!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_EAM_BonnyCastinBullens_2013_FeCrW__SM_699257350704_000 Supported species : Cr Fe W random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTT (Configuration in file "config-Cr-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.0711837672 2^p V(r_1,...,r_N) = -6.0711837672 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 -1.74703968e+00 -2.56810280e+00 -2.89566904e+00 | -1.74703968e+00 -2.56810280e+00 -2.89566904e+00 1 1.11832762e+00 7.87848322e-01 -6.02016673e-01 | 1.11832762e+00 7.87848322e-01 -6.02016673e-01 2 1.47007662e+00 -1.04035099e+00 1.52745119e+00 | 1.47007662e+00 -1.04035099e+00 1.52745119e+00 3 -8.41364569e-01 2.82060547e+00 1.97023452e+00 | -8.41364569e-01 2.82060547e+00 1.97023452e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTF (Configuration in file "config-Cr-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)) = -5.44906277437 2^p V(r_1,...,r_N) = -5.44906277437 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.53692721e+00 -1.73234306e+00 -1.69726515e+00 | -2.53692721e+00 -1.73234306e+00 -1.69726515e+00 1 1.80959292e+00 1.50058924e+00 -2.35632306e+00 | 1.80959292e+00 1.50058924e+00 -2.35632306e+00 2 3.03991053e+00 -3.22135328e+00 2.98196133e+00 | 3.03991053e+00 -3.22135328e+00 2.98196133e+00 3 -2.31257625e+00 3.45310710e+00 1.07162688e+00 | -2.31257625e+00 3.45310710e+00 1.07162688e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFT (Configuration in file "config-Cr-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)) = -4.56996520008 2^p V(r_1,...,r_N) = -4.56996520008 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.81885676e+00 -3.53238563e+00 -4.51172571e+00 | -2.81885676e+00 -3.53238563e+00 -4.51172571e+00 1 3.73917862e+00 3.64658213e+00 -2.11532609e+00 | 3.73917862e+00 3.64658213e+00 -2.11532609e+00 2 2.40096090e+00 -3.11149655e+00 3.34210538e+00 | 2.40096090e+00 -3.11149655e+00 3.34210538e+00 3 -3.32128276e+00 2.99730005e+00 3.28494643e+00 | -3.32128276e+00 2.99730005e+00 3.28494643e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFF (Configuration in file "config-Cr-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)) = -1.46516279994 2^p V(r_1,...,r_N) = -1.46516279994 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 -6.79854074e+00 -5.93808096e+00 -1.04330589e+01 | -6.79854074e+00 -5.93808096e+00 -1.04330589e+01 1 3.74284437e+00 4.53868517e+00 -2.93068515e+00 | 3.74284437e+00 4.53868517e+00 -2.93068515e+00 2 8.25467774e+00 -5.01262092e+00 8.22724480e+00 | 8.25467774e+00 -5.01262092e+00 8.22724480e+00 3 -5.19898137e+00 6.41201670e+00 5.13649928e+00 | -5.19898137e+00 6.41201670e+00 5.13649928e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTT (Configuration in file "config-Cr-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)) = -4.68909143967 2^p V(r_1,...,r_N) = -4.68909143967 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 -3.78418410e+00 -2.64782015e+00 -3.57311661e+00 | -3.78418410e+00 -2.64782015e+00 -3.57311661e+00 1 2.57483369e+00 3.25800546e+00 -2.76360990e+00 | 2.57483369e+00 3.25800546e+00 -2.76360990e+00 2 3.60580953e+00 -3.72386654e+00 3.25973150e+00 | 3.60580953e+00 -3.72386654e+00 3.25973150e+00 3 -2.39645912e+00 3.11368124e+00 3.07699500e+00 | -2.39645912e+00 3.11368124e+00 3.07699500e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTF (Configuration in file "config-Cr-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)) = -5.96638755007 2^p V(r_1,...,r_N) = -5.96638755007 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.65598336e+00 -2.17282431e+00 -1.62391916e+00 | -2.65598336e+00 -2.17282431e+00 -1.62391916e+00 1 1.34196251e+00 2.18739501e+00 -1.57642841e+00 | 1.34196251e+00 2.18739501e+00 -1.57642841e+00 2 1.91639231e+00 -1.01886899e+00 2.77047465e+00 | 1.91639231e+00 -1.01886899e+00 2.77047465e+00 3 -6.02371460e-01 1.00429828e+00 4.29872924e-01 | -6.02371460e-01 1.00429828e+00 4.29872924e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FFT (Configuration in file "config-Cr-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)) = -2.40271307534 2^p V(r_1,...,r_N) = -2.40271307534 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 -3.30995346e+00 -3.02311418e+00 -4.54618241e+00 | -3.30995346e+00 -3.02311418e+00 -4.54618241e+00 1 4.38044805e+00 4.20130873e+00 -3.93082163e+00 | 4.38044805e+00 4.20130873e+00 -3.93082163e+00 2 7.02057742e+00 -8.22574975e+00 5.28551616e+00 | 7.02057742e+00 -8.22574975e+00 5.28551616e+00 3 -8.09107202e+00 7.04755521e+00 3.19148788e+00 | -8.09107202e+00 7.04755521e+00 3.19148788e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTT (Configuration in file "config-Fe-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)) = -4.95338860747 2^p V(r_1,...,r_N) = -4.95338860747 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 -7.07188438e+00 -3.50905666e+00 -7.99114409e+00 | -7.07188438e+00 -3.50905666e+00 -7.99114409e+00 1 2.85368435e+00 4.72869375e+00 -3.38220990e+00 | 2.85368435e+00 4.72869375e+00 -3.38220990e+00 2 9.49327586e+00 -6.59343108e+00 7.99994916e+00 | 9.49327586e+00 -6.59343108e+00 7.99994916e+00 3 -5.27507583e+00 5.37379399e+00 3.37340484e+00 | -5.27507583e+00 5.37379399e+00 3.37340484e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTF (Configuration in file "config-Fe-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)) = -3.92775466632 2^p V(r_1,...,r_N) = -3.92775466632 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 -4.42620222e+00 -3.19085088e+00 -3.86683660e+00 | -4.42620222e+00 -3.19085088e+00 -3.86683660e+00 1 3.25458656e+00 5.43647893e+00 -4.83657781e+00 | 3.25458656e+00 5.43647893e+00 -4.83657781e+00 2 1.37766315e+01 -1.26442236e+01 4.97321365e+00 | 1.37766315e+01 -1.26442236e+01 4.97321365e+00 3 -1.26050159e+01 1.03985955e+01 3.73020076e+00 | -1.26050159e+01 1.03985955e+01 3.73020076e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFT (Configuration in file "config-Fe-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)) = -7.14015008711 2^p V(r_1,...,r_N) = -7.14015008711 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 -8.93568798e-01 -1.39522558e+00 -1.16204333e+00 | -8.93568798e-01 -1.39522558e+00 -1.16204333e+00 1 1.70684814e+00 3.36760427e+00 -6.00203087e+00 | 1.70684814e+00 3.36760427e+00 -6.00203087e+00 2 1.55579446e+00 -4.88789230e+00 5.95408241e+00 | 1.55579446e+00 -4.88789230e+00 5.95408241e+00 3 -2.36907380e+00 2.91551360e+00 1.20999179e+00 | -2.36907380e+00 2.91551360e+00 1.20999179e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFF (Configuration in file "config-Fe-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)) = -6.31495641797 2^p V(r_1,...,r_N) = -6.31495641797 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.02508054e+00 -9.74549045e+00 -8.59672991e+00 | -2.02508054e+00 -9.74549045e+00 -8.59672991e+00 1 1.62311800e+00 1.91289484e+00 -2.36553812e+00 | 1.62311800e+00 1.91289484e+00 -2.36553812e+00 2 1.40078656e+00 -2.25498140e+00 2.27611196e+00 | 1.40078656e+00 -2.25498140e+00 2.27611196e+00 3 -9.98824022e-01 1.00875770e+01 8.68615607e+00 | -9.98824022e-01 1.00875770e+01 8.68615607e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTT (Configuration in file "config-Fe-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.37783177706 2^p V(r_1,...,r_N) = -8.37783177706 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 -4.49988695e-02 -6.83287176e-01 -8.75498831e-01 | -4.49988695e-02 -6.83287176e-01 -8.75498831e-01 1 1.17347978e+00 2.26332773e-01 -1.37299477e+00 | 1.17347978e+00 2.26332773e-01 -1.37299477e+00 2 1.33626921e+00 -1.74088636e+00 3.02744121e-01 | 1.33626921e+00 -1.74088636e+00 3.02744121e-01 3 -2.46475012e+00 2.19784076e+00 1.94574948e+00 | -2.46475012e+00 2.19784076e+00 1.94574948e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTF (Configuration in file "config-Fe-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)) = -4.17348600161 2^p V(r_1,...,r_N) = -4.17348600161 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 -5.26781888e+00 -6.39608728e+00 -2.52202330e+00 | -5.26781888e+00 -6.39608728e+00 -2.52202330e+00 1 5.85469616e+00 5.27941155e+00 -3.27983165e+00 | 5.85469616e+00 5.27941155e+00 -3.27983165e+00 2 1.24029578e+01 -1.33417512e+01 3.96180973e+00 | 1.24029578e+01 -1.33417512e+01 3.96180973e+00 3 -1.29898350e+01 1.44584270e+01 1.84004521e+00 | -1.29898350e+01 1.44584270e+01 1.84004521e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FFT (Configuration in file "config-Fe-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)) = -8.16860952071 2^p V(r_1,...,r_N) = -8.16860952071 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 -1.31188405e+00 -2.14591223e+00 -2.18738395e+00 | -1.31188405e+00 -2.14591223e+00 -2.18738395e+00 1 9.26074254e-01 5.67319358e-01 5.63056470e-02 | 9.26074254e-01 5.67319358e-01 5.63056470e-02 2 1.29683897e+00 -1.14086903e+00 4.87877756e-01 | 1.29683897e+00 -1.14086903e+00 4.87877756e-01 3 -9.11029174e-01 2.71946190e+00 1.64320055e+00 | -9.11029174e-01 2.71946190e+00 1.64320055e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TTT (Configuration in file "config-W-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)) = 12.8969396283 2^p V(r_1,...,r_N) = 12.8969396283 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 -7.12203230e+01 -5.57888861e+01 -5.93818253e+01 | -7.12203230e+01 -5.57888861e+01 -5.93818253e+01 1 3.32945453e+01 4.15047491e+01 -4.62139740e+01 | 3.32945453e+01 4.15047491e+01 -4.62139740e+01 2 5.18864374e+01 -2.80175933e+01 8.13868526e+01 | 5.18864374e+01 -2.80175933e+01 8.13868526e+01 3 -1.39606597e+01 4.23017303e+01 2.42089467e+01 | -1.39606597e+01 4.23017303e+01 2.42089467e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TTF (Configuration in file "config-W-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)) = 15.540732085 2^p V(r_1,...,r_N) = 15.540732085 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 -1.63907822e+01 -2.03865458e+01 -1.07241465e+01 | -1.63907822e+01 -2.03865458e+01 -1.07241465e+01 1 2.14535791e+01 6.98832237e+01 -1.09750543e+02 | 2.14535791e+01 6.98832237e+01 -1.09750543e+02 2 2.67939305e+01 -7.41712388e+01 1.01881927e+02 | 2.67939305e+01 -7.41712388e+01 1.01881927e+02 3 -3.18567273e+01 2.46745609e+01 1.85927621e+01 | -3.18567273e+01 2.46745609e+01 1.85927621e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TFT (Configuration in file "config-W-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)) = 26.8076142786 2^p V(r_1,...,r_N) = 26.8076142786 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 -8.61195197e+01 -1.13401097e+02 -3.14312039e+01 | -8.61195197e+01 -1.13401097e+02 -3.14312039e+01 1 1.10413227e+02 1.17417709e+02 -2.80469322e+01 | 1.10413227e+02 1.17417709e+02 -2.80469322e+01 2 1.53433712e+01 -1.95384431e+01 8.81717773e+00 | 1.53433712e+01 -1.95384431e+01 8.81717773e+00 3 -3.96370788e+01 1.55218308e+01 5.06609584e+01 | -3.96370788e+01 1.55218308e+01 5.06609584e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TFF (Configuration in file "config-W-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)) = 3.59239129493 2^p V(r_1,...,r_N) = 3.59239129493 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 -4.55648554e+01 -5.77168228e+01 -4.74545929e+01 | -4.55648554e+01 -5.77168228e+01 -4.74545929e+01 1 2.87763448e+01 2.71715387e+01 -2.44580252e+01 | 2.87763448e+01 2.71715387e+01 -2.44580252e+01 2 2.98121156e+01 -1.68333842e+01 3.76115051e+01 | 2.98121156e+01 -1.68333842e+01 3.76115051e+01 3 -1.30236050e+01 4.73786683e+01 3.43011130e+01 | -1.30236050e+01 4.73786683e+01 3.43011130e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FTT (Configuration in file "config-W-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)) = -15.2946053474 2^p V(r_1,...,r_N) = -15.2946053474 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 -4.87031372e+00 -6.71832786e+00 -6.12882681e+00 | -4.87031372e+00 -6.71832786e+00 -6.12882681e+00 1 7.62590582e+00 9.13670098e+00 -1.02976718e+01 | 7.62590582e+00 9.13670098e+00 -1.02976718e+01 2 8.18567249e+00 -1.45109336e+01 5.96687165e+00 | 8.18567249e+00 -1.45109336e+01 5.96687165e+00 3 -1.09412646e+01 1.20925605e+01 1.04596269e+01 | -1.09412646e+01 1.20925605e+01 1.04596269e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FTF (Configuration in file "config-W-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)) = 15.776353639 2^p V(r_1,...,r_N) = 15.776353639 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.29516914e+01 -3.25886567e+01 -3.44838654e+01 | -2.29516914e+01 -3.25886567e+01 -3.44838654e+01 1 2.59229024e+01 4.76170507e+01 -7.12274639e+01 | 2.59229024e+01 4.76170507e+01 -7.12274639e+01 2 4.25380224e+01 -8.11621572e+01 7.06959603e+01 | 4.25380224e+01 -8.11621572e+01 7.06959603e+01 3 -4.55092334e+01 6.61337632e+01 3.50153690e+01 | -4.55092334e+01 6.61337632e+01 3.50153690e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FFT (Configuration in file "config-W-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)) = 35.7036978029 2^p V(r_1,...,r_N) = 35.7036978029 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 -4.96575598e+01 -2.80130758e+01 -5.76140490e+01 | -4.96575598e+01 -2.80130758e+01 -5.76140490e+01 1 5.00620369e+01 1.96787167e+01 -6.46715073e+01 | 5.00620369e+01 1.96787167e+01 -6.46715073e+01 2 1.01498435e+02 -1.06505538e+02 9.19077788e+01 | 1.01498435e+02 -1.06505538e+02 9.19077788e+01 3 -1.01902912e+02 1.14839897e+02 3.03777774e+01 | -1.01902912e+02 1.14839897e+02 3.03777774e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = TTT (Configuration in file "config-CrFeW-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)) = 3.94274346848 2^p V(r_1,...,r_N) = 3.94274346848 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 -3.08401317e+01 -1.86041929e+01 -4.98084445e+00 | -3.08401317e+01 -1.86041929e+01 -4.98084445e+00 1 2.36166862e+01 3.41984911e+01 -2.88234168e+01 | 2.36166862e+01 3.41984911e+01 -2.88234168e+01 2 1.17443118e+01 -1.80485014e+01 2.69965939e+01 | 1.17443118e+01 -1.80485014e+01 2.69965939e+01 3 -4.52086622e+00 2.45420326e+00 6.80766741e+00 | -4.52086622e+00 2.45420326e+00 6.80766741e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = TTF (Configuration in file "config-CrFeW-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)) = 11.0280581471 2^p V(r_1,...,r_N) = 11.0280581471 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 -3.02184899e+01 -6.96593709e-01 -2.30064750e+01 | -3.02184899e+01 -6.96593709e-01 -2.30064750e+01 1 7.86452286e-03 2.27285906e+01 -1.35131439e+01 | 7.86452286e-03 2.27285906e+01 -1.35131439e+01 2 3.55663302e+01 -2.78896306e+01 3.37673899e+01 | 3.55663302e+01 -2.78896306e+01 3.37673899e+01 3 -5.35570484e+00 5.85763364e+00 2.75222891e+00 | -5.35570484e+00 5.85763364e+00 2.75222891e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = TFT (Configuration in file "config-CrFeW-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)) = -4.12900114683 2^p V(r_1,...,r_N) = -4.12900114683 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 -1.64306057e+01 -1.87616753e+01 -1.10535347e+01 | -1.64306057e+01 -1.87616753e+01 -1.10535347e+01 1 1.15486387e+01 1.66139138e+01 6.78949416e-01 | 1.15486387e+01 1.66139138e+01 6.78949416e-01 2 6.57123489e+00 -8.76404018e-01 7.44359582e+00 | 6.57123489e+00 -8.76404018e-01 7.44359582e+00 3 -1.68926780e+00 3.02416546e+00 2.93098950e+00 | -1.68926780e+00 3.02416546e+00 2.93098950e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = TFF (Configuration in file "config-CrFeW-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)) = 4.17676510486 2^p V(r_1,...,r_N) = 4.17676510486 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.91103949e+01 -1.05673670e+01 -2.43012926e+01 | -2.91103949e+01 -1.05673670e+01 -2.43012926e+01 1 2.64277172e+01 1.99939528e+01 -2.97474293e+01 | 2.64277172e+01 1.99939528e+01 -2.97474293e+01 2 1.54762957e+01 -2.21998436e+01 3.76608159e+01 | 1.54762957e+01 -2.21998436e+01 3.76608159e+01 3 -1.27936179e+01 1.27732579e+01 1.63879060e+01 | -1.27936179e+01 1.27732579e+01 1.63879060e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = FTT (Configuration in file "config-CrFeW-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.55267238688 2^p V(r_1,...,r_N) = 8.55267238688 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 -1.80272429e+01 -1.00426826e+00 -1.60790492e+01 | -1.80272429e+01 -1.00426826e+00 -1.60790492e+01 1 8.93038539e+00 1.20653403e+01 -1.67244419e+01 | 8.93038539e+00 1.20653403e+01 -1.67244419e+01 2 3.77538392e+01 -3.86494227e+01 1.69949372e+01 | 3.77538392e+01 -3.86494227e+01 1.69949372e+01 3 -2.86569817e+01 2.75883506e+01 1.58085540e+01 | -2.86569817e+01 2.75883506e+01 1.58085540e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = FTF (Configuration in file "config-CrFeW-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)) = -9.19829534353 2^p V(r_1,...,r_N) = -9.19829534353 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 -3.87280806e+00 -5.69486640e+00 -2.91923997e+00 | -3.87280806e+00 -5.69486640e+00 -2.91923997e+00 1 3.33676719e+00 3.67928219e+00 -9.13378860e-01 | 3.33676719e+00 3.67928219e+00 -9.13378860e-01 2 2.06172415e+00 -1.12409808e+00 1.30250098e+00 | 2.06172415e+00 -1.12409808e+00 1.30250098e+00 3 -1.52568328e+00 3.13968228e+00 2.53011786e+00 | -1.52568328e+00 3.13968228e+00 2.53011786e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cr Fe W, PBC = FFT (Configuration in file "config-CrFeW-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 22.770980925 2^p V(r_1,...,r_N) = 22.770980925 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 -5.25920362e+01 -2.11504008e+01 -2.38576530e+01 | -5.25920362e+01 -2.11504008e+01 -2.38576530e+01 1 3.43426624e+01 9.04153424e+01 -6.35468549e+01 | 3.43426624e+01 9.04153424e+01 -6.35468549e+01 2 3.26400814e+01 -8.49603473e+01 8.13262309e+01 | 3.26400814e+01 -8.49603473e+01 8.13262309e+01 3 -1.43907076e+01 1.56954057e+01 6.07827690e+00 | -1.43907076e+01 1.56954057e+01 6.07827690e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.