!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : Sim_LAMMPS_MEAM_GaoOterodelaRozaAouadi_2013_AgTaO__SM_485325656366_000 Supported species : Ag O Ta random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTT (Configuration in file "config-Ag-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)) = 2.63526304789 2^p V(r_1,...,r_N) = 2.63526304789 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 -5.73732477e+00 -2.99317923e+01 -1.98862542e+01 | -5.73732477e+00 -2.99317923e+01 -1.98862542e+01 1 1.01785735e+01 8.47002293e+00 -8.56655585e+00 | 1.01785735e+01 8.47002293e+00 -8.56655585e+00 2 3.33507188e+00 -8.24902973e+00 5.05423785e+00 | 3.33507188e+00 -8.24902973e+00 5.05423785e+00 3 -7.77632063e+00 2.97107991e+01 2.33985722e+01 | -7.77632063e+00 2.97107991e+01 2.33985722e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTF (Configuration in file "config-Ag-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)) = -3.00243513358 2^p V(r_1,...,r_N) = -3.00243513358 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 -2.02990093e+00 -3.24518313e+00 -2.69842761e+00 | -2.02990093e+00 -3.24518313e+00 -2.69842761e+00 1 2.54176625e+00 8.02980020e+00 -9.09204812e+00 | 2.54176625e+00 8.02980020e+00 -9.09204812e+00 2 5.90090849e+00 -1.07857571e+01 9.51271482e+00 | 5.90090849e+00 -1.07857571e+01 9.51271482e+00 3 -6.41277381e+00 6.00114000e+00 2.27776092e+00 | -6.41277381e+00 6.00114000e+00 2.27776092e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFT (Configuration in file "config-Ag-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)) = 18.3678047785 2^p V(r_1,...,r_N) = 18.3678047785 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 -1.54475067e+01 -3.40526782e+01 -2.66675617e+01 | -1.54475067e+01 -3.40526782e+01 -2.66675617e+01 1 2.85707258e+01 8.93729760e+00 -2.75484083e+01 | 2.85707258e+01 8.93729760e+00 -2.75484083e+01 2 3.82740517e+01 -5.04297178e+01 2.20346682e+01 | 3.82740517e+01 -5.04297178e+01 2.20346682e+01 3 -5.13972708e+01 7.55450984e+01 3.21813017e+01 | -5.13972708e+01 7.55450984e+01 3.21813017e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFF (Configuration in file "config-Ag-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.73084487096 2^p V(r_1,...,r_N) = 2.73084487096 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 -1.50851889e+01 -2.05587206e+01 -1.19512311e+01 | -1.50851889e+01 -2.05587206e+01 -1.19512311e+01 1 1.51560451e+01 1.97705754e+01 -9.37127967e+00 | 1.51560451e+01 1.97705754e+01 -9.37127967e+00 2 9.42181975e+00 -8.19605676e+00 1.17081494e+01 | 9.42181975e+00 -8.19605676e+00 1.17081494e+01 3 -9.49267602e+00 8.98420199e+00 9.61436139e+00 | -9.49267602e+00 8.98420199e+00 9.61436139e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTT (Configuration in file "config-Ag-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)) = -0.498825652652 2^p V(r_1,...,r_N) = -0.498825652652 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 -4.05847841e+00 -3.32309299e+00 -5.08931762e+00 | -4.05847841e+00 -3.32309299e+00 -5.08931762e+00 1 7.38520557e+00 9.06682155e+00 -1.23563142e+01 | 7.38520557e+00 9.06682155e+00 -1.23563142e+01 2 1.23119667e+01 -1.13401194e+01 9.96366443e+00 | 1.23119667e+01 -1.13401194e+01 9.96366443e+00 3 -1.56386938e+01 5.59639090e+00 7.48196744e+00 | -1.56386938e+01 5.59639090e+00 7.48196744e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTF (Configuration in file "config-Ag-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)) = 4.24982577626 2^p V(r_1,...,r_N) = 4.24982577626 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 -1.09305354e+01 -1.55740277e+01 -9.02020186e+00 | -1.09305354e+01 -1.55740277e+01 -9.02020186e+00 1 3.98399944e+01 2.03260292e+01 -1.98989823e+01 | 3.98399944e+01 2.03260292e+01 -1.98989823e+01 2 4.07663555e+00 -5.54304274e+00 7.05370082e+00 | 4.07663555e+00 -5.54304274e+00 7.05370082e+00 3 -3.29860946e+01 7.91041297e-01 2.18654833e+01 | -3.29860946e+01 7.91041297e-01 2.18654833e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FFT (Configuration in file "config-Ag-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)) = 2.70723316634 2^p V(r_1,...,r_N) = 2.70723316634 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 -9.12028643e+00 -1.44960822e+01 -1.16364823e+01 | -9.12028643e+00 -1.44960822e+01 -1.16364823e+01 1 2.06401015e+01 9.61995386e+00 -1.89434216e+01 | 2.06401015e+01 9.61995386e+00 -1.89434216e+01 2 7.52003077e+00 -5.81450122e+00 7.77138081e+00 | 7.52003077e+00 -5.81450122e+00 7.77138081e+00 3 -1.90398458e+01 1.06906296e+01 2.28085230e+01 | -1.90398458e+01 1.06906296e+01 2.28085230e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = TTT (Configuration in file "config-O-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)) = -1.54337573055 2^p V(r_1,...,r_N) = -1.54337573055 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 9.31749923e-01 1.19395930e+00 1.14335165e+00 | 9.31749923e-01 1.19395930e+00 1.14335165e+00 1 -1.19255677e+00 -9.04348603e-01 7.96179722e-01 | -1.19255677e+00 -9.04348603e-01 7.96179722e-01 2 -1.04877540e+00 5.56728341e-01 -6.96743182e-01 | -1.04877540e+00 5.56728341e-01 -6.96743182e-01 3 1.30958224e+00 -8.46339037e-01 -1.24278819e+00 | 1.30958224e+00 -8.46339037e-01 -1.24278819e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = TTF (Configuration in file "config-O-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)) = -1.70062312425 2^p V(r_1,...,r_N) = -1.70062312425 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 1.59717470e+00 5.02141218e-01 1.83629335e+00 | 1.59717470e+00 5.02141218e-01 1.83629335e+00 1 -5.18038781e-01 -9.08462963e-01 1.19815608e+00 | -5.18038781e-01 -9.08462963e-01 1.19815608e+00 2 -1.82395825e+00 5.75659278e-01 -2.48772557e+00 | -1.82395825e+00 5.75659278e-01 -2.48772557e+00 3 7.44822334e-01 -1.69337533e-01 -5.46723861e-01 | 7.44822334e-01 -1.69337533e-01 -5.46723861e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = TFT (Configuration in file "config-O-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.93335074008 2^p V(r_1,...,r_N) = -3.93335074008 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 8.89038639e-01 2.31155183e+00 3.16614384e+00 | 8.89038639e-01 2.31155183e+00 3.16614384e+00 1 -5.88304613e-01 -9.54175251e-01 1.23877002e+00 | -5.88304613e-01 -9.54175251e-01 1.23877002e+00 2 -1.79158506e+00 1.91013740e+00 -1.11481907e+00 | -1.79158506e+00 1.91013740e+00 -1.11481907e+00 3 1.49085103e+00 -3.26751398e+00 -3.29009479e+00 | 1.49085103e+00 -3.26751398e+00 -3.29009479e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = TFF (Configuration in file "config-O-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)) = -3.19473272453 2^p V(r_1,...,r_N) = -3.19473272453 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 1.59526727e+00 2.15616848e+00 2.00944699e+00 | 1.59526727e+00 2.15616848e+00 2.00944699e+00 1 -1.92797654e+00 -7.77588272e-01 1.98248378e+00 | -1.92797654e+00 -7.77588272e-01 1.98248378e+00 2 -1.45761529e+00 8.60898160e-01 -5.80126734e-01 | -1.45761529e+00 8.60898160e-01 -5.80126734e-01 3 1.79032456e+00 -2.23947837e+00 -3.41180403e+00 | 1.79032456e+00 -2.23947837e+00 -3.41180403e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = FTT (Configuration in file "config-O-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)) = -2.55138154472 2^p V(r_1,...,r_N) = -2.55138154472 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 1.62109355e+00 1.47608290e+00 1.19719097e+00 | 1.62109355e+00 1.47608290e+00 1.19719097e+00 1 -2.04317429e+00 -8.57862448e-01 2.07908548e+00 | -2.04317429e+00 -8.57862448e-01 2.07908548e+00 2 -7.19348533e-01 1.10673181e+00 -1.15205968e+00 | -7.19348533e-01 1.10673181e+00 -1.15205968e+00 3 1.14142927e+00 -1.72495226e+00 -2.12421676e+00 | 1.14142927e+00 -1.72495226e+00 -2.12421676e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = FTF (Configuration in file "config-O-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)) = -3.86673379109 2^p V(r_1,...,r_N) = -3.86673379109 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 3.00962161e+00 6.94225866e-01 3.43660965e+00 | 3.00962161e+00 6.94225866e-01 3.43660965e+00 1 -1.52707767e+00 -5.87685869e-01 1.90208945e+00 | -1.52707767e+00 -5.87685869e-01 1.90208945e+00 2 -3.47235313e+00 1.04879660e+00 -2.61872753e+00 | -3.47235313e+00 1.04879660e+00 -2.61872753e+00 3 1.98980919e+00 -1.15533660e+00 -2.71997156e+00 | 1.98980919e+00 -1.15533660e+00 -2.71997156e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = FFT (Configuration in file "config-O-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)) = -2.01335855139 2^p V(r_1,...,r_N) = -2.01335855139 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 9.99169352e-01 1.48118374e+00 9.19083047e-01 | 9.99169352e-01 1.48118374e+00 9.19083047e-01 1 -1.78411359e+00 -1.10849675e+00 1.71287502e+00 | -1.78411359e+00 -1.10849675e+00 1.71287502e+00 2 -8.19049461e-01 5.77103876e-01 -6.72721391e-01 | -8.19049461e-01 5.77103876e-01 -6.72721391e-01 3 1.60399370e+00 -9.49790868e-01 -1.95923668e+00 | 1.60399370e+00 -9.49790868e-01 -1.95923668e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTT (Configuration in file "config-Ta-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)) = 13.2655723737 2^p V(r_1,...,r_N) = 13.2655723737 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 -2.91866800e+01 -6.38600546e+01 -4.62619815e+01 | -2.91866800e+01 -6.38600546e+01 -4.62619815e+01 1 7.24947856e+01 5.02739360e+01 -1.45059168e+01 | 7.24947856e+01 5.02739360e+01 -1.45059168e+01 2 8.72452750e+00 -9.37931538e+00 5.26851340e+00 | 8.72452750e+00 -9.37931538e+00 5.26851340e+00 3 -5.20326331e+01 2.29654340e+01 5.54993849e+01 | -5.20326331e+01 2.29654340e+01 5.54993849e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTF (Configuration in file "config-Ta-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)) = 17.52211537 2^p V(r_1,...,r_N) = 17.52211537 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 -9.89476432e+00 -4.02832485e+00 -1.52065901e+01 | -9.89476432e+00 -4.02832485e+00 -1.52065901e+01 1 7.94891877e+00 3.76412742e+00 -9.74584161e+00 | 7.94891877e+00 3.76412742e+00 -9.74584161e+00 2 9.99364992e+01 -1.47221078e+02 1.99902935e+01 | 9.99364992e+01 -1.47221078e+02 1.99902935e+01 3 -9.79906537e+01 1.47485275e+02 4.96213812e+00 | -9.79906537e+01 1.47485275e+02 4.96213812e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFT (Configuration in file "config-Ta-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)) = -12.3125620185 2^p V(r_1,...,r_N) = -12.3125620185 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 -5.11853236e-01 -2.00706866e+00 1.10624199e+00 | -5.11853236e-01 -2.00706866e+00 1.10624199e+00 1 3.13325867e+00 1.04188466e+01 -1.96646611e+01 | 3.13325867e+00 1.04188466e+01 -1.96646611e+01 2 4.62485871e+00 -1.70055917e+01 1.74811295e+01 | 4.62485871e+00 -1.70055917e+01 1.74811295e+01 3 -7.24626415e+00 8.59381371e+00 1.07728955e+00 | -7.24626415e+00 8.59381371e+00 1.07728955e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFF (Configuration in file "config-Ta-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.69912061717 2^p V(r_1,...,r_N) = -9.69912061717 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 -9.20287897e+00 -6.58204669e+00 -1.40470791e+01 | -9.20287897e+00 -6.58204669e+00 -1.40470791e+01 1 2.26245122e+00 4.38406587e+00 -4.35672622e+00 | 2.26245122e+00 4.38406587e+00 -4.35672622e+00 2 2.12052699e+01 -1.50166133e+01 7.36247286e+00 | 2.12052699e+01 -1.50166133e+01 7.36247286e+00 3 -1.42648421e+01 1.72145941e+01 1.10413325e+01 | -1.42648421e+01 1.72145941e+01 1.10413325e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTT (Configuration in file "config-Ta-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.04343884797 2^p V(r_1,...,r_N) = -4.04343884797 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 -1.13398405e+01 -5.16920216e+00 -1.02243626e+01 | -1.13398405e+01 -5.16920216e+00 -1.02243626e+01 1 1.23508450e+01 1.47030391e+01 -2.57605268e+01 | 1.23508450e+01 1.47030391e+01 -2.57605268e+01 2 2.39371245e+01 -2.14471632e+01 1.90649412e+01 | 2.39371245e+01 -2.14471632e+01 1.90649412e+01 3 -2.49481289e+01 1.19133262e+01 1.69199482e+01 | -2.49481289e+01 1.19133262e+01 1.69199482e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTF (Configuration in file "config-Ta-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)) = -10.8727315573 2^p V(r_1,...,r_N) = -10.8727315573 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 -5.92827563e+00 -7.31418641e+00 -7.85640398e+00 | -5.92827563e+00 -7.31418641e+00 -7.85640398e+00 1 6.55698268e+00 1.08337510e+01 -1.63175894e+01 | 6.55698268e+00 1.08337510e+01 -1.63175894e+01 2 9.67124348e+00 -1.79294773e+01 1.62351276e+01 | 9.67124348e+00 -1.79294773e+01 1.62351276e+01 3 -1.02999505e+01 1.44099128e+01 7.93886581e+00 | -1.02999505e+01 1.44099128e+01 7.93886581e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FFT (Configuration in file "config-Ta-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.55852167248 2^p V(r_1,...,r_N) = -3.55852167248 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 -1.86965143e+01 -1.95414808e+01 -4.50968735e+00 | -1.86965143e+01 -1.95414808e+01 -4.50968735e+00 1 1.29372839e+01 4.57201270e+01 -2.76219798e+01 | 1.29372839e+01 4.57201270e+01 -2.76219798e+01 2 2.49950320e+00 -3.34606864e+01 4.06894854e+01 | 2.49950320e+00 -3.34606864e+01 4.06894854e+01 3 3.25972719e+00 7.28204021e+00 -8.55781830e+00 | 3.25972719e+00 7.28204021e+00 -8.55781830e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = TTT (Configuration in file "config-AgOTa-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)) = -8.60270687459 2^p V(r_1,...,r_N) = -8.60270687459 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.13456132e+00 -6.19125778e+00 -6.53871925e+00 | -8.13456132e+00 -6.19125778e+00 -6.53871925e+00 1 4.43123488e+00 6.03378207e+00 -3.09346433e+00 | 4.43123488e+00 6.03378207e+00 -3.09346433e+00 2 2.56738835e+00 -2.31927293e-01 6.52079110e+00 | 2.56738835e+00 -2.31927293e-01 6.52079110e+00 3 1.13593810e+00 3.89403003e-01 3.11139249e+00 | 1.13593810e+00 3.89403003e-01 3.11139249e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = TTF (Configuration in file "config-AgOTa-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)) = 12.7152795242 2^p V(r_1,...,r_N) = 12.7152795242 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 -9.22856152e+00 -6.91303626e+01 -7.20125026e+01 | -9.22856152e+00 -6.91303626e+01 -7.20125026e+01 1 2.41121233e+01 -3.91330840e+01 1.65880709e+01 | 2.41121233e+01 -3.91330840e+01 1.65880709e+01 2 3.63160006e+01 1.81352376e+01 -3.15668134e+01 | 3.63160006e+01 1.81352376e+01 -3.15668134e+01 3 -5.11995624e+01 9.01282091e+01 8.69912451e+01 | -5.11995624e+01 9.01282091e+01 8.69912451e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = TFT (Configuration in file "config-AgOTa-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.64367747924 2^p V(r_1,...,r_N) = -7.64367747924 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 -4.43482644e+00 -6.42823430e+00 -2.56562434e+00 | -4.43482644e+00 -6.42823430e+00 -2.56562434e+00 1 5.71959776e+00 1.05760277e+00 1.25054782e+00 | 5.71959776e+00 1.05760277e+00 1.25054782e+00 2 9.49639357e+00 -8.47701230e+00 -2.80869492e+00 | 9.49639357e+00 -8.47701230e+00 -2.80869492e+00 3 -1.07811649e+01 1.38476438e+01 4.12377143e+00 | -1.07811649e+01 1.38476438e+01 4.12377143e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = TFF (Configuration in file "config-AgOTa-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.61270506476 2^p V(r_1,...,r_N) = -5.61270506476 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 -9.59844796e+00 -6.61877402e+00 -9.97639702e+00 | -9.59844796e+00 -6.61877402e+00 -9.97639702e+00 1 3.27645101e+00 1.34582859e+01 -1.34365937e+01 | 3.27645101e+00 1.34582859e+01 -1.34365937e+01 2 9.91068255e+00 -1.29868219e+01 2.06119955e+01 | 9.91068255e+00 -1.29868219e+01 2.06119955e+01 3 -3.58868561e+00 6.14731000e+00 2.80099516e+00 | -3.58868561e+00 6.14731000e+00 2.80099516e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = FTT (Configuration in file "config-AgOTa-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)) = -1.21434975033 2^p V(r_1,...,r_N) = -1.21434975033 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 -2.09551310e+01 -1.53353365e+01 -9.11017074e+00 | -2.09551310e+01 -1.53353365e+01 -9.11017074e+00 1 1.65821942e+01 1.50757590e+01 -1.29433352e+01 | 1.65821942e+01 1.50757590e+01 -1.29433352e+01 2 1.28697527e+01 -3.64658874e+00 1.26980384e+01 | 1.28697527e+01 -3.64658874e+00 1.26980384e+01 3 -8.49681588e+00 3.90616616e+00 9.35546752e+00 | -8.49681588e+00 3.90616616e+00 9.35546752e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = FTF (Configuration in file "config-AgOTa-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)) = -3.93653877929 2^p V(r_1,...,r_N) = -3.93653877929 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 -1.84004190e+01 -2.43272471e+01 -2.35020001e+01 | -1.84004190e+01 -2.43272471e+01 -2.35020001e+01 1 1.11212889e+01 2.66995139e+00 7.13176353e+00 | 1.11212889e+01 2.66995139e+00 7.13176353e+00 2 1.17037132e+01 8.71422000e+00 3.30374579e+00 | 1.17037132e+01 8.71422000e+00 3.30374579e+00 3 -4.42458315e+00 1.29430757e+01 1.30664908e+01 | -4.42458315e+00 1.29430757e+01 1.30664908e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag O Ta, PBC = FFT (Configuration in file "config-AgOTa-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.65648045514 2^p V(r_1,...,r_N) = 7.65648045514 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 1.85509797e+01 -4.99536376e+01 -2.28550072e+01 | 1.85509797e+01 -4.99536376e+01 -2.28550072e+01 1 1.69023051e+01 1.28415502e+01 -2.34244739e+01 | 1.69023051e+01 1.28415502e+01 -2.34244739e+01 2 2.19535891e+00 -2.97149530e+01 4.90334801e+00 | 2.19535891e+00 -2.97149530e+01 4.90334801e+00 3 -3.76486437e+01 6.68270403e+01 4.13761331e+01 | -3.76486437e+01 6.68270403e+01 4.13761331e+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.