!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MEAM_Wagner_2007_SiC__SM_264944083668_000 Supported species : C Si random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTT (Configuration in file "config-C-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)) = 93.3385532839 2^p V(r_1,...,r_N) = 93.3385532839 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 9.71933094e+01 -6.16276184e+02 -7.32112438e+02 | 9.71933094e+01 -6.16276184e+02 -7.32112438e+02 1 -2.31010693e+01 -3.33140705e+01 -3.13970371e+01 | -2.31010693e+01 -3.33140705e+01 -3.13970371e+01 2 -1.44601944e+02 1.32245816e+02 -1.35127806e+01 | -1.44601944e+02 1.32245816e+02 -1.35127806e+01 3 7.05097043e+01 5.17344438e+02 7.77022255e+02 | 7.05097043e+01 5.17344438e+02 7.77022255e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-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)) = -9.51235359492 2^p V(r_1,...,r_N) = -9.51235359492 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 -4.45046678e+00 -6.25809820e+00 -2.87547040e+00 | -4.45046678e+00 -6.25809820e+00 -2.87547040e+00 1 4.16501096e+00 1.74948368e+01 -1.58685236e+01 | 4.16501096e+00 1.74948368e+01 -1.58685236e+01 2 1.15870998e+01 -2.14882624e+01 1.78514923e+01 | 1.15870998e+01 -2.14882624e+01 1.78514923e+01 3 -1.13016440e+01 1.02515237e+01 8.92501681e-01 | -1.13016440e+01 1.02515237e+01 8.92501681e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFT (Configuration in file "config-C-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)) = -12.0026979587 2^p V(r_1,...,r_N) = -12.0026979587 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 1.02755692e+00 -3.68666780e-01 -8.33082565e-01 | 1.02755692e+00 -3.68666780e-01 -8.33082565e-01 1 2.07621447e+00 7.62247167e+00 -8.52444689e+00 | 2.07621447e+00 7.62247167e+00 -8.52444689e+00 2 1.67390181e+00 -1.00539829e+01 6.88620269e+00 | 1.67390181e+00 -1.00539829e+01 6.88620269e+00 3 -4.77767320e+00 2.80017804e+00 2.47132677e+00 | -4.77767320e+00 2.80017804e+00 2.47132677e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFF (Configuration in file "config-C-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)) = 12.8594391921 2^p V(r_1,...,r_N) = 12.8594391921 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 -3.76421550e+01 -3.14935494e+01 -5.45617955e+00 | -3.76421550e+01 -3.14935494e+01 -5.45617955e+00 1 4.01105224e+01 5.09825117e+01 -2.95759106e+01 | 4.01105224e+01 5.09825117e+01 -2.95759106e+01 2 1.08642236e+02 -1.48864860e+02 8.22243995e+00 | 1.08642236e+02 -1.48864860e+02 8.22243995e+00 3 -1.11110604e+02 1.29375897e+02 2.68096502e+01 | -1.11110604e+02 1.29375897e+02 2.68096502e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTT (Configuration in file "config-C-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 3.39110839219 2^p V(r_1,...,r_N) = 3.39110839219 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 -5.58238508e+01 -1.37581054e+02 -1.05361671e+02 | -5.58238508e+01 -1.37581054e+02 -1.05361671e+02 1 2.31780159e+01 6.20596745e+01 -6.93280758e+01 | 2.31780159e+01 6.20596745e+01 -6.93280758e+01 2 -6.42624176e+01 2.97151648e+01 7.14651203e+01 | -6.42624176e+01 2.97151648e+01 7.14651203e+01 3 9.69082525e+01 4.58062148e+01 1.03224627e+02 | 9.69082525e+01 4.58062148e+01 1.03224627e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTF (Configuration in file "config-C-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)) = 9.28074661668 2^p V(r_1,...,r_N) = 9.28074661668 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 -4.52096118e+01 -5.93228862e+01 -5.26294876e+01 | -4.52096118e+01 -5.93228862e+01 -5.26294876e+01 1 2.62884220e+01 2.58014371e+01 -2.69592827e+01 | 2.62884220e+01 2.58014371e+01 -2.69592827e+01 2 6.05866671e+01 -2.27645914e+01 4.25454472e+01 | 6.05866671e+01 -2.27645914e+01 4.25454472e+01 3 -4.16654773e+01 5.62860404e+01 3.70433231e+01 | -4.16654773e+01 5.62860404e+01 3.70433231e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-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)) = -12.2494059902 2^p V(r_1,...,r_N) = -12.2494059902 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 -2.07570255e+00 -5.01065069e+00 -4.30985214e+00 | -2.07570255e+00 -5.01065069e+00 -4.30985214e+00 1 4.23501262e+00 3.80212268e+00 -4.12741824e+00 | 4.23501262e+00 3.80212268e+00 -4.12741824e+00 2 2.01018054e+00 -1.88990257e+00 2.26417434e+00 | 2.01018054e+00 -1.88990257e+00 2.26417434e+00 3 -4.16949061e+00 3.09843057e+00 6.17309604e+00 | -4.16949061e+00 3.09843057e+00 6.17309604e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTT (Configuration in file "config-Si-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)) = 187.286340804 2^p V(r_1,...,r_N) = 187.286340804 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 -2.40879533e+02 -9.52862810e+01 -2.79038104e+02 | -2.40879533e+02 -9.52862810e+01 -2.79038104e+02 1 -3.69514787e+02 2.55882320e+02 1.26549229e+02 | -3.69514787e+02 2.55882320e+02 1.26549229e+02 2 5.45654977e+02 -4.77842364e+02 4.49956631e+02 | 5.45654977e+02 -4.77842364e+02 4.49956631e+02 3 6.47393430e+01 3.17246325e+02 -2.97467756e+02 | 6.47393430e+01 3.17246325e+02 -2.97467756e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTF (Configuration in file "config-Si-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)) = 176.901529213 2^p V(r_1,...,r_N) = 176.901529213 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 -2.17410641e+02 -1.60219804e+02 -1.65857689e+02 | -2.17410641e+02 -1.60219804e+02 -1.65857689e+02 1 7.71804285e+01 1.61449569e+02 -1.28202617e+01 | 7.71804285e+01 1.61449569e+02 -1.28202617e+01 2 2.06799463e+02 -1.52610547e+02 1.70843804e+02 | 2.06799463e+02 -1.52610547e+02 1.70843804e+02 3 -6.65692509e+01 1.51380781e+02 7.83414703e+00 | -6.65692509e+01 1.51380781e+02 7.83414703e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFT (Configuration in file "config-Si-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)) = 192.062099642 2^p V(r_1,...,r_N) = 192.062099642 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 -4.39551177e+02 -2.77419994e+02 -2.53582785e+02 | -4.39551177e+02 -2.77419994e+02 -2.53582785e+02 1 4.31422033e+02 -2.58432538e+01 9.41106123e+01 | 4.31422033e+02 -2.58432538e+01 9.41106123e+01 2 2.43263273e+02 2.18370698e+02 2.67661786e+01 | 2.43263273e+02 2.18370698e+02 2.67661786e+01 3 -2.35134129e+02 8.48925500e+01 1.32705994e+02 | -2.35134129e+02 8.48925500e+01 1.32705994e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFF (Configuration in file "config-Si-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)) = 20.3618451314 2^p V(r_1,...,r_N) = 20.3618451314 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 -3.75810889e+01 -3.85791643e+01 -4.10133586e+01 | -3.75810889e+01 -3.85791643e+01 -4.10133586e+01 1 2.48379945e+01 9.72564180e+00 -7.19719626e+00 | 2.48379945e+01 9.72564180e+00 -7.19719626e+00 2 3.92967218e+01 -1.81017536e+01 1.74893094e+01 | 3.92967218e+01 -1.81017536e+01 1.74893094e+01 3 -2.65536274e+01 4.69552762e+01 3.07212454e+01 | -2.65536274e+01 4.69552762e+01 3.07212454e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTT (Configuration in file "config-Si-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)) = 41.0064050555 2^p V(r_1,...,r_N) = 41.0064050555 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 -3.30525391e+01 -3.06641572e+01 -2.75789818e+01 | -3.30525391e+01 -3.06641572e+01 -2.75789818e+01 1 5.86920495e+01 4.77602701e+01 -7.05517998e+01 | 5.86920495e+01 4.77602701e+01 -7.05517998e+01 2 1.94278844e+01 -5.12954366e+01 6.07457979e+01 | 1.94278844e+01 -5.12954366e+01 6.07457979e+01 3 -4.50673949e+01 3.41993238e+01 3.73849837e+01 | -4.50673949e+01 3.41993238e+01 3.73849837e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTF (Configuration in file "config-Si-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)) = 254.600705271 2^p V(r_1,...,r_N) = 254.600705271 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 -4.17981447e+02 -1.20632453e+03 -5.51040226e+02 | -4.17981447e+02 -1.20632453e+03 -5.51040226e+02 1 -3.41284706e+02 7.28601686e+02 5.87239624e+02 | -3.41284706e+02 7.28601686e+02 5.87239624e+02 2 2.26046542e+02 -1.64009007e+02 1.73144185e+02 | 2.26046542e+02 -1.64009007e+02 1.73144185e+02 3 5.33219611e+02 6.41731846e+02 -2.09343584e+02 | 5.33219611e+02 6.41731846e+02 -2.09343584e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FFT (Configuration in file "config-Si-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)) = 589.660584092 2^p V(r_1,...,r_N) = 589.660584092 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 1.48815561e+03 3.05810323e+03 -3.06019003e+03 | 1.48815561e+03 3.05810323e+03 -3.06019003e+03 1 -3.11449706e+03 -1.05503311e+03 -2.00810505e+03 | -3.11449706e+03 -1.05503311e+03 -2.00810505e+03 2 1.87166505e+03 -2.44766923e+03 4.91430205e+03 | 1.87166505e+03 -2.44766923e+03 4.91430205e+03 3 -2.45323601e+02 4.44599116e+02 1.53993028e+02 | -2.45323601e+02 4.44599116e+02 1.53993028e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TTT (Configuration in file "config-CSi-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)) = 142.243875157 2^p V(r_1,...,r_N) = 142.243875157 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 -3.09766777e+02 -1.02349296e+02 -2.74569423e+02 | -3.09766777e+02 -1.02349296e+02 -2.74569423e+02 1 7.87795811e+01 8.60099365e+01 -5.55407955e+01 | 7.87795811e+01 8.60099365e+01 -5.55407955e+01 2 1.81972497e+02 5.14979036e+01 3.01205259e+02 | 1.81972497e+02 5.14979036e+01 3.01205259e+02 3 4.90146985e+01 -3.51585442e+01 2.89049597e+01 | 4.90146985e+01 -3.51585442e+01 2.89049597e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TTF (Configuration in file "config-CSi-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)) = 311.166774192 2^p V(r_1,...,r_N) = 311.166774192 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 -1.21346025e+03 -5.66119440e+01 -9.68192748e+02 | -1.21346025e+03 -5.66119440e+01 -9.68192748e+02 1 1.57805273e+03 -1.95172726e+03 1.40523230e+02 | 1.57805273e+03 -1.95172726e+03 1.40523230e+02 2 1.71973518e+03 1.45421452e+03 -1.03049976e+03 | 1.71973518e+03 1.45421452e+03 -1.03049976e+03 3 -2.08432766e+03 5.54124681e+02 1.85816927e+03 | -2.08432766e+03 5.54124681e+02 1.85816927e+03 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TFT (Configuration in file "config-CSi-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)) = 72.0662597836 2^p V(r_1,...,r_N) = 72.0662597836 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 -2.93642572e+02 -3.38747639e+02 1.84146451e+02 | -2.93642572e+02 -3.38747639e+02 1.84146451e+02 1 6.09622302e+02 3.94934468e+02 4.50037104e+01 | 6.09622302e+02 3.94934468e+02 4.50037104e+01 2 -2.75560097e+02 3.26686611e+01 -1.78442273e+02 | -2.75560097e+02 3.26686611e+01 -1.78442273e+02 3 -4.04196335e+01 -8.88554898e+01 -5.07078889e+01 | -4.04196335e+01 -8.88554898e+01 -5.07078889e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = TFF (Configuration in file "config-CSi-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)) = 333.196246006 2^p V(r_1,...,r_N) = 333.196246006 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 -1.67241017e+02 1.83645393e+01 6.45385104e+01 | -1.67241017e+02 1.83645393e+01 6.45385104e+01 1 3.75902071e+02 5.88221295e+02 -1.06288455e+03 | 3.75902071e+02 5.88221295e+02 -1.06288455e+03 2 -2.17690092e+02 -2.48148193e+02 7.87235916e+02 | -2.17690092e+02 -2.48148193e+02 7.87235916e+02 3 9.02903755e+00 -3.58437641e+02 2.11110124e+02 | 9.02903755e+00 -3.58437641e+02 2.11110124e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FTT (Configuration in file "config-CSi-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)) = 82.6324548147 2^p V(r_1,...,r_N) = 82.6324548147 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 -5.12963483e+02 -3.16458414e+02 -1.03022524e+01 | -5.12963483e+02 -3.16458414e+02 -1.03022524e+01 1 2.62630851e+02 3.36961750e+02 1.40957855e+02 | 2.62630851e+02 3.36961750e+02 1.40957855e+02 2 1.13562489e+02 8.06547831e+01 4.44805064e+01 | 1.13562489e+02 8.06547831e+01 4.44805064e+01 3 1.36770143e+02 -1.01158119e+02 -1.75136109e+02 | 1.36770143e+02 -1.01158119e+02 -1.75136109e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FTF (Configuration in file "config-CSi-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)) = 32.4907510182 2^p V(r_1,...,r_N) = 32.4907510182 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 -4.91193497e+01 -3.65052732e+02 -2.66353848e+02 | -4.91193497e+01 -3.65052732e+02 -2.66353848e+02 1 -7.32927389e+01 7.01750128e+01 6.52861671e+01 | -7.32927389e+01 7.01750128e+01 6.52861671e+01 2 -3.04814308e+01 7.73273468e-01 4.57831737e+01 | -3.04814308e+01 7.73273468e-01 4.57831737e+01 3 1.52893519e+02 2.94104446e+02 1.55284507e+02 | 1.52893519e+02 2.94104446e+02 1.55284507e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = C Si, PBC = FFT (Configuration in file "config-CSi-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)) = 299.919863078 2^p V(r_1,...,r_N) = 299.919863078 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 -1.20992125e+02 -3.26398629e+02 -1.03977598e+02 | -1.20992125e+02 -3.26398629e+02 -1.03977598e+02 1 -4.57399892e+02 8.39694647e+02 -1.23567228e+02 | -4.57399892e+02 8.39694647e+02 -1.23567228e+02 2 3.57177328e+02 -1.05708660e+03 5.34404562e+02 | 3.57177328e+02 -1.05708660e+03 5.34404562e+02 3 2.21214688e+02 5.43790581e+02 -3.06859736e+02 | 2.21214688e+02 5.43790581e+02 -3.06859736e+02 ------------------------------------------------------------------------------------------------------------------------ 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.