!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_OnatDurukanoglu_2014_CuNi__MO_592013496703_005 Supported species : Cu Ni 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)) = -2.0720263562 2^p V(r_1,...,r_N) = -2.0720263562 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 -2.68442607e+00 -5.41940549e+00 -5.56556228e+00 | -2.68442607e+00 -5.41940549e+00 -5.56556228e+00 1 2.16710103e+00 1.77785866e+00 -1.58673755e+00 | 2.16710103e+00 1.77785866e+00 -1.58673755e+00 2 1.54705665e+00 -1.93365381e+00 2.76226202e+00 | 1.54705665e+00 -1.93365381e+00 2.76226202e+00 3 -1.02973161e+00 5.57520064e+00 4.39003781e+00 | -1.02973161e+00 5.57520064e+00 4.39003781e+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)) = -2.69297115248 2^p V(r_1,...,r_N) = -2.69297115248 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 7.94760216e-01 5.66199725e-01 6.44609824e-01 | 7.94760216e-01 5.66199725e-01 6.44609824e-01 1 2.16850771e-01 4.05928699e-01 -1.33454907e+00 | 2.16850771e-01 4.05928699e-01 -1.33454907e+00 2 3.08212295e+00 -3.41647054e+00 3.43859846e-01 | 3.08212295e+00 -3.41647054e+00 3.43859846e-01 3 -4.09373393e+00 2.44434211e+00 3.46079396e-01 | -4.09373393e+00 2.44434211e+00 3.46079396e-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)) = 1.03964211515 2^p V(r_1,...,r_N) = 1.03964211515 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 -3.28994645e+00 -4.47239573e+00 -1.60856926e+00 | -3.28994645e+00 -4.47239573e+00 -1.60856926e+00 1 8.26188426e+00 6.52328681e+00 -1.35313142e+01 | 8.26188426e+00 6.52328681e+00 -1.35313142e+01 2 3.11812731e+00 -6.58787283e+00 8.66735861e+00 | 3.11812731e+00 -6.58787283e+00 8.66735861e+00 3 -8.09006512e+00 4.53698175e+00 6.47252486e+00 | -8.09006512e+00 4.53698175e+00 6.47252486e+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)) = -2.05101780628 2^p V(r_1,...,r_N) = -2.05101780628 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 -1.92414882e+00 -1.97271577e+00 -2.07065075e+00 | -1.92414882e+00 -1.97271577e+00 -2.07065075e+00 1 2.85126882e+00 4.52264080e+00 -5.19672418e+00 | 2.85126882e+00 4.52264080e+00 -5.19672418e+00 2 2.71486272e+00 -4.94204111e+00 4.26752950e+00 | 2.71486272e+00 -4.94204111e+00 4.26752950e+00 3 -3.64198272e+00 2.39211608e+00 2.99984544e+00 | -3.64198272e+00 2.39211608e+00 2.99984544e+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)) = -2.80925925982 2^p V(r_1,...,r_N) = -2.80925925982 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 -7.65544163e-01 3.20361617e-01 -5.89518103e-01 | -7.65544163e-01 3.20361617e-01 -5.89518103e-01 1 1.17735228e-01 2.39947217e+00 -2.31036390e+00 | 1.17735228e-01 2.39947217e+00 -2.31036390e+00 2 2.34257409e+00 -4.04130957e+00 2.65479086e+00 | 2.34257409e+00 -4.04130957e+00 2.65479086e+00 3 -1.69476516e+00 1.32147578e+00 2.45091144e-01 | -1.69476516e+00 1.32147578e+00 2.45091144e-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)) = 3.77704854611 2^p V(r_1,...,r_N) = 3.77704854611 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 -4.81868931e+00 -4.20544154e+00 -5.36539368e+00 | -4.81868931e+00 -4.20544154e+00 -5.36539368e+00 1 6.07880536e+00 6.62726979e+00 -5.30385691e+00 | 6.07880536e+00 6.62726979e+00 -5.30385691e+00 2 1.51263929e+01 -1.71796267e+01 7.35121507e+00 | 1.51263929e+01 -1.71796267e+01 7.35121507e+00 3 -1.63865089e+01 1.47577985e+01 3.31803553e+00 | -1.63865089e+01 1.47577985e+01 3.31803553e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.00804459627888 2^p V(r_1,...,r_N) = -0.00804459627888 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 -6.35054631e+00 -3.25897340e+00 -7.36002092e+00 | -6.35054631e+00 -3.25897340e+00 -7.36002092e+00 1 2.54719505e+00 4.79913156e+00 -3.49989410e+00 | 2.54719505e+00 4.79913156e+00 -3.49989410e+00 2 8.78260420e+00 -6.78646612e+00 7.74214006e+00 | 8.78260420e+00 -6.78646612e+00 7.74214006e+00 3 -4.97925294e+00 5.24630796e+00 3.11777496e+00 | -4.97925294e+00 5.24630796e+00 3.11777496e+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)) = 2.85429718327 2^p V(r_1,...,r_N) = 2.85429718327 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 -6.01483130e+00 -4.10738889e+00 -4.59363951e+00 | -6.01483130e+00 -4.10738889e+00 -4.59363951e+00 1 4.09424060e+00 6.88409727e+00 -5.35495044e+00 | 4.09424060e+00 6.88409727e+00 -5.35495044e+00 2 1.29228291e+01 -1.19517359e+01 6.92403344e+00 | 1.29228291e+01 -1.19517359e+01 6.92403344e+00 3 -1.10022384e+01 9.17502747e+00 3.02455651e+00 | -1.10022384e+01 9.17502747e+00 3.02455651e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.604757725747 2^p V(r_1,...,r_N) = -0.604757725747 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 -6.72304159e-01 -1.25324459e+00 -9.59509559e-01 | -6.72304159e-01 -1.25324459e+00 -9.59509559e-01 1 1.66471013e+00 3.91467865e+00 -6.89426972e+00 | 1.66471013e+00 3.91467865e+00 -6.89426972e+00 2 2.12499256e+00 -6.20736524e+00 6.87589857e+00 | 2.12499256e+00 -6.20736524e+00 6.87589857e+00 3 -3.11739853e+00 3.54593119e+00 9.77880712e-01 | -3.11739853e+00 3.54593119e+00 9.77880712e-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)) = -0.847030426544 2^p V(r_1,...,r_N) = -0.847030426544 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 -3.59575061e+00 -4.03795276e+00 -6.63087896e+00 | -3.59575061e+00 -4.03795276e+00 -6.63087896e+00 1 2.31218756e+00 2.84311820e+00 -8.30667846e-01 | 2.31218756e+00 2.84311820e+00 -8.30667846e-01 2 3.68204845e+00 -2.07342465e+00 3.59567096e+00 | 3.68204845e+00 -2.07342465e+00 3.59567096e+00 3 -2.39848539e+00 3.26825921e+00 3.86587585e+00 | -2.39848539e+00 3.26825921e+00 3.86587585e+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)) = -0.183065447075 2^p V(r_1,...,r_N) = -0.183065447075 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 -5.32670748e+00 -2.80111828e+00 -4.56522706e+00 | -5.32670748e+00 -2.80111828e+00 -4.56522706e+00 1 4.06627278e+00 3.26505018e+00 -5.48089979e+00 | 4.06627278e+00 3.26505018e+00 -5.48089979e+00 2 5.04598239e+00 -1.69966411e+00 7.10840196e+00 | 5.04598239e+00 -1.69966411e+00 7.10840196e+00 3 -3.78554769e+00 1.23573221e+00 2.93772489e+00 | -3.78554769e+00 1.23573221e+00 2.93772489e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.992592600036 2^p V(r_1,...,r_N) = -0.992592600036 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 -3.06640377e+00 -4.89433796e+00 -1.11197446e+00 | -3.06640377e+00 -4.89433796e+00 -1.11197446e+00 1 5.60342989e+00 3.68892119e+00 -3.66376624e+00 | 5.60342989e+00 3.68892119e+00 -3.66376624e+00 2 8.20469981e-01 -1.38135464e+00 1.44351720e+00 | 8.20469981e-01 -1.38135464e+00 1.44351720e+00 3 -3.35749611e+00 2.58677142e+00 3.33222350e+00 | -3.35749611e+00 2.58677142e+00 3.33222350e+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)) = 6.61047869261 2^p V(r_1,...,r_N) = 6.61047869261 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 -1.81638950e+01 -1.17317009e+01 -1.67241747e+01 | -1.81638950e+01 -1.17317009e+01 -1.67241747e+01 1 3.71755954e+00 6.21536950e+00 -6.66271547e+00 | 3.71755954e+00 6.21536950e+00 -6.66271547e+00 2 2.24329557e+01 -5.15791847e+00 1.89717651e+01 | 2.24329557e+01 -5.15791847e+00 1.89717651e+01 3 -7.98662030e+00 1.06742499e+01 4.41512497e+00 | -7.98662030e+00 1.06742499e+01 4.41512497e+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)) = -2.33389346067 2^p V(r_1,...,r_N) = -2.33389346067 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 -1.45274768e+00 -2.35931305e-01 -1.14885557e+00 | -1.45274768e+00 -2.35931305e-01 -1.14885557e+00 1 2.91141511e-01 8.12684369e-01 -1.03498553e+00 | 2.91141511e-01 8.12684369e-01 -1.03498553e+00 2 1.84522374e+00 -8.14169934e-01 1.89267502e+00 | 1.84522374e+00 -8.14169934e-01 1.89267502e+00 3 -6.83617573e-01 2.37416869e-01 2.91166077e-01 | -6.83617573e-01 2.37416869e-01 2.91166077e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = TTT (Configuration in file "config-CuNi-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)) = -0.916157163018 2^p V(r_1,...,r_N) = -0.916157163018 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 -7.33866044e-01 -1.27281451e+00 -6.54134299e-01 | -7.33866044e-01 -1.27281451e+00 -6.54134299e-01 1 1.01518207e+00 5.47660513e+00 -8.52395536e+00 | 1.01518207e+00 5.47660513e+00 -8.52395536e+00 2 2.21747663e+00 -6.09587361e+00 7.83087676e+00 | 2.21747663e+00 -6.09587361e+00 7.83087676e+00 3 -2.49879265e+00 1.89208298e+00 1.34721290e+00 | -2.49879265e+00 1.89208298e+00 1.34721290e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = TTF (Configuration in file "config-CuNi-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)) = 1.17721946696 2^p V(r_1,...,r_N) = 1.17721946696 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 -7.35225851e+00 -3.63728573e+00 -6.31587620e+00 | -7.35225851e+00 -3.63728573e+00 -6.31587620e+00 1 3.33742778e+00 9.98218301e+00 -7.28129703e+00 | 3.33742778e+00 9.98218301e+00 -7.28129703e+00 2 6.46120938e+00 -8.45238112e+00 1.12635479e+01 | 6.46120938e+00 -8.45238112e+00 1.12635479e+01 3 -2.44637865e+00 2.10748385e+00 2.33362533e+00 | -2.44637865e+00 2.10748385e+00 2.33362533e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = TFT (Configuration in file "config-CuNi-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)) = -1.74378022991 2^p V(r_1,...,r_N) = -1.74378022991 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 -1.94384285e+00 -2.49570563e+00 -9.94133956e-01 | -1.94384285e+00 -2.49570563e+00 -9.94133956e-01 1 3.55643048e+00 2.32712544e+00 -2.94306562e+00 | 3.55643048e+00 2.32712544e+00 -2.94306562e+00 2 2.28991064e+00 -2.42219658e+00 -9.83313207e-02 | 2.28991064e+00 -2.42219658e+00 -9.83313207e-02 3 -3.90249828e+00 2.59077677e+00 4.03553090e+00 | -3.90249828e+00 2.59077677e+00 4.03553090e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = TFF (Configuration in file "config-CuNi-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)) = 3.17578315818 2^p V(r_1,...,r_N) = 3.17578315818 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 -3.20035606e+00 -6.67833053e+00 -5.85017455e+00 | -3.20035606e+00 -6.67833053e+00 -5.85017455e+00 1 1.65311139e+01 5.70859310e+00 -1.17844743e+01 | 1.65311139e+01 5.70859310e+00 -1.17844743e+01 2 1.70870021e+00 -4.74289820e+00 3.66031453e+00 | 1.70870021e+00 -4.74289820e+00 3.66031453e+00 3 -1.50394580e+01 5.71263563e+00 1.39743343e+01 | -1.50394580e+01 5.71263563e+00 1.39743343e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = FTT (Configuration in file "config-CuNi-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)) = 0.23997016954 2^p V(r_1,...,r_N) = 0.23997016954 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 -4.60249832e+00 -4.32602436e+00 -2.05776635e+00 | -4.60249832e+00 -4.32602436e+00 -2.05776635e+00 1 5.11898834e+00 8.16691045e+00 -9.92966482e+00 | 5.11898834e+00 8.16691045e+00 -9.92966482e+00 2 3.08174614e+00 -6.74193277e+00 9.01433625e+00 | 3.08174614e+00 -6.74193277e+00 9.01433625e+00 3 -3.59823616e+00 2.90104668e+00 2.97309491e+00 | -3.59823616e+00 2.90104668e+00 2.97309491e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = FTF (Configuration in file "config-CuNi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.41967909055 2^p V(r_1,...,r_N) = -2.41967909055 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 -7.51304684e-01 -9.98460767e-01 -8.13031411e-01 | -7.51304684e-01 -9.98460767e-01 -8.13031411e-01 1 3.35572781e+00 1.16418040e+00 -3.29116629e+00 | 3.35572781e+00 1.16418040e+00 -3.29116629e+00 2 7.30421127e-01 -9.88754402e-01 1.21447914e+00 | 7.30421127e-01 -9.88754402e-01 1.21447914e+00 3 -3.33484426e+00 8.23034766e-01 2.88971856e+00 | -3.33484426e+00 8.23034766e-01 2.88971856e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ni, PBC = FFT (Configuration in file "config-CuNi-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)) = 7.80529410025 2^p V(r_1,...,r_N) = 7.80529410025 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 -1.75885983e+01 -1.74575792e+01 -8.84694244e+00 | -1.75885983e+01 -1.74575792e+01 -8.84694244e+00 1 1.93998459e+01 1.23608322e+01 -1.23076293e+01 | 1.93998459e+01 1.23608322e+01 -1.23076293e+01 2 9.50867667e+00 -1.06333718e+01 8.30517386e+00 | 9.50867667e+00 -1.06333718e+01 8.30517386e+00 3 -1.13199243e+01 1.57301189e+01 1.28493979e+01 | -1.13199243e+01 1.57301189e+01 1.28493979e+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.