!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : EAM_Dynamo_HoytGarvinWebb_2003_PbCu__MO_119135752160_005 Supported species : Cu Pb 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)) = -6.08005933616 2^p V(r_1,...,r_N) = -6.08005933616 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 -2.84723892e+00 -5.86151988e+00 -6.00428646e+00 | -2.84723892e+00 -5.86151988e+00 -6.00428646e+00 1 2.28807882e+00 1.80567547e+00 -1.60208299e+00 | 2.28807882e+00 1.80567547e+00 -1.60208299e+00 2 1.67446251e+00 -1.98335889e+00 2.84274582e+00 | 1.67446251e+00 -1.98335889e+00 2.84274582e+00 3 -1.11530241e+00 6.03920330e+00 4.76362363e+00 | -1.11530241e+00 6.03920330e+00 4.76362363e+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)) = -6.5036688272 2^p V(r_1,...,r_N) = -6.5036688272 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 9.61765687e-01 7.07240151e-01 7.88446933e-01 | 9.61765687e-01 7.07240151e-01 7.88446933e-01 1 5.10852252e-01 9.26060850e-01 -2.18791571e+00 | 5.10852252e-01 9.26060850e-01 -2.18791571e+00 2 3.12600137e+00 -4.04817065e+00 8.10837765e-01 | 3.12600137e+00 -4.04817065e+00 8.10837765e-01 3 -4.59861931e+00 2.41486965e+00 5.88631014e-01 | -4.59861931e+00 2.41486965e+00 5.88631014e-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)) = -5.1714224275 2^p V(r_1,...,r_N) = -5.1714224275 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 -3.00044096e+00 -2.93152774e+00 -3.60300354e+00 | -3.00044096e+00 -2.93152774e+00 -3.60300354e+00 1 2.93081686e+00 3.09058630e+00 -4.16122930e+00 | 2.93081686e+00 3.09058630e+00 -4.16122930e+00 2 6.45357154e+00 -5.57873898e+00 3.82042514e+00 | 6.45357154e+00 -5.57873898e+00 3.82042514e+00 3 -6.38394744e+00 5.41968041e+00 3.94380770e+00 | -6.38394744e+00 5.41968041e+00 3.94380770e+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)) = -6.20356946987 2^p V(r_1,...,r_N) = -6.20356946987 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 -2.25397837e+00 -2.40499206e+00 -4.17113081e+00 | -2.25397837e+00 -2.40499206e+00 -4.17113081e+00 1 1.44674546e+00 2.06499201e+00 -2.00919606e+00 | 1.44674546e+00 2.06499201e+00 -2.00919606e+00 2 5.01162558e+00 -4.70040855e+00 2.92001876e+00 | 5.01162558e+00 -4.70040855e+00 2.92001876e+00 3 -4.20439267e+00 5.04040860e+00 3.26030810e+00 | -4.20439267e+00 5.04040860e+00 3.26030810e+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)) = -1.73191556051 2^p V(r_1,...,r_N) = -1.73191556051 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 -4.47183900e+00 -6.09521104e+00 -5.72915359e+00 | -4.47183900e+00 -6.09521104e+00 -5.72915359e+00 1 1.54883618e+01 1.21867110e+00 -1.27237758e+01 | 1.54883618e+01 1.21867110e+00 -1.27237758e+01 2 2.97410937e+00 -2.96463003e+00 2.65561458e+00 | 2.97410937e+00 -2.96463003e+00 2.65561458e+00 3 -1.39906322e+01 7.84116998e+00 1.57973148e+01 | -1.39906322e+01 7.84116998e+00 1.57973148e+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)) = -3.47544513806 2^p V(r_1,...,r_N) = -3.47544513806 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 -5.61502334e+00 -1.20579882e+01 -6.92739306e+00 | -5.61502334e+00 -1.20579882e+01 -6.92739306e+00 1 8.63565724e+00 5.93123264e+00 -5.72403379e+00 | 8.63565724e+00 5.93123264e+00 -5.72403379e+00 2 2.47958660e+00 -8.48189965e-01 2.37719370e+00 | 2.47958660e+00 -8.48189965e-01 2.37719370e+00 3 -5.50022051e+00 6.97494550e+00 1.02742332e+01 | -5.50022051e+00 6.97494550e+00 1.02742332e+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)) = -7.32931865978 2^p V(r_1,...,r_N) = -7.32931865978 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 -1.76837609e+00 -2.93340926e+00 -1.25844830e+00 | -1.76837609e+00 -2.93340926e+00 -1.25844830e+00 1 1.54376120e+00 1.83440130e+00 -1.31523086e+00 | 1.54376120e+00 1.83440130e+00 -1.31523086e+00 2 7.98881218e-01 -4.17226370e-01 1.09612508e+00 | 7.98881218e-01 -4.17226370e-01 1.09612508e+00 3 -5.74266327e-01 1.51623432e+00 1.47755409e+00 | -5.74266327e-01 1.51623432e+00 1.47755409e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TTT (Configuration in file "config-Pb-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)) = 5.62300117559 2^p V(r_1,...,r_N) = 5.62300117559 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 -5.26070990e+00 -5.23768521e+00 -2.93809625e+00 | -5.26070990e+00 -5.23768521e+00 -2.93809625e+00 1 5.07213160e+00 3.18529641e+00 -6.02453811e+00 | 5.07213160e+00 3.18529641e+00 -6.02453811e+00 2 4.56804426e+00 -3.17637530e+00 4.20659892e+00 | 4.56804426e+00 -3.17637530e+00 4.20659892e+00 3 -4.37946597e+00 5.22876410e+00 4.75603544e+00 | -4.37946597e+00 5.22876410e+00 4.75603544e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TTF (Configuration in file "config-Pb-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)) = 9.54590841945 2^p V(r_1,...,r_N) = 9.54590841945 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 -7.44866984e+00 -5.98225166e+00 -5.77683969e+00 | -7.44866984e+00 -5.98225166e+00 -5.77683969e+00 1 7.58801870e+00 4.19373395e+00 -6.95237204e+00 | 7.58801870e+00 4.19373395e+00 -6.95237204e+00 2 5.49550231e+00 -6.08669725e+00 5.36869717e+00 | 5.49550231e+00 -6.08669725e+00 5.36869717e+00 3 -5.63485118e+00 7.87521496e+00 7.36051456e+00 | -5.63485118e+00 7.87521496e+00 7.36051456e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TFT (Configuration in file "config-Pb-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)) = 8.57467543993 2^p V(r_1,...,r_N) = 8.57467543993 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 -6.61473461e+00 -6.90968128e+00 -8.23797503e+00 | -6.61473461e+00 -6.90968128e+00 -8.23797503e+00 1 7.14116328e+00 6.13947146e+00 -3.85373578e+00 | 7.14116328e+00 6.13947146e+00 -3.85373578e+00 2 4.80172884e+00 -5.07281991e+00 6.18898485e+00 | 4.80172884e+00 -5.07281991e+00 6.18898485e+00 3 -5.32815752e+00 5.84302973e+00 5.90272596e+00 | -5.32815752e+00 5.84302973e+00 5.90272596e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TFF (Configuration in file "config-Pb-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)) = 6.92731810399 2^p V(r_1,...,r_N) = 6.92731810399 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 -5.52529744e+00 -3.99134566e+00 -5.51476585e+00 | -5.52529744e+00 -3.99134566e+00 -5.51476585e+00 1 5.39202551e+00 6.24880064e+00 -4.13389912e+00 | 5.39202551e+00 6.24880064e+00 -4.13389912e+00 2 4.78494357e+00 -6.08116737e+00 5.26348148e+00 | 4.78494357e+00 -6.08116737e+00 5.26348148e+00 3 -4.65167164e+00 3.82371239e+00 4.38518349e+00 | -4.65167164e+00 3.82371239e+00 4.38518349e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = FTT (Configuration in file "config-Pb-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)) = 7.40150017332 2^p V(r_1,...,r_N) = 7.40150017332 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 -6.26364971e+00 -4.78484600e+00 -4.29683259e+00 | -6.26364971e+00 -4.78484600e+00 -4.29683259e+00 1 6.54190068e+00 3.49584966e+00 -6.24986569e+00 | 6.54190068e+00 3.49584966e+00 -6.24986569e+00 2 3.74722250e+00 -5.33875469e+00 4.79147227e+00 | 3.74722250e+00 -5.33875469e+00 4.79147227e+00 3 -4.02547346e+00 6.62775103e+00 5.75522602e+00 | -4.02547346e+00 6.62775103e+00 5.75522602e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = FTF (Configuration in file "config-Pb-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.5238135181 2^p V(r_1,...,r_N) = 10.5238135181 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 -7.87931693e+00 -5.97134924e+00 -8.88494142e+00 | -7.87931693e+00 -5.97134924e+00 -8.88494142e+00 1 5.19351161e+00 5.60214347e+00 -6.00675573e+00 | 5.19351161e+00 5.60214347e+00 -6.00675573e+00 2 9.32330696e+00 -7.89642579e+00 6.33348217e+00 | 9.32330696e+00 -7.89642579e+00 6.33348217e+00 3 -6.63750165e+00 8.26563156e+00 8.55821499e+00 | -6.63750165e+00 8.26563156e+00 8.55821499e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = FFT (Configuration in file "config-Pb-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)) = 5.1997156139 2^p V(r_1,...,r_N) = 5.1997156139 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 -3.94959517e+00 -5.48911776e+00 -3.82681808e+00 | -3.94959517e+00 -5.48911776e+00 -3.82681808e+00 1 4.67632943e+00 4.57394427e+00 -5.31361921e+00 | 4.67632943e+00 4.57394427e+00 -5.31361921e+00 2 4.23087819e+00 -3.38067858e+00 3.59509986e+00 | 4.23087819e+00 -3.38067858e+00 3.59509986e+00 3 -4.95761244e+00 4.29585206e+00 5.54533744e+00 | -4.95761244e+00 4.29585206e+00 5.54533744e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = TTT (Configuration in file "config-CuPb-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)) = 1.02478911227 2^p V(r_1,...,r_N) = 1.02478911227 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 -9.58674154e+00 -2.69445875e+00 -1.10952176e+01 | -9.58674154e+00 -2.69445875e+00 -1.10952176e+01 1 3.38356526e+00 5.03997631e+00 -3.22517145e+00 | 3.38356526e+00 5.03997631e+00 -3.22517145e+00 2 1.07497085e+01 -9.85761552e+00 6.99659748e+00 | 1.07497085e+01 -9.85761552e+00 6.99659748e+00 3 -4.54653221e+00 7.51209797e+00 7.32379155e+00 | -4.54653221e+00 7.51209797e+00 7.32379155e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = TTF (Configuration in file "config-CuPb-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.721393828199 2^p V(r_1,...,r_N) = 0.721393828199 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 -7.22293413e+00 -8.04580703e+00 -6.87063392e+00 | -7.22293413e+00 -8.04580703e+00 -6.87063392e+00 1 3.98148774e+00 5.18867414e+00 -3.11444292e+00 | 3.98148774e+00 5.18867414e+00 -3.11444292e+00 2 6.93914896e+00 -3.34643637e+00 6.00788166e+00 | 6.93914896e+00 -3.34643637e+00 6.00788166e+00 3 -3.69770258e+00 6.20356925e+00 3.97719518e+00 | -3.69770258e+00 6.20356925e+00 3.97719518e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = TFT (Configuration in file "config-CuPb-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)) = 0.896025601624 2^p V(r_1,...,r_N) = 0.896025601624 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 -8.48435155e+00 -3.78923399e+00 -6.40794299e+00 | -8.48435155e+00 -3.78923399e+00 -6.40794299e+00 1 5.49281428e+00 8.79454550e+00 -7.56964522e+00 | 5.49281428e+00 8.79454550e+00 -7.56964522e+00 2 7.02576017e+00 -7.15433745e+00 1.08327779e+01 | 7.02576017e+00 -7.15433745e+00 1.08327779e+01 3 -4.03422290e+00 2.14902594e+00 3.14481036e+00 | -4.03422290e+00 2.14902594e+00 3.14481036e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = TFF (Configuration in file "config-CuPb-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)) = 3.43245687568 2^p V(r_1,...,r_N) = 3.43245687568 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 -7.76670051e+00 -6.39760074e+00 -5.53936309e+00 | -7.76670051e+00 -6.39760074e+00 -5.53936309e+00 1 6.92236190e+00 8.47761956e+00 -1.49191949e+01 | 6.92236190e+00 8.47761956e+00 -1.49191949e+01 2 9.78061461e+00 -9.33875776e+00 1.54099284e+01 | 9.78061461e+00 -9.33875776e+00 1.54099284e+01 3 -8.93627600e+00 7.25873895e+00 5.04862962e+00 | -8.93627600e+00 7.25873895e+00 5.04862962e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = FTT (Configuration in file "config-CuPb-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.19333087866 2^p V(r_1,...,r_N) = -1.19333087866 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 -1.79115743e+00 -2.61819750e+00 -2.37756541e+00 | -1.79115743e+00 -2.61819750e+00 -2.37756541e+00 1 3.56202869e+00 3.26225370e+00 -6.22323111e+00 | 3.56202869e+00 3.26225370e+00 -6.22323111e+00 2 2.82998643e+00 -5.68583636e+00 4.67996957e+00 | 2.82998643e+00 -5.68583636e+00 4.67996957e+00 3 -4.60085770e+00 5.04178015e+00 3.92082694e+00 | -4.60085770e+00 5.04178015e+00 3.92082694e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = FTF (Configuration in file "config-CuPb-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.7695823277 2^p V(r_1,...,r_N) = -3.7695823277 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 -5.29014129e-01 -1.03538941e+00 -1.01386278e+00 | -5.29014129e-01 -1.03538941e+00 -1.01386278e+00 1 3.33865545e+00 4.56207610e-01 -3.54245581e+00 | 3.33865545e+00 4.56207610e-01 -3.54245581e+00 2 5.68541854e-01 -1.09780736e+00 4.37885579e-01 | 5.68541854e-01 -1.09780736e+00 4.37885579e-01 3 -3.37818317e+00 1.67698916e+00 4.11843301e+00 | -3.37818317e+00 1.67698916e+00 4.11843301e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Pb, PBC = FFT (Configuration in file "config-CuPb-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.41993961834 2^p V(r_1,...,r_N) = -3.41993961834 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 -1.39127486e+00 -2.21184824e+00 -1.61918551e+00 | -1.39127486e+00 -2.21184824e+00 -1.61918551e+00 1 3.15128244e+00 1.55046501e+00 -2.65965345e+00 | 3.15128244e+00 1.55046501e+00 -2.65965345e+00 2 8.91528123e-01 -9.64822822e-01 1.17179658e+00 | 8.91528123e-01 -9.64822822e-01 1.17179658e+00 3 -2.65153570e+00 1.62620605e+00 3.10704238e+00 | -2.65153570e+00 1.62620605e+00 3.10704238e+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.