!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_IMD_BrommerGaehler_2006B_AlNiCo__MO_128037485276_003 Supported species : Al Co Ni 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=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)) = 0.482084134642 2^p V(r_1,...,r_N) = 0.482084134642 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 -5.72169210e+00 -1.02814993e+01 -1.13006167e+01 | -5.72169210e+00 -1.02814993e+01 -1.13006167e+01 1 4.06552253e+00 2.78028027e+00 -2.56639468e+00 | 4.06552253e+00 2.78028027e+00 -2.56639468e+00 2 4.87999300e+00 -3.69552775e+00 5.47214474e+00 | 4.87999300e+00 -3.69552775e+00 5.47214474e+00 3 -3.22382342e+00 1.11967467e+01 8.39486665e+00 | -3.22382342e+00 1.11967467e+01 8.39486665e+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=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)) = 2.65165011786 2^p V(r_1,...,r_N) = 2.65165011786 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 -8.56601789e+00 -5.69960371e+00 -5.46231159e+00 | -8.56601789e+00 -5.69960371e+00 -5.46231159e+00 1 6.07756313e+00 5.09083400e+00 -7.66421852e+00 | 6.07756313e+00 5.09083400e+00 -7.66421852e+00 2 1.14087582e+01 -1.23775174e+01 9.87104954e+00 | 1.14087582e+01 -1.23775174e+01 9.87104954e+00 3 -8.92030348e+00 1.29862871e+01 3.25548057e+00 | -8.92030348e+00 1.29862871e+01 3.25548057e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 5.39283542032 2^p V(r_1,...,r_N) = 5.39283542032 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 -9.15362425e+00 -1.24394299e+01 -1.56043227e+01 | -9.15362425e+00 -1.24394299e+01 -1.56043227e+01 1 1.22028949e+01 1.24119367e+01 -7.03364930e+00 | 1.22028949e+01 1.24119367e+01 -7.03364930e+00 2 7.47953394e+00 -1.02542571e+01 1.11505945e+01 | 7.47953394e+00 -1.02542571e+01 1.11505945e+01 3 -1.05288046e+01 1.02817504e+01 1.14873775e+01 | -1.05288046e+01 1.02817504e+01 1.14873775e+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=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)) = 15.5326592747 2^p V(r_1,...,r_N) = 15.5326592747 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 -1.93688441e+01 -1.77923443e+01 -3.12400103e+01 | -1.93688441e+01 -1.77923443e+01 -3.12400103e+01 1 1.03983620e+01 1.31136102e+01 -8.42678218e+00 | 1.03983620e+01 1.31136102e+01 -8.42678218e+00 2 2.40414600e+01 -1.47461983e+01 2.41588744e+01 | 2.40414600e+01 -1.47461983e+01 2.41588744e+01 3 -1.50709779e+01 1.94249324e+01 1.55079180e+01 | -1.50709779e+01 1.94249324e+01 1.55079180e+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=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)) = 4.97944490841 2^p V(r_1,...,r_N) = 4.97944490841 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 -1.26672307e+01 -8.91557958e+00 -1.23261089e+01 | -1.26672307e+01 -8.91557958e+00 -1.23261089e+01 1 8.12260043e+00 1.11219839e+01 -9.18824405e+00 | 8.12260043e+00 1.11219839e+01 -9.18824405e+00 2 1.21586884e+01 -1.27979584e+01 1.13676934e+01 | 1.21586884e+01 -1.27979584e+01 1.13676934e+01 3 -7.61405815e+00 1.05915540e+01 1.01466595e+01 | -7.61405815e+00 1.05915540e+01 1.01466595e+01 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 0.389490874524 2^p V(r_1,...,r_N) = 0.389490874524 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 -9.88283739e+00 -7.94105411e+00 -5.56851112e+00 | -9.88283739e+00 -7.94105411e+00 -5.56851112e+00 1 6.14410575e+00 8.04311109e+00 -6.73550809e+00 | 6.14410575e+00 8.04311109e+00 -6.73550809e+00 2 6.73859516e+00 -3.60420371e+00 9.94252999e+00 | 6.73859516e+00 -3.60420371e+00 9.94252999e+00 3 -2.99986351e+00 3.50214674e+00 2.36148923e+00 | -2.99986351e+00 3.50214674e+00 2.36148923e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = 12.9132856377 2^p V(r_1,...,r_N) = 12.9132856377 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 -1.05049674e+01 -9.47772519e+00 -1.26260293e+01 | -1.05049674e+01 -9.47772519e+00 -1.26260293e+01 1 1.34310261e+01 1.34353513e+01 -1.10588148e+01 | 1.34310261e+01 1.34353513e+01 -1.10588148e+01 2 2.16019802e+01 -2.56781803e+01 1.52701083e+01 | 2.16019802e+01 -2.56781803e+01 1.52701083e+01 3 -2.45280389e+01 2.17205541e+01 8.41473582e+00 | -2.45280389e+01 2.17205541e+01 8.41473582e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TTT (Configuration in file "config-Co-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)) = -0.905014991061 2^p V(r_1,...,r_N) = -0.905014991061 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 -1.40024197e+01 -7.88562202e+00 -1.61533462e+01 | -1.40024197e+01 -7.88562202e+00 -1.61533462e+01 1 7.22051657e+00 1.11263469e+01 -8.79689533e+00 | 7.22051657e+00 1.11263469e+01 -8.79689533e+00 2 1.87160804e+01 -1.48515486e+01 1.66571342e+01 | 1.87160804e+01 -1.48515486e+01 1.66571342e+01 3 -1.19341772e+01 1.16108237e+01 8.29310739e+00 | -1.19341772e+01 1.16108237e+01 8.29310739e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TTF (Configuration in file "config-Co-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)) = -0.344095254672 2^p V(r_1,...,r_N) = -0.344095254672 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 -1.17180592e+01 -9.15117553e+00 -1.02847871e+01 | -1.17180592e+01 -9.15117553e+00 -1.02847871e+01 1 9.18615094e+00 1.32148596e+01 -1.12119151e+01 | 9.18615094e+00 1.32148596e+01 -1.12119151e+01 2 2.15238495e+01 -1.99367233e+01 1.37160159e+01 | 2.15238495e+01 -1.99367233e+01 1.37160159e+01 3 -1.89919412e+01 1.58730392e+01 7.78068632e+00 | -1.89919412e+01 1.58730392e+01 7.78068632e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TFT (Configuration in file "config-Co-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)) = -3.8327652288 2^p V(r_1,...,r_N) = -3.8327652288 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 -4.37872154e+00 -4.76728678e+00 -4.07285266e+00 | -4.37872154e+00 -4.76728678e+00 -4.07285266e+00 1 6.06633667e+00 7.85469724e+00 -1.38465478e+01 | 6.06633667e+00 7.85469724e+00 -1.38465478e+01 2 5.86477734e+00 -1.16816347e+01 1.38702699e+01 | 5.86477734e+00 -1.16816347e+01 1.38702699e+01 3 -7.55239247e+00 8.59422420e+00 4.04913057e+00 | -7.55239247e+00 8.59422420e+00 4.04913057e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TFF (Configuration in file "config-Co-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)) = -3.39887697934 2^p V(r_1,...,r_N) = -3.39887697934 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 -5.80826675e+00 -1.61873691e+01 -1.35333664e+01 | -5.80826675e+00 -1.61873691e+01 -1.35333664e+01 1 5.54578355e+00 5.58204450e+00 -6.98155420e+00 | 5.54578355e+00 5.58204450e+00 -6.98155420e+00 2 3.82547707e+00 -5.92528473e+00 5.38876583e+00 | 3.82547707e+00 -5.92528473e+00 5.38876583e+00 3 -3.56299387e+00 1.65306094e+01 1.51261547e+01 | -3.56299387e+00 1.65306094e+01 1.51261547e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FTT (Configuration in file "config-Co-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)) = -5.98934823121 2^p V(r_1,...,r_N) = -5.98934823121 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 -3.83107073e+00 -4.17051932e+00 -2.75375025e+00 | -3.83107073e+00 -4.17051932e+00 -2.75375025e+00 1 6.84829543e+00 5.54646549e+00 -5.13484528e+00 | 6.84829543e+00 5.54646549e+00 -5.13484528e+00 2 1.36103059e+00 -3.99859738e+00 3.45981662e+00 | 1.36103059e+00 -3.99859738e+00 3.45981662e+00 3 -4.37825528e+00 2.62265121e+00 4.42877891e+00 | -4.37825528e+00 2.62265121e+00 4.42877891e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FTF (Configuration in file "config-Co-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)) = -4.45261774483 2^p V(r_1,...,r_N) = -4.45261774483 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 -4.21301623e+00 -1.14276489e+01 -1.07041141e+01 | -4.21301623e+00 -1.14276489e+01 -1.07041141e+01 1 5.21581757e+00 4.35057968e+00 -5.08248529e+00 | 5.21581757e+00 4.35057968e+00 -5.08248529e+00 2 5.21245148e+00 -2.96418331e+00 2.67895471e+00 | 5.21245148e+00 -2.96418331e+00 2.67895471e+00 3 -6.21525282e+00 1.00412525e+01 1.31076447e+01 | -6.21525282e+00 1.00412525e+01 1.31076447e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FFT (Configuration in file "config-Co-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)) = 2.66036990323 2^p V(r_1,...,r_N) = 2.66036990323 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 -1.74929641e+01 -1.34571627e+01 -1.72559969e+01 | -1.74929641e+01 -1.34571627e+01 -1.72559969e+01 1 1.33699513e+01 1.08020269e+01 -1.82367705e+01 | 1.33699513e+01 1.08020269e+01 -1.82367705e+01 2 2.23806245e+01 -2.68057953e+01 2.60532688e+01 | 2.23806245e+01 -2.68057953e+01 2.60532688e+01 3 -1.82576118e+01 2.94609310e+01 9.43949866e+00 | -1.82576118e+01 2.94609310e+01 9.43949866e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-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)) = -8.64244254133 2^p V(r_1,...,r_N) = -8.64244254133 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 -1.35274735e+01 -9.61091873e+00 -7.83593031e+00 | -1.35274735e+01 -9.61091873e+00 -7.83593031e+00 1 7.96380931e+00 1.18545618e+01 -1.63446431e+01 | 7.96380931e+00 1.18545618e+01 -1.63446431e+01 2 1.65159718e+01 -1.44947143e+01 1.14688903e+01 | 1.65159718e+01 -1.44947143e+01 1.14688903e+01 3 -1.09523076e+01 1.22510712e+01 1.27116831e+01 | -1.09523076e+01 1.22510712e+01 1.27116831e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-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)) = -9.11870785685 2^p V(r_1,...,r_N) = -9.11870785685 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 -1.37036118e+01 -1.14835927e+01 -1.25092174e+01 | -1.37036118e+01 -1.14835927e+01 -1.25092174e+01 1 1.50858249e+01 1.42293012e+01 -1.05741176e+01 | 1.50858249e+01 1.42293012e+01 -1.05741176e+01 2 7.49093679e+00 -1.06010316e+01 9.12966883e+00 | 7.49093679e+00 -1.06010316e+01 9.12966883e+00 3 -8.87314985e+00 7.85532311e+00 1.39536662e+01 | -8.87314985e+00 7.85532311e+00 1.39536662e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-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)) = -9.92435799632 2^p V(r_1,...,r_N) = -9.92435799632 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 -1.22333403e+01 -9.58039981e+00 -3.68552358e+00 | -1.22333403e+01 -9.58039981e+00 -3.68552358e+00 1 1.24180126e+01 7.70443459e+00 -9.41727556e+00 | 1.24180126e+01 7.70443459e+00 -9.41727556e+00 2 3.65624176e+00 -5.00347405e+00 4.19249064e+00 | 3.65624176e+00 -5.00347405e+00 4.19249064e+00 3 -3.84091411e+00 6.87943926e+00 8.91030850e+00 | -3.84091411e+00 6.87943926e+00 8.91030850e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-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)) = -8.3817772536 2^p V(r_1,...,r_N) = -8.3817772536 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 -1.37503673e+01 -1.22510751e+01 -1.60132367e+01 | -1.37503673e+01 -1.22510751e+01 -1.60132367e+01 1 1.38080012e+01 1.04387710e+01 -1.03016144e+01 | 1.38080012e+01 1.04387710e+01 -1.03016144e+01 2 1.25353552e+01 -1.41421638e+01 1.35863703e+01 | 1.25353552e+01 -1.41421638e+01 1.35863703e+01 3 -1.25929891e+01 1.59544680e+01 1.27284809e+01 | -1.25929891e+01 1.59544680e+01 1.27284809e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-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)) = -9.42926905881 2^p V(r_1,...,r_N) = -9.42926905881 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 -5.90146725e+00 -5.50371405e+00 -3.79444523e+00 | -5.90146725e+00 -5.50371405e+00 -3.79444523e+00 1 1.17072922e+01 1.06909376e+01 -1.49634865e+01 | 1.17072922e+01 1.06909376e+01 -1.49634865e+01 2 7.79814951e+00 -1.39931753e+01 1.19100278e+01 | 7.79814951e+00 -1.39931753e+01 1.19100278e+01 3 -1.36039745e+01 8.80595172e+00 6.84790395e+00 | -1.36039745e+01 8.80595172e+00 6.84790395e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-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)) = -9.15442519859 2^p V(r_1,...,r_N) = -9.15442519859 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 -1.12742544e+01 -8.46534040e+00 -1.36865062e+01 | -1.12742544e+01 -8.46534040e+00 -1.36865062e+01 1 5.28996068e+00 8.92570932e+00 -7.41737091e+00 | 5.28996068e+00 8.92570932e+00 -7.41737091e+00 2 1.56539856e+01 -1.30024795e+01 1.11179866e+01 | 1.56539856e+01 -1.30024795e+01 1.11179866e+01 3 -9.66969190e+00 1.25421106e+01 9.98589047e+00 | -9.66969190e+00 1.25421106e+01 9.98589047e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-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)) = -8.74677222371 2^p V(r_1,...,r_N) = -8.74677222371 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 -8.73925287e+00 -7.79913481e+00 -8.24020508e+00 | -8.73925287e+00 -7.79913481e+00 -8.24020508e+00 1 8.22890920e+00 1.04877875e+01 -1.58152829e+01 | 8.22890920e+00 1.04877875e+01 -1.58152829e+01 2 1.51857419e+01 -1.43352448e+01 1.10395150e+01 | 1.51857419e+01 -1.43352448e+01 1.10395150e+01 3 -1.46753983e+01 1.16465921e+01 1.30159729e+01 | -1.46753983e+01 1.16465921e+01 1.30159729e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TTT (Configuration in file "config-AlCoNi-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)) = -7.71601145322 2^p V(r_1,...,r_N) = -7.71601145322 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 -4.26916464e+00 -1.20649249e+00 -5.64616453e+00 | -4.26916464e+00 -1.20649249e+00 -5.64616453e+00 1 1.26613029e+00 6.23680076e-01 -1.50882032e+00 | 1.26613029e+00 6.23680076e-01 -1.50882032e+00 2 8.34271754e+00 -2.44961286e+00 5.17567279e+00 | 8.34271754e+00 -2.44961286e+00 5.17567279e+00 3 -5.33968320e+00 3.03242528e+00 1.97931206e+00 | -5.33968320e+00 3.03242528e+00 1.97931206e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TTF (Configuration in file "config-AlCoNi-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)) = -7.10334729113 2^p V(r_1,...,r_N) = -7.10334729113 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 -2.35579657e+00 -1.56839868e+00 -3.77654747e+00 | -2.35579657e+00 -1.56839868e+00 -3.77654747e+00 1 7.82037160e+00 2.65418298e+00 -5.23596016e+00 | 7.82037160e+00 2.65418298e+00 -5.23596016e+00 2 4.00239500e+00 -3.44415284e+00 4.10304246e+00 | 4.00239500e+00 -3.44415284e+00 4.10304246e+00 3 -9.46697003e+00 2.35836854e+00 4.90946518e+00 | -9.46697003e+00 2.35836854e+00 4.90946518e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TFT (Configuration in file "config-AlCoNi-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)) = -1.56330214966 2^p V(r_1,...,r_N) = -1.56330214966 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 -8.75757947e+00 -4.31684530e+00 -5.20532877e+00 | -8.75757947e+00 -4.31684530e+00 -5.20532877e+00 1 1.17928170e+01 1.75989433e+01 -2.10977049e+01 | 1.17928170e+01 1.75989433e+01 -2.10977049e+01 2 5.27624481e+00 -1.86383572e+01 1.83811915e+01 | 5.27624481e+00 -1.86383572e+01 1.83811915e+01 3 -8.31148231e+00 5.35625913e+00 7.92184218e+00 | -8.31148231e+00 5.35625913e+00 7.92184218e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TFF (Configuration in file "config-AlCoNi-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)) = -7.49351756559 2^p V(r_1,...,r_N) = -7.49351756559 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 -4.62195134e+00 -7.51743819e+00 2.69275229e+00 | -4.62195134e+00 -7.51743819e+00 2.69275229e+00 1 5.83020260e+00 7.80981416e+00 1.20805414e+00 | 5.83020260e+00 7.80981416e+00 1.20805414e+00 2 8.42634019e-01 -1.11776970e+00 -2.27613169e+00 | 8.42634019e-01 -1.11776970e+00 -2.27613169e+00 3 -2.05088528e+00 8.25393731e-01 -1.62467474e+00 | -2.05088528e+00 8.25393731e-01 -1.62467474e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = FTT (Configuration in file "config-AlCoNi-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)) = -4.51590698261 2^p V(r_1,...,r_N) = -4.51590698261 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 -7.83543276e+00 -5.76796305e+00 -4.60193366e+00 | -7.83543276e+00 -5.76796305e+00 -4.60193366e+00 1 3.81318349e+00 3.99107007e+00 -6.55503503e-01 | 3.81318349e+00 3.99107007e+00 -6.55503503e-01 2 1.25588679e+01 -9.55989597e+00 2.64261763e+00 | 1.25588679e+01 -9.55989597e+00 2.64261763e+00 3 -8.53661861e+00 1.13367889e+01 2.61481953e+00 | -8.53661861e+00 1.13367889e+01 2.61481953e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = FTF (Configuration in file "config-AlCoNi-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)) = -7.93726712956 2^p V(r_1,...,r_N) = -7.93726712956 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 3.08602975e+00 -5.67304387e+00 -5.88911539e+00 | 3.08602975e+00 -5.67304387e+00 -5.88911539e+00 1 -1.92342279e+00 -3.97645326e-01 -6.36640264e-01 | -1.92342279e+00 -3.97645326e-01 -6.36640264e-01 2 -2.21612813e+00 -2.96239651e-01 -5.69363487e-01 | -2.21612813e+00 -2.96239651e-01 -5.69363487e-01 3 1.05352116e+00 6.36692885e+00 7.09511914e+00 | 1.05352116e+00 6.36692885e+00 7.09511914e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = FFT (Configuration in file "config-AlCoNi-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)) = -2.87069518061 2^p V(r_1,...,r_N) = -2.87069518061 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 -5.81255195e+00 -1.54996123e+01 -6.98917567e+00 | -5.81255195e+00 -1.54996123e+01 -6.98917567e+00 1 1.02939658e+01 1.35268926e+01 -1.33776323e+01 | 1.02939658e+01 1.35268926e+01 -1.33776323e+01 2 5.23368968e+00 -3.79147126e+00 6.20836011e+00 | 5.23368968e+00 -3.79147126e+00 6.20836011e+00 3 -9.71510351e+00 5.76419090e+00 1.41584479e+01 | -9.71510351e+00 5.76419090e+00 1.41584479e+01 ------------------------------------------------------------------------------------------------------------------------ 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.