!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Polymorphic_Zhou_2004_CuTa__SM_453737875254_000 Supported species : Cu Ta random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.73088441988 2^p V(r_1,...,r_N) = -3.73088441988 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 -2.95086805e+00 -5.91645993e+00 -6.08064519e+00 | -2.95086805e+00 -5.91645993e+00 -6.08064519e+00 1 2.38142059e+00 1.88605588e+00 -1.67982005e+00 | 2.38142059e+00 1.88605588e+00 -1.67982005e+00 2 1.72864254e+00 -2.07024260e+00 2.95967193e+00 | 1.72864254e+00 -2.07024260e+00 2.95967193e+00 3 -1.15919507e+00 6.10064666e+00 4.80079331e+00 | -1.15919507e+00 6.10064666e+00 4.80079331e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.21989173576 2^p V(r_1,...,r_N) = -4.21989173576 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 8.78391635e-01 5.93645251e-01 6.57870003e-01 | 8.78391635e-01 5.93645251e-01 6.57870003e-01 1 6.02910892e-01 1.02507529e+00 -2.29444766e+00 | 6.02910892e-01 1.02507529e+00 -2.29444766e+00 2 3.23621836e+00 -4.17172568e+00 8.93214176e-01 | 3.23621836e+00 -4.17172568e+00 8.93214176e-01 3 -4.71752088e+00 2.55300514e+00 7.43363481e-01 | -4.71752088e+00 2.55300514e+00 7.43363481e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.79510598427 2^p V(r_1,...,r_N) = -2.79510598427 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 -3.07502202e+00 -3.00992167e+00 -3.70310296e+00 | -3.07502202e+00 -3.00992167e+00 -3.70310296e+00 1 2.99919019e+00 3.16913769e+00 -4.27078304e+00 | 2.99919019e+00 3.16913769e+00 -4.27078304e+00 2 6.59222533e+00 -5.70108923e+00 3.92464794e+00 | 6.59222533e+00 -5.70108923e+00 3.92464794e+00 3 -6.51639350e+00 5.54187321e+00 4.04923807e+00 | -6.51639350e+00 5.54187321e+00 4.04923807e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.84968974896 2^p V(r_1,...,r_N) = -3.84968974896 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 -2.32592847e+00 -2.46869763e+00 -4.25083930e+00 | -2.32592847e+00 -2.46869763e+00 -4.25083930e+00 1 1.52011836e+00 2.14882118e+00 -2.08035529e+00 | 1.52011836e+00 2.14882118e+00 -2.08035529e+00 2 5.07405575e+00 -4.77622651e+00 2.99924017e+00 | 5.07405575e+00 -4.77622651e+00 2.99924017e+00 3 -4.26824564e+00 5.09610296e+00 3.33195442e+00 | -4.26824564e+00 5.09610296e+00 3.33195442e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.714965517151 2^p V(r_1,...,r_N) = 0.714965517151 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 -4.58611395e+00 -6.23223738e+00 -5.86268645e+00 | -4.58611395e+00 -6.23223738e+00 -5.86268645e+00 1 1.60722340e+01 1.27244444e+00 -1.32170649e+01 | 1.60722340e+01 1.27244444e+00 -1.32170649e+01 2 3.09375496e+00 -3.13667434e+00 2.75763168e+00 | 3.09375496e+00 -3.13667434e+00 2.75763168e+00 3 -1.45798750e+01 8.09646728e+00 1.63221197e+01 | -1.45798750e+01 8.09646728e+00 1.63221197e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.0842591967 2^p V(r_1,...,r_N) = -1.0842591967 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 -5.76846066e+00 -1.22772287e+01 -7.12263169e+00 | -5.76846066e+00 -1.22772287e+01 -7.12263169e+00 1 8.76937684e+00 6.04024772e+00 -5.80441487e+00 | 8.76937684e+00 6.04024772e+00 -5.80441487e+00 2 2.60654802e+00 -9.11967010e-01 2.48926908e+00 | 2.60654802e+00 -9.11967010e-01 2.48926908e+00 3 -5.60746420e+00 7.14894802e+00 1.04377775e+01 | -5.60746420e+00 7.14894802e+00 1.04377775e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.01249975244 2^p V(r_1,...,r_N) = -5.01249975244 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 -1.87181919e+00 -3.07269950e+00 -1.33919649e+00 | -1.87181919e+00 -3.07269950e+00 -1.33919649e+00 1 1.62896453e+00 1.93287138e+00 -1.42155120e+00 | 1.62896453e+00 1.93287138e+00 -1.42155120e+00 2 8.92105613e-01 -4.72318240e-01 1.19274585e+00 | 8.92105613e-01 -4.72318240e-01 1.19274585e+00 3 -6.49250953e-01 1.61214636e+00 1.56800183e+00 | -6.49250953e-01 1.61214636e+00 1.56800183e+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)) = -10.6494919879 2^p V(r_1,...,r_N) = -10.6494919879 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 -1.08986553e+01 -1.07003519e+01 -6.79208624e+00 | -1.08986553e+01 -1.07003519e+01 -6.79208624e+00 1 1.72167361e+01 3.29422271e+00 -1.83461264e+01 | 1.72167361e+01 3.29422271e+00 -1.83461264e+01 2 8.32812270e+00 -3.79146381e+00 7.79866099e+00 | 8.32812270e+00 -3.79146381e+00 7.79866099e+00 3 -1.46462035e+01 1.11975930e+01 1.73395516e+01 | -1.46462035e+01 1.11975930e+01 1.73395516e+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)) = 1.14220663959 2^p V(r_1,...,r_N) = 1.14220663959 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 -2.51313514e+01 -1.70442950e+01 -2.19585338e+01 | -2.51313514e+01 -1.70442950e+01 -2.19585338e+01 1 3.13859411e+01 7.57612858e+00 -2.94228565e+01 | 3.13859411e+01 7.57612858e+00 -2.94228565e+01 2 1.92499649e+01 -1.42521362e+01 1.77080950e+01 | 1.92499649e+01 -1.42521362e+01 1.77080950e+01 3 -2.55045546e+01 2.37203026e+01 3.36732953e+01 | -2.55045546e+01 2.37203026e+01 3.36732953e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.53891342552 2^p V(r_1,...,r_N) = -2.53891342552 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 -2.40674121e+01 -2.92913199e+01 -2.86809182e+01 | -2.40674121e+01 -2.92913199e+01 -2.86809182e+01 1 2.45102621e+01 2.13109107e+01 -7.96516965e+00 | 2.45102621e+01 2.13109107e+01 -7.96516965e+00 2 1.20235235e+01 -1.09823813e+01 1.62273011e+01 | 1.20235235e+01 -1.09823813e+01 1.62273011e+01 3 -1.24663735e+01 1.89627905e+01 2.04187868e+01 | -1.24663735e+01 1.89627905e+01 2.04187868e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -7.71235485185 2^p V(r_1,...,r_N) = -7.71235485185 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 -1.86145800e+01 -1.23047805e+01 -1.24324048e+01 | -1.86145800e+01 -1.23047805e+01 -1.24324048e+01 1 1.64410339e+01 2.36578931e+01 -1.17621315e+01 | 1.64410339e+01 2.36578931e+01 -1.17621315e+01 2 1.19730863e+01 -1.98395561e+01 1.74349092e+01 | 1.19730863e+01 -1.98395561e+01 1.74349092e+01 3 -9.79954018e+00 8.48644343e+00 6.75962715e+00 | -9.79954018e+00 8.48644343e+00 6.75962715e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -6.9663705534 2^p V(r_1,...,r_N) = -6.9663705534 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 -1.76658772e+01 -1.45309502e+01 -9.59475461e+00 | -1.76658772e+01 -1.45309502e+01 -9.59475461e+00 1 2.43462587e+01 8.03874433e+00 -2.09596879e+01 | 2.43462587e+01 8.03874433e+00 -2.09596879e+01 2 8.40280484e+00 -1.16626634e+01 9.34076464e+00 | 8.40280484e+00 -1.16626634e+01 9.34076464e+00 3 -1.50831864e+01 1.81548693e+01 2.12136779e+01 | -1.50831864e+01 1.81548693e+01 2.12136779e+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)) = 6.65005310838 2^p V(r_1,...,r_N) = 6.65005310838 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 -3.68056261e+01 -1.38258852e+01 -4.15339133e+01 | -3.68056261e+01 -1.38258852e+01 -4.15339133e+01 1 1.55136712e+01 1.07331763e+01 -1.85122886e+01 | 1.55136712e+01 1.07331763e+01 -1.85122886e+01 2 4.59900814e+01 -2.44228806e+01 3.07516083e+01 | 4.59900814e+01 -2.44228806e+01 3.07516083e+01 3 -2.46981265e+01 2.75155895e+01 2.92945936e+01 | -2.46981265e+01 2.75155895e+01 2.92945936e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -12.159795068 2^p V(r_1,...,r_N) = -12.159795068 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 -6.20847077e+00 -1.23116840e+01 -7.21623943e+00 | -6.20847077e+00 -1.23116840e+01 -7.21623943e+00 1 1.43100248e+01 8.31381933e+00 -1.42591445e+01 | 1.43100248e+01 8.31381933e+00 -1.42591445e+01 2 4.92847417e+00 -4.44652031e+00 4.23205350e+00 | 4.92847417e+00 -4.44652031e+00 4.23205350e+00 3 -1.30300282e+01 8.44438497e+00 1.72433304e+01 | -1.30300282e+01 8.44438497e+00 1.72433304e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTT (Configuration in file "config-CuTa-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)) = -1.26291953772 2^p V(r_1,...,r_N) = -1.26291953772 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 -1.93751780e+01 -2.60224148e+00 -1.94581833e+01 | -1.93751780e+01 -2.60224148e+00 -1.94581833e+01 1 6.08541008e+00 5.66575308e+00 -3.47316268e+00 | 6.08541008e+00 5.66575308e+00 -3.47316268e+00 2 2.18762697e+01 -1.51434569e+01 1.21808910e+01 | 2.18762697e+01 -1.51434569e+01 1.21808910e+01 3 -8.58650176e+00 1.20799454e+01 1.07504551e+01 | -8.58650176e+00 1.20799454e+01 1.07504551e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTF (Configuration in file "config-CuTa-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)) = -1.56923229502 2^p V(r_1,...,r_N) = -1.56923229502 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 -2.14058722e+01 -1.61372323e+01 -2.08155819e+01 | -2.14058722e+01 -1.61372323e+01 -2.08155819e+01 1 7.87882089e+00 1.05622457e+01 -6.73943209e+00 | 7.87882089e+00 1.05622457e+01 -6.73943209e+00 2 2.16446210e+01 -7.14921447e+00 1.97880978e+01 | 2.16446210e+01 -7.14921447e+00 1.97880978e+01 3 -8.11756975e+00 1.27242010e+01 7.76691617e+00 | -8.11756975e+00 1.27242010e+01 7.76691617e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFT (Configuration in file "config-CuTa-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)) = -3.1574682797 2^p V(r_1,...,r_N) = -3.1574682797 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 -1.09929031e+01 -6.38817190e+00 -7.94188419e+00 | -1.09929031e+01 -6.38817190e+00 -7.94188419e+00 1 9.13565370e+00 1.89850752e+01 -1.51216492e+01 | 9.13565370e+00 1.89850752e+01 -1.51216492e+01 2 8.08856459e+00 -1.61502902e+01 1.80890060e+01 | 8.08856459e+00 -1.61502902e+01 1.80890060e+01 3 -6.23131518e+00 3.55338694e+00 4.97452739e+00 | -6.23131518e+00 3.55338694e+00 4.97452739e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFF (Configuration in file "config-CuTa-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)) = 2.77454063537 2^p V(r_1,...,r_N) = 2.77454063537 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 -1.17840440e+01 -9.82209262e+00 -9.53310306e+00 | -1.17840440e+01 -9.82209262e+00 -9.53310306e+00 1 1.32551501e+01 1.32233721e+01 -2.94861983e+01 | 1.32551501e+01 1.32233721e+01 -2.94861983e+01 2 1.87362313e+01 -1.95631468e+01 2.77937548e+01 | 1.87362313e+01 -1.95631468e+01 2.77937548e+01 3 -2.02073374e+01 1.61618673e+01 1.12255466e+01 | -2.02073374e+01 1.61618673e+01 1.12255466e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTT (Configuration in file "config-CuTa-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)) = -5.83199670674 2^p V(r_1,...,r_N) = -5.83199670674 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 -4.21607171e+00 -5.74896094e+00 -5.58502884e+00 | -4.21607171e+00 -5.74896094e+00 -5.58502884e+00 1 4.56586519e+00 7.63401273e+00 -1.06915846e+01 | 4.56586519e+00 7.63401273e+00 -1.06915846e+01 2 6.57965078e+00 -1.24953745e+01 1.06127269e+01 | 6.57965078e+00 -1.24953745e+01 1.06127269e+01 3 -6.92944426e+00 1.06103227e+01 5.66388650e+00 | -6.92944426e+00 1.06103227e+01 5.66388650e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTF (Configuration in file "config-CuTa-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.13125681556 2^p V(r_1,...,r_N) = -8.13125681556 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 -1.53768861e+00 2.94856493e-01 -4.50447286e-01 | -1.53768861e+00 2.94856493e-01 -4.50447286e-01 1 6.95614877e+00 2.91960284e+00 -7.58956633e+00 | 6.95614877e+00 2.91960284e+00 -7.58956633e+00 2 4.85409516e+00 -6.76415745e+00 1.88145690e+00 | 4.85409516e+00 -6.76415745e+00 1.88145690e+00 3 -1.02725553e+01 3.54969812e+00 6.15855671e+00 | -1.02725553e+01 3.54969812e+00 6.15855671e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FFT (Configuration in file "config-CuTa-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)) = -9.66727963615 2^p V(r_1,...,r_N) = -9.66727963615 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 -7.67100814e+00 -8.37311621e+00 -3.06387088e+00 | -7.67100814e+00 -8.37311621e+00 -3.06387088e+00 1 5.97572968e+00 7.45526906e+00 -2.61082421e+00 | 5.97572968e+00 7.45526906e+00 -2.61082421e+00 2 2.99708308e+00 -8.71614367e-01 3.46522422e+00 | 2.99708308e+00 -8.71614367e-01 3.46522422e+00 3 -1.30180461e+00 1.78946151e+00 2.20947086e+00 | -1.30180461e+00 1.78946151e+00 2.20947086e+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.