!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_AIREBO_LJ_StuartTuteinHarrison_2000_CH__SM_069621990420_000 Supported species : C H random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTT (Configuration in file "config-C-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 3014.021461381404 2^p V(r_1,...,r_N) = 3014.0214613807857 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 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 1 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 2 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 3 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 4 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 5 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 6 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 7 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 8 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 9 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 10 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 11 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 12 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 13 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 14 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 15 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 16 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 17 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 18 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 19 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 20 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 21 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 22 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 23 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 24 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 25 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 26 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 27 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 28 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 | 3.04891806e+02 -3.34548833e+02 -4.09273215e+01 29 -4.90282797e+02 2.43271890e+02 -1.98248019e+02 | -4.90282797e+02 2.43271890e+02 -1.98248019e+02 30 -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 | -4.93475350e+01 -2.43975381e+01 -4.69312493e+01 31 2.34738526e+02 1.15674481e+02 2.86106590e+02 | 2.34738526e+02 1.15674481e+02 2.86106590e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 14595.31945988153 2^p V(r_1,...,r_N) = 14595.319459879902 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 3.80115737e+03 7.51813687e+03 -2.65371465e+03 | 3.80115892e+03 7.51813060e+03 -2.65372190e+03 ERR 1 -5.48376538e+03 -6.01628771e+03 -3.73258339e+03 | -5.48373510e+03 -6.01630277e+03 -3.73258951e+03 ERR 2 -1.49288924e+03 -1.35802924e+03 2.30848568e+03 | -1.49287778e+03 -1.35802805e+03 2.30848024e+03 ERR 3 3.17532998e+03 -1.43691791e+02 4.07787613e+03 | 3.17545396e+03 -1.43799783e+02 4.07783117e+03 ERR 4 3.80125980e+03 7.51802322e+03 -2.65376852e+03 | 3.80115892e+03 7.51813060e+03 -2.65372190e+03 ERR 5 -5.48370670e+03 -6.01627470e+03 -3.73259308e+03 | -5.48373510e+03 -6.01630277e+03 -3.73258951e+03 ERR 6 -1.49286632e+03 -1.35802686e+03 2.30847480e+03 | -1.49287778e+03 -1.35802805e+03 2.30848024e+03 ERR 7 3.17547146e+03 -1.43800976e+02 4.07782759e+03 | 3.17545396e+03 -1.43799783e+02 4.07783117e+03 ERR 8 3.80108715e+03 7.51821622e+03 -2.65368917e+03 | 3.80115892e+03 7.51813060e+03 -2.65372190e+03 ERR 9 -5.48375269e+03 -6.01632579e+03 -3.73258837e+03 | -5.48373510e+03 -6.01630277e+03 -3.73258951e+03 ERR 10 -1.49288259e+03 -1.35802713e+03 2.30848254e+03 | -1.49287778e+03 -1.35802805e+03 2.30848024e+03 ERR 11 3.17547304e+03 -1.43823580e+02 4.07782573e+03 | 3.17545396e+03 -1.43799783e+02 4.07783117e+03 ERR 12 3.80113135e+03 7.51814609e+03 -2.65371529e+03 | 3.80115892e+03 7.51813060e+03 -2.65372190e+03 ERR 13 -5.48371564e+03 -6.01632288e+03 -3.73259319e+03 | -5.48373510e+03 -6.01630277e+03 -3.73258951e+03 ERR 14 -1.49287297e+03 -1.35802897e+03 2.30847794e+03 | -1.49287778e+03 -1.35802805e+03 2.30848024e+03 ERR 15 3.17554138e+03 -1.43882783e+02 4.07779524e+03 | 3.17545396e+03 -1.43799783e+02 4.07783117e+03 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFT (Configuration in file "config-C-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 10845.691065166313 2^p V(r_1,...,r_N) = 10845.691065165176 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 1.87110757e+03 -2.28467396e+03 -1.75793127e+03 | 1.87114271e+03 -2.28468721e+03 -1.75792528e+03 ERR 1 -1.14536267e+03 2.62797864e+03 -5.01681528e+02 | -1.14539381e+03 2.62797452e+03 -5.01659814e+02 ERR 2 -2.91050885e+03 -3.95969725e+03 5.67306952e+02 | -2.91051538e+03 -3.95970287e+03 5.67332719e+02 ERR 3 2.18470675e+03 3.61643029e+03 1.69224234e+03 | 2.18476648e+03 3.61641556e+03 1.69225237e+03 ERR 4 1.87116218e+03 -2.28469119e+03 -1.75795963e+03 | 1.87114271e+03 -2.28468721e+03 -1.75792528e+03 ERR 5 -1.14544062e+03 2.62797967e+03 -5.01678438e+02 | -1.14539381e+03 2.62797452e+03 -5.01659814e+02 ERR 6 -2.91054678e+03 -3.95969788e+03 5.67325964e+02 | -2.91051538e+03 -3.95970287e+03 5.67332719e+02 ERR 7 2.18480134e+03 3.61641142e+03 1.69222989e+03 | 2.18476648e+03 3.61641556e+03 1.69225237e+03 ERR 8 1.87111736e+03 -2.28468720e+03 -1.75789889e+03 | 1.87114271e+03 -2.28468721e+03 -1.75792528e+03 ERR 9 -1.14535637e+03 2.62796381e+03 -5.01647716e+02 | -1.14539381e+03 2.62797452e+03 -5.01659814e+02 ERR 10 -2.91048764e+03 -3.95970936e+03 5.67341188e+02 | -2.91051538e+03 -3.95970287e+03 5.67332719e+02 ERR 11 2.18473141e+03 3.61641978e+03 1.69227513e+03 | 2.18476648e+03 3.61641556e+03 1.69225237e+03 ERR 12 1.87118374e+03 -2.28469649e+03 -1.75791133e+03 | 1.87114271e+03 -2.28468721e+03 -1.75792528e+03 ERR 13 -1.14541557e+03 2.62797596e+03 -5.01631571e+02 | -1.14539381e+03 2.62797452e+03 -5.01659814e+02 ERR 14 -2.91051825e+03 -3.95970696e+03 5.67356769e+02 | -2.91051538e+03 -3.95970287e+03 5.67332719e+02 ERR 15 2.18482642e+03 3.61640074e+03 1.69226214e+03 | 2.18476648e+03 3.61641556e+03 1.69225237e+03 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFF (Configuration in file "config-C-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 3476.3341180594625 2^p V(r_1,...,r_N) = 3476.3341180595166 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 6.99434902e+02 -2.99322709e+03 -1.81397808e+03 | 6.99438934e+02 -2.99322489e+03 -1.81397602e+03 ERR 1 -1.61875860e+03 2.72131299e+03 -1.55051925e+03 | -1.61875638e+03 2.72131256e+03 -1.55051955e+03 ERR 2 -1.37498449e+03 -1.49878882e+03 2.11959011e+03 | -1.37498401e+03 -1.49878866e+03 2.11958985e+03 ERR 3 2.29429568e+03 1.77069939e+03 1.24490370e+03 | 2.29430145e+03 1.77070100e+03 1.24490572e+03 ERR 4 6.99442966e+02 -2.99322270e+03 -1.81397396e+03 | 6.99438934e+02 -2.99322489e+03 -1.81397602e+03 ERR 5 -1.61875416e+03 2.72131213e+03 -1.55051985e+03 | -1.61875638e+03 2.72131256e+03 -1.55051955e+03 ERR 6 -1.37498353e+03 -1.49878850e+03 2.11958959e+03 | -1.37498401e+03 -1.49878866e+03 2.11958985e+03 ERR 7 2.29430722e+03 1.77070260e+03 1.24490774e+03 | 2.29430145e+03 1.77070100e+03 1.24490572e+03 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTT (Configuration in file "config-C-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 10662.568933429739 2^p V(r_1,...,r_N) = 10662.568933428622 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 -6.74795277e+02 -1.04836946e+03 -5.13657248e+02 | -6.74794712e+02 -1.04837192e+03 -5.13663888e+02 ERR 1 -6.18401392e+02 -2.12977243e+03 1.97214820e+03 | -6.18414006e+02 -2.12981987e+03 1.97215327e+03 ERR 2 3.61775859e+03 2.52172100e+03 -2.90154768e+03 | 3.61776223e+03 2.52172295e+03 -2.90155233e+03 ERR 3 -2.32454473e+03 6.56521762e+02 1.44307139e+03 | -2.32455352e+03 6.56468848e+02 1.44306295e+03 ERR 4 -6.74795276e+02 -1.04836945e+03 -5.13657251e+02 | -6.74794712e+02 -1.04837192e+03 -5.13663888e+02 ERR 5 -6.18426057e+02 -2.12986669e+03 1.97215492e+03 | -6.18414006e+02 -2.12981987e+03 1.97215327e+03 ERR 6 3.61775997e+03 2.52173163e+03 -2.90154693e+03 | 3.61776223e+03 2.52172295e+03 -2.90155233e+03 ERR 7 -2.32456888e+03 6.56428036e+02 1.44307494e+03 | -2.32455352e+03 6.56468848e+02 1.44306295e+03 ERR 8 -6.74794147e+02 -1.04837439e+03 -5.13670528e+02 | -6.74794712e+02 -1.04837192e+03 -5.13663888e+02 ERR 9 -6.18401524e+02 -2.12976801e+03 1.97215358e+03 | -6.18414006e+02 -2.12981987e+03 1.97215327e+03 ERR 10 3.61776493e+03 2.52171931e+03 -2.90155578e+03 | 3.61776223e+03 2.52172295e+03 -2.90155233e+03 ERR 11 -2.32453815e+03 6.56509660e+02 1.44305097e+03 | -2.32455352e+03 6.56468848e+02 1.44306295e+03 ERR 12 -6.74794147e+02 -1.04837439e+03 -5.13670525e+02 | -6.74794712e+02 -1.04837192e+03 -5.13663888e+02 ERR 13 -6.18427051e+02 -2.12987237e+03 1.97215638e+03 | -6.18414006e+02 -2.12981987e+03 1.97215327e+03 ERR 14 3.61776545e+03 2.52171985e+03 -2.90155894e+03 | 3.61776223e+03 2.52172295e+03 -2.90155233e+03 ERR 15 -2.32456231e+03 6.56415934e+02 1.44305452e+03 | -2.32455352e+03 6.56468848e+02 1.44306295e+03 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTF (Configuration in file "config-C-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 7352.794041492043 2^p V(r_1,...,r_N) = 7352.794041491955 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 -5.91377321e+03 -1.73010547e+03 -3.05178969e+03 | -5.91377321e+03 -1.73010547e+03 -3.05178969e+03 1 5.97401178e+03 5.36091195e+03 -8.88315732e+03 | 5.97401178e+03 5.36091195e+03 -8.88315732e+03 2 1.11279485e+03 -4.33259891e+03 1.02619856e+04 | 1.11279485e+03 -4.33259891e+03 1.02619856e+04 3 -1.17303342e+03 7.01792429e+02 1.67296144e+03 | -1.17303342e+03 7.01792429e+02 1.67296144e+03 4 -5.91377321e+03 -1.73010547e+03 -3.05178969e+03 | -5.91377321e+03 -1.73010547e+03 -3.05178969e+03 5 5.97401178e+03 5.36091195e+03 -8.88315732e+03 | 5.97401178e+03 5.36091195e+03 -8.88315732e+03 6 1.11279485e+03 -4.33259891e+03 1.02619856e+04 | 1.11279485e+03 -4.33259891e+03 1.02619856e+04 7 -1.17303342e+03 7.01792429e+02 1.67296144e+03 | -1.17303342e+03 7.01792429e+02 1.67296144e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 2216.091925081081 2^p V(r_1,...,r_N) = 2216.0919250811 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 -1.03516614e+03 -9.17744343e+02 3.67028325e+02 | -1.03516614e+03 -9.17744343e+02 3.67028325e+02 1 1.00905659e+03 1.65434378e+03 -1.07134660e+03 | 1.00905673e+03 1.65434296e+03 -1.07134426e+03 ERR 2 1.16752282e+03 -1.96790085e+03 5.98130101e+02 | 1.16752296e+03 -1.96790167e+03 5.98132445e+02 ERR 3 -1.14141354e+03 1.23130306e+03 1.06183485e+02 | -1.14141354e+03 1.23130306e+03 1.06183485e+02 4 -1.03516614e+03 -9.17744343e+02 3.67028325e+02 | -1.03516614e+03 -9.17744343e+02 3.67028325e+02 5 1.00905687e+03 1.65434214e+03 -1.07134191e+03 | 1.00905673e+03 1.65434296e+03 -1.07134426e+03 ERR 6 1.16752309e+03 -1.96790249e+03 5.98134789e+02 | 1.16752296e+03 -1.96790167e+03 5.98132445e+02 ERR 7 -1.14141354e+03 1.23130306e+03 1.06183485e+02 | -1.14141354e+03 1.23130306e+03 1.06183485e+02 ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTT (Configuration in file "config-H-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)) = -0.27714850922412 2^p V(r_1,...,r_N) = -0.2771485092241203 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 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 1 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 2 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 3 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 4 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 5 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 6 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 7 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 8 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 9 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 10 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 11 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 12 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 13 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 14 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 15 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 16 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 17 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 18 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 19 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 20 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 21 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 22 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 23 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 24 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 25 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 26 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 27 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 28 -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 | -3.63529218e-03 -4.64972951e-04 -4.83767398e-04 29 3.16285352e-04 -2.50174563e-03 1.36920479e-04 | 3.16285352e-04 -2.50174563e-03 1.36920479e-04 30 4.51544203e-03 -1.15410729e-03 3.95655049e-03 | 4.51544203e-03 -1.15410729e-03 3.95655049e-03 31 -1.19643521e-03 4.12082586e-03 -3.60970357e-03 | -1.19643521e-03 4.12082586e-03 -3.60970357e-03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTF (Configuration in file "config-H-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)) = 113.90636641643378 2^p V(r_1,...,r_N) = 113.90636641643228 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 6.12248165e+00 1.30258093e+01 -2.26111751e+01 | 6.12331258e+00 1.30355037e+01 -2.26117710e+01 ERR 1 -2.34603046e+00 -1.39719082e+01 -6.82845077e+00 | -2.34556561e+00 -1.39493664e+01 -6.82800710e+00 ERR 2 -3.36024464e+01 4.68127451e+01 3.40374487e+01 | -3.36015185e+01 4.68254487e+01 3.40381686e+01 ERR 3 2.98219295e+01 -4.59026731e+01 -4.59813937e+00 | 2.98237715e+01 -4.59115861e+01 -4.59839051e+00 ERR 4 6.12470392e+00 1.30299935e+01 -2.26120833e+01 | 6.12331258e+00 1.30355037e+01 -2.26117710e+01 ERR 5 -2.34365217e+00 -1.39717165e+01 -6.82746657e+00 | -2.34556561e+00 -1.39493664e+01 -6.82800710e+00 ERR 6 -3.36004908e+01 4.68109106e+01 3.40387880e+01 | -3.36015185e+01 4.68254487e+01 3.40381686e+01 ERR 7 2.98264020e+01 -4.58986092e+01 -4.59872782e+00 | 2.98237715e+01 -4.59115861e+01 -4.59839051e+00 ERR 8 6.12179280e+00 1.30441887e+01 -2.26118262e+01 | 6.12331258e+00 1.30355037e+01 -2.26117710e+01 ERR 9 -2.33882694e+00 -1.39452326e+01 -6.82269295e+00 | -2.34556561e+00 -1.39493664e+01 -6.82800710e+00 ERR 10 -3.36095669e+01 4.68543519e+01 3.40321081e+01 | -3.36015185e+01 4.68254487e+01 3.40381686e+01 ERR 11 2.98205963e+01 -4.59208550e+01 -4.59824090e+00 | 2.98237715e+01 -4.59115861e+01 -4.59839051e+00 ERR 12 6.12427196e+00 1.30420234e+01 -2.26119995e+01 | 6.12331258e+00 1.30355037e+01 -2.26117710e+01 ERR 13 -2.35375285e+00 -1.39086083e+01 -6.83341813e+00 | -2.34556561e+00 -1.39493664e+01 -6.82800710e+00 ERR 14 -3.35935698e+01 4.68237873e+01 3.40443298e+01 | -3.36015185e+01 4.68254487e+01 3.40381686e+01 ERR 15 2.98261583e+01 -4.59242071e+01 -4.59845397e+00 | 2.98237715e+01 -4.59115861e+01 -4.59839051e+00 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFT (Configuration in file "config-H-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)) = 57.918193315340986 2^p V(r_1,...,r_N) = 57.918193315341924 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 1.03211683e+01 -1.44164470e+01 7.31837351e+00 | 1.03529997e+01 -1.44159333e+01 7.32226208e+00 ERR 1 -4.11977196e+00 1.30525576e+01 -2.81714616e+00 | -4.11435803e+00 1.30535045e+01 -2.81386791e+00 ERR 2 -1.06901647e+01 -9.66848160e+00 -4.57346843e+00 | -1.06785416e+01 -9.66861096e+00 -4.58197355e+00 ERR 3 4.40988503e+00 1.10313484e+01 7.59557568e-02 | 4.43989996e+00 1.10310398e+01 7.35793803e-02 ERR 4 1.03851477e+01 -1.44166142e+01 7.31827416e+00 | 1.03529997e+01 -1.44159333e+01 7.32226208e+00 ERR 5 -4.10917282e+00 1.30531609e+01 -2.81670190e+00 | -4.11435803e+00 1.30535045e+01 -2.81386791e+00 ERR 6 -1.06666463e+01 -9.66854167e+00 -4.57310850e+00 | -1.06785416e+01 -9.66861096e+00 -4.58197355e+00 ERR 7 4.46866562e+00 1.10310213e+01 7.80805135e-02 | 4.43989996e+00 1.10310398e+01 7.35793803e-02 ERR 8 1.03207129e+01 -1.44148845e+01 7.32487320e+00 | 1.03529997e+01 -1.44159333e+01 7.32226208e+00 ERR 9 -4.12369283e+00 1.30537631e+01 -2.81317099e+00 | -4.11435803e+00 1.30535045e+01 -2.81386791e+00 ERR 10 -1.06907578e+01 -9.66860826e+00 -4.59201166e+00 | -1.06785416e+01 -9.66861096e+00 -4.58197355e+00 ERR 11 4.41653599e+00 1.10306863e+01 7.14269736e-02 | 4.43989996e+00 1.10310398e+01 7.35793803e-02 ERR 12 1.03849699e+01 -1.44157877e+01 7.32752745e+00 | 1.03529997e+01 -1.44159333e+01 7.32226208e+00 ERR 13 -4.10479451e+00 1.30545363e+01 -2.80845258e+00 | -4.11435803e+00 1.30535045e+01 -2.81386791e+00 ERR 14 -1.06665975e+01 -9.66881230e+00 -4.58930562e+00 | -1.06785416e+01 -9.66861096e+00 -4.58197355e+00 ERR 15 4.46451318e+00 1.10311033e+01 6.88542774e-02 | 4.43989996e+00 1.10310398e+01 7.35793803e-02 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFF (Configuration in file "config-H-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)) = 26.817288513433816 2^p V(r_1,...,r_N) = 26.817288513433887 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 8.30729950e+00 -1.23856644e+01 -9.14146341e+00 | 8.31271893e+00 -1.23857620e+01 -9.14149056e+00 ERR 1 1.24177113e+01 3.09046671e+01 -5.09598958e+00 | 1.24138608e+01 3.09049620e+01 -5.09639692e+00 ERR 2 -9.11370275e+00 -2.11119429e+01 1.47626610e+01 | -9.10944350e+00 -2.11116337e+01 1.47624902e+01 ERR 3 -1.16212550e+01 2.59258530e+00 -5.24313598e-01 | -1.16171362e+01 2.59243379e+00 -5.24602692e-01 ERR 4 8.31813837e+00 -1.23858597e+01 -9.14151772e+00 | 8.31271893e+00 -1.23857620e+01 -9.14149056e+00 ERR 5 1.24100102e+01 3.09052568e+01 -5.09680427e+00 | 1.24138608e+01 3.09049620e+01 -5.09639692e+00 ERR 6 -9.10518425e+00 -2.11113245e+01 1.47623194e+01 | -9.10944350e+00 -2.11116337e+01 1.47624902e+01 ERR 7 -1.16130174e+01 2.59228228e+00 -5.24891785e-01 | -1.16171362e+01 2.59243379e+00 -5.24602692e-01 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTT (Configuration in file "config-H-FTT.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)) = 81.23361824767632 2^p V(r_1,...,r_N) = 81.23361824767433 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 -1.76805462e+01 -1.59086308e+01 -1.12520877e+01 | -1.76807156e+01 -1.58996546e+01 -1.12545260e+01 ERR 1 1.98877770e+01 8.10232815e+00 -1.16552777e+01 | 1.98877781e+01 8.09573960e+00 -1.16514239e+01 ERR 2 1.91577677e+01 -8.40383362e+00 9.90993856e+00 | 1.91581412e+01 -8.39128933e+00 9.90680175e+00 ERR 3 -2.13656820e+01 1.61990593e+01 1.29923254e+01 | -2.13652037e+01 1.61952044e+01 1.29991482e+01 ERR 4 -1.76809108e+01 -1.58911593e+01 -1.12508799e+01 | -1.76807156e+01 -1.58996546e+01 -1.12545260e+01 ERR 5 1.98877925e+01 8.08951122e+00 -1.16524991e+01 | 1.98877781e+01 8.09573960e+00 -1.16514239e+01 ERR 6 1.91578728e+01 -8.37796490e+00 9.90963993e+00 | 1.91581412e+01 -8.39128933e+00 9.90680175e+00 ERR 7 -2.13652914e+01 1.61916411e+01 1.29940775e+01 | -2.13652037e+01 1.61952044e+01 1.29991482e+01 ERR 8 -1.76805517e+01 -1.59058626e+01 -1.12591963e+01 | -1.76807156e+01 -1.58996546e+01 -1.12545260e+01 ERR 9 1.98871324e+01 8.09706353e+00 -1.16482700e+01 | 1.98877781e+01 8.09573960e+00 -1.16514239e+01 ERR 10 1.91586925e+01 -8.40293074e+00 9.90256505e+00 | 1.91581412e+01 -8.39128933e+00 9.90680175e+00 ERR 11 -2.13655133e+01 1.61977239e+01 1.30089998e+01 | -2.13652037e+01 1.61952044e+01 1.29991482e+01 ERR 12 -1.76808538e+01 -1.58929658e+01 -1.12559403e+01 | -1.76807156e+01 -1.58996546e+01 -1.12545260e+01 ERR 13 1.98884103e+01 8.09405551e+00 -1.16496487e+01 | 1.98877781e+01 8.09573960e+00 -1.16514239e+01 ERR 14 1.91582320e+01 -8.38042808e+00 9.90506348e+00 | 1.91581412e+01 -8.39128933e+00 9.90680175e+00 ERR 15 -2.13643280e+01 1.61923930e+01 1.30011901e+01 | -2.13652037e+01 1.61952044e+01 1.29991482e+01 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTF (Configuration in file "config-H-FTF.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)) = 19.95977583385635 2^p V(r_1,...,r_N) = 19.959775833856327 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 -1.42289653e+01 -4.29713337e-01 -1.43721569e+01 | -1.42289792e+01 -4.29863822e-01 -1.43721662e+01 ERR 1 7.13608785e+00 -3.24510912e+00 -7.01118363e+00 | 7.13609303e+00 -3.25213164e+00 -7.01118784e+00 ERR 2 1.37008582e+01 2.10916003e-01 1.23262794e+01 | 1.37006500e+01 2.37213016e-01 1.23263414e+01 ERR 3 -6.60757478e+00 3.44629795e+00 9.05694546e+00 | -6.60776392e+00 3.44478245e+00 9.05701260e+00 ERR 4 -1.42289930e+01 -4.30014307e-01 -1.43721755e+01 | -1.42289792e+01 -4.29863822e-01 -1.43721662e+01 ERR 5 7.13609821e+00 -3.25915417e+00 -7.01119205e+00 | 7.13609303e+00 -3.25213164e+00 -7.01118784e+00 ERR 6 1.37004419e+01 2.63510029e-01 1.23264035e+01 | 1.37006500e+01 2.37213016e-01 1.23263414e+01 ERR 7 -6.60795305e+00 3.44326694e+00 9.05707974e+00 | -6.60776392e+00 3.44478245e+00 9.05701260e+00 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FFT (Configuration in file "config-H-FFT.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)) = 32.66397368916847 2^p V(r_1,...,r_N) = 32.66397368916848 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 -1.81971046e+01 -2.22829812e+01 -1.08602836e+01 | -1.81971764e+01 -2.22830194e+01 -1.08630743e+01 ERR 1 4.48543326e+00 2.06111175e+01 -5.91817957e+00 | 4.48552325e+00 2.06106876e+01 -5.91578000e+00 ERR 2 3.22534612e+01 -8.98055979e+00 4.44627112e+00 | 3.22531910e+01 -8.98087909e+00 4.44988189e+00 ERR 3 -1.85412510e+01 1.06530583e+01 1.23249652e+01 | -1.85415379e+01 1.06532109e+01 1.23289725e+01 ERR 4 -1.81972482e+01 -2.22830576e+01 -1.08658651e+01 | -1.81971764e+01 -2.22830194e+01 -1.08630743e+01 ERR 5 4.48561323e+00 2.06102576e+01 -5.91338044e+00 | 4.48552325e+00 2.06106876e+01 -5.91578000e+00 ERR 6 3.22529209e+01 -8.98119838e+00 4.45349267e+00 | 3.22531910e+01 -8.98087909e+00 4.44988189e+00 ERR 7 -1.85418248e+01 1.06533635e+01 1.23329797e+01 | -1.85415379e+01 1.06532109e+01 1.23289725e+01 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = TTT (Configuration in file "config-CH-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)) = 1094.6171140412926 2^p V(r_1,...,r_N) = 1094.6171140413958 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 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 1 -4.52837397e+02 1.64911840e+02 -4.68715495e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 2 -5.40614009e+00 -1.06087849e+01 2.06217361e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 3 4.50202883e+02 -1.55096518e+02 4.54973043e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 4 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 5 -4.52838557e+02 1.64911063e+02 -4.68720781e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 6 -5.41688790e+00 -1.06214952e+01 2.06221394e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 ERR 7 4.50214791e+02 -1.55083031e+02 4.54977926e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 ERR 8 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 9 -4.52840922e+02 1.64901594e+02 -4.68719077e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 10 -5.40614009e+00 -1.06087849e+01 2.06217361e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 11 4.50202883e+02 -1.55096518e+02 4.54973043e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 12 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 13 -4.52838557e+02 1.64911063e+02 -4.68720781e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 14 -5.42806296e+00 -1.06124424e+01 2.06187336e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 ERR 15 4.50222441e+02 -1.55102330e+02 4.54977750e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 ERR 16 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 17 -4.52837397e+02 1.64911840e+02 -4.68715495e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 18 -5.40614009e+00 -1.06087849e+01 2.06217361e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 19 4.50202883e+02 -1.55096518e+02 4.54973043e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 20 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 21 -4.52839762e+02 1.64902371e+02 -4.68713790e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 22 -5.39539228e+00 -1.05960747e+01 2.06213328e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 ERR 23 4.50194500e+02 -1.55099759e+02 4.54971742e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 ERR 24 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 25 -4.52840922e+02 1.64901594e+02 -4.68719077e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 26 -5.40614009e+00 -1.06087849e+01 2.06217361e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 27 4.50202883e+02 -1.55096518e+02 4.54973043e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 28 8.04241659e+00 7.98586186e-01 -6.87749316e+00 | 8.04241659e+00 7.98586186e-01 -6.87749316e+00 29 -4.52839762e+02 1.64902371e+02 -4.68713790e+02 | -4.52839160e+02 1.64906717e+02 -4.68717286e+02 ERR 30 -5.38421721e+00 -1.06051275e+01 2.06247386e+01 | -5.40614009e+00 -1.06087849e+01 2.06217361e+01 ERR 31 4.50179800e+02 -1.55100953e+02 4.54964754e+02 | 4.50202883e+02 -1.55096518e+02 4.54973043e+02 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = TTF (Configuration in file "config-CH-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)) = 2340.2209153530303 2^p V(r_1,...,r_N) = 2340.220915353139 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 5.95781964e+02 -1.01080645e+03 -1.35171662e+03 | 5.95821951e+02 -1.01081448e+03 -1.35172695e+03 ERR 1 -2.34272275e+02 4.50033994e+02 -3.21498798e+02 | -2.34270731e+02 4.50036432e+02 -3.21498930e+02 ERR 2 2.94647455e+02 -4.72030099e+02 3.35634571e+02 | 2.94647441e+02 -4.72030160e+02 3.35634499e+02 ERR 3 -6.56212248e+02 1.03281362e+03 1.33759486e+03 | -6.56198660e+02 1.03280820e+03 1.33759138e+03 ERR 4 5.95833867e+02 -1.01082251e+03 -1.35173026e+03 | 5.95821951e+02 -1.01081448e+03 -1.35172695e+03 ERR 5 -2.34272307e+02 4.50033999e+02 -3.21498802e+02 | -2.34270731e+02 4.50036432e+02 -3.21498930e+02 ERR 6 2.94647426e+02 -4.72030166e+02 3.35634498e+02 | 2.94647441e+02 -4.72030160e+02 3.35634499e+02 ERR 7 -6.56160124e+02 1.03279801e+03 1.33758122e+03 | -6.56198660e+02 1.03280820e+03 1.33759138e+03 ERR 8 5.95835675e+02 -1.01081464e+03 -1.35173040e+03 | 5.95821951e+02 -1.01081448e+03 -1.35172695e+03 ERR 9 -2.34269156e+02 4.50038865e+02 -3.21499059e+02 | -2.34270731e+02 4.50036432e+02 -3.21498930e+02 ERR 10 2.94647458e+02 -4.72030226e+02 3.35634432e+02 | 2.94647441e+02 -4.72030160e+02 3.35634499e+02 ERR 11 -6.56211337e+02 1.03281065e+03 1.33759477e+03 | -6.56198660e+02 1.03280820e+03 1.33759138e+03 ERR 12 5.95836298e+02 -1.01081431e+03 -1.35173050e+03 | 5.95821951e+02 -1.01081448e+03 -1.35172695e+03 ERR 13 -2.34269188e+02 4.50038871e+02 -3.21499063e+02 | -2.34270731e+02 4.50036432e+02 -3.21498930e+02 ERR 14 2.94647424e+02 -4.72030148e+02 3.35634496e+02 | 2.94647441e+02 -4.72030160e+02 3.35634499e+02 ERR 15 -6.56210933e+02 1.03281053e+03 1.33759466e+03 | -6.56198660e+02 1.03280820e+03 1.33759138e+03 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = TFT (Configuration in file "config-CH-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)) = 1250.8347499460415 2^p V(r_1,...,r_N) = 1250.8347499460726 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 -3.22021826e+01 -2.10373863e+01 1.99799158e+00 | -3.21941453e+01 -2.10336837e+01 2.01414886e+00 ERR 1 3.11836609e+02 7.62767193e+02 3.69941778e+02 | 3.11834849e+02 7.62766277e+02 3.69944998e+02 ERR 2 -2.65139332e+02 -8.61488425e+02 -3.44644846e+02 | -2.65139562e+02 -8.61488487e+02 -3.44644661e+02 ERR 3 -1.45011414e+01 1.19755894e+02 -2.73148383e+01 | -1.45011414e+01 1.19755894e+02 -2.73144862e+01 ERR 4 -3.21926778e+01 -2.10328510e+01 2.01074308e+00 | -3.21941453e+01 -2.10336837e+01 2.01414886e+00 ERR 5 3.11826726e+02 7.62762546e+02 3.69929192e+02 | 3.11834849e+02 7.62766277e+02 3.69944998e+02 ERR 6 -2.65139586e+02 -8.61488493e+02 -3.44644642e+02 | -2.65139562e+02 -8.61488487e+02 -3.44644661e+02 ERR 7 -1.45011414e+01 1.19755894e+02 -2.73148383e+01 | -1.45011414e+01 1.19755894e+02 -2.73144862e+01 ERR 8 -3.21956129e+01 -2.10345164e+01 2.01755465e+00 | -3.21941453e+01 -2.10336837e+01 2.01414886e+00 ERR 9 3.11842910e+02 7.62769985e+02 3.69960785e+02 | 3.11834849e+02 7.62766277e+02 3.69944998e+02 ERR 10 -2.65139477e+02 -8.61488459e+02 -3.44644660e+02 | -2.65139562e+02 -8.61488487e+02 -3.44644661e+02 ERR 11 -1.45011414e+01 1.19755894e+02 -2.73141341e+01 | -1.45011414e+01 1.19755894e+02 -2.73144862e+01 ERR 12 -3.21861080e+01 -2.10299810e+01 2.03030615e+00 | -3.21941453e+01 -2.10336837e+01 2.01414886e+00 ERR 13 3.11833151e+02 7.62765382e+02 3.69948237e+02 | 3.11834849e+02 7.62766277e+02 3.69944998e+02 ERR 14 -2.65139855e+02 -8.61488570e+02 -3.44644495e+02 | -2.65139562e+02 -8.61488487e+02 -3.44644661e+02 ERR 15 -1.45011414e+01 1.19755894e+02 -2.73141341e+01 | -1.45011414e+01 1.19755894e+02 -2.73144862e+01 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = TFF (Configuration in file "config-CH-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)) = 257.6242628789304 2^p V(r_1,...,r_N) = 257.6242628789309 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 9.99887629e+01 -3.78085898e+02 -3.05362157e+02 | 9.99887629e+01 -3.78085898e+02 -3.05362157e+02 1 -1.90845467e+01 2.31735783e+01 -4.65375833e+01 | -1.90845467e+01 2.31735783e+01 -4.65375833e+01 2 7.36691943e+00 -2.32634551e+01 3.28462197e+01 | 7.36691943e+00 -2.32634551e+01 3.28462197e+01 3 -8.82711356e+01 3.78175775e+02 3.19053521e+02 | -8.82711356e+01 3.78175775e+02 3.19053521e+02 4 9.99887629e+01 -3.78085898e+02 -3.05362157e+02 | 9.99887629e+01 -3.78085898e+02 -3.05362157e+02 5 -1.90845467e+01 2.31735783e+01 -4.65375833e+01 | -1.90845467e+01 2.31735783e+01 -4.65375833e+01 6 7.36691943e+00 -2.32634551e+01 3.28462197e+01 | 7.36691943e+00 -2.32634551e+01 3.28462197e+01 7 -8.82711356e+01 3.78175775e+02 3.19053521e+02 | -8.82711356e+01 3.78175775e+02 3.19053521e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = FTT (Configuration in file "config-CH-FTT.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)) = 1757.5417148643844 2^p V(r_1,...,r_N) = 1757.541714864409 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 -7.20204644e+01 -5.00216044e+01 -1.70497987e+01 | -7.20204643e+01 -5.00215944e+01 -1.70496244e+01 ERR 1 1.32547258e+02 -1.77677162e+02 6.76995459e+02 | 1.32547258e+02 -1.77677162e+02 6.76995459e+02 2 6.06143212e+00 2.01746793e+02 -7.02759478e+02 | 6.06143212e+00 2.01746793e+02 -7.02759478e+02 3 -6.65882263e+01 2.59519528e+01 4.28134694e+01 | -6.65882262e+01 2.59519628e+01 4.28136437e+01 ERR 4 -7.20204644e+01 -5.00216044e+01 -1.70497987e+01 | -7.20204643e+01 -5.00215944e+01 -1.70496244e+01 ERR 5 1.32547258e+02 -1.77677162e+02 6.76995459e+02 | 1.32547258e+02 -1.77677162e+02 6.76995459e+02 6 6.06143212e+00 2.01746793e+02 -7.02759478e+02 | 6.06143212e+00 2.01746793e+02 -7.02759478e+02 7 -6.65882263e+01 2.59519528e+01 4.28134694e+01 | -6.65882262e+01 2.59519628e+01 4.28136437e+01 ERR 8 -7.20204641e+01 -5.00215844e+01 -1.70494501e+01 | -7.20204643e+01 -5.00215944e+01 -1.70496244e+01 ERR 9 1.32547258e+02 -1.77677162e+02 6.76995459e+02 | 1.32547258e+02 -1.77677162e+02 6.76995459e+02 10 6.06143212e+00 2.01746793e+02 -7.02759478e+02 | 6.06143212e+00 2.01746793e+02 -7.02759478e+02 11 -6.65882260e+01 2.59519728e+01 4.28138180e+01 | -6.65882262e+01 2.59519628e+01 4.28136437e+01 ERR 12 -7.20204641e+01 -5.00215844e+01 -1.70494501e+01 | -7.20204643e+01 -5.00215944e+01 -1.70496244e+01 ERR 13 1.32547258e+02 -1.77677162e+02 6.76995459e+02 | 1.32547258e+02 -1.77677162e+02 6.76995459e+02 14 6.06143212e+00 2.01746793e+02 -7.02759478e+02 | 6.06143212e+00 2.01746793e+02 -7.02759478e+02 15 -6.65882260e+01 2.59519728e+01 4.28138180e+01 | -6.65882262e+01 2.59519628e+01 4.28136437e+01 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = FTF (Configuration in file "config-CH-FTF.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)) = 440.99603218613237 2^p V(r_1,...,r_N) = 440.9960321861326 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 -6.76224131e+02 1.35348886e+02 -8.27198897e+01 | -6.76224131e+02 1.35348886e+02 -8.27198897e+01 1 6.66779252e+02 -8.52706310e+01 -3.58843228e+01 | 6.66779252e+02 -8.52706310e+01 -3.58843228e+01 2 3.49619011e+01 -3.11468413e+01 6.42320692e+01 | 3.49619011e+01 -3.11468413e+01 6.42320692e+01 3 -2.55170213e+01 -1.89314134e+01 5.43721432e+01 | -2.55170213e+01 -1.89314134e+01 5.43721432e+01 4 -6.76224131e+02 1.35348886e+02 -8.27198897e+01 | -6.76224131e+02 1.35348886e+02 -8.27198897e+01 5 6.66779252e+02 -8.52706310e+01 -3.58843228e+01 | 6.66779252e+02 -8.52706310e+01 -3.58843228e+01 6 3.49619011e+01 -3.11468413e+01 6.42320692e+01 | 3.49619011e+01 -3.11468413e+01 6.42320692e+01 7 -2.55170213e+01 -1.89314134e+01 5.43721432e+01 | -2.55170213e+01 -1.89314134e+01 5.43721432e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C H, PBC = FFT (Configuration in file "config-CH-FFT.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)) = 4026.644270307699 2^p V(r_1,...,r_N) = 4026.644270307686 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 -1.77631303e+02 -3.92046750e+01 2.62713748e+01 | -1.77631303e+02 -3.92046750e+01 2.62711106e+01 ERR 1 -1.30168827e+03 9.40123061e+03 -6.49182328e+03 | -1.30168810e+03 9.40122950e+03 -6.49181761e+03 ERR 2 1.57599799e+03 -9.38281287e+03 6.46953695e+03 | 1.57599816e+03 -9.38281398e+03 6.46954262e+03 ERR 3 -9.66787610e+01 2.07891549e+01 -3.99639180e+00 | -9.66787610e+01 2.07891549e+01 -3.99612758e+00 ERR 4 -1.77631303e+02 -3.92046750e+01 2.62708464e+01 | -1.77631303e+02 -3.92046750e+01 2.62711106e+01 ERR 5 -1.30168792e+03 9.40122839e+03 -6.49181193e+03 | -1.30168810e+03 9.40122950e+03 -6.49181761e+03 ERR 6 1.57599834e+03 -9.38281509e+03 6.46954830e+03 | 1.57599816e+03 -9.38281398e+03 6.46954262e+03 ERR 7 -9.66787610e+01 2.07891549e+01 -3.99586335e+00 | -9.66787610e+01 2.07891549e+01 -3.99612758e+00 ERR ------------------------------------------------------------------------------------------------------------------------ FAIL: Energies and/or forces differ by more than 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: F Comment: Periodic boundary conditions were NOT supported correctly for at least one configuration that the model was able to compute. This is an error in the implementation of the model.