!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_SchopfBrommerFrigan_2012_AlMnPd__MO_137572817842_000 Supported species : Al Mn Pd 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)) = -3.8933284738 2^p V(r_1,...,r_N) = -3.8933284738 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 -7.06201792e+00 -3.83715769e+00 -6.26877271e+00 | -7.06201792e+00 -3.83715769e+00 -6.26877271e+00 1 4.37058412e+00 3.03356239e+00 -2.61289296e+00 | 4.37058412e+00 3.03356239e+00 -2.61289296e+00 2 5.67812363e+00 -4.03163735e+00 6.21899356e+00 | 5.67812363e+00 -4.03163735e+00 6.21899356e+00 3 -2.98668983e+00 4.83523265e+00 2.66267211e+00 | -2.98668983e+00 4.83523265e+00 2.66267211e+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)) = -1.75994518824 2^p V(r_1,...,r_N) = -1.75994518824 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 -1.02408990e+01 -6.63653404e+00 -6.51361145e+00 | -1.02408990e+01 -6.63653404e+00 -6.51361145e+00 1 7.03505757e+00 6.10510737e+00 -8.91895042e+00 | 7.03505757e+00 6.10510737e+00 -8.91895042e+00 2 1.29787857e-01 3.32702516e+00 1.13960854e+01 | 1.29787857e-01 3.32702516e+00 1.13960854e+01 3 3.07605359e+00 -2.79559848e+00 4.03647642e+00 | 3.07605359e+00 -2.79559848e+00 4.03647642e+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)) = 0.649601167562 2^p V(r_1,...,r_N) = 0.649601167562 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 -1.31282768e+01 -1.24345624e+01 -8.43941314e+00 | -1.31282768e+01 -1.24345624e+01 -8.43941314e+00 1 1.47351345e+01 1.42266963e+01 -1.62160117e+01 | 1.47351345e+01 1.42266963e+01 -1.62160117e+01 2 -4.19302234e+01 6.15761678e+01 1.69577940e+01 | -4.19302234e+01 6.15761678e+01 1.69577940e+01 3 4.03233656e+01 -6.33683017e+01 7.69763079e+00 | 4.03233656e+01 -6.33683017e+01 7.69763079e+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)) = -3.30522745112 2^p V(r_1,...,r_N) = -3.30522745112 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 -1.03306005e+01 -1.26405049e+01 -7.63669819e+00 | -1.03306005e+01 -1.26405049e+01 -7.63669819e+00 1 1.08286789e+01 1.28539188e+01 -7.19986756e+00 | 1.08286789e+01 1.28539188e+01 -7.19986756e+00 2 6.85773304e+00 -5.60428269e+00 8.25194400e+00 | 6.85773304e+00 -5.60428269e+00 8.25194400e+00 3 -7.35581154e+00 5.39086878e+00 6.58462176e+00 | -7.35581154e+00 5.39086878e+00 6.58462176e+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)) = -5.07679167252 2^p V(r_1,...,r_N) = -5.07679167252 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 -2.31868449e+00 -3.93857062e+00 -3.32661176e+00 | -2.31868449e+00 -3.93857062e+00 -3.32661176e+00 1 5.88865546e+00 7.78338477e+00 -8.85741155e+00 | 5.88865546e+00 7.78338477e+00 -8.85741155e+00 2 7.78207245e+00 -8.86134510e+00 5.97264512e+00 | 7.78207245e+00 -8.86134510e+00 5.97264512e+00 3 -1.13520434e+01 5.01653095e+00 6.21137819e+00 | -1.13520434e+01 5.01653095e+00 6.21137819e+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)) = -4.29541222353 2^p V(r_1,...,r_N) = -4.29541222353 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 -3.71165995e+00 -8.04258600e+00 -5.80158704e+00 | -3.71165995e+00 -8.04258600e+00 -5.80158704e+00 1 -9.45525477e+00 5.28948833e+00 8.72908382e+00 | -9.45525477e+00 5.28948833e+00 8.72908382e+00 2 1.39263949e+00 -1.96912776e+00 2.14999911e+00 | 1.39263949e+00 -1.96912776e+00 2.14999911e+00 3 1.17742752e+01 4.72222544e+00 -5.07749589e+00 | 1.17742752e+01 4.72222544e+00 -5.07749589e+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)) = -5.11426854726 2^p V(r_1,...,r_N) = -5.11426854726 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 -9.46117314e+00 -6.91472829e+00 -9.25568340e+00 | -9.46117314e+00 -6.91472829e+00 -9.25568340e+00 1 5.12034262e+00 5.59298145e+00 -5.28079724e+00 | 5.12034262e+00 5.59298145e+00 -5.28079724e+00 2 8.78552733e+00 -3.19256900e+00 9.63549975e+00 | 8.78552733e+00 -3.19256900e+00 9.63549975e+00 3 -4.44469681e+00 4.51431584e+00 4.90098088e+00 | -4.44469681e+00 4.51431584e+00 4.90098088e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TTT (Configuration in file "config-Mn-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -12.9932666836 2^p V(r_1,...,r_N) = -12.9932666836 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 6.28375671e+00 7.03146133e+00 4.57740009e+00 | 6.28375671e+00 7.03146133e+00 4.57740009e+00 1 -6.26046521e+00 -5.71085051e+00 6.89681111e+00 | -6.26046521e+00 -5.71085051e+00 6.89681111e+00 2 -6.11496131e+00 5.60625484e+00 -6.18397985e+00 | -6.11496131e+00 5.60625484e+00 -6.18397985e+00 3 6.09166981e+00 -6.92686565e+00 -5.29023135e+00 | 6.09166981e+00 -6.92686565e+00 -5.29023135e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TTF (Configuration in file "config-Mn-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)) = -14.0717685964 2^p V(r_1,...,r_N) = -14.0717685964 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 6.98792096e+00 6.20600442e+00 5.07888235e+00 | 6.98792096e+00 6.20600442e+00 5.07888235e+00 1 -4.94575706e+00 -5.79524183e+00 6.66347570e+00 | -4.94575706e+00 -5.79524183e+00 6.66347570e+00 2 -6.63529455e+00 5.76470679e+00 -5.45061167e+00 | -6.63529455e+00 5.76470679e+00 -5.45061167e+00 3 4.59313065e+00 -6.17546938e+00 -6.29174639e+00 | 4.59313065e+00 -6.17546938e+00 -6.29174639e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TFT (Configuration in file "config-Mn-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)) = -19.022226866 2^p V(r_1,...,r_N) = -19.022226866 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 3.29757839e+00 2.03593734e+00 4.37484261e+00 | 3.29757839e+00 2.03593734e+00 4.37484261e+00 1 -3.76694663e+00 -3.46652281e+00 5.80147277e+00 | -3.76694663e+00 -3.46652281e+00 5.80147277e+00 2 -4.62163194e+00 4.33095273e+00 -4.00439192e+00 | -4.62163194e+00 4.33095273e+00 -4.00439192e+00 3 5.09100018e+00 -2.90036725e+00 -6.17192346e+00 | 5.09100018e+00 -2.90036725e+00 -6.17192346e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = TFF (Configuration in file "config-Mn-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)) = -15.3431380753 2^p V(r_1,...,r_N) = -15.3431380753 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 6.17094876e+00 5.93380937e+00 5.89929822e+00 | 6.17094876e+00 5.93380937e+00 5.89929822e+00 1 -5.35670269e+00 -6.18223402e+00 6.24391604e+00 | -5.35670269e+00 -6.18223402e+00 6.24391604e+00 2 -5.90692777e+00 5.62852354e+00 -5.52713983e+00 | -5.90692777e+00 5.62852354e+00 -5.52713983e+00 3 5.09268170e+00 -5.38009889e+00 -6.61607443e+00 | 5.09268170e+00 -5.38009889e+00 -6.61607443e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = FTT (Configuration in file "config-Mn-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)) = -25.4167292609 2^p V(r_1,...,r_N) = -25.4167292609 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 2.90856798e+01 4.71648641e+01 1.72031392e+01 | 2.90856798e+01 4.71648641e+01 1.72031392e+01 1 -4.56836246e+01 -2.42263412e+01 2.24078765e+01 | -4.56836246e+01 -2.42263412e+01 2.24078765e+01 2 -1.27402426e+01 1.62389880e+01 1.63266479e+00 | -1.27402426e+01 1.62389880e+01 1.63266479e+00 3 2.93381874e+01 -3.91775109e+01 -4.12436805e+01 | 2.93381874e+01 -3.91775109e+01 -4.12436805e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = FTF (Configuration in file "config-Mn-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)) = -18.1036890768 2^p V(r_1,...,r_N) = -18.1036890768 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 5.79075206e+00 5.70028829e+00 3.54204186e+00 | 5.79075206e+00 5.70028829e+00 3.54204186e+00 1 -4.26103406e+00 -3.85493715e+00 5.03321397e+00 | -4.26103406e+00 -3.85493715e+00 5.03321397e+00 2 -4.41656857e+00 2.75367445e+00 -2.73633877e+00 | -4.41656857e+00 2.75367445e+00 -2.73633877e+00 3 2.88685057e+00 -4.59902559e+00 -5.83891706e+00 | 2.88685057e+00 -4.59902559e+00 -5.83891706e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mn, PBC = FFT (Configuration in file "config-Mn-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)) = -17.2489598618 2^p V(r_1,...,r_N) = -17.2489598618 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 5.45340462e+00 3.73934363e+00 5.61681005e+00 | 5.45340462e+00 3.73934363e+00 5.61681005e+00 1 -4.56130787e+00 -5.11375112e+00 3.90078802e+00 | -4.56130787e+00 -5.11375112e+00 3.90078802e+00 2 -5.43493235e+00 6.37088371e+00 -4.12279816e+00 | -5.43493235e+00 6.37088371e+00 -4.12279816e+00 3 4.54283560e+00 -4.99647622e+00 -5.39479991e+00 | 4.54283560e+00 -4.99647622e+00 -5.39479991e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTT (Configuration in file "config-Pd-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)) = -89.6093845109 2^p V(r_1,...,r_N) = -89.6093845109 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 4.35186439e+02 3.00176509e+02 -6.06706366e+01 | 4.35186439e+02 3.00176509e+02 -6.06706366e+01 1 -4.48586899e+02 -2.98650961e+02 6.47006543e+01 | -4.48586899e+02 -2.98650961e+02 6.47006543e+01 2 1.45298845e-01 -3.01416481e-01 6.46949725e+00 | 1.45298845e-01 -3.01416481e-01 6.46949725e+00 3 1.32551604e+01 -1.22413165e+00 -1.04995149e+01 | 1.32551604e+01 -1.22413165e+00 -1.04995149e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTF (Configuration in file "config-Pd-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)) = -98.554677156 2^p V(r_1,...,r_N) = -98.554677156 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 3.24660981e+02 1.23649192e+02 2.33097103e+02 | 3.24660981e+02 1.23649192e+02 2.33097103e+02 1 -1.80368911e+02 -1.71549771e+02 -2.50393394e+01 | -1.80368911e+02 -1.71549771e+02 -2.50393394e+01 2 -3.04094808e+02 3.01404926e+02 -1.69044498e+02 | -3.04094808e+02 3.01404926e+02 -1.69044498e+02 3 1.59802739e+02 -2.53504347e+02 -3.90132656e+01 | 1.59802739e+02 -2.53504347e+02 -3.90132656e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFT (Configuration in file "config-Pd-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)) = -136.148532053 2^p V(r_1,...,r_N) = -136.148532053 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 2.48550840e+02 1.71752853e+02 2.74790675e+02 | 2.48550840e+02 1.71752853e+02 2.74790675e+02 1 -1.63292622e+02 -3.91626391e+02 3.38348626e+02 | -1.63292622e+02 -3.91626391e+02 3.38348626e+02 2 -2.51590142e+02 4.19191448e+02 -5.38338073e+02 | -2.51590142e+02 4.19191448e+02 -5.38338073e+02 3 1.66331923e+02 -1.99317911e+02 -7.48012280e+01 | 1.66331923e+02 -1.99317911e+02 -7.48012280e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFF (Configuration in file "config-Pd-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)) = -53.304663715 2^p V(r_1,...,r_N) = -53.304663715 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 2.12469102e+02 1.51161845e+02 2.08093452e+02 | 2.12469102e+02 1.51161845e+02 2.08093452e+02 1 -1.52119514e+02 -1.21574740e+02 1.15763338e+02 | -1.52119514e+02 -1.21574740e+02 1.15763338e+02 2 -1.44173488e+02 -3.25393049e+01 -2.30436796e+02 | -1.44173488e+02 -3.25393049e+01 -2.30436796e+02 3 8.38238998e+01 2.95219970e+00 -9.34199929e+01 | 8.38238998e+01 2.95219970e+00 -9.34199929e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTT (Configuration in file "config-Pd-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)) = -3.73978473026 2^p V(r_1,...,r_N) = -3.73978473026 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 -1.08204753e+01 -1.02416647e+01 -5.40514551e+00 | -1.08204753e+01 -1.02416647e+01 -5.40514551e+00 1 1.33137544e+01 -1.87798707e+01 3.05871709e+01 | 1.33137544e+01 -1.87798707e+01 3.05871709e+01 2 -2.00581842e+01 4.08599471e+01 -3.06775697e+01 | -2.00581842e+01 4.08599471e+01 -3.06775697e+01 3 1.75649051e+01 -1.18384117e+01 5.49554433e+00 | 1.75649051e+01 -1.18384117e+01 5.49554433e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTF (Configuration in file "config-Pd-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)) = -3.94508653763 2^p V(r_1,...,r_N) = -3.94508653763 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 -9.93612287e+00 -9.93122141e+00 -1.12337295e+01 | -9.93612287e+00 -9.93122141e+00 -1.12337295e+01 1 7.81121478e+00 6.61465430e+00 -6.07674992e+00 | 7.81121478e+00 6.61465430e+00 -6.07674992e+00 2 7.47555223e+00 -3.78778541e+00 8.63517813e+00 | 7.47555223e+00 -3.78778541e+00 8.63517813e+00 3 -5.35064414e+00 7.10435252e+00 8.67530127e+00 | -5.35064414e+00 7.10435252e+00 8.67530127e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FFT (Configuration in file "config-Pd-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)) = -555.922045899 2^p V(r_1,...,r_N) = -555.922045899 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 3.79427577e+02 2.01738034e+02 4.27463860e+02 | 3.79427577e+02 2.01738034e+02 4.27463860e+02 1 -4.41909757e+02 -3.87085958e+02 6.89562649e+02 | -4.41909757e+02 -3.87085958e+02 6.89562649e+02 2 -9.38230513e+02 1.25566919e+03 -6.06698024e+02 | -9.38230513e+02 1.25566919e+03 -6.06698024e+02 3 1.00071269e+03 -1.07032127e+03 -5.10328485e+02 | 1.00071269e+03 -1.07032127e+03 -5.10328485e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TTT (Configuration in file "config-AlMnPd-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)) = -10.4414952752 2^p V(r_1,...,r_N) = -10.4414952752 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 -8.55999104e-01 -1.33918152e+00 -7.30013860e-01 | -8.55999104e-01 -1.33918152e+00 -7.30013860e-01 1 4.34230446e+00 -5.23644526e+00 3.94454518e+00 | 4.34230446e+00 -5.23644526e+00 3.94454518e+00 2 -5.85723920e-01 4.04518922e+00 -6.53713208e+00 | -5.85723920e-01 4.04518922e+00 -6.53713208e+00 3 -2.90058144e+00 2.53043755e+00 3.32260076e+00 | -2.90058144e+00 2.53043755e+00 3.32260076e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TTF (Configuration in file "config-AlMnPd-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)) = -8.75013119047 2^p V(r_1,...,r_N) = -8.75013119047 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 -1.30097163e+01 -1.15690205e+01 -1.10880509e+01 | -1.30097163e+01 -1.15690205e+01 -1.10880509e+01 1 -1.55616062e+01 1.65935216e+01 1.25389488e+01 | -1.55616062e+01 1.65935216e+01 1.25389488e+01 2 -5.18223985e+01 3.38598603e+01 2.96286830e+01 | -5.18223985e+01 3.38598603e+01 2.96286830e+01 3 8.03937210e+01 -3.88843614e+01 -3.10795809e+01 | 8.03937210e+01 -3.88843614e+01 -3.10795809e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TFT (Configuration in file "config-AlMnPd-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)) = -8.9456171254 2^p V(r_1,...,r_N) = -8.9456171254 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 -9.30405180e+00 -1.17561023e+01 -2.96466185e+00 | -9.30405180e+00 -1.17561023e+01 -2.96466185e+00 1 9.02570863e+00 1.20280591e+01 -6.03351241e+00 | 9.02570863e+00 1.20280591e+01 -6.03351241e+00 2 -1.95465233e+01 1.83715221e+01 3.55789894e+00 | -1.95465233e+01 1.83715221e+01 3.55789894e+00 3 1.98248665e+01 -1.86434789e+01 5.44027532e+00 | 1.98248665e+01 -1.86434789e+01 5.44027532e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = TFF (Configuration in file "config-AlMnPd-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)) = -13.9620159812 2^p V(r_1,...,r_N) = -13.9620159812 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 -2.38104068e+00 5.42034593e+01 2.86241966e+01 | -2.38104068e+00 5.42034593e+01 2.86241966e+01 1 5.30692386e+00 2.49076074e+00 -7.15013519e+00 | 5.30692386e+00 2.49076074e+00 -7.15013519e+00 2 9.91309333e+00 -6.44458031e+00 9.21450174e+00 | 9.91309333e+00 -6.44458031e+00 9.21450174e+00 3 -1.28389765e+01 -5.02496397e+01 -3.06885632e+01 | -1.28389765e+01 -5.02496397e+01 -3.06885632e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = FTT (Configuration in file "config-AlMnPd-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)) = -4.85298454817 2^p V(r_1,...,r_N) = -4.85298454817 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 -1.51585557e+01 -1.18043120e+01 -8.34310277e+00 | -1.51585557e+01 -1.18043120e+01 -8.34310277e+00 1 9.44002391e+00 1.50120257e+01 -5.34932095e+00 | 9.44002391e+00 1.50120257e+01 -5.34932095e+00 2 6.23395251e+00 -5.97078243e+00 1.13973349e+01 | 6.23395251e+00 -5.97078243e+00 1.13973349e+01 3 -5.15420721e-01 2.76306869e+00 2.29508887e+00 | -5.15420721e-01 2.76306869e+00 2.29508887e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = FTF (Configuration in file "config-AlMnPd-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)) = -28.1129802381 2^p V(r_1,...,r_N) = -28.1129802381 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 1.17653073e+02 9.23833937e+01 3.37096915e+01 | 1.17653073e+02 9.23833937e+01 3.37096915e+01 1 -9.40260736e+01 -1.65965534e+02 1.39430175e+02 | -9.40260736e+01 -1.65965534e+02 1.39430175e+02 2 -4.95807866e+01 6.56754026e+01 -1.35003884e+02 | -4.95807866e+01 6.56754026e+01 -1.35003884e+02 3 2.59537876e+01 7.90673780e+00 -3.81359829e+01 | 2.59537876e+01 7.90673780e+00 -3.81359829e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mn Pd, PBC = FFT (Configuration in file "config-AlMnPd-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)) = -8.62824840628 2^p V(r_1,...,r_N) = -8.62824840628 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 1.94784121e+01 3.21145558e+01 -1.36338276e+01 | 1.94784121e+01 3.21145558e+01 -1.36338276e+01 1 -2.23518988e+01 -3.28096748e+01 1.30077208e-01 | -2.23518988e+01 -3.28096748e+01 1.30077208e-01 2 1.12990226e+01 -7.10717272e+00 4.21768809e+00 | 1.12990226e+01 -7.10717272e+00 4.21768809e+00 3 -8.42553593e+00 7.80229173e+00 9.28606231e+00 | -8.42553593e+00 7.80229173e+00 9.28606231e+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.