!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005 Supported species : Cu Fe Ni random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.93457435467 2^p V(r_1,...,r_N) = -4.93457435467 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 -3.54011030e+00 -7.63165617e+00 -7.76862321e+00 | -3.54011030e+00 -7.63165617e+00 -7.76862321e+00 1 2.85177603e+00 2.33840620e+00 -2.08496228e+00 | 2.85177603e+00 2.33840620e+00 -2.08496228e+00 2 2.04034677e+00 -2.53674233e+00 3.64209695e+00 | 2.04034677e+00 -2.53674233e+00 3.64209695e+00 3 -1.35201250e+00 7.82999230e+00 6.21148854e+00 | -1.35201250e+00 7.82999230e+00 6.21148854e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.60851441264 2^p V(r_1,...,r_N) = -5.60851441264 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 1.00283997e+00 7.04541670e-01 7.86492990e-01 | 1.00283997e+00 7.04541670e-01 7.86492990e-01 1 8.31865618e-01 1.39090534e+00 -2.94028699e+00 | 8.31865618e-01 1.39090534e+00 -2.94028699e+00 2 4.31990253e+00 -5.44719365e+00 1.22358094e+00 | 4.31990253e+00 -5.44719365e+00 1.22358094e+00 3 -6.15460812e+00 3.35174664e+00 9.30213064e-01 | -6.15460812e+00 3.35174664e+00 9.30213064e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.83741169046 2^p V(r_1,...,r_N) = -3.83741169046 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 -3.85112178e+00 -3.74976959e+00 -4.55762746e+00 | -3.85112178e+00 -3.74976959e+00 -4.55762746e+00 1 3.76474852e+00 3.95694419e+00 -5.27314016e+00 | 3.76474852e+00 3.95694419e+00 -5.27314016e+00 2 8.09487107e+00 -6.97291630e+00 4.83977340e+00 | 8.09487107e+00 -6.97291630e+00 4.83977340e+00 3 -8.00849781e+00 6.76574169e+00 4.99099422e+00 | -8.00849781e+00 6.76574169e+00 4.99099422e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.11897967342 2^p V(r_1,...,r_N) = -5.11897967342 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 -2.81732193e+00 -3.03763232e+00 -5.22327242e+00 | -2.81732193e+00 -3.03763232e+00 -5.22327242e+00 1 1.80827731e+00 2.61427797e+00 -2.51671147e+00 | 1.80827731e+00 2.61427797e+00 -2.51671147e+00 2 6.28835174e+00 -5.93559444e+00 3.65451841e+00 | 6.28835174e+00 -5.93559444e+00 3.65451841e+00 3 -5.27930712e+00 6.35894879e+00 4.08546549e+00 | -5.27930712e+00 6.35894879e+00 4.08546549e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.968271733531 2^p V(r_1,...,r_N) = 0.968271733531 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 -5.45274128e+00 -7.52015654e+00 -7.22238308e+00 | -5.45274128e+00 -7.52015654e+00 -7.22238308e+00 1 2.26662713e+01 1.25602500e+00 -1.87625987e+01 | 2.26662713e+01 1.25602500e+00 -1.87625987e+01 2 3.67993203e+00 -3.48646126e+00 3.23144502e+00 | 3.67993203e+00 -3.48646126e+00 3.23144502e+00 3 -2.08934621e+01 9.75059280e+00 2.27535368e+01 | -2.08934621e+01 9.75059280e+00 2.27535368e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.67540293783 2^p V(r_1,...,r_N) = -1.67540293783 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 -7.09859382e+00 -1.54967471e+01 -8.91081468e+00 | -7.09859382e+00 -1.54967471e+01 -8.91081468e+00 1 1.09601183e+01 7.54057080e+00 -7.25457115e+00 | 1.09601183e+01 7.54057080e+00 -7.25457115e+00 2 3.07690806e+00 -1.01196453e+00 2.98259750e+00 | 3.07690806e+00 -1.01196453e+00 2.98259750e+00 3 -6.93843252e+00 8.96814082e+00 1.31827883e+01 | -6.93843252e+00 8.96814082e+00 1.31827883e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.57289354833 2^p V(r_1,...,r_N) = -6.57289354833 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 -2.37713392e+00 -3.93218297e+00 -1.71095865e+00 | -2.37713392e+00 -3.93218297e+00 -1.71095865e+00 1 2.07739153e+00 2.47537803e+00 -1.82838038e+00 | 2.07739153e+00 2.47537803e+00 -1.82838038e+00 2 1.16139364e+00 -6.36957642e-01 1.52879141e+00 | 1.16139364e+00 -6.36957642e-01 1.52879141e+00 3 -8.61651246e-01 2.09376258e+00 2.01054762e+00 | -8.61651246e-01 2.09376258e+00 2.01054762e+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)) = -7.83006415405 2^p V(r_1,...,r_N) = -7.83006415405 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 -2.26067262e+00 -2.05349396e+00 -1.29545626e+00 | -2.26067262e+00 -2.05349396e+00 -1.29545626e+00 1 3.05608093e+00 5.85589507e-01 -3.23345704e+00 | 3.05608093e+00 5.85589507e-01 -3.23345704e+00 2 1.40818600e+00 -3.94405426e-01 1.52437281e+00 | 1.40818600e+00 -3.94405426e-01 1.52437281e+00 3 -2.20359431e+00 1.86230988e+00 3.00454049e+00 | -2.20359431e+00 1.86230988e+00 3.00454049e+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)) = -7.43669565644 2^p V(r_1,...,r_N) = -7.43669565644 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 -4.42297039e+00 -3.91449947e+00 -1.85933221e+00 | -4.42297039e+00 -3.91449947e+00 -1.85933221e+00 1 2.98812021e+00 3.73339812e+00 -1.42197350e+00 | 2.98812021e+00 3.73339812e+00 -1.42197350e+00 2 2.89758994e+00 -1.46984225e+00 3.02495429e+00 | 2.89758994e+00 -1.46984225e+00 3.02495429e+00 3 -1.46273976e+00 1.65094359e+00 2.56351416e-01 | -1.46273976e+00 1.65094359e+00 2.56351416e-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)) = -2.94823658591 2^p V(r_1,...,r_N) = -2.94823658591 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 -8.82961889e+00 -5.45134508e+00 -8.30753420e+00 | -8.82961889e+00 -5.45134508e+00 -8.30753420e+00 1 1.08806105e+01 5.40867527e+00 -1.08673713e+01 | 1.08806105e+01 5.40867527e+00 -1.08673713e+01 2 7.55567189e+00 -6.96487478e+00 9.99339948e+00 | 7.55567189e+00 -6.96487478e+00 9.99339948e+00 3 -9.60666346e+00 7.00754458e+00 9.18150598e+00 | -9.60666346e+00 7.00754458e+00 9.18150598e+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)) = -7.83304746461 2^p V(r_1,...,r_N) = -7.83304746461 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 -2.36205584e+00 -3.48937194e+00 -2.77429176e+00 | -2.36205584e+00 -3.48937194e+00 -2.77429176e+00 1 3.04633076e+00 1.75410320e+00 -1.63926651e+00 | 3.04633076e+00 1.75410320e+00 -1.63926651e+00 2 1.71349670e+00 -8.03231128e-01 1.63109396e+00 | 1.71349670e+00 -8.03231128e-01 1.63109396e+00 3 -2.39777162e+00 2.53849987e+00 2.78246431e+00 | -2.39777162e+00 2.53849987e+00 2.78246431e+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)) = -3.93542183721 2^p V(r_1,...,r_N) = -3.93542183721 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 -1.24908353e+01 -1.90613166e+00 -1.30692019e+01 | -1.24908353e+01 -1.90613166e+00 -1.30692019e+01 1 2.94785246e+00 1.62620708e+00 -3.56329469e+00 | 2.94785246e+00 1.62620708e+00 -3.56329469e+00 2 1.48637433e+01 -5.37824505e+00 1.09124087e+01 | 1.48637433e+01 -5.37824505e+00 1.09124087e+01 3 -5.32076052e+00 5.65816963e+00 5.72008784e+00 | -5.32076052e+00 5.65816963e+00 5.72008784e+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)) = -7.97071546796 2^p V(r_1,...,r_N) = -7.97071546796 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 -1.25933612e+00 -2.35343782e+00 -1.56349808e+00 | -1.25933612e+00 -2.35343782e+00 -1.56349808e+00 1 2.16198159e+00 2.00066689e+00 -2.79206041e+00 | 2.16198159e+00 2.00066689e+00 -2.79206041e+00 2 1.05252165e+00 -1.21810670e+00 1.25706481e+00 | 1.05252165e+00 -1.21810670e+00 1.25706481e+00 3 -1.95516713e+00 1.57087763e+00 3.09849368e+00 | -1.95516713e+00 1.57087763e+00 3.09849368e+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)) = -5.949337504 2^p V(r_1,...,r_N) = -5.949337504 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 -4.87343667e+00 -3.62928777e+00 -4.74635411e+00 | -4.87343667e+00 -3.62928777e+00 -4.74635411e+00 1 3.90056684e+00 5.43485297e+00 -3.99453775e+00 | 3.90056684e+00 5.43485297e+00 -3.99453775e+00 2 3.40559524e+00 -5.48187757e+00 5.29168043e+00 | 3.40559524e+00 -5.48187757e+00 5.29168043e+00 3 -2.43272542e+00 3.67631237e+00 3.44921143e+00 | -2.43272542e+00 3.67631237e+00 3.44921143e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.0667969683 2^p V(r_1,...,r_N) = 10.0667969683 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 -1.41768002e+01 -4.24919643e+01 -4.55750360e+01 | -1.41768002e+01 -4.24919643e+01 -4.55750360e+01 1 8.89264595e+00 1.30086726e+01 -1.27549368e+01 | 8.89264595e+00 1.30086726e+01 -1.27549368e+01 2 1.60731965e+01 -1.47809166e+01 1.41214582e+01 | 1.60731965e+01 -1.47809166e+01 1.41214582e+01 3 -1.07890422e+01 4.42642084e+01 4.42085147e+01 | -1.07890422e+01 4.42642084e+01 4.42085147e+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)) = -2.19421072013 2^p V(r_1,...,r_N) = -2.19421072013 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 -1.13917206e+01 -2.74574079e+00 -1.41945311e+01 | -1.13917206e+01 -2.74574079e+00 -1.41945311e+01 1 3.82920922e+00 4.35154451e+00 -1.03628899e+00 | 3.82920922e+00 4.35154451e+00 -1.03628899e+00 2 1.61919444e+01 -1.48483163e+01 1.16403818e+01 | 1.61919444e+01 -1.48483163e+01 1.16403818e+01 3 -8.62943297e+00 1.32425126e+01 3.59043826e+00 | -8.62943297e+00 1.32425126e+01 3.59043826e+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)) = 1.16391472174 2^p V(r_1,...,r_N) = 1.16391472174 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 -1.05212919e+01 -2.69356964e+01 -2.06626339e+01 | -1.05212919e+01 -2.69356964e+01 -2.06626339e+01 1 1.09449211e+01 1.23798276e+01 -1.02061545e+01 | 1.09449211e+01 1.23798276e+01 -1.02061545e+01 2 3.43648953e+00 -6.96179663e+00 7.71948059e+00 | 3.43648953e+00 -6.96179663e+00 7.71948059e+00 3 -3.86011873e+00 2.15176654e+01 2.31493078e+01 | -3.86011873e+00 2.15176654e+01 2.31493078e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.817759305091 2^p V(r_1,...,r_N) = -0.817759305091 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 -9.22260505e+00 -7.24025786e+00 -5.28378708e+00 | -9.22260505e+00 -7.24025786e+00 -5.28378708e+00 1 1.08189218e+01 1.21744454e+01 -2.25730874e+01 | 1.08189218e+01 1.21744454e+01 -2.25730874e+01 2 9.87366510e+00 -1.20535340e+01 2.02217752e+01 | 9.87366510e+00 -1.20535340e+01 2.02217752e+01 3 -1.14699818e+01 7.11934647e+00 7.63509925e+00 | -1.14699818e+01 7.11934647e+00 7.63509925e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 9.86022215926 2^p V(r_1,...,r_N) = 9.86022215926 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 -2.14247491e+01 -9.43199766e+00 -2.89641146e+01 | -2.14247491e+01 -9.43199766e+00 -2.89641146e+01 1 2.03857009e+01 2.72555240e+01 -2.47389786e+01 | 2.03857009e+01 2.72555240e+01 -2.47389786e+01 2 1.65324823e+01 -3.37191361e+01 4.70170863e+01 | 1.65324823e+01 -3.37191361e+01 4.70170863e+01 3 -1.54934341e+01 1.58956098e+01 6.68600685e+00 | -1.54934341e+01 1.58956098e+01 6.68600685e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.11262885534 2^p V(r_1,...,r_N) = -0.11262885534 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 -1.64096192e+01 -1.30001004e+01 -4.78387026e+00 | -1.64096192e+01 -1.30001004e+01 -4.78387026e+00 1 1.73110253e+01 1.99775892e+01 -1.19683776e+01 | 1.73110253e+01 1.99775892e+01 -1.19683776e+01 2 8.93428435e+00 -1.50940900e+01 1.36375836e+01 | 8.93428435e+00 -1.50940900e+01 1.36375836e+01 3 -9.83569046e+00 8.11660119e+00 3.11466428e+00 | -9.83569046e+00 8.11660119e+00 3.11466428e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.01108557885 2^p V(r_1,...,r_N) = -5.01108557885 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 -4.25992565e+00 -3.79050231e+00 -5.21992413e+00 | -4.25992565e+00 -3.79050231e+00 -5.21992413e+00 1 7.25867967e+00 2.57599075e+00 -7.80751386e+00 | 7.25867967e+00 2.57599075e+00 -7.80751386e+00 2 6.99441597e+00 -4.71610036e+00 4.24687023e+00 | 6.99441597e+00 -4.71610036e+00 4.24687023e+00 3 -9.99317000e+00 5.93061193e+00 8.78056776e+00 | -9.99317000e+00 5.93061193e+00 8.78056776e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = TTT (Configuration in file "config-CuFeNi-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)) = -6.14185776795 2^p V(r_1,...,r_N) = -6.14185776795 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 -5.69188031e+00 -1.83236630e+00 -4.70644821e+00 | -5.69188031e+00 -1.83236630e+00 -4.70644821e+00 1 1.65989622e+00 1.77761377e+00 -2.80312626e+00 | 1.65989622e+00 1.77761377e+00 -2.80312626e+00 2 8.81115497e+00 -3.70997099e+00 3.39189597e+00 | 8.81115497e+00 -3.70997099e+00 3.39189597e+00 3 -4.77917088e+00 3.76472353e+00 4.11767850e+00 | -4.77917088e+00 3.76472353e+00 4.11767850e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = TTF (Configuration in file "config-CuFeNi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.2344888889 2^p V(r_1,...,r_N) = -2.2344888889 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 -1.89771855e+01 -3.85406298e+00 -1.59694516e+01 | -1.89771855e+01 -3.85406298e+00 -1.59694516e+01 1 3.76829427e+00 4.97298987e+00 -4.13949505e+00 | 3.76829427e+00 4.97298987e+00 -4.13949505e+00 2 2.29892332e+01 -1.07892471e+01 1.66983191e+01 | 2.29892332e+01 -1.07892471e+01 1.66983191e+01 3 -7.78034194e+00 9.67032024e+00 3.41062751e+00 | -7.78034194e+00 9.67032024e+00 3.41062751e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = TFT (Configuration in file "config-CuFeNi-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)) = -4.95774828808 2^p V(r_1,...,r_N) = -4.95774828808 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 -3.40427027e+00 -3.12510513e+00 -2.90961265e+00 | -3.40427027e+00 -3.12510513e+00 -2.90961265e+00 1 3.04634995e+00 1.77479311e+00 -2.90778427e+00 | 3.04634995e+00 1.77479311e+00 -2.90778427e+00 2 1.09645681e+01 -1.13525863e+01 1.29615305e+00 | 1.09645681e+01 -1.13525863e+01 1.29615305e+00 3 -1.06066478e+01 1.27028984e+01 4.52124387e+00 | -1.06066478e+01 1.27028984e+01 4.52124387e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = TFF (Configuration in file "config-CuFeNi-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)) = -1.04585664365 2^p V(r_1,...,r_N) = -1.04585664365 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 -1.89259740e+01 -8.36871353e+00 -3.06247123e+01 | -1.89259740e+01 -8.36871353e+00 -3.06247123e+01 1 6.09016898e+00 6.54442447e+00 -1.58125963e+00 | 6.09016898e+00 6.54442447e+00 -1.58125963e+00 2 1.82012651e+01 -7.64539540e+00 2.05560497e+01 | 1.82012651e+01 -7.64539540e+00 2.05560497e+01 3 -5.36546003e+00 9.46968445e+00 1.16499223e+01 | -5.36546003e+00 9.46968445e+00 1.16499223e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = FTT (Configuration in file "config-CuFeNi-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)) = -1.14136290686 2^p V(r_1,...,r_N) = -1.14136290686 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 -4.40947459e+00 -2.05910772e+01 -1.71112837e+01 | -4.40947459e+00 -2.05910772e+01 -1.71112837e+01 1 7.30302583e+00 4.97404933e+00 -7.83511822e+00 | 7.30302583e+00 4.97404933e+00 -7.83511822e+00 2 1.22952269e+01 -1.32908113e+01 1.01177712e+01 | 1.22952269e+01 -1.32908113e+01 1.01177712e+01 3 -1.51887782e+01 2.89078392e+01 1.48286307e+01 | -1.51887782e+01 2.89078392e+01 1.48286307e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = FTF (Configuration in file "config-CuFeNi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.79492894631 2^p V(r_1,...,r_N) = -5.79492894631 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 -2.24343795e+00 -1.30498692e+00 -1.73264041e+00 | -2.24343795e+00 -1.30498692e+00 -1.73264041e+00 1 6.75272121e+00 6.35651610e+00 -1.19060972e+01 | 6.75272121e+00 6.35651610e+00 -1.19060972e+01 2 2.93996151e+00 -8.23117370e+00 7.06035256e+00 | 2.93996151e+00 -8.23117370e+00 7.06035256e+00 3 -7.44924478e+00 3.17964452e+00 6.57838507e+00 | -7.44924478e+00 3.17964452e+00 6.57838507e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Fe Ni, PBC = FFT (Configuration in file "config-CuFeNi-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)) = -4.55611666343 2^p V(r_1,...,r_N) = -4.55611666343 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 -3.36953220e+00 -1.61386780e+01 -1.41786575e+01 | -3.36953220e+00 -1.61386780e+01 -1.41786575e+01 1 5.97517250e+00 3.91965854e+00 -9.26585944e-01 | 5.97517250e+00 3.91965854e+00 -9.26585944e-01 2 -1.21743302e-01 9.79440483e-02 -5.37285083e-01 | -1.21743302e-01 9.79440483e-02 -5.37285083e-01 3 -2.48389701e+00 1.21210754e+01 1.56425285e+01 | -2.48389701e+00 1.21210754e+01 1.56425285e+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.