!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_AngeloMoodyBaskes_1995_NiAlH__MO_418978237058_005 Supported species : Al H Ni random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -2.6366259304 2^p V(r_1,...,r_N) = -2.6366259304 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 -3.73295363e+00 -7.05434290e+00 -7.72169019e+00 | -3.73295363e+00 -7.05434290e+00 -7.72169019e+00 1 2.27604969e+00 1.53645481e+00 -1.09270883e+00 | 2.27604969e+00 1.53645481e+00 -1.09270883e+00 2 3.12716932e+00 -1.92361703e+00 3.20372010e+00 | 3.12716932e+00 -1.92361703e+00 3.20372010e+00 3 -1.67026538e+00 7.44150512e+00 5.61067892e+00 | -1.67026538e+00 7.44150512e+00 5.61067892e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -1.31132316181 2^p V(r_1,...,r_N) = -1.31132316181 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 -5.56111276e+00 -3.54289054e+00 -3.83798204e+00 | -5.56111276e+00 -3.54289054e+00 -3.83798204e+00 1 3.68556867e+00 3.28528952e+00 -5.11837594e+00 | 3.68556867e+00 3.28528952e+00 -5.11837594e+00 2 8.30783946e+00 -9.05452157e+00 6.95701387e+00 | 8.30783946e+00 -9.05452157e+00 6.95701387e+00 3 -6.43229537e+00 9.31212258e+00 1.99934411e+00 | -6.43229537e+00 9.31212258e+00 1.99934411e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.673169214272 2^p V(r_1,...,r_N) = 0.673169214272 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 -7.22061409e+00 -9.74317222e+00 -1.21813098e+01 | -7.22061409e+00 -9.74317222e+00 -1.21813098e+01 1 9.62536761e+00 9.63127622e+00 -5.41595127e+00 | 9.62536761e+00 9.63127622e+00 -5.41595127e+00 2 5.88485618e+00 -7.91189916e+00 8.62293635e+00 | 5.88485618e+00 -7.91189916e+00 8.62293635e+00 3 -8.28960970e+00 8.02379516e+00 8.97432471e+00 | -8.28960970e+00 8.02379516e+00 8.97432471e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 8.70303670562 2^p V(r_1,...,r_N) = 8.70303670562 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 -1.50305930e+01 -1.41342578e+01 -2.44481214e+01 | -1.50305930e+01 -1.41342578e+01 -2.44481214e+01 1 8.34883680e+00 1.03502332e+01 -6.72559959e+00 | 8.34883680e+00 1.03502332e+01 -6.72559959e+00 2 1.89100850e+01 -1.17398127e+01 1.87630612e+01 | 1.89100850e+01 -1.17398127e+01 1.87630612e+01 3 -1.22283288e+01 1.55238373e+01 1.24106597e+01 | -1.22283288e+01 1.55238373e+01 1.24106597e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-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)) = 0.356714174107 2^p V(r_1,...,r_N) = 0.356714174107 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 -9.91327150e+00 -6.81975370e+00 -9.56607969e+00 | -9.91327150e+00 -6.81975370e+00 -9.56607969e+00 1 6.27237006e+00 8.53499509e+00 -7.04826009e+00 | 6.27237006e+00 8.53499509e+00 -7.04826009e+00 2 9.52717964e+00 -9.84142093e+00 8.84046367e+00 | 9.52717964e+00 -9.84142093e+00 8.84046367e+00 3 -5.88627820e+00 8.12617953e+00 7.77387612e+00 | -5.88627820e+00 8.12617953e+00 7.77387612e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-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)) = -2.71212996118 2^p V(r_1,...,r_N) = -2.71212996118 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 -6.52800662e+00 -5.02862867e+00 -3.64553213e+00 | -6.52800662e+00 -5.02862867e+00 -3.64553213e+00 1 3.73396044e+00 5.08885653e+00 -3.97131571e+00 | 3.73396044e+00 5.08885653e+00 -3.97131571e+00 2 4.27983939e+00 -2.05128767e+00 6.40737319e+00 | 4.27983939e+00 -2.05128767e+00 6.40737319e+00 3 -1.48579321e+00 1.99105981e+00 1.20947465e+00 | -1.48579321e+00 1.99105981e+00 1.20947465e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-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)) = 6.53597488228 2^p V(r_1,...,r_N) = 6.53597488228 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 -8.28601493e+00 -7.52898825e+00 -1.02295270e+01 | -8.28601493e+00 -7.52898825e+00 -1.02295270e+01 1 1.07861807e+01 1.06216458e+01 -9.03533611e+00 | 1.07861807e+01 1.06216458e+01 -9.03533611e+00 2 1.63859596e+01 -1.96728532e+01 1.22608360e+01 | 1.63859596e+01 -1.96728532e+01 1.22608360e+01 3 -1.88861254e+01 1.65801957e+01 7.00402715e+00 | -1.88861254e+01 1.65801957e+01 7.00402715e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within 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=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)) = -2.38093568461 2^p V(r_1,...,r_N) = -2.38093568461 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 2.05868868e+00 1.45280702e+00 2.37878833e+00 | 2.05868868e+00 1.45280702e+00 2.37878833e+00 1 -1.22594492e+00 -1.85160300e+00 1.31546706e+00 | -1.22594492e+00 -1.85160300e+00 1.31546706e+00 2 -2.52133715e+00 2.20996961e+00 -2.33502192e+00 | -2.52133715e+00 2.20996961e+00 -2.33502192e+00 3 1.68859338e+00 -1.81117364e+00 -1.35923347e+00 | 1.68859338e+00 -1.81117364e+00 -1.35923347e+00 ------------------------------------------------------------------------------------------------------------------------ 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=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)) = -2.5609689806 2^p V(r_1,...,r_N) = -2.5609689806 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 1.93363021e+00 1.55817392e+00 1.57866924e+00 | 1.93363021e+00 1.55817392e+00 1.57866924e+00 1 -1.49585756e+00 -2.07107319e+00 1.53178583e+00 | -1.49585756e+00 -2.07107319e+00 1.53178583e+00 2 -2.64353379e+00 2.42304055e+00 -2.09168161e+00 | -2.64353379e+00 2.42304055e+00 -2.09168161e+00 3 2.20576113e+00 -1.91014127e+00 -1.01877346e+00 | 2.20576113e+00 -1.91014127e+00 -1.01877346e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within 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=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)) = -1.4296212226 2^p V(r_1,...,r_N) = -1.4296212226 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 7.75601104e-01 9.84007783e-01 8.07720607e-01 | 7.75601104e-01 9.84007783e-01 8.07720607e-01 1 -1.05718411e+00 -1.27783536e+00 2.22463626e+00 | -1.05718411e+00 -1.27783536e+00 2.22463626e+00 2 -1.11759840e+00 2.02658808e+00 -2.20851725e+00 | -1.11759840e+00 2.02658808e+00 -2.20851725e+00 3 1.39918141e+00 -1.73276051e+00 -8.23839617e-01 | 1.39918141e+00 -1.73276051e+00 -8.23839617e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within 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=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)) = -1.59849265645 2^p V(r_1,...,r_N) = -1.59849265645 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 8.47761270e-01 2.24608720e+00 1.87210339e+00 | 8.47761270e-01 2.24608720e+00 1.87210339e+00 1 -1.02376465e+00 -1.17742949e+00 1.51642465e+00 | -1.02376465e+00 -1.17742949e+00 1.51642465e+00 2 -6.03886658e-01 1.23829791e+00 -1.13069898e+00 | -6.03886658e-01 1.23829791e+00 -1.13069898e+00 3 7.79890039e-01 -2.30695561e+00 -2.25782906e+00 | 7.79890039e-01 -2.30695561e+00 -2.25782906e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within 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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.676656478321 2^p V(r_1,...,r_N) = -0.676656478321 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 8.48341947e-01 9.10993087e-01 4.94328594e-01 | 8.48341947e-01 9.10993087e-01 4.94328594e-01 1 -1.61399219e+00 -1.30806421e+00 1.20753285e+00 | -1.61399219e+00 -1.30806421e+00 1.20753285e+00 2 -1.77567870e-01 8.46344965e-01 -7.44879427e-01 | -1.77567870e-01 8.46344965e-01 -7.44879427e-01 3 9.43218108e-01 -4.49273837e-01 -9.56982021e-01 | 9.43218108e-01 -4.49273837e-01 -9.56982021e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within 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=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)) = -1.21307273863 2^p V(r_1,...,r_N) = -1.21307273863 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 7.90247558e-01 1.90800050e+00 1.81236913e+00 | 7.90247558e-01 1.90800050e+00 1.81236913e+00 1 -1.08182306e+00 -7.79827875e-01 1.01975353e+00 | -1.08182306e+00 -7.79827875e-01 1.01975353e+00 2 -1.02314299e+00 5.30362143e-01 -4.71073537e-01 | -1.02314299e+00 5.30362143e-01 -4.71073537e-01 3 1.31471849e+00 -1.65853476e+00 -2.36104912e+00 | 1.31471849e+00 -1.65853476e+00 -2.36104912e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within 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=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)) = -3.3838352493 2^p V(r_1,...,r_N) = -3.3838352493 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 2.08500837e+00 1.77488307e+00 2.05420405e+00 | 2.08500837e+00 1.77488307e+00 2.05420405e+00 1 -1.84357282e+00 -1.24533104e+00 2.27583942e+00 | -1.84357282e+00 -1.24533104e+00 2.27583942e+00 2 -2.23341774e+00 2.69604653e+00 -2.90866674e+00 | -2.23341774e+00 2.69604653e+00 -2.90866674e+00 3 1.99198219e+00 -3.22559856e+00 -1.42137673e+00 | 1.99198219e+00 -3.22559856e+00 -1.42137673e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-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)) = -5.39589859656 2^p V(r_1,...,r_N) = -5.39589859656 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 -1.60197576e+00 -4.37336603e-01 -8.31259524e-01 | -1.60197576e+00 -4.37336603e-01 -8.31259524e-01 1 4.65025976e-01 2.29584731e+00 -3.15360291e+00 | 4.65025976e-01 2.29584731e+00 -3.15360291e+00 2 3.44123356e+00 -3.85182954e+00 2.59338318e+00 | 3.44123356e+00 -3.85182954e+00 2.59338318e+00 3 -2.30428377e+00 1.99331884e+00 1.39147925e+00 | -2.30428377e+00 1.99331884e+00 1.39147925e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-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)) = -5.71718293152 2^p V(r_1,...,r_N) = -5.71718293152 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 -2.81372442e+00 -2.09079973e+00 -2.26935194e+00 | -2.81372442e+00 -2.09079973e+00 -2.26935194e+00 1 1.01843598e+00 1.59946426e+00 -1.50428328e+00 | 1.01843598e+00 1.59946426e+00 -1.50428328e+00 2 2.15571674e+00 -1.22572174e+00 3.08428216e+00 | 2.15571674e+00 -1.22572174e+00 3.08428216e+00 3 -3.60428302e-01 1.71705721e+00 6.89353059e-01 | -3.60428302e-01 1.71705721e+00 6.89353059e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-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)) = -3.76553558317 2^p V(r_1,...,r_N) = -3.76553558317 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 -2.35846980e+00 -4.07952503e+00 -4.16697729e+00 | -2.35846980e+00 -4.07952503e+00 -4.16697729e+00 1 2.39085234e+00 3.03708512e+00 -4.24745118e+00 | 2.39085234e+00 3.03708512e+00 -4.24745118e+00 2 4.45151007e+00 -4.76352542e+00 5.40012888e+00 | 4.45151007e+00 -4.76352542e+00 5.40012888e+00 3 -4.48389260e+00 5.80596533e+00 3.01429959e+00 | -4.48389260e+00 5.80596533e+00 3.01429959e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-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)) = -4.56266728396 2^p V(r_1,...,r_N) = -4.56266728396 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 -3.67032492e+00 -3.88527869e+00 -5.17672469e+00 | -3.67032492e+00 -3.88527869e+00 -5.17672469e+00 1 5.96304891e-01 1.59461901e+00 -1.19195185e+00 | 5.96304891e-01 1.59461901e+00 -1.19195185e+00 2 5.14026899e+00 -1.22227024e+00 4.71309156e+00 | 5.14026899e+00 -1.22227024e+00 4.71309156e+00 3 -2.06624896e+00 3.51292993e+00 1.65558499e+00 | -2.06624896e+00 3.51292993e+00 1.65558499e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-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)) = -5.96785817313 2^p V(r_1,...,r_N) = -5.96785817313 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 7.84678174e-01 5.06374466e-01 1.15514396e+00 | 7.84678174e-01 5.06374466e-01 1.15514396e+00 1 -7.55766634e-01 -4.54550773e-01 1.08530736e+00 | -7.55766634e-01 -4.54550773e-01 1.08530736e+00 2 -6.32161265e-01 5.75761876e-01 -1.11532864e+00 | -6.32161265e-01 5.75761876e-01 -1.11532864e+00 3 6.03249725e-01 -6.27585569e-01 -1.12512267e+00 | 6.03249725e-01 -6.27585569e-01 -1.12512267e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-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)) = -5.01628621087 2^p V(r_1,...,r_N) = -5.01628621087 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 6.19684608e-01 -2.72797851e+00 -3.29305088e+00 | 6.19684608e-01 -2.72797851e+00 -3.29305088e+00 1 -4.04005038e-01 -7.88020530e-01 9.55969321e-01 | -4.04005038e-01 -7.88020530e-01 9.55969321e-01 2 -7.88154553e-01 8.61714914e-01 -9.26972529e-01 | -7.88154553e-01 8.61714914e-01 -9.26972529e-01 3 5.72474984e-01 2.65428413e+00 3.26405409e+00 | 5.72474984e-01 2.65428413e+00 3.26405409e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-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)) = -4.4910792463 2^p V(r_1,...,r_N) = -4.4910792463 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 -2.84049108e+00 -4.36364985e+00 -4.81447538e+00 | -2.84049108e+00 -4.36364985e+00 -4.81447538e+00 1 3.40781254e+00 2.61674562e+00 -1.87396236e+00 | 3.40781254e+00 2.61674562e+00 -1.87396236e+00 2 3.64537615e+00 -2.71478116e+00 4.41129234e+00 | 3.64537615e+00 -2.71478116e+00 4.41129234e+00 3 -4.21269762e+00 4.46168539e+00 2.27714539e+00 | -4.21269762e+00 4.46168539e+00 2.27714539e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = TTT (Configuration in file "config-AlHNi-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)) = -3.31489924058 2^p V(r_1,...,r_N) = -3.31489924058 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 -3.48475628e+00 -5.79884970e+00 -8.52786881e+00 | -3.48475628e+00 -5.79884970e+00 -8.52786881e+00 1 -2.67306044e-02 5.08227106e-01 -1.59751703e-01 | -2.67306044e-02 5.08227106e-01 -1.59751703e-01 2 5.89333314e+00 -3.84026410e+00 8.17051445e-01 | 5.89333314e+00 -3.84026410e+00 8.17051445e-01 3 -2.38184626e+00 9.13088670e+00 7.87056907e+00 | -2.38184626e+00 9.13088670e+00 7.87056907e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = TTF (Configuration in file "config-AlHNi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.196876252471 2^p V(r_1,...,r_N) = -0.196876252471 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 -9.68511312e+00 -1.08737191e+01 -3.68727283e+00 | -9.68511312e+00 -1.08737191e+01 -3.68727283e+00 1 7.02167617e+00 1.72381515e+01 -8.80144238e+00 | 7.02167617e+00 1.72381515e+01 -8.80144238e+00 2 4.83499516e+00 -6.61543798e+00 1.17778212e+01 | 4.83499516e+00 -6.61543798e+00 1.17778212e+01 3 -2.17155821e+00 2.51005545e-01 7.10894024e-01 | -2.17155821e+00 2.51005545e-01 7.10894024e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = TFT (Configuration in file "config-AlHNi-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.8993917146 2^p V(r_1,...,r_N) = -5.8993917146 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 4.26098781e-01 -1.97886999e-01 2.62504334e-01 | 4.26098781e-01 -1.97886999e-01 2.62504334e-01 1 4.13481108e-01 -1.19801104e-01 -7.47510012e-02 | 4.13481108e-01 -1.19801104e-01 -7.47510012e-02 2 3.37991132e-01 -7.52665087e-01 -7.46289964e-01 | 3.37991132e-01 -7.52665087e-01 -7.46289964e-01 3 -1.17757102e+00 1.07035319e+00 5.58536632e-01 | -1.17757102e+00 1.07035319e+00 5.58536632e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = TFF (Configuration in file "config-AlHNi-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)) = -3.83034791866 2^p V(r_1,...,r_N) = -3.83034791866 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 -4.96249169e+00 -1.31107213e+00 -5.92236326e+00 | -4.96249169e+00 -1.31107213e+00 -5.92236326e+00 1 4.19064544e-01 4.61050359e-01 -1.12339302e+00 | 4.19064544e-01 4.61050359e-01 -1.12339302e+00 2 7.20411197e+00 -5.54403403e+00 4.90253038e+00 | 7.20411197e+00 -5.54403403e+00 4.90253038e+00 3 -2.66068483e+00 6.39405581e+00 2.14322589e+00 | -2.66068483e+00 6.39405581e+00 2.14322589e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = FTT (Configuration in file "config-AlHNi-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)) = -4.62896769255 2^p V(r_1,...,r_N) = -4.62896769255 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 -3.60886182e+00 -5.27119362e+00 -1.70013890e+00 | -3.60886182e+00 -5.27119362e+00 -1.70013890e+00 1 5.08628682e+00 2.64548175e+00 -2.68509118e+00 | 5.08628682e+00 2.64548175e+00 -2.68509118e+00 2 1.00538416e+00 -9.78567766e-02 5.23008036e-01 | 1.00538416e+00 -9.78567766e-02 5.23008036e-01 3 -2.48280916e+00 2.72356865e+00 3.86222204e+00 | -2.48280916e+00 2.72356865e+00 3.86222204e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = FTF (Configuration in file "config-AlHNi-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)) = -5.80279363381 2^p V(r_1,...,r_N) = -5.80279363381 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 -1.73105788e+00 -1.02687488e+00 -1.36261597e+00 | -1.73105788e+00 -1.02687488e+00 -1.36261597e+00 1 8.54076904e-01 1.68840377e+00 -1.16789503e+00 | 8.54076904e-01 1.68840377e+00 -1.16789503e+00 2 8.02594008e-01 -7.42031175e-01 2.07190901e+00 | 8.02594008e-01 -7.42031175e-01 2.07190901e+00 3 7.43869643e-02 8.05022850e-02 4.58601991e-01 | 7.43869643e-02 8.05022850e-02 4.58601991e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al H Ni, PBC = FFT (Configuration in file "config-AlHNi-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)) = -3.85024536441 2^p V(r_1,...,r_N) = -3.85024536441 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 -1.29286176e+00 -5.66387326e+00 -7.64447330e+00 | -1.29286176e+00 -5.66387326e+00 -7.64447330e+00 1 1.14584190e-02 6.96212162e-01 -2.64038077e-01 | 1.14584190e-02 6.96212162e-01 -2.64038077e-01 2 4.89934108e+00 -2.97587898e+00 1.92317291e+00 | 4.89934108e+00 -2.97587898e+00 1.92317291e+00 3 -3.61793774e+00 7.94354008e+00 5.98533847e+00 | -3.61793774e+00 7.94354008e+00 5.98533847e+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.