!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BOP_ZhouWardFoster_2016_AlCu__SM_566399258279_001 Supported species : Al Cu random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 13.967515657071155 2^p V(r_1,...,r_N) = 13.96751565707118 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 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 1 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 2 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 3 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 4 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 5 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 6 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 7 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 8 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 9 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 10 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 11 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 12 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 13 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 14 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 15 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 16 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 17 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 18 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 19 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 20 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 21 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 22 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 23 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 24 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 25 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 26 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 27 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 28 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 | 4.10681033e-01 -8.67939724e-01 -6.30830824e-01 29 -1.52331638e+00 8.59396166e-01 9.81474963e-01 | -1.52331638e+00 8.59396166e-01 9.81474963e-01 30 5.34784653e-01 2.92787928e-01 -8.62097357e-01 | 5.34784653e-01 2.92787928e-01 -8.62097357e-01 31 5.77850692e-01 -2.84244370e-01 5.11453218e-01 | 5.77850692e-01 -2.84244370e-01 5.11453218e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = -20.20769117640641 2^p V(r_1,...,r_N) = -20.20769117640642 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 -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 | -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 1 1.51834545e+00 1.76111539e+00 -4.22908478e+00 | 1.51834545e+00 1.76111539e+00 -4.22908478e+00 2 2.96746025e-01 -1.04589738e+00 3.77446573e+00 | 2.96746025e-01 -1.04589738e+00 3.77446573e+00 3 -8.54383110e-01 3.85221245e-01 3.82318107e+00 | -8.54383110e-01 3.85221245e-01 3.82318107e+00 4 -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 | -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 5 1.51834545e+00 1.76111539e+00 -4.22908478e+00 | 1.51834545e+00 1.76111539e+00 -4.22908478e+00 6 2.96746025e-01 -1.04589738e+00 3.77446573e+00 | 2.96746025e-01 -1.04589738e+00 3.77446573e+00 7 -8.54383110e-01 3.85221245e-01 3.82318107e+00 | -8.54383110e-01 3.85221245e-01 3.82318107e+00 8 -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 | -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 9 1.51834545e+00 1.76111539e+00 -4.22908478e+00 | 1.51834545e+00 1.76111539e+00 -4.22908478e+00 10 2.96746025e-01 -1.04589738e+00 3.77446573e+00 | 2.96746025e-01 -1.04589738e+00 3.77446573e+00 11 -8.54383110e-01 3.85221245e-01 3.82318107e+00 | -8.54383110e-01 3.85221245e-01 3.82318107e+00 12 -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 | -9.60708363e-01 -1.10043926e+00 -3.36856201e+00 13 1.51834545e+00 1.76111539e+00 -4.22908478e+00 | 1.51834545e+00 1.76111539e+00 -4.22908478e+00 14 2.96746025e-01 -1.04589738e+00 3.77446573e+00 | 2.96746025e-01 -1.04589738e+00 3.77446573e+00 15 -8.54383110e-01 3.85221245e-01 3.82318107e+00 | -8.54383110e-01 3.85221245e-01 3.82318107e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -15.669517554505862 2^p V(r_1,...,r_N) = -15.669517554505877 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 -1.25359451e+00 -3.97199599e+00 7.84207247e-01 | -1.25359451e+00 -3.97199599e+00 7.84207247e-01 1 1.05232888e+00 4.21578534e+00 7.58044343e-01 | 1.05232888e+00 4.21578534e+00 7.58044343e-01 2 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 | 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 3 -1.41895844e+00 4.12786998e+00 -4.44498777e-01 | -1.41895844e+00 4.12786998e+00 -4.44498777e-01 4 -1.25359451e+00 -3.97199599e+00 7.84207247e-01 | -1.25359451e+00 -3.97199599e+00 7.84207247e-01 5 1.05232888e+00 4.21578534e+00 7.58044343e-01 | 1.05232888e+00 4.21578534e+00 7.58044343e-01 6 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 | 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 7 -1.41895844e+00 4.12786998e+00 -4.44498777e-01 | -1.41895844e+00 4.12786998e+00 -4.44498777e-01 8 -1.25359451e+00 -3.97199599e+00 7.84207247e-01 | -1.25359451e+00 -3.97199599e+00 7.84207247e-01 9 1.05232888e+00 4.21578534e+00 7.58044343e-01 | 1.05232888e+00 4.21578534e+00 7.58044343e-01 10 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 | 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 11 -1.41895844e+00 4.12786998e+00 -4.44498777e-01 | -1.41895844e+00 4.12786998e+00 -4.44498777e-01 12 -1.25359451e+00 -3.97199599e+00 7.84207247e-01 | -1.25359451e+00 -3.97199599e+00 7.84207247e-01 13 1.05232888e+00 4.21578534e+00 7.58044343e-01 | 1.05232888e+00 4.21578534e+00 7.58044343e-01 14 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 | 1.62022407e+00 -4.37165933e+00 -1.09775281e+00 15 -1.41895844e+00 4.12786998e+00 -4.44498777e-01 | -1.41895844e+00 4.12786998e+00 -4.44498777e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -15.357612177600215 2^p V(r_1,...,r_N) = -15.357612177600211 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 -6.25146010e-01 -2.49160686e+00 -1.32588765e+00 | -6.25146010e-01 -2.49160686e+00 -1.32588765e+00 1 8.45353379e-01 2.62049099e+00 -1.90851506e+00 | 8.45353379e-01 2.62049099e+00 -1.90851506e+00 2 4.53435672e-01 -2.10896704e+00 1.58406640e+00 | 4.53435672e-01 -2.10896704e+00 1.58406640e+00 3 -6.73643041e-01 1.98008291e+00 1.65033631e+00 | -6.73643041e-01 1.98008291e+00 1.65033631e+00 4 -6.25146010e-01 -2.49160686e+00 -1.32588765e+00 | -6.25146010e-01 -2.49160686e+00 -1.32588765e+00 5 8.45353379e-01 2.62049099e+00 -1.90851506e+00 | 8.45353379e-01 2.62049099e+00 -1.90851506e+00 6 4.53435672e-01 -2.10896704e+00 1.58406640e+00 | 4.53435672e-01 -2.10896704e+00 1.58406640e+00 7 -6.73643041e-01 1.98008291e+00 1.65033631e+00 | -6.73643041e-01 1.98008291e+00 1.65033631e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ERROR: Unable to perform verification check. Message = ERROR: Unable to scale configuration down to nonzero forces.