!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MendelevFangYe_2015_AlSm__MO_338600200739_000 Supported species : Al Sm 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)) = -4.31824862531 2^p V(r_1,...,r_N) = -4.31824862531 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 -4.66100680e+00 -7.93921367e+00 -8.64171564e+00 | -4.66100680e+00 -7.93921367e+00 -8.64171564e+00 1 3.42695756e+00 2.38403004e+00 -2.20074482e+00 | 3.42695756e+00 2.38403004e+00 -2.20074482e+00 2 3.95287797e+00 -3.17593706e+00 4.45147944e+00 | 3.95287797e+00 -3.17593706e+00 4.45147944e+00 3 -2.71882873e+00 8.73112070e+00 6.39098102e+00 | -2.71882873e+00 8.73112070e+00 6.39098102e+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)) = -2.54555819838 2^p V(r_1,...,r_N) = -2.54555819838 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 -6.70821960e+00 -4.66943271e+00 -4.34267320e+00 | -6.70821960e+00 -4.66943271e+00 -4.34267320e+00 1 4.93544540e+00 3.94613939e+00 -6.14306992e+00 | 4.93544540e+00 3.94613939e+00 -6.14306992e+00 2 8.70011294e+00 -9.46462646e+00 7.59647196e+00 | 8.70011294e+00 -9.46462646e+00 7.59647196e+00 3 -6.92733874e+00 1.01879198e+01 2.88927117e+00 | -6.92733874e+00 1.01879198e+01 2.88927117e+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)) = -0.364102933378 2^p V(r_1,...,r_N) = -0.364102933378 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 -6.85488460e+00 -9.28947343e+00 -1.17084475e+01 | -6.85488460e+00 -9.28947343e+00 -1.17084475e+01 1 9.22736127e+00 9.28673388e+00 -5.34866720e+00 | 9.22736127e+00 9.28673388e+00 -5.34866720e+00 2 5.79716470e+00 -7.84666610e+00 8.40052330e+00 | 5.79716470e+00 -7.84666610e+00 8.40052330e+00 3 -8.16964136e+00 7.84940565e+00 8.65659141e+00 | -8.16964136e+00 7.84940565e+00 8.65659141e+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)) = 7.52026031386 2^p V(r_1,...,r_N) = 7.52026031386 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 -1.65640396e+01 -1.38017205e+01 -2.66186720e+01 | -1.65640396e+01 -1.38017205e+01 -2.66186720e+01 1 7.99118400e+00 9.76416081e+00 -6.45178800e+00 | 7.99118400e+00 9.76416081e+00 -6.45178800e+00 2 2.02223921e+01 -1.10528179e+01 2.05543303e+01 | 2.02223921e+01 -1.10528179e+01 2.05543303e+01 3 -1.16495365e+01 1.50903776e+01 1.25161296e+01 | -1.16495365e+01 1.50903776e+01 1.25161296e+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)) = -0.688276140699 2^p V(r_1,...,r_N) = -0.688276140699 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 -9.51990448e+00 -6.73210824e+00 -9.19638443e+00 | -9.51990448e+00 -6.73210824e+00 -9.19638443e+00 1 6.37306921e+00 8.36821929e+00 -7.10043378e+00 | 6.37306921e+00 8.36821929e+00 -7.10043378e+00 2 9.09135386e+00 -9.57767571e+00 8.46205657e+00 | 9.09135386e+00 -9.57767571e+00 8.46205657e+00 3 -5.94451859e+00 7.94156466e+00 7.83476164e+00 | -5.94451859e+00 7.94156466e+00 7.83476164e+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)) = -4.29668177972 2^p V(r_1,...,r_N) = -4.29668177972 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 -7.41367938e+00 -6.18370586e+00 -4.44468886e+00 | -7.41367938e+00 -6.18370586e+00 -4.44468886e+00 1 4.53878615e+00 6.11039702e+00 -5.06909000e+00 | 4.53878615e+00 6.11039702e+00 -5.06909000e+00 2 5.35856860e+00 -2.91838670e+00 7.59293694e+00 | 5.35856860e+00 -2.91838670e+00 7.59293694e+00 3 -2.48367537e+00 2.99169555e+00 1.92084191e+00 | -2.48367537e+00 2.99169555e+00 1.92084191e+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)) = 5.7875693788 2^p V(r_1,...,r_N) = 5.7875693788 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 -7.84443276e+00 -7.13380104e+00 -9.55708769e+00 | -7.84443276e+00 -7.13380104e+00 -9.55708769e+00 1 1.01498951e+01 9.99612504e+00 -8.35127672e+00 | 1.01498951e+01 9.99612504e+00 -8.35127672e+00 2 2.01509158e+01 -2.27643298e+01 1.13619758e+01 | 2.01509158e+01 -2.27643298e+01 1.13619758e+01 3 -2.24563782e+01 1.99020058e+01 6.54638859e+00 | -2.24563782e+01 1.99020058e+01 6.54638859e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = TTT (Configuration in file "config-Sm-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)) = 42.5157153799 2^p V(r_1,...,r_N) = 42.5157153799 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 -3.67192985e+01 -2.38384771e+01 -4.23235387e+01 | -3.67192985e+01 -2.38384771e+01 -4.23235387e+01 1 2.34323762e+01 3.09410315e+01 -2.51607356e+01 | 2.34323762e+01 3.09410315e+01 -2.51607356e+01 2 4.58395064e+01 -3.76500759e+01 4.17044531e+01 | 4.58395064e+01 -3.76500759e+01 4.17044531e+01 3 -3.25525841e+01 3.05475215e+01 2.57798212e+01 | -3.25525841e+01 3.05475215e+01 2.57798212e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = TTF (Configuration in file "config-Sm-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)) = 46.1562935366 2^p V(r_1,...,r_N) = 46.1562935366 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 -3.16102523e+01 -2.64443595e+01 -2.95907203e+01 | -3.16102523e+01 -2.64443595e+01 -2.95907203e+01 1 2.66926782e+01 3.47229510e+01 -3.06327508e+01 | 2.66926782e+01 3.47229510e+01 -3.06327508e+01 2 5.34474993e+01 -4.86921047e+01 3.60653966e+01 | 5.34474993e+01 -4.86921047e+01 3.60653966e+01 3 -4.85299251e+01 4.04135132e+01 2.41580746e+01 | -4.85299251e+01 4.04135132e+01 2.41580746e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = TFT (Configuration in file "config-Sm-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)) = 27.2153014362 2^p V(r_1,...,r_N) = 27.2153014362 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 -1.62231369e+01 -1.63460676e+01 -1.44430964e+01 | -1.62231369e+01 -1.63460676e+01 -1.44430964e+01 1 2.00023292e+01 2.04472036e+01 -3.61507755e+01 | 2.00023292e+01 2.04472036e+01 -3.61507755e+01 2 1.89858096e+01 -3.02161281e+01 3.64851786e+01 | 1.89858096e+01 -3.02161281e+01 3.64851786e+01 3 -2.27650019e+01 2.61149922e+01 1.41086933e+01 | -2.27650019e+01 2.61149922e+01 1.41086933e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = TFF (Configuration in file "config-Sm-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)) = 29.6551125662 2^p V(r_1,...,r_N) = 29.6551125662 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 -1.95027694e+01 -4.05594766e+01 -3.41225870e+01 | -1.95027694e+01 -4.05594766e+01 -3.41225870e+01 1 1.92030232e+01 1.81946061e+01 -2.20771608e+01 | 1.92030232e+01 1.81946061e+01 -2.20771608e+01 2 1.46995309e+01 -1.94124400e+01 1.77815214e+01 | 1.46995309e+01 -1.94124400e+01 1.77815214e+01 3 -1.43997848e+01 4.17773105e+01 3.84182264e+01 | -1.43997848e+01 4.17773105e+01 3.84182264e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = FTT (Configuration in file "config-Sm-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)) = 14.7152963324 2^p V(r_1,...,r_N) = 14.7152963324 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 -1.47033203e+01 -1.43583422e+01 -1.27537071e+01 | -1.47033203e+01 -1.43583422e+01 -1.27537071e+01 1 2.22034197e+01 1.80515186e+01 -1.67152751e+01 | 2.22034197e+01 1.80515186e+01 -1.67152751e+01 2 8.52191878e+00 -1.51655467e+01 1.39734742e+01 | 8.52191878e+00 -1.51655467e+01 1.39734742e+01 3 -1.60220182e+01 1.14723703e+01 1.54955080e+01 | -1.60220182e+01 1.14723703e+01 1.54955080e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = FTF (Configuration in file "config-Sm-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)) = 23.5839883127 2^p V(r_1,...,r_N) = 23.5839883127 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 -1.47385368e+01 -3.08246383e+01 -2.82728435e+01 | -1.47385368e+01 -3.08246383e+01 -2.82728435e+01 1 1.64974371e+01 1.67940345e+01 -1.77210662e+01 | 1.64974371e+01 1.67940345e+01 -1.77210662e+01 2 1.84434181e+01 -1.20619790e+01 1.10120145e+01 | 1.84434181e+01 -1.20619790e+01 1.10120145e+01 3 -2.02023184e+01 2.60925828e+01 3.49818951e+01 | -2.02023184e+01 2.60925828e+01 3.49818951e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Sm, PBC = FFT (Configuration in file "config-Sm-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)) = 62.6960129724 2^p V(r_1,...,r_N) = 62.6960129724 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 -4.53840372e+01 -3.56891038e+01 -4.22236867e+01 | -4.53840372e+01 -3.56891038e+01 -4.22236867e+01 1 3.78246403e+01 2.74671378e+01 -4.64826015e+01 | 3.78246403e+01 2.74671378e+01 -4.64826015e+01 2 5.44771562e+01 -6.52240187e+01 6.29452546e+01 | 5.44771562e+01 -6.52240187e+01 6.29452546e+01 3 -4.69177593e+01 7.34459846e+01 2.57610336e+01 | -4.69177593e+01 7.34459846e+01 2.57610336e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = TTT (Configuration in file "config-AlSm-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)) = 23.4703384711 2^p V(r_1,...,r_N) = 23.4703384711 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 -9.95245160e+00 -7.18966996e+00 -6.70453074e+00 | -9.95245160e+00 -7.18966996e+00 -6.70453074e+00 1 1.60654115e+01 3.44012660e+01 -4.70190284e+01 | 1.60654115e+01 3.44012660e+01 -4.70190284e+01 2 1.67152393e+01 -4.30468355e+01 4.33795753e+01 | 1.67152393e+01 -4.30468355e+01 4.33795753e+01 3 -2.28281992e+01 1.58352394e+01 1.03439838e+01 | -2.28281992e+01 1.58352394e+01 1.03439838e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = TTF (Configuration in file "config-AlSm-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)) = 14.4729895035 2^p V(r_1,...,r_N) = 14.4729895035 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 -1.68225815e+01 -2.48218136e+01 -2.29812716e+01 | -1.68225815e+01 -2.48218136e+01 -2.29812716e+01 1 1.51465501e+01 1.06783773e+01 -8.83639211e+00 | 1.51465501e+01 1.06783773e+01 -8.83639211e+00 2 1.36704430e+01 -1.21102771e+01 1.21084203e+01 | 1.36704430e+01 -1.21102771e+01 1.21084203e+01 3 -1.19944117e+01 2.62537133e+01 1.97092435e+01 | -1.19944117e+01 2.62537133e+01 1.97092435e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = TFT (Configuration in file "config-AlSm-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 13.9212769268 2^p V(r_1,...,r_N) = 13.9212769268 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 -1.36639505e+01 -2.16067480e+01 -2.69722066e+01 | -1.36639505e+01 -2.16067480e+01 -2.69722066e+01 1 1.24628295e+01 7.29338696e+00 -6.77434617e+00 | 1.24628295e+01 7.29338696e+00 -6.77434617e+00 2 1.44951559e+01 -1.26646566e+01 1.04998896e+01 | 1.44951559e+01 -1.26646566e+01 1.04998896e+01 3 -1.32940349e+01 2.69780177e+01 2.32466632e+01 | -1.32940349e+01 2.69780177e+01 2.32466632e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = TFF (Configuration in file "config-AlSm-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)) = -0.15636263758 2^p V(r_1,...,r_N) = -0.15636263758 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 -6.67883334e+00 -9.43879263e+00 -1.21191623e+01 | -6.67883334e+00 -9.43879263e+00 -1.21191623e+01 1 6.16488876e+00 5.89730218e+00 -3.91178196e+00 | 6.16488876e+00 5.89730218e+00 -3.91178196e+00 2 6.87152193e+00 -5.17517383e+00 3.93788564e+00 | 6.87152193e+00 -5.17517383e+00 3.93788564e+00 3 -6.35757735e+00 8.71666428e+00 1.20930586e+01 | -6.35757735e+00 8.71666428e+00 1.20930586e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = FTT (Configuration in file "config-AlSm-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.09141922378 2^p V(r_1,...,r_N) = -2.09141922378 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 -7.10142832e+00 -7.27924908e+00 -7.12027163e+00 | -7.10142832e+00 -7.27924908e+00 -7.12027163e+00 1 7.07431733e+00 3.93033412e+00 -2.96770862e+00 | 7.07431733e+00 3.93033412e+00 -2.96770862e+00 2 5.79973618e+00 -5.44275237e+00 2.72789550e+00 | 5.79973618e+00 -5.44275237e+00 2.72789550e+00 3 -5.77262519e+00 8.79166733e+00 7.36008474e+00 | -5.77262519e+00 8.79166733e+00 7.36008474e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = FTF (Configuration in file "config-AlSm-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)) = 5.38625916646 2^p V(r_1,...,r_N) = 5.38625916646 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 -6.97816174e+00 -1.19825006e+01 -1.12205541e+01 | -6.97816174e+00 -1.19825006e+01 -1.12205541e+01 1 9.33185516e+00 8.23426737e+00 -1.13302553e+01 | 9.33185516e+00 8.23426737e+00 -1.13302553e+01 2 1.26035457e+01 -8.09308186e+00 1.17664264e+01 | 1.26035457e+01 -8.09308186e+00 1.17664264e+01 3 -1.49572391e+01 1.18413151e+01 1.07843830e+01 | -1.49572391e+01 1.18413151e+01 1.07843830e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Sm, PBC = FFT (Configuration in file "config-AlSm-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.58565864409 2^p V(r_1,...,r_N) = 7.58565864409 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 -9.09468403e+00 -7.41357575e+00 -7.60563859e+00 | -9.09468403e+00 -7.41357575e+00 -7.60563859e+00 1 6.03873244e+00 1.17571130e+01 -1.70406409e+01 | 6.03873244e+00 1.17571130e+01 -1.70406409e+01 2 1.66230335e+01 -1.53611125e+01 1.02063576e+01 | 1.66230335e+01 -1.53611125e+01 1.02063576e+01 3 -1.35670819e+01 1.10175752e+01 1.44399219e+01 | -1.35670819e+01 1.10175752e+01 1.44399219e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.