!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Dynamo_ZhouWadleyJohnson_2001_CuTa__MO_547744193826_000 Supported species : Cu Ta random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-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)) = -3.73088293863 2^p V(r_1,...,r_N) = -3.73088293863 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 -2.95101600e+00 -5.91652130e+00 -6.08063955e+00 | -2.95101600e+00 -5.91652130e+00 -6.08063955e+00 1 2.38162463e+00 1.88614325e+00 -1.67989091e+00 | 2.38162463e+00 1.88614325e+00 -1.67989091e+00 2 1.72872235e+00 -2.07035048e+00 2.95972354e+00 | 1.72872235e+00 -2.07035048e+00 2.95972354e+00 3 -1.15933098e+00 6.10072853e+00 4.80080692e+00 | -1.15933098e+00 6.10072853e+00 4.80080692e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -4.21989112642 2^p V(r_1,...,r_N) = -4.21989112642 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 8.78398433e-01 5.93646248e-01 6.57873395e-01 | 8.78398433e-01 5.93646248e-01 6.57873395e-01 1 6.02893713e-01 1.02509483e+00 -2.29445763e+00 | 6.02893713e-01 1.02509483e+00 -2.29445763e+00 2 3.23640364e+00 -4.17190229e+00 8.93236151e-01 | 3.23640364e+00 -4.17190229e+00 8.93236151e-01 3 -4.71769578e+00 2.55316120e+00 7.43348081e-01 | -4.71769578e+00 2.55316120e+00 7.43348081e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -2.79510573811 2^p V(r_1,...,r_N) = -2.79510573811 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 -3.07511861e+00 -3.01002067e+00 -3.70320567e+00 | -3.07511861e+00 -3.01002067e+00 -3.70320567e+00 1 2.99917939e+00 3.16895673e+00 -4.27065089e+00 | 2.99917939e+00 3.16895673e+00 -4.27065089e+00 2 6.59242047e+00 -5.70097262e+00 3.92456758e+00 | 6.59242047e+00 -5.70097262e+00 3.92456758e+00 3 -6.51648125e+00 5.54203657e+00 4.04928898e+00 | -6.51648125e+00 5.54203657e+00 4.04928898e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -3.84968782527 2^p V(r_1,...,r_N) = -3.84968782527 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 -2.32584055e+00 -2.46881574e+00 -4.25090380e+00 | -2.32584055e+00 -2.46881574e+00 -4.25090380e+00 1 1.52011284e+00 2.14880783e+00 -2.08035201e+00 | 1.52011284e+00 2.14880783e+00 -2.08035201e+00 2 5.07393872e+00 -4.77618595e+00 2.99915173e+00 | 5.07393872e+00 -4.77618595e+00 2.99915173e+00 3 -4.26821100e+00 5.09619387e+00 3.33210408e+00 | -4.26821100e+00 5.09619387e+00 3.33210408e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 0.714968164663 2^p V(r_1,...,r_N) = 0.714968164663 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 -4.58628104e+00 -6.23219955e+00 -5.86279772e+00 | -4.58628104e+00 -6.23219955e+00 -5.86279772e+00 1 1.60724649e+01 1.27248828e+00 -1.32172406e+01 | 1.60724649e+01 1.27248828e+00 -1.32172406e+01 2 3.09387620e+00 -3.13668036e+00 2.75777252e+00 | 3.09387620e+00 -3.13668036e+00 2.75777252e+00 3 -1.45800600e+01 8.09639163e+00 1.63222658e+01 | -1.45800600e+01 8.09639163e+00 1.63222658e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -1.08425692839 2^p V(r_1,...,r_N) = -1.08425692839 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 -5.76861421e+00 -1.22775746e+01 -7.12267307e+00 | -5.76861421e+00 -1.22775746e+01 -7.12267307e+00 1 8.76947400e+00 6.04047289e+00 -5.80436646e+00 | 8.76947400e+00 6.04047289e+00 -5.80436646e+00 2 2.60650110e+00 -9.11916687e-01 2.48924769e+00 | 2.60650110e+00 -9.11916687e-01 2.48924769e+00 3 -5.60736089e+00 7.14901841e+00 1.04377918e+01 | -5.60736089e+00 7.14901841e+00 1.04377918e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -5.01249903268 2^p V(r_1,...,r_N) = -5.01249903268 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 -1.87175000e+00 -3.07254451e+00 -1.33912556e+00 | -1.87175000e+00 -3.07254451e+00 -1.33912556e+00 1 1.62892324e+00 1.93278586e+00 -1.42151797e+00 | 1.62892324e+00 1.93278586e+00 -1.42151797e+00 2 8.92066832e-01 -4.72289381e-01 1.19269872e+00 | 8.92066832e-01 -4.72289381e-01 1.19269872e+00 3 -6.49240074e-01 1.61204804e+00 1.56794481e+00 | -6.49240074e-01 1.61204804e+00 1.56794481e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTT (Configuration in file "config-Ta-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)) = -10.6494986206 2^p V(r_1,...,r_N) = -10.6494986206 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 -1.08987966e+01 -1.07000865e+01 -6.79207133e+00 | -1.08987966e+01 -1.07000865e+01 -6.79207133e+00 1 1.72173645e+01 3.29394986e+00 -1.83465981e+01 | 1.72173645e+01 3.29394986e+00 -1.83465981e+01 2 8.32822307e+00 -3.79128181e+00 7.79863245e+00 | 8.32822307e+00 -3.79128181e+00 7.79863245e+00 3 -1.46467909e+01 1.11974185e+01 1.73400370e+01 | -1.46467909e+01 1.11974185e+01 1.73400370e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTF (Configuration in file "config-Ta-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.14219519583 2^p V(r_1,...,r_N) = 1.14219519583 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 -2.51313627e+01 -1.70451055e+01 -2.19588615e+01 | -2.51313627e+01 -1.70451055e+01 -2.19588615e+01 1 3.13855405e+01 7.57580745e+00 -2.94221321e+01 | 3.13855405e+01 7.57580745e+00 -2.94221321e+01 2 1.92498589e+01 -1.42517721e+01 1.77076267e+01 | 1.92498589e+01 -1.42517721e+01 1.77076267e+01 3 -2.55040367e+01 2.37210702e+01 3.36733670e+01 | -2.55040367e+01 2.37210702e+01 3.36733670e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFT (Configuration in file "config-Ta-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)) = -2.53892247102 2^p V(r_1,...,r_N) = -2.53892247102 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 -2.40680335e+01 -2.92907162e+01 -2.86810101e+01 | -2.40680335e+01 -2.92907162e+01 -2.86810101e+01 1 2.45104822e+01 2.13110271e+01 -7.96545682e+00 | 2.45104822e+01 2.13110271e+01 -7.96545682e+00 2 1.20242892e+01 -1.09829429e+01 1.62280535e+01 | 1.20242892e+01 -1.09829429e+01 1.62280535e+01 3 -1.24667380e+01 1.89626320e+01 2.04184134e+01 | -1.24667380e+01 1.89626320e+01 2.04184134e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFF (Configuration in file "config-Ta-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)) = -7.71236165981 2^p V(r_1,...,r_N) = -7.71236165981 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 -1.86140568e+01 -1.23045850e+01 -1.24318453e+01 | -1.86140568e+01 -1.23045850e+01 -1.24318453e+01 1 1.64408725e+01 2.36574545e+01 -1.17619637e+01 | 1.64408725e+01 2.36574545e+01 -1.17619637e+01 2 1.19731620e+01 -1.98395815e+01 1.74341483e+01 | 1.19731620e+01 -1.98395815e+01 1.74341483e+01 3 -9.79997776e+00 8.48671211e+00 6.75966076e+00 | -9.79997776e+00 8.48671211e+00 6.75966076e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTT (Configuration in file "config-Ta-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)) = -6.96637752106 2^p V(r_1,...,r_N) = -6.96637752106 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 -1.76667528e+01 -1.45311723e+01 -9.59449343e+00 | -1.76667528e+01 -1.45311723e+01 -9.59449343e+00 1 2.43475592e+01 8.03947182e+00 -2.09605525e+01 | 2.43475592e+01 8.03947182e+00 -2.09605525e+01 2 8.40283556e+00 -1.16627293e+01 9.34113524e+00 | 8.40283556e+00 -1.16627293e+01 9.34113524e+00 3 -1.50836420e+01 1.81544298e+01 2.12139107e+01 | -1.50836420e+01 1.81544298e+01 2.12139107e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTF (Configuration in file "config-Ta-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)) = 6.65002750461 2^p V(r_1,...,r_N) = 6.65002750461 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 -3.68058739e+01 -1.38258400e+01 -4.15342583e+01 | -3.68058739e+01 -1.38258400e+01 -4.15342583e+01 1 1.55141534e+01 1.07332119e+01 -1.85129138e+01 | 1.55141534e+01 1.07332119e+01 -1.85129138e+01 2 4.59906229e+01 -2.44231673e+01 3.07518063e+01 | 4.59906229e+01 -2.44231673e+01 3.07518063e+01 3 -2.46989024e+01 2.75157955e+01 2.92953657e+01 | -2.46989024e+01 2.75157955e+01 2.92953657e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FFT (Configuration in file "config-Ta-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)) = -12.1598022837 2^p V(r_1,...,r_N) = -12.1598022837 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 -6.20815594e+00 -1.23107370e+01 -7.21547496e+00 | -6.20815594e+00 -1.23107370e+01 -7.21547496e+00 1 1.43097433e+01 8.31350977e+00 -1.42588335e+01 | 1.43097433e+01 8.31350977e+00 -1.42588335e+01 2 4.92837294e+00 -4.44647770e+00 4.23181177e+00 | 4.92837294e+00 -4.44647770e+00 4.23181177e+00 3 -1.30299603e+01 8.44370496e+00 1.72424967e+01 | -1.30299603e+01 8.44370496e+00 1.72424967e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTT (Configuration in file "config-CuTa-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)) = -1.26291861656 2^p V(r_1,...,r_N) = -1.26291861656 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 -1.93751989e+01 -2.60219504e+00 -1.94585556e+01 | -1.93751989e+01 -2.60219504e+00 -1.94585556e+01 1 6.08541348e+00 5.66589812e+00 -3.47347571e+00 | 6.08541348e+00 5.66589812e+00 -3.47347571e+00 2 2.18766569e+01 -1.51441239e+01 1.21810832e+01 | 2.18766569e+01 -1.51441239e+01 1.21810832e+01 3 -8.58687148e+00 1.20804209e+01 1.07509482e+01 | -8.58687148e+00 1.20804209e+01 1.07509482e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTF (Configuration in file "config-CuTa-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.56923332597 2^p V(r_1,...,r_N) = -1.56923332597 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 -2.14058003e+01 -1.61372697e+01 -2.08151936e+01 | -2.14058003e+01 -1.61372697e+01 -2.08151936e+01 1 7.87890054e+00 1.05623809e+01 -6.73935445e+00 | 7.87890054e+00 1.05623809e+01 -6.73935445e+00 2 2.16442444e+01 -7.14907428e+00 1.97878111e+01 | 2.16442444e+01 -7.14907428e+00 1.97878111e+01 3 -8.11734462e+00 1.27239630e+01 7.76673692e+00 | -8.11734462e+00 1.27239630e+01 7.76673692e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFT (Configuration in file "config-CuTa-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)) = -3.15746920054 2^p V(r_1,...,r_N) = -3.15746920054 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 -1.09924668e+01 -6.38762605e+00 -7.94162558e+00 | -1.09924668e+01 -6.38762605e+00 -7.94162558e+00 1 9.13545143e+00 1.89845080e+01 -1.51216178e+01 | 9.13545143e+00 1.89845080e+01 -1.51216178e+01 2 8.08838318e+00 -1.61500647e+01 1.80887543e+01 | 8.08838318e+00 -1.61500647e+01 1.80887543e+01 3 -6.23136784e+00 3.55318273e+00 4.97448903e+00 | -6.23136784e+00 3.55318273e+00 4.97448903e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFF (Configuration in file "config-CuTa-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)) = 2.77454131248 2^p V(r_1,...,r_N) = 2.77454131248 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 -1.17842768e+01 -9.82227262e+00 -9.53343503e+00 | -1.17842768e+01 -9.82227262e+00 -9.53343503e+00 1 1.32553203e+01 1.32232724e+01 -2.94864089e+01 | 1.32553203e+01 1.32232724e+01 -2.94864089e+01 2 1.87369172e+01 -1.95635021e+01 2.77940804e+01 | 1.87369172e+01 -1.95635021e+01 2.77940804e+01 3 -2.02079607e+01 1.61625023e+01 1.12257636e+01 | -2.02079607e+01 1.61625023e+01 1.12257636e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTT (Configuration in file "config-CuTa-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)) = -5.83199775325 2^p V(r_1,...,r_N) = -5.83199775325 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 -4.21614738e+00 -5.74915005e+00 -5.58522354e+00 | -4.21614738e+00 -5.74915005e+00 -5.58522354e+00 1 4.56608804e+00 7.63385457e+00 -1.06915578e+01 | 4.56608804e+00 7.63385457e+00 -1.06915578e+01 2 6.57973681e+00 -1.24952772e+01 1.06125008e+01 | 6.57973681e+00 -1.24952772e+01 1.06125008e+01 3 -6.92967747e+00 1.06105727e+01 5.66428050e+00 | -6.92967747e+00 1.06105727e+01 5.66428050e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTF (Configuration in file "config-CuTa-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)) = -8.13125712846 2^p V(r_1,...,r_N) = -8.13125712846 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 -1.53767181e+00 2.94860464e-01 -4.50351337e-01 | -1.53767181e+00 2.94860464e-01 -4.50351337e-01 1 6.95631389e+00 2.91965132e+00 -7.58969215e+00 | 6.95631389e+00 2.91965132e+00 -7.58969215e+00 2 4.85399312e+00 -6.76407257e+00 1.88140829e+00 | 4.85399312e+00 -6.76407257e+00 1.88140829e+00 3 -1.02726352e+01 3.54956079e+00 6.15863520e+00 | -1.02726352e+01 3.54956079e+00 6.15863520e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FFT (Configuration in file "config-CuTa-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)) = -9.6672807094 2^p V(r_1,...,r_N) = -9.6672807094 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 -7.67095391e+00 -8.37296247e+00 -3.06383876e+00 | -7.67095391e+00 -8.37296247e+00 -3.06383876e+00 1 5.97566247e+00 7.45518300e+00 -2.61083019e+00 | 5.97566247e+00 7.45518300e+00 -2.61083019e+00 2 2.99707435e+00 -8.71606132e-01 3.46524327e+00 | 2.99707435e+00 -8.71606132e-01 3.46524327e+00 3 -1.30178291e+00 1.78938560e+00 2.20942569e+00 | -1.30178291e+00 1.78938560e+00 2.20942569e+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.