!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_CaiYe_1996_AlCu__MO_942551040047_005 Supported species : Al Cu random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-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)) = -5.53311632005 2^p V(r_1,...,r_N) = -5.53311632005 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 -5.27513329e+00 -9.92470951e+00 -1.08023765e+01 | -5.27513329e+00 -9.92470951e+00 -1.08023765e+01 1 3.74668506e+00 2.51798193e+00 -2.29879031e+00 | 3.74668506e+00 2.51798193e+00 -2.29879031e+00 2 4.60863470e+00 -3.44823400e+00 5.00276171e+00 | 4.60863470e+00 -3.44823400e+00 5.00276171e+00 3 -3.08018647e+00 1.08549616e+01 8.09840514e+00 | -3.08018647e+00 1.08549616e+01 8.09840514e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-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)) = -3.48889948057 2^p V(r_1,...,r_N) = -3.48889948057 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 -8.04120917e+00 -5.46452634e+00 -5.23980201e+00 | -8.04120917e+00 -5.46452634e+00 -5.23980201e+00 1 5.76779383e+00 4.73769159e+00 -7.30635232e+00 | 5.76779383e+00 4.73769159e+00 -7.30635232e+00 2 1.10685294e+01 -1.21054044e+01 9.28656315e+00 | 1.10685294e+01 -1.21054044e+01 9.28656315e+00 3 -8.79511405e+00 1.28322392e+01 3.25959118e+00 | -8.79511405e+00 1.28322392e+01 3.25959118e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.869283277797 2^p V(r_1,...,r_N) = -0.869283277797 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 -8.65959454e+00 -1.19632989e+01 -1.49753280e+01 | -8.65959454e+00 -1.19632989e+01 -1.49753280e+01 1 1.16257374e+01 1.17682494e+01 -6.67247478e+00 | 1.16257374e+01 1.17682494e+01 -6.67247478e+00 2 7.17316057e+00 -9.77407780e+00 1.05628061e+01 | 7.17316057e+00 -9.77407780e+00 1.05628061e+01 3 -1.01393034e+01 9.96912727e+00 1.10849967e+01 | -1.01393034e+01 9.96912727e+00 1.10849967e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 9.49573704705 2^p V(r_1,...,r_N) = 9.49573704705 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 -2.15387336e+01 -1.80453593e+01 -3.51027148e+01 | -2.15387336e+01 -1.80453593e+01 -3.51027148e+01 1 1.00110756e+01 1.24422322e+01 -8.10863962e+00 | 1.00110756e+01 1.24422322e+01 -8.10863962e+00 2 2.65757629e+01 -1.43196648e+01 2.68537999e+01 | 2.65757629e+01 -1.43196648e+01 2.68537999e+01 3 -1.50481049e+01 1.99227919e+01 1.63575545e+01 | -1.50481049e+01 1.99227919e+01 1.63575545e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-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)) = -1.27644503492 2^p V(r_1,...,r_N) = -1.27644503492 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 -1.20602164e+01 -8.43897125e+00 -1.17114506e+01 | -1.20602164e+01 -8.43897125e+00 -1.17114506e+01 1 7.82478980e+00 1.05632881e+01 -8.84918030e+00 | 7.82478980e+00 1.05632881e+01 -8.84918030e+00 2 1.15655845e+01 -1.21423113e+01 1.08315341e+01 | 1.15655845e+01 -1.21423113e+01 1.08315341e+01 3 -7.33015787e+00 1.00179945e+01 9.72909675e+00 | -7.33015787e+00 1.00179945e+01 9.72909675e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-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)) = -5.64203924254 2^p V(r_1,...,r_N) = -5.64203924254 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 -9.19433710e+00 -7.33801989e+00 -5.16670052e+00 | -9.19433710e+00 -7.33801989e+00 -5.16670052e+00 1 5.72978795e+00 7.44699797e+00 -6.27926973e+00 | 5.72978795e+00 7.44699797e+00 -6.27926973e+00 2 6.24237200e+00 -3.31241499e+00 9.24777546e+00 | 6.24237200e+00 -3.31241499e+00 9.24777546e+00 3 -2.77782286e+00 3.20343691e+00 2.19819479e+00 | -2.77782286e+00 3.20343691e+00 2.19819479e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.20082844415 2^p V(r_1,...,r_N) = 7.20082844415 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 -9.98419103e+00 -9.04335124e+00 -1.20355247e+01 | -9.98419103e+00 -9.04335124e+00 -1.20355247e+01 1 1.29196669e+01 1.29206807e+01 -1.07676840e+01 | 1.29196669e+01 1.29206807e+01 -1.07676840e+01 2 2.61692417e+01 -2.97230980e+01 1.46352835e+01 | 2.61692417e+01 -2.97230980e+01 1.46352835e+01 3 -2.91047176e+01 2.58457686e+01 8.16792515e+00 | -2.91047176e+01 2.58457686e+01 8.16792515e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ 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)) = -3.88674118139 2^p V(r_1,...,r_N) = -3.88674118139 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 -8.40781787e+00 -4.49772794e+00 -9.75044737e+00 | -8.40781787e+00 -4.49772794e+00 -9.75044737e+00 1 3.80893287e+00 6.38708449e+00 -4.85549749e+00 | 3.80893287e+00 6.38708449e+00 -4.85549749e+00 2 1.13929817e+01 -8.76906302e+00 1.00654498e+01 | 1.13929817e+01 -8.76906302e+00 1.00654498e+01 3 -6.79409674e+00 6.87970647e+00 4.54049507e+00 | -6.79409674e+00 6.87970647e+00 4.54049507e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.86577592714 2^p V(r_1,...,r_N) = -2.86577592714 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 -6.89068771e+00 -5.00733659e+00 -5.75605214e+00 | -6.89068771e+00 -5.00733659e+00 -5.75605214e+00 1 5.00887825e+00 7.77807537e+00 -6.40857128e+00 | 5.00887825e+00 7.77807537e+00 -6.40857128e+00 2 1.37729758e+01 -1.26865796e+01 8.10584768e+00 | 1.37729758e+01 -1.26865796e+01 8.10584768e+00 3 -1.18911664e+01 9.91584078e+00 4.05877573e+00 | -1.18911664e+01 9.91584078e+00 4.05877573e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -6.74110447077 2^p V(r_1,...,r_N) = -6.74110447077 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 -1.23797929e+00 -1.59946056e+00 -1.32345101e+00 | -1.23797929e+00 -1.59946056e+00 -1.32345101e+00 1 2.32658452e+00 4.15821787e+00 -7.47776523e+00 | 2.32658452e+00 4.15821787e+00 -7.47776523e+00 2 2.69379932e+00 -6.60348413e+00 7.42838132e+00 | 2.69379932e+00 -6.60348413e+00 7.42838132e+00 3 -3.78240456e+00 4.04472681e+00 1.37283492e+00 | -3.78240456e+00 4.04472681e+00 1.37283492e+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)) = -6.03610685965 2^p V(r_1,...,r_N) = -6.03610685965 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 -2.37061795e+00 -9.45539407e+00 -7.84270161e+00 | -2.37061795e+00 -9.45539407e+00 -7.84270161e+00 1 2.43838823e+00 2.33367879e+00 -3.26847337e+00 | 2.43838823e+00 2.33367879e+00 -3.26847337e+00 2 1.12692452e+00 -2.41831594e+00 2.18549562e+00 | 1.12692452e+00 -2.41831594e+00 2.18549562e+00 3 -1.19469480e+00 9.54003122e+00 8.92567935e+00 | -1.19469480e+00 9.54003122e+00 8.92567935e+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)) = -7.81193098058 2^p V(r_1,...,r_N) = -7.81193098058 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 -2.49569228e+00 -3.07113893e+00 -2.64986503e+00 | -2.49569228e+00 -3.07113893e+00 -2.64986503e+00 1 3.80631142e+00 2.85566243e+00 -2.53729362e+00 | 3.80631142e+00 2.85566243e+00 -2.53729362e+00 2 1.41766110e+00 -2.41026531e+00 2.02083227e+00 | 1.41766110e+00 -2.41026531e+00 2.02083227e+00 3 -2.72828024e+00 2.62574181e+00 3.16632639e+00 | -2.72828024e+00 2.62574181e+00 3.16632639e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -4.86212317597 2^p V(r_1,...,r_N) = -4.86212317597 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 -3.60744311e+00 -4.03193542e+00 -1.39050596e+00 | -3.60744311e+00 -4.03193542e+00 -1.39050596e+00 1 1.39952368e+00 1.13168144e+01 -1.06238362e+01 | 1.39952368e+00 1.13168144e+01 -1.06238362e+01 2 7.64266880e+00 -9.41021851e+00 7.74814390e+00 | 7.64266880e+00 -9.41021851e+00 7.74814390e+00 3 -5.43474938e+00 2.12533957e+00 4.26619825e+00 | -5.43474938e+00 2.12533957e+00 4.26619825e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.708407672023 2^p V(r_1,...,r_N) = 0.708407672023 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 -1.24361538e+01 -1.37029000e+01 -1.02727034e+01 | -1.24361538e+01 -1.37029000e+01 -1.02727034e+01 1 1.94020426e+01 1.79856364e+01 -1.15335565e+01 | 1.94020426e+01 1.79856364e+01 -1.15335565e+01 2 5.08752535e+00 -9.61698053e+00 1.20271780e+01 | 5.08752535e+00 -9.61698053e+00 1.20271780e+01 3 -1.20534141e+01 5.33424411e+00 9.77908186e+00 | -1.20534141e+01 5.33424411e+00 9.77908186e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TTT (Configuration in file "config-AlCu-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)) = -1.84729871068 2^p V(r_1,...,r_N) = -1.84729871068 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 -8.32990062e+00 -4.36287266e+00 -1.40105756e+01 | -8.32990062e+00 -4.36287266e+00 -1.40105756e+01 1 1.12232610e+01 4.35360021e+00 -8.70871067e+00 | 1.12232610e+01 4.35360021e+00 -8.70871067e+00 2 1.03072706e+01 -7.98525305e+00 1.17743520e+01 | 1.03072706e+01 -7.98525305e+00 1.17743520e+01 3 -1.32006310e+01 7.99452550e+00 1.09449343e+01 | -1.32006310e+01 7.99452550e+00 1.09449343e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TTF (Configuration in file "config-AlCu-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)) = -4.50833437665 2^p V(r_1,...,r_N) = -4.50833437665 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 -2.33618902e+00 -4.87795767e+00 -4.21518786e+00 | -2.33618902e+00 -4.87795767e+00 -4.21518786e+00 1 1.28933845e+01 3.85221032e+00 -1.05912966e+01 | 1.28933845e+01 3.85221032e+00 -1.05912966e+01 2 2.07209571e+00 -4.02469413e+00 2.31569118e+00 | 2.07209571e+00 -4.02469413e+00 2.31569118e+00 3 -1.26292911e+01 5.05044148e+00 1.24907933e+01 | -1.26292911e+01 5.05044148e+00 1.24907933e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TFT (Configuration in file "config-AlCu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.53833699891 2^p V(r_1,...,r_N) = -7.53833699891 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 -1.44872404e+00 -2.60084465e+00 -1.80110773e+00 | -1.44872404e+00 -2.60084465e+00 -1.80110773e+00 1 6.29350881e+00 2.75456063e+00 -6.00847882e+00 | 6.29350881e+00 2.75456063e+00 -6.00847882e+00 2 1.06606056e+00 -3.28316497e+00 2.99051422e+00 | 1.06606056e+00 -3.28316497e+00 2.99051422e+00 3 -5.91084533e+00 3.12944899e+00 4.81907233e+00 | -5.91084533e+00 3.12944899e+00 4.81907233e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TFF (Configuration in file "config-AlCu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.32765933869 2^p V(r_1,...,r_N) = -9.32765933869 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 -9.10134563e-01 -9.60502070e-01 -3.29911765e-01 | -9.10134563e-01 -9.60502070e-01 -3.29911765e-01 1 1.20801825e+00 8.76565892e-01 -6.03399701e-01 | 1.20801825e+00 8.76565892e-01 -6.03399701e-01 2 6.77524375e-01 -1.07804223e+00 3.91988963e-01 | 6.77524375e-01 -1.07804223e+00 3.91988963e-01 3 -9.75408060e-01 1.16197841e+00 5.41322502e-01 | -9.75408060e-01 1.16197841e+00 5.41322502e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = FTT (Configuration in file "config-AlCu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.26666501008 2^p V(r_1,...,r_N) = -6.26666501008 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 -3.38633194e+00 -3.51612902e+00 -4.03798302e+00 | -3.38633194e+00 -3.51612902e+00 -4.03798302e+00 1 2.97969395e+00 4.77821838e+00 -6.81002866e+00 | 2.97969395e+00 4.77821838e+00 -6.81002866e+00 2 4.92937927e+00 -7.86418259e+00 7.32348716e+00 | 4.92937927e+00 -7.86418259e+00 7.32348716e+00 3 -4.52274128e+00 6.60209324e+00 3.52452453e+00 | -4.52274128e+00 6.60209324e+00 3.52452453e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = FTF (Configuration in file "config-AlCu-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)) = -8.12498335426 2^p V(r_1,...,r_N) = -8.12498335426 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 -1.67488770e+00 -1.24145387e+00 -7.83254796e-01 | -1.67488770e+00 -1.24145387e+00 -7.83254796e-01 1 5.19078880e+00 2.29110279e+00 -5.07872017e+00 | 5.19078880e+00 2.29110279e+00 -5.07872017e+00 2 9.54233426e-01 -2.89654205e+00 1.91048386e+00 | 9.54233426e-01 -2.89654205e+00 1.91048386e+00 3 -4.47013453e+00 1.84689313e+00 3.95149111e+00 | -4.47013453e+00 1.84689313e+00 3.95149111e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = FFT (Configuration in file "config-AlCu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.92960362099 2^p V(r_1,...,r_N) = -8.92960362099 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 -2.64320943e+00 -2.25266386e+00 -2.82084495e+00 | -2.64320943e+00 -2.25266386e+00 -2.82084495e+00 1 1.50096132e+00 1.61705252e+00 -1.13569535e+00 | 1.50096132e+00 1.61705252e+00 -1.13569535e+00 2 2.09529971e+00 -9.94158766e-01 2.32424470e+00 | 2.09529971e+00 -9.94158766e-01 2.32424470e+00 3 -9.53051598e-01 1.62977011e+00 1.63229559e+00 | -9.53051598e-01 1.62977011e+00 1.63229559e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.