!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_TseplyaevStarikova_2016_UN__SM_474015477315_000 Supported species : N U random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TTT (Configuration in file "config-N-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)) = -7.89724064195 2^p V(r_1,...,r_N) = -7.89724064195 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 7.12921378e+00 4.09207975e+00 6.31491282e+00 | 7.12921378e+00 4.09207975e+00 6.31491282e+00 1 -4.55002429e+00 -3.35662679e+00 2.89640981e+00 | -4.55002429e+00 -3.35662679e+00 2.89640981e+00 2 -5.68655656e+00 4.40319183e+00 -6.46285557e+00 | -5.68655656e+00 4.40319183e+00 -6.46285557e+00 3 3.10736707e+00 -5.13864479e+00 -2.74846705e+00 | 3.10736707e+00 -5.13864479e+00 -2.74846705e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TTF (Configuration in file "config-N-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)) = -10.1554545059 2^p V(r_1,...,r_N) = -10.1554545059 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 9.39436498e+00 6.40379161e+00 5.45668317e+00 | 9.39436498e+00 6.40379161e+00 5.45668317e+00 1 -6.90685225e+00 -5.78589218e+00 8.09856700e+00 | -6.90685225e+00 -5.78589218e+00 8.09856700e+00 2 -4.75335294e+00 3.62864466e+00 -9.92656930e+00 | -4.75335294e+00 3.62864466e+00 -9.92656930e+00 3 2.26584021e+00 -4.24654409e+00 -3.62868086e+00 | 2.26584021e+00 -4.24654409e+00 -3.62868086e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TFT (Configuration in file "config-N-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)) = -13.2872795048 2^p V(r_1,...,r_N) = -13.2872795048 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 8.03975407e+00 6.12737943e+00 8.91614314e+00 | 8.03975407e+00 6.12737943e+00 8.91614314e+00 1 -1.00617379e+01 -9.89521950e+00 6.49494321e+00 | -1.00617379e+01 -9.89521950e+00 6.49494321e+00 2 -7.12109646e+00 9.37961195e+00 -9.71646822e+00 | -7.12109646e+00 9.37961195e+00 -9.71646822e+00 3 9.14308032e+00 -5.61177189e+00 -5.69461813e+00 | 9.14308032e+00 -5.61177189e+00 -5.69461813e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TFF (Configuration in file "config-N-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)) = -12.2487270441 2^p V(r_1,...,r_N) = -12.2487270441 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 -8.16674987e+00 -9.34119792e-01 -2.24847830e+01 | -8.16674987e+00 -9.34119792e-01 -2.24847830e+01 1 -7.63491280e+00 -9.24325329e+00 6.12967950e+00 | -7.63491280e+00 -9.24325329e+00 6.12967950e+00 2 1.59854659e+01 3.48723749e+00 1.14709894e+01 | 1.59854659e+01 3.48723749e+00 1.14709894e+01 3 -1.83803221e-01 6.69013559e+00 4.88411413e+00 | -1.83803221e-01 6.69013559e+00 4.88411413e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FTT (Configuration in file "config-N-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)) = -8.01013758171 2^p V(r_1,...,r_N) = -8.01013758171 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 7.90557949e+00 6.03579730e+00 4.57575810e+00 | 7.90557949e+00 6.03579730e+00 4.57575810e+00 1 -7.28125401e+00 -5.51925181e+00 7.10432282e+00 | -7.28125401e+00 -5.51925181e+00 7.10432282e+00 2 -7.45382514e+00 7.06052905e+00 -4.78171359e+00 | -7.45382514e+00 7.06052905e+00 -4.78171359e+00 3 6.82949966e+00 -7.57707455e+00 -6.89836733e+00 | 6.82949966e+00 -7.57707455e+00 -6.89836733e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FTF (Configuration in file "config-N-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)) = -7.59905358304 2^p V(r_1,...,r_N) = -7.59905358304 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 2.99415485e+00 2.21514476e+00 4.88071544e+00 | 2.99415485e+00 2.21514476e+00 4.88071544e+00 1 -5.97447201e+00 -2.15554375e+00 5.05035097e+00 | -5.97447201e+00 -2.15554375e+00 5.05035097e+00 2 -5.48428407e+00 6.19691108e+00 -6.44769339e+00 | -5.48428407e+00 6.19691108e+00 -6.44769339e+00 3 8.46460123e+00 -6.25651209e+00 -3.48337301e+00 | 8.46460123e+00 -6.25651209e+00 -3.48337301e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FFT (Configuration in file "config-N-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)) = -9.97384207672 2^p V(r_1,...,r_N) = -9.97384207672 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 7.20496031e+00 9.00302210e+00 8.84345177e+00 | 7.20496031e+00 9.00302210e+00 8.84345177e+00 1 -4.42826587e+00 -5.38196073e+00 2.69659868e+00 | -4.42826587e+00 -5.38196073e+00 2.69659868e+00 2 -6.38667741e+00 2.17482727e+00 -5.69811404e+00 | -6.38667741e+00 2.17482727e+00 -5.69811404e+00 3 3.60998297e+00 -5.79588864e+00 -5.84193641e+00 | 3.60998297e+00 -5.79588864e+00 -5.84193641e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = TTT (Configuration in file "config-U-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)) = 6.53276887442 2^p V(r_1,...,r_N) = 6.53276887442 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 -2.39330130e+01 -3.54209006e+01 -2.73661367e+01 | -2.39330130e+01 -3.54209006e+01 -2.73661367e+01 1 7.74571690e+01 2.65823074e+01 -7.57056823e+01 | 7.74571690e+01 2.65823074e+01 -7.57056823e+01 2 1.66054533e+01 -1.09659744e+01 1.84783628e+01 | 1.66054533e+01 -1.09659744e+01 1.84783628e+01 3 -7.01296093e+01 1.98045676e+01 8.45934561e+01 | -7.01296093e+01 1.98045676e+01 8.45934561e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = TTF (Configuration in file "config-U-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)) = -10.3214980362 2^p V(r_1,...,r_N) = -10.3214980362 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 -5.31417614e+00 -8.03078444e+00 -7.03729025e+00 | -5.31417614e+00 -8.03078444e+00 -7.03729025e+00 1 7.81796991e+00 6.22139047e+00 -5.76992696e+00 | 7.81796991e+00 6.22139047e+00 -5.76992696e+00 2 5.65890853e+00 -3.44289736e+00 4.08526498e+00 | 5.65890853e+00 -3.44289736e+00 4.08526498e+00 3 -8.16270230e+00 5.25229134e+00 8.72195223e+00 | -8.16270230e+00 5.25229134e+00 8.72195223e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = TFT (Configuration in file "config-U-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)) = -5.44367889043 2^p V(r_1,...,r_N) = -5.44367889043 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 -2.43202684e+01 -1.29527037e+01 -2.65675910e+01 | -2.43202684e+01 -1.29527037e+01 -2.65675910e+01 1 4.46619198e+00 1.82837573e+01 -1.62482073e+01 | 4.46619198e+00 1.82837573e+01 -1.62482073e+01 2 2.74135588e+01 -8.82337314e+00 3.82152915e+01 | 2.74135588e+01 -8.82337314e+00 3.82152915e+01 3 -7.55948240e+00 3.49231953e+00 4.60050677e+00 | -7.55948240e+00 3.49231953e+00 4.60050677e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = TFF (Configuration in file "config-U-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)) = 77.5320486035 2^p V(r_1,...,r_N) = 77.5320486035 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 -1.73206040e+02 -7.13957204e+01 -1.52590299e+02 | -1.73206040e+02 -7.13957204e+01 -1.52590299e+02 1 2.30893387e+02 8.20362174e+01 -2.32616720e+02 | 2.30893387e+02 8.20362174e+01 -2.32616720e+02 2 1.52112804e+02 -1.15595786e+02 1.98252026e+02 | 1.52112804e+02 -1.15595786e+02 1.98252026e+02 3 -2.09800150e+02 1.04955289e+02 1.86954994e+02 | -2.09800150e+02 1.04955289e+02 1.86954994e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = FTT (Configuration in file "config-U-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)) = -8.63066916004 2^p V(r_1,...,r_N) = -8.63066916004 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 -1.69166433e+01 -1.56769853e+01 -1.02328232e+01 | -1.69166433e+01 -1.56769853e+01 -1.02328232e+01 1 1.42792686e+01 1.36513078e+01 -5.37377508e+00 | 1.42792686e+01 1.36513078e+01 -5.37377508e+00 2 7.10270118e+00 -2.27856916e+00 1.07471819e+01 | 7.10270118e+00 -2.27856916e+00 1.07471819e+01 3 -4.46532641e+00 4.30424668e+00 4.85941640e+00 | -4.46532641e+00 4.30424668e+00 4.85941640e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = FTF (Configuration in file "config-U-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)) = 73.2733763272 2^p V(r_1,...,r_N) = 73.2733763272 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 -9.98704110e+01 -1.27275257e+02 -3.40091833e+01 | -9.98704110e+01 -1.27275257e+02 -3.40091833e+01 1 5.69269293e+00 3.42610472e+02 -2.68469829e+02 | 5.69269293e+00 3.42610472e+02 -2.68469829e+02 2 1.89102870e+02 -2.64952962e+02 2.46101428e+02 | 1.89102870e+02 -2.64952962e+02 2.46101428e+02 3 -9.49251519e+01 4.96177470e+01 5.63775845e+01 | -9.49251519e+01 4.96177470e+01 5.63775845e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = U, PBC = FFT (Configuration in file "config-U-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)) = -5.04027418448 2^p V(r_1,...,r_N) = -5.04027418448 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 -8.16189740e+00 -1.80535766e+01 -1.03761546e+01 | -8.16189740e+00 -1.80535766e+01 -1.03761546e+01 1 3.12590218e+01 1.17316257e+01 -3.13083232e+01 | 3.12590218e+01 1.17316257e+01 -3.13083232e+01 2 5.63716237e+00 -5.17633463e+00 4.79568006e+00 | 5.63716237e+00 -5.17633463e+00 4.79568006e+00 3 -2.87342867e+01 1.14982855e+01 3.68887977e+01 | -2.87342867e+01 1.14982855e+01 3.68887977e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = TTT (Configuration in file "config-NU-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)) = -22.1174503912 2^p V(r_1,...,r_N) = -22.1174503912 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 -7.46451194e+00 -2.16218565e+00 -8.07418010e+00 | -7.46451194e+00 -2.16218565e+00 -8.07418010e+00 1 4.87697015e+00 5.60420594e+00 -6.01704461e+00 | 4.87697015e+00 5.60420594e+00 -6.01704461e+00 2 8.75755654e+00 -1.11178848e+01 4.00215244e+00 | 8.75755654e+00 -1.11178848e+01 4.00215244e+00 3 -6.17001475e+00 7.67586447e+00 1.00890723e+01 | -6.17001475e+00 7.67586447e+00 1.00890723e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = TTF (Configuration in file "config-NU-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.221335775977 2^p V(r_1,...,r_N) = -0.221335775977 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 -7.76382435e+01 -1.21802626e+02 -3.41700382e+01 | -7.76382435e+01 -1.21802626e+02 -3.41700382e+01 1 1.01608245e+02 1.11112773e+02 -1.95450392e+01 | 1.01608245e+02 1.11112773e+02 -1.95450392e+01 2 1.96509382e+01 -1.75796083e+01 1.86820470e+01 | 1.96509382e+01 -1.75796083e+01 1.86820470e+01 3 -4.36209402e+01 2.82694616e+01 3.50330304e+01 | -4.36209402e+01 2.82694616e+01 3.50330304e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = TFT (Configuration in file "config-NU-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)) = -22.7061286065 2^p V(r_1,...,r_N) = -22.7061286065 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 -3.07384316e+00 -9.64202782e+00 -8.07805624e+00 | -3.07384316e+00 -9.64202782e+00 -8.07805624e+00 1 2.96410477e+00 6.63277000e+00 -4.40033201e+00 | 2.96410477e+00 6.63277000e+00 -4.40033201e+00 2 2.67664251e+00 -4.83671035e+00 7.62390794e+00 | 2.67664251e+00 -4.83671035e+00 7.62390794e+00 3 -2.56690412e+00 7.84596816e+00 4.85448031e+00 | -2.56690412e+00 7.84596816e+00 4.85448031e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = TFF (Configuration in file "config-NU-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)) = -17.5172156288 2^p V(r_1,...,r_N) = -17.5172156288 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 -3.53115604e+01 -2.31373678e+01 3.60293881e+00 | -3.53115604e+01 -2.31373678e+01 3.60293881e+00 1 3.61019641e+01 2.17240864e+01 9.33570114e+00 | 3.61019641e+01 2.17240864e+01 9.33570114e+00 2 -3.11718675e+00 5.17579105e+00 -8.06003953e+00 | -3.11718675e+00 5.17579105e+00 -8.06003953e+00 3 2.32678307e+00 -3.76250962e+00 -4.87860042e+00 | 2.32678307e+00 -3.76250962e+00 -4.87860042e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = FTT (Configuration in file "config-NU-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)) = -7.57657364088 2^p V(r_1,...,r_N) = -7.57657364088 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 -2.85300540e+01 -1.27098263e+01 -2.01086361e+01 | -2.85300540e+01 -1.27098263e+01 -2.01086361e+01 1 5.49356179e+01 2.47093655e+01 -8.08981484e+01 | 5.49356179e+01 2.47093655e+01 -8.08981484e+01 2 2.91818205e+01 -1.68405818e+01 2.05358431e+01 | 2.91818205e+01 -1.68405818e+01 2.05358431e+01 3 -5.55873844e+01 4.84104264e+00 8.04709415e+01 | -5.55873844e+01 4.84104264e+00 8.04709415e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = FTF (Configuration in file "config-NU-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)) = -20.411476757 2^p V(r_1,...,r_N) = -20.411476757 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 -3.20637976e+00 -4.63437100e+00 1.01922074e+01 | -3.20637976e+00 -4.63437100e+00 1.01922074e+01 1 4.38183910e+00 6.74320444e+00 4.94574650e+00 | 4.38183910e+00 6.74320444e+00 4.94574650e+00 2 -4.87660891e+00 2.05584017e+00 -7.64162947e+00 | -4.87660891e+00 2.05584017e+00 -7.64162947e+00 3 3.70114957e+00 -4.16467360e+00 -7.49632444e+00 | 3.70114957e+00 -4.16467360e+00 -7.49632444e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = N U, PBC = FFT (Configuration in file "config-NU-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)) = -22.3457826437 2^p V(r_1,...,r_N) = -22.3457826437 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 -4.66832404e+00 -9.33755294e+00 -1.26450830e+01 | -4.66832404e+00 -9.33755294e+00 -1.26450830e+01 1 1.82705612e+00 2.74987834e+00 -2.35664380e+00 | 1.82705612e+00 2.74987834e+00 -2.35664380e+00 2 6.17991761e+00 -3.42346257e+00 4.85256310e+00 | 6.17991761e+00 -3.42346257e+00 4.85256310e+00 3 -3.33864969e+00 1.00111372e+01 1.01491637e+01 | -3.33864969e+00 1.00111372e+01 1.01491637e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.