!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LiuOhotnickyAdams_1997_AlMg__MO_559870613549_000 Supported species : Al Mg 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)) = 0.0556827748411 2^p V(r_1,...,r_N) = 0.0556827748411 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 -6.81850694e+00 -6.97599039e+00 -8.47984895e+00 | -6.81850694e+00 -6.97599039e+00 -8.47984895e+00 1 4.81198597e+00 3.35418572e+00 -3.02827435e+00 | 4.81198597e+00 3.35418572e+00 -3.02827435e+00 2 5.54667968e+00 -4.42212702e+00 6.20434674e+00 | 5.54667968e+00 -4.42212702e+00 6.20434674e+00 3 -3.54015871e+00 8.04393169e+00 5.30377656e+00 | -3.54015871e+00 8.04393169e+00 5.30377656e+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)) = 2.3999543145 2^p V(r_1,...,r_N) = 2.3999543145 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 -9.26587155e+00 -6.48225912e+00 -5.88608956e+00 | -9.26587155e+00 -6.48225912e+00 -5.88608956e+00 1 6.86287679e+00 5.50243744e+00 -8.42356226e+00 | 6.86287679e+00 5.50243744e+00 -8.42356226e+00 2 8.13035573e+00 -7.98282664e+00 1.02359108e+01 | 8.13035573e+00 -7.98282664e+00 1.02359108e+01 3 -5.72736096e+00 8.96264832e+00 4.07374102e+00 | -5.72736096e+00 8.96264832e+00 4.07374102e+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)) = 5.58304000046 2^p V(r_1,...,r_N) = 5.58304000046 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 -8.75814005e+00 -8.89859387e+00 -1.23128219e+01 | -8.75814005e+00 -8.89859387e+00 -1.23128219e+01 1 1.13298999e+01 1.09462754e+01 -6.94902560e+00 | 1.13298999e+01 1.09462754e+01 -6.94902560e+00 2 7.85854687e+00 -1.00314769e+01 1.07059759e+01 | 7.85854687e+00 -1.00314769e+01 1.07059759e+01 3 -1.04303067e+01 7.98379537e+00 8.55587158e+00 | -1.04303067e+01 7.98379537e+00 8.55587158e+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)) = 10.8356272455 2^p V(r_1,...,r_N) = 10.8356272455 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 -8.64610413e+00 -9.61723893e+00 -1.00670054e+01 | -8.64610413e+00 -9.61723893e+00 -1.00670054e+01 1 9.15061594e+00 1.07055102e+01 -7.41391067e+00 | 9.15061594e+00 1.07055102e+01 -7.41391067e+00 2 9.41149186e+00 -1.03606066e+01 1.01194049e+01 | 9.41149186e+00 -1.03606066e+01 1.01194049e+01 3 -9.91600367e+00 9.27233538e+00 7.36151125e+00 | -9.91600367e+00 9.27233538e+00 7.36151125e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 5.28341418918 2^p V(r_1,...,r_N) = 5.28341418918 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 -1.11484827e+01 -8.53014625e+00 -1.02281771e+01 | -1.11484827e+01 -8.53014625e+00 -1.02281771e+01 1 8.54197087e+00 9.82047127e+00 -8.32449844e+00 | 8.54197087e+00 9.82047127e+00 -8.32449844e+00 2 1.05157430e+01 -1.11137726e+01 8.75945947e+00 | 1.05157430e+01 -1.11137726e+01 8.75945947e+00 3 -7.90923122e+00 9.82344762e+00 9.79321607e+00 | -7.90923122e+00 9.82344762e+00 9.79321607e+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)) = 0.493893426385 2^p V(r_1,...,r_N) = 0.493893426385 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 -9.56633385e+00 -8.15283036e+00 -6.25563570e+00 | -9.56633385e+00 -8.15283036e+00 -6.25563570e+00 1 5.75614000e+00 7.97903532e+00 -6.91091396e+00 | 5.75614000e+00 7.97903532e+00 -6.91091396e+00 2 7.40155133e+00 -4.12961865e+00 1.03814385e+01 | 7.40155133e+00 -4.12961865e+00 1.03814385e+01 3 -3.59135748e+00 4.30341369e+00 2.78511117e+00 | -3.59135748e+00 4.30341369e+00 2.78511117e+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)) = 8.89647524192 2^p V(r_1,...,r_N) = 8.89647524192 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 -8.99052642e+00 -8.37353853e+00 -1.23124067e+01 | -8.99052642e+00 -8.37353853e+00 -1.23124067e+01 1 1.11659594e+01 9.42084056e+00 -7.98555830e+00 | 1.11659594e+01 9.42084056e+00 -7.98555830e+00 2 7.43518086e+00 -9.07788869e+00 1.16563936e+01 | 7.43518086e+00 -9.07788869e+00 1.16563936e+01 3 -9.61061382e+00 8.03058666e+00 8.64157133e+00 | -9.61061382e+00 8.03058666e+00 8.64157133e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTT (Configuration in file "config-Mg-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)) = 9.15882120991 2^p V(r_1,...,r_N) = 9.15882120991 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 -5.78822784e+00 -5.35706231e+00 -6.60219482e+00 | -5.78822784e+00 -5.35706231e+00 -6.60219482e+00 1 5.13963015e+00 5.78861421e+00 -4.28287296e+00 | 5.13963015e+00 5.78861421e+00 -4.28287296e+00 2 5.60876254e+00 -5.41234128e+00 5.61748570e+00 | 5.60876254e+00 -5.41234128e+00 5.61748570e+00 3 -4.96016485e+00 4.98078938e+00 5.26758208e+00 | -4.96016485e+00 4.98078938e+00 5.26758208e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTF (Configuration in file "config-Mg-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)) = 9.26645339163 2^p V(r_1,...,r_N) = 9.26645339163 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 -5.46986774e+00 -5.22484088e+00 -5.82195105e+00 | -5.46986774e+00 -5.22484088e+00 -5.82195105e+00 1 5.00477518e+00 5.53668228e+00 -4.96335119e+00 | 5.00477518e+00 5.53668228e+00 -4.96335119e+00 2 5.36001118e+00 -4.64401592e+00 6.23138246e+00 | 5.36001118e+00 -4.64401592e+00 6.23138246e+00 3 -4.89491862e+00 4.33217452e+00 4.55391978e+00 | -4.89491862e+00 4.33217452e+00 4.55391978e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFT (Configuration in file "config-Mg-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)) = 5.95906612359 2^p V(r_1,...,r_N) = 5.95906612359 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 -4.23045756e+00 -4.26307751e+00 -3.73764639e+00 | -4.23045756e+00 -4.26307751e+00 -3.73764639e+00 1 4.72395273e+00 3.04679741e+00 -5.40137163e+00 | 4.72395273e+00 3.04679741e+00 -5.40137163e+00 2 4.31885665e+00 -4.60748120e+00 5.37875965e+00 | 4.31885665e+00 -4.60748120e+00 5.37875965e+00 3 -4.81235182e+00 5.82376130e+00 3.76025837e+00 | -4.81235182e+00 5.82376130e+00 3.76025837e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFF (Configuration in file "config-Mg-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.03856695275 2^p V(r_1,...,r_N) = 6.03856695275 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 -4.14168595e+00 -4.42761802e+00 -3.74854636e+00 | -4.14168595e+00 -4.42761802e+00 -3.74854636e+00 1 4.86439061e+00 4.42496247e+00 -5.37338992e+00 | 4.86439061e+00 4.42496247e+00 -5.37338992e+00 2 3.78560294e+00 -4.75766221e+00 4.32836602e+00 | 3.78560294e+00 -4.75766221e+00 4.32836602e+00 3 -4.50830761e+00 4.76031776e+00 4.79357027e+00 | -4.50830761e+00 4.76031776e+00 4.79357027e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTT (Configuration in file "config-Mg-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)) = 3.30548390508 2^p V(r_1,...,r_N) = 3.30548390508 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 -3.61845590e+00 -3.73165710e+00 -3.15273800e+00 | -3.61845590e+00 -3.73165710e+00 -3.15273800e+00 1 5.66490984e+00 4.65744664e+00 -4.30476246e+00 | 5.66490984e+00 4.65744664e+00 -4.30476246e+00 2 1.99698269e+00 -3.85597709e+00 3.45082184e+00 | 1.99698269e+00 -3.85597709e+00 3.45082184e+00 3 -4.04343663e+00 2.93018754e+00 4.00667861e+00 | -4.04343663e+00 2.93018754e+00 4.00667861e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTF (Configuration in file "config-Mg-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)) = 5.16137402145 2^p V(r_1,...,r_N) = 5.16137402145 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 -3.82062608e+00 -5.06447290e+00 -4.47677754e+00 | -3.82062608e+00 -5.06447290e+00 -4.47677754e+00 1 4.09363802e+00 4.20073289e+00 -4.25739188e+00 | 4.09363802e+00 4.20073289e+00 -4.25739188e+00 2 4.85557294e+00 -3.06501275e+00 2.81209889e+00 | 4.85557294e+00 -3.06501275e+00 2.81209889e+00 3 -5.12858489e+00 3.92875276e+00 5.92207054e+00 | -5.12858489e+00 3.92875276e+00 5.92207054e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FFT (Configuration in file "config-Mg-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)) = 12.0424123992 2^p V(r_1,...,r_N) = 12.0424123992 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 -6.49200643e+00 -5.74668745e+00 -5.02802945e+00 | -6.49200643e+00 -5.74668745e+00 -5.02802945e+00 1 7.04671452e+00 3.53373671e+00 -6.35204702e+00 | 7.04671452e+00 3.53373671e+00 -6.35204702e+00 2 4.84761503e+00 -5.60600639e+00 6.56572376e+00 | 4.84761503e+00 -5.60600639e+00 6.56572376e+00 3 -5.40232313e+00 7.81895713e+00 4.81435271e+00 | -5.40232313e+00 7.81895713e+00 4.81435271e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TTT (Configuration in file "config-AlMg-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.39312307734 2^p V(r_1,...,r_N) = 6.39312307734 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 -5.32233490e+00 -5.13838807e+00 -4.86497554e+00 | -5.32233490e+00 -5.13838807e+00 -4.86497554e+00 1 6.75109348e+00 4.63703508e+00 -6.59125022e+00 | 6.75109348e+00 4.63703508e+00 -6.59125022e+00 2 5.69125217e+00 -5.60144868e+00 5.28328269e+00 | 5.69125217e+00 -5.60144868e+00 5.28328269e+00 3 -7.12001074e+00 6.10280167e+00 6.17294307e+00 | -7.12001074e+00 6.10280167e+00 6.17294307e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TTF (Configuration in file "config-AlMg-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.47035145902 2^p V(r_1,...,r_N) = 6.47035145902 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 -7.09478270e+00 -5.17219071e+00 -5.27483009e+00 | -7.09478270e+00 -5.17219071e+00 -5.27483009e+00 1 7.97593831e+00 8.10218790e+00 -6.00500190e+00 | 7.97593831e+00 8.10218790e+00 -6.00500190e+00 2 4.55613540e+00 -8.09012505e+00 6.48859431e+00 | 4.55613540e+00 -8.09012505e+00 6.48859431e+00 3 -5.43729102e+00 5.16012786e+00 4.79123769e+00 | -5.43729102e+00 5.16012786e+00 4.79123769e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TFT (Configuration in file "config-AlMg-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)) = 5.06787285318 2^p V(r_1,...,r_N) = 5.06787285318 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 -7.08077782e+00 -5.27936466e+00 -7.02799915e+00 | -7.08077782e+00 -5.27936466e+00 -7.02799915e+00 1 6.97898155e+00 5.38920665e+00 -5.14660800e+00 | 6.97898155e+00 5.38920665e+00 -5.14660800e+00 2 5.99866180e+00 -6.75400773e+00 6.92993126e+00 | 5.99866180e+00 -6.75400773e+00 6.92993126e+00 3 -5.89686552e+00 6.64416574e+00 5.24467589e+00 | -5.89686552e+00 6.64416574e+00 5.24467589e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TFF (Configuration in file "config-AlMg-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)) = -0.350817619567 2^p V(r_1,...,r_N) = -0.350817619567 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 -3.09074816e+00 -3.30981976e+00 -3.59877042e+00 | -3.09074816e+00 -3.30981976e+00 -3.59877042e+00 1 2.64959970e+00 4.94100395e+00 -3.67670083e+00 | 2.64959970e+00 4.94100395e+00 -3.67670083e+00 2 3.17831929e+00 -4.55553101e+00 3.75031629e+00 | 3.17831929e+00 -4.55553101e+00 3.75031629e+00 3 -2.73717083e+00 2.92434682e+00 3.52515496e+00 | -2.73717083e+00 2.92434682e+00 3.52515496e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FTT (Configuration in file "config-AlMg-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)) = -1.23956113937 2^p V(r_1,...,r_N) = -1.23956113937 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 -3.29221387e+00 -2.79153367e+00 -1.95516220e+00 | -3.29221387e+00 -2.79153367e+00 -1.95516220e+00 1 3.45350571e+00 2.66724791e+00 -1.97310795e+00 | 3.45350571e+00 2.66724791e+00 -1.97310795e+00 2 2.70509610e+00 -3.41538045e+00 1.85801860e+00 | 2.70509610e+00 -3.41538045e+00 1.85801860e+00 3 -2.86638794e+00 3.53966621e+00 2.07025156e+00 | -2.86638794e+00 3.53966621e+00 2.07025156e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FTF (Configuration in file "config-AlMg-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)) = 3.82609345497 2^p V(r_1,...,r_N) = 3.82609345497 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 -4.68336467e+00 -6.43931554e+00 -7.51183318e+00 | -4.68336467e+00 -6.43931554e+00 -7.51183318e+00 1 3.18861292e+00 3.64442835e+00 -3.46625970e+00 | 3.18861292e+00 3.64442835e+00 -3.46625970e+00 2 7.27882518e+00 -3.16152055e+00 7.38365681e+00 | 7.27882518e+00 -3.16152055e+00 7.38365681e+00 3 -5.78407343e+00 5.95640774e+00 3.59443607e+00 | -5.78407343e+00 5.95640774e+00 3.59443607e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FFT (Configuration in file "config-AlMg-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)) = 4.17356503828 2^p V(r_1,...,r_N) = 4.17356503828 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 -7.15409040e+00 -7.20841964e+00 -3.96474548e+00 | -7.15409040e+00 -7.20841964e+00 -3.96474548e+00 1 5.05464542e+00 9.48444747e+00 -7.26315016e+00 | 5.05464542e+00 9.48444747e+00 -7.26315016e+00 2 6.66464215e+00 -5.44877780e+00 5.61837568e+00 | 6.66464215e+00 -5.44877780e+00 5.61837568e+00 3 -4.56519717e+00 3.17274997e+00 5.60951995e+00 | -4.56519717e+00 3.17274997e+00 5.60951995e+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.