!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : Sim_LAMMPS_MEAM_JelinekGrohHorstemeyer_2012_AlSiMgCuFe__SM_656517352485_000 Supported species : Al Cu Fe Mg Si random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 264.8706528368411 2^p V(r_1,...,r_N) = 264.8706528368413 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 1 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 2 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 3 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 4 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 5 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 6 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 7 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 8 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 9 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 10 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 11 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 12 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 13 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 14 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 15 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 16 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 17 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 18 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 19 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 20 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 21 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 22 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 23 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 24 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 25 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 26 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 27 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 28 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 | 6.63385744e+00 -3.42816786e+00 -1.33483074e+01 29 -1.26607633e+01 -4.75751196e-01 1.91308353e+01 | -1.26607633e+01 -4.75751196e-01 1.91308353e+01 30 -1.14983088e+01 6.44887573e+00 -1.84907991e+00 | -1.14983088e+01 6.44887573e+00 -1.84907991e+00 31 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 | 1.75252146e+01 -2.54495668e+00 -3.93344793e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 116.04373411119295 2^p V(r_1,...,r_N) = 116.04373411119293 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 | 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 1 -9.19691804e+00 6.87046776e+00 -2.51351629e+01 | -9.19691804e+00 6.87046776e+00 -2.51351629e+01 2 -2.05524537e+01 -8.18580700e+00 3.20316126e+01 | -2.05524537e+01 -8.18580700e+00 3.20316126e+01 3 6.54883767e+00 7.06287257e+00 2.66013738e+01 | 6.54883767e+00 7.06287257e+00 2.66013738e+01 4 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 | 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 5 -9.19691804e+00 6.87046776e+00 -2.51351629e+01 | -9.19691804e+00 6.87046776e+00 -2.51351629e+01 6 -2.05524537e+01 -8.18580700e+00 3.20316126e+01 | -2.05524537e+01 -8.18580700e+00 3.20316126e+01 7 6.54883767e+00 7.06287257e+00 2.66013738e+01 | 6.54883767e+00 7.06287257e+00 2.66013738e+01 8 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 | 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 9 -9.19691804e+00 6.87046776e+00 -2.51351629e+01 | -9.19691804e+00 6.87046776e+00 -2.51351629e+01 10 -2.05524537e+01 -8.18580700e+00 3.20316126e+01 | -2.05524537e+01 -8.18580700e+00 3.20316126e+01 11 6.54883767e+00 7.06287257e+00 2.66013738e+01 | 6.54883767e+00 7.06287257e+00 2.66013738e+01 12 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 | 2.32005341e+01 -5.74753334e+00 -3.34978236e+01 13 -9.19691804e+00 6.87046776e+00 -2.51351629e+01 | -9.19691804e+00 6.87046776e+00 -2.51351629e+01 14 -2.05524537e+01 -8.18580700e+00 3.20316126e+01 | -2.05524537e+01 -8.18580700e+00 3.20316126e+01 15 6.54883767e+00 7.06287257e+00 2.66013738e+01 | 6.54883767e+00 7.06287257e+00 2.66013738e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 122.38764789717368 2^p V(r_1,...,r_N) = 122.38764789717362 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 | 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 1 -1.23265070e+01 3.53033633e+01 -6.60814655e+00 | -1.23265070e+01 3.53033633e+01 -6.60814655e+00 2 -2.30811690e+01 -3.43172710e+01 6.87763010e+00 | -2.30811690e+01 -3.43172710e+01 6.87763010e+00 3 1.47502566e+01 2.53605500e+01 1.28172568e+01 | 1.47502566e+01 2.53605500e+01 1.28172568e+01 4 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 | 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 5 -1.23265070e+01 3.53033633e+01 -6.60814655e+00 | -1.23265070e+01 3.53033633e+01 -6.60814655e+00 6 -2.30811690e+01 -3.43172710e+01 6.87763010e+00 | -2.30811690e+01 -3.43172710e+01 6.87763010e+00 7 1.47502566e+01 2.53605500e+01 1.28172568e+01 | 1.47502566e+01 2.53605500e+01 1.28172568e+01 8 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 | 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 9 -1.23265070e+01 3.53033633e+01 -6.60814655e+00 | -1.23265070e+01 3.53033633e+01 -6.60814655e+00 10 -2.30811690e+01 -3.43172710e+01 6.87763010e+00 | -2.30811690e+01 -3.43172710e+01 6.87763010e+00 11 1.47502566e+01 2.53605500e+01 1.28172568e+01 | 1.47502566e+01 2.53605500e+01 1.28172568e+01 12 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 | 2.06574193e+01 -2.63466423e+01 -1.30867404e+01 13 -1.23265070e+01 3.53033633e+01 -6.60814655e+00 | -1.23265070e+01 3.53033633e+01 -6.60814655e+00 14 -2.30811690e+01 -3.43172710e+01 6.87763010e+00 | -2.30811690e+01 -3.43172710e+01 6.87763010e+00 15 1.47502566e+01 2.53605500e+01 1.28172568e+01 | 1.47502566e+01 2.53605500e+01 1.28172568e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 40.33948401688952 2^p V(r_1,...,r_N) = 40.33948401688953 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 9.64511131e+00 -2.72481837e+01 -2.24411656e+01 | 9.64511131e+00 -2.72481837e+01 -2.24411656e+01 1 -1.30869643e+01 2.52080112e+01 -1.52688731e+01 | -1.30869643e+01 2.52080112e+01 -1.52688731e+01 2 -1.08290499e+01 -1.54198447e+01 2.30983492e+01 | -1.08290499e+01 -1.54198447e+01 2.30983492e+01 3 1.42709030e+01 1.74600171e+01 1.46116895e+01 | 1.42709030e+01 1.74600171e+01 1.46116895e+01 4 9.64511131e+00 -2.72481837e+01 -2.24411656e+01 | 9.64511131e+00 -2.72481837e+01 -2.24411656e+01 5 -1.30869643e+01 2.52080112e+01 -1.52688731e+01 | -1.30869643e+01 2.52080112e+01 -1.52688731e+01 6 -1.08290499e+01 -1.54198447e+01 2.30983492e+01 | -1.08290499e+01 -1.54198447e+01 2.30983492e+01 7 1.42709030e+01 1.74600171e+01 1.46116895e+01 | 1.42709030e+01 1.74600171e+01 1.46116895e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 103.50660901749754 2^p V(r_1,...,r_N) = 103.50660901749745 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 | -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 1 1.68770526e+01 -4.74281768e+00 5.10931204e+00 | 1.68770526e+01 -4.74281768e+00 5.10931204e+00 2 2.85473339e+01 1.06495862e+01 -1.04997237e+01 | 2.85473339e+01 1.06495862e+01 -1.04997237e+01 3 -2.78011393e+01 -1.15684585e+00 6.75325168e+00 | -2.78011393e+01 -1.15684585e+00 6.75325168e+00 4 -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 | -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 5 1.68770526e+01 -4.74281768e+00 5.10931204e+00 | 1.68770526e+01 -4.74281768e+00 5.10931204e+00 6 2.85473339e+01 1.06495862e+01 -1.04997237e+01 | 2.85473339e+01 1.06495862e+01 -1.04997237e+01 7 -2.78011393e+01 -1.15684585e+00 6.75325168e+00 | -2.78011393e+01 -1.15684585e+00 6.75325168e+00 8 -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 | -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 9 1.68770526e+01 -4.74281768e+00 5.10931204e+00 | 1.68770526e+01 -4.74281768e+00 5.10931204e+00 10 2.85473339e+01 1.06495862e+01 -1.04997237e+01 | 2.85473339e+01 1.06495862e+01 -1.04997237e+01 11 -2.78011393e+01 -1.15684585e+00 6.75325168e+00 | -2.78011393e+01 -1.15684585e+00 6.75325168e+00 12 -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 | -1.76232473e+01 -4.74992268e+00 -1.36283998e+00 13 1.68770526e+01 -4.74281768e+00 5.10931204e+00 | 1.68770526e+01 -4.74281768e+00 5.10931204e+00 14 2.85473339e+01 1.06495862e+01 -1.04997237e+01 | 2.85473339e+01 1.06495862e+01 -1.04997237e+01 15 -2.78011393e+01 -1.15684585e+00 6.75325168e+00 | -2.78011393e+01 -1.15684585e+00 6.75325168e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 65.79513347281492 2^p V(r_1,...,r_N) = 65.795133472815 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.38222245e+01 -7.50369390e+00 -2.40488504e+01 | -2.38222245e+01 -7.50369390e+00 -2.40488504e+01 1 2.10977984e+01 1.25462730e+01 -3.03372027e+01 | 2.10977984e+01 1.25462730e+01 -3.03372027e+01 2 3.17190130e+01 -1.30958597e+01 1.89768019e+01 | 3.17190130e+01 -1.30958597e+01 1.89768019e+01 3 -2.89945869e+01 8.05328064e+00 3.54092512e+01 | -2.89945869e+01 8.05328064e+00 3.54092512e+01 4 -2.38222245e+01 -7.50369390e+00 -2.40488504e+01 | -2.38222245e+01 -7.50369390e+00 -2.40488504e+01 5 2.10977984e+01 1.25462730e+01 -3.03372027e+01 | 2.10977984e+01 1.25462730e+01 -3.03372027e+01 6 3.17190130e+01 -1.30958597e+01 1.89768019e+01 | 3.17190130e+01 -1.30958597e+01 1.89768019e+01 7 -2.89945869e+01 8.05328064e+00 3.54092512e+01 | -2.89945869e+01 8.05328064e+00 3.54092512e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 26.142835661307306 2^p V(r_1,...,r_N) = 26.142835661307323 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.64353820e+01 -1.76954297e+01 4.79565897e+00 | -1.64353820e+01 -1.76954297e+01 4.79565897e+00 1 1.42848201e+01 1.67087305e+01 -6.58931149e+00 | 1.42848201e+01 1.67087305e+01 -6.58931149e+00 2 1.67897398e+01 -1.86401929e+01 4.05429241e+00 | 1.67897398e+01 -1.86401929e+01 4.05429241e+00 3 -1.46391779e+01 1.96268921e+01 -2.26063989e+00 | -1.46391779e+01 1.96268921e+01 -2.26063989e+00 4 -1.64353820e+01 -1.76954297e+01 4.79565897e+00 | -1.64353820e+01 -1.76954297e+01 4.79565897e+00 5 1.42848201e+01 1.67087305e+01 -6.58931149e+00 | 1.42848201e+01 1.67087305e+01 -6.58931149e+00 6 1.67897398e+01 -1.86401929e+01 4.05429241e+00 | 1.67897398e+01 -1.86401929e+01 4.05429241e+00 7 -1.46391779e+01 1.96268921e+01 -2.26063989e+00 | -1.46391779e+01 1.96268921e+01 -2.26063989e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 51.10078788416412 2^p V(r_1,...,r_N) = 51.10078788416423 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 1 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 2 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 3 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 4 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 5 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 6 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 7 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 8 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 9 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 10 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 11 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 12 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 13 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 14 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 15 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 16 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 17 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 18 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 19 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 20 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 21 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 22 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 23 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 24 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 25 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 26 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 27 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 28 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 | 3.04006977e+01 -7.38132376e+00 -3.96932044e+01 29 -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 | -9.13139726e+00 -3.38784842e+00 -4.75709908e+00 30 -3.36820879e+01 -8.94187491e+00 2.75793094e+01 | -3.36820879e+01 -8.94187491e+00 2.75793094e+01 31 1.24127875e+01 1.97110471e+01 1.68709942e+01 | 1.24127875e+01 1.97110471e+01 1.68709942e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 88.35018215815194 2^p V(r_1,...,r_N) = 88.35018215815191 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 1.76797763e+01 1.95415420e+01 -2.92751535e+01 | 1.76797763e+01 1.95415420e+01 -2.92751535e+01 1 -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 | -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 2 -7.78598246e+01 7.89197168e+01 4.01879249e+01 | -7.78598246e+01 7.89197168e+01 4.01879249e+01 3 8.12738442e+01 -8.22961672e+01 1.74242705e+01 | 8.12738442e+01 -8.22961672e+01 1.74242705e+01 4 1.76797763e+01 1.95415420e+01 -2.92751535e+01 | 1.76797763e+01 1.95415420e+01 -2.92751535e+01 5 -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 | -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 6 -7.78598246e+01 7.89197168e+01 4.01879249e+01 | -7.78598246e+01 7.89197168e+01 4.01879249e+01 7 8.12738442e+01 -8.22961672e+01 1.74242705e+01 | 8.12738442e+01 -8.22961672e+01 1.74242705e+01 8 1.76797763e+01 1.95415420e+01 -2.92751535e+01 | 1.76797763e+01 1.95415420e+01 -2.92751535e+01 9 -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 | -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 10 -7.78598246e+01 7.89197168e+01 4.01879249e+01 | -7.78598246e+01 7.89197168e+01 4.01879249e+01 11 8.12738442e+01 -8.22961672e+01 1.74242705e+01 | 8.12738442e+01 -8.22961672e+01 1.74242705e+01 12 1.76797763e+01 1.95415420e+01 -2.92751535e+01 | 1.76797763e+01 1.95415420e+01 -2.92751535e+01 13 -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 | -2.10937959e+01 -1.61650916e+01 -2.83370418e+01 14 -7.78598246e+01 7.89197168e+01 4.01879249e+01 | -7.78598246e+01 7.89197168e+01 4.01879249e+01 15 8.12738442e+01 -8.22961672e+01 1.74242705e+01 | 8.12738442e+01 -8.22961672e+01 1.74242705e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.6725451806702931 2^p V(r_1,...,r_N) = -0.6725451806703159 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 1.14430098e+01 -1.16092666e+01 1.50967032e+01 | 1.14430098e+01 -1.16092666e+01 1.50967032e+01 1 -2.59545779e+00 9.19307389e+00 1.72201713e+00 | -2.59545779e+00 9.19307389e+00 1.72201713e+00 2 -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 | -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 3 4.29303541e+00 1.33921047e+01 -3.12396208e+00 | 4.29303541e+00 1.33921047e+01 -3.12396208e+00 4 1.14430098e+01 -1.16092666e+01 1.50967032e+01 | 1.14430098e+01 -1.16092666e+01 1.50967032e+01 5 -2.59545779e+00 9.19307389e+00 1.72201713e+00 | -2.59545779e+00 9.19307389e+00 1.72201713e+00 6 -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 | -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 7 4.29303541e+00 1.33921047e+01 -3.12396208e+00 | 4.29303541e+00 1.33921047e+01 -3.12396208e+00 8 1.14430098e+01 -1.16092666e+01 1.50967032e+01 | 1.14430098e+01 -1.16092666e+01 1.50967032e+01 9 -2.59545779e+00 9.19307389e+00 1.72201713e+00 | -2.59545779e+00 9.19307389e+00 1.72201713e+00 10 -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 | -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 11 4.29303541e+00 1.33921047e+01 -3.12396208e+00 | 4.29303541e+00 1.33921047e+01 -3.12396208e+00 12 1.14430098e+01 -1.16092666e+01 1.50967032e+01 | 1.14430098e+01 -1.16092666e+01 1.50967032e+01 13 -2.59545779e+00 9.19307389e+00 1.72201713e+00 | -2.59545779e+00 9.19307389e+00 1.72201713e+00 14 -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 | -1.31405875e+01 -1.09759120e+01 -1.36947583e+01 15 4.29303541e+00 1.33921047e+01 -3.12396208e+00 | 4.29303541e+00 1.33921047e+01 -3.12396208e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.122694975403599 2^p V(r_1,...,r_N) = 7.122694975403578 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 1.88775892e+01 -1.77230393e+01 -1.41788142e+01 | 1.88775892e+01 -1.77230393e+01 -1.41788142e+01 1 -5.61940225e-01 3.84538628e+01 -1.96790642e+01 | -5.61940225e-01 3.84538628e+01 -1.96790642e+01 2 -1.56661237e+01 -2.61327705e+01 2.99638813e+01 | -1.56661237e+01 -2.61327705e+01 2.99638813e+01 3 -2.64952535e+00 5.40194698e+00 3.89399710e+00 | -2.64952535e+00 5.40194698e+00 3.89399710e+00 4 1.88775892e+01 -1.77230393e+01 -1.41788142e+01 | 1.88775892e+01 -1.77230393e+01 -1.41788142e+01 5 -5.61940225e-01 3.84538628e+01 -1.96790642e+01 | -5.61940225e-01 3.84538628e+01 -1.96790642e+01 6 -1.56661237e+01 -2.61327705e+01 2.99638813e+01 | -1.56661237e+01 -2.61327705e+01 2.99638813e+01 7 -2.64952535e+00 5.40194698e+00 3.89399710e+00 | -2.64952535e+00 5.40194698e+00 3.89399710e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -13.265819818484358 2^p V(r_1,...,r_N) = -13.265819818484355 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.61191882e+00 4.62362043e+00 8.37855977e+00 | -8.61191882e+00 4.62362043e+00 8.37855977e+00 1 8.79512174e+00 -6.40936094e+00 5.62141655e+00 | 8.79512174e+00 -6.40936094e+00 5.62141655e+00 2 7.15609912e+00 6.66616463e+00 -6.42957251e+00 | 7.15609912e+00 6.66616463e+00 -6.42957251e+00 3 -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 | -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 4 -8.61191882e+00 4.62362043e+00 8.37855977e+00 | -8.61191882e+00 4.62362043e+00 8.37855977e+00 5 8.79512174e+00 -6.40936094e+00 5.62141655e+00 | 8.79512174e+00 -6.40936094e+00 5.62141655e+00 6 7.15609912e+00 6.66616463e+00 -6.42957251e+00 | 7.15609912e+00 6.66616463e+00 -6.42957251e+00 7 -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 | -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 8 -8.61191882e+00 4.62362043e+00 8.37855977e+00 | -8.61191882e+00 4.62362043e+00 8.37855977e+00 9 8.79512174e+00 -6.40936094e+00 5.62141655e+00 | 8.79512174e+00 -6.40936094e+00 5.62141655e+00 10 7.15609912e+00 6.66616463e+00 -6.42957251e+00 | 7.15609912e+00 6.66616463e+00 -6.42957251e+00 11 -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 | -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 12 -8.61191882e+00 4.62362043e+00 8.37855977e+00 | -8.61191882e+00 4.62362043e+00 8.37855977e+00 13 8.79512174e+00 -6.40936094e+00 5.62141655e+00 | 8.79512174e+00 -6.40936094e+00 5.62141655e+00 14 7.15609912e+00 6.66616463e+00 -6.42957251e+00 | 7.15609912e+00 6.66616463e+00 -6.42957251e+00 15 -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 | -7.33930204e+00 -4.88042411e+00 -7.57040380e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 16.040169458088208 2^p V(r_1,...,r_N) = 16.040169458088215 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.66993478e+01 -1.72490169e+01 -4.43036750e+01 | -4.66993478e+01 -1.72490169e+01 -4.43036750e+01 1 1.19303069e+01 1.33953203e+01 -1.47349942e+01 | 1.19303069e+01 1.33953203e+01 -1.47349942e+01 2 4.65524371e+01 -6.12021259e+00 4.79375168e+01 | 4.65524371e+01 -6.12021259e+00 4.79375168e+01 3 -1.17833962e+01 9.97390917e+00 1.11011524e+01 | -1.17833962e+01 9.97390917e+00 1.11011524e+01 4 -4.66993478e+01 -1.72490169e+01 -4.43036750e+01 | -4.66993478e+01 -1.72490169e+01 -4.43036750e+01 5 1.19303069e+01 1.33953203e+01 -1.47349942e+01 | 1.19303069e+01 1.33953203e+01 -1.47349942e+01 6 4.65524371e+01 -6.12021259e+00 4.79375168e+01 | 4.65524371e+01 -6.12021259e+00 4.79375168e+01 7 -1.17833962e+01 9.97390917e+00 1.11011524e+01 | -1.17833962e+01 9.97390917e+00 1.11011524e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.6958599266059435 2^p V(r_1,...,r_N) = -5.695859926605936 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.84770467e+00 -1.17051372e+01 -5.60061742e+00 | -6.84770467e+00 -1.17051372e+01 -5.60061742e+00 1 6.96406344e+00 7.47619081e+00 -5.10529386e+00 | 6.96406344e+00 7.47619081e+00 -5.10529386e+00 2 7.28914139e+00 -7.20058249e+00 4.19619582e+00 | 7.28914139e+00 -7.20058249e+00 4.19619582e+00 3 -7.40550017e+00 1.14295289e+01 6.50971547e+00 | -7.40550017e+00 1.14295289e+01 6.50971547e+00 4 -6.84770467e+00 -1.17051372e+01 -5.60061742e+00 | -6.84770467e+00 -1.17051372e+01 -5.60061742e+00 5 6.96406344e+00 7.47619081e+00 -5.10529386e+00 | 6.96406344e+00 7.47619081e+00 -5.10529386e+00 6 7.28914139e+00 -7.20058249e+00 4.19619582e+00 | 7.28914139e+00 -7.20058249e+00 4.19619582e+00 7 -7.40550017e+00 1.14295289e+01 6.50971547e+00 | -7.40550017e+00 1.14295289e+01 6.50971547e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTT (Configuration in file "config-Fe-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 166.8378892597291 2^p V(r_1,...,r_N) = 166.83788925972934 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 1 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 2 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 3 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 4 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 5 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 6 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 7 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 8 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 9 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 10 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 11 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 12 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 13 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 14 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 15 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 16 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 17 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 18 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 19 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 20 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 21 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 22 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 23 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 24 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 25 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 26 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 27 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 28 -1.77806582e+01 -5.31767828e+01 4.85082072e+01 | -1.77806582e+01 -5.31767828e+01 4.85082072e+01 29 2.63448463e+01 -1.11803823e+01 3.79857882e+01 | 2.63448463e+01 -1.11803823e+01 3.79857882e+01 30 1.78230787e+01 3.95883520e+01 -2.73378761e+01 | 1.78230787e+01 3.95883520e+01 -2.73378761e+01 31 -2.63872669e+01 2.47688131e+01 -5.91561193e+01 | -2.63872669e+01 2.47688131e+01 -5.91561193e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTF (Configuration in file "config-Fe-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 100.55011958298162 2^p V(r_1,...,r_N) = 100.5501195829816 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 2.98208546e+01 5.18778071e+01 -4.93802990e+01 | 2.98208546e+01 5.18778071e+01 -4.93802990e+01 1 -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 | -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 2 -2.35316756e+01 -1.61629022e+01 3.19033554e+01 | -2.35316756e+01 -1.61629022e+01 3.19033554e+01 3 4.64745344e+01 -9.29834753e+00 6.92496904e+01 | 4.64745344e+01 -9.29834753e+00 6.92496904e+01 4 2.98208546e+01 5.18778071e+01 -4.93802990e+01 | 2.98208546e+01 5.18778071e+01 -4.93802990e+01 5 -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 | -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 6 -2.35316756e+01 -1.61629022e+01 3.19033554e+01 | -2.35316756e+01 -1.61629022e+01 3.19033554e+01 7 4.64745344e+01 -9.29834753e+00 6.92496904e+01 | 4.64745344e+01 -9.29834753e+00 6.92496904e+01 8 2.98208546e+01 5.18778071e+01 -4.93802990e+01 | 2.98208546e+01 5.18778071e+01 -4.93802990e+01 9 -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 | -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 10 -2.35316756e+01 -1.61629022e+01 3.19033554e+01 | -2.35316756e+01 -1.61629022e+01 3.19033554e+01 11 4.64745344e+01 -9.29834753e+00 6.92496904e+01 | 4.64745344e+01 -9.29834753e+00 6.92496904e+01 12 2.98208546e+01 5.18778071e+01 -4.93802990e+01 | 2.98208546e+01 5.18778071e+01 -4.93802990e+01 13 -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 | -5.27637135e+01 -2.64165574e+01 -5.17727469e+01 14 -2.35316756e+01 -1.61629022e+01 3.19033554e+01 | -2.35316756e+01 -1.61629022e+01 3.19033554e+01 15 4.64745344e+01 -9.29834753e+00 6.92496904e+01 | 4.64745344e+01 -9.29834753e+00 6.92496904e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFT (Configuration in file "config-Fe-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.767794671989558 2^p V(r_1,...,r_N) = -2.767794671989542 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.18805063e+00 -2.42355864e+01 6.54246276e+00 | -9.18805063e+00 -2.42355864e+01 6.54246276e+00 1 3.54714250e+00 1.98382226e+01 -5.74420539e+00 | 3.54714250e+00 1.98382226e+01 -5.74420539e+00 2 1.70348381e+01 -3.00932067e+01 9.30887522e+00 | 1.70348381e+01 -3.00932067e+01 9.30887522e+00 3 -1.13939300e+01 3.44905705e+01 -1.01071326e+01 | -1.13939300e+01 3.44905705e+01 -1.01071326e+01 4 -9.18805063e+00 -2.42355864e+01 6.54246276e+00 | -9.18805063e+00 -2.42355864e+01 6.54246276e+00 5 3.54714250e+00 1.98382226e+01 -5.74420539e+00 | 3.54714250e+00 1.98382226e+01 -5.74420539e+00 6 1.70348381e+01 -3.00932067e+01 9.30887522e+00 | 1.70348381e+01 -3.00932067e+01 9.30887522e+00 7 -1.13939300e+01 3.44905705e+01 -1.01071326e+01 | -1.13939300e+01 3.44905705e+01 -1.01071326e+01 8 -9.18805063e+00 -2.42355864e+01 6.54246276e+00 | -9.18805063e+00 -2.42355864e+01 6.54246276e+00 9 3.54714250e+00 1.98382226e+01 -5.74420539e+00 | 3.54714250e+00 1.98382226e+01 -5.74420539e+00 10 1.70348381e+01 -3.00932067e+01 9.30887522e+00 | 1.70348381e+01 -3.00932067e+01 9.30887522e+00 11 -1.13939300e+01 3.44905705e+01 -1.01071326e+01 | -1.13939300e+01 3.44905705e+01 -1.01071326e+01 12 -9.18805063e+00 -2.42355864e+01 6.54246276e+00 | -9.18805063e+00 -2.42355864e+01 6.54246276e+00 13 3.54714250e+00 1.98382226e+01 -5.74420539e+00 | 3.54714250e+00 1.98382226e+01 -5.74420539e+00 14 1.70348381e+01 -3.00932067e+01 9.30887522e+00 | 1.70348381e+01 -3.00932067e+01 9.30887522e+00 15 -1.13939300e+01 3.44905705e+01 -1.01071326e+01 | -1.13939300e+01 3.44905705e+01 -1.01071326e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFF (Configuration in file "config-Fe-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 16.356346494445763 2^p V(r_1,...,r_N) = 16.356346494445795 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 3.11532915e+01 -3.07575963e+01 -2.68910135e+01 | 3.11532915e+01 -3.07575963e+01 -2.68910135e+01 1 -2.97671040e+01 4.39995479e+01 -3.29893534e+01 | -2.97671040e+01 4.39995479e+01 -3.29893534e+01 2 -3.39652230e+01 -4.59398326e+01 3.21782161e+01 | -3.39652230e+01 -4.59398326e+01 3.21782161e+01 3 3.25790355e+01 3.26978810e+01 2.77021507e+01 | 3.25790355e+01 3.26978810e+01 2.77021507e+01 4 3.11532915e+01 -3.07575963e+01 -2.68910135e+01 | 3.11532915e+01 -3.07575963e+01 -2.68910135e+01 5 -2.97671040e+01 4.39995479e+01 -3.29893534e+01 | -2.97671040e+01 4.39995479e+01 -3.29893534e+01 6 -3.39652230e+01 -4.59398326e+01 3.21782161e+01 | -3.39652230e+01 -4.59398326e+01 3.21782161e+01 7 3.25790355e+01 3.26978810e+01 2.77021507e+01 | 3.25790355e+01 3.26978810e+01 2.77021507e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTT (Configuration in file "config-Fe-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 333.16741539435003 2^p V(r_1,...,r_N) = 333.16741539435037 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.75882903e+02 4.92541608e+01 -1.58826526e+02 | -1.75882903e+02 4.92541608e+01 -1.58826526e+02 1 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 | 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 2 1.49033325e+02 4.11303361e+01 1.65508455e+02 | 1.49033325e+02 4.11303361e+01 1.65508455e+02 3 -9.17176063e+01 -1.96508967e+01 7.90336732e+01 | -9.17176063e+01 -1.96508967e+01 7.90336732e+01 4 -1.75882903e+02 4.92541608e+01 -1.58826526e+02 | -1.75882903e+02 4.92541608e+01 -1.58826526e+02 5 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 | 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 6 1.49033325e+02 4.11303361e+01 1.65508455e+02 | 1.49033325e+02 4.11303361e+01 1.65508455e+02 7 -9.17176063e+01 -1.96508967e+01 7.90336732e+01 | -9.17176063e+01 -1.96508967e+01 7.90336732e+01 8 -1.75882903e+02 4.92541608e+01 -1.58826526e+02 | -1.75882903e+02 4.92541608e+01 -1.58826526e+02 9 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 | 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 10 1.49033325e+02 4.11303361e+01 1.65508455e+02 | 1.49033325e+02 4.11303361e+01 1.65508455e+02 11 -9.17176063e+01 -1.96508967e+01 7.90336732e+01 | -9.17176063e+01 -1.96508967e+01 7.90336732e+01 12 -1.75882903e+02 4.92541608e+01 -1.58826526e+02 | -1.75882903e+02 4.92541608e+01 -1.58826526e+02 13 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 | 1.18567184e+02 -7.07336001e+01 -8.57156024e+01 14 1.49033325e+02 4.11303361e+01 1.65508455e+02 | 1.49033325e+02 4.11303361e+01 1.65508455e+02 15 -9.17176063e+01 -1.96508967e+01 7.90336732e+01 | -9.17176063e+01 -1.96508967e+01 7.90336732e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTF (Configuration in file "config-Fe-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 15.421691531387436 2^p V(r_1,...,r_N) = 15.421691531387458 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.41305489e+01 -2.55916403e+01 -2.93800449e+01 | -2.41305489e+01 -2.55916403e+01 -2.93800449e+01 1 1.58776549e+01 3.10638813e+01 -3.30952781e+01 | 1.58776549e+01 3.10638813e+01 -3.30952781e+01 2 4.67783261e+01 -4.63667401e+01 2.91761178e+01 | 4.67783261e+01 -4.63667401e+01 2.91761178e+01 3 -3.85254321e+01 4.08944992e+01 3.32992051e+01 | -3.85254321e+01 4.08944992e+01 3.32992051e+01 4 -2.41305489e+01 -2.55916403e+01 -2.93800449e+01 | -2.41305489e+01 -2.55916403e+01 -2.93800449e+01 5 1.58776549e+01 3.10638813e+01 -3.30952781e+01 | 1.58776549e+01 3.10638813e+01 -3.30952781e+01 6 4.67783261e+01 -4.63667401e+01 2.91761178e+01 | 4.67783261e+01 -4.63667401e+01 2.91761178e+01 7 -3.85254321e+01 4.08944992e+01 3.32992051e+01 | -3.85254321e+01 4.08944992e+01 3.32992051e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FFT (Configuration in file "config-Fe-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 56.56288313683686 2^p V(r_1,...,r_N) = 56.56288313683687 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.89630433e+01 -4.52681479e+01 4.61944650e+01 | -6.89630433e+01 -4.52681479e+01 4.61944650e+01 1 3.73257380e+01 3.85942869e+01 1.43600694e+01 | 3.73257380e+01 3.85942869e+01 1.43600694e+01 2 8.30013720e+01 -7.42489349e+01 -4.61178792e+01 | 8.30013720e+01 -7.42489349e+01 -4.61178792e+01 3 -5.13640668e+01 8.09227959e+01 -1.44366552e+01 | -5.13640668e+01 8.09227959e+01 -1.44366552e+01 4 -6.89630433e+01 -4.52681479e+01 4.61944650e+01 | -6.89630433e+01 -4.52681479e+01 4.61944650e+01 5 3.73257380e+01 3.85942869e+01 1.43600694e+01 | 3.73257380e+01 3.85942869e+01 1.43600694e+01 6 8.30013720e+01 -7.42489349e+01 -4.61178792e+01 | 8.30013720e+01 -7.42489349e+01 -4.61178792e+01 7 -5.13640668e+01 8.09227959e+01 -1.44366552e+01 | -5.13640668e+01 8.09227959e+01 -1.44366552e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTT (Configuration in file "config-Mg-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 325.0771064247562 2^p V(r_1,...,r_N) = 325.07710642475575 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 1 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 2 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 3 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 4 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 5 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 6 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 7 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 8 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 9 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 10 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 11 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 12 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 13 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 14 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 15 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 16 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 17 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 18 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 19 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 20 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 21 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 22 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 23 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 24 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 25 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 26 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 27 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 28 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 | 5.19708106e+00 -5.59855453e+00 -1.23167221e+01 29 -3.26994237e+00 2.41307207e+00 -8.62436148e+00 | -3.26994237e+00 2.41307207e+00 -8.62436148e+00 30 -1.21490045e+01 -8.52339163e+00 8.97246155e+00 | -1.21490045e+01 -8.52339163e+00 8.97246155e+00 31 1.02218658e+01 1.17088741e+01 1.19686221e+01 | 1.02218658e+01 1.17088741e+01 1.19686221e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTF (Configuration in file "config-Mg-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 110.938178754604 2^p V(r_1,...,r_N) = 110.93817875460408 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.20721151e-01 5.97814592e+00 -2.19965317e+01 | -7.20721151e-01 5.97814592e+00 -2.19965317e+01 1 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 | 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 2 -5.07285133e+00 7.38610983e+00 1.77323949e+01 | -5.07285133e+00 7.38610983e+00 1.77323949e+01 3 3.46796778e+00 -8.41754519e+00 2.11931286e+01 | 3.46796778e+00 -8.41754519e+00 2.11931286e+01 4 -7.20721151e-01 5.97814592e+00 -2.19965317e+01 | -7.20721151e-01 5.97814592e+00 -2.19965317e+01 5 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 | 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 6 -5.07285133e+00 7.38610983e+00 1.77323949e+01 | -5.07285133e+00 7.38610983e+00 1.77323949e+01 7 3.46796778e+00 -8.41754519e+00 2.11931286e+01 | 3.46796778e+00 -8.41754519e+00 2.11931286e+01 8 -7.20721151e-01 5.97814592e+00 -2.19965317e+01 | -7.20721151e-01 5.97814592e+00 -2.19965317e+01 9 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 | 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 10 -5.07285133e+00 7.38610983e+00 1.77323949e+01 | -5.07285133e+00 7.38610983e+00 1.77323949e+01 11 3.46796778e+00 -8.41754519e+00 2.11931286e+01 | 3.46796778e+00 -8.41754519e+00 2.11931286e+01 12 -7.20721151e-01 5.97814592e+00 -2.19965317e+01 | -7.20721151e-01 5.97814592e+00 -2.19965317e+01 13 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 | 2.32560469e+00 -4.94671056e+00 -1.69289917e+01 14 -5.07285133e+00 7.38610983e+00 1.77323949e+01 | -5.07285133e+00 7.38610983e+00 1.77323949e+01 15 3.46796778e+00 -8.41754519e+00 2.11931286e+01 | 3.46796778e+00 -8.41754519e+00 2.11931286e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFT (Configuration in file "config-Mg-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 150.95524028065998 2^p V(r_1,...,r_N) = 150.95524028065995 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 | -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 1 1.28681092e+01 2.33158185e+01 -8.94510082e+00 | 1.28681092e+01 2.33158185e+01 -8.94510082e+00 2 7.36335789e+00 -2.66340319e+01 1.12833236e+01 | 7.36335789e+00 -2.66340319e+01 1.12833236e+01 3 -8.30880322e+00 2.47884053e+01 5.50123102e+00 | -8.30880322e+00 2.47884053e+01 5.50123102e+00 4 -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 | -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 5 1.28681092e+01 2.33158185e+01 -8.94510082e+00 | 1.28681092e+01 2.33158185e+01 -8.94510082e+00 6 7.36335789e+00 -2.66340319e+01 1.12833236e+01 | 7.36335789e+00 -2.66340319e+01 1.12833236e+01 7 -8.30880322e+00 2.47884053e+01 5.50123102e+00 | -8.30880322e+00 2.47884053e+01 5.50123102e+00 8 -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 | -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 9 1.28681092e+01 2.33158185e+01 -8.94510082e+00 | 1.28681092e+01 2.33158185e+01 -8.94510082e+00 10 7.36335789e+00 -2.66340319e+01 1.12833236e+01 | 7.36335789e+00 -2.66340319e+01 1.12833236e+01 11 -8.30880322e+00 2.47884053e+01 5.50123102e+00 | -8.30880322e+00 2.47884053e+01 5.50123102e+00 12 -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 | -1.19226638e+01 -2.14701918e+01 -7.83945383e+00 13 1.28681092e+01 2.33158185e+01 -8.94510082e+00 | 1.28681092e+01 2.33158185e+01 -8.94510082e+00 14 7.36335789e+00 -2.66340319e+01 1.12833236e+01 | 7.36335789e+00 -2.66340319e+01 1.12833236e+01 15 -8.30880322e+00 2.47884053e+01 5.50123102e+00 | -8.30880322e+00 2.47884053e+01 5.50123102e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFF (Configuration in file "config-Mg-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 53.4416661799891 2^p V(r_1,...,r_N) = 53.441666179989085 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 6.93124474e+00 -1.60777076e+01 -1.66741147e+01 | 6.93124474e+00 -1.60777076e+01 -1.66741147e+01 1 -9.90074365e+00 1.98660087e+01 -1.68588827e+01 | -9.90074365e+00 1.98660087e+01 -1.68588827e+01 2 -7.92025414e+00 -2.13295651e+01 1.42389829e+01 | -7.92025414e+00 -2.13295651e+01 1.42389829e+01 3 1.08897531e+01 1.75412640e+01 1.92940145e+01 | 1.08897531e+01 1.75412640e+01 1.92940145e+01 4 6.93124474e+00 -1.60777076e+01 -1.66741147e+01 | 6.93124474e+00 -1.60777076e+01 -1.66741147e+01 5 -9.90074365e+00 1.98660087e+01 -1.68588827e+01 | -9.90074365e+00 1.98660087e+01 -1.68588827e+01 6 -7.92025414e+00 -2.13295651e+01 1.42389829e+01 | -7.92025414e+00 -2.13295651e+01 1.42389829e+01 7 1.08897531e+01 1.75412640e+01 1.92940145e+01 | 1.08897531e+01 1.75412640e+01 1.92940145e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTT (Configuration in file "config-Mg-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 162.78016726847173 2^p V(r_1,...,r_N) = 162.78016726847167 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.43621016e+01 1.53706059e+01 -7.63500701e+00 | -2.43621016e+01 1.53706059e+01 -7.63500701e+00 1 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 | 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 2 3.26777203e+01 1.34324033e+01 6.35140746e+00 | 3.26777203e+01 1.34324033e+01 6.35140746e+00 3 -2.85151108e+01 -1.59901780e+01 7.38341951e+00 | -2.85151108e+01 -1.59901780e+01 7.38341951e+00 4 -2.43621016e+01 1.53706059e+01 -7.63500701e+00 | -2.43621016e+01 1.53706059e+01 -7.63500701e+00 5 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 | 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 6 3.26777203e+01 1.34324033e+01 6.35140746e+00 | 3.26777203e+01 1.34324033e+01 6.35140746e+00 7 -2.85151108e+01 -1.59901780e+01 7.38341951e+00 | -2.85151108e+01 -1.59901780e+01 7.38341951e+00 8 -2.43621016e+01 1.53706059e+01 -7.63500701e+00 | -2.43621016e+01 1.53706059e+01 -7.63500701e+00 9 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 | 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 10 3.26777203e+01 1.34324033e+01 6.35140746e+00 | 3.26777203e+01 1.34324033e+01 6.35140746e+00 11 -2.85151108e+01 -1.59901780e+01 7.38341951e+00 | -2.85151108e+01 -1.59901780e+01 7.38341951e+00 12 -2.43621016e+01 1.53706059e+01 -7.63500701e+00 | -2.43621016e+01 1.53706059e+01 -7.63500701e+00 13 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 | 2.01994920e+01 -1.28128312e+01 -6.09981996e+00 14 3.26777203e+01 1.34324033e+01 6.35140746e+00 | 3.26777203e+01 1.34324033e+01 6.35140746e+00 15 -2.85151108e+01 -1.59901780e+01 7.38341951e+00 | -2.85151108e+01 -1.59901780e+01 7.38341951e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTF (Configuration in file "config-Mg-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 67.26603357537299 2^p V(r_1,...,r_N) = 67.26603357537297 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.18134844e+01 1.27955292e+01 -2.36335925e+01 | -2.18134844e+01 1.27955292e+01 -2.36335925e+01 1 2.50178968e+01 -5.83405152e+00 -1.56554308e+01 | 2.50178968e+01 -5.83405152e+00 -1.56554308e+01 2 2.01490884e+01 5.12847791e+00 2.05106562e+01 | 2.01490884e+01 5.12847791e+00 2.05106562e+01 3 -2.33535007e+01 -1.20899556e+01 1.87783671e+01 | -2.33535007e+01 -1.20899556e+01 1.87783671e+01 4 -2.18134844e+01 1.27955292e+01 -2.36335925e+01 | -2.18134844e+01 1.27955292e+01 -2.36335925e+01 5 2.50178968e+01 -5.83405152e+00 -1.56554308e+01 | 2.50178968e+01 -5.83405152e+00 -1.56554308e+01 6 2.01490884e+01 5.12847791e+00 2.05106562e+01 | 2.01490884e+01 5.12847791e+00 2.05106562e+01 7 -2.33535007e+01 -1.20899556e+01 1.87783671e+01 | -2.33535007e+01 -1.20899556e+01 1.87783671e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FFT (Configuration in file "config-Mg-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 59.8110691982248 2^p V(r_1,...,r_N) = 59.811069198224814 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.71574936e+01 -2.57095030e+01 -5.43145751e+00 | -1.71574936e+01 -2.57095030e+01 -5.43145751e+00 1 1.82523324e+01 2.27817092e+01 -1.05777111e+01 | 1.82523324e+01 2.27817092e+01 -1.05777111e+01 2 1.94244477e+01 -1.54207406e+01 5.76421457e+00 | 1.94244477e+01 -1.54207406e+01 5.76421457e+00 3 -2.05192864e+01 1.83485344e+01 1.02449540e+01 | -2.05192864e+01 1.83485344e+01 1.02449540e+01 4 -1.71574936e+01 -2.57095030e+01 -5.43145751e+00 | -1.71574936e+01 -2.57095030e+01 -5.43145751e+00 5 1.82523324e+01 2.27817092e+01 -1.05777111e+01 | 1.82523324e+01 2.27817092e+01 -1.05777111e+01 6 1.94244477e+01 -1.54207406e+01 5.76421457e+00 | 1.94244477e+01 -1.54207406e+01 5.76421457e+00 7 -2.05192864e+01 1.83485344e+01 1.02449540e+01 | -2.05192864e+01 1.83485344e+01 1.02449540e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTT (Configuration in file "config-Si-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1034.6969563918055 2^p V(r_1,...,r_N) = 1034.696956391806 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 1 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 2 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 3 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 4 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 5 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 6 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 7 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 8 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 9 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 10 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 11 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 12 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 13 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 14 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 15 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 16 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 17 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 18 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 19 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 20 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 21 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 22 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 23 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 24 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 25 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 26 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 27 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 28 3.24248208e+02 1.06482547e+02 -6.99801473e+01 | 3.24248208e+02 1.06482547e+02 -6.99801473e+01 29 -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 | -1.42338174e+02 -3.28315411e+02 -1.74114614e+02 30 -1.24771312e+02 7.94386307e+01 3.05710299e+02 | -1.24771312e+02 7.94386307e+01 3.05710299e+02 31 -5.71387221e+01 1.42394234e+02 -6.16155382e+01 | -5.71387221e+01 1.42394234e+02 -6.16155382e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTF (Configuration in file "config-Si-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 338.43768224441146 2^p V(r_1,...,r_N) = 338.43768224441123 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.18052927e+01 5.19554635e+01 -8.56005005e+01 | -1.18052927e+01 5.19554635e+01 -8.56005005e+01 1 -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 | -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 2 -5.22689017e+01 3.22151882e+01 9.85841518e+01 | -5.22689017e+01 3.22151882e+01 9.85841518e+01 3 6.52952014e+01 -5.03238433e+01 1.02853930e+02 | 6.52952014e+01 -5.03238433e+01 1.02853930e+02 4 -1.18052927e+01 5.19554635e+01 -8.56005005e+01 | -1.18052927e+01 5.19554635e+01 -8.56005005e+01 5 -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 | -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 6 -5.22689017e+01 3.22151882e+01 9.85841518e+01 | -5.22689017e+01 3.22151882e+01 9.85841518e+01 7 6.52952014e+01 -5.03238433e+01 1.02853930e+02 | 6.52952014e+01 -5.03238433e+01 1.02853930e+02 8 -1.18052927e+01 5.19554635e+01 -8.56005005e+01 | -1.18052927e+01 5.19554635e+01 -8.56005005e+01 9 -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 | -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 10 -5.22689017e+01 3.22151882e+01 9.85841518e+01 | -5.22689017e+01 3.22151882e+01 9.85841518e+01 11 6.52952014e+01 -5.03238433e+01 1.02853930e+02 | 6.52952014e+01 -5.03238433e+01 1.02853930e+02 12 -1.18052927e+01 5.19554635e+01 -8.56005005e+01 | -1.18052927e+01 5.19554635e+01 -8.56005005e+01 13 -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 | -1.22100699e+00 -3.38468084e+01 -1.15837582e+02 14 -5.22689017e+01 3.22151882e+01 9.85841518e+01 | -5.22689017e+01 3.22151882e+01 9.85841518e+01 15 6.52952014e+01 -5.03238433e+01 1.02853930e+02 | 6.52952014e+01 -5.03238433e+01 1.02853930e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFT (Configuration in file "config-Si-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 245.03850573481517 2^p V(r_1,...,r_N) = 245.03850573481515 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 | 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 1 -1.56915973e+00 1.00792511e+02 -7.06261056e+01 | -1.56915973e+00 1.00792511e+02 -7.06261056e+01 2 6.45794568e+00 -9.49468067e+01 7.02328747e+01 | 6.45794568e+00 -9.49468067e+01 7.02328747e+01 3 -1.93794281e+01 6.17412511e+01 3.18610245e+01 | -1.93794281e+01 6.17412511e+01 3.18610245e+01 4 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 | 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 5 -1.56915973e+00 1.00792511e+02 -7.06261056e+01 | -1.56915973e+00 1.00792511e+02 -7.06261056e+01 6 6.45794568e+00 -9.49468067e+01 7.02328747e+01 | 6.45794568e+00 -9.49468067e+01 7.02328747e+01 7 -1.93794281e+01 6.17412511e+01 3.18610245e+01 | -1.93794281e+01 6.17412511e+01 3.18610245e+01 8 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 | 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 9 -1.56915973e+00 1.00792511e+02 -7.06261056e+01 | -1.56915973e+00 1.00792511e+02 -7.06261056e+01 10 6.45794568e+00 -9.49468067e+01 7.02328747e+01 | 6.45794568e+00 -9.49468067e+01 7.02328747e+01 11 -1.93794281e+01 6.17412511e+01 3.18610245e+01 | -1.93794281e+01 6.17412511e+01 3.18610245e+01 12 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 | 1.44906422e+01 -6.75869550e+01 -3.14677936e+01 13 -1.56915973e+00 1.00792511e+02 -7.06261056e+01 | -1.56915973e+00 1.00792511e+02 -7.06261056e+01 14 6.45794568e+00 -9.49468067e+01 7.02328747e+01 | 6.45794568e+00 -9.49468067e+01 7.02328747e+01 15 -1.93794281e+01 6.17412511e+01 3.18610245e+01 | -1.93794281e+01 6.17412511e+01 3.18610245e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFF (Configuration in file "config-Si-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 130.57239609752096 2^p V(r_1,...,r_N) = 130.5723960975209 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -5.44429320e+01 -5.18178300e+01 -5.78648230e+01 | -5.44429320e+01 -5.18178300e+01 -5.78648230e+01 1 -2.51998210e+01 1.03549962e+02 -1.28948378e+02 | -2.51998210e+01 1.03549962e+02 -1.28948378e+02 2 1.86814930e+01 -8.57008769e+01 1.22622567e+02 | 1.86814930e+01 -8.57008769e+01 1.22622567e+02 3 6.09612600e+01 3.39687450e+01 6.41906343e+01 | 6.09612600e+01 3.39687450e+01 6.41906343e+01 4 -5.44429320e+01 -5.18178300e+01 -5.78648230e+01 | -5.44429320e+01 -5.18178300e+01 -5.78648230e+01 5 -2.51998210e+01 1.03549962e+02 -1.28948378e+02 | -2.51998210e+01 1.03549962e+02 -1.28948378e+02 6 1.86814930e+01 -8.57008769e+01 1.22622567e+02 | 1.86814930e+01 -8.57008769e+01 1.22622567e+02 7 6.09612600e+01 3.39687450e+01 6.41906343e+01 | 6.09612600e+01 3.39687450e+01 6.41906343e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTT (Configuration in file "config-Si-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 359.6107258508706 2^p V(r_1,...,r_N) = 359.61072585087055 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.10381811e+02 2.50907246e+01 1.34855645e+02 | -1.10381811e+02 2.50907246e+01 1.34855645e+02 1 5.79551205e+01 6.35388207e+00 -3.31661985e+01 | 5.79551205e+01 6.35388207e+00 -3.31661985e+01 2 1.21852224e+02 1.96251656e+01 -5.74302747e+01 | 1.21852224e+02 1.96251656e+01 -5.74302747e+01 3 -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 | -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 4 -1.10381811e+02 2.50907246e+01 1.34855645e+02 | -1.10381811e+02 2.50907246e+01 1.34855645e+02 5 5.79551205e+01 6.35388207e+00 -3.31661985e+01 | 5.79551205e+01 6.35388207e+00 -3.31661985e+01 6 1.21852224e+02 1.96251656e+01 -5.74302747e+01 | 1.21852224e+02 1.96251656e+01 -5.74302747e+01 7 -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 | -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 8 -1.10381811e+02 2.50907246e+01 1.34855645e+02 | -1.10381811e+02 2.50907246e+01 1.34855645e+02 9 5.79551205e+01 6.35388207e+00 -3.31661985e+01 | 5.79551205e+01 6.35388207e+00 -3.31661985e+01 10 1.21852224e+02 1.96251656e+01 -5.74302747e+01 | 1.21852224e+02 1.96251656e+01 -5.74302747e+01 11 -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 | -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 12 -1.10381811e+02 2.50907246e+01 1.34855645e+02 | -1.10381811e+02 2.50907246e+01 1.34855645e+02 13 5.79551205e+01 6.35388207e+00 -3.31661985e+01 | 5.79551205e+01 6.35388207e+00 -3.31661985e+01 14 1.21852224e+02 1.96251656e+01 -5.74302747e+01 | 1.21852224e+02 1.96251656e+01 -5.74302747e+01 15 -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 | -6.94255327e+01 -5.10697723e+01 -4.42591717e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTF (Configuration in file "config-Si-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 191.29724243814965 2^p V(r_1,...,r_N) = 191.29724243814965 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.73342538e+01 -3.85179132e+01 -1.74198803e+02 | -6.73342538e+01 -3.85179132e+01 -1.74198803e+02 1 5.16787940e+01 -3.51865685e+01 -7.67554074e+01 | 5.16787940e+01 -3.51865685e+01 -7.67554074e+01 2 8.17516649e+01 -2.94993320e+01 1.24816519e+02 | 8.17516649e+01 -2.94993320e+01 1.24816519e+02 3 -6.60962050e+01 1.03203814e+02 1.26137692e+02 | -6.60962050e+01 1.03203814e+02 1.26137692e+02 4 -6.73342538e+01 -3.85179132e+01 -1.74198803e+02 | -6.73342538e+01 -3.85179132e+01 -1.74198803e+02 5 5.16787940e+01 -3.51865685e+01 -7.67554074e+01 | 5.16787940e+01 -3.51865685e+01 -7.67554074e+01 6 8.17516649e+01 -2.94993320e+01 1.24816519e+02 | 8.17516649e+01 -2.94993320e+01 1.24816519e+02 7 -6.60962050e+01 1.03203814e+02 1.26137692e+02 | -6.60962050e+01 1.03203814e+02 1.26137692e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FFT (Configuration in file "config-Si-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 192.06145451960185 2^p V(r_1,...,r_N) = 192.06145451960188 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.92013366e+01 -5.27408829e+01 -5.40904291e+01 | -6.92013366e+01 -5.27408829e+01 -5.40904291e+01 1 3.94560105e+01 8.62404681e+01 5.93566132e+01 | 3.94560105e+01 8.62404681e+01 5.93566132e+01 2 1.28908217e+02 -1.36838963e+02 -9.53311098e+01 | 1.28908217e+02 -1.36838963e+02 -9.53311098e+01 3 -9.91628909e+01 1.03339378e+02 9.00649257e+01 | -9.91628909e+01 1.03339378e+02 9.00649257e+01 4 -6.92013366e+01 -5.27408829e+01 -5.40904291e+01 | -6.92013366e+01 -5.27408829e+01 -5.40904291e+01 5 3.94560105e+01 8.62404681e+01 5.93566132e+01 | 3.94560105e+01 8.62404681e+01 5.93566132e+01 6 1.28908217e+02 -1.36838963e+02 -9.53311098e+01 | 1.28908217e+02 -1.36838963e+02 -9.53311098e+01 7 -9.91628909e+01 1.03339378e+02 9.00649257e+01 | -9.91628909e+01 1.03339378e+02 9.00649257e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = TTT (Configuration in file "config-AlCuFeMgSi-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1845.9586589119547 2^p V(r_1,...,r_N) = 1845.9586589119635 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 | 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 1 -1.90349679e+01 2.85115386e+01 -3.21711204e+00 | -1.90349679e+01 2.85115386e+01 -3.21711204e+00 2 -5.86487470e+00 2.48840512e+01 -8.15606774e+00 | -5.86487470e+00 2.48840512e+01 -8.15606774e+00 3 -2.01503207e+01 7.97636516e+00 3.41055634e+01 | -2.01503207e+01 7.97636516e+00 3.41055634e+01 4 -2.31663820e+01 -7.00102428e+01 1.09479754e+01 | -2.31663820e+01 -7.00102428e+01 1.09479754e+01 5 7.61379129e+01 5.16494709e+01 7.97127254e+00 | 7.61379129e+01 5.16494709e+01 7.97127254e+00 6 -1.37355515e+01 2.65332105e+01 4.33058829e+01 | -1.37355515e+01 2.65332105e+01 4.33058829e+01 7 -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 | -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 8 -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 | -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 9 3.27571057e+01 -2.07310843e+00 2.41709578e+01 | 3.27571057e+01 -2.07310843e+00 2.41709578e+01 10 7.48637010e+00 -7.50319842e+00 5.02331345e+00 | 7.48637010e+00 -7.50319842e+00 5.02331345e+00 11 1.95176703e+01 1.23633205e+01 5.93400157e+00 | 1.95176703e+01 1.23633205e+01 5.93400157e+00 12 1.46276639e-01 1.44680169e+01 -1.80461771e+01 | 1.46276639e-01 1.44680169e+01 -1.80461771e+01 13 -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 | -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 14 3.57114820e+00 -6.36895924e+00 3.53819978e-02 | 3.57114820e+00 -6.36895924e+00 3.53819978e-02 15 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 | 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 16 -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 | -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 17 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 | 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 18 -2.12861925e+01 4.18211577e+01 1.03427815e+01 | -2.12861925e+01 4.18211577e+01 1.03427815e+01 19 -2.44590588e+01 6.96975903e+00 2.48647632e+01 | -2.44590588e+01 6.96975903e+00 2.48647632e+01 20 7.11843779e+00 1.47032162e+00 -4.92873299e-01 | 7.11843779e+00 1.47032162e+00 -4.92873299e-01 21 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 | 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 22 8.65226824e+01 4.64901511e+01 5.88316440e+00 | 8.65226824e+01 4.64901511e+01 5.88316440e+00 23 4.10401614e+00 -1.13357420e+01 1.36665096e+01 | 4.10401614e+00 -1.13357420e+01 1.36665096e+01 24 9.51689632e+00 -9.14499160e-01 9.28937374e-01 | 9.51689632e+00 -9.14499160e-01 9.28937374e-01 25 -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 | -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 26 -3.68656127e+01 -1.72107073e+01 3.16353938e+01 | -3.68656127e+01 -1.72107073e+01 3.16353938e+01 27 -5.11401567e+01 1.50057168e+01 -3.85166735e+01 | -5.11401567e+01 1.50057168e+01 -3.85166735e+01 28 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 | 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 29 -1.60446084e+01 1.72160056e+01 1.39454702e+01 | -1.60446084e+01 1.72160056e+01 1.39454702e+01 30 4.97981943e+00 1.12947573e+01 2.22145044e+01 | 4.97981943e+00 1.12947573e+01 2.22145044e+01 31 -1.96598837e+01 -5.47048658e+01 3.38496776e+01 | -1.96598837e+01 -5.47048658e+01 3.38496776e+01 32 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 | 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 33 -1.90349679e+01 2.85115386e+01 -3.21711204e+00 | -1.90349679e+01 2.85115386e+01 -3.21711204e+00 34 -5.86487470e+00 2.48840512e+01 -8.15606774e+00 | -5.86487470e+00 2.48840512e+01 -8.15606774e+00 35 -2.01503207e+01 7.97636516e+00 3.41055634e+01 | -2.01503207e+01 7.97636516e+00 3.41055634e+01 36 -2.31663820e+01 -7.00102428e+01 1.09479754e+01 | -2.31663820e+01 -7.00102428e+01 1.09479754e+01 37 7.61379129e+01 5.16494709e+01 7.97127254e+00 | 7.61379129e+01 5.16494709e+01 7.97127254e+00 38 -1.37355515e+01 2.65332105e+01 4.33058829e+01 | -1.37355515e+01 2.65332105e+01 4.33058829e+01 39 -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 | -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 40 -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 | -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 41 3.27571057e+01 -2.07310843e+00 2.41709578e+01 | 3.27571057e+01 -2.07310843e+00 2.41709578e+01 42 7.48637010e+00 -7.50319842e+00 5.02331345e+00 | 7.48637010e+00 -7.50319842e+00 5.02331345e+00 43 1.95176703e+01 1.23633205e+01 5.93400157e+00 | 1.95176703e+01 1.23633205e+01 5.93400157e+00 44 1.46276639e-01 1.44680169e+01 -1.80461771e+01 | 1.46276639e-01 1.44680169e+01 -1.80461771e+01 45 -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 | -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 46 3.57114820e+00 -6.36895924e+00 3.53819978e-02 | 3.57114820e+00 -6.36895924e+00 3.53819978e-02 47 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 | 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 48 -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 | -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 49 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 | 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 50 -2.12861925e+01 4.18211577e+01 1.03427815e+01 | -2.12861925e+01 4.18211577e+01 1.03427815e+01 51 -2.44590588e+01 6.96975903e+00 2.48647632e+01 | -2.44590588e+01 6.96975903e+00 2.48647632e+01 52 7.11843779e+00 1.47032162e+00 -4.92873299e-01 | 7.11843779e+00 1.47032162e+00 -4.92873299e-01 53 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 | 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 54 8.65226824e+01 4.64901511e+01 5.88316440e+00 | 8.65226824e+01 4.64901511e+01 5.88316440e+00 55 4.10401614e+00 -1.13357420e+01 1.36665096e+01 | 4.10401614e+00 -1.13357420e+01 1.36665096e+01 56 9.51689632e+00 -9.14499160e-01 9.28937374e-01 | 9.51689632e+00 -9.14499160e-01 9.28937374e-01 57 -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 | -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 58 -3.68656127e+01 -1.72107073e+01 3.16353938e+01 | -3.68656127e+01 -1.72107073e+01 3.16353938e+01 59 -5.11401567e+01 1.50057168e+01 -3.85166735e+01 | -5.11401567e+01 1.50057168e+01 -3.85166735e+01 60 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 | 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 61 -1.60446084e+01 1.72160056e+01 1.39454702e+01 | -1.60446084e+01 1.72160056e+01 1.39454702e+01 62 4.97981943e+00 1.12947573e+01 2.22145044e+01 | 4.97981943e+00 1.12947573e+01 2.22145044e+01 63 -1.96598837e+01 -5.47048658e+01 3.38496776e+01 | -1.96598837e+01 -5.47048658e+01 3.38496776e+01 64 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 | 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 65 -1.90349679e+01 2.85115386e+01 -3.21711204e+00 | -1.90349679e+01 2.85115386e+01 -3.21711204e+00 66 -5.86487470e+00 2.48840512e+01 -8.15606774e+00 | -5.86487470e+00 2.48840512e+01 -8.15606774e+00 67 -2.01503207e+01 7.97636516e+00 3.41055634e+01 | -2.01503207e+01 7.97636516e+00 3.41055634e+01 68 -2.31663820e+01 -7.00102428e+01 1.09479754e+01 | -2.31663820e+01 -7.00102428e+01 1.09479754e+01 69 7.61379129e+01 5.16494709e+01 7.97127254e+00 | 7.61379129e+01 5.16494709e+01 7.97127254e+00 70 -1.37355515e+01 2.65332105e+01 4.33058829e+01 | -1.37355515e+01 2.65332105e+01 4.33058829e+01 71 -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 | -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 72 -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 | -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 73 3.27571057e+01 -2.07310843e+00 2.41709578e+01 | 3.27571057e+01 -2.07310843e+00 2.41709578e+01 74 7.48637010e+00 -7.50319842e+00 5.02331345e+00 | 7.48637010e+00 -7.50319842e+00 5.02331345e+00 75 1.95176703e+01 1.23633205e+01 5.93400157e+00 | 1.95176703e+01 1.23633205e+01 5.93400157e+00 76 1.46276639e-01 1.44680169e+01 -1.80461771e+01 | 1.46276639e-01 1.44680169e+01 -1.80461771e+01 77 -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 | -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 78 3.57114820e+00 -6.36895924e+00 3.53819978e-02 | 3.57114820e+00 -6.36895924e+00 3.53819978e-02 79 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 | 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 80 -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 | -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 81 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 | 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 82 -2.12861925e+01 4.18211577e+01 1.03427815e+01 | -2.12861925e+01 4.18211577e+01 1.03427815e+01 83 -2.44590588e+01 6.96975903e+00 2.48647632e+01 | -2.44590588e+01 6.96975903e+00 2.48647632e+01 84 7.11843779e+00 1.47032162e+00 -4.92873299e-01 | 7.11843779e+00 1.47032162e+00 -4.92873299e-01 85 7.45628764e+00 -1.88968878e+01 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-8.68611432e+00 -4.29438042e+01 -4.53820630e+01 206 3.57114820e+00 -6.36895924e+00 3.53819978e-02 | 3.57114820e+00 -6.36895924e+00 3.53819978e-02 207 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 | 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 208 -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 | -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 209 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 | 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 210 -2.12861925e+01 4.18211577e+01 1.03427815e+01 | -2.12861925e+01 4.18211577e+01 1.03427815e+01 211 -2.44590588e+01 6.96975903e+00 2.48647632e+01 | -2.44590588e+01 6.96975903e+00 2.48647632e+01 212 7.11843779e+00 1.47032162e+00 -4.92873299e-01 | 7.11843779e+00 1.47032162e+00 -4.92873299e-01 213 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 | 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 214 8.65226824e+01 4.64901511e+01 5.88316440e+00 | 8.65226824e+01 4.64901511e+01 5.88316440e+00 215 4.10401614e+00 -1.13357420e+01 1.36665096e+01 | 4.10401614e+00 -1.13357420e+01 1.36665096e+01 216 9.51689632e+00 -9.14499160e-01 9.28937374e-01 | 9.51689632e+00 -9.14499160e-01 9.28937374e-01 217 -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 | -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 218 -3.68656127e+01 -1.72107073e+01 3.16353938e+01 | -3.68656127e+01 -1.72107073e+01 3.16353938e+01 219 -5.11401567e+01 1.50057168e+01 -3.85166735e+01 | -5.11401567e+01 1.50057168e+01 -3.85166735e+01 220 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 | 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 221 -1.60446084e+01 1.72160056e+01 1.39454702e+01 | -1.60446084e+01 1.72160056e+01 1.39454702e+01 222 4.97981943e+00 1.12947573e+01 2.22145044e+01 | 4.97981943e+00 1.12947573e+01 2.22145044e+01 223 -1.96598837e+01 -5.47048658e+01 3.38496776e+01 | -1.96598837e+01 -5.47048658e+01 3.38496776e+01 224 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 | 1.27441763e+01 -1.91397619e+01 -3.19750445e+01 225 -1.90349679e+01 2.85115386e+01 -3.21711204e+00 | -1.90349679e+01 2.85115386e+01 -3.21711204e+00 226 -5.86487470e+00 2.48840512e+01 -8.15606774e+00 | -5.86487470e+00 2.48840512e+01 -8.15606774e+00 227 -2.01503207e+01 7.97636516e+00 3.41055634e+01 | -2.01503207e+01 7.97636516e+00 3.41055634e+01 228 -2.31663820e+01 -7.00102428e+01 1.09479754e+01 | -2.31663820e+01 -7.00102428e+01 1.09479754e+01 229 7.61379129e+01 5.16494709e+01 7.97127254e+00 | 7.61379129e+01 5.16494709e+01 7.97127254e+00 230 -1.37355515e+01 2.65332105e+01 4.33058829e+01 | -1.37355515e+01 2.65332105e+01 4.33058829e+01 231 -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 | -3.81786471e+00 -1.38096996e+01 -1.52023388e+01 232 -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 | -7.15475526e+00 -4.18585099e+00 -1.61617928e+00 233 3.27571057e+01 -2.07310843e+00 2.41709578e+01 | 3.27571057e+01 -2.07310843e+00 2.41709578e+01 234 7.48637010e+00 -7.50319842e+00 5.02331345e+00 | 7.48637010e+00 -7.50319842e+00 5.02331345e+00 235 1.95176703e+01 1.23633205e+01 5.93400157e+00 | 1.95176703e+01 1.23633205e+01 5.93400157e+00 236 1.46276639e-01 1.44680169e+01 -1.80461771e+01 | 1.46276639e-01 1.44680169e+01 -1.80461771e+01 237 -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 | -8.68611432e+00 -4.29438042e+01 -4.53820630e+01 238 3.57114820e+00 -6.36895924e+00 3.53819978e-02 | 3.57114820e+00 -6.36895924e+00 3.53819978e-02 239 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 | 1.71955531e+01 -2.40400137e+00 -2.07175765e+00 240 -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 | -1.90896262e+01 -8.13288212e+00 -1.60465638e+01 241 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 | 2.70439199e+01 -1.67277603e+01 -1.89838997e+01 242 -2.12861925e+01 4.18211577e+01 1.03427815e+01 | -2.12861925e+01 4.18211577e+01 1.03427815e+01 243 -2.44590588e+01 6.96975903e+00 2.48647632e+01 | -2.44590588e+01 6.96975903e+00 2.48647632e+01 244 7.11843779e+00 1.47032162e+00 -4.92873299e-01 | 7.11843779e+00 1.47032162e+00 -4.92873299e-01 245 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 | 7.45628764e+00 -1.88968878e+01 -1.07438733e+01 246 8.65226824e+01 4.64901511e+01 5.88316440e+00 | 8.65226824e+01 4.64901511e+01 5.88316440e+00 247 4.10401614e+00 -1.13357420e+01 1.36665096e+01 | 4.10401614e+00 -1.13357420e+01 1.36665096e+01 248 9.51689632e+00 -9.14499160e-01 9.28937374e-01 | 9.51689632e+00 -9.14499160e-01 9.28937374e-01 249 -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 | -4.71523712e+01 -6.26387667e+00 -5.20991353e+01 250 -3.68656127e+01 -1.72107073e+01 3.16353938e+01 | -3.68656127e+01 -1.72107073e+01 3.16353938e+01 251 -5.11401567e+01 1.50057168e+01 -3.85166735e+01 | -5.11401567e+01 1.50057168e+01 -3.85166735e+01 252 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 | 2.10100682e+01 -4.02799464e+00 -2.62757924e+01 253 -1.60446084e+01 1.72160056e+01 1.39454702e+01 | -1.60446084e+01 1.72160056e+01 1.39454702e+01 254 4.97981943e+00 1.12947573e+01 2.22145044e+01 | 4.97981943e+00 1.12947573e+01 2.22145044e+01 255 -1.96598837e+01 -5.47048658e+01 3.38496776e+01 | -1.96598837e+01 -5.47048658e+01 3.38496776e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = TTF (Configuration in file "config-AlCuFeMgSi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 796.949771781673 2^p V(r_1,...,r_N) = 796.9497717816736 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 | 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 1 1.76678171e+01 1.19724988e+01 -5.64116377e+01 | 1.76678171e+01 1.19724988e+01 -5.64116377e+01 2 -1.52925547e+00 -3.00048136e+01 2.87705788e+01 | -1.52925547e+00 -3.00048136e+01 2.87705788e+01 3 -1.55609838e+01 1.08066713e+01 2.80600717e+01 | -1.55609838e+01 1.08066713e+01 2.80600717e+01 4 -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 | -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 5 2.26272524e+01 5.99977219e+01 -6.36518804e+01 | 2.26272524e+01 5.99977219e+01 -6.36518804e+01 6 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 | 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 7 -2.83924675e+01 3.38157555e+01 1.80608729e+01 | -2.83924675e+01 3.38157555e+01 1.80608729e+01 8 -4.71303197e+00 2.04849655e+01 -9.48269394e+00 | -4.71303197e+00 2.04849655e+01 -9.48269394e+00 9 -5.12891970e+01 3.60623668e+01 -2.04041455e+01 | -5.12891970e+01 3.60623668e+01 -2.04041455e+01 10 1.70146839e+00 -1.53298215e+01 1.42098925e+01 | 1.70146839e+00 -1.53298215e+01 1.42098925e+01 11 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 | 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 12 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 | 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 13 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 | 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 14 -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 | -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 15 -4.35279039e+01 3.90460575e+00 2.90446234e+01 | -4.35279039e+01 3.90460575e+00 2.90446234e+01 16 -9.82025026e+00 2.55251625e+01 1.56919583e+01 | -9.82025026e+00 2.55251625e+01 1.56919583e+01 17 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 | 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 18 -7.93246478e+00 3.03273962e+00 1.32336613e+01 | -7.93246478e+00 3.03273962e+00 1.32336613e+01 19 -2.15870560e+01 1.54293143e+01 8.13967850e+00 | -2.15870560e+01 1.54293143e+01 8.13967850e+00 20 1.09010080e+01 9.77598143e+00 3.50204482e+01 | 1.09010080e+01 9.77598143e+00 3.50204482e+01 21 -8.56965726e+00 2.52384254e+01 5.34050625e+01 | -8.56965726e+00 2.52384254e+01 5.34050625e+01 22 -1.40389372e+00 -1.11953525e+01 8.36297927e+00 | -1.40389372e+00 -1.11953525e+01 8.36297927e+00 23 3.88844417e+00 6.28882467e+00 1.06180645e+01 | 3.88844417e+00 6.28882467e+00 1.06180645e+01 24 -1.59817035e+01 -7.26870878e+00 1.08710286e+01 | -1.59817035e+01 -7.26870878e+00 1.08710286e+01 25 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 | 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 26 -1.99308091e+01 -1.53504161e+01 1.09765946e+01 | -1.99308091e+01 -1.53504161e+01 1.09765946e+01 27 -1.63971887e+00 -3.57229669e+00 4.91146610e+00 | -1.63971887e+00 -3.57229669e+00 4.91146610e+00 28 1.47932181e+01 6.10512327e+00 -1.59815817e+01 | 1.47932181e+01 6.10512327e+00 -1.59815817e+01 29 1.10599321e+00 4.67920905e+00 4.89419235e+00 | 1.10599321e+00 4.67920905e+00 4.89419235e+00 30 5.30684876e+00 6.20844456e+00 2.66180373e+00 | 5.30684876e+00 6.20844456e+00 2.66180373e+00 31 2.16185879e+01 1.09025460e+01 1.14024142e+01 | 2.16185879e+01 1.09025460e+01 1.14024142e+01 32 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 | 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 33 1.76678171e+01 1.19724988e+01 -5.64116377e+01 | 1.76678171e+01 1.19724988e+01 -5.64116377e+01 34 -1.52925547e+00 -3.00048136e+01 2.87705788e+01 | -1.52925547e+00 -3.00048136e+01 2.87705788e+01 35 -1.55609838e+01 1.08066713e+01 2.80600717e+01 | -1.55609838e+01 1.08066713e+01 2.80600717e+01 36 -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 | -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 37 2.26272524e+01 5.99977219e+01 -6.36518804e+01 | 2.26272524e+01 5.99977219e+01 -6.36518804e+01 38 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 | 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 39 -2.83924675e+01 3.38157555e+01 1.80608729e+01 | -2.83924675e+01 3.38157555e+01 1.80608729e+01 40 -4.71303197e+00 2.04849655e+01 -9.48269394e+00 | -4.71303197e+00 2.04849655e+01 -9.48269394e+00 41 -5.12891970e+01 3.60623668e+01 -2.04041455e+01 | -5.12891970e+01 3.60623668e+01 -2.04041455e+01 42 1.70146839e+00 -1.53298215e+01 1.42098925e+01 | 1.70146839e+00 -1.53298215e+01 1.42098925e+01 43 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 | 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 44 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 | 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 45 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 | 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 46 -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 | -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 47 -4.35279039e+01 3.90460575e+00 2.90446234e+01 | -4.35279039e+01 3.90460575e+00 2.90446234e+01 48 -9.82025026e+00 2.55251625e+01 1.56919583e+01 | -9.82025026e+00 2.55251625e+01 1.56919583e+01 49 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 | 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 50 -7.93246478e+00 3.03273962e+00 1.32336613e+01 | -7.93246478e+00 3.03273962e+00 1.32336613e+01 51 -2.15870560e+01 1.54293143e+01 8.13967850e+00 | -2.15870560e+01 1.54293143e+01 8.13967850e+00 52 1.09010080e+01 9.77598143e+00 3.50204482e+01 | 1.09010080e+01 9.77598143e+00 3.50204482e+01 53 -8.56965726e+00 2.52384254e+01 5.34050625e+01 | -8.56965726e+00 2.52384254e+01 5.34050625e+01 54 -1.40389372e+00 -1.11953525e+01 8.36297927e+00 | -1.40389372e+00 -1.11953525e+01 8.36297927e+00 55 3.88844417e+00 6.28882467e+00 1.06180645e+01 | 3.88844417e+00 6.28882467e+00 1.06180645e+01 56 -1.59817035e+01 -7.26870878e+00 1.08710286e+01 | -1.59817035e+01 -7.26870878e+00 1.08710286e+01 57 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 | 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 58 -1.99308091e+01 -1.53504161e+01 1.09765946e+01 | -1.99308091e+01 -1.53504161e+01 1.09765946e+01 59 -1.63971887e+00 -3.57229669e+00 4.91146610e+00 | -1.63971887e+00 -3.57229669e+00 4.91146610e+00 60 1.47932181e+01 6.10512327e+00 -1.59815817e+01 | 1.47932181e+01 6.10512327e+00 -1.59815817e+01 61 1.10599321e+00 4.67920905e+00 4.89419235e+00 | 1.10599321e+00 4.67920905e+00 4.89419235e+00 62 5.30684876e+00 6.20844456e+00 2.66180373e+00 | 5.30684876e+00 6.20844456e+00 2.66180373e+00 63 2.16185879e+01 1.09025460e+01 1.14024142e+01 | 2.16185879e+01 1.09025460e+01 1.14024142e+01 64 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 | 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 65 1.76678171e+01 1.19724988e+01 -5.64116377e+01 | 1.76678171e+01 1.19724988e+01 -5.64116377e+01 66 -1.52925547e+00 -3.00048136e+01 2.87705788e+01 | -1.52925547e+00 -3.00048136e+01 2.87705788e+01 67 -1.55609838e+01 1.08066713e+01 2.80600717e+01 | -1.55609838e+01 1.08066713e+01 2.80600717e+01 68 -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 | -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 69 2.26272524e+01 5.99977219e+01 -6.36518804e+01 | 2.26272524e+01 5.99977219e+01 -6.36518804e+01 70 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 | 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 71 -2.83924675e+01 3.38157555e+01 1.80608729e+01 | -2.83924675e+01 3.38157555e+01 1.80608729e+01 72 -4.71303197e+00 2.04849655e+01 -9.48269394e+00 | -4.71303197e+00 2.04849655e+01 -9.48269394e+00 73 -5.12891970e+01 3.60623668e+01 -2.04041455e+01 | -5.12891970e+01 3.60623668e+01 -2.04041455e+01 74 1.70146839e+00 -1.53298215e+01 1.42098925e+01 | 1.70146839e+00 -1.53298215e+01 1.42098925e+01 75 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 | 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 76 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 | 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 77 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 | 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 78 -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 | -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 79 -4.35279039e+01 3.90460575e+00 2.90446234e+01 | -4.35279039e+01 3.90460575e+00 2.90446234e+01 80 -9.82025026e+00 2.55251625e+01 1.56919583e+01 | -9.82025026e+00 2.55251625e+01 1.56919583e+01 81 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 | 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 82 -7.93246478e+00 3.03273962e+00 1.32336613e+01 | -7.93246478e+00 3.03273962e+00 1.32336613e+01 83 -2.15870560e+01 1.54293143e+01 8.13967850e+00 | -2.15870560e+01 1.54293143e+01 8.13967850e+00 84 1.09010080e+01 9.77598143e+00 3.50204482e+01 | 1.09010080e+01 9.77598143e+00 3.50204482e+01 85 -8.56965726e+00 2.52384254e+01 5.34050625e+01 | -8.56965726e+00 2.52384254e+01 5.34050625e+01 86 -1.40389372e+00 -1.11953525e+01 8.36297927e+00 | -1.40389372e+00 -1.11953525e+01 8.36297927e+00 87 3.88844417e+00 6.28882467e+00 1.06180645e+01 | 3.88844417e+00 6.28882467e+00 1.06180645e+01 88 -1.59817035e+01 -7.26870878e+00 1.08710286e+01 | -1.59817035e+01 -7.26870878e+00 1.08710286e+01 89 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 | 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 90 -1.99308091e+01 -1.53504161e+01 1.09765946e+01 | -1.99308091e+01 -1.53504161e+01 1.09765946e+01 91 -1.63971887e+00 -3.57229669e+00 4.91146610e+00 | -1.63971887e+00 -3.57229669e+00 4.91146610e+00 92 1.47932181e+01 6.10512327e+00 -1.59815817e+01 | 1.47932181e+01 6.10512327e+00 -1.59815817e+01 93 1.10599321e+00 4.67920905e+00 4.89419235e+00 | 1.10599321e+00 4.67920905e+00 4.89419235e+00 94 5.30684876e+00 6.20844456e+00 2.66180373e+00 | 5.30684876e+00 6.20844456e+00 2.66180373e+00 95 2.16185879e+01 1.09025460e+01 1.14024142e+01 | 2.16185879e+01 1.09025460e+01 1.14024142e+01 96 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 | 2.26255796e+01 -1.39323730e+01 -3.02763668e+00 97 1.76678171e+01 1.19724988e+01 -5.64116377e+01 | 1.76678171e+01 1.19724988e+01 -5.64116377e+01 98 -1.52925547e+00 -3.00048136e+01 2.87705788e+01 | -1.52925547e+00 -3.00048136e+01 2.87705788e+01 99 -1.55609838e+01 1.08066713e+01 2.80600717e+01 | -1.55609838e+01 1.08066713e+01 2.80600717e+01 100 -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 | -2.16586396e+01 -6.72900166e+00 -1.77555880e+00 101 2.26272524e+01 5.99977219e+01 -6.36518804e+01 | 2.26272524e+01 5.99977219e+01 -6.36518804e+01 102 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 | 5.59547076e+00 -8.21789905e+01 -7.27223283e+01 103 -2.83924675e+01 3.38157555e+01 1.80608729e+01 | -2.83924675e+01 3.38157555e+01 1.80608729e+01 104 -4.71303197e+00 2.04849655e+01 -9.48269394e+00 | -4.71303197e+00 2.04849655e+01 -9.48269394e+00 105 -5.12891970e+01 3.60623668e+01 -2.04041455e+01 | -5.12891970e+01 3.60623668e+01 -2.04041455e+01 106 1.70146839e+00 -1.53298215e+01 1.42098925e+01 | 1.70146839e+00 -1.53298215e+01 1.42098925e+01 107 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 | 7.80028977e+00 -1.07161833e+01 -1.87385391e+01 108 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 | 2.04970444e+01 -3.79486757e+01 -7.31820570e+00 109 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 | 7.31910734e+01 -1.02388223e+01 -3.00068235e+01 110 -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 | -5.26947474e+00 -1.32630707e+01 -2.07663025e+00 111 -4.35279039e+01 3.90460575e+00 2.90446234e+01 | -4.35279039e+01 3.90460575e+00 2.90446234e+01 112 -9.82025026e+00 2.55251625e+01 1.56919583e+01 | -9.82025026e+00 2.55251625e+01 1.56919583e+01 113 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 | 2.27693566e+01 -3.14900690e+01 -1.86486950e+00 114 -7.93246478e+00 3.03273962e+00 1.32336613e+01 | -7.93246478e+00 3.03273962e+00 1.32336613e+01 115 -2.15870560e+01 1.54293143e+01 8.13967850e+00 | -2.15870560e+01 1.54293143e+01 8.13967850e+00 116 1.09010080e+01 9.77598143e+00 3.50204482e+01 | 1.09010080e+01 9.77598143e+00 3.50204482e+01 117 -8.56965726e+00 2.52384254e+01 5.34050625e+01 | -8.56965726e+00 2.52384254e+01 5.34050625e+01 118 -1.40389372e+00 -1.11953525e+01 8.36297927e+00 | -1.40389372e+00 -1.11953525e+01 8.36297927e+00 119 3.88844417e+00 6.28882467e+00 1.06180645e+01 | 3.88844417e+00 6.28882467e+00 1.06180645e+01 120 -1.59817035e+01 -7.26870878e+00 1.08710286e+01 | -1.59817035e+01 -7.26870878e+00 1.08710286e+01 121 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 | 6.71705485e+00 -1.01176100e+00 -4.87286048e+00 122 -1.99308091e+01 -1.53504161e+01 1.09765946e+01 | -1.99308091e+01 -1.53504161e+01 1.09765946e+01 123 -1.63971887e+00 -3.57229669e+00 4.91146610e+00 | -1.63971887e+00 -3.57229669e+00 4.91146610e+00 124 1.47932181e+01 6.10512327e+00 -1.59815817e+01 | 1.47932181e+01 6.10512327e+00 -1.59815817e+01 125 1.10599321e+00 4.67920905e+00 4.89419235e+00 | 1.10599321e+00 4.67920905e+00 4.89419235e+00 126 5.30684876e+00 6.20844456e+00 2.66180373e+00 | 5.30684876e+00 6.20844456e+00 2.66180373e+00 127 2.16185879e+01 1.09025460e+01 1.14024142e+01 | 2.16185879e+01 1.09025460e+01 1.14024142e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = TFT (Configuration in file "config-AlCuFeMgSi-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 641.7538753915279 2^p V(r_1,...,r_N) = 641.7538753915267 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 2.10997138e+01 -2.18084833e+01 2.50380318e+01 | 2.10997138e+01 -2.18084833e+01 2.50380318e+01 1 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 | 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 2 -4.09397670e-01 -1.62058117e+01 2.49803024e+00 | -4.09397670e-01 -1.62058117e+01 2.49803024e+00 3 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 | 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 4 -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 | -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 5 -4.01696096e+00 2.36236635e+01 5.90962233e+00 | -4.01696096e+00 2.36236635e+01 5.90962233e+00 6 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 | 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 7 -1.75376524e+01 2.39695007e+01 -1.24776786e+01 | -1.75376524e+01 2.39695007e+01 -1.24776786e+01 8 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 | 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 9 2.77863205e+00 6.21342250e+00 7.00130601e+00 | 2.77863205e+00 6.21342250e+00 7.00130601e+00 10 7.33011428e+00 5.30937703e+01 6.12431878e+01 | 7.33011428e+00 5.30937703e+01 6.12431878e+01 11 5.59806670e-01 1.10236288e+01 1.88310481e+00 | 5.59806670e-01 1.10236288e+01 1.88310481e+00 12 -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 | -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 13 4.18202524e+00 1.33570960e+01 -5.92947061e+00 | 4.18202524e+00 1.33570960e+01 -5.92947061e+00 14 -1.12226470e+01 1.89433985e+01 4.02923933e+01 | -1.12226470e+01 1.89433985e+01 4.02923933e+01 15 8.78943563e+00 1.83193426e+01 1.25512529e+01 | 8.78943563e+00 1.83193426e+01 1.25512529e+01 16 3.04966687e+01 -2.33834603e+01 1.24787616e+01 | 3.04966687e+01 -2.33834603e+01 1.24787616e+01 17 -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 | -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 18 -1.29361365e+01 -2.37452320e+01 7.56075530e+00 | -1.29361365e+01 -2.37452320e+01 7.56075530e+00 19 -1.08947706e+01 4.59355847e+00 -2.07556214e+01 | -1.08947706e+01 4.59355847e+00 -2.07556214e+01 20 1.77347272e+01 -3.96261171e+01 2.11690511e+01 | 1.77347272e+01 -3.96261171e+01 2.11690511e+01 21 -2.07749399e+01 2.02986257e+01 2.32875723e+01 | -2.07749399e+01 2.02986257e+01 2.32875723e+01 22 -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 | -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 23 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 | 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 24 7.29330862e+00 2.23718144e+01 1.90816448e-01 | 7.29330862e+00 2.23718144e+01 1.90816448e-01 25 2.70901510e+01 1.67031886e+01 -2.21451616e+01 | 2.70901510e+01 1.67031886e+01 -2.21451616e+01 26 -1.32732268e+01 7.36201578e+01 2.84155606e+01 | -1.32732268e+01 7.36201578e+01 2.84155606e+01 27 -1.05453911e+00 1.63850616e+01 2.30953297e+01 | -1.05453911e+00 1.63850616e+01 2.30953297e+01 28 -1.11650067e+01 -6.96998574e+00 2.85665460e+01 | -1.11650067e+01 -6.96998574e+00 2.85665460e+01 29 -7.69536770e+00 1.13515061e+01 -3.87922792e-01 | -7.69536770e+00 1.13515061e+01 -3.87922792e-01 30 -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 | -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 31 -3.83469399e+00 1.15036220e+01 5.14668352e+00 | -3.83469399e+00 1.15036220e+01 5.14668352e+00 32 2.10997138e+01 -2.18084833e+01 2.50380318e+01 | 2.10997138e+01 -2.18084833e+01 2.50380318e+01 33 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 | 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 34 -4.09397670e-01 -1.62058117e+01 2.49803024e+00 | -4.09397670e-01 -1.62058117e+01 2.49803024e+00 35 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 | 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 36 -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 | -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 37 -4.01696096e+00 2.36236635e+01 5.90962233e+00 | -4.01696096e+00 2.36236635e+01 5.90962233e+00 38 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 | 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 39 -1.75376524e+01 2.39695007e+01 -1.24776786e+01 | -1.75376524e+01 2.39695007e+01 -1.24776786e+01 40 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 | 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 41 2.77863205e+00 6.21342250e+00 7.00130601e+00 | 2.77863205e+00 6.21342250e+00 7.00130601e+00 42 7.33011428e+00 5.30937703e+01 6.12431878e+01 | 7.33011428e+00 5.30937703e+01 6.12431878e+01 43 5.59806670e-01 1.10236288e+01 1.88310481e+00 | 5.59806670e-01 1.10236288e+01 1.88310481e+00 44 -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 | -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 45 4.18202524e+00 1.33570960e+01 -5.92947061e+00 | 4.18202524e+00 1.33570960e+01 -5.92947061e+00 46 -1.12226470e+01 1.89433985e+01 4.02923933e+01 | -1.12226470e+01 1.89433985e+01 4.02923933e+01 47 8.78943563e+00 1.83193426e+01 1.25512529e+01 | 8.78943563e+00 1.83193426e+01 1.25512529e+01 48 3.04966687e+01 -2.33834603e+01 1.24787616e+01 | 3.04966687e+01 -2.33834603e+01 1.24787616e+01 49 -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 | -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 50 -1.29361365e+01 -2.37452320e+01 7.56075530e+00 | -1.29361365e+01 -2.37452320e+01 7.56075530e+00 51 -1.08947706e+01 4.59355847e+00 -2.07556214e+01 | -1.08947706e+01 4.59355847e+00 -2.07556214e+01 52 1.77347272e+01 -3.96261171e+01 2.11690511e+01 | 1.77347272e+01 -3.96261171e+01 2.11690511e+01 53 -2.07749399e+01 2.02986257e+01 2.32875723e+01 | -2.07749399e+01 2.02986257e+01 2.32875723e+01 54 -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 | -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 55 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 | 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 56 7.29330862e+00 2.23718144e+01 1.90816448e-01 | 7.29330862e+00 2.23718144e+01 1.90816448e-01 57 2.70901510e+01 1.67031886e+01 -2.21451616e+01 | 2.70901510e+01 1.67031886e+01 -2.21451616e+01 58 -1.32732268e+01 7.36201578e+01 2.84155606e+01 | -1.32732268e+01 7.36201578e+01 2.84155606e+01 59 -1.05453911e+00 1.63850616e+01 2.30953297e+01 | -1.05453911e+00 1.63850616e+01 2.30953297e+01 60 -1.11650067e+01 -6.96998574e+00 2.85665460e+01 | -1.11650067e+01 -6.96998574e+00 2.85665460e+01 61 -7.69536770e+00 1.13515061e+01 -3.87922792e-01 | -7.69536770e+00 1.13515061e+01 -3.87922792e-01 62 -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 | -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 63 -3.83469399e+00 1.15036220e+01 5.14668352e+00 | -3.83469399e+00 1.15036220e+01 5.14668352e+00 64 2.10997138e+01 -2.18084833e+01 2.50380318e+01 | 2.10997138e+01 -2.18084833e+01 2.50380318e+01 65 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 | 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 66 -4.09397670e-01 -1.62058117e+01 2.49803024e+00 | -4.09397670e-01 -1.62058117e+01 2.49803024e+00 67 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 | 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 68 -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 | -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 69 -4.01696096e+00 2.36236635e+01 5.90962233e+00 | -4.01696096e+00 2.36236635e+01 5.90962233e+00 70 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 | 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 71 -1.75376524e+01 2.39695007e+01 -1.24776786e+01 | -1.75376524e+01 2.39695007e+01 -1.24776786e+01 72 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 | 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 73 2.77863205e+00 6.21342250e+00 7.00130601e+00 | 2.77863205e+00 6.21342250e+00 7.00130601e+00 74 7.33011428e+00 5.30937703e+01 6.12431878e+01 | 7.33011428e+00 5.30937703e+01 6.12431878e+01 75 5.59806670e-01 1.10236288e+01 1.88310481e+00 | 5.59806670e-01 1.10236288e+01 1.88310481e+00 76 -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 | -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 77 4.18202524e+00 1.33570960e+01 -5.92947061e+00 | 4.18202524e+00 1.33570960e+01 -5.92947061e+00 78 -1.12226470e+01 1.89433985e+01 4.02923933e+01 | -1.12226470e+01 1.89433985e+01 4.02923933e+01 79 8.78943563e+00 1.83193426e+01 1.25512529e+01 | 8.78943563e+00 1.83193426e+01 1.25512529e+01 80 3.04966687e+01 -2.33834603e+01 1.24787616e+01 | 3.04966687e+01 -2.33834603e+01 1.24787616e+01 81 -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 | -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 82 -1.29361365e+01 -2.37452320e+01 7.56075530e+00 | -1.29361365e+01 -2.37452320e+01 7.56075530e+00 83 -1.08947706e+01 4.59355847e+00 -2.07556214e+01 | -1.08947706e+01 4.59355847e+00 -2.07556214e+01 84 1.77347272e+01 -3.96261171e+01 2.11690511e+01 | 1.77347272e+01 -3.96261171e+01 2.11690511e+01 85 -2.07749399e+01 2.02986257e+01 2.32875723e+01 | -2.07749399e+01 2.02986257e+01 2.32875723e+01 86 -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 | -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 87 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 | 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 88 7.29330862e+00 2.23718144e+01 1.90816448e-01 | 7.29330862e+00 2.23718144e+01 1.90816448e-01 89 2.70901510e+01 1.67031886e+01 -2.21451616e+01 | 2.70901510e+01 1.67031886e+01 -2.21451616e+01 90 -1.32732268e+01 7.36201578e+01 2.84155606e+01 | -1.32732268e+01 7.36201578e+01 2.84155606e+01 91 -1.05453911e+00 1.63850616e+01 2.30953297e+01 | -1.05453911e+00 1.63850616e+01 2.30953297e+01 92 -1.11650067e+01 -6.96998574e+00 2.85665460e+01 | -1.11650067e+01 -6.96998574e+00 2.85665460e+01 93 -7.69536770e+00 1.13515061e+01 -3.87922792e-01 | -7.69536770e+00 1.13515061e+01 -3.87922792e-01 94 -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 | -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 95 -3.83469399e+00 1.15036220e+01 5.14668352e+00 | -3.83469399e+00 1.15036220e+01 5.14668352e+00 96 2.10997138e+01 -2.18084833e+01 2.50380318e+01 | 2.10997138e+01 -2.18084833e+01 2.50380318e+01 97 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 | 1.20581701e+01 -4.84940385e+01 -6.86357649e+01 98 -4.09397670e-01 -1.62058117e+01 2.49803024e+00 | -4.09397670e-01 -1.62058117e+01 2.49803024e+00 99 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 | 9.68521059e+00 -1.08518225e+01 -2.44510701e+01 100 -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 | -2.58702571e+01 -1.85568621e+01 -7.22351816e+00 101 -4.01696096e+00 2.36236635e+01 5.90962233e+00 | -4.01696096e+00 2.36236635e+01 5.90962233e+00 102 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 | 1.62176158e+01 -1.44841850e+00 -1.10702907e+01 103 -1.75376524e+01 2.39695007e+01 -1.24776786e+01 | -1.75376524e+01 2.39695007e+01 -1.24776786e+01 104 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 | 9.41632060e+00 -9.88593343e+00 -5.68455595e+00 105 2.77863205e+00 6.21342250e+00 7.00130601e+00 | 2.77863205e+00 6.21342250e+00 7.00130601e+00 106 7.33011428e+00 5.30937703e+01 6.12431878e+01 | 7.33011428e+00 5.30937703e+01 6.12431878e+01 107 5.59806670e-01 1.10236288e+01 1.88310481e+00 | 5.59806670e-01 1.10236288e+01 1.88310481e+00 108 -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 | -2.69227128e+01 -2.47890016e+01 -3.46811255e+01 109 4.18202524e+00 1.33570960e+01 -5.92947061e+00 | 4.18202524e+00 1.33570960e+01 -5.92947061e+00 110 -1.12226470e+01 1.89433985e+01 4.02923933e+01 | -1.12226470e+01 1.89433985e+01 4.02923933e+01 111 8.78943563e+00 1.83193426e+01 1.25512529e+01 | 8.78943563e+00 1.83193426e+01 1.25512529e+01 112 3.04966687e+01 -2.33834603e+01 1.24787616e+01 | 3.04966687e+01 -2.33834603e+01 1.24787616e+01 113 -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 | -3.18701037e+00 -3.16237415e+01 -6.27074623e+01 114 -1.29361365e+01 -2.37452320e+01 7.56075530e+00 | -1.29361365e+01 -2.37452320e+01 7.56075530e+00 115 -1.08947706e+01 4.59355847e+00 -2.07556214e+01 | -1.08947706e+01 4.59355847e+00 -2.07556214e+01 116 1.77347272e+01 -3.96261171e+01 2.11690511e+01 | 1.77347272e+01 -3.96261171e+01 2.11690511e+01 117 -2.07749399e+01 2.02986257e+01 2.32875723e+01 | -2.07749399e+01 2.02986257e+01 2.32875723e+01 118 -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 | -2.46809039e+01 -2.33182016e+01 -2.57704941e+01 119 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 | 5.17458656e+01 -1.91287253e+01 -2.53840165e+00 120 7.29330862e+00 2.23718144e+01 1.90816448e-01 | 7.29330862e+00 2.23718144e+01 1.90816448e-01 121 2.70901510e+01 1.67031886e+01 -2.21451616e+01 | 2.70901510e+01 1.67031886e+01 -2.21451616e+01 122 -1.32732268e+01 7.36201578e+01 2.84155606e+01 | -1.32732268e+01 7.36201578e+01 2.84155606e+01 123 -1.05453911e+00 1.63850616e+01 2.30953297e+01 | -1.05453911e+00 1.63850616e+01 2.30953297e+01 124 -1.11650067e+01 -6.96998574e+00 2.85665460e+01 | -1.11650067e+01 -6.96998574e+00 2.85665460e+01 125 -7.69536770e+00 1.13515061e+01 -3.87922792e-01 | -7.69536770e+00 1.13515061e+01 -3.87922792e-01 126 -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 | -3.10015422e+01 -2.55355224e+01 -1.86946732e+00 127 -3.83469399e+00 1.15036220e+01 5.14668352e+00 | -3.83469399e+00 1.15036220e+01 5.14668352e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = TFF (Configuration in file "config-AlCuFeMgSi-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 220.76085393036095 2^p V(r_1,...,r_N) = 220.76085393036067 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.55426628e+01 -1.82378961e+01 -6.72880287e+00 | -1.55426628e+01 -1.82378961e+01 -6.72880287e+00 1 2.36077319e+01 4.15486104e+01 -4.07353473e+01 | 2.36077319e+01 4.15486104e+01 -4.07353473e+01 2 -1.38809510e+01 -3.14233529e+01 2.76453507e+01 | -1.38809510e+01 -3.14233529e+01 2.76453507e+01 3 9.66742012e+00 -2.54374086e+00 2.90902252e+00 | 9.66742012e+00 -2.54374086e+00 2.90902252e+00 4 -5.45475547e+00 -8.55366803e+00 -2.11251996e+01 | -5.45475547e+00 -8.55366803e+00 -2.11251996e+01 5 1.90594045e+01 -3.87030435e+01 -3.18002309e+01 | 1.90594045e+01 -3.87030435e+01 -3.18002309e+01 6 -8.23769380e+00 -4.02221426e+00 8.40599668e+00 | -8.23769380e+00 -4.02221426e+00 8.40599668e+00 7 3.27941023e+01 -2.07827215e+01 -1.87064973e+01 | 3.27941023e+01 -2.07827215e+01 -1.87064973e+01 8 5.85726080e+00 1.22765101e+01 -5.53004061e+00 | 5.85726080e+00 1.22765101e+01 -5.53004061e+00 9 1.15194814e+01 -2.38166618e+00 -3.06261213e+01 | 1.15194814e+01 -2.38166618e+00 -3.06261213e+01 10 -1.00777932e+01 2.43770210e+01 -1.32028653e+01 | -1.00777932e+01 2.43770210e+01 -1.32028653e+01 11 -1.65758583e+01 9.43023392e+00 2.06627642e+01 | -1.65758583e+01 9.43023392e+00 2.06627642e+01 12 -2.27161781e+01 6.09518148e+00 -1.67767804e+01 | -2.27161781e+01 6.09518148e+00 -1.67767804e+01 13 9.65302996e+00 7.02589815e+00 -6.78765935e+00 | 9.65302996e+00 7.02589815e+00 -6.78765935e+00 14 -5.20646367e+00 2.04228939e+01 1.63926656e+01 | -5.20646367e+00 2.04228939e+01 1.63926656e+01 15 4.44418602e+00 1.43741214e+01 1.33804789e+01 | 4.44418602e+00 1.43741214e+01 1.33804789e+01 16 1.96151049e+01 -4.46689066e+01 -9.70463360e+00 | 1.96151049e+01 -4.46689066e+01 -9.70463360e+00 17 -3.37020736e+01 -2.04660522e+01 4.19690075e+01 | -3.37020736e+01 -2.04660522e+01 4.19690075e+01 18 -8.10651802e+00 -5.05799497e+00 1.01744847e+01 | -8.10651802e+00 -5.05799497e+00 1.01744847e+01 19 -3.70906903e+00 1.02063157e+01 1.87724231e+01 | -3.70906903e+00 1.02063157e+01 1.87724231e+01 20 1.31956789e+01 -1.52666744e+01 -1.56590114e+01 | 1.31956789e+01 -1.52666744e+01 -1.56590114e+01 21 -4.07069464e+00 1.24116207e+01 5.29903167e+00 | -4.07069464e+00 1.24116207e+01 5.29903167e+00 22 1.24191625e+01 -2.10425933e+01 1.02951219e+01 | 1.24191625e+01 -2.10425933e+01 1.02951219e+01 23 -2.56041727e+01 -1.09385623e+01 2.00553646e+01 | -2.56041727e+01 -1.09385623e+01 2.00553646e+01 24 -9.33001661e+00 4.27377194e+00 -6.82579660e+00 | -9.33001661e+00 4.27377194e+00 -6.82579660e+00 25 3.22091628e+00 1.51737865e+01 -8.37668002e+00 | 3.22091628e+00 1.51737865e+01 -8.37668002e+00 26 -8.98379163e+00 -1.26622045e+01 1.32707572e+01 | -8.98379163e+00 -1.26622045e+01 1.32707572e+01 27 9.29791085e+00 1.41572862e+01 1.05382667e+01 | 9.29791085e+00 1.41572862e+01 1.05382667e+01 28 1.03484937e+01 -5.61420986e+00 1.46886110e+01 | 1.03484937e+01 -5.61420986e+00 1.46886110e+01 29 9.90802673e+00 2.27210455e+01 -8.72969027e+00 | 9.90802673e+00 2.27210455e+01 -8.72969027e+00 30 -8.40291486e+00 2.45933176e+01 -1.26013985e+01 | -8.40291486e+00 2.45933176e+01 -1.26013985e+01 31 4.99369669e+00 2.32778867e+01 1.94574081e+01 | 4.99369669e+00 2.32778867e+01 1.94574081e+01 32 -1.55426628e+01 -1.82378961e+01 -6.72880287e+00 | -1.55426628e+01 -1.82378961e+01 -6.72880287e+00 33 2.36077319e+01 4.15486104e+01 -4.07353473e+01 | 2.36077319e+01 4.15486104e+01 -4.07353473e+01 34 -1.38809510e+01 -3.14233529e+01 2.76453507e+01 | -1.38809510e+01 -3.14233529e+01 2.76453507e+01 35 9.66742012e+00 -2.54374086e+00 2.90902252e+00 | 9.66742012e+00 -2.54374086e+00 2.90902252e+00 36 -5.45475547e+00 -8.55366803e+00 -2.11251996e+01 | -5.45475547e+00 -8.55366803e+00 -2.11251996e+01 37 1.90594045e+01 -3.87030435e+01 -3.18002309e+01 | 1.90594045e+01 -3.87030435e+01 -3.18002309e+01 38 -8.23769380e+00 -4.02221426e+00 8.40599668e+00 | -8.23769380e+00 -4.02221426e+00 8.40599668e+00 39 3.27941023e+01 -2.07827215e+01 -1.87064973e+01 | 3.27941023e+01 -2.07827215e+01 -1.87064973e+01 40 5.85726080e+00 1.22765101e+01 -5.53004061e+00 | 5.85726080e+00 1.22765101e+01 -5.53004061e+00 41 1.15194814e+01 -2.38166618e+00 -3.06261213e+01 | 1.15194814e+01 -2.38166618e+00 -3.06261213e+01 42 -1.00777932e+01 2.43770210e+01 -1.32028653e+01 | -1.00777932e+01 2.43770210e+01 -1.32028653e+01 43 -1.65758583e+01 9.43023392e+00 2.06627642e+01 | -1.65758583e+01 9.43023392e+00 2.06627642e+01 44 -2.27161781e+01 6.09518148e+00 -1.67767804e+01 | -2.27161781e+01 6.09518148e+00 -1.67767804e+01 45 9.65302996e+00 7.02589815e+00 -6.78765935e+00 | 9.65302996e+00 7.02589815e+00 -6.78765935e+00 46 -5.20646367e+00 2.04228939e+01 1.63926656e+01 | -5.20646367e+00 2.04228939e+01 1.63926656e+01 47 4.44418602e+00 1.43741214e+01 1.33804789e+01 | 4.44418602e+00 1.43741214e+01 1.33804789e+01 48 1.96151049e+01 -4.46689066e+01 -9.70463360e+00 | 1.96151049e+01 -4.46689066e+01 -9.70463360e+00 49 -3.37020736e+01 -2.04660522e+01 4.19690075e+01 | -3.37020736e+01 -2.04660522e+01 4.19690075e+01 50 -8.10651802e+00 -5.05799497e+00 1.01744847e+01 | -8.10651802e+00 -5.05799497e+00 1.01744847e+01 51 -3.70906903e+00 1.02063157e+01 1.87724231e+01 | -3.70906903e+00 1.02063157e+01 1.87724231e+01 52 1.31956789e+01 -1.52666744e+01 -1.56590114e+01 | 1.31956789e+01 -1.52666744e+01 -1.56590114e+01 53 -4.07069464e+00 1.24116207e+01 5.29903167e+00 | -4.07069464e+00 1.24116207e+01 5.29903167e+00 54 1.24191625e+01 -2.10425933e+01 1.02951219e+01 | 1.24191625e+01 -2.10425933e+01 1.02951219e+01 55 -2.56041727e+01 -1.09385623e+01 2.00553646e+01 | -2.56041727e+01 -1.09385623e+01 2.00553646e+01 56 -9.33001661e+00 4.27377194e+00 -6.82579660e+00 | -9.33001661e+00 4.27377194e+00 -6.82579660e+00 57 3.22091628e+00 1.51737865e+01 -8.37668002e+00 | 3.22091628e+00 1.51737865e+01 -8.37668002e+00 58 -8.98379163e+00 -1.26622045e+01 1.32707572e+01 | -8.98379163e+00 -1.26622045e+01 1.32707572e+01 59 9.29791085e+00 1.41572862e+01 1.05382667e+01 | 9.29791085e+00 1.41572862e+01 1.05382667e+01 60 1.03484937e+01 -5.61420986e+00 1.46886110e+01 | 1.03484937e+01 -5.61420986e+00 1.46886110e+01 61 9.90802673e+00 2.27210455e+01 -8.72969027e+00 | 9.90802673e+00 2.27210455e+01 -8.72969027e+00 62 -8.40291486e+00 2.45933176e+01 -1.26013985e+01 | -8.40291486e+00 2.45933176e+01 -1.26013985e+01 63 4.99369669e+00 2.32778867e+01 1.94574081e+01 | 4.99369669e+00 2.32778867e+01 1.94574081e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = FTT (Configuration in file "config-AlCuFeMgSi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 821.7449751382449 2^p V(r_1,...,r_N) = 821.7449751382454 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.08268208e+01 -1.13696273e+00 1.54345594e+00 | -1.08268208e+01 -1.13696273e+00 1.54345594e+00 1 -7.53357660e+00 1.10391830e+01 1.20380351e+01 | -7.53357660e+00 1.10391830e+01 1.20380351e+01 2 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 | 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 3 -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 | -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 4 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 | 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 5 2.15005168e+01 -1.16733573e+01 3.04400351e+01 | 2.15005168e+01 -1.16733573e+01 3.04400351e+01 6 3.94793591e+01 5.15651247e+01 -4.32499398e+01 | 3.94793591e+01 5.15651247e+01 -4.32499398e+01 7 -5.47304957e+00 4.65021775e+00 -4.38657853e+00 | -5.47304957e+00 4.65021775e+00 -4.38657853e+00 8 -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 | -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 9 1.46359479e+01 5.52631774e+01 4.78336668e+01 | 1.46359479e+01 5.52631774e+01 4.78336668e+01 10 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 | 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 11 -2.57225421e+01 8.56523335e+00 -5.79017421e+00 | -2.57225421e+01 8.56523335e+00 -5.79017421e+00 12 -4.55524507e+01 6.83577002e+01 1.05962059e+02 | -4.55524507e+01 6.83577002e+01 1.05962059e+02 13 3.94616791e+00 -7.66610716e+00 6.97886949e+00 | 3.94616791e+00 -7.66610716e+00 6.97886949e+00 14 7.49891823e+00 5.87513182e-01 -2.07274371e+01 | 7.49891823e+00 5.87513182e-01 -2.07274371e+01 15 -5.01998153e+00 1.75324654e+00 -2.42590725e+00 | -5.01998153e+00 1.75324654e+00 -2.42590725e+00 16 -1.44163047e+01 -1.01118557e+01 1.44433395e+01 | -1.44163047e+01 -1.01118557e+01 1.44433395e+01 17 3.47583454e+01 1.88187007e+01 4.41683677e+01 | 3.47583454e+01 1.88187007e+01 4.41683677e+01 18 -2.67853024e+01 2.31196471e+00 1.77276812e+01 | -2.67853024e+01 2.31196471e+00 1.77276812e+01 19 -3.36082016e+00 8.65263830e+00 2.93979226e+00 | -3.36082016e+00 8.65263830e+00 2.93979226e+00 20 -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 | -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 21 3.13966653e+01 -4.24281073e+00 1.12931853e+01 | 3.13966653e+01 -4.24281073e+00 1.12931853e+01 22 5.46620035e+00 1.34116136e+01 -5.21589746e+00 | 5.46620035e+00 1.34116136e+01 -5.21589746e+00 23 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 | 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 24 -1.02219625e+02 -2.18228128e+01 6.98405269e+01 | -1.02219625e+02 -2.18228128e+01 6.98405269e+01 25 3.77982500e+01 1.50266741e+01 -7.40905021e+00 | 3.77982500e+01 1.50266741e+01 -7.40905021e+00 26 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 | 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 27 -2.25442184e+01 3.30184086e+01 2.58086111e+01 | -2.25442184e+01 3.30184086e+01 2.58086111e+01 28 -4.10470147e+00 -2.24765568e-01 2.01488029e+01 | -4.10470147e+00 -2.24765568e-01 2.01488029e+01 29 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 | 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 30 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 | 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 31 -2.82209006e+01 1.54907324e+00 3.81980847e+01 | -2.82209006e+01 1.54907324e+00 3.81980847e+01 32 -1.08268208e+01 -1.13696273e+00 1.54345594e+00 | -1.08268208e+01 -1.13696273e+00 1.54345594e+00 33 -7.53357660e+00 1.10391830e+01 1.20380351e+01 | -7.53357660e+00 1.10391830e+01 1.20380351e+01 34 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 | 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 35 -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 | -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 36 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 | 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 37 2.15005168e+01 -1.16733573e+01 3.04400351e+01 | 2.15005168e+01 -1.16733573e+01 3.04400351e+01 38 3.94793591e+01 5.15651247e+01 -4.32499398e+01 | 3.94793591e+01 5.15651247e+01 -4.32499398e+01 39 -5.47304957e+00 4.65021775e+00 -4.38657853e+00 | -5.47304957e+00 4.65021775e+00 -4.38657853e+00 40 -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 | -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 41 1.46359479e+01 5.52631774e+01 4.78336668e+01 | 1.46359479e+01 5.52631774e+01 4.78336668e+01 42 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 | 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 43 -2.57225421e+01 8.56523335e+00 -5.79017421e+00 | -2.57225421e+01 8.56523335e+00 -5.79017421e+00 44 -4.55524507e+01 6.83577002e+01 1.05962059e+02 | -4.55524507e+01 6.83577002e+01 1.05962059e+02 45 3.94616791e+00 -7.66610716e+00 6.97886949e+00 | 3.94616791e+00 -7.66610716e+00 6.97886949e+00 46 7.49891823e+00 5.87513182e-01 -2.07274371e+01 | 7.49891823e+00 5.87513182e-01 -2.07274371e+01 47 -5.01998153e+00 1.75324654e+00 -2.42590725e+00 | -5.01998153e+00 1.75324654e+00 -2.42590725e+00 48 -1.44163047e+01 -1.01118557e+01 1.44433395e+01 | -1.44163047e+01 -1.01118557e+01 1.44433395e+01 49 3.47583454e+01 1.88187007e+01 4.41683677e+01 | 3.47583454e+01 1.88187007e+01 4.41683677e+01 50 -2.67853024e+01 2.31196471e+00 1.77276812e+01 | -2.67853024e+01 2.31196471e+00 1.77276812e+01 51 -3.36082016e+00 8.65263830e+00 2.93979226e+00 | -3.36082016e+00 8.65263830e+00 2.93979226e+00 52 -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 | -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 53 3.13966653e+01 -4.24281073e+00 1.12931853e+01 | 3.13966653e+01 -4.24281073e+00 1.12931853e+01 54 5.46620035e+00 1.34116136e+01 -5.21589746e+00 | 5.46620035e+00 1.34116136e+01 -5.21589746e+00 55 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 | 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 56 -1.02219625e+02 -2.18228128e+01 6.98405269e+01 | -1.02219625e+02 -2.18228128e+01 6.98405269e+01 57 3.77982500e+01 1.50266741e+01 -7.40905021e+00 | 3.77982500e+01 1.50266741e+01 -7.40905021e+00 58 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 | 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 59 -2.25442184e+01 3.30184086e+01 2.58086111e+01 | -2.25442184e+01 3.30184086e+01 2.58086111e+01 60 -4.10470147e+00 -2.24765568e-01 2.01488029e+01 | -4.10470147e+00 -2.24765568e-01 2.01488029e+01 61 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 | 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 62 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 | 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 63 -2.82209006e+01 1.54907324e+00 3.81980847e+01 | -2.82209006e+01 1.54907324e+00 3.81980847e+01 64 -1.08268208e+01 -1.13696273e+00 1.54345594e+00 | -1.08268208e+01 -1.13696273e+00 1.54345594e+00 65 -7.53357660e+00 1.10391830e+01 1.20380351e+01 | -7.53357660e+00 1.10391830e+01 1.20380351e+01 66 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 | 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 67 -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 | -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 68 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 | 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 69 2.15005168e+01 -1.16733573e+01 3.04400351e+01 | 2.15005168e+01 -1.16733573e+01 3.04400351e+01 70 3.94793591e+01 5.15651247e+01 -4.32499398e+01 | 3.94793591e+01 5.15651247e+01 -4.32499398e+01 71 -5.47304957e+00 4.65021775e+00 -4.38657853e+00 | -5.47304957e+00 4.65021775e+00 -4.38657853e+00 72 -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 | -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 73 1.46359479e+01 5.52631774e+01 4.78336668e+01 | 1.46359479e+01 5.52631774e+01 4.78336668e+01 74 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 | 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 75 -2.57225421e+01 8.56523335e+00 -5.79017421e+00 | -2.57225421e+01 8.56523335e+00 -5.79017421e+00 76 -4.55524507e+01 6.83577002e+01 1.05962059e+02 | -4.55524507e+01 6.83577002e+01 1.05962059e+02 77 3.94616791e+00 -7.66610716e+00 6.97886949e+00 | 3.94616791e+00 -7.66610716e+00 6.97886949e+00 78 7.49891823e+00 5.87513182e-01 -2.07274371e+01 | 7.49891823e+00 5.87513182e-01 -2.07274371e+01 79 -5.01998153e+00 1.75324654e+00 -2.42590725e+00 | -5.01998153e+00 1.75324654e+00 -2.42590725e+00 80 -1.44163047e+01 -1.01118557e+01 1.44433395e+01 | -1.44163047e+01 -1.01118557e+01 1.44433395e+01 81 3.47583454e+01 1.88187007e+01 4.41683677e+01 | 3.47583454e+01 1.88187007e+01 4.41683677e+01 82 -2.67853024e+01 2.31196471e+00 1.77276812e+01 | -2.67853024e+01 2.31196471e+00 1.77276812e+01 83 -3.36082016e+00 8.65263830e+00 2.93979226e+00 | -3.36082016e+00 8.65263830e+00 2.93979226e+00 84 -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 | -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 85 3.13966653e+01 -4.24281073e+00 1.12931853e+01 | 3.13966653e+01 -4.24281073e+00 1.12931853e+01 86 5.46620035e+00 1.34116136e+01 -5.21589746e+00 | 5.46620035e+00 1.34116136e+01 -5.21589746e+00 87 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 | 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 88 -1.02219625e+02 -2.18228128e+01 6.98405269e+01 | -1.02219625e+02 -2.18228128e+01 6.98405269e+01 89 3.77982500e+01 1.50266741e+01 -7.40905021e+00 | 3.77982500e+01 1.50266741e+01 -7.40905021e+00 90 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 | 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 91 -2.25442184e+01 3.30184086e+01 2.58086111e+01 | -2.25442184e+01 3.30184086e+01 2.58086111e+01 92 -4.10470147e+00 -2.24765568e-01 2.01488029e+01 | -4.10470147e+00 -2.24765568e-01 2.01488029e+01 93 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 | 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 94 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 | 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 95 -2.82209006e+01 1.54907324e+00 3.81980847e+01 | -2.82209006e+01 1.54907324e+00 3.81980847e+01 96 -1.08268208e+01 -1.13696273e+00 1.54345594e+00 | -1.08268208e+01 -1.13696273e+00 1.54345594e+00 97 -7.53357660e+00 1.10391830e+01 1.20380351e+01 | -7.53357660e+00 1.10391830e+01 1.20380351e+01 98 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 | 6.63755745e+00 -1.16545552e+00 -5.25032895e+00 99 -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 | -6.07319078e+01 -1.27300479e+01 -6.68485237e+01 100 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 | 1.55244564e+01 -4.61821944e+00 -5.25186178e+00 101 2.15005168e+01 -1.16733573e+01 3.04400351e+01 | 2.15005168e+01 -1.16733573e+01 3.04400351e+01 102 3.94793591e+01 5.15651247e+01 -4.32499398e+01 | 3.94793591e+01 5.15651247e+01 -4.32499398e+01 103 -5.47304957e+00 4.65021775e+00 -4.38657853e+00 | -5.47304957e+00 4.65021775e+00 -4.38657853e+00 104 -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 | -1.32455735e+01 -1.03658273e+01 -7.46809285e+00 105 1.46359479e+01 5.52631774e+01 4.78336668e+01 | 1.46359479e+01 5.52631774e+01 4.78336668e+01 106 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 | 8.49894015e+01 -3.40866081e+01 -8.55514443e+01 107 -2.57225421e+01 8.56523335e+00 -5.79017421e+00 | -2.57225421e+01 8.56523335e+00 -5.79017421e+00 108 -4.55524507e+01 6.83577002e+01 1.05962059e+02 | -4.55524507e+01 6.83577002e+01 1.05962059e+02 109 3.94616791e+00 -7.66610716e+00 6.97886949e+00 | 3.94616791e+00 -7.66610716e+00 6.97886949e+00 110 7.49891823e+00 5.87513182e-01 -2.07274371e+01 | 7.49891823e+00 5.87513182e-01 -2.07274371e+01 111 -5.01998153e+00 1.75324654e+00 -2.42590725e+00 | -5.01998153e+00 1.75324654e+00 -2.42590725e+00 112 -1.44163047e+01 -1.01118557e+01 1.44433395e+01 | -1.44163047e+01 -1.01118557e+01 1.44433395e+01 113 3.47583454e+01 1.88187007e+01 4.41683677e+01 | 3.47583454e+01 1.88187007e+01 4.41683677e+01 114 -2.67853024e+01 2.31196471e+00 1.77276812e+01 | -2.67853024e+01 2.31196471e+00 1.77276812e+01 115 -3.36082016e+00 8.65263830e+00 2.93979226e+00 | -3.36082016e+00 8.65263830e+00 2.93979226e+00 116 -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 | -2.23392922e+00 -2.08107197e+01 -7.02704121e+00 117 3.13966653e+01 -4.24281073e+00 1.12931853e+01 | 3.13966653e+01 -4.24281073e+00 1.12931853e+01 118 5.46620035e+00 1.34116136e+01 -5.21589746e+00 | 5.46620035e+00 1.34116136e+01 -5.21589746e+00 119 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 | 3.15007046e+01 -3.40203298e+01 -9.22791334e+01 120 -1.02219625e+02 -2.18228128e+01 6.98405269e+01 | -1.02219625e+02 -2.18228128e+01 6.98405269e+01 121 3.77982500e+01 1.50266741e+01 -7.40905021e+00 | 3.77982500e+01 1.50266741e+01 -7.40905021e+00 122 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 | 2.50167398e-01 -6.01346484e+01 -4.16052773e+01 123 -2.25442184e+01 3.30184086e+01 2.58086111e+01 | -2.25442184e+01 3.30184086e+01 2.58086111e+01 124 -4.10470147e+00 -2.24765568e-01 2.01488029e+01 | -4.10470147e+00 -2.24765568e-01 2.01488029e+01 125 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 | 1.62685440e+01 -4.52607049e+01 -6.25302036e+00 126 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 | 2.63405022e+01 -1.44992364e+01 -4.26248045e+01 127 -2.82209006e+01 1.54907324e+00 3.81980847e+01 | -2.82209006e+01 1.54907324e+00 3.81980847e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = FTF (Configuration in file "config-AlCuFeMgSi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 381.94057992493003 2^p V(r_1,...,r_N) = 381.9405799249301 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -5.29711439e+00 2.98406413e+01 -3.73182727e+01 | -5.29711439e+00 2.98406413e+01 -3.73182727e+01 1 -8.94220860e+00 4.14073375e+01 -3.02956459e+01 | -8.94220860e+00 4.14073375e+01 -3.02956459e+01 2 -5.00470153e+01 -1.02796975e+01 -4.62367874e+01 | -5.00470153e+01 -1.02796975e+01 -4.62367874e+01 3 -4.74039101e+01 -3.62462105e+01 6.70375925e+01 | -4.74039101e+01 -3.62462105e+01 6.70375925e+01 4 9.22949146e+00 -3.37288080e+01 -2.79063505e+01 | 9.22949146e+00 -3.37288080e+01 -2.79063505e+01 5 3.49820830e+01 1.11040105e+01 -3.67414059e+01 | 3.49820830e+01 1.11040105e+01 -3.67414059e+01 6 3.11274245e+01 2.63353686e+01 3.32997029e+01 | 3.11274245e+01 2.63353686e+01 3.32997029e+01 7 -3.20950236e+01 1.45198792e+01 2.94828801e+01 | -3.20950236e+01 1.45198792e+01 2.94828801e+01 8 -4.53092929e+01 1.08218980e+01 -8.28290488e+01 | -4.53092929e+01 1.08218980e+01 -8.28290488e+01 9 4.23063593e+01 1.61036833e+01 -2.81537574e+01 | 4.23063593e+01 1.61036833e+01 -2.81537574e+01 10 3.52203818e+01 -3.00734652e+01 2.85532382e+01 | 3.52203818e+01 -3.00734652e+01 2.85532382e+01 11 -4.31668571e+01 -4.00314121e+01 4.54767826e+01 | -4.31668571e+01 -4.00314121e+01 4.54767826e+01 12 2.80570407e+01 -2.41252982e-01 -1.10046272e+01 | 2.80570407e+01 -2.41252982e-01 -1.10046272e+01 13 8.51323579e-01 -2.57962826e+01 -2.89976443e+01 | 8.51323579e-01 -2.57962826e+01 -2.89976443e+01 14 6.66438072e+00 7.42718638e+00 1.56373321e+01 | 6.66438072e+00 7.42718638e+00 1.56373321e+01 15 -3.27842794e+00 -1.19270957e+01 7.02605788e-01 | -3.27842794e+00 -1.19270957e+01 7.02605788e-01 16 -1.94916856e+01 -9.35732610e+00 7.69052933e+00 | -1.94916856e+01 -9.35732610e+00 7.69052933e+00 17 8.37968678e+00 2.40647827e+00 -5.05827413e+00 | 8.37968678e+00 2.40647827e+00 -5.05827413e+00 18 8.89162386e+00 1.09561352e+01 1.65233340e+01 | 8.89162386e+00 1.09561352e+01 1.65233340e+01 19 -8.57215764e+00 -2.61215726e+00 1.07870725e+01 | -8.57215764e+00 -2.61215726e+00 1.07870725e+01 20 6.64313623e+01 2.18442469e+01 3.95482115e+01 | 6.64313623e+01 2.18442469e+01 3.95482115e+01 21 3.87562436e+00 9.65638207e+00 -5.36443142e+00 | 3.87562436e+00 9.65638207e+00 -5.36443142e+00 22 1.73848539e+01 5.11079456e+00 1.93927044e+01 | 1.73848539e+01 5.11079456e+00 1.93927044e+01 23 -1.40876881e+01 -2.10164051e+01 1.39285066e+01 | -1.40876881e+01 -2.10164051e+01 1.39285066e+01 24 -1.79623237e+01 7.75977874e+00 -2.09848518e+00 | -1.79623237e+01 7.75977874e+00 -2.09848518e+00 25 -1.27584392e+01 3.77852687e+00 -2.68238117e+01 | -1.27584392e+01 3.77852687e+00 -2.68238117e+01 26 2.49549478e+01 -2.11805400e+01 3.48921171e+01 | 2.49549478e+01 -2.11805400e+01 3.48921171e+01 27 -5.07896518e+01 1.02143440e+01 1.41397429e+01 | -5.07896518e+01 1.02143440e+01 1.41397429e+01 28 1.79028834e+01 9.72494065e+00 -1.22163130e+01 | 1.79028834e+01 9.72494065e+00 -1.22163130e+01 29 1.08611094e+01 -4.16073246e+00 -1.32831220e+01 | 1.08611094e+01 -4.16073246e+00 -1.32831220e+01 30 2.12496810e+01 1.15958837e+01 8.27778786e+00 | 2.12496810e+01 1.15958837e+01 8.27778786e+00 31 -9.16846174e+00 -3.95613017e+00 8.95783736e+00 | -9.16846174e+00 -3.95613017e+00 8.95783736e+00 32 -5.29711439e+00 2.98406413e+01 -3.73182727e+01 | -5.29711439e+00 2.98406413e+01 -3.73182727e+01 33 -8.94220860e+00 4.14073375e+01 -3.02956459e+01 | -8.94220860e+00 4.14073375e+01 -3.02956459e+01 34 -5.00470153e+01 -1.02796975e+01 -4.62367874e+01 | -5.00470153e+01 -1.02796975e+01 -4.62367874e+01 35 -4.74039101e+01 -3.62462105e+01 6.70375925e+01 | -4.74039101e+01 -3.62462105e+01 6.70375925e+01 36 9.22949146e+00 -3.37288080e+01 -2.79063505e+01 | 9.22949146e+00 -3.37288080e+01 -2.79063505e+01 37 3.49820830e+01 1.11040105e+01 -3.67414059e+01 | 3.49820830e+01 1.11040105e+01 -3.67414059e+01 38 3.11274245e+01 2.63353686e+01 3.32997029e+01 | 3.11274245e+01 2.63353686e+01 3.32997029e+01 39 -3.20950236e+01 1.45198792e+01 2.94828801e+01 | -3.20950236e+01 1.45198792e+01 2.94828801e+01 40 -4.53092929e+01 1.08218980e+01 -8.28290488e+01 | -4.53092929e+01 1.08218980e+01 -8.28290488e+01 41 4.23063593e+01 1.61036833e+01 -2.81537574e+01 | 4.23063593e+01 1.61036833e+01 -2.81537574e+01 42 3.52203818e+01 -3.00734652e+01 2.85532382e+01 | 3.52203818e+01 -3.00734652e+01 2.85532382e+01 43 -4.31668571e+01 -4.00314121e+01 4.54767826e+01 | -4.31668571e+01 -4.00314121e+01 4.54767826e+01 44 2.80570407e+01 -2.41252982e-01 -1.10046272e+01 | 2.80570407e+01 -2.41252982e-01 -1.10046272e+01 45 8.51323579e-01 -2.57962826e+01 -2.89976443e+01 | 8.51323579e-01 -2.57962826e+01 -2.89976443e+01 46 6.66438072e+00 7.42718638e+00 1.56373321e+01 | 6.66438072e+00 7.42718638e+00 1.56373321e+01 47 -3.27842794e+00 -1.19270957e+01 7.02605788e-01 | -3.27842794e+00 -1.19270957e+01 7.02605788e-01 48 -1.94916856e+01 -9.35732610e+00 7.69052933e+00 | -1.94916856e+01 -9.35732610e+00 7.69052933e+00 49 8.37968678e+00 2.40647827e+00 -5.05827413e+00 | 8.37968678e+00 2.40647827e+00 -5.05827413e+00 50 8.89162386e+00 1.09561352e+01 1.65233340e+01 | 8.89162386e+00 1.09561352e+01 1.65233340e+01 51 -8.57215764e+00 -2.61215726e+00 1.07870725e+01 | -8.57215764e+00 -2.61215726e+00 1.07870725e+01 52 6.64313623e+01 2.18442469e+01 3.95482115e+01 | 6.64313623e+01 2.18442469e+01 3.95482115e+01 53 3.87562436e+00 9.65638207e+00 -5.36443142e+00 | 3.87562436e+00 9.65638207e+00 -5.36443142e+00 54 1.73848539e+01 5.11079456e+00 1.93927044e+01 | 1.73848539e+01 5.11079456e+00 1.93927044e+01 55 -1.40876881e+01 -2.10164051e+01 1.39285066e+01 | -1.40876881e+01 -2.10164051e+01 1.39285066e+01 56 -1.79623237e+01 7.75977874e+00 -2.09848518e+00 | -1.79623237e+01 7.75977874e+00 -2.09848518e+00 57 -1.27584392e+01 3.77852687e+00 -2.68238117e+01 | -1.27584392e+01 3.77852687e+00 -2.68238117e+01 58 2.49549478e+01 -2.11805400e+01 3.48921171e+01 | 2.49549478e+01 -2.11805400e+01 3.48921171e+01 59 -5.07896518e+01 1.02143440e+01 1.41397429e+01 | -5.07896518e+01 1.02143440e+01 1.41397429e+01 60 1.79028834e+01 9.72494065e+00 -1.22163130e+01 | 1.79028834e+01 9.72494065e+00 -1.22163130e+01 61 1.08611094e+01 -4.16073246e+00 -1.32831220e+01 | 1.08611094e+01 -4.16073246e+00 -1.32831220e+01 62 2.12496810e+01 1.15958837e+01 8.27778786e+00 | 2.12496810e+01 1.15958837e+01 8.27778786e+00 63 -9.16846174e+00 -3.95613017e+00 8.95783736e+00 | -9.16846174e+00 -3.95613017e+00 8.95783736e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu Fe Mg Si, PBC = FFT (Configuration in file "config-AlCuFeMgSi-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 349.09533856767763 2^p V(r_1,...,r_N) = 349.09533856767854 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.80050528e+00 -7.55559227e+00 -7.71792008e+00 | -8.80050528e+00 -7.55559227e+00 -7.71792008e+00 1 1.15273254e+01 1.57722355e+01 -1.29856525e+01 | 1.15273254e+01 1.57722355e+01 -1.29856525e+01 2 -7.33314312e+01 -8.53459778e+01 -1.12246711e+02 | -7.33314312e+01 -8.53459778e+01 -1.12246711e+02 3 -2.02117809e+01 -1.50696951e+00 4.53242394e+00 | -2.02117809e+01 -1.50696951e+00 4.53242394e+00 4 2.46145843e+00 -9.03623927e+00 -1.23892427e+01 | 2.46145843e+00 -9.03623927e+00 -1.23892427e+01 5 4.17414531e+00 -3.63533388e+00 4.37896811e+00 | 4.17414531e+00 -3.63533388e+00 4.37896811e+00 6 4.42967362e+01 -1.64226412e+01 -6.05336886e+00 | 4.42967362e+01 -1.64226412e+01 -6.05336886e+00 7 -1.88027307e+01 1.03003629e+01 -9.76116540e+00 | -1.88027307e+01 1.03003629e+01 -9.76116540e+00 8 -7.70599259e+00 1.04402167e+01 -1.05595215e+01 | -7.70599259e+00 1.04402167e+01 -1.05595215e+01 9 -2.54948433e+01 2.73285407e+00 -1.79734633e+01 | -2.54948433e+01 2.73285407e+00 -1.79734633e+01 10 2.76373556e+01 1.42979547e+01 -4.51751222e+00 | 2.76373556e+01 1.42979547e+01 -4.51751222e+00 11 -1.40540345e+01 1.68689208e+01 -7.67819267e+00 | -1.40540345e+01 1.68689208e+01 -7.67819267e+00 12 7.50696552e+00 -1.67485182e+00 3.05096632e+01 | 7.50696552e+00 -1.67485182e+00 3.05096632e+01 13 1.50162015e+01 9.53561878e+00 7.30353092e+00 | 1.50162015e+01 9.53561878e+00 7.30353092e+00 14 1.45795233e+01 1.37261812e+01 -4.21836031e+00 | 1.45795233e+01 1.37261812e+01 -4.21836031e+00 15 1.74252504e+01 5.27174600e-01 8.10770166e+00 | 1.74252504e+01 5.27174600e-01 8.10770166e+00 16 -3.10795731e+01 -7.48381468e+01 -3.28915232e+01 | -3.10795731e+01 -7.48381468e+01 -3.28915232e+01 17 2.01597865e+01 4.44298883e+01 4.59505224e+01 | 2.01597865e+01 4.44298883e+01 4.59505224e+01 18 -6.22186844e-02 -1.40987640e+01 3.33344404e+00 | -6.22186844e-02 -1.40987640e+01 3.33344404e+00 19 4.03762772e+00 4.29722376e+01 3.52503641e+01 | 4.03762772e+00 4.29722376e+01 3.52503641e+01 20 2.52872209e+01 2.66563097e+01 8.48411696e+01 | 2.52872209e+01 2.66563097e+01 8.48411696e+01 21 3.20737212e+01 -1.92878311e+00 -1.01229596e+01 | 3.20737212e+01 -1.92878311e+00 -1.01229596e+01 22 4.25341938e+00 -1.29239187e+01 -5.72043289e+00 | 4.25341938e+00 -1.29239187e+01 -5.72043289e+00 23 2.22638234e+01 -3.68167708e+01 2.76848457e+01 | 2.22638234e+01 -3.68167708e+01 2.76848457e+01 24 -7.67538106e+01 -5.30377208e+01 -5.30433895e+00 | -7.67538106e+01 -5.30377208e+01 -5.30433895e+00 25 4.95668213e+01 5.11667030e+01 2.97006938e+00 | 4.95668213e+01 5.11667030e+01 2.97006938e+00 26 -3.73973588e+01 1.12737425e+01 1.27830367e+01 | -3.73973588e+01 1.12737425e+01 1.27830367e+01 27 -5.30523811e+00 1.32416378e+00 -1.29095093e-01 | -5.30523811e+00 1.32416378e+00 -1.29095093e-01 28 4.48746085e+00 2.49510416e+01 -1.58740869e+01 | 4.48746085e+00 2.49510416e+01 -1.58740869e+01 29 1.19178565e+01 1.29726711e+00 6.45851469e+00 | 1.19178565e+01 1.29726711e+00 6.45851469e+00 30 -1.65412196e+00 1.56443646e+00 -4.16025528e+00 | -1.65412196e+00 1.56443646e+00 -4.16025528e+00 31 1.98094033e+00 1.89844007e+01 6.19954812e+00 | 1.98094033e+00 1.89844007e+01 6.19954812e+00 32 -8.80050528e+00 -7.55559227e+00 -7.71792008e+00 | -8.80050528e+00 -7.55559227e+00 -7.71792008e+00 33 1.15273254e+01 1.57722355e+01 -1.29856525e+01 | 1.15273254e+01 1.57722355e+01 -1.29856525e+01 34 -7.33314312e+01 -8.53459778e+01 -1.12246711e+02 | -7.33314312e+01 -8.53459778e+01 -1.12246711e+02 35 -2.02117809e+01 -1.50696951e+00 4.53242394e+00 | -2.02117809e+01 -1.50696951e+00 4.53242394e+00 36 2.46145843e+00 -9.03623927e+00 -1.23892427e+01 | 2.46145843e+00 -9.03623927e+00 -1.23892427e+01 37 4.17414531e+00 -3.63533388e+00 4.37896811e+00 | 4.17414531e+00 -3.63533388e+00 4.37896811e+00 38 4.42967362e+01 -1.64226412e+01 -6.05336886e+00 | 4.42967362e+01 -1.64226412e+01 -6.05336886e+00 39 -1.88027307e+01 1.03003629e+01 -9.76116540e+00 | -1.88027307e+01 1.03003629e+01 -9.76116540e+00 40 -7.70599259e+00 1.04402167e+01 -1.05595215e+01 | -7.70599259e+00 1.04402167e+01 -1.05595215e+01 41 -2.54948433e+01 2.73285407e+00 -1.79734633e+01 | -2.54948433e+01 2.73285407e+00 -1.79734633e+01 42 2.76373556e+01 1.42979547e+01 -4.51751222e+00 | 2.76373556e+01 1.42979547e+01 -4.51751222e+00 43 -1.40540345e+01 1.68689208e+01 -7.67819267e+00 | -1.40540345e+01 1.68689208e+01 -7.67819267e+00 44 7.50696552e+00 -1.67485182e+00 3.05096632e+01 | 7.50696552e+00 -1.67485182e+00 3.05096632e+01 45 1.50162015e+01 9.53561878e+00 7.30353092e+00 | 1.50162015e+01 9.53561878e+00 7.30353092e+00 46 1.45795233e+01 1.37261812e+01 -4.21836031e+00 | 1.45795233e+01 1.37261812e+01 -4.21836031e+00 47 1.74252504e+01 5.27174600e-01 8.10770166e+00 | 1.74252504e+01 5.27174600e-01 8.10770166e+00 48 -3.10795731e+01 -7.48381468e+01 -3.28915232e+01 | -3.10795731e+01 -7.48381468e+01 -3.28915232e+01 49 2.01597865e+01 4.44298883e+01 4.59505224e+01 | 2.01597865e+01 4.44298883e+01 4.59505224e+01 50 -6.22186844e-02 -1.40987640e+01 3.33344404e+00 | -6.22186844e-02 -1.40987640e+01 3.33344404e+00 51 4.03762772e+00 4.29722376e+01 3.52503641e+01 | 4.03762772e+00 4.29722376e+01 3.52503641e+01 52 2.52872209e+01 2.66563097e+01 8.48411696e+01 | 2.52872209e+01 2.66563097e+01 8.48411696e+01 53 3.20737212e+01 -1.92878311e+00 -1.01229596e+01 | 3.20737212e+01 -1.92878311e+00 -1.01229596e+01 54 4.25341938e+00 -1.29239187e+01 -5.72043289e+00 | 4.25341938e+00 -1.29239187e+01 -5.72043289e+00 55 2.22638234e+01 -3.68167708e+01 2.76848457e+01 | 2.22638234e+01 -3.68167708e+01 2.76848457e+01 56 -7.67538106e+01 -5.30377208e+01 -5.30433895e+00 | -7.67538106e+01 -5.30377208e+01 -5.30433895e+00 57 4.95668213e+01 5.11667030e+01 2.97006938e+00 | 4.95668213e+01 5.11667030e+01 2.97006938e+00 58 -3.73973588e+01 1.12737425e+01 1.27830367e+01 | -3.73973588e+01 1.12737425e+01 1.27830367e+01 59 -5.30523811e+00 1.32416378e+00 -1.29095093e-01 | -5.30523811e+00 1.32416378e+00 -1.29095093e-01 60 4.48746085e+00 2.49510416e+01 -1.58740869e+01 | 4.48746085e+00 2.49510416e+01 -1.58740869e+01 61 1.19178565e+01 1.29726711e+00 6.45851469e+00 | 1.19178565e+01 1.29726711e+00 6.45851469e+00 62 -1.65412196e+00 1.56443646e+00 -4.16025528e+00 | -1.65412196e+00 1.56443646e+00 -4.16025528e+00 63 1.98094033e+00 1.89844007e+01 6.19954812e+00 | 1.98094033e+00 1.89844007e+01 6.19954812e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.