!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyCastinTerentyev_2013_FeNiCr__MO_763197941039_000 Supported species : Cr Fe Ni random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTT (Configuration in file "config-Cr-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)) = 27.7368458933 2^p V(r_1,...,r_N) = 27.7368458933 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 -7.04101535e+01 -9.90490829e+01 -9.35725251e+01 | -7.04101535e+01 -9.90490829e+01 -9.35725251e+01 1 8.12227584e+01 3.86694950e+01 -5.77994604e+01 | 8.12227584e+01 3.86694950e+01 -5.77994604e+01 2 4.71093797e+01 -5.67342080e+01 5.74126190e+01 | 4.71093797e+01 -5.67342080e+01 5.74126190e+01 3 -5.79219845e+01 1.17113796e+02 9.39593665e+01 | -5.79219845e+01 1.17113796e+02 9.39593665e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTF (Configuration in file "config-Cr-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)) = 91.1677071086 2^p V(r_1,...,r_N) = 91.1677071086 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 -1.03247503e+02 -9.76396424e+01 -1.72687768e+02 | -1.03247503e+02 -9.76396424e+01 -1.72687768e+02 1 7.79692574e+01 6.38579299e+01 -8.00806324e+01 | 7.79692574e+01 6.38579299e+01 -8.00806324e+01 2 1.64799150e+02 -1.27575781e+02 1.34327836e+02 | 1.64799150e+02 -1.27575781e+02 1.34327836e+02 3 -1.39520905e+02 1.61357493e+02 1.18440564e+02 | -1.39520905e+02 1.61357493e+02 1.18440564e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFT (Configuration in file "config-Cr-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)) = 21.9722939647 2^p V(r_1,...,r_N) = 21.9722939647 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 -5.93570609e+00 -1.50429758e+01 -1.36460137e+01 | -5.93570609e+00 -1.50429758e+01 -1.36460137e+01 1 6.10553700e+01 4.84514721e+01 -9.69123971e+01 | 6.10553700e+01 4.84514721e+01 -9.69123971e+01 2 5.87639085e+01 -5.67448836e+01 1.48896944e+01 | 5.87639085e+01 -5.67448836e+01 1.48896944e+01 3 -1.13883572e+02 2.33363873e+01 9.56687163e+01 | -1.13883572e+02 2.33363873e+01 9.56687163e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFF (Configuration in file "config-Cr-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)) = 37.3677981704 2^p V(r_1,...,r_N) = 37.3677981704 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 -1.05859502e+02 -7.40954415e+01 -1.05980944e+02 | -1.05859502e+02 -7.40954415e+01 -1.05980944e+02 1 5.10471449e+01 9.31022093e+01 -6.25436360e+01 | 5.10471449e+01 9.31022093e+01 -6.25436360e+01 2 1.03386654e+02 -1.09261234e+02 9.82122854e+01 | 1.03386654e+02 -1.09261234e+02 9.82122854e+01 3 -4.85742967e+01 9.02544663e+01 7.03122943e+01 | -4.85742967e+01 9.02544663e+01 7.03122943e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTT (Configuration in file "config-Cr-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)) = 26.3789953193 2^p V(r_1,...,r_N) = 26.3789953193 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 -8.23664788e+01 -8.98078801e+01 -7.17600497e+01 | -8.23664788e+01 -8.98078801e+01 -7.17600497e+01 1 5.24925528e+01 6.77838713e+01 -5.38300982e+01 | 5.24925528e+01 6.77838713e+01 -5.38300982e+01 2 1.01048706e+02 -5.76833153e+01 7.94427052e+01 | 1.01048706e+02 -5.76833153e+01 7.94427052e+01 3 -7.11747801e+01 7.97073241e+01 4.61474428e+01 | -7.11747801e+01 7.97073241e+01 4.61474428e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTF (Configuration in file "config-Cr-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)) = 13.6781927571 2^p V(r_1,...,r_N) = 13.6781927571 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 -7.97522091e+01 -4.99979613e+01 -6.01831464e+01 | -7.97522091e+01 -4.99979613e+01 -6.01831464e+01 1 5.10049490e+01 3.72491973e+01 -6.30603387e+01 | 5.10049490e+01 3.72491973e+01 -6.30603387e+01 2 6.61741082e+01 -9.40753390e+00 7.83688963e+01 | 6.61741082e+01 -9.40753390e+00 7.83688963e+01 3 -3.74268481e+01 2.21562980e+01 4.48745888e+01 | -3.74268481e+01 2.21562980e+01 4.48745888e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FFT (Configuration in file "config-Cr-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)) = 67.1271143825 2^p V(r_1,...,r_N) = 67.1271143825 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.87682647e+01 -6.16273377e+01 -6.50258153e+01 | -9.87682647e+01 -6.16273377e+01 -6.50258153e+01 1 6.52854486e+01 1.05913874e+02 -7.62604126e+01 | 6.52854486e+01 1.05913874e+02 -7.62604126e+01 2 1.41621114e+02 -1.31671884e+02 1.16415204e+02 | 1.41621114e+02 -1.31671884e+02 1.16415204e+02 3 -1.08138298e+02 8.73853477e+01 2.48710242e+01 | -1.08138298e+02 8.73853477e+01 2.48710242e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.47018198908 2^p V(r_1,...,r_N) = -2.47018198908 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 -2.54923228e+00 -4.39603462e+00 -3.42796478e+00 | -2.54923228e+00 -4.39603462e+00 -3.42796478e+00 1 5.39925791e+00 1.11198779e+01 -1.96452891e+01 | 5.39925791e+00 1.11198779e+01 -1.96452891e+01 2 7.05522982e+00 -1.81465888e+01 1.95399291e+01 | 7.05522982e+00 -1.81465888e+01 1.95399291e+01 3 -9.90525546e+00 1.14227456e+01 3.53332477e+00 | -9.90525546e+00 1.14227456e+01 3.53332477e+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)) = 0.0578964184553 2^p V(r_1,...,r_N) = 0.0578964184553 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 -6.85838230e+00 -2.26814494e+01 -2.05599255e+01 | -6.85838230e+00 -2.26814494e+01 -2.05599255e+01 1 6.42832610e+00 6.60673107e+00 -9.50591919e+00 | 6.42832610e+00 6.60673107e+00 -9.50591919e+00 2 5.42031717e+00 -9.04248105e+00 8.05505195e+00 | 5.42031717e+00 -9.04248105e+00 8.05505195e+00 3 -4.99026097e+00 2.51171994e+01 2.20107928e+01 | -4.99026097e+00 2.51171994e+01 2.20107928e+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)) = 6.25834216126 2^p V(r_1,...,r_N) = 6.25834216126 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 -1.16100004e+01 -5.90609050e+00 -1.26814888e+01 | -1.16100004e+01 -5.90609050e+00 -1.26814888e+01 1 1.68104878e+01 1.46204650e+01 -2.68891100e+01 | 1.68104878e+01 1.46204650e+01 -2.68891100e+01 2 2.65931341e+01 -2.65737424e+01 2.07219333e+01 | 2.65931341e+01 -2.65737424e+01 2.07219333e+01 3 -3.17936215e+01 1.78593679e+01 1.88486655e+01 | -3.17936215e+01 1.78593679e+01 1.88486655e+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)) = -3.32260976068 2^p V(r_1,...,r_N) = -3.32260976068 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 -3.93821083e+00 -5.67509836e+00 -9.40465735e+00 | -3.93821083e+00 -5.67509836e+00 -9.40465735e+00 1 6.54066919e+00 1.49130398e+01 -1.25979286e+01 | 6.54066919e+00 1.49130398e+01 -1.25979286e+01 2 3.99778842e+00 -1.82404433e+01 1.55953459e+01 | 3.99778842e+00 -1.82404433e+01 1.55953459e+01 3 -6.60024678e+00 9.00250185e+00 6.40724008e+00 | -6.60024678e+00 9.00250185e+00 6.40724008e+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)) = 32.123229134 2^p V(r_1,...,r_N) = 32.123229134 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 -2.88276497e+01 -9.00073441e+01 -6.85297712e+01 | -2.88276497e+01 -9.00073441e+01 -6.85297712e+01 1 2.69873629e+01 1.89250580e+01 -2.38922758e+01 | 2.69873629e+01 1.89250580e+01 -2.38922758e+01 2 2.43495595e+01 -1.30758718e+01 1.32878005e+01 | 2.43495595e+01 -1.30758718e+01 1.32878005e+01 3 -2.25092727e+01 8.41581579e+01 7.91342466e+01 | -2.25092727e+01 8.41581579e+01 7.91342466e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 6.31255338099 2^p V(r_1,...,r_N) = 6.31255338099 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 -4.92852760e+00 -4.80889157e+00 -3.88067211e+00 | -4.92852760e+00 -4.80889157e+00 -3.88067211e+00 1 1.30833152e+01 2.08457233e+01 -3.26306650e+01 | 1.30833152e+01 2.08457233e+01 -3.26306650e+01 2 1.95023365e+01 -3.61402039e+01 2.56381315e+01 | 1.95023365e+01 -3.61402039e+01 2.56381315e+01 3 -2.76571241e+01 2.01033722e+01 1.08732057e+01 | -2.76571241e+01 2.01033722e+01 1.08732057e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 40.1420155485 2^p V(r_1,...,r_N) = 40.1420155485 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 -5.13224737e+01 -6.90194916e+01 -3.69164518e+01 | -5.13224737e+01 -6.90194916e+01 -3.69164518e+01 1 6.05506451e+01 3.95397032e+01 -5.94034281e+01 | 6.05506451e+01 3.95397032e+01 -5.94034281e+01 2 2.65305502e+01 -2.47749347e+01 2.28261496e+01 | 2.65305502e+01 -2.47749347e+01 2.28261496e+01 3 -3.57587216e+01 5.42547231e+01 7.34937304e+01 | -3.57587216e+01 5.42547231e+01 7.34937304e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.65980549709 2^p V(r_1,...,r_N) = -2.65980549709 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 -5.71877976e+00 -7.63343400e+00 -4.05597797e+00 | -5.71877976e+00 -7.63343400e+00 -4.05597797e+00 1 1.24711334e+01 1.08134952e+01 -2.09157725e+01 | 1.24711334e+01 1.08134952e+01 -2.09157725e+01 2 6.23916150e+00 -8.45406918e+00 7.55921485e+00 | 6.23916150e+00 -8.45406918e+00 7.55921485e+00 3 -1.29915152e+01 5.27400802e+00 1.74125356e+01 | -1.29915152e+01 5.27400802e+00 1.74125356e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.35529379961 2^p V(r_1,...,r_N) = -6.35529379961 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 -1.35708326e-01 1.98848747e-01 -1.06157752e-01 | -1.35708326e-01 1.98848747e-01 -1.06157752e-01 1 5.06111749e+00 1.92097491e+00 -9.69342093e+00 | 5.06111749e+00 1.92097491e+00 -9.69342093e+00 2 6.11133945e+00 -7.13317833e+00 1.63563621e+00 | 6.11133945e+00 -7.13317833e+00 1.63563621e+00 3 -1.10367486e+01 5.01335466e+00 8.16394247e+00 | -1.10367486e+01 5.01335466e+00 8.16394247e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.95547929344 2^p V(r_1,...,r_N) = -5.95547929344 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 -5.23652236e+00 -5.85528151e+00 -2.31671656e+00 | -5.23652236e+00 -5.85528151e+00 -2.31671656e+00 1 8.01921240e+00 5.50000801e+00 -5.58581041e+00 | 8.01921240e+00 5.50000801e+00 -5.58581041e+00 2 5.59402091e+00 -5.44929762e+00 3.99563759e-02 | 5.59402091e+00 -5.44929762e+00 3.99563759e-02 3 -8.37671095e+00 5.80457111e+00 7.86257059e+00 | -8.37671095e+00 5.80457111e+00 7.86257059e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.63855313358 2^p V(r_1,...,r_N) = -2.63855313358 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 -6.51627323e+00 -5.17780976e+00 -7.13853230e+00 | -6.51627323e+00 -5.17780976e+00 -7.13853230e+00 1 1.48640864e+01 7.15060605e+00 -1.03228717e+01 | 1.48640864e+01 7.15060605e+00 -1.03228717e+01 2 6.62719746e+00 -1.61433327e+01 5.26766164e+00 | 6.62719746e+00 -1.61433327e+01 5.26766164e+00 3 -1.49750107e+01 1.41705364e+01 1.21937423e+01 | -1.49750107e+01 1.41705364e+01 1.21937423e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.01543543576 2^p V(r_1,...,r_N) = 1.01543543576 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 -2.19735232e+01 -8.18234676e+00 -1.61383809e+01 | -2.19735232e+01 -8.18234676e+00 -1.61383809e+01 1 1.16940570e+01 1.67608841e+01 -1.58152394e+01 | 1.16940570e+01 1.67608841e+01 -1.58152394e+01 2 2.03229496e+01 -1.25556544e+01 1.95847372e+01 | 2.03229496e+01 -1.25556544e+01 1.95847372e+01 3 -1.00434833e+01 3.97711705e+00 1.23688831e+01 | -1.00434833e+01 3.97711705e+00 1.23688831e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.39945119008 2^p V(r_1,...,r_N) = -2.39945119008 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 -4.87359425e+00 -1.35974780e+01 -1.31335434e+01 | -4.87359425e+00 -1.35974780e+01 -1.31335434e+01 1 6.20178474e+00 5.06893791e+00 -7.32758289e+00 | 6.20178474e+00 5.06893791e+00 -7.32758289e+00 2 1.21604697e+01 -7.99316732e+00 1.02208556e+01 | 1.21604697e+01 -7.99316732e+00 1.02208556e+01 3 -1.34886601e+01 1.65217074e+01 1.02402706e+01 | -1.34886601e+01 1.65217074e+01 1.02402706e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.87201823492 2^p V(r_1,...,r_N) = -3.87201823492 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 -4.68619851e+00 -4.62657553e+00 -2.91487962e+00 | -4.68619851e+00 -4.62657553e+00 -2.91487962e+00 1 7.17261801e+00 1.16038311e+01 -1.20107739e+01 | 7.17261801e+00 1.16038311e+01 -1.20107739e+01 2 1.01569265e+01 -1.50060248e+01 8.74666874e+00 | 1.01569265e+01 -1.50060248e+01 8.74666874e+00 3 -1.26433460e+01 8.02876917e+00 6.17898474e+00 | -1.26433460e+01 8.02876917e+00 6.17898474e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = TTT (Configuration in file "config-CrFeNi-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)) = -6.03768488173 2^p V(r_1,...,r_N) = -6.03768488173 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 -8.02557785e+00 -9.77561876e+00 -9.23733062e+00 | -8.02557785e+00 -9.77561876e+00 -9.23733062e+00 1 6.25733369e+00 1.03117026e+00 -5.71896765e+00 | 6.25733369e+00 1.03117026e+00 -5.71896765e+00 2 7.94886353e+00 -5.94906221e+00 4.96197586e+00 | 7.94886353e+00 -5.94906221e+00 4.96197586e+00 3 -6.18061936e+00 1.46935107e+01 9.99432241e+00 | -6.18061936e+00 1.46935107e+01 9.99432241e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = TTF (Configuration in file "config-CrFeNi-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)) = -3.54331462536 2^p V(r_1,...,r_N) = -3.54331462536 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 3.43983069e-01 -1.44189510e+01 -1.48869601e+01 | 3.43983069e-01 -1.44189510e+01 -1.48869601e+01 1 9.76547675e+00 1.18993647e+01 -1.42117352e+01 | 9.76547675e+00 1.18993647e+01 -1.42117352e+01 2 3.61552058e+00 -1.66715280e+01 1.38687748e+01 | 3.61552058e+00 -1.66715280e+01 1.38687748e+01 3 -1.37249804e+01 1.91911143e+01 1.52299205e+01 | -1.37249804e+01 1.91911143e+01 1.52299205e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = TFT (Configuration in file "config-CrFeNi-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)) = 26.2893873358 2^p V(r_1,...,r_N) = 26.2893873358 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 -8.28360662e+01 -2.30112908e+01 -1.07571539e+02 | -8.28360662e+01 -2.30112908e+01 -1.07571539e+02 1 1.01776977e+01 9.38833709e+00 -5.93555805e+00 | 1.01776977e+01 9.38833709e+00 -5.93555805e+00 2 8.76779551e+01 -2.08675766e+01 9.82783327e+01 | 8.76779551e+01 -2.08675766e+01 9.82783327e+01 3 -1.50195866e+01 3.44905303e+01 1.52287640e+01 | -1.50195866e+01 3.44905303e+01 1.52287640e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = TFF (Configuration in file "config-CrFeNi-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)) = 0.259574468089 2^p V(r_1,...,r_N) = 0.259574468089 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 -1.48253338e+00 -1.22290189e+01 -1.41190988e+01 | -1.48253338e+00 -1.22290189e+01 -1.41190988e+01 1 1.35661407e+01 4.11953573e+01 -3.57321584e+01 | 1.35661407e+01 4.11953573e+01 -3.57321584e+01 2 2.96764931e+00 -4.61886761e+01 3.34109139e+01 | 2.96764931e+00 -4.61886761e+01 3.34109139e+01 3 -1.50512567e+01 1.72223376e+01 1.64403433e+01 | -1.50512567e+01 1.72223376e+01 1.64403433e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = FTT (Configuration in file "config-CrFeNi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 4.3049973704 2^p V(r_1,...,r_N) = 4.3049973704 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 -1.35301152e+01 -2.59731607e+01 -1.21920404e+01 | -1.35301152e+01 -2.59731607e+01 -1.21920404e+01 1 2.50202193e+01 1.93317838e+01 -2.82348406e+01 | 2.50202193e+01 1.93317838e+01 -2.82348406e+01 2 1.29321229e+01 -1.64682591e+01 1.08198281e+01 | 1.29321229e+01 -1.64682591e+01 1.08198281e+01 3 -2.44222270e+01 2.31096360e+01 2.96070528e+01 | -2.44222270e+01 2.31096360e+01 2.96070528e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = FTF (Configuration in file "config-CrFeNi-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)) = 2.49475811907 2^p V(r_1,...,r_N) = 2.49475811907 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 -8.81825488e+00 -1.18313555e+01 -8.47199366e+00 | -8.81825488e+00 -1.18313555e+01 -8.47199366e+00 1 1.76404868e+01 1.81986971e+01 -3.07241243e+01 | 1.76404868e+01 1.81986971e+01 -3.07241243e+01 2 1.13258653e+01 -2.73196515e+01 2.17172656e+01 | 1.13258653e+01 -2.73196515e+01 2.17172656e+01 3 -2.01480972e+01 2.09523098e+01 1.74788524e+01 | -2.01480972e+01 2.09523098e+01 1.74788524e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe Ni, PBC = FFT (Configuration in file "config-CrFeNi-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)) = 50.7478392874 2^p V(r_1,...,r_N) = 50.7478392874 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 -1.15380556e+02 -4.88363920e+01 -9.60313973e+01 | -1.15380556e+02 -4.88363920e+01 -9.60313973e+01 1 2.52042001e+01 4.59526179e+01 -3.52915401e+01 | 2.52042001e+01 4.59526179e+01 -3.52915401e+01 2 1.09004524e+02 -1.48400282e+01 1.14322200e+02 | 1.09004524e+02 -1.48400282e+01 1.14322200e+02 3 -1.88281672e+01 1.77238023e+01 1.70007378e+01 | -1.88281672e+01 1.77238023e+01 1.70007378e+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.