!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_ADP_SmirnovaStarikov_2017_ZrNb__SM_937902197407_000 Supported species : Nb Zr random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTT (Configuration in file "config-Nb-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)) = 341.274074915 2^p V(r_1,...,r_N) = 341.274074915 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 -7.27723004e+02 -2.77567481e+03 -2.15404507e+03 | -7.27723004e+02 -2.77567481e+03 -2.15404507e+03 1 4.01090431e+02 5.17296334e+03 -6.33943204e+03 | 4.01090431e+02 5.17296334e+03 -6.33943204e+03 2 2.47422740e+02 -4.95566074e+03 6.13124970e+03 | 2.47422740e+02 -4.95566074e+03 6.13124970e+03 3 7.92098325e+01 2.55837220e+03 2.36222740e+03 | 7.92098325e+01 2.55837220e+03 2.36222740e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTF (Configuration in file "config-Nb-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.13641635297 2^p V(r_1,...,r_N) = -6.13641635297 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 -2.99323009e+02 -2.26922199e+02 -5.40945114e+01 | -2.99323009e+02 -2.26922199e+02 -5.40945114e+01 1 2.72164158e+02 2.33217498e+02 -1.43662377e+00 | 2.72164158e+02 2.33217498e+02 -1.43662377e+00 2 3.47002621e+01 -1.55505325e+01 4.70787075e+01 | 3.47002621e+01 -1.55505325e+01 4.70787075e+01 3 -7.54141043e+00 9.25523347e+00 8.45242763e+00 | -7.54141043e+00 9.25523347e+00 8.45242763e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFT (Configuration in file "config-Nb-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)) = 111.312080599 2^p V(r_1,...,r_N) = 111.312080599 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 -1.39057876e+03 -1.14534893e+03 -3.97283969e+02 | -1.39057876e+03 -1.14534893e+03 -3.97283969e+02 1 1.81271209e+03 1.70409143e+03 -1.63523084e+03 | 1.81271209e+03 1.70409143e+03 -1.63523084e+03 2 2.60536388e+02 -8.10026204e+02 1.21866136e+03 | 2.60536388e+02 -8.10026204e+02 1.21866136e+03 3 -6.82669718e+02 2.51283710e+02 8.13853445e+02 | -6.82669718e+02 2.51283710e+02 8.13853445e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFF (Configuration in file "config-Nb-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)) = 2254322.58131 2^p V(r_1,...,r_N) = 2254322.58131 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 -1.38452730e+07 -5.88181702e+06 -1.39525619e+07 | -1.38452730e+07 -5.88181702e+06 -1.39525619e+07 1 2.63136852e+07 7.26174826e+06 -3.04953891e+07 | 2.63136852e+07 7.26174826e+06 -3.04953891e+07 2 2.41994137e+07 -3.60111749e+06 1.54536680e+07 | 2.41994137e+07 -3.60111749e+06 1.54536680e+07 3 -3.66678259e+07 2.22118626e+06 2.89942830e+07 | -3.66678259e+07 2.22118626e+06 2.89942830e+07 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTT (Configuration in file "config-Nb-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)) = -19.0142485577 2^p V(r_1,...,r_N) = -19.0142485577 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 -4.58382867e+00 -1.68273452e+00 -5.79276339e+00 | -4.58382867e+00 -1.68273452e+00 -5.79276339e+00 1 4.57273649e+00 1.65393508e+01 -1.11551252e+01 | 4.57273649e+00 1.65393508e+01 -1.11551252e+01 2 2.07537481e+01 -3.25211050e+01 1.02902896e+01 | 2.07537481e+01 -3.25211050e+01 1.02902896e+01 3 -2.07426559e+01 1.76644888e+01 6.65759908e+00 | -2.07426559e+01 1.76644888e+01 6.65759908e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTF (Configuration in file "config-Nb-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)) = -20.4295940147 2^p V(r_1,...,r_N) = -20.4295940147 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 2.20264648e+00 5.37637721e+00 5.57580404e+00 | 2.20264648e+00 5.37637721e+00 5.57580404e+00 1 -3.59589691e+00 -4.31086702e+00 6.45457911e+00 | -3.59589691e+00 -4.31086702e+00 6.45457911e+00 2 -4.87596558e+00 7.67026798e+00 -5.08806693e+00 | -4.87596558e+00 7.67026798e+00 -5.08806693e+00 3 6.26921601e+00 -8.73577816e+00 -6.94231623e+00 | 6.26921601e+00 -8.73577816e+00 -6.94231623e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FFT (Configuration in file "config-Nb-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)) = -21.45588452 2^p V(r_1,...,r_N) = -21.45588452 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 -1.84047693e+00 -1.78859990e+00 -2.08827390e+00 | -1.84047693e+00 -1.78859990e+00 -2.08827390e+00 1 7.70666914e-01 1.11436252e+00 -1.03998952e+00 | 7.70666914e-01 1.11436252e+00 -1.03998952e+00 2 2.38929881e+00 -1.78822561e+00 1.60328849e+00 | 2.38929881e+00 -1.78822561e+00 1.60328849e+00 3 -1.31948880e+00 2.46246299e+00 1.52497493e+00 | -1.31948880e+00 2.46246299e+00 1.52497493e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TTT (Configuration in file "config-Zr-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)) = -7.87814865079 2^p V(r_1,...,r_N) = -7.87814865079 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 -7.75341313e+00 -3.78665312e+00 -7.78277952e+00 | -7.75341313e+00 -3.78665312e+00 -7.78277952e+00 1 6.62145198e+00 7.50433760e+00 -5.32617569e+00 | 6.62145198e+00 7.50433760e+00 -5.32617569e+00 2 6.23524925e+00 -7.97391113e+00 8.06739522e+00 | 6.23524925e+00 -7.97391113e+00 8.06739522e+00 3 -5.10328809e+00 4.25622665e+00 5.04155999e+00 | -5.10328809e+00 4.25622665e+00 5.04155999e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TTF (Configuration in file "config-Zr-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.96583210919 2^p V(r_1,...,r_N) = 5.96583210919 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 -1.48453017e+01 -1.53638543e+01 -1.45073645e+01 | -1.48453017e+01 -1.53638543e+01 -1.45073645e+01 1 1.62324111e+01 1.74602623e+01 -1.47014911e+01 | 1.62324111e+01 1.74602623e+01 -1.47014911e+01 2 1.52120446e+01 -1.44832705e+01 1.84654958e+01 | 1.52120446e+01 -1.44832705e+01 1.84654958e+01 3 -1.65991540e+01 1.23868625e+01 1.07433598e+01 | -1.65991540e+01 1.23868625e+01 1.07433598e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TFT (Configuration in file "config-Zr-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)) = -11.7207664879 2^p V(r_1,...,r_N) = -11.7207664879 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 -3.60591457e+00 -2.96217653e+00 -3.12804894e+00 | -3.60591457e+00 -2.96217653e+00 -3.12804894e+00 1 2.37579618e+00 2.94957153e+00 -2.77481160e+00 | 2.37579618e+00 2.94957153e+00 -2.77481160e+00 2 3.58257198e+00 -2.61703391e+00 3.96593857e+00 | 3.58257198e+00 -2.61703391e+00 3.96593857e+00 3 -2.35245359e+00 2.62963891e+00 1.93692197e+00 | -2.35245359e+00 2.62963891e+00 1.93692197e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TFF (Configuration in file "config-Zr-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.60539952051 2^p V(r_1,...,r_N) = -6.60539952051 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 -4.33015803e+00 -1.06962069e+01 -1.16055271e+01 | -4.33015803e+00 -1.06962069e+01 -1.16055271e+01 1 6.93719810e+00 6.38908913e+00 -4.78486104e+00 | 6.93719810e+00 6.38908913e+00 -4.78486104e+00 2 3.85227028e+00 -4.11027934e+00 3.26012428e+00 | 3.85227028e+00 -4.11027934e+00 3.26012428e+00 3 -6.45931034e+00 8.41739707e+00 1.31302639e+01 | -6.45931034e+00 8.41739707e+00 1.31302639e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FTT (Configuration in file "config-Zr-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)) = -8.76378551772 2^p V(r_1,...,r_N) = -8.76378551772 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 -7.09370827e+00 -5.60768990e+00 -5.87566867e+00 | -7.09370827e+00 -5.60768990e+00 -5.87566867e+00 1 6.83047989e+00 6.36358122e+00 -5.80445662e+00 | 6.83047989e+00 6.36358122e+00 -5.80445662e+00 2 4.51166986e+00 -5.36347672e+00 6.08889626e+00 | 4.51166986e+00 -5.36347672e+00 6.08889626e+00 3 -4.24844148e+00 4.60758541e+00 5.59122903e+00 | -4.24844148e+00 4.60758541e+00 5.59122903e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FTF (Configuration in file "config-Zr-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)) = -6.24138418937 2^p V(r_1,...,r_N) = -6.24138418937 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 -9.82965548e+00 -1.02225181e+01 -6.92749416e+00 | -9.82965548e+00 -1.02225181e+01 -6.92749416e+00 1 1.10278428e+01 9.59755810e+00 -5.79065797e+00 | 1.10278428e+01 9.59755810e+00 -5.79065797e+00 2 4.40069672e+00 -4.83700986e+00 6.07350734e+00 | 4.40069672e+00 -4.83700986e+00 6.07350734e+00 3 -5.59888400e+00 5.46196986e+00 6.64464479e+00 | -5.59888400e+00 5.46196986e+00 6.64464479e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FFT (Configuration in file "config-Zr-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.05016359599 2^p V(r_1,...,r_N) = -3.05016359599 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 -1.00463304e+01 -8.71830738e+00 -8.47202311e+00 | -1.00463304e+01 -8.71830738e+00 -8.47202311e+00 1 9.17072283e+00 8.78603405e+00 -1.30152748e+01 | 9.17072283e+00 8.78603405e+00 -1.30152748e+01 2 1.11826739e+01 -7.60085452e+00 8.24974346e+00 | 1.11826739e+01 -7.60085452e+00 8.24974346e+00 3 -1.03070664e+01 7.53312785e+00 1.32375545e+01 | -1.03070664e+01 7.53312785e+00 1.32375545e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = TTT (Configuration in file "config-NbZr-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)) = -7.01405267486 2^p V(r_1,...,r_N) = -7.01405267486 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 -8.04453374e+00 -9.69156783e+00 1.33942810e+00 | -8.04453374e+00 -9.69156783e+00 1.33942810e+00 1 8.24670893e+00 9.38656517e+00 2.30095747e+00 | 8.24670893e+00 9.38656517e+00 2.30095747e+00 2 -1.20813085e+01 1.19431747e+01 -1.86432106e+00 | -1.20813085e+01 1.19431747e+01 -1.86432106e+00 3 1.18791333e+01 -1.16381721e+01 -1.77606452e+00 | 1.18791333e+01 -1.16381721e+01 -1.77606452e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = TTF (Configuration in file "config-NbZr-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)) = 201.24135363 2^p V(r_1,...,r_N) = 201.24135363 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 -3.88846339e+03 -5.88271507e+03 -6.21056242e+02 | -3.88846339e+03 -5.88271507e+03 -6.21056242e+02 1 3.88723154e+03 5.88674068e+03 6.02086744e+02 | 3.88723154e+03 5.88674068e+03 6.02086744e+02 2 1.08565613e+01 -1.30551038e+01 1.12382698e+01 | 1.08565613e+01 -1.30551038e+01 1.12382698e+01 3 -9.62471341e+00 9.02949739e+00 7.73122852e+00 | -9.62471341e+00 9.02949739e+00 7.73122852e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = TFT (Configuration in file "config-NbZr-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 3.51019717953 2^p V(r_1,...,r_N) = 3.51019717953 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 -8.19120115e+00 -2.53677658e+01 -1.75497853e+01 | -8.19120115e+00 -2.53677658e+01 -1.75497853e+01 1 1.94347182e+01 1.56085639e+02 -1.33143870e+02 | 1.94347182e+01 1.56085639e+02 -1.33143870e+02 2 3.31098971e+00 -1.54281311e+02 1.35741550e+02 | 3.31098971e+00 -1.54281311e+02 1.35741550e+02 3 -1.45545068e+01 2.35634376e+01 1.49521059e+01 | -1.45545068e+01 2.35634376e+01 1.49521059e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = TFF (Configuration in file "config-NbZr-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)) = -13.3883256183 2^p V(r_1,...,r_N) = -13.3883256183 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 -1.33368978e+01 -8.30378165e+00 -1.05731744e+01 | -1.33368978e+01 -8.30378165e+00 -1.05731744e+01 1 2.64952221e+00 5.57730044e+00 -4.57566103e+00 | 2.64952221e+00 5.57730044e+00 -4.57566103e+00 2 1.44058694e+01 -4.01402443e+00 1.03012525e+01 | 1.44058694e+01 -4.01402443e+00 1.03012525e+01 3 -3.71849384e+00 6.74050565e+00 4.84758293e+00 | -3.71849384e+00 6.74050565e+00 4.84758293e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = FTT (Configuration in file "config-NbZr-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -14.6316718205 2^p V(r_1,...,r_N) = -14.6316718205 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 -7.89089185e+00 -8.35880311e+00 -2.76042291e+00 | -7.89089185e+00 -8.35880311e+00 -2.76042291e+00 1 7.91938328e+00 7.62109407e+00 -3.43495304e+00 | 7.91938328e+00 7.62109407e+00 -3.43495304e+00 2 -2.94855139e+00 2.89528357e+00 2.41172972e+00 | -2.94855139e+00 2.89528357e+00 2.41172972e+00 3 2.92005995e+00 -2.15757453e+00 3.78364623e+00 | 2.92005995e+00 -2.15757453e+00 3.78364623e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = FTF (Configuration in file "config-NbZr-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)) = 89166.4209427 2^p V(r_1,...,r_N) = 89166.4209427 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 -1.17668209e+01 -2.07674790e+01 -1.24719115e+01 | -1.17668209e+01 -2.07674790e+01 -1.24719115e+01 1 1.36105723e+01 1.88982770e+01 -1.32235916e+01 | 1.36105723e+01 1.88982770e+01 -1.32235916e+01 2 2.19053291e+06 -2.00815539e+06 3.20108492e+05 | 2.19053291e+06 -2.00815539e+06 3.20108492e+05 3 -2.19053475e+06 2.00815726e+06 -3.20082796e+05 | -2.19053475e+06 2.00815726e+06 -3.20082796e+05 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Nb Zr, PBC = FFT (Configuration in file "config-NbZr-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)) = 615.319270894 2^p V(r_1,...,r_N) = 615.319270894 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 -1.43128174e+04 -1.45115361e+04 2.22711831e+03 | -1.43128174e+04 -1.45115361e+04 2.22711831e+03 1 1.43121003e+04 1.45093536e+04 -2.25370363e+03 | 1.43121003e+04 1.45093536e+04 -2.25370363e+03 2 2.86594747e+01 -2.77082051e+01 1.81212740e+01 | 2.86594747e+01 -2.77082051e+01 1.81212740e+01 3 -2.79424055e+01 2.98907312e+01 8.46404668e+00 | -2.79424055e+01 2.98907312e+01 8.46404668e+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.