!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_IMD_BrommerBoissieuEuchner_2009_MgZn__MO_710767216198_003 Supported species : Mg Zn random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ 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)) = 11.1677436868 2^p V(r_1,...,r_N) = 11.1677436868 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 -1.36140834e+03 -2.43258255e+03 -2.82086318e+03 | -1.36140834e+03 -2.43258255e+03 -2.82086318e+03 1 9.40980306e+02 8.30548027e+02 -6.54330262e+02 | 9.40980306e+02 8.30548027e+02 -6.54330262e+02 2 1.00921059e+03 -9.23174649e+02 1.48551324e+03 | 1.00921059e+03 -9.23174649e+02 1.48551324e+03 3 -5.88782550e+02 2.52520918e+03 1.98968019e+03 | -5.88782550e+02 2.52520918e+03 1.98968019e+03 ------------------------------------------------------------------------------------------------------------------------ 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)) = 13.5565719903 2^p V(r_1,...,r_N) = 13.5565719903 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 -8.30385784e+02 -1.26770271e+03 -6.77716305e+02 | -8.30385784e+02 -1.26770271e+03 -6.77716305e+02 1 1.94272170e+03 1.81582269e+03 -2.40401582e+03 | 1.94272170e+03 1.81582269e+03 -2.40401582e+03 2 1.59621713e+03 -1.84463038e+03 1.31117650e+03 | 1.59621713e+03 -1.84463038e+03 1.31117650e+03 3 -2.70855305e+03 1.29651040e+03 1.77055562e+03 | -2.70855305e+03 1.29651040e+03 1.77055562e+03 ------------------------------------------------------------------------------------------------------------------------ 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)) = 15.7598889021 2^p V(r_1,...,r_N) = 15.7598889021 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 -1.76090169e+03 -2.30926822e+03 -8.53444206e+02 | -1.76090169e+03 -2.30926822e+03 -8.53444206e+02 1 3.36053718e+03 2.53902861e+03 -3.66501484e+03 | 3.36053718e+03 2.53902861e+03 -3.66501484e+03 2 1.25925635e+03 -2.15598499e+03 2.42629963e+03 | 1.25925635e+03 -2.15598499e+03 2.42629963e+03 3 -2.85889184e+03 1.92622460e+03 2.09215942e+03 | -2.85889184e+03 1.92622460e+03 2.09215942e+03 ------------------------------------------------------------------------------------------------------------------------ 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)) = 11.6336858952 2^p V(r_1,...,r_N) = 11.6336858952 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 -2.15304454e+03 -2.56816278e+03 -1.53043856e+03 | -2.15304454e+03 -2.56816278e+03 -1.53043856e+03 1 2.23655239e+03 2.64626114e+03 -1.46226257e+03 | 2.23655239e+03 2.64626114e+03 -1.46226257e+03 2 1.33293922e+03 -1.07011109e+03 1.68555506e+03 | 1.33293922e+03 -1.07011109e+03 1.68555506e+03 3 -1.41644707e+03 9.92012734e+02 1.30714606e+03 | -1.41644707e+03 9.92012734e+02 1.30714606e+03 ------------------------------------------------------------------------------------------------------------------------ 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)) = 10.6263161404 2^p V(r_1,...,r_N) = 10.6263161404 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 -6.31237997e+02 -9.81852758e+02 -5.69732126e+02 | -6.31237997e+02 -9.81852758e+02 -5.69732126e+02 1 1.41852358e+03 1.98007861e+03 -1.83063739e+03 | 1.41852358e+03 1.98007861e+03 -1.83063739e+03 2 1.66125535e+03 -1.90255363e+03 1.28698393e+03 | 1.66125535e+03 -1.90255363e+03 1.28698393e+03 3 -2.44854093e+03 9.04327775e+02 1.11338558e+03 | -2.44854093e+03 9.04327775e+02 1.11338558e+03 ------------------------------------------------------------------------------------------------------------------------ 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)) = 13.3994228259 2^p V(r_1,...,r_N) = 13.3994228259 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 -1.53687867e+03 -6.20117177e+02 -1.95087403e+03 | -1.53687867e+03 -6.20117177e+02 -1.95087403e+03 1 6.64361918e+02 1.70170721e+03 -1.56833404e+03 | 6.64361918e+02 1.70170721e+03 -1.56833404e+03 2 2.97278397e+03 -2.79734635e+03 2.59806030e+03 | 2.97278397e+03 -2.79734635e+03 2.59806030e+03 3 -2.10026722e+03 1.71575632e+03 9.21147778e+02 | -2.10026722e+03 1.71575632e+03 9.21147778e+02 ------------------------------------------------------------------------------------------------------------------------ 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)) = 13.3513631652 2^p V(r_1,...,r_N) = 13.3513631652 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 -2.01441649e+03 -1.65961588e+03 -2.28289509e+03 | -2.01441649e+03 -1.65961588e+03 -2.28289509e+03 1 1.52789378e+03 2.90994780e+03 -1.79034653e+03 | 1.52789378e+03 2.90994780e+03 -1.79034653e+03 2 2.98600956e+03 -3.48503261e+03 2.63585026e+03 | 2.98600956e+03 -3.48503261e+03 2.63585026e+03 3 -2.49948685e+03 2.23470069e+03 1.43739136e+03 | -2.49948685e+03 2.23470069e+03 1.43739136e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = TTT (Configuration in file "config-Zn-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)) = 3.68401393001 2^p V(r_1,...,r_N) = 3.68401393001 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 -2.03806311e+01 -4.08919988e+00 -3.03703244e+01 | -2.03806311e+01 -4.08919988e+00 -3.03703244e+01 1 6.87916186e+00 2.83600998e+01 -2.80374727e+01 | 6.87916186e+00 2.83600998e+01 -2.80374727e+01 2 4.17327781e+02 -3.67446073e+02 -2.95909721e+01 | 4.17327781e+02 -3.67446073e+02 -2.95909721e+01 3 -4.03826312e+02 3.43175173e+02 8.79987692e+01 | -4.03826312e+02 3.43175173e+02 8.79987692e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = TTF (Configuration in file "config-Zn-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)) = 28.1415769183 2^p V(r_1,...,r_N) = 28.1415769183 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 -2.52258889e+03 -1.73241745e+03 -2.70612951e+03 | -2.52258889e+03 -1.73241745e+03 -2.70612951e+03 1 9.56461094e+02 1.47913920e+03 -9.03542137e+02 | 9.56461094e+02 1.47913920e+03 -9.03542137e+02 2 2.70620079e+03 -1.24906031e+03 2.58155628e+03 | 2.70620079e+03 -1.24906031e+03 2.58155628e+03 3 -1.14007300e+03 1.50233857e+03 1.02811537e+03 | -1.14007300e+03 1.50233857e+03 1.02811537e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = TFT (Configuration in file "config-Zn-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.70110341084 2^p V(r_1,...,r_N) = -1.70110341084 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 -1.14758719e+00 -1.84056437e+00 -1.47967879e+00 | -1.14758719e+00 -1.84056437e+00 -1.47967879e+00 1 1.97545596e+00 1.45491249e+00 -2.06820892e+00 | 1.97545596e+00 1.45491249e+00 -2.06820892e+00 2 1.28244364e+00 -1.53845900e+00 2.15611833e+00 | 1.28244364e+00 -1.53845900e+00 2.15611833e+00 3 -2.11031241e+00 1.92411088e+00 1.39176937e+00 | -2.11031241e+00 1.92411088e+00 1.39176937e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = TFF (Configuration in file "config-Zn-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)) = 10.871027813 2^p V(r_1,...,r_N) = 10.871027813 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 -8.42565172e+02 -3.23496661e+02 -6.89413112e+02 | -8.42565172e+02 -3.23496661e+02 -6.89413112e+02 1 3.37899339e+01 2.29176929e+02 -5.20057038e+01 | 3.37899339e+01 2.29176929e+02 -5.20057038e+01 2 8.16411738e+02 8.64629337e+01 7.33217512e+02 | 8.16411738e+02 8.64629337e+01 7.33217512e+02 3 -7.63650008e+00 7.85679874e+00 8.20130337e+00 | -7.63650008e+00 7.85679874e+00 8.20130337e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = FTT (Configuration in file "config-Zn-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)) = 6.90444846549 2^p V(r_1,...,r_N) = 6.90444846549 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 -3.85570100e+02 -1.35785289e+02 -3.42669884e+02 | -3.85570100e+02 -1.35785289e+02 -3.42669884e+02 1 7.55374615e+01 2.03762985e+02 -3.40388115e+02 | 7.55374615e+01 2.03762985e+02 -3.40388115e+02 2 4.21085732e+02 -2.25527840e+02 6.56829516e+02 | 4.21085732e+02 -2.25527840e+02 6.56829516e+02 3 -1.11053094e+02 1.57550144e+02 2.62284826e+01 | -1.11053094e+02 1.57550144e+02 2.62284826e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = FTF (Configuration in file "config-Zn-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)) = 26.9695425711 2^p V(r_1,...,r_N) = 26.9695425711 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 -2.18349957e+03 -1.91787576e+03 -1.76858631e+03 | -2.18349957e+03 -1.91787576e+03 -1.76858631e+03 1 1.63923974e+03 2.87893653e+03 -1.12850191e+03 | 1.63923974e+03 2.87893653e+03 -1.12850191e+03 2 1.28978690e+03 -1.67578601e+03 1.78892008e+03 | 1.28978690e+03 -1.67578601e+03 1.78892008e+03 3 -7.45527074e+02 7.14725245e+02 1.10816814e+03 | -7.45527074e+02 7.14725245e+02 1.10816814e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zn, PBC = FFT (Configuration in file "config-Zn-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)) = 26.8315796769 2^p V(r_1,...,r_N) = 26.8315796769 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 -2.81325304e+03 -2.30429919e+03 -1.94419484e+03 | -2.81325304e+03 -2.30429919e+03 -1.94419484e+03 1 1.43630559e+03 2.26528688e+03 -1.42914830e+03 | 1.43630559e+03 2.26528688e+03 -1.42914830e+03 2 1.75225541e+03 -8.47259760e+02 2.70013487e+03 | 1.75225541e+03 -8.47259760e+02 2.70013487e+03 3 -3.75307969e+02 8.86272075e+02 6.73208271e+02 | -3.75307969e+02 8.86272075e+02 6.73208271e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = TTT (Configuration in file "config-MgZn-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)) = 19.1914121284 2^p V(r_1,...,r_N) = 19.1914121284 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 -4.96333127e+03 -4.04834090e+03 -5.29987560e+03 | -4.96333127e+03 -4.04834090e+03 -5.29987560e+03 1 2.45858543e+03 5.18118989e+03 -5.80253709e+03 | 2.45858543e+03 5.18118989e+03 -5.80253709e+03 2 6.26440695e+03 -4.65222312e+03 4.60110130e+03 | 6.26440695e+03 -4.65222312e+03 4.60110130e+03 3 -3.75966111e+03 3.51937413e+03 6.50131140e+03 | -3.75966111e+03 3.51937413e+03 6.50131140e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = TTF (Configuration in file "config-MgZn-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)) = 16.6532148318 2^p V(r_1,...,r_N) = 16.6532148318 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 -2.80976919e+03 -2.83861102e+03 -3.02979437e+03 | -2.80976919e+03 -2.83861102e+03 -3.02979437e+03 1 1.63600611e+03 1.84276497e+03 -1.12824279e+03 | 1.63600611e+03 1.84276497e+03 -1.12824279e+03 2 4.84769783e+03 -2.43406536e+03 1.44808935e+03 | 4.84769783e+03 -2.43406536e+03 1.44808935e+03 3 -3.67393475e+03 3.42991140e+03 2.70994781e+03 | -3.67393475e+03 3.42991140e+03 2.70994781e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = TFT (Configuration in file "config-MgZn-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)) = 17.0570632258 2^p V(r_1,...,r_N) = 17.0570632258 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 -2.64104378e+03 -2.40269836e+03 -6.77749849e+03 | -2.64104378e+03 -2.40269836e+03 -6.77749849e+03 1 1.43010338e+03 8.92954760e+02 -8.88828091e+02 | 1.43010338e+03 8.92954760e+02 -8.88828091e+02 2 4.06733587e+03 -2.96618384e+03 3.24905904e+03 | 4.06733587e+03 -2.96618384e+03 3.24905904e+03 3 -2.85639547e+03 4.47592744e+03 4.41726755e+03 | -2.85639547e+03 4.47592744e+03 4.41726755e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = TFF (Configuration in file "config-MgZn-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)) = 16.1529610446 2^p V(r_1,...,r_N) = 16.1529610446 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 -3.67488974e+03 -2.28118635e+03 -4.31030865e+03 | -3.67488974e+03 -2.28118635e+03 -4.31030865e+03 1 2.13048646e+03 4.18789743e+03 -4.18331780e+03 | 2.13048646e+03 4.18789743e+03 -4.18331780e+03 2 4.33525035e+03 -3.78037630e+03 4.51055547e+03 | 4.33525035e+03 -3.78037630e+03 4.51055547e+03 3 -2.79084707e+03 1.87366522e+03 3.98307097e+03 | -2.79084707e+03 1.87366522e+03 3.98307097e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = FTT (Configuration in file "config-MgZn-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)) = 19.041717402 2^p V(r_1,...,r_N) = 19.041717402 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 -5.19303671e+03 -4.42121416e+03 -3.89572068e+03 | -5.19303671e+03 -4.42121416e+03 -3.89572068e+03 1 6.04979441e+03 4.13453101e+03 -5.24152309e+03 | 6.04979441e+03 4.13453101e+03 -5.24152309e+03 2 4.63141816e+03 -4.14705220e+03 3.83199396e+03 | 4.63141816e+03 -4.14705220e+03 3.83199396e+03 3 -5.48817586e+03 4.43373536e+03 5.30524981e+03 | -5.48817586e+03 4.43373536e+03 5.30524981e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = FTF (Configuration in file "config-MgZn-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)) = 16.7800830546 2^p V(r_1,...,r_N) = 16.7800830546 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 -2.50298184e+03 -2.04551981e+03 -4.06581078e+02 | -2.50298184e+03 -2.04551981e+03 -4.06581078e+02 1 4.21096844e+03 3.99738829e+03 -4.81137426e+03 | 4.21096844e+03 3.99738829e+03 -4.81137426e+03 2 1.47127220e+03 -5.31081704e+03 2.65712737e+03 | 1.47127220e+03 -5.31081704e+03 2.65712737e+03 3 -3.17925880e+03 3.35894857e+03 2.56082797e+03 | -3.17925880e+03 3.35894857e+03 2.56082797e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Mg Zn, PBC = FFT (Configuration in file "config-MgZn-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)) = 16.4003028701 2^p V(r_1,...,r_N) = 16.4003028701 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 -5.26724513e+03 -2.18862233e+03 -3.98411501e+03 | -5.26724513e+03 -2.18862233e+03 -3.98411501e+03 1 2.65859206e+03 2.86706624e+03 -1.31360196e+03 | 2.65859206e+03 2.86706624e+03 -1.31360196e+03 2 3.63886728e+03 -1.93583113e+03 4.26012207e+03 | 3.63886728e+03 -1.93583113e+03 4.26012207e+03 3 -1.03021421e+03 1.25738722e+03 1.03759490e+03 | -1.03021421e+03 1.25738722e+03 1.03759490e+03 ------------------------------------------------------------------------------------------------------------------------ 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.