!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BorovikovMendelevKing_2016_CuZr__MO_097471813275_000 Supported species : Cu Zr random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-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)) = -5.71854043158 2^p V(r_1,...,r_N) = -5.71854043158 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 -1.79527451e+00 -6.25482455e+00 -5.56997621e+00 | -1.79527451e+00 -6.25482455e+00 -5.56997621e+00 1 1.92111681e+00 1.28846531e+00 -9.50094407e-01 | 1.92111681e+00 1.28846531e+00 -9.50094407e-01 2 1.03418798e+00 -1.01837365e+00 1.44644662e+00 | 1.03418798e+00 -1.01837365e+00 1.44644662e+00 3 -1.16003028e+00 5.98473290e+00 5.07362399e+00 | -1.16003028e+00 5.98473290e+00 5.07362399e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-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)) = 1.42404960801 2^p V(r_1,...,r_N) = 1.42404960801 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 -1.36055232e+00 -2.06982644e+00 -1.64939111e+00 | -1.36055232e+00 -2.06982644e+00 -1.64939111e+00 1 2.76629873e+01 8.96568574e+00 -3.23941716e+01 | 2.76629873e+01 8.96568574e+00 -3.23941716e+01 2 6.19504770e+00 -6.38212991e+00 2.83626450e+00 | 6.19504770e+00 -6.38212991e+00 2.83626450e+00 3 -3.24974826e+01 -5.13729396e-01 3.12072982e+01 | -3.24974826e+01 -5.13729396e-01 3.12072982e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-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)) = 3.13550794792 2^p V(r_1,...,r_N) = 3.13550794792 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 -2.21283542e+01 -1.30154415e+01 -3.77316868e+01 | -2.21283542e+01 -1.30154415e+01 -3.77316868e+01 1 4.23849454e+00 6.39291034e+00 -3.77255303e+00 | 4.23849454e+00 6.39291034e+00 -3.77255303e+00 2 2.67258042e+01 -8.71016727e+00 2.82308274e+01 | 2.67258042e+01 -8.71016727e+00 2.82308274e+01 3 -8.83594453e+00 1.53326984e+01 1.32734124e+01 | -8.83594453e+00 1.53326984e+01 1.32734124e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-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)) = -6.62237168032 2^p V(r_1,...,r_N) = -6.62237168032 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 -1.29308793e+00 -1.08220114e+00 -6.18221241e-01 | -1.29308793e+00 -1.08220114e+00 -6.18221241e-01 1 1.38488434e+00 9.52830923e-01 -1.27688074e+00 | 1.38488434e+00 9.52830923e-01 -1.27688074e+00 2 1.65689924e+00 -1.88929504e+00 6.05003528e-01 | 1.65689924e+00 -1.88929504e+00 6.05003528e-01 3 -1.74869565e+00 2.01866526e+00 1.29009846e+00 | -1.74869565e+00 2.01866526e+00 1.29009846e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-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)) = -4.91856107916 2^p V(r_1,...,r_N) = -4.91856107916 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 -4.55694492e+00 -2.44991419e+00 -7.52922723e+00 | -4.55694492e+00 -2.44991419e+00 -7.52922723e+00 1 5.16066340e+00 1.41143534e+00 -3.74968262e+00 | 5.16066340e+00 1.41143534e+00 -3.74968262e+00 2 4.36664024e+00 -1.40457254e+00 7.81810881e+00 | 4.36664024e+00 -1.40457254e+00 7.81810881e+00 3 -4.97035872e+00 2.44305139e+00 3.46080104e+00 | -4.97035872e+00 2.44305139e+00 3.46080104e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-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)) = -4.71525600907 2^p V(r_1,...,r_N) = -4.71525600907 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 -9.95787028e-01 -9.63236614e+00 -9.82576526e+00 | -9.95787028e-01 -9.63236614e+00 -9.82576526e+00 1 2.31454784e+00 2.03305853e+00 -7.85004280e-01 | 2.31454784e+00 2.03305853e+00 -7.85004280e-01 2 2.40359223e+00 -7.79756607e-01 2.59020097e+00 | 2.40359223e+00 -7.79756607e-01 2.59020097e+00 3 -3.72235304e+00 8.37906422e+00 8.02056857e+00 | -3.72235304e+00 8.37906422e+00 8.02056857e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-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)) = 1.42245030873 2^p V(r_1,...,r_N) = 1.42245030873 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 -3.32971100e+00 -2.98955455e+00 -2.84805330e+00 | -3.32971100e+00 -2.98955455e+00 -2.84805330e+00 1 1.74337717e+01 1.70237744e+01 -2.74101355e+01 | 1.74337717e+01 1.70237744e+01 -2.74101355e+01 2 7.00417016e+00 -2.26054891e+01 1.28758142e+01 | 7.00417016e+00 -2.26054891e+01 1.28758142e+01 3 -2.11082308e+01 8.57126922e+00 1.73823746e+01 | -2.11082308e+01 8.57126922e+00 1.73823746e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 8.45481628713 2^p V(r_1,...,r_N) = 8.45481628713 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 -1.38981540e+01 -1.96970343e+01 -2.16429126e+01 | -1.38981540e+01 -1.96970343e+01 -2.16429126e+01 1 2.91034930e+01 2.95503252e+01 -2.18478015e+01 | 2.91034930e+01 2.95503252e+01 -2.18478015e+01 2 1.67978753e+01 -2.61268928e+01 1.55522107e+01 | 1.67978753e+01 -2.61268928e+01 1.55522107e+01 3 -3.20032143e+01 1.62736020e+01 2.79385034e+01 | -3.20032143e+01 1.62736020e+01 2.79385034e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 2.89676609569 2^p V(r_1,...,r_N) = 2.89676609569 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 -2.06145061e+01 -2.28639241e+01 -3.21594500e+01 | -2.06145061e+01 -2.28639241e+01 -3.21594500e+01 1 1.48969604e+01 1.85176185e+01 -7.51869555e+00 | 1.48969604e+01 1.85176185e+01 -7.51869555e+00 2 2.28203545e+01 -1.53011685e+01 1.93564137e+01 | 2.28203545e+01 -1.53011685e+01 1.93564137e+01 3 -1.71028088e+01 1.96474740e+01 2.03217319e+01 | -1.71028088e+01 1.96474740e+01 2.03217319e+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)) = -10.8334635518 2^p V(r_1,...,r_N) = -10.8334635518 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 -3.55602702e+00 -8.62540748e+00 -9.29750222e+00 | -3.55602702e+00 -8.62540748e+00 -9.29750222e+00 1 5.58475195e+00 2.51743743e+00 -5.82679556e+00 | 5.58475195e+00 2.51743743e+00 -5.82679556e+00 2 7.58595599e+00 -7.78016450e+00 2.37458869e+00 | 7.58595599e+00 -7.78016450e+00 2.37458869e+00 3 -9.61468092e+00 1.38881346e+01 1.27497091e+01 | -9.61468092e+00 1.38881346e+01 1.27497091e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 7.59512125053 2^p V(r_1,...,r_N) = 7.59512125053 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 -3.53307212e+01 -2.21644321e+01 -3.32194482e+01 | -3.53307212e+01 -2.21644321e+01 -3.32194482e+01 1 1.01473836e+01 1.45004479e+01 -1.56362634e+01 | 1.01473836e+01 1.45004479e+01 -1.56362634e+01 2 4.29782225e+01 -1.29166247e+01 2.88804188e+01 | 4.29782225e+01 -1.29166247e+01 2.88804188e+01 3 -1.77948849e+01 2.05806089e+01 1.99752928e+01 | -1.77948849e+01 2.05806089e+01 1.99752928e+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)) = 35.8446104054 2^p V(r_1,...,r_N) = 35.8446104054 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 -3.89505926e+01 -4.03397883e+01 -4.69539257e+01 | -3.89505926e+01 -4.03397883e+01 -4.69539257e+01 1 5.40694505e+01 5.72768815e+01 -3.21988794e+01 | 5.40694505e+01 5.72768815e+01 -3.21988794e+01 2 2.75632188e+01 -4.26562791e+01 5.09201244e+01 | 2.75632188e+01 -4.26562791e+01 5.09201244e+01 3 -4.26820767e+01 2.57191859e+01 2.82326808e+01 | -4.26820767e+01 2.57191859e+01 2.82326808e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 21.3860794748 2^p V(r_1,...,r_N) = 21.3860794748 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 -2.34447197e+01 -2.07547164e+01 -2.08929137e+01 | -2.34447197e+01 -2.07547164e+01 -2.08929137e+01 1 2.65000907e+01 3.16669814e+01 -3.61269975e+01 | 2.65000907e+01 3.16669814e+01 -3.61269975e+01 2 3.53078142e+01 -4.57268009e+01 3.32613327e+01 | 3.53078142e+01 -4.57268009e+01 3.32613327e+01 3 -3.83631852e+01 3.48145358e+01 2.37585785e+01 | -3.83631852e+01 3.48145358e+01 2.37585785e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 3.18835756253 2^p V(r_1,...,r_N) = 3.18835756253 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 -2.02475683e+01 -1.64572038e+01 -2.21966855e+01 | -2.02475683e+01 -1.64572038e+01 -2.21966855e+01 1 1.20943703e+01 1.29628343e+01 -8.31182289e+00 | 1.20943703e+01 1.29628343e+01 -8.31182289e+00 2 2.99553393e+01 -2.65461510e+01 1.65911818e+01 | 2.99553393e+01 -2.65461510e+01 1.65911818e+01 3 -2.18021413e+01 3.00405204e+01 1.39173265e+01 | -2.18021413e+01 3.00405204e+01 1.39173265e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TTT (Configuration in file "config-CuZr-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)) = -2.78622375771 2^p V(r_1,...,r_N) = -2.78622375771 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 -6.66674562e+00 -1.36857702e+01 -1.09281871e+01 | -6.66674562e+00 -1.36857702e+01 -1.09281871e+01 1 1.51630857e+01 5.97148622e+00 -1.41236176e+01 | 1.51630857e+01 5.97148622e+00 -1.41236176e+01 2 6.74905767e+00 -6.68139401e+00 3.52088231e+00 | 6.74905767e+00 -6.68139401e+00 3.52088231e+00 3 -1.52453978e+01 1.43956780e+01 2.15309223e+01 | -1.52453978e+01 1.43956780e+01 2.15309223e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TTF (Configuration in file "config-CuZr-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)) = 6.40451195169 2^p V(r_1,...,r_N) = 6.40451195169 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 -7.72004654e+00 -8.13339213e+00 -8.77146428e+00 | -7.72004654e+00 -8.13339213e+00 -8.77146428e+00 1 1.57708761e+01 1.91386996e+01 -2.75466812e+01 | 1.57708761e+01 1.91386996e+01 -2.75466812e+01 2 2.83791214e+01 -2.76662424e+01 2.10900315e+01 | 2.83791214e+01 -2.76662424e+01 2.10900315e+01 3 -3.64299510e+01 1.66609350e+01 1.52281140e+01 | -3.64299510e+01 1.66609350e+01 1.52281140e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TFT (Configuration in file "config-CuZr-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.74831992558 2^p V(r_1,...,r_N) = 5.74831992558 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 -1.81329643e+01 -7.73315490e+00 -1.62354145e+01 | -1.81329643e+01 -7.73315490e+00 -1.62354145e+01 1 1.00553580e+01 1.23384110e+01 -1.99767763e+01 | 1.00553580e+01 1.23384110e+01 -1.99767763e+01 2 3.30669887e+01 -2.85213462e+01 2.03958946e+01 | 3.30669887e+01 -2.85213462e+01 2.03958946e+01 3 -2.49893824e+01 2.39160901e+01 1.58162963e+01 | -2.49893824e+01 2.39160901e+01 1.58162963e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TFF (Configuration in file "config-CuZr-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.0594074938975 2^p V(r_1,...,r_N) = 0.0594074938975 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 -1.70739634e+01 -1.16463294e+01 -1.50324875e+01 | -1.70739634e+01 -1.16463294e+01 -1.50324875e+01 1 2.81816813e+01 1.51492948e+01 -1.41457020e+01 | 2.81816813e+01 1.51492948e+01 -1.41457020e+01 2 3.01590234e+00 -1.35251118e+01 9.92331359e+00 | 3.01590234e+00 -1.35251118e+01 9.92331359e+00 3 -1.41236202e+01 1.00221464e+01 1.92548758e+01 | -1.41236202e+01 1.00221464e+01 1.92548758e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = FTT (Configuration in file "config-CuZr-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)) = 11.2883653856 2^p V(r_1,...,r_N) = 11.2883653856 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 -3.42995963e+01 -2.96149109e+01 -1.35477136e+01 | -3.42995963e+01 -2.96149109e+01 -1.35477136e+01 1 3.88247016e+01 3.67744433e+01 -2.67312035e+01 | 3.88247016e+01 3.67744433e+01 -2.67312035e+01 2 6.79727069e+00 -1.61227104e+01 2.58417760e+01 | 6.79727069e+00 -1.61227104e+01 2.58417760e+01 3 -1.13223760e+01 8.96317796e+00 1.44371411e+01 | -1.13223760e+01 8.96317796e+00 1.44371411e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = FTF (Configuration in file "config-CuZr-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)) = 2.46998682359 2^p V(r_1,...,r_N) = 2.46998682359 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 -9.72548208e+00 -9.08688011e+00 -8.74524541e+00 | -9.72548208e+00 -9.08688011e+00 -8.74524541e+00 1 1.65507536e+01 1.96203711e+01 -2.36328099e+01 | 1.65507536e+01 1.96203711e+01 -2.36328099e+01 2 1.38263173e+01 -2.95532570e+01 1.44491666e+01 | 1.38263173e+01 -2.95532570e+01 1.44491666e+01 3 -2.06515888e+01 1.90197660e+01 1.79288887e+01 | -2.06515888e+01 1.90197660e+01 1.79288887e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = FFT (Configuration in file "config-CuZr-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)) = 2.65115219233 2^p V(r_1,...,r_N) = 2.65115219233 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 -1.87698431e+01 -1.39774480e+01 -1.80725995e+01 | -1.87698431e+01 -1.39774480e+01 -1.80725995e+01 1 2.78190506e+01 6.38972020e+00 -1.91215153e+01 | 2.78190506e+01 6.38972020e+00 -1.91215153e+01 2 1.60562697e+01 -2.81943264e+00 1.40589375e+01 | 1.60562697e+01 -2.81943264e+00 1.40589375e+01 3 -2.51054772e+01 1.04071604e+01 2.31351773e+01 | -2.51054772e+01 1.04071604e+01 2.31351773e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.