!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Vashishta_VashishtaKaliaNakano_2007_SiC__SM_196548226654_000 Supported species : C Si random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTT (Configuration in file "config-C-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 39.6707158692 2^p V(r_1,...,r_N) = 39.6707158692 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 -1.48478059e+01 -2.46263477e+01 -2.62763561e+01 | -1.48478059e+01 -2.46263477e+01 -2.62763561e+01 1 1.31293741e+01 8.54178075e+00 -9.43866754e+00 | 1.31293741e+01 8.54178075e+00 -9.43866754e+00 2 1.24750570e+01 -1.15361109e+01 1.50144709e+01 | 1.24750570e+01 -1.15361109e+01 1.50144709e+01 3 -1.07566252e+01 2.76206778e+01 2.07005527e+01 | -1.07566252e+01 2.76206778e+01 2.07005527e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 45.5471452089 2^p V(r_1,...,r_N) = 45.5471452089 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 -2.03560842e+01 -1.49353218e+01 -1.34904346e+01 | -2.03560842e+01 -1.49353218e+01 -1.34904346e+01 1 1.57319321e+01 1.17213696e+01 -1.93178788e+01 | 1.57319321e+01 1.17213696e+01 -1.93178788e+01 2 2.63659862e+01 -2.89036759e+01 2.25915907e+01 | 2.63659862e+01 -2.89036759e+01 2.25915907e+01 3 -2.17418340e+01 3.21176281e+01 1.02167227e+01 | -2.17418340e+01 3.21176281e+01 1.02167227e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFT (Configuration in file "config-C-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 52.1905051078 2^p V(r_1,...,r_N) = 52.1905051078 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 -1.98612922e+01 -2.73989987e+01 -3.45121749e+01 | -1.98612922e+01 -2.73989987e+01 -3.45121749e+01 1 2.69962920e+01 2.70934893e+01 -1.57029747e+01 | 2.69962920e+01 2.70934893e+01 -1.57029747e+01 2 1.71716205e+01 -2.31680608e+01 2.45343388e+01 | 1.71716205e+01 -2.31680608e+01 2.45343388e+01 3 -2.43066203e+01 2.34735701e+01 2.56808107e+01 | -2.43066203e+01 2.34735701e+01 2.56808107e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFF (Configuration in file "config-C-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 77.1492892203 2^p V(r_1,...,r_N) = 77.1492892203 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 -5.91879092e+01 -4.29967609e+01 -9.51815252e+01 | -5.91879092e+01 -4.29967609e+01 -9.51815252e+01 1 2.37498602e+01 2.81423478e+01 -1.92045863e+01 | 2.37498602e+01 2.81423478e+01 -1.92045863e+01 2 7.13800220e+01 -3.28358851e+01 7.32169966e+01 | 7.13800220e+01 -3.28358851e+01 7.32169966e+01 3 -3.59419730e+01 4.76902982e+01 4.11691150e+01 | -3.59419730e+01 4.76902982e+01 4.11691150e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTT (Configuration in file "config-C-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 51.1943562576 2^p V(r_1,...,r_N) = 51.1943562576 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 -2.78422723e+01 -1.97094589e+01 -2.68620710e+01 | -2.78422723e+01 -1.97094589e+01 -2.68620710e+01 1 1.91533641e+01 2.45371228e+01 -2.13008015e+01 | 1.91533641e+01 2.45371228e+01 -2.13008015e+01 2 2.65245467e+01 -2.80035891e+01 2.47555498e+01 | 2.65245467e+01 -2.80035891e+01 2.47555498e+01 3 -1.78356385e+01 2.31759253e+01 2.34073227e+01 | -1.78356385e+01 2.31759253e+01 2.34073227e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTF (Configuration in file "config-C-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 39.0729027322 2^p V(r_1,...,r_N) = 39.0729027322 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 -2.17776352e+01 -1.91832263e+01 -1.40027675e+01 | -2.17776352e+01 -1.91832263e+01 -1.40027675e+01 1 1.57936212e+01 1.80233717e+01 -1.74877175e+01 | 1.57936212e+01 1.80233717e+01 -1.74877175e+01 2 1.69667139e+01 -9.49109213e+00 2.26321132e+01 | 1.69667139e+01 -9.49109213e+00 2.26321132e+01 3 -1.09827000e+01 1.06509468e+01 8.85837179e+00 | -1.09827000e+01 1.06509468e+01 8.85837179e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 73.1158452924 2^p V(r_1,...,r_N) = 73.1158452924 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 -2.27602580e+01 -2.08270389e+01 -2.76262170e+01 | -2.27602580e+01 -2.08270389e+01 -2.76262170e+01 1 2.98099868e+01 2.93432133e+01 -2.46381081e+01 | 2.98099868e+01 2.93432133e+01 -2.46381081e+01 2 8.05049852e+01 -8.65113873e+01 3.29068258e+01 | 8.05049852e+01 -8.65113873e+01 3.29068258e+01 3 -8.75547139e+01 7.79952130e+01 1.93574994e+01 | -8.75547139e+01 7.79952130e+01 1.93574994e+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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 28.3756626434 2^p V(r_1,...,r_N) = 28.3756626434 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 -5.86867335e+00 -4.83502114e+00 -6.73992665e+00 | -5.86867335e+00 -4.83502114e+00 -6.73992665e+00 1 5.55194823e+00 5.62662143e+00 -5.08741797e+00 | 5.55194823e+00 5.62662143e+00 -5.08741797e+00 2 6.32740107e+00 -5.73319431e+00 6.08167069e+00 | 6.32740107e+00 -5.73319431e+00 6.08167069e+00 3 -6.01067594e+00 4.94159403e+00 5.74567393e+00 | -6.01067594e+00 4.94159403e+00 5.74567393e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 28.6983776722 2^p V(r_1,...,r_N) = 28.6983776722 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 -5.38464452e+00 -5.36211511e+00 -6.02965052e+00 | -5.38464452e+00 -5.36211511e+00 -6.02965052e+00 1 5.51765827e+00 5.68420226e+00 -5.77521654e+00 | 5.51765827e+00 5.68420226e+00 -5.77521654e+00 2 6.52695018e+00 -5.81258044e+00 6.15772417e+00 | 6.52695018e+00 -5.81258044e+00 6.15772417e+00 3 -6.65996393e+00 5.49049329e+00 5.64714288e+00 | -6.65996393e+00 5.49049329e+00 5.64714288e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 25.3470425708 2^p V(r_1,...,r_N) = 25.3470425708 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 -5.06191657e+00 -4.49600022e+00 -4.13858027e+00 | -5.06191657e+00 -4.49600022e+00 -4.13858027e+00 1 5.42282658e+00 3.48356847e+00 -6.18283360e+00 | 5.42282658e+00 3.48356847e+00 -6.18283360e+00 2 4.63702057e+00 -4.71090386e+00 6.34849039e+00 | 4.63702057e+00 -4.71090386e+00 6.34849039e+00 3 -4.99793058e+00 5.72333562e+00 3.97292348e+00 | -4.99793058e+00 5.72333562e+00 3.97292348e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 25.4828653243 2^p V(r_1,...,r_N) = 25.4828653243 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 -5.37589654e+00 -5.74262018e+00 -4.93800180e+00 | -5.37589654e+00 -5.74262018e+00 -4.93800180e+00 1 5.15320593e+00 4.42655872e+00 -4.90344076e+00 | 5.15320593e+00 4.42655872e+00 -4.90344076e+00 2 4.77152911e+00 -4.79404421e+00 4.41707832e+00 | 4.77152911e+00 -4.79404421e+00 4.41707832e+00 3 -4.54883849e+00 6.11010568e+00 5.42436424e+00 | -4.54883849e+00 6.11010568e+00 5.42436424e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 22.3354180845 2^p V(r_1,...,r_N) = 22.3354180845 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 -4.23338091e+00 -3.88914439e+00 -4.57597683e+00 | -4.23338091e+00 -3.88914439e+00 -4.57597683e+00 1 5.19438017e+00 4.32924532e+00 -4.00524066e+00 | 5.19438017e+00 4.32924532e+00 -4.00524066e+00 2 3.55150942e+00 -4.52074549e+00 4.30478930e+00 | 3.55150942e+00 -4.52074549e+00 4.30478930e+00 3 -4.51250868e+00 4.08064457e+00 4.27642819e+00 | -4.51250868e+00 4.08064457e+00 4.27642819e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 24.4459609005 2^p V(r_1,...,r_N) = 24.4459609005 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 -4.33558251e+00 -5.75411805e+00 -4.98545700e+00 | -4.33558251e+00 -5.75411805e+00 -4.98545700e+00 1 3.84747728e+00 5.23119244e+00 -4.62163446e+00 | 3.84747728e+00 5.23119244e+00 -4.62163446e+00 2 5.38808711e+00 -3.96344742e+00 3.70913631e+00 | 5.38808711e+00 -3.96344742e+00 3.70913631e+00 3 -4.89998189e+00 4.48637304e+00 5.89795516e+00 | -4.89998189e+00 4.48637304e+00 5.89795516e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 31.6129173647 2^p V(r_1,...,r_N) = 31.6129173647 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 -7.32827455e+00 -6.14200161e+00 -5.62690730e+00 | -7.32827455e+00 -6.14200161e+00 -5.62690730e+00 1 7.23699182e+00 4.22017821e+00 -6.81823665e+00 | 7.23699182e+00 4.22017821e+00 -6.81823665e+00 2 6.16633774e+00 -7.25728309e+00 7.84248519e+00 | 6.16633774e+00 -7.25728309e+00 7.84248519e+00 3 -6.07505501e+00 9.17910649e+00 4.60265876e+00 | -6.07505501e+00 9.17910649e+00 4.60265876e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TTT (Configuration in file "config-CSi-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -8.24758536951 2^p V(r_1,...,r_N) = -8.24758536951 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 4.19974947e+00 -2.86200810e+00 -3.35213492e+00 | 4.19974947e+00 -2.86200810e+00 -3.35213492e+00 1 -5.32836660e+00 1.42902035e+00 -2.19998802e+00 | -5.32836660e+00 1.42902035e+00 -2.19998802e+00 2 -3.83379033e+00 -2.92032053e+00 2.24968351e+00 | -3.83379033e+00 -2.92032053e+00 2.24968351e+00 3 4.96240746e+00 4.35330828e+00 3.30243943e+00 | 4.96240746e+00 4.35330828e+00 3.30243943e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TTF (Configuration in file "config-CSi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -1.64146884449 2^p V(r_1,...,r_N) = -1.64146884449 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 5.47761991e+00 -4.80582398e+00 -2.39554651e+00 | 5.47761991e+00 -4.80582398e+00 -2.39554651e+00 1 -4.73860472e+00 2.01205878e+01 -1.08770631e+01 | -4.73860472e+00 2.01205878e+01 -1.08770631e+01 2 -5.81084476e+00 -1.93653768e+01 1.16175538e+01 | -5.81084476e+00 -1.93653768e+01 1.16175538e+01 3 5.07182957e+00 4.05061295e+00 1.65505578e+00 | 5.07182957e+00 4.05061295e+00 1.65505578e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TFT (Configuration in file "config-CSi-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -8.07612973895 2^p V(r_1,...,r_N) = -8.07612973895 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 3.84142722e-01 4.87417016e+00 -1.29645158e+00 | 3.84142722e-01 4.87417016e+00 -1.29645158e+00 1 2.08437269e+00 -7.10934660e+00 -3.19555267e+00 | 2.08437269e+00 -7.10934660e+00 -3.19555267e+00 2 9.26775650e-01 5.67836669e+00 -8.75516244e-03 | 9.26775650e-01 5.67836669e+00 -8.75516244e-03 3 -3.39529106e+00 -3.44319025e+00 4.50075941e+00 | -3.39529106e+00 -3.44319025e+00 4.50075941e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TFF (Configuration in file "config-CSi-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -6.95055795565 2^p V(r_1,...,r_N) = -6.95055795565 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 4.80840790e+00 -3.98516401e-01 -1.09389081e+00 | 4.80840790e+00 -3.98516401e-01 -1.09389081e+00 1 -5.17432210e+00 2.23133442e+00 -4.57694744e+00 | -5.17432210e+00 2.23133442e+00 -4.57694744e+00 2 -5.30942699e+00 -1.26265705e+00 4.31298265e+00 | -5.30942699e+00 -1.26265705e+00 4.31298265e+00 3 5.67534119e+00 -5.70160970e-01 1.35785559e+00 | 5.67534119e+00 -5.70160970e-01 1.35785559e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FTT (Configuration in file "config-CSi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -11.5554892232 2^p V(r_1,...,r_N) = -11.5554892232 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 -1.69731564e+00 5.73094808e-01 2.81131999e+00 | -1.69731564e+00 5.73094808e-01 2.81131999e+00 1 1.19964540e-01 -4.59953601e-01 4.20642223e+00 | 1.19964540e-01 -4.59953601e-01 4.20642223e+00 2 6.80121020e+00 -5.55478749e+00 -3.53884481e+00 | 6.80121020e+00 -5.55478749e+00 -3.53884481e+00 3 -5.22385910e+00 5.44164629e+00 -3.47889741e+00 | -5.22385910e+00 5.44164629e+00 -3.47889741e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FTF (Configuration in file "config-CSi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -2.40926216366 2^p V(r_1,...,r_N) = -2.40926216366 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 -2.08485806e+01 5.03944668e+00 -2.73308143e+01 | -2.08485806e+01 5.03944668e+00 -2.73308143e+01 1 -5.62987533e-01 -5.47777899e+00 9.34313282e-01 | -5.62987533e-01 -5.47777899e+00 9.34313282e-01 2 2.02406631e+01 5.94149389e+00 2.68842983e+01 | 2.02406631e+01 5.94149389e+00 2.68842983e+01 3 1.17090510e+00 -5.50316159e+00 -4.87797305e-01 | 1.17090510e+00 -5.50316159e+00 -4.87797305e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FFT (Configuration in file "config-CSi-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = 2.63540265819 2^p V(r_1,...,r_N) = 2.63540265819 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 -9.01155348e+00 -6.78178784e+00 1.88474165e+00 | -9.01155348e+00 -6.78178784e+00 1.88474165e+00 1 9.15109988e+00 7.03523367e+00 -6.37561781e-01 | 9.15109988e+00 7.03523367e+00 -6.37561781e-01 2 3.02092342e+01 -3.66060225e+01 1.13301648e+00 | 3.02092342e+01 -3.66060225e+01 1.13301648e+00 3 -3.03487806e+01 3.63525767e+01 -2.38019635e+00 | -3.03487806e+01 3.63525767e+01 -2.38019635e+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.