!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_PunMishin_2009_NiAl__MO_751354403791_005 Supported species : Al Ni random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.5321152892 2^p V(r_1,...,r_N) = -2.5321152892 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 -4.04795907e+00 -3.24940740e+00 -3.71034369e+00 | -4.04795907e+00 -3.24940740e+00 -3.71034369e+00 1 3.70524030e+00 2.51731422e+00 -2.71801511e+00 | 3.70524030e+00 2.51731422e+00 -2.71801511e+00 2 3.21624779e+00 -3.37475117e+00 3.93952271e+00 | 3.21624779e+00 -3.37475117e+00 3.93952271e+00 3 -2.87352901e+00 4.10684435e+00 2.48883609e+00 | -2.87352901e+00 4.10684435e+00 2.48883609e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.05535733227 2^p V(r_1,...,r_N) = -1.05535733227 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 -4.67231316e+00 -3.92326626e+00 -3.22114493e+00 | -4.67231316e+00 -3.92326626e+00 -3.22114493e+00 1 4.06488299e+00 2.61879096e+00 -4.81261811e+00 | 4.06488299e+00 2.61879096e+00 -4.81261811e+00 2 3.39958004e+00 -3.34500041e+00 4.79851008e+00 | 3.39958004e+00 -3.34500041e+00 4.79851008e+00 3 -2.79214987e+00 4.64947571e+00 3.23525296e+00 | -2.79214987e+00 4.64947571e+00 3.23525296e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.644899539675 2^p V(r_1,...,r_N) = 0.644899539675 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 -3.61288044e+00 -3.58923348e+00 -5.01213078e+00 | -3.61288044e+00 -3.58923348e+00 -5.01213078e+00 1 4.97503691e+00 4.49282647e+00 -3.06083625e+00 | 4.97503691e+00 4.49282647e+00 -3.06083625e+00 2 3.76442301e+00 -4.58231083e+00 4.45447249e+00 | 3.76442301e+00 -4.58231083e+00 4.45447249e+00 3 -5.12657948e+00 3.67871784e+00 3.61849454e+00 | -5.12657948e+00 3.67871784e+00 3.61849454e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.61743742594 2^p V(r_1,...,r_N) = 2.61743742594 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 -3.60861329e+00 -3.84065982e+00 -4.03949512e+00 | -3.60861329e+00 -3.84065982e+00 -4.03949512e+00 1 4.63118947e+00 4.49469908e+00 -3.69927055e+00 | 4.63118947e+00 4.49469908e+00 -3.69927055e+00 2 3.85461927e+00 -4.22541265e+00 4.17400346e+00 | 3.85461927e+00 -4.22541265e+00 4.17400346e+00 3 -4.87719545e+00 3.57137339e+00 3.56476220e+00 | -4.87719545e+00 3.57137339e+00 3.56476220e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.477845744245 2^p V(r_1,...,r_N) = 0.477845744245 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 -4.72517806e+00 -3.63304435e+00 -4.16288984e+00 | -4.72517806e+00 -3.63304435e+00 -4.16288984e+00 1 4.33317608e+00 4.16607547e+00 -4.09951253e+00 | 4.33317608e+00 4.16607547e+00 -4.09951253e+00 2 4.28663558e+00 -4.52992093e+00 3.56319018e+00 | 4.28663558e+00 -4.52992093e+00 3.56319018e+00 3 -3.89463360e+00 3.99688981e+00 4.69921219e+00 | -3.89463360e+00 3.99688981e+00 4.69921219e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.20321440295 2^p V(r_1,...,r_N) = -2.20321440295 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 -3.79264821e+00 -4.07133916e+00 -3.42103113e+00 | -3.79264821e+00 -4.07133916e+00 -3.42103113e+00 1 2.45240648e+00 3.42284824e+00 -3.20993457e+00 | 2.45240648e+00 3.42284824e+00 -3.20993457e+00 2 4.03131858e+00 -2.43903603e+00 4.58765040e+00 | 4.03131858e+00 -2.43903603e+00 4.58765040e+00 3 -2.69107686e+00 3.08752695e+00 2.04331530e+00 | -2.69107686e+00 3.08752695e+00 2.04331530e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.96065488722 2^p V(r_1,...,r_N) = 1.96065488722 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 -3.70206545e+00 -3.68637407e+00 -5.53342727e+00 | -3.70206545e+00 -3.68637407e+00 -5.53342727e+00 1 5.07988053e+00 3.84019199e+00 -3.71132488e+00 | 5.07988053e+00 3.84019199e+00 -3.71132488e+00 2 3.28624925e+00 -3.82716824e+00 4.81472064e+00 | 3.28624925e+00 -3.82716824e+00 4.81472064e+00 3 -4.66406434e+00 3.67335032e+00 4.43003151e+00 | -4.66406434e+00 3.67335032e+00 4.43003151e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-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)) = -5.41294474451 2^p V(r_1,...,r_N) = -5.41294474451 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 -3.33745217e+00 -2.26742949e+00 -3.89245738e+00 | -3.33745217e+00 -2.26742949e+00 -3.89245738e+00 1 1.57385351e+00 2.90021694e+00 -1.80136816e+00 | 1.57385351e+00 2.90021694e+00 -1.80136816e+00 2 4.14165128e+00 -3.55856296e+00 3.85419195e+00 | 4.14165128e+00 -3.55856296e+00 3.85419195e+00 3 -2.37805262e+00 2.92577551e+00 1.83963359e+00 | -2.37805262e+00 2.92577551e+00 1.83963359e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-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)) = -5.18118052575 2^p V(r_1,...,r_N) = -5.18118052575 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 -3.13935744e+00 -2.31949170e+00 -2.53643138e+00 | -3.13935744e+00 -2.31949170e+00 -2.53643138e+00 1 2.10731492e+00 3.32560611e+00 -2.35317604e+00 | 2.10731492e+00 3.32560611e+00 -2.35317604e+00 2 4.16615941e+00 -3.82369261e+00 3.69827356e+00 | 4.16615941e+00 -3.82369261e+00 3.69827356e+00 3 -3.13411690e+00 2.81757819e+00 1.19133386e+00 | -3.13411690e+00 2.81757819e+00 1.19133386e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-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)) = -6.83846337939 2^p V(r_1,...,r_N) = -6.83846337939 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 -5.05375974e-01 -9.55254084e-01 -7.03708777e-01 | -5.05375974e-01 -9.55254084e-01 -7.03708777e-01 1 1.02614677e+00 1.65888716e+00 -2.96379482e+00 | 1.02614677e+00 1.65888716e+00 -2.96379482e+00 2 1.32636484e+00 -2.91728326e+00 2.85126548e+00 | 1.32636484e+00 -2.91728326e+00 2.85126548e+00 3 -1.84713563e+00 2.21365019e+00 8.16238114e-01 | -1.84713563e+00 2.21365019e+00 8.16238114e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-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)) = -6.47278935188 2^p V(r_1,...,r_N) = -6.47278935188 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 -1.19945436e+00 -2.89052419e+00 -2.80011362e+00 | -1.19945436e+00 -2.89052419e+00 -2.80011362e+00 1 1.33757774e+00 1.31793648e+00 -1.94947989e+00 | 1.33757774e+00 1.31793648e+00 -1.94947989e+00 2 1.23732738e+00 -1.89144428e+00 1.67688284e+00 | 1.23732738e+00 -1.89144428e+00 1.67688284e+00 3 -1.37545076e+00 3.46403199e+00 3.07271067e+00 | -1.37545076e+00 3.46403199e+00 3.07271067e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.30282949058 2^p V(r_1,...,r_N) = -5.30282949058 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 -1.90064662e+00 -1.06221850e+00 -2.11020779e+00 | -1.90064662e+00 -1.06221850e+00 -2.11020779e+00 1 2.41443377e+00 2.39118948e+00 -4.02003612e+00 | 2.41443377e+00 2.39118948e+00 -4.02003612e+00 2 3.91980743e+00 -3.89914676e+00 3.39571475e+00 | 3.91980743e+00 -3.89914676e+00 3.39571475e+00 3 -4.43359457e+00 2.57017578e+00 2.73452916e+00 | -4.43359457e+00 2.57017578e+00 2.73452916e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-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)) = -6.95658106497 2^p V(r_1,...,r_N) = -6.95658106497 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 -8.99082430e-01 -1.18288322e+00 -1.99765559e+00 | -8.99082430e-01 -1.18288322e+00 -1.99765559e+00 1 1.17218115e+00 2.35800335e+00 -1.92690432e+00 | 1.17218115e+00 2.35800335e+00 -1.92690432e+00 2 1.10808664e+00 -3.04410066e+00 2.61445039e+00 | 1.10808664e+00 -3.04410066e+00 2.61445039e+00 3 -1.38118536e+00 1.86898053e+00 1.31010952e+00 | -1.38118536e+00 1.86898053e+00 1.31010952e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-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)) = -3.30059858568 2^p V(r_1,...,r_N) = -3.30059858568 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 -3.52454407e+00 -5.78449158e+00 -3.30590274e+00 | -3.52454407e+00 -5.78449158e+00 -3.30590274e+00 1 3.90837416e+00 2.84806952e+00 -3.59123777e+00 | 3.90837416e+00 2.84806952e+00 -3.59123777e+00 2 2.94866819e+00 -1.53351330e+00 1.62220871e+00 | 2.94866819e+00 -1.53351330e+00 1.62220871e+00 3 -3.33249828e+00 4.46993535e+00 5.27493179e+00 | -3.33249828e+00 4.46993535e+00 5.27493179e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = TTT (Configuration in file "config-AlNi-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)) = -5.31376390763 2^p V(r_1,...,r_N) = -5.31376390763 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 -3.10964120e+00 -3.24802938e+00 -2.68031108e+00 | -3.10964120e+00 -3.24802938e+00 -2.68031108e+00 1 5.45632399e+00 2.81285821e+00 -4.14447004e+00 | 5.45632399e+00 2.81285821e+00 -4.14447004e+00 2 1.43461263e+00 -3.38688052e+00 3.14960086e+00 | 1.43461263e+00 -3.38688052e+00 3.14960086e+00 3 -3.78129542e+00 3.82205169e+00 3.67518025e+00 | -3.78129542e+00 3.82205169e+00 3.67518025e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = TTF (Configuration in file "config-AlNi-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)) = -5.31416442986 2^p V(r_1,...,r_N) = -5.31416442986 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 -1.23735601e+01 -8.96025105e+00 -1.00215645e+00 | -1.23735601e+01 -8.96025105e+00 -1.00215645e+00 1 1.16670842e+01 8.69762915e+00 -2.52056541e+00 | 1.16670842e+01 8.69762915e+00 -2.52056541e+00 2 1.14779165e+00 -1.38319192e+00 1.63562810e+00 | 1.14779165e+00 -1.38319192e+00 1.63562810e+00 3 -4.41315752e-01 1.64581381e+00 1.88709375e+00 | -4.41315752e-01 1.64581381e+00 1.88709375e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = TFT (Configuration in file "config-AlNi-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)) = -6.34863195586 2^p V(r_1,...,r_N) = -6.34863195586 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 -1.38550349e+00 -1.48815658e+00 -1.08524971e+00 | -1.38550349e+00 -1.48815658e+00 -1.08524971e+00 1 2.80393608e+00 2.43342084e+00 -4.12919179e+00 | 2.80393608e+00 2.43342084e+00 -4.12919179e+00 2 1.87571889e+00 -3.27209867e+00 3.12584618e+00 | 1.87571889e+00 -3.27209867e+00 3.12584618e+00 3 -3.29415148e+00 2.32683440e+00 2.08859532e+00 | -3.29415148e+00 2.32683440e+00 2.08859532e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = TFF (Configuration in file "config-AlNi-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)) = -7.75335052485 2^p V(r_1,...,r_N) = -7.75335052485 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 -5.59466289e-01 -4.57090371e-01 4.73530045e-01 | -5.59466289e-01 -4.57090371e-01 4.73530045e-01 1 7.82188434e-01 1.49925685e+00 -1.07186560e+00 | 7.82188434e-01 1.49925685e+00 -1.07186560e+00 2 3.89214768e-01 -1.67014114e+00 9.68641080e-01 | 3.89214768e-01 -1.67014114e+00 9.68641080e-01 3 -6.11936913e-01 6.27974657e-01 -3.70305526e-01 | -6.11936913e-01 6.27974657e-01 -3.70305526e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = FTT (Configuration in file "config-AlNi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.67903444951 2^p V(r_1,...,r_N) = -5.67903444951 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 -1.77575056e+00 -2.09476303e+00 -2.85394320e+00 | -1.77575056e+00 -2.09476303e+00 -2.85394320e+00 1 7.68807204e-01 7.40683294e-01 -4.05967278e-01 | 7.68807204e-01 7.40683294e-01 -4.05967278e-01 2 3.28902128e+00 -1.27910208e+00 2.49711580e+00 | 3.28902128e+00 -1.27910208e+00 2.49711580e+00 3 -2.28207792e+00 2.63318182e+00 7.62794685e-01 | -2.28207792e+00 2.63318182e+00 7.62794685e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = FTF (Configuration in file "config-AlNi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.52730007106 2^p V(r_1,...,r_N) = -5.52730007106 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 -2.86968190e+00 -2.52781530e+00 -1.09699161e+00 | -2.86968190e+00 -2.52781530e+00 -1.09699161e+00 1 2.40510510e+00 4.29347456e+00 -4.13382556e+00 | 2.40510510e+00 4.29347456e+00 -4.13382556e+00 2 2.45763409e+00 -2.28603508e+00 2.70850859e+00 | 2.45763409e+00 -2.28603508e+00 2.70850859e+00 3 -1.99305728e+00 5.20375813e-01 2.52230858e+00 | -1.99305728e+00 5.20375813e-01 2.52230858e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ni, PBC = FFT (Configuration in file "config-AlNi-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)) = -7.30663160751 2^p V(r_1,...,r_N) = -7.30663160751 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 -7.50263543e-01 -5.75149059e-01 -3.03194315e-01 | -7.50263543e-01 -5.75149059e-01 -3.03194315e-01 1 2.16375616e+00 8.08910268e-01 -2.50247965e+00 | 2.16375616e+00 8.08910268e-01 -2.50247965e+00 2 1.23004134e+00 -1.58733217e+00 9.24566969e-01 | 1.23004134e+00 -1.58733217e+00 9.24566969e-01 3 -2.64353396e+00 1.35357096e+00 1.88110700e+00 | -2.64353396e+00 1.35357096e+00 1.88110700e+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.