!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_VashishtaKaliaRino_1990_SiO__SM_887826436433_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)) = 33.3574978304 2^p V(r_1,...,r_N) = 33.3574978304 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 -1.54742956e+01 -3.01457099e+01 -3.19350723e+01 | -1.54742956e+01 -3.01457099e+01 -3.19350723e+01 1 1.26421936e+01 8.38355032e+00 -8.67081047e+00 | 1.26421936e+01 8.38355032e+00 -8.67081047e+00 2 1.32487846e+01 -1.12630895e+01 1.54677672e+01 | 1.32487846e+01 -1.12630895e+01 1.54677672e+01 3 -1.04166826e+01 3.30252491e+01 2.51381156e+01 | -1.04166826e+01 3.30252491e+01 2.51381156e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 39.5350396816 2^p V(r_1,...,r_N) = 39.5350396816 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 -2.24156845e+01 -1.56612234e+01 -1.45690265e+01 | -2.24156845e+01 -1.56612234e+01 -1.45690265e+01 1 1.65806941e+01 1.30867746e+01 -2.05799226e+01 | 1.65806941e+01 1.30867746e+01 -2.05799226e+01 2 3.24766766e+01 -3.60989846e+01 2.54106679e+01 | 3.24766766e+01 -3.60989846e+01 2.54106679e+01 3 -2.66416862e+01 3.86734334e+01 9.73828120e+00 | -2.66416862e+01 3.86734334e+01 9.73828120e+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)) = 46.6025709247 2^p V(r_1,...,r_N) = 46.6025709247 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 -2.30633393e+01 -3.35787739e+01 -4.16957968e+01 | -2.30633393e+01 -3.35787739e+01 -4.16957968e+01 1 3.12857994e+01 3.20062334e+01 -1.79938984e+01 | 3.12857994e+01 3.20062334e+01 -1.79938984e+01 2 1.91527377e+01 -2.64510528e+01 2.85129868e+01 | 1.91527377e+01 -2.64510528e+01 2.85129868e+01 3 -2.73751977e+01 2.80235933e+01 3.11767084e+01 | -2.73751977e+01 2.80235933e+01 3.11767084e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 79.2976706019 2^p V(r_1,...,r_N) = 79.2976706019 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 -8.05722328e+01 -5.56167186e+01 -1.31576115e+02 | -8.05722328e+01 -5.56167186e+01 -1.31576115e+02 1 2.70090252e+01 3.34346108e+01 -2.19061662e+01 | 2.70090252e+01 3.34346108e+01 -2.19061662e+01 2 9.75198455e+01 -4.05334450e+01 9.99113427e+01 | 9.75198455e+01 -4.05334450e+01 9.99113427e+01 3 -4.39566379e+01 6.27155529e+01 5.35709380e+01 | -4.39566379e+01 6.27155529e+01 5.35709380e+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)) = 45.4300270569 2^p V(r_1,...,r_N) = 45.4300270569 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 -3.27659648e+01 -2.28401032e+01 -3.20908667e+01 | -3.27659648e+01 -2.28401032e+01 -3.20908667e+01 1 2.11506247e+01 2.88708605e+01 -2.44018586e+01 | 2.11506247e+01 2.88708605e+01 -2.44018586e+01 2 3.14757598e+01 -3.32238643e+01 2.99102196e+01 | 3.14757598e+01 -3.32238643e+01 2.99102196e+01 3 -1.98604196e+01 2.71931070e+01 2.65825057e+01 | -1.98604196e+01 2.71931070e+01 2.65825057e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 32.561039707 2^p V(r_1,...,r_N) = 32.561039707 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 -2.55454356e+01 -2.14511104e+01 -1.50714877e+01 | -2.55454356e+01 -2.14511104e+01 -1.50714877e+01 1 1.74866460e+01 2.09187200e+01 -1.89286965e+01 | 1.74866460e+01 2.09187200e+01 -1.89286965e+01 2 1.83647801e+01 -1.00300696e+01 2.57355342e+01 | 1.83647801e+01 -1.00300696e+01 2.57355342e+01 3 -1.03059904e+01 1.05624599e+01 8.26465006e+00 | -1.03059904e+01 1.05624599e+01 8.26465006e+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)) = 74.7272398429 2^p V(r_1,...,r_N) = 74.7272398429 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 -2.69802255e+01 -2.43216932e+01 -3.14800720e+01 | -2.69802255e+01 -2.43216932e+01 -3.14800720e+01 1 3.50561885e+01 3.59739251e+01 -2.96203919e+01 | 3.50561885e+01 3.59739251e+01 -2.96203919e+01 2 1.13233448e+02 -1.20427505e+02 3.96933767e+01 | 1.13233448e+02 -1.20427505e+02 3.96933767e+01 3 -1.21309411e+02 1.08775273e+02 2.14070873e+01 | -1.21309411e+02 1.08775273e+02 2.14070873e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 69.4446994347 2^p V(r_1,...,r_N) = 69.4446994347 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 -1.24472816e+01 -1.03637278e+01 -1.43009115e+01 | -1.24472816e+01 -1.03637278e+01 -1.43009115e+01 1 1.18950729e+01 1.20208199e+01 -1.08582617e+01 | 1.18950729e+01 1.20208199e+01 -1.08582617e+01 2 1.33324116e+01 -1.21698616e+01 1.28630901e+01 | 1.33324116e+01 -1.21698616e+01 1.28630901e+01 3 -1.27802028e+01 1.05127695e+01 1.22960831e+01 | -1.27802028e+01 1.05127695e+01 1.22960831e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 70.0881884718 2^p V(r_1,...,r_N) = 70.0881884718 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 -1.15014119e+01 -1.14765131e+01 -1.28981239e+01 | -1.15014119e+01 -1.14765131e+01 -1.28981239e+01 1 1.17975668e+01 1.21072909e+01 -1.22970786e+01 | 1.17975668e+01 1.21072909e+01 -1.22970786e+01 2 1.34494228e+01 -1.19759412e+01 1.31985160e+01 | 1.34494228e+01 -1.19759412e+01 1.31985160e+01 3 -1.37455778e+01 1.13451634e+01 1.19966866e+01 | -1.37455778e+01 1.13451634e+01 1.19966866e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 62.962855183 2^p V(r_1,...,r_N) = 62.962855183 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 -1.08575590e+01 -9.64808712e+00 -8.87945110e+00 | -1.08575590e+01 -9.64808712e+00 -8.87945110e+00 1 1.16158971e+01 7.39268396e+00 -1.31235008e+01 | 1.16158971e+01 7.39268396e+00 -1.31235008e+01 2 9.94948764e+00 -1.00140395e+01 1.34756152e+01 | 9.94948764e+00 -1.00140395e+01 1.34756152e+01 3 -1.07078257e+01 1.22694427e+01 8.52733669e+00 | -1.07078257e+01 1.22694427e+01 8.52733669e+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)) = 63.2262028838 2^p V(r_1,...,r_N) = 63.2262028838 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 -1.14783723e+01 -1.19701015e+01 -1.03003585e+01 | -1.14783723e+01 -1.19701015e+01 -1.03003585e+01 1 1.10569349e+01 9.49476720e+00 -1.05214755e+01 | 1.10569349e+01 9.49476720e+00 -1.05214755e+01 2 1.02326361e+01 -1.02831398e+01 9.47390547e+00 | 1.02326361e+01 -1.02831398e+01 9.47390547e+00 3 -9.81119875e+00 1.27584741e+01 1.13479286e+01 | -9.81119875e+00 1.27584741e+01 1.13479286e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 56.5149859717 2^p V(r_1,...,r_N) = 56.5149859717 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 -9.08628503e+00 -8.34384604e+00 -9.81644006e+00 | -9.08628503e+00 -8.34384604e+00 -9.81644006e+00 1 1.11498943e+01 9.29315618e+00 -8.59762947e+00 | 1.11498943e+01 9.29315618e+00 -8.59762947e+00 2 7.61812511e+00 -9.69951519e+00 9.23935013e+00 | 7.61812511e+00 -9.69951519e+00 9.23935013e+00 3 -9.68173442e+00 8.75020506e+00 9.17471939e+00 | -9.68173442e+00 8.75020506e+00 9.17471939e+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)) = 61.0331902043 2^p V(r_1,...,r_N) = 61.0331902043 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 -9.29895386e+00 -1.22487962e+01 -1.06027255e+01 | -9.29895386e+00 -1.22487962e+01 -1.06027255e+01 1 8.25418440e+00 1.12199803e+01 -9.91294493e+00 | 8.25418440e+00 1.12199803e+01 -9.91294493e+00 2 1.15610775e+01 -8.50226020e+00 7.95587806e+00 | 1.15610775e+01 -8.50226020e+00 7.95587806e+00 3 -1.05163081e+01 9.53107608e+00 1.25597924e+01 | -1.05163081e+01 9.53107608e+00 1.25597924e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 76.2836740996 2^p V(r_1,...,r_N) = 76.2836740996 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 -1.54757071e+01 -1.30610869e+01 -1.18200798e+01 | -1.54757071e+01 -1.30610869e+01 -1.18200798e+01 1 1.54219973e+01 8.86738540e+00 -1.43696339e+01 | 1.54219973e+01 8.86738540e+00 -1.43696339e+01 2 1.26063162e+01 -1.47902697e+01 1.63228767e+01 | 1.26063162e+01 -1.47902697e+01 1.63228767e+01 3 -1.25526063e+01 1.89839712e+01 9.86683696e+00 | -1.25526063e+01 1.89839712e+01 9.86683696e+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)) = -6.82588642991 2^p V(r_1,...,r_N) = -6.82588642991 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 4.58553538e+00 -2.45610349e+00 -3.35465286e+00 | 4.58553538e+00 -2.45610349e+00 -3.35465286e+00 1 -4.00027373e+00 5.39471432e+00 -9.53738545e+00 | -4.00027373e+00 5.39471432e+00 -9.53738545e+00 2 -7.04233771e+00 -4.75588098e+00 8.24348355e+00 | -7.04233771e+00 -4.75588098e+00 8.24348355e+00 3 6.45707606e+00 1.81727015e+00 4.64855476e+00 | 6.45707606e+00 1.81727015e+00 4.64855476e+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)) = -1.83527544136 2^p V(r_1,...,r_N) = -1.83527544136 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 8.63627600e+00 -8.87220699e+00 -1.45250392e+00 | 8.63627600e+00 -8.87220699e+00 -1.45250392e+00 1 -3.37174690e+00 2.65973310e+01 -1.36438395e+01 | -3.37174690e+00 2.65973310e+01 -1.36438395e+01 2 -1.15360732e+01 -2.33149587e+01 1.21699661e+01 | -1.15360732e+01 -2.33149587e+01 1.21699661e+01 3 6.27154414e+00 5.58983474e+00 2.92637730e+00 | 6.27154414e+00 5.58983474e+00 2.92637730e+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)) = -8.91862863256 2^p V(r_1,...,r_N) = -8.91862863256 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 -4.71731031e+00 6.22447009e+00 -6.29306755e+00 | -4.71731031e+00 6.22447009e+00 -6.29306755e+00 1 1.89717795e+00 -4.93794859e+00 -3.76916319e+00 | 1.89717795e+00 -4.93794859e+00 -3.76916319e+00 2 5.45477460e+00 3.65598037e+00 6.69226195e+00 | 5.45477460e+00 3.65598037e+00 6.69226195e+00 3 -2.63464225e+00 -4.94250187e+00 3.36996878e+00 | -2.63464225e+00 -4.94250187e+00 3.36996878e+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)) = 1.36097282632 2^p V(r_1,...,r_N) = 1.36097282632 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 -3.21477502e+01 2.44481919e+00 -2.73448220e+01 | -3.21477502e+01 2.44481919e+00 -2.73448220e+01 1 9.05821100e+00 -1.28411778e+01 -2.92404414e+00 | 9.05821100e+00 -1.28411778e+01 -2.92404414e+00 2 3.20291721e+01 1.11424969e+01 2.45887782e+01 | 3.20291721e+01 1.11424969e+01 2.45887782e+01 3 -8.93963295e+00 -7.46138317e-01 5.68008799e+00 | -8.93963295e+00 -7.46138317e-01 5.68008799e+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)) = -6.76696477333 2^p V(r_1,...,r_N) = -6.76696477333 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 -4.48552766e+00 -9.11461766e+00 5.10721856e+00 | -4.48552766e+00 -9.11461766e+00 5.10721856e+00 1 8.53431536e+00 6.53514806e+00 3.95866285e+00 | 8.53431536e+00 6.53514806e+00 3.95866285e+00 2 7.03055443e+00 -6.10682986e+00 -1.11030064e+01 | 7.03055443e+00 -6.10682986e+00 -1.11030064e+01 3 -1.10793421e+01 8.68629945e+00 2.03712501e+00 | -1.10793421e+01 8.68629945e+00 2.03712501e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -6.48196517988 2^p V(r_1,...,r_N) = -6.48196517988 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 6.00413836e+00 -1.06703770e+01 -1.48043886e+01 | 6.00413836e+00 -1.06703770e+01 -1.48043886e+01 1 -5.17611154e+00 1.80884510e+00 -2.32842953e+00 | -5.17611154e+00 1.80884510e+00 -2.32842953e+00 2 -8.35705125e+00 -1.27153042e+00 3.80644122e+00 | -8.35705125e+00 -1.27153042e+00 3.80644122e+00 3 7.52902443e+00 1.01330623e+01 1.33263769e+01 | 7.52902443e+00 1.01330623e+01 1.33263769e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.167611921784 2^p V(r_1,...,r_N) = -0.167611921784 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 4.60203209e+00 -5.33878307e+01 -3.72404547e+01 | 4.60203209e+00 -5.33878307e+01 -3.72404547e+01 1 -6.89298423e+00 7.52159215e+00 -1.68038782e+00 | -6.89298423e+00 7.52159215e+00 -1.68038782e+00 2 -5.88631100e+00 -8.07692206e+00 1.89696493e+00 | -5.88631100e+00 -8.07692206e+00 1.89696493e+00 3 8.17726314e+00 5.39431606e+01 3.70238776e+01 | 8.17726314e+00 5.39431606e+01 3.70238776e+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.