!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_SchopfBrommerFrigan_2012_AlMnPd__MO_878712978062_003 Supported species : Al Mn Pd 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)) = -3.47654589868 2^p V(r_1,...,r_N) = -3.47654589868 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 -6.39826333e+00 -1.59273530e+01 -1.67293577e+01 | -6.39826333e+00 -1.59273530e+01 -1.67293577e+01 1 4.37053362e+00 3.03350927e+00 -2.61285283e+00 | 4.37053362e+00 3.03350927e+00 -2.61285283e+00 2 5.67815899e+00 -4.03161922e+00 6.21898740e+00 | 5.67815899e+00 -4.03161922e+00 6.21898740e+00 3 -3.65042928e+00 1.69254629e+01 1.31232231e+01 | -3.65042928e+00 1.69254629e+01 1.31232231e+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)) = -0.883081641055 2^p V(r_1,...,r_N) = -0.883081641055 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 -1.02275557e+01 -6.57729969e+00 -6.45545079e+00 | -1.02275557e+01 -6.57729969e+00 -6.45545079e+00 1 7.02085772e+00 6.10042497e+00 -8.90065350e+00 | 7.02085772e+00 6.10042497e+00 -8.90065350e+00 2 1.73441803e+01 -1.96038892e+01 1.20026115e+01 | 1.73441803e+01 -1.96038892e+01 1.20026115e+01 3 -1.41374823e+01 2.00807640e+01 3.35349281e+00 | -1.41374823e+01 2.00807640e+01 3.35349281e+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)) = 2.17359884814 2^p V(r_1,...,r_N) = 2.17359884814 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 -1.14227130e+01 -1.78268530e+01 -2.17531657e+01 | -1.14227130e+01 -1.78268530e+01 -2.17531657e+01 1 1.54582082e+01 1.62081900e+01 -8.74357617e+00 | 1.54582082e+01 1.62081900e+01 -8.74357617e+00 2 8.96537909e+00 -1.27909578e+01 1.41298355e+01 | 8.96537909e+00 -1.27909578e+01 1.41298355e+01 3 -1.30008742e+01 1.44096208e+01 1.63669064e+01 | -1.30008742e+01 1.44096208e+01 1.63669064e+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)) = 21.1171559281 2^p V(r_1,...,r_N) = 21.1171559281 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 -4.95069667e+01 -3.17308931e+01 -8.17085741e+01 | -4.95069667e+01 -3.17308931e+01 -8.17085741e+01 1 1.30452970e+01 1.71109291e+01 -1.06187218e+01 | 1.30452970e+01 1.71109291e+01 -1.06187218e+01 2 5.99467175e+01 -2.18646677e+01 6.14149872e+01 | 5.99467175e+01 -2.18646677e+01 6.14149872e+01 3 -2.34850478e+01 3.64846317e+01 3.09123088e+01 | -2.34850478e+01 3.64846317e+01 3.09123088e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.5818448384 2^p V(r_1,...,r_N) = 1.5818448384 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 -1.65204423e+01 -1.12688210e+01 -1.64881934e+01 | -1.65204423e+01 -1.12688210e+01 -1.64881934e+01 1 9.74259551e+00 1.45418167e+01 -1.18563944e+01 | 9.74259551e+00 1.45418167e+01 -1.18563944e+01 2 1.60421858e+01 -1.69161280e+01 1.55902925e+01 | 1.60421858e+01 -1.69161280e+01 1.55902925e+01 3 -9.26433901e+00 1.36431322e+01 1.27542953e+01 | -9.26433901e+00 1.36431322e+01 1.27542953e+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)) = -3.91691297128 2^p V(r_1,...,r_N) = -3.91691297128 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 -1.27550930e+01 -9.95739145e+00 -6.59386930e+00 | -1.27550930e+01 -9.95739145e+00 -6.59386930e+00 1 7.93792094e+00 1.02767216e+01 -8.28829037e+00 | 7.93792094e+00 1.02767216e+01 -8.28829037e+00 2 8.09927081e+00 -4.22378025e+00 1.22965975e+01 | 8.09927081e+00 -4.22378025e+00 1.22965975e+01 3 -3.28209879e+00 3.90445010e+00 2.58556213e+00 | -3.28209879e+00 3.90445010e+00 2.58556213e+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)) = 19.0483509467 2^p V(r_1,...,r_N) = 19.0483509467 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 -1.37482231e+01 -1.21561116e+01 -1.52549506e+01 | -1.37482231e+01 -1.21561116e+01 -1.52549506e+01 1 1.77079477e+01 1.91362496e+01 -1.54403147e+01 | 1.77079477e+01 1.91362496e+01 -1.54403147e+01 2 7.26416820e+01 -7.60904094e+01 2.07236250e+01 | 7.26416820e+01 -7.60904094e+01 2.07236250e+01 3 -7.66014067e+01 6.91102714e+01 9.97164034e+00 | -7.66014067e+01 6.91102714e+01 9.97164034e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TTT (Configuration in file "config-Mn-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)) = -19.3418989443 2^p V(r_1,...,r_N) = -19.3418989443 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 2.03838638e+00 3.37825436e+00 2.30685751e+00 | 2.03838638e+00 3.37825436e+00 2.30685751e+00 1 -4.32944023e+00 -3.09029232e+00 3.05381495e+00 | -4.32944023e+00 -3.09029232e+00 3.05381495e+00 2 -1.00279078e+00 1.90667589e+00 -1.12180482e+00 | -1.00279078e+00 1.90667589e+00 -1.12180482e+00 3 3.29384462e+00 -2.19463794e+00 -4.23886765e+00 | 3.29384462e+00 -2.19463794e+00 -4.23886765e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TTF (Configuration in file "config-Mn-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)) = -14.7158170951 2^p V(r_1,...,r_N) = -14.7158170951 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 6.01131062e+00 6.88677534e+00 4.89267832e+00 | 6.01131062e+00 6.88677534e+00 4.89267832e+00 1 -5.23303171e+00 -5.39135393e+00 7.06525528e+00 | -5.23303171e+00 -5.39135393e+00 7.06525528e+00 2 -6.63715161e+00 4.95336881e+00 -6.31638706e+00 | -6.63715161e+00 4.95336881e+00 -6.31638706e+00 3 5.85887271e+00 -6.44879022e+00 -5.64154655e+00 | 5.85887271e+00 -6.44879022e+00 -5.64154655e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TFT (Configuration in file "config-Mn-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)) = -19.3166919789 2^p V(r_1,...,r_N) = -19.3166919789 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 2.33805894e+00 -8.75283580e-01 7.57768232e-01 | 2.33805894e+00 -8.75283580e-01 7.57768232e-01 1 3.56394538e+00 -1.65480275e+00 -1.79266930e+00 | 3.56394538e+00 -1.65480275e+00 -1.79266930e+00 2 -4.55284711e+00 2.74860360e+00 -3.49717334e+00 | -4.55284711e+00 2.74860360e+00 -3.49717334e+00 3 -1.34915721e+00 -2.18517272e-01 4.53207441e+00 | -1.34915721e+00 -2.18517272e-01 4.53207441e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TFF (Configuration in file "config-Mn-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)) = -17.595800803 2^p V(r_1,...,r_N) = -17.595800803 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 3.73245903e+00 4.11582312e+00 4.58201478e+00 | 3.73245903e+00 4.11582312e+00 4.58201478e+00 1 -5.12085007e+00 -6.16851602e+00 4.80531014e+00 | -5.12085007e+00 -6.16851602e+00 4.80531014e+00 2 -4.79162354e+00 5.68282354e+00 -4.52233226e+00 | -4.79162354e+00 5.68282354e+00 -4.52233226e+00 3 6.18001458e+00 -3.63013064e+00 -4.86499266e+00 | 6.18001458e+00 -3.63013064e+00 -4.86499266e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = FTT (Configuration in file "config-Mn-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)) = -11.3456324678 2^p V(r_1,...,r_N) = -11.3456324678 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 6.60053732e+00 5.99536305e+00 6.22223509e+00 | 6.60053732e+00 5.99536305e+00 6.22223509e+00 1 -6.47110460e+00 -6.01959365e+00 6.60964952e+00 | -6.47110460e+00 -6.01959365e+00 6.60964952e+00 2 -6.32943532e+00 6.72791403e+00 -5.76676010e+00 | -6.32943532e+00 6.72791403e+00 -5.76676010e+00 3 6.20000260e+00 -6.70368343e+00 -7.06512451e+00 | 6.20000260e+00 -6.70368343e+00 -7.06512451e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = FTF (Configuration in file "config-Mn-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)) = -17.7464335042 2^p V(r_1,...,r_N) = -17.7464335042 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 1.77616863e+00 5.07660548e+00 1.51185775e+00 | 1.77616863e+00 5.07660548e+00 1.51185775e+00 1 -4.40343356e+00 -5.91533700e+00 5.78913746e+00 | -4.40343356e+00 -5.91533700e+00 5.78913746e+00 2 -2.73943994e+00 4.87226036e+00 -2.02652815e+00 | -2.73943994e+00 4.87226036e+00 -2.02652815e+00 3 5.36670487e+00 -4.03352884e+00 -5.27446706e+00 | 5.36670487e+00 -4.03352884e+00 -5.27446706e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = FFT (Configuration in file "config-Mn-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)) = -19.0145843141 2^p V(r_1,...,r_N) = -19.0145843141 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 -4.45708668e+00 -6.90653742e+00 -8.16746711e+00 | -4.45708668e+00 -6.90653742e+00 -8.16746711e+00 1 5.81249396e+00 6.80476281e+00 -2.66322633e+00 | 5.81249396e+00 6.80476281e+00 -2.66322633e+00 2 3.14727259e+00 -3.94235504e+00 5.16413700e+00 | 3.14727259e+00 -3.94235504e+00 5.16413700e+00 3 -4.50267987e+00 4.04412964e+00 5.66655644e+00 | -4.50267987e+00 4.04412964e+00 5.66655644e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTT (Configuration in file "config-Pd-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)) = 58.2450489 2^p V(r_1,...,r_N) = 58.2450489 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 -4.75937461e+01 -5.36561993e+01 -5.05431906e+01 | -4.75937461e+01 -5.36561993e+01 -5.05431906e+01 1 5.55334509e+01 1.18871845e+02 -1.55247006e+02 | 5.55334509e+01 1.18871845e+02 -1.55247006e+02 2 9.54397748e+01 -1.77266085e+02 1.46265587e+02 | 9.54397748e+01 -1.77266085e+02 1.46265587e+02 3 -1.03379480e+02 1.12050439e+02 5.95246099e+01 | -1.03379480e+02 1.12050439e+02 5.95246099e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTF (Configuration in file "config-Pd-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.09850720113 2^p V(r_1,...,r_N) = -3.09850720113 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 -5.21991128e+00 -1.02919999e+01 -1.14011862e+01 | -5.21991128e+00 -1.02919999e+01 -1.14011862e+01 1 1.55905557e+00 1.16961621e+01 -1.04047674e+01 | 1.55905557e+00 1.16961621e+01 -1.04047674e+01 2 7.78887798e+00 -1.14903168e+01 9.50402508e+00 | 7.78887798e+00 -1.14903168e+01 9.50402508e+00 3 -4.12802227e+00 1.00861546e+01 1.23019285e+01 | -4.12802227e+00 1.00861546e+01 1.23019285e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFT (Configuration in file "config-Pd-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)) = 25.7041199883 2^p V(r_1,...,r_N) = 25.7041199883 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 -9.82192464e+01 -1.09968150e+02 -5.76252815e+01 | -9.82192464e+01 -1.09968150e+02 -5.76252815e+01 1 9.77453298e+01 1.07625007e+02 -1.14423411e+00 | 9.77453298e+01 1.07625007e+02 -1.14423411e+00 2 1.76510040e+01 -1.79755667e+01 2.38768321e+01 | 1.76510040e+01 -1.79755667e+01 2.38768321e+01 3 -1.71770873e+01 2.03187092e+01 3.48926835e+01 | -1.71770873e+01 2.03187092e+01 3.48926835e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFF (Configuration in file "config-Pd-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)) = 14.7540762549 2^p V(r_1,...,r_N) = 14.7540762549 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 -1.53232774e+01 -1.47703797e+01 -6.81701845e+00 | -1.53232774e+01 -1.47703797e+01 -6.81701845e+00 1 3.59085309e+01 5.61285125e+01 -7.39453014e+01 | 3.59085309e+01 5.61285125e+01 -7.39453014e+01 2 1.23681584e+01 -6.02109422e+01 6.00565553e+01 | 1.23681584e+01 -6.02109422e+01 6.00565553e+01 3 -3.29534120e+01 1.88528094e+01 2.07057646e+01 | -3.29534120e+01 1.88528094e+01 2.07057646e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTT (Configuration in file "config-Pd-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.97202124347 2^p V(r_1,...,r_N) = -3.97202124347 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 -1.21029609e+01 -1.00205364e+01 -7.12002722e+00 | -1.21029609e+01 -1.00205364e+01 -7.12002722e+00 1 7.14464219e+00 9.59872428e+00 -6.23141397e+00 | 7.14464219e+00 9.59872428e+00 -6.23141397e+00 2 9.30522222e+00 -6.31807264e+00 5.22355899e+00 | 9.30522222e+00 -6.31807264e+00 5.22355899e+00 3 -4.34690354e+00 6.73988472e+00 8.12788220e+00 | -4.34690354e+00 6.73988472e+00 8.12788220e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTF (Configuration in file "config-Pd-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)) = 96.3221295398 2^p V(r_1,...,r_N) = 96.3221295398 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 -1.26122208e+02 -7.42421707e+01 -9.70035078e+01 | -1.26122208e+02 -7.42421707e+01 -9.70035078e+01 1 3.35510535e+01 1.33059969e+02 -1.34860054e+02 | 3.35510535e+01 1.33059969e+02 -1.34860054e+02 2 3.23374250e+02 -2.34366176e+02 6.23816645e+01 | 3.23374250e+02 -2.34366176e+02 6.23816645e+01 3 -2.30803096e+02 1.75548378e+02 1.69481898e+02 | -2.30803096e+02 1.75548378e+02 1.69481898e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FFT (Configuration in file "config-Pd-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)) = 33.1894202768 2^p V(r_1,...,r_N) = 33.1894202768 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 -7.57597573e+01 -3.10514627e+01 -5.41638209e+01 | -7.57597573e+01 -3.10514627e+01 -5.41638209e+01 1 4.48268369e+01 6.55424853e+01 -8.61843113e+01 | 4.48268369e+01 6.55424853e+01 -8.61843113e+01 2 7.40130473e+01 -7.35738590e+01 8.62969618e+01 | 7.40130473e+01 -7.35738590e+01 8.62969618e+01 3 -4.30801268e+01 3.90828364e+01 5.40511703e+01 | -4.30801268e+01 3.90828364e+01 5.40511703e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TTT (Configuration in file "config-AlMnPd-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)) = -8.96205989819 2^p V(r_1,...,r_N) = -8.96205989819 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 -9.25129788e-01 -2.49526226e+00 -4.33966727e+00 | -9.25129788e-01 -2.49526226e+00 -4.33966727e+00 1 4.56733029e+00 1.02272673e+00 -3.57761626e+00 | 4.56733029e+00 1.02272673e+00 -3.57761626e+00 2 3.38518855e+00 -2.48380196e+00 2.27649269e+00 | 3.38518855e+00 -2.48380196e+00 2.27649269e+00 3 -7.02738906e+00 3.95633749e+00 5.64079084e+00 | -7.02738906e+00 3.95633749e+00 5.64079084e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TTF (Configuration in file "config-AlMnPd-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)) = -8.9646140041 2^p V(r_1,...,r_N) = -8.9646140041 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 -3.16429491e+00 -4.90523257e+00 -3.83522666e+00 | -3.16429491e+00 -4.90523257e+00 -3.83522666e+00 1 5.65946843e+00 5.28612265e+00 -4.67852497e+00 | 5.65946843e+00 5.28612265e+00 -4.67852497e+00 2 1.92755456e+00 -3.50458434e+00 4.17967050e+00 | 1.92755456e+00 -3.50458434e+00 4.17967050e+00 3 -4.42272808e+00 3.12369425e+00 4.33408113e+00 | -4.42272808e+00 3.12369425e+00 4.33408113e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TFT (Configuration in file "config-AlMnPd-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)) = -4.17221700898 2^p V(r_1,...,r_N) = -4.17221700898 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 -1.23057944e+01 -1.00276701e+01 -1.58699724e+01 | -1.23057944e+01 -1.00276701e+01 -1.58699724e+01 1 9.32729943e+00 7.36636280e+00 -5.34143220e+00 | 9.32729943e+00 7.36636280e+00 -5.34143220e+00 2 1.36087024e+01 -5.79285716e+00 1.39102110e+01 | 1.36087024e+01 -5.79285716e+00 1.39102110e+01 3 -1.06302074e+01 8.45416444e+00 7.30119353e+00 | -1.06302074e+01 8.45416444e+00 7.30119353e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TFF (Configuration in file "config-AlMnPd-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)) = -4.13175067514 2^p V(r_1,...,r_N) = -4.13175067514 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 -1.15095710e+01 -1.50988872e+01 -1.35836260e+01 | -1.15095710e+01 -1.50988872e+01 -1.35836260e+01 1 7.69076668e+00 5.76991577e+00 -2.91596441e+00 | 7.69076668e+00 5.76991577e+00 -2.91596441e+00 2 9.87692380e+00 -6.26690137e+00 3.48906338e+00 | 9.87692380e+00 -6.26690137e+00 3.48906338e+00 3 -6.05811942e+00 1.55958728e+01 1.30105271e+01 | -6.05811942e+00 1.55958728e+01 1.30105271e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = FTT (Configuration in file "config-AlMnPd-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.23008693129 2^p V(r_1,...,r_N) = -7.23008693129 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 -5.95495478e+00 -8.60483970e+00 -8.21268672e+00 | -5.95495478e+00 -8.60483970e+00 -8.21268672e+00 1 4.21349472e+00 2.33519566e+00 -2.90226210e+00 | 4.21349472e+00 2.33519566e+00 -2.90226210e+00 2 4.50787156e+00 -1.92405123e+00 1.41204391e+00 | 4.50787156e+00 -1.92405123e+00 1.41204391e+00 3 -2.76641149e+00 8.19369527e+00 9.70290491e+00 | -2.76641149e+00 8.19369527e+00 9.70290491e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = FTF (Configuration in file "config-AlMnPd-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 4.08494929653 2^p V(r_1,...,r_N) = 4.08494929653 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 -1.65651769e+01 -2.48302056e+01 -3.14516132e+01 | -1.65651769e+01 -2.48302056e+01 -3.14516132e+01 1 5.28612921e+00 4.24331079e+00 -8.08394341e+00 | 5.28612921e+00 4.24331079e+00 -8.08394341e+00 2 2.31678408e+01 -2.33363394e+01 5.43332992e+00 | 2.31678408e+01 -2.33363394e+01 5.43332992e+00 3 -1.18887930e+01 4.39232342e+01 3.41022267e+01 | -1.18887930e+01 4.39232342e+01 3.41022267e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = FFT (Configuration in file "config-AlMnPd-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.14118111033 2^p V(r_1,...,r_N) = -8.14118111033 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 -4.30385658e+00 -3.67577413e+00 -1.11082234e+00 | -4.30385658e+00 -3.67577413e+00 -1.11082234e+00 1 8.75007449e+00 3.52453234e+00 -9.62362837e+00 | 8.75007449e+00 3.52453234e+00 -9.62362837e+00 2 1.71172917e+00 -1.49031334e+00 1.88727006e+00 | 1.71172917e+00 -1.49031334e+00 1.88727006e+00 3 -6.15794709e+00 1.64155514e+00 8.84718065e+00 | -6.15794709e+00 1.64155514e+00 8.84718065e+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.