!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_StarikovKolotovaKuksin_2017_UMo__SM_682749584055_000 Supported species : Mo U random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = TTT (Configuration in file "config-Mo-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)) = -14.9140807621 2^p V(r_1,...,r_N) = -14.9140807621 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 -5.20679127e+00 -5.76743865e+00 -7.28838275e+00 | -5.20679127e+00 -5.76743865e+00 -7.28838275e+00 1 3.57468538e+00 2.16449425e+00 -2.11258531e+00 | 3.57468538e+00 2.16449425e+00 -2.11258531e+00 2 5.02327557e+00 -3.71123332e+00 4.78506579e+00 | 5.02327557e+00 -3.71123332e+00 4.78506579e+00 3 -3.39116969e+00 7.31417771e+00 4.61590227e+00 | -3.39116969e+00 7.31417771e+00 4.61590227e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = TTF (Configuration in file "config-Mo-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)) = -12.8379069543 2^p V(r_1,...,r_N) = -12.8379069543 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 -8.33817085e+00 -6.30477196e+00 -6.50936597e+00 | -8.33817085e+00 -6.30477196e+00 -6.50936597e+00 1 6.37317725e+00 4.64097985e+00 -8.93080921e+00 | 6.37317725e+00 4.64097985e+00 -8.93080921e+00 2 8.53383423e+00 -8.63711057e+00 1.02881529e+01 | 8.53383423e+00 -8.63711057e+00 1.02881529e+01 3 -6.56884064e+00 1.03009027e+01 5.15202227e+00 | -6.56884064e+00 1.03009027e+01 5.15202227e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = TFT (Configuration in file "config-Mo-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)) = -9.5172031271 2^p V(r_1,...,r_N) = -9.5172031271 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 -5.96824647e+00 -6.21108587e+00 -8.48206049e+00 | -5.96824647e+00 -6.21108587e+00 -8.48206049e+00 1 1.02804183e+01 9.55761651e+00 -7.76893060e+00 | 1.02804183e+01 9.55761651e+00 -7.76893060e+00 2 7.20115680e+00 -1.06353997e+01 9.03966198e+00 | 7.20115680e+00 -1.06353997e+01 9.03966198e+00 3 -1.15133287e+01 7.28886906e+00 7.21132912e+00 | -1.15133287e+01 7.28886906e+00 7.21132912e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = TFF (Configuration in file "config-Mo-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)) = -6.95392891317 2^p V(r_1,...,r_N) = -6.95392891317 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 -5.15890125e+00 -5.15930924e+00 -3.81423482e+00 | -5.15890125e+00 -5.15930924e+00 -3.81423482e+00 1 7.59311467e+00 7.53941481e+00 -6.07537297e+00 | 7.59311467e+00 7.53941481e+00 -6.07537297e+00 2 3.18358998e+00 -5.43630622e+00 5.59467594e+00 | 3.18358998e+00 -5.43630622e+00 5.59467594e+00 3 -5.61780340e+00 3.05620065e+00 4.29493185e+00 | -5.61780340e+00 3.05620065e+00 4.29493185e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = FTT (Configuration in file "config-Mo-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.80602625109 2^p V(r_1,...,r_N) = -9.80602625109 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 -1.03605509e+01 -9.45312633e+00 -9.49557131e+00 | -1.03605509e+01 -9.45312633e+00 -9.49557131e+00 1 9.91654978e+00 8.49130849e+00 -7.69540650e+00 | 9.91654978e+00 8.49130849e+00 -7.69540650e+00 2 7.49030831e+00 -7.42310830e+00 6.31575734e+00 | 7.49030831e+00 -7.42310830e+00 6.31575734e+00 3 -7.04630723e+00 8.38492613e+00 1.08752205e+01 | -7.04630723e+00 8.38492613e+00 1.08752205e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = FTF (Configuration in file "config-Mo-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)) = -14.6025136695 2^p V(r_1,...,r_N) = -14.6025136695 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 -7.66602799e+00 -5.61678350e+00 -4.57389685e+00 | -7.66602799e+00 -5.61678350e+00 -4.57389685e+00 1 4.28563620e+00 5.86980544e+00 -5.11504305e+00 | 4.28563620e+00 5.86980544e+00 -5.11504305e+00 2 5.23677811e+00 -2.49859821e+00 8.15430567e+00 | 5.23677811e+00 -2.49859821e+00 8.15430567e+00 3 -1.85638632e+00 2.24557626e+00 1.53463422e+00 | -1.85638632e+00 2.24557626e+00 1.53463422e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mo, PBC = FFT (Configuration in file "config-Mo-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)) = -7.4196822831 2^p V(r_1,...,r_N) = -7.4196822831 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 -9.44635108e+00 -8.80752574e+00 -9.75737506e+00 | -9.44635108e+00 -8.80752574e+00 -9.75737506e+00 1 1.29064545e+01 1.03792943e+01 -7.64173981e+00 | 1.29064545e+01 1.03792943e+01 -7.64173981e+00 2 3.39135702e+00 -6.07888785e+00 9.50583739e+00 | 3.39135702e+00 -6.07888785e+00 9.50583739e+00 3 -6.85146048e+00 4.50711930e+00 7.89327749e+00 | -6.85146048e+00 4.50711930e+00 7.89327749e+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)) = 26.4525871695 2^p V(r_1,...,r_N) = 26.4525871695 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 -4.23534707e+01 -3.35330189e+01 -5.02946629e+01 | -4.23534707e+01 -3.35330189e+01 -5.02946629e+01 1 3.00761832e+01 3.97536994e+01 -2.97877875e+01 | 3.00761832e+01 3.97536994e+01 -2.97877875e+01 2 4.86211125e+01 -4.39247718e+01 4.66284094e+01 | 4.86211125e+01 -4.39247718e+01 4.66284094e+01 3 -3.63438250e+01 3.77040914e+01 3.34540411e+01 | -3.63438250e+01 3.77040914e+01 3.34540411e+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)) = 28.9421921421 2^p V(r_1,...,r_N) = 28.9421921421 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 -4.36049700e+01 -3.48564309e+01 -3.77793648e+01 | -4.36049700e+01 -3.48564309e+01 -3.77793648e+01 1 3.42932082e+01 4.47347081e+01 -3.53705824e+01 | 3.42932082e+01 4.47347081e+01 -3.53705824e+01 2 4.95654073e+01 -4.42111723e+01 4.98195702e+01 | 4.95654073e+01 -4.42111723e+01 4.98195702e+01 3 -4.02536455e+01 3.43328951e+01 2.33303770e+01 | -4.02536455e+01 3.43328951e+01 2.33303770e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 9.89261240155 2^p V(r_1,...,r_N) = 9.89261240155 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 -1.34597711e+01 -1.50214306e+01 -1.33041074e+01 | -1.34597711e+01 -1.50214306e+01 -1.33041074e+01 1 1.80811796e+01 2.03578655e+01 -3.70971942e+01 | 1.80811796e+01 2.03578655e+01 -3.70971942e+01 2 2.32454992e+01 -3.60732929e+01 3.73223234e+01 | 2.32454992e+01 -3.60732929e+01 3.73223234e+01 3 -2.78669077e+01 3.07368580e+01 1.30789782e+01 | -2.78669077e+01 3.07368580e+01 1.30789782e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 11.6377270146 2^p V(r_1,...,r_N) = 11.6377270146 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 -1.61029825e+01 -3.42532405e+01 -2.83858859e+01 | -1.61029825e+01 -3.42532405e+01 -2.83858859e+01 1 2.12669915e+01 1.96840582e+01 -2.64182315e+01 | 2.12669915e+01 1.96840582e+01 -2.64182315e+01 2 1.22047676e+01 -2.06306359e+01 1.87501685e+01 | 1.22047676e+01 -2.06306359e+01 1.87501685e+01 3 -1.73687766e+01 3.51998182e+01 3.60539489e+01 | -1.73687766e+01 3.51998182e+01 3.60539489e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.70205186425 2^p V(r_1,...,r_N) = -2.70205186425 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 -1.35954242e+01 -1.25433266e+01 -8.65663782e+00 | -1.35954242e+01 -1.25433266e+01 -8.65663782e+00 1 2.31374758e+01 1.77844316e+01 -1.66948559e+01 | 2.31374758e+01 1.77844316e+01 -1.66948559e+01 2 5.02375769e+00 -1.24743217e+01 1.17860089e+01 | 5.02375769e+00 -1.24743217e+01 1.17860089e+01 3 -1.45658093e+01 7.23321667e+00 1.35654848e+01 | -1.45658093e+01 7.23321667e+00 1.35654848e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 6.30382127064 2^p V(r_1,...,r_N) = 6.30382127064 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 -1.22123053e+01 -3.13622010e+01 -2.90647307e+01 | -1.22123053e+01 -3.13622010e+01 -2.90647307e+01 1 1.88710893e+01 1.48450150e+01 -1.95532055e+01 | 1.88710893e+01 1.48450150e+01 -1.95532055e+01 2 1.60057058e+01 -9.91618465e+00 8.33256225e+00 | 1.60057058e+01 -9.91618465e+00 8.33256225e+00 3 -2.26644898e+01 2.64333706e+01 4.02853739e+01 | -2.26644898e+01 2.64333706e+01 4.02853739e+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)) = 43.5283747103 2^p V(r_1,...,r_N) = 43.5283747103 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 -5.26589670e+01 -4.32665013e+01 -4.98146323e+01 | -5.26589670e+01 -4.32665013e+01 -4.98146323e+01 1 4.68452273e+01 2.62192990e+01 -5.19140109e+01 | 4.68452273e+01 2.62192990e+01 -5.19140109e+01 2 5.19378997e+01 -5.40999646e+01 6.49229907e+01 | 5.19378997e+01 -5.40999646e+01 6.49229907e+01 3 -4.61241600e+01 7.11471670e+01 3.68056525e+01 | -4.61241600e+01 7.11471670e+01 3.68056525e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = TTT (Configuration in file "config-MoU-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)) = 14.7245363644 2^p V(r_1,...,r_N) = 14.7245363644 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 -1.45866557e+01 -1.08210933e+01 -1.01178186e+01 | -1.45866557e+01 -1.08210933e+01 -1.01178186e+01 1 2.15116211e+01 3.14114600e+01 -4.37081605e+01 | 2.15116211e+01 3.14114600e+01 -4.37081605e+01 2 1.82381995e+01 -3.72002734e+01 3.90813569e+01 | 1.82381995e+01 -3.72002734e+01 3.90813569e+01 3 -2.51631649e+01 1.66099067e+01 1.47446222e+01 | -2.51631649e+01 1.66099067e+01 1.47446222e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = TTF (Configuration in file "config-MoU-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.10172937165 2^p V(r_1,...,r_N) = 6.10172937165 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 -1.97089078e+01 -2.99572475e+01 -2.56437991e+01 | -1.97089078e+01 -2.99572475e+01 -2.56437991e+01 1 1.90905676e+01 7.51886713e+00 -6.90318266e+00 | 1.90905676e+01 7.51886713e+00 -6.90318266e+00 2 1.58456419e+01 -8.75195545e+00 9.59699511e+00 | 1.58456419e+01 -8.75195545e+00 9.59699511e+00 3 -1.52273016e+01 3.11903358e+01 2.29499867e+01 | -1.52273016e+01 3.11903358e+01 2.29499867e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = TFT (Configuration in file "config-MoU-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)) = 5.91901167528 2^p V(r_1,...,r_N) = 5.91901167528 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 -1.91308548e+01 -2.74686997e+01 -3.34001504e+01 | -1.91308548e+01 -2.74686997e+01 -3.34001504e+01 1 1.85198540e+01 1.12575687e+01 -1.05034645e+01 | 1.85198540e+01 1.12575687e+01 -1.05034645e+01 2 1.73761829e+01 -1.56455528e+01 1.45525551e+01 | 1.73761829e+01 -1.56455528e+01 1.45525551e+01 3 -1.67651821e+01 3.18566838e+01 2.93510598e+01 | -1.67651821e+01 3.18566838e+01 2.93510598e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = TFF (Configuration in file "config-MoU-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)) = -10.7968487708 2^p V(r_1,...,r_N) = -10.7968487708 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 -5.78202397e+00 -6.28337686e+00 -7.91343994e+00 | -5.78202397e+00 -6.28337686e+00 -7.91343994e+00 1 5.23697600e+00 5.41689899e+00 -3.96445659e+00 | 5.23697600e+00 5.41689899e+00 -3.96445659e+00 2 5.80219761e+00 -4.73149229e+00 4.01667254e+00 | 5.80219761e+00 -4.73149229e+00 4.01667254e+00 3 -5.25714964e+00 5.59797016e+00 7.86122400e+00 | -5.25714964e+00 5.59797016e+00 7.86122400e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = FTT (Configuration in file "config-MoU-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)) = -11.787295227 2^p V(r_1,...,r_N) = -11.787295227 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 -4.62323342e+00 -3.14086779e+00 -2.39496095e+00 | -4.62323342e+00 -3.14086779e+00 -2.39496095e+00 1 4.92632611e+00 2.99291006e+00 -2.53442635e+00 | 4.92632611e+00 2.99291006e+00 -2.53442635e+00 2 3.93290082e+00 -4.03456919e+00 2.30016895e+00 | 3.93290082e+00 -4.03456919e+00 2.30016895e+00 3 -4.23599350e+00 4.18252692e+00 2.62921835e+00 | -4.23599350e+00 4.18252692e+00 2.62921835e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = FTF (Configuration in file "config-MoU-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)) = -4.55657832655 2^p V(r_1,...,r_N) = -4.55657832656 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 -6.40979941e+00 -1.42535518e+01 -1.19333986e+01 | -6.40979941e+00 -1.42535518e+01 -1.19333986e+01 1 7.16620991e+00 9.31847326e+00 -9.49335554e+00 | 7.16620991e+00 9.31847326e+00 -9.49335554e+00 2 1.57764291e+01 -1.30273232e+01 1.27452041e+01 | 1.57764291e+01 -1.30273232e+01 1.27452041e+01 3 -1.65328396e+01 1.79624017e+01 8.68154996e+00 | -1.65328396e+01 1.79624017e+01 8.68154996e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mo U, PBC = FFT (Configuration in file "config-MoU-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)) = -1.80961852284 2^p V(r_1,...,r_N) = -1.80961852284 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 -1.03906945e+01 -7.72487535e+00 -9.96462445e+00 | -1.03906945e+01 -7.72487535e+00 -9.96462445e+00 1 5.14897782e+00 1.21473739e+01 -1.81982672e+01 | 5.14897782e+00 1.21473739e+01 -1.81982672e+01 2 1.76817410e+01 -1.50903643e+01 1.31489275e+01 | 1.76817410e+01 -1.50903643e+01 1.31489275e+01 3 -1.24400243e+01 1.06678657e+01 1.50139642e+01 | -1.24400243e+01 1.06678657e+01 1.50139642e+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.