!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Vashishta_BroughtonMeliVashishta_1997_SiO__SM_422553794879_000 Supported species : O Si random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ 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)) = 5.53909201944 2^p V(r_1,...,r_N) = 5.53909201944 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 -2.98281569e+00 -5.75719364e+00 -6.10338365e+00 | -2.98281569e+00 -5.75719364e+00 -6.10338365e+00 1 2.44072507e+00 1.61867902e+00 -1.67576952e+00 | 2.44072507e+00 1.61867902e+00 -1.67576952e+00 2 2.55098704e+00 -2.17458709e+00 2.98013029e+00 | 2.55098704e+00 -2.17458709e+00 2.98013029e+00 3 -2.00889642e+00 6.31310171e+00 4.79902289e+00 | -2.00889642e+00 6.31310171e+00 4.79902289e+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)) = 6.72808321134 2^p V(r_1,...,r_N) = 6.72808321134 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 -4.30887384e+00 -3.01659674e+00 -2.80200099e+00 | -4.30887384e+00 -3.01659674e+00 -2.80200099e+00 1 3.19296896e+00 2.51475853e+00 -3.96080563e+00 | 3.19296896e+00 2.51475853e+00 -3.96080563e+00 2 6.20190579e+00 -6.88768880e+00 4.87951206e+00 | 6.20190579e+00 -6.88768880e+00 4.87951206e+00 3 -5.08600091e+00 7.38952701e+00 1.88329457e+00 | -5.08600091e+00 7.38952701e+00 1.88329457e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 8.08917794721 2^p V(r_1,...,r_N) = 8.08917794721 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 -4.42129593e+00 -6.41563322e+00 -7.97306105e+00 | -4.42129593e+00 -6.41563322e+00 -7.97306105e+00 1 5.99747972e+00 6.12912320e+00 -3.45177707e+00 | 5.99747972e+00 6.12912320e+00 -3.45177707e+00 2 3.67926920e+00 -5.07463519e+00 5.46536662e+00 | 3.67926920e+00 -5.07463519e+00 5.46536662e+00 3 -5.25545299e+00 5.36114521e+00 5.95947151e+00 | -5.25545299e+00 5.36114521e+00 5.95947151e+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)) = 14.3090237797 2^p V(r_1,...,r_N) = 14.3090237797 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 -1.52853984e+01 -1.05876093e+01 -2.49402872e+01 | -1.52853984e+01 -1.05876093e+01 -2.49402872e+01 1 5.17989452e+00 6.39999346e+00 -4.20070534e+00 | 5.17989452e+00 6.39999346e+00 -4.20070534e+00 2 1.84980128e+01 -7.73998527e+00 1.89520154e+01 | 1.84980128e+01 -7.73998527e+00 1.89520154e+01 3 -8.39250888e+00 1.19276011e+01 1.01889772e+01 | -8.39250888e+00 1.19276011e+01 1.01889772e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 7.86477714027 2^p V(r_1,...,r_N) = 7.86477714027 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 -6.27566471e+00 -4.37870038e+00 -6.14120106e+00 | -6.27566471e+00 -4.37870038e+00 -6.14120106e+00 1 4.06457886e+00 5.52967847e+00 -4.67910766e+00 | 4.06457886e+00 5.52967847e+00 -4.67910766e+00 2 6.02580497e+00 -6.36056914e+00 5.71999408e+00 | 6.02580497e+00 -6.36056914e+00 5.71999408e+00 3 -3.81471912e+00 5.20959105e+00 5.10031464e+00 | -3.81471912e+00 5.20959105e+00 5.10031464e+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)) = 5.39126316651 2^p V(r_1,...,r_N) = 5.39126316651 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 -4.89477038e+00 -4.11861356e+00 -2.89958377e+00 | -4.89477038e+00 -4.11861356e+00 -2.89958377e+00 1 3.34825655e+00 4.01143638e+00 -3.63049545e+00 | 3.34825655e+00 4.01143638e+00 -3.63049545e+00 2 3.53163449e+00 -1.93121070e+00 4.93935721e+00 | 3.53163449e+00 -1.93121070e+00 4.93935721e+00 3 -1.98512066e+00 2.03838788e+00 1.59072201e+00 | -1.98512066e+00 2.03838788e+00 1.59072201e+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)) = 13.4298640807 2^p V(r_1,...,r_N) = 13.4298640807 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 -5.16548951e+00 -4.66021160e+00 -6.04063810e+00 | -5.16548951e+00 -4.66021160e+00 -6.04063810e+00 1 6.71325422e+00 6.87291099e+00 -5.66399134e+00 | 6.71325422e+00 6.87291099e+00 -5.66399134e+00 2 2.14364786e+01 -2.28155187e+01 7.59082046e+00 | 2.14364786e+01 -2.28155187e+01 7.59082046e+00 3 -2.29842434e+01 2.06028193e+01 4.11380898e+00 | -2.29842434e+01 2.06028193e+01 4.11380898e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTT (Configuration in file "config-Si-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)) = 9.96938117147 2^p V(r_1,...,r_N) = 9.96938117147 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 -2.64915757e+00 -2.17078608e+00 -3.04603112e+00 | -2.64915757e+00 -2.17078608e+00 -3.04603112e+00 1 2.43869234e+00 2.53539167e+00 -2.24847701e+00 | 2.43869234e+00 2.53539167e+00 -2.24847701e+00 2 2.87437127e+00 -2.60572916e+00 2.76159093e+00 | 2.87437127e+00 -2.60572916e+00 2.76159093e+00 3 -2.66390605e+00 2.24112357e+00 2.53291721e+00 | -2.66390605e+00 2.24112357e+00 2.53291721e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTF (Configuration in file "config-Si-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.1125707734 2^p V(r_1,...,r_N) = 10.1125707734 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 -2.44425687e+00 -2.39640295e+00 -2.68913488e+00 | -2.44425687e+00 -2.39640295e+00 -2.68913488e+00 1 2.45002971e+00 2.57755756e+00 -2.56546219e+00 | 2.45002971e+00 2.57755756e+00 -2.56546219e+00 2 2.91697868e+00 -2.60464220e+00 2.80685466e+00 | 2.91697868e+00 -2.60464220e+00 2.80685466e+00 3 -2.92275152e+00 2.42348759e+00 2.44774241e+00 | -2.92275152e+00 2.42348759e+00 2.44774241e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFT (Configuration in file "config-Si-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)) = 8.60988141119 2^p V(r_1,...,r_N) = 8.60988141119 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 -2.18319372e+00 -1.96581418e+00 -1.79971862e+00 | -2.18319372e+00 -1.96581418e+00 -1.79971862e+00 1 2.36123597e+00 1.55972547e+00 -2.76804440e+00 | 2.36123597e+00 1.55972547e+00 -2.76804440e+00 2 2.04216774e+00 -2.14366517e+00 2.83259626e+00 | 2.04216774e+00 -2.14366517e+00 2.83259626e+00 3 -2.22020999e+00 2.54975388e+00 1.73516676e+00 | -2.22020999e+00 2.54975388e+00 1.73516676e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFF (Configuration in file "config-Si-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)) = 8.67631290797 2^p V(r_1,...,r_N) = 8.67631290797 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 -2.31504230e+00 -2.55118093e+00 -2.18805184e+00 | -2.31504230e+00 -2.55118093e+00 -2.18805184e+00 1 2.25445563e+00 1.95251765e+00 -2.18751001e+00 | 2.25445563e+00 1.95251765e+00 -2.18751001e+00 2 2.04812222e+00 -2.11182237e+00 1.94311662e+00 | 2.04812222e+00 -2.11182237e+00 1.94311662e+00 3 -1.98753555e+00 2.71048564e+00 2.43244523e+00 | -1.98753555e+00 2.71048564e+00 2.43244523e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTT (Configuration in file "config-Si-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.29069734909 2^p V(r_1,...,r_N) = 7.29069734909 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 -1.82795518e+00 -1.70088702e+00 -1.93442478e+00 | -1.82795518e+00 -1.70088702e+00 -1.93442478e+00 1 2.30939768e+00 1.92063752e+00 -1.77695354e+00 | 2.30939768e+00 1.92063752e+00 -1.77695354e+00 2 1.47744142e+00 -1.95128513e+00 1.84609784e+00 | 1.47744142e+00 -1.95128513e+00 1.84609784e+00 3 -1.95888392e+00 1.73153462e+00 1.86528049e+00 | -1.95888392e+00 1.73153462e+00 1.86528049e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTF (Configuration in file "config-Si-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)) = 8.21576323789 2^p V(r_1,...,r_N) = 8.21576323789 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 -1.88151015e+00 -2.56368923e+00 -2.23303364e+00 | -1.88151015e+00 -2.56368923e+00 -2.23303364e+00 1 1.70877617e+00 2.24742905e+00 -2.01660723e+00 | 1.70877617e+00 2.24742905e+00 -2.01660723e+00 2 2.34112580e+00 -1.69504610e+00 1.58339359e+00 | 2.34112580e+00 -1.69504610e+00 1.58339359e+00 3 -2.16839182e+00 2.01130628e+00 2.66624729e+00 | -2.16839182e+00 2.01130628e+00 2.66624729e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FFT (Configuration in file "config-Si-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)) = 11.4172995758 2^p V(r_1,...,r_N) = 11.4172995758 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 -3.27349758e+00 -2.75765544e+00 -2.55611182e+00 | -3.27349758e+00 -2.75765544e+00 -2.55611182e+00 1 3.22664605e+00 1.87950023e+00 -3.07592604e+00 | 3.22664605e+00 1.87950023e+00 -3.07592604e+00 2 2.75209581e+00 -3.23285686e+00 3.54244313e+00 | 2.75209581e+00 -3.23285686e+00 3.54244313e+00 3 -2.70524427e+00 4.11101207e+00 2.08959473e+00 | -2.70524427e+00 4.11101207e+00 2.08959473e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = TTT (Configuration in file "config-OSi-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)) = 1.11173909871 2^p V(r_1,...,r_N) = 1.11173909871 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 -6.78794851e-01 -1.24345649e+00 -1.70559249e+00 | -6.78794851e-01 -1.24345649e+00 -1.70559249e+00 1 2.86127160e+00 2.17329774e+00 -5.80852585e+00 | 2.86127160e+00 2.17329774e+00 -5.80852585e+00 2 1.04896362e+00 -2.99752756e+00 3.62264318e+00 | 1.04896362e+00 -2.99752756e+00 3.62264318e+00 3 -3.23144037e+00 2.06768631e+00 3.89147517e+00 | -3.23144037e+00 2.06768631e+00 3.89147517e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = TTF (Configuration in file "config-OSi-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)) = 1.27636685097 2^p V(r_1,...,r_N) = 1.27636685097 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 -2.59483981e+00 -6.17480529e+00 -7.60567526e-01 | -2.59483981e+00 -6.17480529e+00 -7.60567526e-01 1 4.14164901e+00 8.24769479e+00 -3.58209724e+00 | 4.14164901e+00 8.24769479e+00 -3.58209724e+00 2 8.51430832e-01 -8.46433105e+00 2.50412621e+00 | 8.51430832e-01 -8.46433105e+00 2.50412621e+00 3 -2.39824004e+00 6.39144155e+00 1.83853856e+00 | -2.39824004e+00 6.39144155e+00 1.83853856e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = TFT (Configuration in file "config-OSi-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)) = 2.17104860497 2^p V(r_1,...,r_N) = 2.17104860497 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 -5.17450022e+00 -5.22877598e+00 -1.80528476e+00 | -5.17450022e+00 -5.22877598e+00 -1.80528476e+00 1 3.44704094e+00 6.90910018e+00 -8.13459749e-01 | 3.44704094e+00 6.90910018e+00 -8.13459749e-01 2 4.01525211e+00 -3.96782273e+00 3.62154156e+00 | 4.01525211e+00 -3.96782273e+00 3.62154156e+00 3 -2.28779282e+00 2.28749853e+00 -1.00279705e+00 | -2.28779282e+00 2.28749853e+00 -1.00279705e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = TFF (Configuration in file "config-OSi-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.2254101933 2^p V(r_1,...,r_N) = -0.2254101933 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 -1.06693006e+00 7.04375058e-01 -3.07187771e+00 | -1.06693006e+00 7.04375058e-01 -3.07187771e+00 1 4.04127540e-01 -7.70325802e-01 -5.39723016e-01 | 4.04127540e-01 -7.70325802e-01 -5.39723016e-01 2 2.54936290e+00 -6.48368769e-01 2.49832613e+00 | 2.54936290e+00 -6.48368769e-01 2.49832613e+00 3 -1.88656037e+00 7.14319513e-01 1.11327460e+00 | -1.88656037e+00 7.14319513e-01 1.11327460e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = FTT (Configuration in file "config-OSi-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)) = -0.647717213875 2^p V(r_1,...,r_N) = -0.647717213875 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 -1.85596153e+00 -6.13823147e-01 -1.33312910e+00 | -1.85596153e+00 -6.13823147e-01 -1.33312910e+00 1 2.24557121e+00 6.93756214e-01 -9.39997894e-01 | 2.24557121e+00 6.93756214e-01 -9.39997894e-01 2 5.14771712e-01 6.05149533e-01 1.50094797e+00 | 5.14771712e-01 6.05149533e-01 1.50094797e+00 3 -9.04381394e-01 -6.85082599e-01 7.72179033e-01 | -9.04381394e-01 -6.85082599e-01 7.72179033e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = FTF (Configuration in file "config-OSi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.1211441738 2^p V(r_1,...,r_N) = 0.1211441738 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 -3.89007469e+00 -2.05651093e+00 -9.58986758e-01 | -3.89007469e+00 -2.05651093e+00 -9.58986758e-01 1 2.58884268e+00 4.40629194e+00 -1.03647323e-02 | 2.58884268e+00 4.40629194e+00 -1.03647323e-02 2 3.09048801e+00 -3.89908211e+00 2.66958974e+00 | 3.09048801e+00 -3.89908211e+00 2.66958974e+00 3 -1.78925600e+00 1.54930111e+00 -1.70023825e+00 | -1.78925600e+00 1.54930111e+00 -1.70023825e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Si, PBC = FFT (Configuration in file "config-OSi-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)) = 0.531349931191 2^p V(r_1,...,r_N) = 0.531349931191 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 -2.46724269e+00 -2.48604845e+00 -3.39743732e+00 | -2.46724269e+00 -2.48604845e+00 -3.39743732e+00 1 7.71772989e-01 1.94225547e+00 -2.95820018e+00 | 7.71772989e-01 1.94225547e+00 -2.95820018e+00 2 3.90972498e+00 -2.87487558e+00 4.39837526e+00 | 3.90972498e+00 -2.87487558e+00 4.39837526e+00 3 -2.21425528e+00 3.41866856e+00 1.95726225e+00 | -2.21425528e+00 3.41866856e+00 1.95726225e+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.