!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : Sim_LAMMPS_MEAM_KimJungLee_2009_FeTiC__SM_531038274471_000 Supported species : C Fe Ti 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)) = -13.0970831408 2^p V(r_1,...,r_N) = -13.0970831408 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 8.83039569e-01 -1.81118920e+00 -2.10630365e+00 | 8.83039569e-01 -1.81118920e+00 -2.10630365e+00 1 -7.07650969e-01 -1.40057611e+00 9.49211429e-01 | -7.07650969e-01 -1.40057611e+00 9.49211429e-01 2 7.40445127e-01 3.32543788e-01 -9.67164132e-01 | 7.40445127e-01 3.32543788e-01 -9.67164132e-01 3 -9.15833727e-01 2.87922153e+00 2.12425636e+00 | -9.15833727e-01 2.87922153e+00 2.12425636e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -12.9884691222 2^p V(r_1,...,r_N) = -12.9884691222 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 1.69102464e-01 -1.33249037e+00 -1.63496656e+00 | 1.69102464e-01 -1.33249037e+00 -1.63496656e+00 1 -1.62374831e-01 -2.12431469e-01 -7.13322629e-01 | -1.62374831e-01 -2.12431469e-01 -7.13322629e-01 2 2.96754214e+00 -4.29656018e+00 5.83543245e-01 | 2.96754214e+00 -4.29656018e+00 5.83543245e-01 3 -2.97426977e+00 5.84148201e+00 1.76474595e+00 | -2.97426977e+00 5.84148201e+00 1.76474595e+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)) = -11.6365949461 2^p V(r_1,...,r_N) = -11.6365949461 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 -8.21224301e+00 -4.73907597e+00 -1.01538225e+01 | -8.21224301e+00 -4.73907597e+00 -1.01538225e+01 1 1.79590587e+00 4.92525006e+00 -3.42472798e+00 | 1.79590587e+00 4.92525006e+00 -3.42472798e+00 2 1.08701328e+01 -4.98995266e+00 9.24801712e+00 | 1.08701328e+01 -4.98995266e+00 9.24801712e+00 3 -4.45379565e+00 4.80377856e+00 4.33053334e+00 | -4.45379565e+00 4.80377856e+00 4.33053334e+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)) = -12.8250614899 2^p V(r_1,...,r_N) = -12.8250614899 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 -2.12294488e+00 -1.84508289e+00 -1.64286523e+00 | -2.12294488e+00 -1.84508289e+00 -1.64286523e+00 1 3.16375747e+00 4.77302950e+00 -5.17998604e+00 | 3.16375747e+00 4.77302950e+00 -5.17998604e+00 2 3.05157267e+00 -5.28679899e+00 4.16612794e+00 | 3.05157267e+00 -5.28679899e+00 4.16612794e+00 3 -4.09238525e+00 2.35885238e+00 2.65672332e+00 | -4.09238525e+00 2.35885238e+00 2.65672332e+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)) = -11.9501648162 2^p V(r_1,...,r_N) = -11.9501648162 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 2.10550173e+00 2.53577485e+00 2.44295491e+00 | 2.10550173e+00 2.53577485e+00 2.44295491e+00 1 -2.11629670e+00 -2.75943578e+00 2.43822744e+00 | -2.11629670e+00 -2.75943578e+00 2.43822744e+00 2 -2.20526134e+00 2.24311813e+00 -2.06294031e+00 | -2.20526134e+00 2.24311813e+00 -2.06294031e+00 3 2.21605632e+00 -2.01945719e+00 -2.81824203e+00 | 2.21605632e+00 -2.01945719e+00 -2.81824203e+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)) = -11.101869319 2^p V(r_1,...,r_N) = -11.101869319 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 -2.09701403e+00 -3.35610956e+00 -3.25621492e+00 | -2.09701403e+00 -3.35610956e+00 -3.25621492e+00 1 4.00973778e+00 2.61245335e+00 -3.18345756e+00 | 4.00973778e+00 2.61245335e+00 -3.18345756e+00 2 8.52481298e+00 -7.55076298e+00 -4.23919808e-01 | 8.52481298e+00 -7.55076298e+00 -4.23919808e-01 3 -1.04375367e+01 8.29441920e+00 6.86359229e+00 | -1.04375367e+01 8.29441920e+00 6.86359229e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -11.3399160198 2^p V(r_1,...,r_N) = -11.3399160198 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 -8.75862838e+00 -6.28880181e+00 -1.09309538e+01 | -8.75862838e+00 -6.28880181e+00 -1.09309538e+01 1 4.27637865e+00 5.43476967e+00 -3.12985887e+00 | 4.27637865e+00 5.43476967e+00 -3.12985887e+00 2 9.53878304e+00 -5.56607114e+00 8.37177979e+00 | 9.53878304e+00 -5.56607114e+00 8.37177979e+00 3 -5.05653331e+00 6.42010327e+00 5.68903288e+00 | -5.05653331e+00 6.42010327e+00 5.68903288e+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)) = -2.90740268426 2^p V(r_1,...,r_N) = -2.90740268426 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 -5.76859204e+00 -3.80095983e+00 -4.43007304e+00 | -5.76859204e+00 -3.80095983e+00 -4.43007304e+00 1 3.76631858e+00 6.56219616e+00 -5.12533458e+00 | 3.76631858e+00 6.56219616e+00 -5.12533458e+00 2 1.23458228e+01 -1.13972313e+01 6.86011040e+00 | 1.23458228e+01 -1.13972313e+01 6.86011040e+00 3 -1.03435493e+01 8.63599495e+00 2.69529723e+00 | -1.03435493e+01 8.63599495e+00 2.69529723e+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)) = -6.19010505838 2^p V(r_1,...,r_N) = -6.19010505838 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 -5.83642250e-01 -1.07053063e+00 -8.12000728e-01 | -5.83642250e-01 -1.07053063e+00 -8.12000728e-01 1 1.47092891e+00 3.59886298e+00 -6.30091627e+00 | 1.47092891e+00 3.59886298e+00 -6.30091627e+00 2 1.95773361e+00 -5.71862458e+00 6.31529406e+00 | 1.95773361e+00 -5.71862458e+00 6.31529406e+00 3 -2.84502027e+00 3.19029222e+00 7.97622930e-01 | -2.84502027e+00 3.19029222e+00 7.97622930e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFT (Configuration in file "config-Fe-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.40675519862 2^p V(r_1,...,r_N) = -6.40675519862 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 -3.33632312e+00 -3.74393209e+00 -6.14799005e+00 | -3.33632312e+00 -3.74393209e+00 -6.14799005e+00 1 2.14357100e+00 2.63187976e+00 -7.65300078e-01 | 2.14357100e+00 2.63187976e+00 -7.65300078e-01 2 3.41814433e+00 -1.91998778e+00 3.33105956e+00 | 3.41814433e+00 -1.91998778e+00 3.33105956e+00 3 -2.22539221e+00 3.03204011e+00 3.58223058e+00 | -2.22539221e+00 3.03204011e+00 3.58223058e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -5.81477946872 2^p V(r_1,...,r_N) = -5.81477946872 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 -4.93301452e+00 -2.66401736e+00 -4.19314487e+00 | -4.93301452e+00 -2.66401736e+00 -4.19314487e+00 1 3.76489383e+00 3.13154080e+00 -5.08501585e+00 | 3.76489383e+00 3.13154080e+00 -5.08501585e+00 2 4.65040694e+00 -1.64094012e+00 6.58372444e+00 | 4.65040694e+00 -1.64094012e+00 6.58372444e+00 3 -3.48228625e+00 1.17341669e+00 2.69443627e+00 | -3.48228625e+00 1.17341669e+00 2.69443627e+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)) = -6.53498946207 2^p V(r_1,...,r_N) = -6.53498946207 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 -2.77832813e+00 -4.49838300e+00 -9.47086842e-01 | -2.77832813e+00 -4.49838300e+00 -9.47086842e-01 1 5.17694305e+00 3.42098445e+00 -3.39816085e+00 | 5.17694305e+00 3.42098445e+00 -3.39816085e+00 2 6.68772248e-01 -1.27372530e+00 1.27141127e+00 | 6.68772248e-01 -1.27372530e+00 1.27141127e+00 3 -3.06738717e+00 2.35112384e+00 3.07383642e+00 | -3.06738717e+00 2.35112384e+00 3.07383642e+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)) = 0.756571794883 2^p V(r_1,...,r_N) = 0.756571794883 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 -1.76909798e+01 -1.17366739e+01 -1.63008178e+01 | -1.76909798e+01 -1.17366739e+01 -1.63008178e+01 1 3.80316940e+00 6.17704592e+00 -6.59173095e+00 | 3.80316940e+00 6.17704592e+00 -6.59173095e+00 2 2.16375094e+01 -4.95201624e+00 1.83853575e+01 | 2.16375094e+01 -4.95201624e+00 1.83853575e+01 3 -7.74969899e+00 1.05116442e+01 4.50719126e+00 | -7.74969899e+00 1.05116442e+01 4.50719126e+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)) = -7.14353411968 2^p V(r_1,...,r_N) = -7.14353411968 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 -2.60955163e+00 -1.95768466e+00 -1.07710381e+00 | -2.60955163e+00 -1.95768466e+00 -1.07710381e+00 1 2.75314717e+00 2.24974577e+00 -2.77555615e+00 | 2.75314717e+00 2.24974577e+00 -2.77555615e+00 2 1.47907041e+00 -4.93211521e-01 1.79978605e+00 | 1.47907041e+00 -4.93211521e-01 1.79978605e+00 3 -1.62266595e+00 2.01150416e-01 2.05287392e+00 | -1.62266595e+00 2.01150416e-01 2.05287392e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTT (Configuration in file "config-Ti-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.8375259231 2^p V(r_1,...,r_N) = 7.8375259231 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 -1.03726554e+01 -1.33799473e+01 -7.60192429e+00 | -1.03726554e+01 -1.33799473e+01 -7.60192429e+00 1 1.73250749e+01 1.28341828e+01 -1.63801725e+01 | 1.73250749e+01 1.28341828e+01 -1.63801725e+01 2 7.31589948e+00 -1.34713157e+01 1.22782765e+01 | 7.31589948e+00 -1.34713157e+01 1.22782765e+01 3 -1.42683190e+01 1.40170802e+01 1.17038203e+01 | -1.42683190e+01 1.40170802e+01 1.17038203e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTF (Configuration in file "config-Ti-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)) = 0.789272264726 2^p V(r_1,...,r_N) = 0.789272264726 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 -1.06649426e+01 -1.09812519e+01 -1.02915512e+01 | -1.06649426e+01 -1.09812519e+01 -1.02915512e+01 1 6.92362399e+00 7.92800179e+00 -7.15929446e+00 | 6.92362399e+00 7.92800179e+00 -7.15929446e+00 2 1.12934136e+01 -6.28429542e+00 1.02743477e+01 | 1.12934136e+01 -6.28429542e+00 1.02743477e+01 3 -7.55209495e+00 9.33754557e+00 7.17649796e+00 | -7.55209495e+00 9.33754557e+00 7.17649796e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFT (Configuration in file "config-Ti-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)) = -4.6520818538 2^p V(r_1,...,r_N) = -4.6520818538 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 -1.21388051e+00 -1.25769019e+00 -9.79685766e-01 | -1.21388051e+00 -1.25769019e+00 -9.79685766e-01 1 4.01306693e+00 3.23386004e+00 -8.44542280e+00 | 4.01306693e+00 3.23386004e+00 -8.44542280e+00 2 5.60049081e+00 -6.81017199e+00 2.75962838e+00 | 5.60049081e+00 -6.81017199e+00 2.75962838e+00 3 -8.39967723e+00 4.83400214e+00 6.66548018e+00 | -8.39967723e+00 4.83400214e+00 6.66548018e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFF (Configuration in file "config-Ti-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)) = -3.68554632237 2^p V(r_1,...,r_N) = -3.68554632237 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 -7.01297402e+00 -7.67940026e+00 -5.91175789e+00 | -7.01297402e+00 -7.67940026e+00 -5.91175789e+00 1 5.67040948e+00 4.81738559e+00 -5.08714968e+00 | 5.67040948e+00 4.81738559e+00 -5.08714968e+00 2 4.88618725e+00 -3.91385238e+00 6.09938009e+00 | 4.88618725e+00 -3.91385238e+00 6.09938009e+00 3 -3.54362271e+00 6.77586705e+00 4.89952748e+00 | -3.54362271e+00 6.77586705e+00 4.89952748e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTT (Configuration in file "config-Ti-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)) = -7.34614411149 2^p V(r_1,...,r_N) = -7.34614411149 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 -2.18032095e+00 -2.09876281e+00 -2.26627764e+00 | -2.18032095e+00 -2.09876281e+00 -2.26627764e+00 1 2.62268257e+00 2.70909657e+00 -2.99146805e+00 | 2.62268257e+00 2.70909657e+00 -2.99146805e+00 2 2.51775487e+00 -3.76528736e+00 2.07625810e+00 | 2.51775487e+00 -3.76528736e+00 2.07625810e+00 3 -2.96011649e+00 3.15495361e+00 3.18148760e+00 | -2.96011649e+00 3.15495361e+00 3.18148760e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTF (Configuration in file "config-Ti-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)) = -2.08489183555 2^p V(r_1,...,r_N) = -2.08489183555 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 -5.36540903e+00 -5.05211141e+00 -5.63106422e+00 | -5.36540903e+00 -5.05211141e+00 -5.63106422e+00 1 5.51442924e+00 5.58253746e+00 -8.70886395e+00 | 5.51442924e+00 5.58253746e+00 -8.70886395e+00 2 6.18573587e+00 -8.84139415e+00 8.52572359e+00 | 6.18573587e+00 -8.84139415e+00 8.52572359e+00 3 -6.33475609e+00 8.31096810e+00 5.81420459e+00 | -6.33475609e+00 8.31096810e+00 5.81420459e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FFT (Configuration in file "config-Ti-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)) = 0.386767367623 2^p V(r_1,...,r_N) = 0.386767367623 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 -6.69057107e+00 -5.80773214e+00 -7.15861853e+00 | -6.69057107e+00 -5.80773214e+00 -7.15861853e+00 1 7.41831632e+00 4.18146129e+00 -8.82745748e+00 | 7.41831632e+00 4.18146129e+00 -8.82745748e+00 2 9.64797161e+00 -1.09345491e+01 1.09050363e+01 | 9.64797161e+00 -1.09345491e+01 1.09050363e+01 3 -1.03757169e+01 1.25608200e+01 5.08103973e+00 | -1.03757169e+01 1.25608200e+01 5.08103973e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = TTT (Configuration in file "config-CFeTi-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)) = -11.1813029553 2^p V(r_1,...,r_N) = -11.1813029553 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 -4.62634708e+00 -6.55945754e+00 -4.06434993e+00 | -4.62634708e+00 -6.55945754e+00 -4.06434993e+00 1 4.27918745e+00 1.04695701e+01 -1.13941904e+01 | 4.27918745e+00 1.04695701e+01 -1.13941904e+01 2 1.07931744e+00 -8.05195698e+00 9.87481247e+00 | 1.07931744e+00 -8.05195698e+00 9.87481247e+00 3 -7.32157822e-01 4.14184445e+00 5.58372787e+00 | -7.32157822e-01 4.14184445e+00 5.58372787e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = TTF (Configuration in file "config-CFeTi-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)) = -12.9692748867 2^p V(r_1,...,r_N) = -12.9692748867 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 -1.79114744e+00 1.17605712e+00 -1.84056755e+00 | -1.79114744e+00 1.17605712e+00 -1.84056755e+00 1 4.36205746e-01 -1.43082299e+00 1.28832220e-01 | 4.36205746e-01 -1.43082299e+00 1.28832220e-01 2 1.22208376e+00 1.71831653e+00 1.40664225e+00 | 1.22208376e+00 1.71831653e+00 1.40664225e+00 3 1.32857936e-01 -1.46355066e+00 3.05093081e-01 | 1.32857936e-01 -1.46355066e+00 3.05093081e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = TFT (Configuration in file "config-CFeTi-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)) = -11.8166186839 2^p V(r_1,...,r_N) = -11.8166186839 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 2.56256727e-01 -2.79572742e+00 3.65669317e-01 | 2.56256727e-01 -2.79572742e+00 3.65669317e-01 1 3.50996005e+00 1.78266500e+00 -2.12355152e+00 | 3.50996005e+00 1.78266500e+00 -2.12355152e+00 2 4.50280221e+00 -5.16186578e+00 -1.83815037e+00 | 4.50280221e+00 -5.16186578e+00 -1.83815037e+00 3 -8.26901898e+00 6.17492820e+00 3.59603257e+00 | -8.26901898e+00 6.17492820e+00 3.59603257e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = TFF (Configuration in file "config-CFeTi-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)) = -10.302067057 2^p V(r_1,...,r_N) = -10.302067057 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 -5.23580936e+00 -7.61570918e+00 -8.57662030e+00 | -5.23580936e+00 -7.61570918e+00 -8.57662030e+00 1 2.41378208e+00 1.35440734e+01 -1.00168035e+01 | 2.41378208e+00 1.35440734e+01 -1.00168035e+01 2 8.32229463e+00 -1.33302219e+01 1.11962489e+01 | 8.32229463e+00 -1.33302219e+01 1.11962489e+01 3 -5.50026734e+00 7.40185768e+00 7.39717485e+00 | -5.50026734e+00 7.40185768e+00 7.39717485e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = FTT (Configuration in file "config-CFeTi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.14032255583 2^p V(r_1,...,r_N) = -9.14032255583 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 -6.92052573e+00 -7.68899618e+00 -7.89434476e+00 | -6.92052573e+00 -7.68899618e+00 -7.89434476e+00 1 9.19924763e+00 2.42998951e+00 -1.27463990e+01 | 9.19924763e+00 2.42998951e+00 -1.27463990e+01 2 1.15970517e+01 -2.63806134e+00 5.14615659e+00 | 1.15970517e+01 -2.63806134e+00 5.14615659e+00 3 -1.38757736e+01 7.89706801e+00 1.54945871e+01 | -1.38757736e+01 7.89706801e+00 1.54945871e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = FTF (Configuration in file "config-CFeTi-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)) = -14.1122520774 2^p V(r_1,...,r_N) = -14.1122520774 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 1.48554005e+00 -1.33583126e+00 -1.10405287e+00 | 1.48554005e+00 -1.33583126e+00 -1.10405287e+00 1 -1.23864917e+00 1.30953114e+00 -1.31727602e+00 | -1.23864917e+00 1.30953114e+00 -1.31727602e+00 2 -1.33605846e+00 -8.08777892e-01 1.03650758e+00 | -1.33605846e+00 -8.08777892e-01 1.03650758e+00 3 1.08916757e+00 8.35078011e-01 1.38482130e+00 | 1.08916757e+00 8.35078011e-01 1.38482130e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Fe Ti, PBC = FFT (Configuration in file "config-CFeTi-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)) = -13.0993054795 2^p V(r_1,...,r_N) = -13.0993054795 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 -5.31778758e+00 -1.07150611e+00 -2.45232215e+00 | -5.31778758e+00 -1.07150611e+00 -2.45232215e+00 1 7.82216252e+00 4.34760328e+00 -7.92144057e+00 | 7.82216252e+00 4.34760328e+00 -7.92144057e+00 2 2.63255334e+00 -1.94829565e+00 6.17488484e+00 | 2.63255334e+00 -1.94829565e+00 6.17488484e+00 3 -5.13692828e+00 -1.32780153e+00 4.19887788e+00 | -5.13692828e+00 -1.32780153e+00 4.19887788e+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.