!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_HepburnAckland_2008_FeC__MO_143977152728_005 Supported species : C Fe random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTT (Configuration in file "config-C-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.95339365081 2^p V(r_1,...,r_N) = -8.95339365081 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 -1.76645635e+00 -1.05900887e+00 -1.24724470e+00 | -1.76645635e+00 -1.05900887e+00 -1.24724470e+00 1 1.76964709e+00 1.14386489e+00 -1.33894718e+00 | 1.76964709e+00 1.14386489e+00 -1.33894718e+00 2 1.37605649e+00 -1.53941917e+00 1.73922285e+00 | 1.37605649e+00 -1.53941917e+00 1.73922285e+00 3 -1.37924723e+00 1.45456315e+00 8.46969031e-01 | -1.37924723e+00 1.45456315e+00 8.46969031e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.30980013801 2^p V(r_1,...,r_N) = -8.30980013801 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 -1.92929802e+00 -1.69912997e+00 -1.35317203e+00 | -1.92929802e+00 -1.69912997e+00 -1.35317203e+00 1 1.75174928e+00 1.06704989e+00 -2.05017216e+00 | 1.75174928e+00 1.06704989e+00 -2.05017216e+00 2 1.07715052e+00 -9.82003245e-01 1.92400118e+00 | 1.07715052e+00 -9.82003245e-01 1.92400118e+00 3 -8.99601772e-01 1.61408332e+00 1.47934301e+00 | -8.99601772e-01 1.61408332e+00 1.47934301e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFT (Configuration in file "config-C-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.5841331874 2^p V(r_1,...,r_N) = -7.5841331874 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 -1.35671355e+00 -1.13970446e+00 -1.69645408e+00 | -1.35671355e+00 -1.13970446e+00 -1.69645408e+00 1 1.88664323e+00 1.62158036e+00 -1.18645376e+00 | 1.88664323e+00 1.62158036e+00 -1.18645376e+00 2 1.52806038e+00 -1.79147778e+00 1.67489779e+00 | 1.52806038e+00 -1.79147778e+00 1.67489779e+00 3 -2.05799007e+00 1.30960189e+00 1.20801004e+00 | -2.05799007e+00 1.30960189e+00 1.20801004e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFF (Configuration in file "config-C-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.4125290991 2^p V(r_1,...,r_N) = -7.4125290991 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 6.22469233e+00 5.76675541e+00 8.79961337e+00 | 6.22469233e+00 5.76675541e+00 8.79961337e+00 1 -1.48455668e+00 -2.47029671e+00 -4.44281954e-01 | -1.48455668e+00 -2.47029671e+00 -4.44281954e-01 2 -5.36109356e+00 8.59059567e-01 -5.28134842e+00 | -5.36109356e+00 8.59059567e-01 -5.28134842e+00 3 6.20957912e-01 -4.15551826e+00 -3.07398300e+00 | 6.20957912e-01 -4.15551826e+00 -3.07398300e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTT (Configuration in file "config-C-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.80016017694 2^p V(r_1,...,r_N) = -8.80016017694 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 -1.76800094e+00 -1.55781577e+00 -1.44966325e+00 | -1.76800094e+00 -1.55781577e+00 -1.44966325e+00 1 1.39724210e+00 1.44792887e+00 -1.81538945e+00 | 1.39724210e+00 1.44792887e+00 -1.81538945e+00 2 1.50888744e+00 -1.58727570e+00 1.52714515e+00 | 1.50888744e+00 -1.58727570e+00 1.52714515e+00 3 -1.13812861e+00 1.69716260e+00 1.73790755e+00 | -1.13812861e+00 1.69716260e+00 1.73790755e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTF (Configuration in file "config-C-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.16648817236 2^p V(r_1,...,r_N) = -9.16648817236 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 -1.00661332e+00 -1.33525346e+00 -1.59297471e+00 | -1.00661332e+00 -1.33525346e+00 -1.59297471e+00 1 1.28525259e+00 1.24180415e+00 -1.05389506e+00 | 1.28525259e+00 1.24180415e+00 -1.05389506e+00 2 1.04057324e+00 -1.47895837e+00 1.82824500e+00 | 1.04057324e+00 -1.47895837e+00 1.82824500e+00 3 -1.31921251e+00 1.57240768e+00 8.18624772e-01 | -1.31921251e+00 1.57240768e+00 8.18624772e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.51954811817 2^p V(r_1,...,r_N) = -8.51954811817 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 -1.32084055e+00 -1.94321497e+00 -1.52333683e+00 | -1.32084055e+00 -1.94321497e+00 -1.52333683e+00 1 9.86463292e-01 1.71509211e+00 -1.00578479e+00 | 9.86463292e-01 1.71509211e+00 -1.00578479e+00 2 1.55945669e+00 -1.33388201e+00 1.32133885e+00 | 1.55945669e+00 -1.33388201e+00 1.32133885e+00 3 -1.22507943e+00 1.56200487e+00 1.20778276e+00 | -1.22507943e+00 1.56200487e+00 1.20778276e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTT (Configuration in file "config-Fe-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.7427545964 2^p V(r_1,...,r_N) = -6.7427545964 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 -2.67179830e+00 -3.82972320e+00 -3.30926514e+00 | -2.67179830e+00 -3.82972320e+00 -3.30926514e+00 1 4.91088657e+00 2.24555338e+00 -3.98242753e+00 | 4.91088657e+00 2.24555338e+00 -3.98242753e+00 2 1.91642916e+00 -8.60612253e-01 1.93619915e+00 | 1.91642916e+00 -8.60612253e-01 1.93619915e+00 3 -4.15551743e+00 2.44478208e+00 5.35549353e+00 | -4.15551743e+00 2.44478208e+00 5.35549353e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTF (Configuration in file "config-Fe-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.32515396671 2^p V(r_1,...,r_N) = -8.32515396671 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 -6.17781820e-01 -9.50248915e-01 -7.78087880e-01 | -6.17781820e-01 -9.50248915e-01 -7.78087880e-01 1 1.05376767e+00 6.22410718e-01 -6.86933869e-01 | 1.05376767e+00 6.22410718e-01 -6.86933869e-01 2 1.51504664e+00 -9.44022906e-01 4.10510480e-01 | 1.51504664e+00 -9.44022906e-01 4.10510480e-01 3 -1.95103249e+00 1.27186110e+00 1.05451127e+00 | -1.95103249e+00 1.27186110e+00 1.05451127e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFT (Configuration in file "config-Fe-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.16199474779 2^p V(r_1,...,r_N) = -8.16199474779 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 -3.88295452e-01 2.87594966e-01 -2.12174754e-01 | -3.88295452e-01 2.87594966e-01 -2.12174754e-01 1 3.21317887e-01 1.74937548e+00 -1.90802753e+00 | 3.21317887e-01 1.74937548e+00 -1.90802753e+00 2 5.72700142e-01 -2.00000374e+00 1.80310629e+00 | 5.72700142e-01 -2.00000374e+00 1.80310629e+00 3 -5.05722576e-01 -3.69667096e-02 3.17095993e-01 | -5.05722576e-01 -3.69667096e-02 3.17095993e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFF (Configuration in file "config-Fe-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.533018553532 2^p V(r_1,...,r_N) = -0.533018553532 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 -2.41756998e+01 -7.07169010e+00 -2.30692077e+01 | -2.41756998e+01 -7.07169010e+00 -2.30692077e+01 1 4.30251467e+00 7.83876801e+00 -4.16855833e+00 | 4.30251467e+00 7.83876801e+00 -4.16855833e+00 2 2.36622265e+01 -5.21110047e+00 2.40195369e+01 | 2.36622265e+01 -5.21110047e+00 2.40195369e+01 3 -3.78904134e+00 4.44402256e+00 3.21822920e+00 | -3.78904134e+00 4.44402256e+00 3.21822920e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTT (Configuration in file "config-Fe-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.50205502696 2^p V(r_1,...,r_N) = -6.50205502696 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 -6.15469913e+00 -2.62377326e+00 -5.27303552e+00 | -6.15469913e+00 -2.62377326e+00 -5.27303552e+00 1 3.85418865e+00 2.47406119e+00 -3.81643751e+00 | 3.85418865e+00 2.47406119e+00 -3.81643751e+00 2 5.41462355e+00 -9.44873499e-01 6.42395086e+00 | 5.41462355e+00 -9.44873499e-01 6.42395086e+00 3 -3.11411307e+00 1.09458556e+00 2.66552217e+00 | -3.11411307e+00 1.09458556e+00 2.66552217e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTF (Configuration in file "config-Fe-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.31872086908 2^p V(r_1,...,r_N) = -3.31872086908 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 -6.08671006e+00 -7.33030878e+00 -2.44503920e+00 | -6.08671006e+00 -7.33030878e+00 -2.44503920e+00 1 6.69417229e+00 6.21115371e+00 -3.37239686e+00 | 6.69417229e+00 6.21115371e+00 -3.37239686e+00 2 1.34710338e+01 -1.45567577e+01 4.14883908e+00 | 1.34710338e+01 -1.45567577e+01 4.14883908e+00 3 -1.40784961e+01 1.56759128e+01 1.66859697e+00 | -1.40784961e+01 1.56759128e+01 1.66859697e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FFT (Configuration in file "config-Fe-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.90018248153 2^p V(r_1,...,r_N) = -7.90018248153 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 -1.35924707e+00 -2.61068760e+00 -2.74308990e+00 | -1.35924707e+00 -2.61068760e+00 -2.74308990e+00 1 9.65217686e-01 5.93979732e-01 2.81478184e-02 | 9.65217686e-01 5.93979732e-01 2.81478184e-02 2 1.34240110e+00 -1.19258708e+00 5.34059438e-01 | 1.34240110e+00 -1.19258708e+00 5.34059438e-01 3 -9.48371719e-01 3.20929496e+00 2.18088264e+00 | -9.48371719e-01 3.20929496e+00 2.18088264e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TTT (Configuration in file "config-CFe-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.85148135396 2^p V(r_1,...,r_N) = -8.85148135396 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 -1.27914122e-01 1.73773658e+00 -2.96054778e-01 | -1.27914122e-01 1.73773658e+00 -2.96054778e-01 1 -2.22694087e+00 1.95808158e-02 1.02287662e-01 | -2.22694087e+00 1.95808158e-02 1.02287662e-01 2 1.66257697e+00 -1.42580740e+00 1.85718690e+00 | 1.66257697e+00 -1.42580740e+00 1.85718690e+00 3 6.92278028e-01 -3.31509997e-01 -1.66341979e+00 | 6.92278028e-01 -3.31509997e-01 -1.66341979e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TTF (Configuration in file "config-CFe-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.47772244308 2^p V(r_1,...,r_N) = -9.47772244308 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 -7.00584632e-01 -1.97812207e+00 -1.12041102e+00 | -7.00584632e-01 -1.97812207e+00 -1.12041102e+00 1 1.93209588e+00 1.02461913e+00 -2.16499468e-01 | 1.93209588e+00 1.02461913e+00 -2.16499468e-01 2 -8.39474686e+00 5.39037556e+00 -1.25175574e+00 | -8.39474686e+00 5.39037556e+00 -1.25175574e+00 3 7.16323561e+00 -4.43687262e+00 2.58866622e+00 | 7.16323561e+00 -4.43687262e+00 2.58866622e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TFT (Configuration in file "config-CFe-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.01445545672 2^p V(r_1,...,r_N) = -7.01445545672 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 -3.16116328e+00 -1.43568634e+00 -5.05070358e-01 | -3.16116328e+00 -1.43568634e+00 -5.05070358e-01 1 8.05310660e+00 2.23922958e+01 -1.84848680e+01 | 8.05310660e+00 2.23922958e+01 -1.84848680e+01 2 -1.12666405e+01 -1.68076853e+01 2.22331002e+01 | -1.12666405e+01 -1.68076853e+01 2.22331002e+01 3 6.37469717e+00 -4.14892419e+00 -3.24316190e+00 | 6.37469717e+00 -4.14892419e+00 -3.24316190e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = TFF (Configuration in file "config-CFe-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.65497961711 2^p V(r_1,...,r_N) = -9.65497961711 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 3.81691230e+00 1.04725159e+01 1.23035886e+01 | 3.81691230e+00 1.04725159e+01 1.23035886e+01 1 -5.36580786e-01 -4.23671439e-01 1.42086914e+00 | -5.36580786e-01 -4.23671439e-01 1.42086914e+00 2 -3.67913543e+00 -2.19383917e+00 -6.24710728e+00 | -3.67913543e+00 -2.19383917e+00 -6.24710728e+00 3 3.98803914e-01 -7.85500531e+00 -7.47735051e+00 | 3.98803914e-01 -7.85500531e+00 -7.47735051e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = FTT (Configuration in file "config-CFe-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.90757928228 2^p V(r_1,...,r_N) = -3.90757928228 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 -3.30797336e+01 -1.60626113e+01 -1.32857152e+01 | -3.30797336e+01 -1.60626113e+01 -1.32857152e+01 1 1.94760094e+01 2.06551353e+01 -3.80749127e+00 | 1.94760094e+01 2.06551353e+01 -3.80749127e+00 2 3.92597272e+01 -2.89443553e+01 1.78695507e+01 | 3.92597272e+01 -2.89443553e+01 1.78695507e+01 3 -2.56560030e+01 2.43518313e+01 -7.76344175e-01 | -2.56560030e+01 2.43518313e+01 -7.76344175e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = FTF (Configuration in file "config-CFe-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.09585945461 2^p V(r_1,...,r_N) = -5.09585945461 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 -1.65692707e+01 -1.63943105e+01 -2.27025372e+01 | -1.65692707e+01 -1.63943105e+01 -2.27025372e+01 1 -6.98479849e-02 2.53461810e-01 -5.07919278e-01 | -6.98479849e-02 2.53461810e-01 -5.07919278e-01 2 1.78310812e+01 1.48870637e+00 1.27738159e+01 | 1.78310812e+01 1.48870637e+00 1.27738159e+01 3 -1.19196250e+00 1.46521424e+01 1.04366406e+01 | -1.19196250e+00 1.46521424e+01 1.04366406e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe, PBC = FFT (Configuration in file "config-CFe-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.36097176708 2^p V(r_1,...,r_N) = -9.36097176708 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 6.36912419e-01 2.07195885e-02 -9.88896343e-01 | 6.36912419e-01 2.07195885e-02 -9.88896343e-01 1 -6.51507072e-01 -3.99160162e-01 -1.63131258e-01 | -6.51507072e-01 -3.99160162e-01 -1.63131258e-01 2 1.26870406e+00 -1.28176273e+00 2.70047448e-01 | 1.26870406e+00 -1.28176273e+00 2.70047448e-01 3 -1.25410941e+00 1.66020330e+00 8.81980154e-01 | -1.25410941e+00 1.66020330e+00 8.81980154e-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.