!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LiyanageSeongGonHouze_2014_FeC__SM_652425777808_000 Supported species : C Fe 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)) = -15.383753239 2^p V(r_1,...,r_N) = -15.383753239 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 9.17039964e-01 3.78615685e+00 1.07217838e+00 | 9.17039964e-01 3.78615685e+00 1.07217838e+00 1 -2.67035177e+00 -4.18448730e+00 3.99272111e+00 | -2.67035177e+00 -4.18448730e+00 3.99272111e+00 2 -2.59720796e+00 7.66856390e+00 -3.77388183e+00 | -2.59720796e+00 7.66856390e+00 -3.77388183e+00 3 4.35051977e+00 -7.27023344e+00 -1.29101766e+00 | 4.35051977e+00 -7.27023344e+00 -1.29101766e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -16.3609288401 2^p V(r_1,...,r_N) = -16.3609288401 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 -1.03485098e+01 -1.32270878e+01 -5.53420442e+00 | -1.03485098e+01 -1.32270878e+01 -5.53420442e+00 1 8.76620671e+00 1.28826819e+01 4.71093915e+00 | 8.76620671e+00 1.28826819e+01 4.71093915e+00 2 -2.63523222e+00 3.61617362e+00 1.14565686e+00 | -2.63523222e+00 3.61617362e+00 1.14565686e+00 3 4.21753533e+00 -3.27176769e+00 -3.22391586e-01 | 4.21753533e+00 -3.27176769e+00 -3.22391586e-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)) = -16.5578302793 2^p V(r_1,...,r_N) = -16.5578302793 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 1.63874411e-01 2.94110099e+00 3.58255618e+00 | 1.63874411e-01 2.94110099e+00 3.58255618e+00 1 4.53824773e+00 -4.11246546e+00 1.85482651e+00 | 4.53824773e+00 -4.11246546e+00 1.85482651e+00 2 -5.57568407e-01 4.55016032e+00 -4.38567608e+00 | -5.57568407e-01 4.55016032e+00 -4.38567608e+00 3 -4.14455373e+00 -3.37879585e+00 -1.05170662e+00 | -4.14455373e+00 -3.37879585e+00 -1.05170662e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -17.4420542261 2^p V(r_1,...,r_N) = -17.4420542261 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 3.26633294e+00 3.63925914e+00 2.79202705e+00 | 3.26633294e+00 3.63925914e+00 2.79202705e+00 1 -4.73868532e+00 -3.08589264e+00 2.47167776e+00 | -4.73868532e+00 -3.08589264e+00 2.47167776e+00 2 -1.93368533e+00 1.56368537e+00 -1.34202489e+00 | -1.93368533e+00 1.56368537e+00 -1.34202489e+00 3 3.40603770e+00 -2.11705187e+00 -3.92167992e+00 | 3.40603770e+00 -2.11705187e+00 -3.92167992e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -17.1060225062 2^p V(r_1,...,r_N) = -17.1060225062 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 1.92499239e+00 -1.02356063e-01 2.97758625e+00 | 1.92499239e+00 -1.02356063e-01 2.97758625e+00 1 1.12151056e+01 1.56634365e+00 -9.07836332e+00 | 1.12151056e+01 1.56634365e+00 -9.07836332e+00 2 -3.20018831e+00 1.31369708e+00 -2.23833522e+00 | -3.20018831e+00 1.31369708e+00 -2.23833522e+00 3 -9.93990964e+00 -2.77768467e+00 8.33911230e+00 | -9.93990964e+00 -2.77768467e+00 8.33911230e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -16.6233722636 2^p V(r_1,...,r_N) = -16.6233722636 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 2.41107431e+00 -4.10202579e+00 2.19661422e+00 | 2.41107431e+00 -4.10202579e+00 2.19661422e+00 1 1.58573016e+00 1.36790143e+00 -1.08371834e+00 | 1.58573016e+00 1.36790143e+00 -1.08371834e+00 2 -2.98440716e+00 7.64290946e-01 -3.39858921e+00 | -2.98440716e+00 7.64290946e-01 -3.39858921e+00 3 -1.01239731e+00 1.96983342e+00 2.28569333e+00 | -1.01239731e+00 1.96983342e+00 2.28569333e+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)) = -16.6759172735 2^p V(r_1,...,r_N) = -16.6759172735 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 1.54145186e+00 -2.31765200e+00 -8.84860831e-01 | 1.54145186e+00 -2.31765200e+00 -8.84860831e-01 1 -4.14556634e+00 -7.17027870e-01 3.27327975e+00 | -4.14556634e+00 -7.17027870e-01 3.27327975e+00 2 -4.30127403e+00 3.03797278e+00 -1.86476722e+00 | -4.30127403e+00 3.03797278e+00 -1.86476722e+00 3 6.90538850e+00 -3.29290785e-03 -5.23651699e-01 | 6.90538850e+00 -3.29290785e-03 -5.23651699e-01 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 6.04374465367 2^p V(r_1,...,r_N) = 6.04374465367 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 -1.56465347e+01 -9.90584302e+00 -1.13029812e+01 | -1.56465347e+01 -9.90584302e+00 -1.13029812e+01 1 1.01474486e+01 1.89417370e+01 -1.49888919e+01 | 1.01474486e+01 1.89417370e+01 -1.49888919e+01 2 4.40341487e+01 -4.08171582e+01 1.76410399e+01 | 4.40341487e+01 -4.08171582e+01 1.76410399e+01 3 -3.85350626e+01 3.17812643e+01 8.65083326e+00 | -3.85350626e+01 3.17812643e+01 8.65083326e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 0.932600808082 2^p V(r_1,...,r_N) = 0.932600808082 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 -6.67048775e+00 -2.31669970e+01 -1.92321709e+01 | -6.67048775e+00 -2.31669970e+01 -1.92321709e+01 1 6.11217009e+00 1.18949207e+01 -2.08891519e+01 | 6.11217009e+00 1.18949207e+01 -2.08891519e+01 2 4.61591712e+00 -1.67004658e+01 2.12946070e+01 | 4.61591712e+00 -1.67004658e+01 2.12946070e+01 3 -4.05759946e+00 2.79725422e+01 1.88267158e+01 | -4.05759946e+00 2.79725422e+01 1.88267158e+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=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)) = -1.33751110765 2^p V(r_1,...,r_N) = -1.33751110765 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 -1.66048989e+01 -2.35303057e+01 -2.11223271e+01 | -1.66048989e+01 -2.35303057e+01 -2.11223271e+01 1 1.73671668e+01 1.58446701e+01 -1.94047224e+00 | 1.73671668e+01 1.58446701e+01 -1.94047224e+00 2 4.80253261e+00 -4.64774263e+00 8.47162171e+00 | 4.80253261e+00 -4.64774263e+00 8.47162171e+00 3 -5.56480054e+00 1.23333783e+01 1.45911776e+01 | -5.56480054e+00 1.23333783e+01 1.45911776e+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=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)) = -2.40908132647 2^p V(r_1,...,r_N) = -2.40908132647 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 -1.40895537e+01 -7.93578447e+00 -1.39511676e+01 | -1.40895537e+01 -7.93578447e+00 -1.39511676e+01 1 1.05401921e+01 7.97007314e+00 -1.42608999e+01 | 1.05401921e+01 7.97007314e+00 -1.42608999e+01 2 1.49808097e+01 -4.21607323e+00 1.92604494e+01 | 1.49808097e+01 -4.21607323e+00 1.92604494e+01 3 -1.14314482e+01 4.18178456e+00 8.95161809e+00 | -1.14314482e+01 4.18178456e+00 8.95161809e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 1.39398717154 2^p V(r_1,...,r_N) = 1.39398717154 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 -6.39653715e+00 -7.34367631e+00 -2.36721260e+00 | -6.39653715e+00 -7.34367631e+00 -2.36721260e+00 1 -3.39266477e+00 3.39293554e+01 -3.44138801e+01 | -3.39266477e+00 3.39293554e+01 -3.44138801e+01 2 1.93996517e+01 -3.20196119e+01 2.98643692e+01 | 1.93996517e+01 -3.20196119e+01 2.98643692e+01 3 -9.61044976e+00 5.43393279e+00 6.91672351e+00 | -9.61044976e+00 5.43393279e+00 6.91672351e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = -1.75674499589 2^p V(r_1,...,r_N) = -1.75674499589 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 -1.98047069e+01 -1.61051597e+01 -8.23940291e+00 | -1.98047069e+01 -1.61051597e+01 -8.23940291e+00 1 1.44683414e+01 2.00742902e+01 -4.72416618e+00 | 1.44683414e+01 2.00742902e+01 -4.72416618e+00 2 1.49572241e+01 -1.27774925e+01 7.35420531e+00 | 1.49572241e+01 -1.27774925e+01 7.35420531e+00 3 -9.62085856e+00 8.80836194e+00 5.60936379e+00 | -9.62085856e+00 8.80836194e+00 5.60936379e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 5.34321631871 2^p V(r_1,...,r_N) = 5.34321631871 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 -2.93911973e+01 -1.46980492e+01 -4.26737583e+01 | -2.93911973e+01 -1.46980492e+01 -4.26737583e+01 1 1.79981508e+01 1.42910645e+01 -7.58675438e+00 | 1.79981508e+01 1.42910645e+01 -7.58675438e+00 2 2.54066375e+01 -2.15101694e+01 1.36423724e+01 | 2.54066375e+01 -2.15101694e+01 1.36423724e+01 3 -1.40135910e+01 2.19171541e+01 3.66181402e+01 | -1.40135910e+01 2.19171541e+01 3.66181402e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TTT (Configuration in file "config-CFe-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)) = -10.4096522043 2^p V(r_1,...,r_N) = -10.4096522043 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 -1.29247462e+01 -2.09173368e+01 -6.86440685e+00 | -1.29247462e+01 -2.09173368e+01 -6.86440685e+00 1 2.34058377e+01 2.08474367e+01 -9.88812100e+00 | 2.34058377e+01 2.08474367e+01 -9.88812100e+00 2 4.13203737e+00 -4.88869265e+00 5.35540311e+00 | 4.13203737e+00 -4.88869265e+00 5.35540311e+00 3 -1.46131288e+01 4.95859280e+00 1.13971247e+01 | -1.46131288e+01 4.95859280e+00 1.13971247e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TTF (Configuration in file "config-CFe-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)) = -14.0933339215 2^p V(r_1,...,r_N) = -14.0933339215 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 1.39247180e+00 1.82754703e+00 5.95003420e-01 | 1.39247180e+00 1.82754703e+00 5.95003420e-01 1 -2.47153503e+00 -1.81578747e+00 7.48603944e-01 | -2.47153503e+00 -1.81578747e+00 7.48603944e-01 2 -3.10954300e+00 3.17827992e+00 -8.05248613e-01 | -3.10954300e+00 3.17827992e+00 -8.05248613e-01 3 4.18860623e+00 -3.19003949e+00 -5.38358752e-01 | 4.18860623e+00 -3.19003949e+00 -5.38358752e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TFT (Configuration in file "config-CFe-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)) = -13.9796505943 2^p V(r_1,...,r_N) = -13.9796505943 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 1.27032512e+00 1.87437369e+00 1.12817995e+00 | 1.27032512e+00 1.87437369e+00 1.12817995e+00 1 -5.30411304e-01 -3.06150837e+00 1.65803122e+00 | -5.30411304e-01 -3.06150837e+00 1.65803122e+00 2 8.41767062e-01 1.50842951e+00 -2.19539018e+00 | 8.41767062e-01 1.50842951e+00 -2.19539018e+00 3 -1.58168088e+00 -3.21294826e-01 -5.90820983e-01 | -1.58168088e+00 -3.21294826e-01 -5.90820983e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TFF (Configuration in file "config-CFe-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)) = -13.2958141542 2^p V(r_1,...,r_N) = -13.2958141542 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 3.30949025e+00 9.13544378e-01 2.16824343e+00 | 3.30949025e+00 9.13544378e-01 2.16824343e+00 1 -1.26226773e+00 -1.36424723e+00 -5.93717862e-03 | -1.26226773e+00 -1.36424723e+00 -5.93717862e-03 2 -2.11770985e-02 -2.19547847e+00 -1.65861944e+00 | -2.11770985e-02 -2.19547847e+00 -1.65861944e+00 3 -2.02604542e+00 2.64618132e+00 -5.03686810e-01 | -2.02604542e+00 2.64618132e+00 -5.03686810e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = FTT (Configuration in file "config-CFe-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)) = -11.1515775114 2^p V(r_1,...,r_N) = -11.1515775114 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 -2.11757488e+01 -6.09727836e-01 -1.50799522e+01 | -2.11757488e+01 -6.09727836e-01 -1.50799522e+01 1 1.92965753e+00 -3.82028927e+00 6.53485650e+00 | 1.92965753e+00 -3.82028927e+00 6.53485650e+00 2 1.43019501e+01 6.83824085e+00 8.87938746e+00 | 1.43019501e+01 6.83824085e+00 8.87938746e+00 3 4.94414114e+00 -2.40822375e+00 -3.34291729e-01 | 4.94414114e+00 -2.40822375e+00 -3.34291729e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = FTF (Configuration in file "config-CFe-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)) = -11.9221370839 2^p V(r_1,...,r_N) = -11.9221370839 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 -8.15045189e+00 -4.82350941e+00 -5.46505171e+00 | -8.15045189e+00 -4.82350941e+00 -5.46505171e+00 1 -1.80303316e+00 3.91170272e+00 6.73161023e+00 | -1.80303316e+00 3.91170272e+00 6.73161023e+00 2 3.00453145e+00 3.55243795e+00 5.72001494e+00 | 3.00453145e+00 3.55243795e+00 5.72001494e+00 3 6.94895360e+00 -2.64063126e+00 -6.98657347e+00 | 6.94895360e+00 -2.64063126e+00 -6.98657347e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = FFT (Configuration in file "config-CFe-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)) = -11.3090637823 2^p V(r_1,...,r_N) = -11.3090637823 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 -1.14338755e-01 4.13628798e+00 -4.57433577e+00 | -1.14338755e-01 4.13628798e+00 -4.57433577e+00 1 -9.98945916e+00 7.39342913e+00 -1.05642007e+01 | -9.98945916e+00 7.39342913e+00 -1.05642007e+01 2 5.16193272e+00 -1.02598450e+01 1.81947111e+01 | 5.16193272e+00 -1.02598450e+01 1.81947111e+01 3 4.94186520e+00 -1.26987210e+00 -3.05617465e+00 | 4.94186520e+00 -1.26987210e+00 -3.05617465e+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.