!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_IMD_BrommerGaehler_2006A_AlNiCo__MO_122703700223_003 Supported species : Al Co Ni 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)) = 8.1224352472 2^p V(r_1,...,r_N) = 8.1224352472 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 -5.63532674e+00 -1.38680776e+01 -1.46517690e+01 | -5.63532674e+00 -1.38680776e+01 -1.46517690e+01 1 4.68639293e+00 3.03703922e+00 -3.43408466e+00 | 4.68639293e+00 3.03703922e+00 -3.43408466e+00 2 5.06800760e+00 -4.21575572e+00 6.11000445e+00 | 5.06800760e+00 -4.21575572e+00 6.11000445e+00 3 -4.11907379e+00 1.50467941e+01 1.19758492e+01 | -4.11907379e+00 1.50467941e+01 1.19758492e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 10.5443192172 2^p V(r_1,...,r_N) = 10.5443192172 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 -9.18288122e+00 -5.97662800e+00 -5.97812704e+00 | -9.18288122e+00 -5.97662800e+00 -5.97812704e+00 1 6.42825289e+00 5.34084122e+00 -8.24014189e+00 | 6.42825289e+00 5.34084122e+00 -8.24014189e+00 2 1.50142887e+01 -1.67608231e+01 1.08164690e+01 | 1.50142887e+01 -1.67608231e+01 1.08164690e+01 3 -1.22596604e+01 1.73966099e+01 3.40179992e+00 | -1.22596604e+01 1.73966099e+01 3.40179992e+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)) = 13.3200294073 2^p V(r_1,...,r_N) = 13.3200294073 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 -1.06337805e+01 -1.61043264e+01 -1.96400535e+01 | -1.06337805e+01 -1.61043264e+01 -1.96400535e+01 1 1.41339981e+01 1.49899771e+01 -7.99691224e+00 | 1.41339981e+01 1.49899771e+01 -7.99691224e+00 2 8.02391811e+00 -1.16201308e+01 1.30264194e+01 | 8.02391811e+00 -1.16201308e+01 1.30264194e+01 3 -1.15241357e+01 1.27344801e+01 1.46105463e+01 | -1.15241357e+01 1.27344801e+01 1.46105463e+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)) = 27.5169239887 2^p V(r_1,...,r_N) = 27.5169239887 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 -2.78436847e+01 -2.43942042e+01 -4.72782332e+01 | -2.78436847e+01 -2.43942042e+01 -4.72782332e+01 1 1.20259024e+01 1.57710744e+01 -9.79546085e+00 | 1.20259024e+01 1.57710744e+01 -9.79546085e+00 2 3.51323955e+01 -1.86196998e+01 3.51915561e+01 | 3.51323955e+01 -1.86196998e+01 3.51915561e+01 3 -1.93146132e+01 2.72428296e+01 2.18821379e+01 | -1.93146132e+01 2.72428296e+01 2.18821379e+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)) = 12.8071297193 2^p V(r_1,...,r_N) = 12.8071297193 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 -1.51523038e+01 -1.03741590e+01 -1.52262477e+01 | -1.51523038e+01 -1.03741590e+01 -1.52262477e+01 1 8.70849673e+00 1.33539533e+01 -1.07052816e+01 | 8.70849673e+00 1.33539533e+01 -1.07052816e+01 2 1.47808137e+01 -1.56063745e+01 1.43558321e+01 | 1.47808137e+01 -1.56063745e+01 1.43558321e+01 3 -8.33700662e+00 1.26265802e+01 1.15756972e+01 | -8.33700662e+00 1.26265802e+01 1.15756972e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 7.46900974182 2^p V(r_1,...,r_N) = 7.46900974182 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 -1.18431599e+01 -9.19387531e+00 -5.99492781e+00 | -1.18431599e+01 -9.19387531e+00 -5.99492781e+00 1 7.82787525e+00 9.46009263e+00 -8.02851284e+00 | 7.82787525e+00 9.46009263e+00 -8.02851284e+00 2 7.49417260e+00 -3.88629533e+00 1.12642512e+01 | 7.49417260e+00 -3.88629533e+00 1.12642512e+01 3 -3.47888796e+00 3.62007801e+00 2.75918946e+00 | -3.47888796e+00 3.62007801e+00 2.75918946e+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)) = 24.3269231002 2^p V(r_1,...,r_N) = 24.3269231002 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 -1.26515689e+01 -1.10792017e+01 -1.38097634e+01 | -1.26515689e+01 -1.10792017e+01 -1.38097634e+01 1 1.59009609e+01 1.71875321e+01 -1.34428533e+01 | 1.59009609e+01 1.71875321e+01 -1.34428533e+01 2 3.30320712e+01 -3.87396309e+01 1.87359642e+01 | 3.30320712e+01 -3.87396309e+01 1.87359642e+01 3 -3.62814632e+01 3.26313005e+01 8.51665242e+00 | -3.62814632e+01 3.26313005e+01 8.51665242e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TTT (Configuration in file "config-Co-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)) = -4.24087698568 2^p V(r_1,...,r_N) = -4.24087698568 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 -6.58657777e+00 -3.21298484e+00 -6.50636470e+00 | -6.58657777e+00 -3.21298484e+00 -6.50636470e+00 1 1.98975927e+00 4.26403630e+00 -2.21383086e+00 | 1.98975927e+00 4.26403630e+00 -2.21383086e+00 2 7.34217073e+00 -4.23731517e+00 6.91830546e+00 | 7.34217073e+00 -4.23731517e+00 6.91830546e+00 3 -2.74535223e+00 3.18626370e+00 1.80189011e+00 | -2.74535223e+00 3.18626370e+00 1.80189011e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TTF (Configuration in file "config-Co-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)) = -4.35751660913 2^p V(r_1,...,r_N) = -4.35751660913 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 5.34169206e-01 1.00619520e+00 6.92601549e-01 | 5.34169206e-01 1.00619520e+00 6.92601549e-01 1 -1.13253222e+00 -3.20729934e-01 5.04710099e-01 | -1.13253222e+00 -3.20729934e-01 5.04710099e-01 2 -1.52685349e-02 -3.77663148e-02 1.25529660e-01 | -1.52685349e-02 -3.77663148e-02 1.25529660e-01 3 6.13631547e-01 -6.47698951e-01 -1.32284131e+00 | 6.13631547e-01 -6.47698951e-01 -1.32284131e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TFT (Configuration in file "config-Co-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)) = -4.53563521195 2^p V(r_1,...,r_N) = -4.53563521195 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 -1.87766154e-02 5.32539080e-01 3.66608139e-01 | -1.87766154e-02 5.32539080e-01 3.66608139e-01 1 -7.28840766e-01 4.08424289e-02 6.45179245e-01 | -7.28840766e-01 4.08424289e-02 6.45179245e-01 2 -1.20266034e-01 1.06500340e-01 1.33104527e-01 | -1.20266034e-01 1.06500340e-01 1.33104527e-01 3 8.67883416e-01 -6.79881849e-01 -1.14489191e+00 | 8.67883416e-01 -6.79881849e-01 -1.14489191e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TFF (Configuration in file "config-Co-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)) = -4.91248823004 2^p V(r_1,...,r_N) = -4.91248823004 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 9.71495634e-02 4.39930878e-02 1.44232266e-01 | 9.71495634e-02 4.39930878e-02 1.44232266e-01 1 5.01632782e-02 8.85087431e-02 -1.30690526e-01 | 5.01632782e-02 8.85087431e-02 -1.30690526e-01 2 -4.55716860e-02 -1.08945449e-01 -3.14798135e-02 | -4.55716860e-02 -1.08945449e-01 -3.14798135e-02 3 -1.01741156e-01 -2.35563817e-02 1.79380737e-02 | -1.01741156e-01 -2.35563817e-02 1.79380737e-02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FTT (Configuration in file "config-Co-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)) = -1.64690219516 2^p V(r_1,...,r_N) = -1.64690219516 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 -3.49895813e+00 -2.76755249e+00 -3.39357241e+00 | -3.49895813e+00 -2.76755249e+00 -3.39357241e+00 1 7.66700243e+00 9.83170184e+00 -1.14151941e+01 | 7.66700243e+00 9.83170184e+00 -1.14151941e+01 2 4.66121707e+00 -1.20368570e+01 1.16105552e+01 | 4.66121707e+00 -1.20368570e+01 1.16105552e+01 3 -8.82926136e+00 4.97270767e+00 3.19821128e+00 | -8.82926136e+00 4.97270767e+00 3.19821128e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FTF (Configuration in file "config-Co-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)) = -3.5725070866 2^p V(r_1,...,r_N) = -3.5725070866 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 1.20463577e+00 1.06784920e+00 8.49469400e-01 | 1.20463577e+00 1.06784920e+00 8.49469400e-01 1 -1.34163125e+00 -1.26876938e+00 1.30017882e+00 | -1.34163125e+00 -1.26876938e+00 1.30017882e+00 2 -1.01146535e+00 1.32752238e+00 -1.17072937e+00 | -1.01146535e+00 1.32752238e+00 -1.17072937e+00 3 1.14846083e+00 -1.12660219e+00 -9.78918846e-01 | 1.14846083e+00 -1.12660219e+00 -9.78918846e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FFT (Configuration in file "config-Co-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)) = -4.19784879818 2^p V(r_1,...,r_N) = -4.19784879818 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 1.17065611e+00 1.25216816e+00 1.22132771e+00 | 1.17065611e+00 1.25216816e+00 1.22132771e+00 1 -1.27498569e+00 -4.84956042e-01 5.73650520e-01 | -1.27498569e+00 -4.84956042e-01 5.73650520e-01 2 -8.47860738e-01 3.91077022e-01 -6.79581851e-01 | -8.47860738e-01 3.91077022e-01 -6.79581851e-01 3 9.52190324e-01 -1.15828914e+00 -1.11539638e+00 | 9.52190324e-01 -1.15828914e+00 -1.11539638e+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)) = -2.06163247524 2^p V(r_1,...,r_N) = -2.06163247524 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 2.10166156e+00 2.59064043e+00 1.75205920e+00 | 2.10166156e+00 2.59064043e+00 1.75205920e+00 1 -1.34603498e+00 -2.60075216e+00 1.76174647e+00 | -1.34603498e+00 -2.60075216e+00 1.76174647e+00 2 -2.09114604e+00 1.35949625e+00 -1.96206413e+00 | -2.09114604e+00 1.35949625e+00 -1.96206413e+00 3 1.33551946e+00 -1.34938452e+00 -1.55174153e+00 | 1.33551946e+00 -1.34938452e+00 -1.55174153e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.948931521135 2^p V(r_1,...,r_N) = -0.948931521135 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 -1.77447027e+01 -3.40970137e+00 -1.16199647e+01 | -1.77447027e+01 -3.40970137e+00 -1.16199647e+01 1 2.74583589e+00 4.74523146e+00 -3.99583282e+00 | 2.74583589e+00 4.74523146e+00 -3.99583282e+00 2 1.62708034e+01 -3.66562997e+00 1.50681068e+01 | 1.62708034e+01 -3.66562997e+00 1.50681068e+01 3 -1.27193661e+00 2.33009988e+00 5.47690676e-01 | -1.27193661e+00 2.33009988e+00 5.47690676e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.76984814966 2^p V(r_1,...,r_N) = -1.76984814966 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 2.17157218e+00 2.60517328e+00 2.09125904e+00 | 2.17157218e+00 2.60517328e+00 2.09125904e+00 1 -1.72163593e+00 -2.04016655e+00 1.98308758e+00 | -1.72163593e+00 -2.04016655e+00 1.98308758e+00 2 -2.44228274e+00 1.78234712e+00 -2.26552904e+00 | -2.44228274e+00 1.78234712e+00 -2.26552904e+00 3 1.99234648e+00 -2.34735385e+00 -1.80881758e+00 | 1.99234648e+00 -2.34735385e+00 -1.80881758e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.435189771556 2^p V(r_1,...,r_N) = -0.435189771556 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 4.31060080e-01 4.46632159e-01 3.21004123e-01 | 4.31060080e-01 4.46632159e-01 3.21004123e-01 1 -9.35561631e-01 -9.44593033e-01 2.18328040e+00 | -9.35561631e-01 -9.44593033e-01 2.18328040e+00 2 -1.55343782e+00 1.85095904e+00 -8.62264228e-01 | -1.55343782e+00 1.85095904e+00 -8.62264228e-01 3 2.05793937e+00 -1.35299816e+00 -1.64202030e+00 | 2.05793937e+00 -1.35299816e+00 -1.64202030e+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)) = -1.73328005322 2^p V(r_1,...,r_N) = -1.73328005322 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 1.64382319e+00 1.75923670e+00 1.91978196e+00 | 1.64382319e+00 1.75923670e+00 1.91978196e+00 1 -1.88013753e+00 -1.99678932e+00 1.92802286e+00 | -1.88013753e+00 -1.99678932e+00 1.92802286e+00 2 -2.12895985e+00 2.08419934e+00 -2.42469640e+00 | -2.12895985e+00 2.08419934e+00 -2.42469640e+00 3 2.36527419e+00 -1.84664672e+00 -1.42310842e+00 | 2.36527419e+00 -1.84664672e+00 -1.42310842e+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)) = -0.0432937575045 2^p V(r_1,...,r_N) = -0.0432937575045 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 -3.92266166e+00 -3.00336671e+00 -6.50645757e+00 | -3.92266166e+00 -3.00336671e+00 -6.50645757e+00 1 1.62687956e+00 4.05781371e+00 -7.16901760e+00 | 1.62687956e+00 4.05781371e+00 -7.16901760e+00 2 1.74003909e+01 -1.38482652e+01 3.55801380e+00 | 1.74003909e+01 -1.38482652e+01 3.55801380e+00 3 -1.51046088e+01 1.27938182e+01 1.01174614e+01 | -1.51046088e+01 1.27938182e+01 1.01174614e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.29377126063 2^p V(r_1,...,r_N) = -2.29377126063 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 2.58171756e+00 2.17565473e+00 1.73462032e+00 | 2.58171756e+00 2.17565473e+00 1.73462032e+00 1 -2.13664982e+00 -2.03955509e+00 2.39621788e+00 | -2.13664982e+00 -2.03955509e+00 2.39621788e+00 2 -2.40482892e+00 2.43779606e+00 -1.84040310e+00 | -2.40482892e+00 2.43779606e+00 -1.84040310e+00 3 1.95976118e+00 -2.57389571e+00 -2.29043510e+00 | 1.95976118e+00 -2.57389571e+00 -2.29043510e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TTT (Configuration in file "config-AlCoNi-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)) = -1.83995027717 2^p V(r_1,...,r_N) = -1.83995027717 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 -3.60555343e+00 -2.72770672e+00 -3.74451868e+00 | -3.60555343e+00 -2.72770672e+00 -3.74451868e+00 1 6.59390964e-01 4.37976436e+00 -8.98043098e-01 | 6.59390964e-01 4.37976436e+00 -8.98043098e-01 2 1.72801326e+00 -2.88489812e+00 4.68915598e+00 | 1.72801326e+00 -2.88489812e+00 4.68915598e+00 3 1.21814920e+00 1.23284048e+00 -4.65941988e-02 | 1.21814920e+00 1.23284048e+00 -4.65941988e-02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TTF (Configuration in file "config-AlCoNi-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)) = 1.38588124561 2^p V(r_1,...,r_N) = 1.38588124561 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 -7.94703970e+00 -2.21120904e+00 -5.14702227e+00 | -7.94703970e+00 -2.21120904e+00 -5.14702227e+00 1 2.00211861e+00 9.60812275e+00 -4.90984978e+00 | 2.00211861e+00 9.60812275e+00 -4.90984978e+00 2 5.60053761e+00 -8.67464922e+00 1.09324899e+01 | 5.60053761e+00 -8.67464922e+00 1.09324899e+01 3 3.44383474e-01 1.27773552e+00 -8.75617810e-01 | 3.44383474e-01 1.27773552e+00 -8.75617810e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TFT (Configuration in file "config-AlCoNi-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)) = -2.12077415122 2^p V(r_1,...,r_N) = -2.12077415122 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 2.16149092e-03 1.76528556e+00 1.82298837e+00 | 2.16149092e-03 1.76528556e+00 1.82298837e+00 1 6.61668540e-01 2.64320075e+00 -2.77611783e+00 | 6.61668540e-01 2.64320075e+00 -2.77611783e+00 2 -6.72990318e-01 -2.80835651e+00 2.71132270e+00 | -6.72990318e-01 -2.80835651e+00 2.71132270e+00 3 9.16028658e-03 -1.60012981e+00 -1.75819325e+00 | 9.16028658e-03 -1.60012981e+00 -1.75819325e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = TFF (Configuration in file "config-AlCoNi-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)) = 1.62911871522 2^p V(r_1,...,r_N) = 1.62911871522 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 -9.02766699e+00 -1.06180089e+01 -1.03912127e+01 | -9.02766699e+00 -1.06180089e+01 -1.03912127e+01 1 9.64455416e+00 4.60362101e+00 -1.84633192e+00 | 9.64455416e+00 4.60362101e+00 -1.84633192e+00 2 6.80094111e+00 -6.61928057e-01 1.18416140e+00 | 6.80094111e+00 -6.61928057e-01 1.18416140e+00 3 -7.41782828e+00 6.67631594e+00 1.10533833e+01 | -7.41782828e+00 6.67631594e+00 1.10533833e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = FTT (Configuration in file "config-AlCoNi-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)) = -0.735947172598 2^p V(r_1,...,r_N) = -0.735947172598 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 -3.65774239e+00 -5.02653556e+00 -3.45467950e+00 | -3.65774239e+00 -5.02653556e+00 -3.45467950e+00 1 5.20065299e+00 3.67406989e+00 -7.30627915e-01 | 5.20065299e+00 3.67406989e+00 -7.30627915e-01 2 -6.39698179e-01 -5.99668442e-01 6.12994109e-01 | -6.39698179e-01 -5.99668442e-01 6.12994109e-01 3 -9.03212425e-01 1.95213411e+00 3.57231331e+00 | -9.03212425e-01 1.95213411e+00 3.57231331e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = FTF (Configuration in file "config-AlCoNi-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)) = -1.61012254179 2^p V(r_1,...,r_N) = -1.61012254179 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 -2.65375759e+00 -1.71564234e+00 1.04215151e+00 | -2.65375759e+00 -1.71564234e+00 1.04215151e+00 1 2.21514739e+00 4.38607574e+00 -1.87764952e+00 | 2.21514739e+00 4.38607574e+00 -1.87764952e+00 2 1.89560609e-01 -1.82139538e+00 1.78543696e+00 | 1.89560609e-01 -1.82139538e+00 1.78543696e+00 3 2.49049593e-01 -8.49038022e-01 -9.49938949e-01 | 2.49049593e-01 -8.49038022e-01 -9.49938949e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Ni, PBC = FFT (Configuration in file "config-AlCoNi-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)) = -2.38953594337 2^p V(r_1,...,r_N) = -2.38953594337 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 -4.34620461e-01 -1.12864633e+00 -1.83493765e+00 | -4.34620461e-01 -1.12864633e+00 -1.83493765e+00 1 -3.12235122e-01 -6.26935583e-01 7.52136345e-01 | -3.12235122e-01 -6.26935583e-01 7.52136345e-01 2 9.97817106e-01 1.79785283e-01 3.67342808e-01 | 9.97817106e-01 1.79785283e-01 3.67342808e-01 3 -2.50961524e-01 1.57579663e+00 7.15458497e-01 | -2.50961524e-01 1.57579663e+00 7.15458497e-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.