!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ADP_PunDarlingKecskes_2015_CuTa__SM_399364650444_000 Supported species : Cu Ta random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.93327404623 2^p V(r_1,...,r_N) = -4.93327404623 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 -3.54101719e+00 -7.63302632e+00 -7.77007378e+00 | -3.54101719e+00 -7.63302632e+00 -7.77007378e+00 1 2.85265184e+00 2.33900829e+00 -2.08560240e+00 | 2.85265184e+00 2.33900829e+00 -2.08560240e+00 2 2.04092068e+00 -2.53749398e+00 3.64304396e+00 | 2.04092068e+00 -2.53749398e+00 3.64304396e+00 3 -1.35255533e+00 7.83151200e+00 6.21263222e+00 | -1.35255533e+00 7.83151200e+00 6.21263222e+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)) = -5.60760379449 2^p V(r_1,...,r_N) = -5.60760379449 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 1.00270546e+00 7.04370440e-01 7.86292464e-01 | 1.00270546e+00 7.04370440e-01 7.86292464e-01 1 8.32307960e-01 1.39145364e+00 -2.94107644e+00 | 8.32307960e-01 1.39145364e+00 -2.94107644e+00 2 4.32085108e+00 -5.44833901e+00 1.22406554e+00 | 4.32085108e+00 -5.44833901e+00 1.22406554e+00 3 -6.15586451e+00 3.35251493e+00 9.30718432e-01 | -6.15586451e+00 3.35251493e+00 9.30718432e-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)) = -3.83589923611 2^p V(r_1,...,r_N) = -3.83589923611 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 -3.85201249e+00 -3.75068148e+00 -4.55857217e+00 | -3.85201249e+00 -3.75068148e+00 -4.55857217e+00 1 3.76560848e+00 3.95787390e+00 -5.27421775e+00 | 3.76560848e+00 3.95787390e+00 -5.27421775e+00 2 8.09641869e+00 -6.97425461e+00 4.84076760e+00 | 8.09641869e+00 -6.97425461e+00 4.84076760e+00 3 -8.01001468e+00 6.76706219e+00 4.99202232e+00 | -8.01001468e+00 6.76706219e+00 4.99202232e+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)) = -5.11767733491 2^p V(r_1,...,r_N) = -5.11767733491 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 -2.81808850e+00 -3.03840217e+00 -5.22442610e+00 | -2.81808850e+00 -3.03840217e+00 -5.22442610e+00 1 1.80891957e+00 2.61504199e+00 -2.51740527e+00 | 1.80891957e+00 2.61504199e+00 -2.51740527e+00 2 6.28960665e+00 -5.93682321e+00 3.65539667e+00 | 6.28960665e+00 -5.93682321e+00 3.65539667e+00 3 -5.28043772e+00 6.36018338e+00 4.08643470e+00 | -5.28043772e+00 6.36018338e+00 4.08643470e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.970513539404 2^p V(r_1,...,r_N) = 0.970513539404 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 -5.45393839e+00 -7.52151744e+00 -7.22371803e+00 | -5.45393839e+00 -7.52151744e+00 -7.22371803e+00 1 2.26694768e+01 1.25652959e+00 -1.87652299e+01 | 2.26694768e+01 1.25652959e+00 -1.87652299e+01 2 3.68075102e+00 -3.48738444e+00 3.23227405e+00 | 3.68075102e+00 -3.48738444e+00 3.23227405e+00 3 -2.08962895e+01 9.75237229e+00 2.27566739e+01 | -2.08962895e+01 9.75237229e+00 2.27566739e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.67352755629 2^p V(r_1,...,r_N) = -1.67352755629 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 -7.09990159e+00 -1.54992391e+01 -8.91237385e+00 | -7.09990159e+00 -1.54992391e+01 -8.91237385e+00 1 1.09619639e+01 7.54195819e+00 -7.25593905e+00 | 1.09619639e+01 7.54195819e+00 -7.25593905e+00 2 3.07768885e+00 -1.01244479e+00 2.98338082e+00 | 3.07768885e+00 -1.01244479e+00 2.98338082e+00 3 -6.93975120e+00 8.96972567e+00 1.31849321e+01 | -6.93975120e+00 8.96972567e+00 1.31849321e+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)) = -6.57196407777 2^p V(r_1,...,r_N) = -6.57196407777 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 -2.37783287e+00 -3.93319215e+00 -1.71148839e+00 | -2.37783287e+00 -3.93319215e+00 -1.71148839e+00 1 2.07800188e+00 2.47607159e+00 -1.82908078e+00 | 2.07800188e+00 2.47607159e+00 -1.82908078e+00 2 1.16197795e+00 -6.37315042e-01 1.52939415e+00 | 1.16197795e+00 -6.37315042e-01 1.52939415e+00 3 -8.62146957e-01 2.09443560e+00 2.01117502e+00 | -8.62146957e-01 2.09443560e+00 2.01117502e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTT (Configuration in file "config-Ta-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.94470398871 2^p V(r_1,...,r_N) = -1.94470398871 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 -1.21370165e+01 -1.22479616e+01 -6.61865422e+00 | -1.21370165e+01 -1.22479616e+01 -6.61865422e+00 1 1.17793613e+01 6.99890239e+00 -1.31908395e+01 | 1.17793613e+01 6.99890239e+00 -1.31908395e+01 2 9.34373378e+00 -5.64516518e+00 8.86953284e+00 | 9.34373378e+00 -5.64516518e+00 8.86953284e+00 3 -8.98607860e+00 1.08942244e+01 1.09399609e+01 | -8.98607860e+00 1.08942244e+01 1.09399609e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTF (Configuration in file "config-Ta-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.88165933031 2^p V(r_1,...,r_N) = 6.88165933031 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 -1.69241865e+01 -1.31716136e+01 -1.19935043e+01 | -1.69241865e+01 -1.31716136e+01 -1.19935043e+01 1 1.50556194e+01 1.10098858e+01 -1.34361121e+01 | 1.50556194e+01 1.10098858e+01 -1.34361121e+01 2 1.22383843e+01 -1.46277398e+01 1.22958750e+01 | 1.22383843e+01 -1.46277398e+01 1.22958750e+01 3 -1.03698172e+01 1.67894676e+01 1.31337414e+01 | -1.03698172e+01 1.67894676e+01 1.31337414e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFT (Configuration in file "config-Ta-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 4.33234108313 2^p V(r_1,...,r_N) = 4.33234108313 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 -1.24245864e+01 -1.23074112e+01 -1.55612133e+01 | -1.24245864e+01 -1.23074112e+01 -1.55612133e+01 1 1.50260432e+01 1.28836732e+01 -1.02928355e+01 | 1.50260432e+01 1.28836732e+01 -1.02928355e+01 2 1.04545516e+01 -1.26167782e+01 1.37975945e+01 | 1.04545516e+01 -1.26167782e+01 1.37975945e+01 3 -1.30560084e+01 1.20405162e+01 1.20564543e+01 | -1.30560084e+01 1.20405162e+01 1.20564543e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFF (Configuration in file "config-Ta-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.13402664686 2^p V(r_1,...,r_N) = 1.13402664686 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 -1.37957232e+01 -9.14359986e+00 -1.32173966e+01 | -1.37957232e+01 -9.14359986e+00 -1.32173966e+01 1 1.24294551e+01 1.48060000e+01 -9.26429999e+00 | 1.24294551e+01 1.48060000e+01 -9.26429999e+00 2 1.16124952e+01 -1.41489498e+01 1.31387740e+01 | 1.16124952e+01 -1.41489498e+01 1.31387740e+01 3 -1.02462271e+01 8.48654966e+00 9.34292261e+00 | -1.02462271e+01 8.48654966e+00 9.34292261e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTT (Configuration in file "config-Ta-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.18655680797 2^p V(r_1,...,r_N) = 2.18655680797 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 -1.54124319e+01 -1.22337972e+01 -1.09194124e+01 | -1.54124319e+01 -1.22337972e+01 -1.09194124e+01 1 1.53681483e+01 8.71375561e+00 -1.44521651e+01 | 1.53681483e+01 8.71375561e+00 -1.44521651e+01 2 9.01889959e+00 -1.28501050e+01 1.16184859e+01 | 9.01889959e+00 -1.28501050e+01 1.16184859e+01 3 -8.97461598e+00 1.63701466e+01 1.37530916e+01 | -8.97461598e+00 1.63701466e+01 1.37530916e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTF (Configuration in file "config-Ta-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.48689061677 2^p V(r_1,...,r_N) = 8.48689061677 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 -1.22580425e+01 -1.18471034e+01 -1.43939902e+01 | -1.22580425e+01 -1.18471034e+01 -1.43939902e+01 1 9.60280085e+00 1.05935650e+01 -1.09371382e+01 | 9.60280085e+00 1.05935650e+01 -1.09371382e+01 2 1.41775089e+01 -1.37219020e+01 9.44973783e+00 | 1.41775089e+01 -1.37219020e+01 9.44973783e+00 3 -1.15222673e+01 1.49754404e+01 1.58813905e+01 | -1.15222673e+01 1.49754404e+01 1.58813905e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FFT (Configuration in file "config-Ta-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.90733540868 2^p V(r_1,...,r_N) = -2.90733540868 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 -8.49553147e+00 -1.32801152e+01 -8.33842985e+00 | -8.49553147e+00 -1.32801152e+01 -8.33842985e+00 1 1.14391874e+01 1.03321855e+01 -1.19501925e+01 | 1.14391874e+01 1.03321855e+01 -1.19501925e+01 2 8.08282173e+00 -6.74579959e+00 6.89268935e+00 | 8.08282173e+00 -6.74579959e+00 6.89268935e+00 3 -1.10264777e+01 9.69372931e+00 1.33959330e+01 | -1.10264777e+01 9.69372931e+00 1.33959330e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTT (Configuration in file "config-CuTa-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 51.4893614369 2^p V(r_1,...,r_N) = 51.4893614369 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 -2.13818288e+02 4.66266516e+01 -1.94422183e+02 | -2.13818288e+02 4.66266516e+01 -1.94422183e+02 1 4.57974132e+01 3.76187227e+01 -3.36808398e+01 | 4.57974132e+01 3.76187227e+01 -3.36808398e+01 2 2.43778131e+02 -1.44598030e+02 1.73017593e+02 | 2.43778131e+02 -1.44598030e+02 1.73017593e+02 3 -7.57572559e+01 6.03526556e+01 5.50854301e+01 | -7.57572559e+01 6.03526556e+01 5.50854301e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTF (Configuration in file "config-CuTa-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 37.6155451694 2^p V(r_1,...,r_N) = 37.6155451694 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 -1.55405886e+02 -1.04923849e+02 -2.17027386e+01 | -1.55405886e+02 -1.04923849e+02 -2.17027386e+01 1 1.57872724e+02 8.99891786e+01 -6.66433266e+01 | 1.57872724e+02 8.99891786e+01 -6.66433266e+01 2 6.73831223e+01 -2.50408770e+01 4.18122540e+01 | 6.73831223e+01 -2.50408770e+01 4.18122540e+01 3 -6.98499601e+01 3.99755470e+01 4.65338112e+01 | -6.98499601e+01 3.99755470e+01 4.65338112e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFT (Configuration in file "config-CuTa-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.49401898636 2^p V(r_1,...,r_N) = 6.49401898636 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 -5.65314416e+01 -1.78732372e+01 -5.95488136e+01 | -5.65314416e+01 -1.78732372e+01 -5.95488136e+01 1 7.01685491e+00 1.87073959e+01 -1.68826837e+01 | 7.01685491e+00 1.87073959e+01 -1.68826837e+01 2 5.70571529e+01 -1.52911448e+01 6.05406543e+01 | 5.70571529e+01 -1.52911448e+01 6.05406543e+01 3 -7.54256620e+00 1.44569860e+01 1.58908430e+01 | -7.54256620e+00 1.44569860e+01 1.58908430e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFF (Configuration in file "config-CuTa-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 384.781247948 2^p V(r_1,...,r_N) = 384.781247948 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 -9.16783222e+02 -5.14394006e+02 -1.15052171e+03 | -9.16783222e+02 -5.14394006e+02 -1.15052171e+03 1 6.28366335e+02 6.56732820e+02 -7.98907173e+02 | 6.28366335e+02 6.56732820e+02 -7.98907173e+02 2 7.38404887e+02 -2.57603164e+02 1.52246954e+03 | 7.38404887e+02 -2.57603164e+02 1.52246954e+03 3 -4.49988000e+02 1.15264350e+02 4.26959335e+02 | -4.49988000e+02 1.15264350e+02 4.26959335e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTT (Configuration in file "config-CuTa-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.02823688983 2^p V(r_1,...,r_N) = -9.02823688983 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 -5.60606760e+00 -3.97403248e+00 -4.73524968e+00 | -5.60606760e+00 -3.97403248e+00 -4.73524968e+00 1 5.97640741e+00 5.38299618e+00 -2.86249371e+00 | 5.97640741e+00 5.38299618e+00 -2.86249371e+00 2 3.27449682e+00 -4.39335268e+00 4.51664280e+00 | 3.27449682e+00 -4.39335268e+00 4.51664280e+00 3 -3.64483664e+00 2.98438898e+00 3.08110059e+00 | -3.64483664e+00 2.98438898e+00 3.08110059e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTF (Configuration in file "config-CuTa-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.03207049674 2^p V(r_1,...,r_N) = -7.03207049674 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 -4.67093848e+00 -1.33935666e+01 -6.97868736e+00 | -4.67093848e+00 -1.33935666e+01 -6.97868736e+00 1 8.93772660e+00 8.40704704e+00 -6.73287662e+00 | 8.93772660e+00 8.40704704e+00 -6.73287662e+00 2 1.47687658e+00 -4.36283287e+00 3.27332047e+00 | 1.47687658e+00 -4.36283287e+00 3.27332047e+00 3 -5.74366471e+00 9.34935239e+00 1.04382435e+01 | -5.74366471e+00 9.34935239e+00 1.04382435e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FFT (Configuration in file "config-CuTa-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 158.600002962 2^p V(r_1,...,r_N) = 158.600002962 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 -4.80251185e+01 -1.56628165e+02 -2.03290015e+02 | -4.80251185e+01 -1.56628165e+02 -2.03290015e+02 1 3.53297943e+02 2.87329959e+02 -6.87151630e+02 | 3.53297943e+02 2.87329959e+02 -6.87151630e+02 2 8.04543595e+01 -2.31924648e+02 2.57092511e+02 | 8.04543595e+01 -2.31924648e+02 2.57092511e+02 3 -3.85727184e+02 1.01222855e+02 6.33349134e+02 | -3.85727184e+02 1.01222855e+02 6.33349134e+02 ------------------------------------------------------------------------------------------------------------------------ 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.