!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_EDIP_JiangMorganSzlufarska_2012_SiC__SM_435704953434_000 Supported species : C Si random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTT (Configuration in file "config-C-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)) = -4.55102418885 2^p V(r_1,...,r_N) = -4.55102418885 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 1.04027326e+01 1.43249614e+01 1.21213442e+01 | 1.04027326e+01 1.43249614e+01 1.21213442e+01 1 -1.49632473e+01 -4.41777058e+00 8.80593643e+00 | -1.49632473e+01 -4.41777058e+00 8.80593643e+00 2 -6.67242940e+00 6.96179848e+00 -5.97018177e+00 | -6.67242940e+00 6.96179848e+00 -5.97018177e+00 3 1.12329442e+01 -1.68689893e+01 -1.49570988e+01 | 1.12329442e+01 -1.68689893e+01 -1.49570988e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-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)) = -12.8383557242 2^p V(r_1,...,r_N) = -12.8383557242 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 3.48944154e+00 4.81565910e+00 1.03841909e+01 | 3.48944154e+00 4.81565910e+00 1.03841909e+01 1 -8.69221329e+00 -4.46764220e+00 1.10346748e+01 | -8.69221329e+00 -4.46764220e+00 1.10346748e+01 2 -7.80678481e+00 8.45174798e+00 -8.62399291e+00 | -7.80678481e+00 8.45174798e+00 -8.62399291e+00 3 1.30095566e+01 -8.79976487e+00 -1.27948728e+01 | 1.30095566e+01 -8.79976487e+00 -1.27948728e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFT (Configuration in file "config-C-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)) = -5.05790120505 2^p V(r_1,...,r_N) = -5.05790120505 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 1.06119656e+00 5.59794596e+00 7.04909842e+00 | 1.06119656e+00 5.59794596e+00 7.04909842e+00 1 -7.11047326e+00 -6.98488940e+00 1.35835855e+01 | -7.11047326e+00 -6.98488940e+00 1.35835855e+01 2 -1.21650016e+01 1.15548978e+01 -2.18116300e+00 | -1.21650016e+01 1.15548978e+01 -2.18116300e+00 3 1.82142783e+01 -1.01679543e+01 -1.84515209e+01 | 1.82142783e+01 -1.01679543e+01 -1.84515209e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFF (Configuration in file "config-C-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)) = -9.53403318431 2^p V(r_1,...,r_N) = -9.53403318431 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 1.11363752e+01 9.19008229e+00 7.27883736e+00 | 1.11363752e+01 9.19008229e+00 7.27883736e+00 1 -1.40990653e+01 -1.77886790e+01 1.06549822e+01 | -1.40990653e+01 -1.77886790e+01 1.06549822e+01 2 -1.24449991e+01 1.86887393e+01 -6.56114084e+00 | -1.24449991e+01 1.86887393e+01 -6.56114084e+00 3 1.54076892e+01 -1.00901426e+01 -1.13726787e+01 | 1.54076892e+01 -1.00901426e+01 -1.13726787e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTT (Configuration in file "config-C-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)) = -11.5163739916 2^p V(r_1,...,r_N) = -11.5163739916 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 1.13582710e+01 1.38120487e+01 1.45299574e+01 | 1.13582710e+01 1.38120487e+01 1.45299574e+01 1 -1.42325595e+01 -8.84976699e+00 8.25058433e+00 | -1.42325595e+01 -8.84976699e+00 8.25058433e+00 2 -7.32581691e+00 -2.55844835e-01 -9.17726907e+00 | -7.32581691e+00 -2.55844835e-01 -9.17726907e+00 3 1.02001054e+01 -4.70643686e+00 -1.36032727e+01 | 1.02001054e+01 -4.70643686e+00 -1.36032727e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTF (Configuration in file "config-C-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)) = -3.9774851942 2^p V(r_1,...,r_N) = -3.9774851942 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 1.10935611e+01 6.37057381e-01 1.28956620e+01 | 1.10935611e+01 6.37057381e-01 1.28956620e+01 1 -4.40982741e-01 -1.99309387e+00 1.75176747e+00 | -4.40982741e-01 -1.99309387e+00 1.75176747e+00 2 -2.25212483e+01 1.25204303e+01 -9.63989565e+00 | -2.25212483e+01 1.25204303e+01 -9.63989565e+00 3 1.18686699e+01 -1.11643938e+01 -5.00753379e+00 | 1.18686699e+01 -1.11643938e+01 -5.00753379e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-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)) = -3.12204486689 2^p V(r_1,...,r_N) = -3.12204486689 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 1.08716021e+00 9.91439190e-01 2.54956048e-01 | 1.08716021e+00 9.91439190e-01 2.54956048e-01 1 -8.92161011e+00 -1.16044922e+01 1.62468775e+01 | -8.92161011e+00 -1.16044922e+01 1.62468775e+01 2 -4.60828532e+00 1.66204764e+01 -1.18101043e+01 | -4.60828532e+00 1.66204764e+01 -1.18101043e+01 3 1.24427352e+01 -6.00742339e+00 -4.69172922e+00 | 1.24427352e+01 -6.00742339e+00 -4.69172922e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTT (Configuration in file "config-Si-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.723971425928 2^p V(r_1,...,r_N) = -0.723971425928 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 -1.41625460e+01 -1.47939772e+01 -1.63342528e+01 | -1.41625460e+01 -1.47939772e+01 -1.63342528e+01 1 1.88793599e+01 1.36668785e+01 -1.96903189e+01 | 1.88793599e+01 1.36668785e+01 -1.96903189e+01 2 1.56044001e+01 -1.23748705e+01 1.46100103e+01 | 1.56044001e+01 -1.23748705e+01 1.46100103e+01 3 -2.03212140e+01 1.35019692e+01 2.14145614e+01 | -2.03212140e+01 1.35019692e+01 2.14145614e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTF (Configuration in file "config-Si-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 12.927376241 2^p V(r_1,...,r_N) = 12.927376241 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 -1.55561716e+01 -2.26782186e+01 -2.38810180e+01 | -1.55561716e+01 -2.26782186e+01 -2.38810180e+01 1 1.83718692e+01 2.37412048e+01 -1.95467520e+01 | 1.83718692e+01 2.37412048e+01 -1.95467520e+01 2 1.18543597e+01 -2.48651010e+01 9.97986677e+00 | 1.18543597e+01 -2.48651010e+01 9.97986677e+00 3 -1.46700573e+01 2.38021148e+01 3.34479032e+01 | -1.46700573e+01 2.38021148e+01 3.34479032e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFT (Configuration in file "config-Si-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.526919256628 2^p V(r_1,...,r_N) = 0.526919256628 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 -1.61630126e+01 -2.41984253e+01 -2.59584144e+01 | -1.61630126e+01 -2.41984253e+01 -2.59584144e+01 1 1.22775875e+01 2.88080436e+01 -2.45664977e+01 | 1.22775875e+01 2.88080436e+01 -2.45664977e+01 2 1.54070461e+01 -2.22742145e+01 2.28142849e+01 | 1.54070461e+01 -2.22742145e+01 2.28142849e+01 3 -1.15216210e+01 1.76645961e+01 2.77106273e+01 | -1.15216210e+01 1.76645961e+01 2.77106273e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFF (Configuration in file "config-Si-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 12.8205131191 2^p V(r_1,...,r_N) = 12.8205131191 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 -2.84235659e+01 -1.31139230e+01 -3.20406517e+01 | -2.84235659e+01 -1.31139230e+01 -3.20406517e+01 1 3.79664609e+01 1.91301837e+01 -3.10202836e+01 | 3.79664609e+01 1.91301837e+01 -3.10202836e+01 2 3.19318338e+01 -1.78043211e+01 3.65483934e+01 | 3.19318338e+01 -1.78043211e+01 3.65483934e+01 3 -4.14747288e+01 1.17880604e+01 2.65125419e+01 | -4.14747288e+01 1.17880604e+01 2.65125419e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTT (Configuration in file "config-Si-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.19616380062 2^p V(r_1,...,r_N) = -6.19616380062 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 -6.24592015e+00 -8.37586957e+00 -1.32734517e+01 | -6.24592015e+00 -8.37586957e+00 -1.32734517e+01 1 8.87312802e+00 1.04994155e+01 -1.11773924e+01 | 8.87312802e+00 1.04994155e+01 -1.11773924e+01 2 5.59351452e+00 -1.39436232e+01 1.47793692e+01 | 5.59351452e+00 -1.39436232e+01 1.47793692e+01 3 -8.22072239e+00 1.18200773e+01 9.67147485e+00 | -8.22072239e+00 1.18200773e+01 9.67147485e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTF (Configuration in file "config-Si-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 28.6632375253 2^p V(r_1,...,r_N) = 28.6632375253 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 -1.94887235e+01 -3.79582183e+01 -3.28013720e+01 | -1.94887235e+01 -3.79582183e+01 -3.28013720e+01 1 3.48237795e+01 3.42076843e+01 -2.45428654e+01 | 3.48237795e+01 3.42076843e+01 -2.45428654e+01 2 2.53758388e+01 -3.73503559e+01 2.16142896e+01 | 2.53758388e+01 -3.73503559e+01 2.16142896e+01 3 -4.07108947e+01 4.11008899e+01 3.57299478e+01 | -4.07108947e+01 4.11008899e+01 3.57299478e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FFT (Configuration in file "config-Si-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 46.4327425266 2^p V(r_1,...,r_N) = 46.4327425266 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 -4.29224345e+01 -3.67509236e+01 -4.40192710e+01 | -4.29224345e+01 -3.67509236e+01 -4.40192710e+01 1 2.44636265e+01 1.54974498e+01 -4.09065866e+01 | 2.44636265e+01 1.54974498e+01 -4.09065866e+01 2 3.99078242e+01 -2.69267643e+01 3.84046514e+01 | 3.99078242e+01 -2.69267643e+01 3.84046514e+01 3 -2.14490162e+01 4.81802381e+01 4.65212062e+01 | -2.14490162e+01 4.81802381e+01 4.65212062e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TTT (Configuration in file "config-CSi-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)) = 13.1367245322 2^p V(r_1,...,r_N) = 13.1367245322 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 -3.89683950e+01 -2.60688778e+01 -3.09940012e+01 | -3.89683950e+01 -2.60688778e+01 -3.09940012e+01 1 3.38762492e+01 3.02754825e+01 -2.99133233e+01 | 3.38762492e+01 3.02754825e+01 -2.99133233e+01 2 3.39144859e+01 -3.29496398e+01 2.72773630e+01 | 3.39144859e+01 -3.29496398e+01 2.72773630e+01 3 -2.88223402e+01 2.87430350e+01 3.36299615e+01 | -2.88223402e+01 2.87430350e+01 3.36299615e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TTF (Configuration in file "config-CSi-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)) = -8.69553067336 2^p V(r_1,...,r_N) = -8.69553067336 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 3.02932843e+00 -1.61899921e+00 6.99856323e+00 | 3.02932843e+00 -1.61899921e+00 6.99856323e+00 1 -8.50248240e+00 1.41373384e+00 7.96046447e+00 | -8.50248240e+00 1.41373384e+00 7.96046447e+00 2 -4.87831733e+00 2.24443207e+00 -6.30088066e+00 | -4.87831733e+00 2.24443207e+00 -6.30088066e+00 3 1.03514713e+01 -2.03916670e+00 -8.65814704e+00 | 1.03514713e+01 -2.03916670e+00 -8.65814704e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TFT (Configuration in file "config-CSi-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)) = -9.35005497391 2^p V(r_1,...,r_N) = -9.35005497391 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 1.35262646e+01 8.61433643e+00 2.78688107e+00 | 1.35262646e+01 8.61433643e+00 2.78688107e+00 1 -1.00065417e+01 -1.30595689e+01 1.63116671e+01 | -1.00065417e+01 -1.30595689e+01 1.63116671e+01 2 -2.43638173e+00 1.24420111e+00 -1.37789276e+01 | -2.43638173e+00 1.24420111e+00 -1.37789276e+01 3 -1.08334122e+00 3.20103137e+00 -5.31962058e+00 | -1.08334122e+00 3.20103137e+00 -5.31962058e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TFF (Configuration in file "config-CSi-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)) = -10.2425184419 2^p V(r_1,...,r_N) = -10.2425184419 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 -6.41792219e+00 -4.61316815e+00 -8.10494912e+00 | -6.41792219e+00 -4.61316815e+00 -8.10494912e+00 1 6.12394749e+00 6.57803854e+00 -7.95854901e+00 | 6.12394749e+00 6.57803854e+00 -7.95854901e+00 2 8.96571851e+00 -7.95296608e+00 7.56836468e+00 | 8.96571851e+00 -7.95296608e+00 7.56836468e+00 3 -8.67174381e+00 5.98809569e+00 8.49513345e+00 | -8.67174381e+00 5.98809569e+00 8.49513345e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FTT (Configuration in file "config-CSi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.02592787657 2^p V(r_1,...,r_N) = -6.02592787657 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 -1.15311015e+01 -1.47409817e+01 -4.79654391e+00 | -1.15311015e+01 -1.47409817e+01 -4.79654391e+00 1 2.28489769e+01 6.27494818e+00 9.09757602e-01 | 2.28489769e+01 6.27494818e+00 9.09757602e-01 2 -2.12144363e+00 5.95718452e+00 -5.09803068e+00 | -2.12144363e+00 5.95718452e+00 -5.09803068e+00 3 -9.19643178e+00 2.50884896e+00 8.98481698e+00 | -9.19643178e+00 2.50884896e+00 8.98481698e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FTF (Configuration in file "config-CSi-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)) = -11.1353748833 2^p V(r_1,...,r_N) = -11.1353748833 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 7.50218882e+00 6.96676970e+00 8.60187802e-01 | 7.50218882e+00 6.96676970e+00 8.60187802e-01 1 -5.96756352e+00 -7.19875643e+00 -4.93634649e-02 | -5.96756352e+00 -7.19875643e+00 -4.93634649e-02 2 6.44455135e-01 6.84721070e-01 -1.59744700e+00 | 6.44455135e-01 6.84721070e-01 -1.59744700e+00 3 -2.17908043e+00 -4.52734345e-01 7.86622663e-01 | -2.17908043e+00 -4.52734345e-01 7.86622663e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FFT (Configuration in file "config-CSi-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)) = -8.99282755926 2^p V(r_1,...,r_N) = -8.99282755926 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 6.67714051e+00 1.84257086e+00 6.50918852e+00 | 6.67714051e+00 1.84257086e+00 6.50918852e+00 1 7.51484810e+00 6.14032488e+00 -9.49263741e+00 | 7.51484810e+00 6.14032488e+00 -9.49263741e+00 2 6.23233898e-02 -1.91380850e+01 -1.02031887e+00 | 6.23233898e-02 -1.91380850e+01 -1.02031887e+00 3 -1.42543120e+01 1.11551892e+01 4.00376776e+00 | -1.42543120e+01 1.11551892e+01 4.00376776e+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.