!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : Sim_LAMMPS_MEAM_ZhangTrinkle_2016_TiO__SM_513612626462_000 Supported species : O Ti 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)) = -0.903067980453 2^p V(r_1,...,r_N) = -0.903067980453 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 -1.58575182e+01 -1.35345645e+01 -1.21780492e+01 | -1.58575182e+01 -1.35345645e+01 -1.21780492e+01 1 1.27852695e+01 9.83516720e+00 -6.99651489e+00 | 1.27852695e+01 9.83516720e+00 -6.99651489e+00 2 1.18209460e+01 -1.20402317e+01 1.21882174e+01 | 1.18209460e+01 -1.20402317e+01 1.21882174e+01 3 -8.74869730e+00 1.57396290e+01 6.98634668e+00 | -8.74869730e+00 1.57396290e+01 6.98634668e+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)) = 4.30172650145 2^p V(r_1,...,r_N) = 4.30172650145 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 -1.14836531e+01 -1.30831414e+01 -7.35779689e+00 | -1.14836531e+01 -1.30831414e+01 -7.35779689e+00 1 1.29378356e+01 6.86686040e+00 -1.30893148e+01 | 1.29378356e+01 6.86686040e+00 -1.30893148e+01 2 9.29099403e+00 -1.22633109e+01 8.80567373e+00 | 9.29099403e+00 -1.22633109e+01 8.80567373e+00 3 -1.07451765e+01 1.84795919e+01 1.16414380e+01 | -1.07451765e+01 1.84795919e+01 1.16414380e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = O, PBC = TFT (Configuration in file "config-O-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.49495478016 2^p V(r_1,...,r_N) = 8.49495478016 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 -3.99851200e+00 -8.24428771e+00 -9.66208615e+00 | -3.99851200e+00 -8.24428771e+00 -9.66208615e+00 1 7.87908791e+00 6.41998788e+00 -4.50204454e+00 | 7.87908791e+00 6.41998788e+00 -4.50204454e+00 2 7.85984585e+00 -9.02066453e+00 5.64531006e+00 | 7.85984585e+00 -9.02066453e+00 5.64531006e+00 3 -1.17404218e+01 1.08449644e+01 8.51882063e+00 | -1.17404218e+01 1.08449644e+01 8.51882063e+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)) = 16.2481078646 2^p V(r_1,...,r_N) = 16.2481078646 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 -1.27076146e+01 -1.60364774e+01 -2.87815724e+01 | -1.27076146e+01 -1.60364774e+01 -2.87815724e+01 1 1.05585416e+01 7.71950183e+00 -8.24798441e+00 | 1.05585416e+01 7.71950183e+00 -8.24798441e+00 2 1.82719733e+01 -8.97409357e+00 1.78146233e+01 | 1.82719733e+01 -8.97409357e+00 1.78146233e+01 3 -1.61229004e+01 1.72910692e+01 1.92149335e+01 | -1.61229004e+01 1.72910692e+01 1.92149335e+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)) = 7.72644364288 2^p V(r_1,...,r_N) = 7.72644364288 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 -6.57229259e+00 -4.27304389e+00 -6.76965711e+00 | -6.57229259e+00 -4.27304389e+00 -6.76965711e+00 1 9.30891553e+00 6.05046380e+00 -1.09464075e+01 | 9.30891553e+00 6.05046380e+00 -1.09464075e+01 2 6.42411591e+00 -6.91260455e+00 6.73400388e+00 | 6.42411591e+00 -6.91260455e+00 6.73400388e+00 3 -9.16073884e+00 5.13518464e+00 1.09820607e+01 | -9.16073884e+00 5.13518464e+00 1.09820607e+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)) = 1.53653861807 2^p V(r_1,...,r_N) = 1.53653861807 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 -2.90752665e+00 -1.08487220e+01 -9.80081588e+00 | -2.90752665e+00 -1.08487220e+01 -9.80081588e+00 1 1.56607366e+00 5.10411072e+00 -3.06571300e+00 | 1.56607366e+00 5.10411072e+00 -3.06571300e+00 2 1.10779135e+01 -7.73163679e+00 5.69772312e+00 | 1.10779135e+01 -7.73163679e+00 5.69772312e+00 3 -9.73646048e+00 1.34762481e+01 7.16880576e+00 | -9.73646048e+00 1.34762481e+01 7.16880576e+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)) = 15.0910597194 2^p V(r_1,...,r_N) = 15.0910597194 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 -5.24096662e+00 -6.62733941e+00 -8.08627603e+00 | -5.24096662e+00 -6.62733941e+00 -8.08627603e+00 1 1.17528311e+01 9.27083318e+00 -1.12953031e+01 | 1.17528311e+01 9.27083318e+00 -1.12953031e+01 2 1.44278227e+01 -1.90666407e+01 9.35003672e+00 | 1.44278227e+01 -1.90666407e+01 9.35003672e+00 3 -2.09396872e+01 1.64231469e+01 1.00315424e+01 | -2.09396872e+01 1.64231469e+01 1.00315424e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTT (Configuration in file "config-Ti-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)) = -0.6315319478 2^p V(r_1,...,r_N) = -0.6315319478 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 2.83264850e+00 2.38453257e+00 2.70255395e+00 | 2.83264850e+00 2.38453257e+00 2.70255395e+00 1 -2.91122365e+00 -2.99867550e+00 2.48199353e+00 | -2.91122365e+00 -2.99867550e+00 2.48199353e+00 2 -2.22491858e+00 2.44133441e+00 -2.79810048e+00 | -2.22491858e+00 2.44133441e+00 -2.79810048e+00 3 2.30349373e+00 -1.82719149e+00 -2.38644700e+00 | 2.30349373e+00 -1.82719149e+00 -2.38644700e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTF (Configuration in file "config-Ti-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)) = -0.634198684336 2^p V(r_1,...,r_N) = -0.634198684336 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 1.91718052e+00 1.78489366e+00 2.26569756e+00 | 1.91718052e+00 1.78489366e+00 2.26569756e+00 1 -1.66937247e+00 -1.83370866e+00 1.79780354e+00 | -1.66937247e+00 -1.83370866e+00 1.79780354e+00 2 -1.97010424e+00 1.58140530e+00 -2.37578987e+00 | -1.97010424e+00 1.58140530e+00 -2.37578987e+00 3 1.72229619e+00 -1.53259030e+00 -1.68771122e+00 | 1.72229619e+00 -1.53259030e+00 -1.68771122e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFT (Configuration in file "config-Ti-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)) = 0.660208400353 2^p V(r_1,...,r_N) = 0.660208400353 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 1.92202832e+00 1.93531976e+00 1.52240543e+00 | 1.92202832e+00 1.93531976e+00 1.52240543e+00 1 -2.90722111e+00 -1.32516888e+00 2.99268234e+00 | -2.90722111e+00 -1.32516888e+00 2.99268234e+00 2 -1.79458968e+00 2.08017782e+00 -2.32487727e+00 | -1.79458968e+00 2.08017782e+00 -2.32487727e+00 3 2.77978248e+00 -2.69032870e+00 -2.19021050e+00 | 2.77978248e+00 -2.69032870e+00 -2.19021050e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFF (Configuration in file "config-Ti-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)) = 0.701416824123 2^p V(r_1,...,r_N) = 0.701416824123 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 2.53768250e+00 2.33821115e+00 1.87686290e+00 | 2.53768250e+00 2.33821115e+00 1.87686290e+00 1 -2.32497364e+00 -1.69380652e+00 1.65508891e+00 | -2.32497364e+00 -1.69380652e+00 1.65508891e+00 2 -1.77276493e+00 1.44385880e+00 -1.52644743e+00 | -1.77276493e+00 1.44385880e+00 -1.52644743e+00 3 1.56005607e+00 -2.08826343e+00 -2.00550437e+00 | 1.56005607e+00 -2.08826343e+00 -2.00550437e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTT (Configuration in file "config-Ti-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)) = 1.47625826539 2^p V(r_1,...,r_N) = 1.47625826539 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 1.44754148e+00 1.36920904e+00 1.05377231e+00 | 1.44754148e+00 1.36920904e+00 1.05377231e+00 1 -2.32786247e+00 -1.95063562e+00 1.80443010e+00 | -2.32786247e+00 -1.95063562e+00 1.80443010e+00 2 -6.86823305e-01 1.51820583e+00 -1.39903212e+00 | -6.86823305e-01 1.51820583e+00 -1.39903212e+00 3 1.56714430e+00 -9.36779254e-01 -1.45917029e+00 | 1.56714430e+00 -9.36779254e-01 -1.45917029e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTF (Configuration in file "config-Ti-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)) = 0.90176204308 2^p V(r_1,...,r_N) = 0.90176204308 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 1.98553222e+00 2.57308627e+00 2.22638580e+00 | 1.98553222e+00 2.57308627e+00 2.22638580e+00 1 -1.50652142e+00 -1.75240800e+00 1.27418754e+00 | -1.50652142e+00 -1.75240800e+00 1.27418754e+00 2 -2.02423508e+00 1.04371948e+00 -1.24697035e+00 | -2.02423508e+00 1.04371948e+00 -1.24697035e+00 3 1.54522428e+00 -1.86439775e+00 -2.25360299e+00 | 1.54522428e+00 -1.86439775e+00 -2.25360299e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FFT (Configuration in file "config-Ti-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)) = -1.87824355845 2^p V(r_1,...,r_N) = -1.87824355845 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 3.20827830e+00 2.78805484e+00 2.21413864e+00 | 3.20827830e+00 2.78805484e+00 2.21413864e+00 1 -3.45293055e+00 -1.78956911e+00 2.86516051e+00 | -3.45293055e+00 -1.78956911e+00 2.86516051e+00 2 -2.13079148e+00 2.46876106e+00 -2.92333459e+00 | -2.13079148e+00 2.46876106e+00 -2.92333459e+00 3 2.37544373e+00 -3.46724679e+00 -2.15596455e+00 | 2.37544373e+00 -3.46724679e+00 -2.15596455e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = TTT (Configuration in file "config-OTi-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)) = 0.943513234585 2^p V(r_1,...,r_N) = 0.943513234585 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 -1.01737061e+01 -1.36415425e+01 -1.41095120e+01 | -1.01737061e+01 -1.36415425e+01 -1.41095120e+01 1 8.42658300e+00 1.94948402e+00 -2.45456838e+00 | 8.42658300e+00 1.94948402e+00 -2.45456838e+00 2 9.34807164e+00 -1.85639125e+00 1.52890559e+00 | 9.34807164e+00 -1.85639125e+00 1.52890559e+00 3 -7.60094853e+00 1.35484497e+01 1.50351747e+01 | -7.60094853e+00 1.35484497e+01 1.50351747e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = TTF (Configuration in file "config-OTi-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)) = -0.825303951806 2^p V(r_1,...,r_N) = -0.825303951806 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 -9.48451095e+00 -5.49740409e+00 -5.73729929e+00 | -9.48451095e+00 -5.49740409e+00 -5.73729929e+00 1 6.40553785e+00 2.60347577e+00 -9.65013028e-01 | 6.40553785e+00 2.60347577e+00 -9.65013028e-01 2 3.87798221e+00 -9.72036674e-01 2.30381688e+00 | 3.87798221e+00 -9.72036674e-01 2.30381688e+00 3 -7.99009110e-01 3.86596499e+00 4.39849543e+00 | -7.99009110e-01 3.86596499e+00 4.39849543e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = TFT (Configuration in file "config-OTi-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)) = 1.04535620445 2^p V(r_1,...,r_N) = 1.04535620445 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 -6.94818458e+00 -6.56246262e+00 -8.89888324e+00 | -6.94818458e+00 -6.56246262e+00 -8.89888324e+00 1 6.47829926e+00 6.79073043e+00 -8.29475738e+00 | 6.47829926e+00 6.79073043e+00 -8.29475738e+00 2 1.28384759e+00 -9.59687954e-01 9.63642359e+00 | 1.28384759e+00 -9.59687954e-01 9.63642359e+00 3 -8.13962271e-01 7.31420146e-01 7.55721704e+00 | -8.13962271e-01 7.31420146e-01 7.55721704e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = TFF (Configuration in file "config-OTi-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)) = 0.696647031873 2^p V(r_1,...,r_N) = 0.696647031873 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 -3.95625953e+00 -1.24057815e+01 -1.63001208e+01 | -3.95625953e+00 -1.24057815e+01 -1.63001208e+01 1 7.80633976e+00 4.78885424e+00 -2.19655303e+00 | 7.80633976e+00 4.78885424e+00 -2.19655303e+00 2 6.50109511e+00 -3.25256637e+00 3.82172565e+00 | 6.50109511e+00 -3.25256637e+00 3.82172565e+00 3 -1.03511753e+01 1.08694936e+01 1.46749481e+01 | -1.03511753e+01 1.08694936e+01 1.46749481e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = FTT (Configuration in file "config-OTi-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)) = 3.9722188149 2^p V(r_1,...,r_N) = 3.9722188149 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 -2.50409243e+00 -1.07110296e+00 -8.63358188e+00 | -2.50409243e+00 -1.07110296e+00 -8.63358188e+00 1 4.72585120e+00 3.59382753e+00 -8.15351976e+00 | 4.72585120e+00 3.59382753e+00 -8.15351976e+00 2 5.81584867e+00 -1.23391241e+01 7.48404168e+00 | 5.81584867e+00 -1.23391241e+01 7.48404168e+00 3 -8.03760744e+00 9.81639958e+00 9.30305996e+00 | -8.03760744e+00 9.81639958e+00 9.30305996e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = FTF (Configuration in file "config-OTi-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)) = 2.0026568384 2^p V(r_1,...,r_N) = 2.0026568384 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 -6.92829898e+00 -7.36845095e+00 -6.93170886e+00 | -6.92829898e+00 -7.36845095e+00 -6.93170886e+00 1 4.03920535e+00 8.61160663e+00 -9.03771321e+00 | 4.03920535e+00 8.61160663e+00 -9.03771321e+00 2 4.60632607e+00 -2.68983963e+00 8.08107861e+00 | 4.60632607e+00 -2.68983963e+00 8.08107861e+00 3 -1.71723244e+00 1.44668395e+00 7.88834346e+00 | -1.71723244e+00 1.44668395e+00 7.88834346e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = O Ti, PBC = FFT (Configuration in file "config-OTi-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.49829288402 2^p V(r_1,...,r_N) = -2.49829288402 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 -8.65120979e+00 -3.94891314e+00 -8.24201921e+00 | -8.65120979e+00 -3.94891314e+00 -8.24201921e+00 1 2.59410340e-01 3.56185160e+00 7.26133683e-01 | 2.59410340e-01 3.56185160e+00 7.26133683e-01 2 7.85769980e+00 -2.93317680e+00 7.33229661e+00 | 7.85769980e+00 -2.93317680e+00 7.33229661e+00 3 5.34099650e-01 3.32023834e+00 1.83588923e-01 | 5.34099650e-01 3.32023834e+00 1.83588923e-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.