!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : Sim_LAMMPS_ADP_ApostolMishin_2011_AlCu__SM_667696763561_000 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)) = -2.53211528526 2^p V(r_1,...,r_N) = -2.53211528526 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 -4.04795940e+00 -3.24940796e+00 -3.71034445e+00 | -4.04795940e+00 -3.24940796e+00 -3.71034445e+00 1 3.70524093e+00 2.51731379e+00 -2.71801513e+00 | 3.70524093e+00 2.51731379e+00 -2.71801513e+00 2 3.21624801e+00 -3.37475062e+00 3.93952247e+00 | 3.21624801e+00 -3.37475062e+00 3.93952247e+00 3 -2.87352954e+00 4.10684479e+00 2.48883711e+00 | -2.87352954e+00 4.10684479e+00 2.48883711e+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)) = -1.05535733355 2^p V(r_1,...,r_N) = -1.05535733355 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 -4.67231248e+00 -3.92326678e+00 -3.22114452e+00 | -4.67231248e+00 -3.92326678e+00 -3.22114452e+00 1 4.06488357e+00 2.61879139e+00 -4.81261951e+00 | 4.06488357e+00 2.61879139e+00 -4.81261951e+00 2 3.39957951e+00 -3.34500169e+00 4.79851012e+00 | 3.39957951e+00 -3.34500169e+00 4.79851012e+00 3 -2.79215059e+00 4.64947708e+00 3.23525392e+00 | -2.79215059e+00 4.64947708e+00 3.23525392e+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)) = 0.644899535188 2^p V(r_1,...,r_N) = 0.644899535188 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 -3.61288179e+00 -3.58923366e+00 -5.01213223e+00 | -3.61288179e+00 -3.58923366e+00 -5.01213223e+00 1 4.97503638e+00 4.49282633e+00 -3.06083536e+00 | 4.97503638e+00 4.49282633e+00 -3.06083536e+00 2 3.76442472e+00 -4.58231118e+00 4.45447354e+00 | 3.76442472e+00 -4.58231118e+00 4.45447354e+00 3 -5.12657931e+00 3.67871850e+00 3.61849405e+00 | -5.12657931e+00 3.67871850e+00 3.61849405e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 2.61743742248 2^p V(r_1,...,r_N) = 2.61743742248 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 -3.60861426e+00 -3.84065936e+00 -4.03949517e+00 | -3.60861426e+00 -3.84065936e+00 -4.03949517e+00 1 4.63118951e+00 4.49469840e+00 -3.69926985e+00 | 4.63118951e+00 4.49469840e+00 -3.69926985e+00 2 3.85461954e+00 -4.22541140e+00 4.17400339e+00 | 3.85461954e+00 -4.22541140e+00 4.17400339e+00 3 -4.87719479e+00 3.57137236e+00 3.56476164e+00 | -4.87719479e+00 3.57137236e+00 3.56476164e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.477845745973 2^p V(r_1,...,r_N) = 0.477845745973 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 -4.72517915e+00 -3.63304393e+00 -4.16288991e+00 | -4.72517915e+00 -3.63304393e+00 -4.16288991e+00 1 4.33317536e+00 4.16607512e+00 -4.09951108e+00 | 4.33317536e+00 4.16607512e+00 -4.09951108e+00 2 4.28663691e+00 -4.52992090e+00 3.56319034e+00 | 4.28663691e+00 -4.52992090e+00 3.56319034e+00 3 -3.89463313e+00 3.99688971e+00 4.69921065e+00 | -3.89463313e+00 3.99688971e+00 4.69921065e+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)) = -2.20321440318 2^p V(r_1,...,r_N) = -2.20321440318 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 -3.79264978e+00 -4.07134003e+00 -3.42103263e+00 | -3.79264978e+00 -4.07134003e+00 -3.42103263e+00 1 2.45240661e+00 3.42284800e+00 -3.20993335e+00 | 2.45240661e+00 3.42284800e+00 -3.20993335e+00 2 4.03131900e+00 -2.43903459e+00 4.58765068e+00 | 4.03131900e+00 -2.43903459e+00 4.58765068e+00 3 -2.69107583e+00 3.08752663e+00 2.04331531e+00 | -2.69107583e+00 3.08752663e+00 2.04331531e+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)) = 1.96065488588 2^p V(r_1,...,r_N) = 1.96065488588 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 -3.70206688e+00 -3.68637469e+00 -5.53342694e+00 | -3.70206688e+00 -3.68637469e+00 -5.53342694e+00 1 5.07988062e+00 3.84019265e+00 -3.71132316e+00 | 5.07988062e+00 3.84019265e+00 -3.71132316e+00 2 3.28624824e+00 -3.82716674e+00 4.81472033e+00 | 3.28624824e+00 -3.82716674e+00 4.81472033e+00 3 -4.66406198e+00 3.67334878e+00 4.43002978e+00 | -4.66406198e+00 3.67334878e+00 4.43002978e+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)) = -2.15026786643 2^p V(r_1,...,r_N) = -2.15026786643 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 -8.90093817e+00 -4.35164254e+00 -1.02889979e+01 | -8.90093817e+00 -4.35164254e+00 -1.02889979e+01 1 3.48179303e+00 6.52035812e+00 -4.86200181e+00 | 3.48179303e+00 6.52035812e+00 -4.86200181e+00 2 1.24462425e+01 -9.40508872e+00 1.08674481e+01 | 1.24462425e+01 -9.40508872e+00 1.08674481e+01 3 -7.02709737e+00 7.23637314e+00 4.28355155e+00 | -7.02709737e+00 7.23637314e+00 4.28355155e+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)) = -0.889267445983 2^p V(r_1,...,r_N) = -0.889267445983 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 -7.11433729e+00 -4.87812786e+00 -5.51134437e+00 | -7.11433729e+00 -4.87812786e+00 -5.51134437e+00 1 4.89415339e+00 8.14481308e+00 -6.43795638e+00 | 4.89415339e+00 8.14481308e+00 -6.43795638e+00 2 1.59686587e+01 -1.46851303e+01 8.10554989e+00 | 1.59686587e+01 -1.46851303e+01 8.10554989e+00 3 -1.37484748e+01 1.14184451e+01 3.84375086e+00 | -1.37484748e+01 1.14184451e+01 3.84375086e+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)) = -5.01093564731 2^p V(r_1,...,r_N) = -5.01093564731 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 -7.50127772e-01 -1.36766217e+00 -1.06641093e+00 | -7.50127772e-01 -1.36766217e+00 -1.06641093e+00 1 1.92926507e+00 4.57542846e+00 -8.11952857e+00 | 1.92926507e+00 4.57542846e+00 -8.11952857e+00 2 2.48042536e+00 -7.27087828e+00 8.09634369e+00 | 2.48042536e+00 -7.27087828e+00 8.09634369e+00 3 -3.65956266e+00 4.06311200e+00 1.08959582e+00 | -3.65956266e+00 4.06311200e+00 1.08959582e+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)) = -5.29365568775 2^p V(r_1,...,r_N) = -5.29365568775 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 -4.21318000e+00 -4.72712889e+00 -7.77081152e+00 | -4.21318000e+00 -4.72712889e+00 -7.77081152e+00 1 2.69647137e+00 3.31054999e+00 -9.54191842e-01 | 2.69647137e+00 3.31054999e+00 -9.54191842e-01 2 4.31448279e+00 -2.41200329e+00 4.20423238e+00 | 4.31448279e+00 -2.41200329e+00 4.20423238e+00 3 -2.79777416e+00 3.82858220e+00 4.52077098e+00 | -2.79777416e+00 3.82858220e+00 4.52077098e+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)) = -4.52881056471 2^p V(r_1,...,r_N) = -4.52881056471 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 -6.26532552e+00 -3.33406466e+00 -5.35691604e+00 | -6.26532552e+00 -3.33406466e+00 -5.35691604e+00 1 4.74729290e+00 3.89096409e+00 -6.41611501e+00 | 4.74729290e+00 3.89096409e+00 -6.41611501e+00 2 5.94364637e+00 -2.04395625e+00 8.35793446e+00 | 5.94364637e+00 -2.04395625e+00 8.35793446e+00 3 -4.42561375e+00 1.48705682e+00 3.41509658e+00 | -4.42561375e+00 1.48705682e+00 3.41509658e+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)) = -5.46678085474 2^p V(r_1,...,r_N) = -5.46678085474 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 -3.59777037e+00 -5.69547607e+00 -1.32021624e+00 | -3.59777037e+00 -5.69547607e+00 -1.32021624e+00 1 6.55267889e+00 4.26702723e+00 -4.24680485e+00 | 6.55267889e+00 4.26702723e+00 -4.24680485e+00 2 9.27286287e-01 -1.54165058e+00 1.65658504e+00 | 9.27286287e-01 -1.54165058e+00 1.65658504e+00 3 -3.88219481e+00 2.97009942e+00 3.91043605e+00 | -3.88219481e+00 2.97009942e+00 3.91043605e+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)) = 3.80387588033 2^p V(r_1,...,r_N) = 3.80387588033 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 -2.36912714e+01 -1.45696292e+01 -2.17630096e+01 | -2.36912714e+01 -1.45696292e+01 -2.17630096e+01 1 4.50757350e+00 7.41273134e+00 -8.01116615e+00 | 4.50757350e+00 7.41273134e+00 -8.01116615e+00 2 2.88474109e+01 -5.64654876e+00 2.44323069e+01 | 2.88474109e+01 -5.64654876e+00 2.44323069e+01 3 -9.66371300e+00 1.28034466e+01 5.34186888e+00 | -9.66371300e+00 1.28034466e+01 5.34186888e+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)) = -4.633119441 2^p V(r_1,...,r_N) = -4.633119441 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 -6.98500407e+00 -5.45494135e+00 -2.11217453e+00 | -6.98500407e+00 -5.45494135e+00 -2.11217453e+00 1 3.53769895e+00 7.62466107e+00 -3.67445454e+00 | 3.53769895e+00 7.62466107e+00 -3.67445454e+00 2 5.68815050e+00 -3.58242746e+00 4.74846880e+00 | 5.68815050e+00 -3.58242746e+00 4.74846880e+00 3 -2.24084539e+00 1.41270775e+00 1.03816027e+00 | -2.24084539e+00 1.41270775e+00 1.03816027e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -6.00287812225 2^p V(r_1,...,r_N) = -6.00287812225 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 8.05312774e-01 3.08115067e-01 1.13591929e+00 | 8.05312774e-01 3.08115067e-01 1.13591929e+00 1 2.27284454e-01 1.62237038e+00 -2.68204723e+00 | 2.27284454e-01 1.62237038e+00 -2.68204723e+00 2 1.59217757e+00 -3.42341203e+00 1.72338791e+00 | 1.59217757e+00 -3.42341203e+00 1.72338791e+00 3 -2.62477480e+00 1.49292658e+00 -1.77259960e-01 | -2.62477480e+00 1.49292658e+00 -1.77259960e-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)) = -5.03718666577 2^p V(r_1,...,r_N) = -5.03718666577 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 -1.48713778e+00 -2.25170636e+00 -2.27608576e-01 | -1.48713778e+00 -2.25170636e+00 -2.27608576e-01 1 2.73896338e+00 2.64129543e+00 -1.81777207e+00 | 2.73896338e+00 2.64129543e+00 -1.81777207e+00 2 8.07602522e-01 -1.35436225e+00 2.48179337e-01 | 8.07602522e-01 -1.35436225e+00 2.48179337e-01 3 -2.05942812e+00 9.64773175e-01 1.79720131e+00 | -2.05942812e+00 9.64773175e-01 1.79720131e+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)) = -5.83920939673 2^p V(r_1,...,r_N) = -5.83920939673 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 -8.02334036e-01 -7.28379341e-01 -1.05336191e+00 | -8.02334036e-01 -7.28379341e-01 -1.05336191e+00 1 1.12472840e+00 2.50642383e+00 -2.25496234e+00 | 1.12472840e+00 2.50642383e+00 -2.25496234e+00 2 4.22036599e-01 -2.79076431e+00 2.57087068e+00 | 4.22036599e-01 -2.79076431e+00 2.57087068e+00 3 -7.44430965e-01 1.01271982e+00 7.37453566e-01 | -7.44430965e-01 1.01271982e+00 7.37453566e-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)) = -6.53344363654 2^p V(r_1,...,r_N) = -6.53344363654 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 -2.12895292e+00 -6.85130637e-01 -1.64069115e+00 | -2.12895292e+00 -6.85130637e-01 -1.64069115e+00 1 9.97390749e-01 1.19721281e+00 -1.63478998e+00 | 9.97390749e-01 1.19721281e+00 -1.63478998e+00 2 2.09103152e+00 -1.57869888e+00 2.69824665e+00 | 2.09103152e+00 -1.57869888e+00 2.69824665e+00 3 -9.59469353e-01 1.06661670e+00 5.77234483e-01 | -9.59469353e-01 1.06661670e+00 5.77234483e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -6.6631173774 2^p V(r_1,...,r_N) = -6.6631173774 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 -1.94463477e-01 -2.91119878e-01 2.76834075e-01 | -1.94463477e-01 -2.91119878e-01 2.76834075e-01 1 1.29060224e+00 2.24795729e+00 -2.30596511e+00 | 1.29060224e+00 2.24795729e+00 -2.30596511e+00 2 -1.35361120e-01 -2.14002380e+00 1.40498475e+00 | -1.35361120e-01 -2.14002380e+00 1.40498475e+00 3 -9.60777645e-01 1.83186395e-01 6.24146283e-01 | -9.60777645e-01 1.83186395e-01 6.24146283e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -4.84287343176 2^p V(r_1,...,r_N) = -4.84287343176 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 -2.65542276e+00 -6.62219345e-01 -2.36000013e+00 | -2.65542276e+00 -6.62219345e-01 -2.36000013e+00 1 2.01375103e+00 1.99205481e+00 -3.04866759e+00 | 2.01375103e+00 1.99205481e+00 -3.04866759e+00 2 3.24169149e+00 -3.11645090e+00 3.26140729e+00 | 3.24169149e+00 -3.11645090e+00 3.26140729e+00 3 -2.60001976e+00 1.78661543e+00 2.14726043e+00 | -2.60001976e+00 1.78661543e+00 2.14726043e+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.