!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Wagner_2007_Cu__SM_521856783904_000 Supported species : Cu random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.10097082247 2^p V(r_1,...,r_N) = -6.10097082247 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 -2.77264987e-01 -4.54384761e+00 -4.21207268e+00 | -2.77264987e-01 -4.54384761e+00 -4.21207268e+00 1 4.65174323e+00 7.05287092e-01 -4.62569954e+00 | 4.65174323e+00 7.05287092e-01 -4.62569954e+00 2 2.20361453e+00 -3.90921871e+00 2.18099639e+00 | 2.20361453e+00 -3.90921871e+00 2.18099639e+00 3 -6.57809278e+00 7.74777923e+00 6.65677583e+00 | -6.57809278e+00 7.74777923e+00 6.65677583e+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)) = -7.26249825973 2^p V(r_1,...,r_N) = -7.26249825973 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 1.48088792e+00 1.27170131e+00 -3.52067359e-01 | 1.48088792e+00 1.27170131e+00 -3.52067359e-01 1 -9.16812098e-03 -5.63030784e-01 -2.90441499e+00 | -9.16812098e-03 -5.63030784e-01 -2.90441499e+00 2 4.42528847e+00 -4.13190444e+00 1.04353396e+00 | 4.42528847e+00 -4.13190444e+00 1.04353396e+00 3 -5.89700827e+00 3.42323391e+00 2.21294839e+00 | -5.89700827e+00 3.42323391e+00 2.21294839e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -3.20657951771 2^p V(r_1,...,r_N) = -3.20657951771 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 -1.90014747e+00 -3.57768379e+00 -2.15245473e+00 | -1.90014747e+00 -3.57768379e+00 -2.15245473e+00 1 7.42344619e+00 6.63919878e+00 -1.79581684e+01 | 7.42344619e+00 6.63919878e+00 -1.79581684e+01 2 3.72886902e+00 -8.41427234e+00 1.19390363e+01 | 3.72886902e+00 -8.41427234e+00 1.19390363e+01 3 -9.25216774e+00 5.35275735e+00 8.17158688e+00 | -9.25216774e+00 5.35275735e+00 8.17158688e+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)) = -5.78127676418 2^p V(r_1,...,r_N) = -5.78127676418 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 -3.27103749e+00 -3.75425697e+00 -2.76280946e+00 | -3.27103749e+00 -3.75425697e+00 -2.76280946e+00 1 4.23445680e+00 6.28314120e+00 -5.64187420e+00 | 4.23445680e+00 6.28314120e+00 -5.64187420e+00 2 4.33272518e+00 -6.79927254e+00 4.72181315e+00 | 4.33272518e+00 -6.79927254e+00 4.72181315e+00 3 -5.29614449e+00 4.27038830e+00 3.68287051e+00 | -5.29614449e+00 4.27038830e+00 3.68287051e+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)) = -7.62071968796 2^p V(r_1,...,r_N) = -7.62071968796 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 -5.75148862e-01 7.85267019e-01 9.24961953e-01 | -5.75148862e-01 7.85267019e-01 9.24961953e-01 1 3.12885219e-01 2.92932229e+00 -2.53421786e+00 | 3.12885219e-01 2.92932229e+00 -2.53421786e+00 2 1.48826420e+00 -3.30773668e+00 2.42550576e+00 | 1.48826420e+00 -3.30773668e+00 2.42550576e+00 3 -1.22600056e+00 -4.06852631e-01 -8.16249849e-01 | -1.22600056e+00 -4.06852631e-01 -8.16249849e-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)) = 0.76219573028 2^p V(r_1,...,r_N) = 0.76219573028 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 -9.11296487e+00 -4.38484494e+00 -9.31865163e+00 | -9.11296487e+00 -4.38484494e+00 -9.31865163e+00 1 7.53522345e+00 2.54239185e+01 -2.29593865e+01 | 7.53522345e+00 2.54239185e+01 -2.29593865e+01 2 4.66325281e+00 -2.80942055e+01 2.66251878e+01 | 4.66325281e+00 -2.80942055e+01 2.66251878e+01 3 -3.08551139e+00 7.05513201e+00 5.65285034e+00 | -3.08551139e+00 7.05513201e+00 5.65285034e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -3.59778498178 2^p V(r_1,...,r_N) = -3.59778498178 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 -1.62540255e+00 -1.25002654e+01 -7.76359376e+00 | -1.62540255e+00 -1.25002654e+01 -7.76359376e+00 1 4.93050725e+00 6.85654518e+00 -5.65879979e+00 | 4.93050725e+00 6.85654518e+00 -5.65879979e+00 2 4.49284832e+00 -6.74776319e+00 5.38897751e+00 | 4.49284832e+00 -6.74776319e+00 5.38897751e+00 3 -7.79795302e+00 1.23914834e+01 8.03341604e+00 | -7.79795302e+00 1.23914834e+01 8.03341604e+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.