!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LiuAdams_1998_AlMg__MO_019873715786_000 Supported species : Al Mg 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)) = 0.494763322614 2^p V(r_1,...,r_N) = 0.494763322614 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 -7.04608946e+00 -7.21832222e+00 -8.77558292e+00 | -7.04608946e+00 -7.21832222e+00 -8.77558292e+00 1 4.96508535e+00 3.46416370e+00 -3.12346046e+00 | 4.96508535e+00 3.46416370e+00 -3.12346046e+00 2 5.73345695e+00 -4.56751546e+00 6.41229889e+00 | 5.73345695e+00 -4.56751546e+00 6.41229889e+00 3 -3.65245283e+00 8.32167397e+00 5.48674449e+00 | -3.65245283e+00 8.32167397e+00 5.48674449e+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)) = 2.91729699196 2^p V(r_1,...,r_N) = 2.91729699196 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 -9.58273621e+00 -6.70061827e+00 -6.08523857e+00 | -9.58273621e+00 -6.70061827e+00 -6.08523857e+00 1 7.09498232e+00 5.69077425e+00 -8.70741064e+00 | 7.09498232e+00 5.69077425e+00 -8.70741064e+00 2 8.41218276e+00 -8.25902709e+00 1.05855752e+01 | 8.41218276e+00 -8.25902709e+00 1.05855752e+01 3 -5.92442887e+00 9.26887111e+00 4.20707402e+00 | -5.92442887e+00 9.26887111e+00 4.20707402e+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)) = 6.20798457379 2^p V(r_1,...,r_N) = 6.20798457379 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 -9.05723992e+00 -9.20209456e+00 -1.27339814e+01 | -9.05723992e+00 -9.20209456e+00 -1.27339814e+01 1 1.17146316e+01 1.13231600e+01 -7.18806326e+00 | 1.17146316e+01 1.13231600e+01 -7.18806326e+00 2 8.12330094e+00 -1.03743945e+01 1.10748483e+01 | 8.12330094e+00 -1.03743945e+01 1.10748483e+01 3 -1.07806926e+01 8.25332909e+00 8.84719639e+00 | -1.07806926e+01 8.25332909e+00 8.84719639e+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)) = 11.6316165826 2^p V(r_1,...,r_N) = 11.6316165826 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 -8.91379537e+00 -9.92327477e+00 -1.03738683e+01 | -8.91379537e+00 -9.92327477e+00 -1.03738683e+01 1 9.44326584e+00 1.10524402e+01 -7.65332231e+00 | 9.44326584e+00 1.10524402e+01 -7.65332231e+00 2 9.70030317e+00 -1.06947347e+01 1.04349962e+01 | 9.70030317e+00 -1.06947347e+01 1.04349962e+01 3 -1.02297736e+01 9.56556930e+00 7.59219444e+00 | -1.02297736e+01 9.56556930e+00 7.59219444e+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)) = 5.89842525611 2^p V(r_1,...,r_N) = 5.89842525611 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 -1.15287821e+01 -8.82422245e+00 -1.05797427e+01 | -1.15287821e+01 -8.82422245e+00 -1.05797427e+01 1 8.82988424e+00 1.01577380e+01 -8.60601821e+00 | 8.82988424e+00 1.01577380e+01 -8.60601821e+00 2 1.08755718e+01 -1.14966411e+01 9.05920861e+00 | 1.08755718e+01 -1.14966411e+01 9.05920861e+00 3 -8.17667397e+00 1.01631255e+01 1.01265523e+01 | -8.17667397e+00 1.01631255e+01 1.01265523e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.954152869665 2^p V(r_1,...,r_N) = 0.954152869665 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 -9.90393419e+00 -8.43301870e+00 -6.46972597e+00 | -9.90393419e+00 -8.43301870e+00 -6.46972597e+00 1 5.96260593e+00 8.25585079e+00 -7.15419352e+00 | 5.96260593e+00 8.25585079e+00 -7.15419352e+00 2 7.65559444e+00 -4.26796217e+00 1.07425936e+01 | 7.65559444e+00 -4.26796217e+00 1.07425936e+01 3 -3.71426618e+00 4.44513008e+00 2.88132593e+00 | -3.71426618e+00 4.44513008e+00 2.88132593e+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)) = 9.63119774103 2^p V(r_1,...,r_N) = 9.63119774103 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 -9.29235995e+00 -8.65471839e+00 -1.27135400e+01 | -9.29235995e+00 -8.65471839e+00 -1.27135400e+01 1 1.15349959e+01 9.73413701e+00 -8.23739841e+00 | 1.15349959e+01 9.73413701e+00 -8.23739841e+00 2 7.67105143e+00 -9.36654829e+00 1.20317556e+01 | 7.67105143e+00 -9.36654829e+00 1.20317556e+01 3 -9.91368734e+00 8.28712967e+00 8.91918280e+00 | -9.91368734e+00 8.28712967e+00 8.91918280e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTT (Configuration in file "config-Mg-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 9.15882120825 2^p V(r_1,...,r_N) = 9.15882120825 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 -5.78822679e+00 -5.35706175e+00 -6.60219360e+00 | -5.78822679e+00 -5.35706175e+00 -6.60219360e+00 1 5.13962972e+00 5.78861347e+00 -4.28287245e+00 | 5.13962972e+00 5.78861347e+00 -4.28287245e+00 2 5.60876128e+00 -5.41234038e+00 5.61748446e+00 | 5.60876128e+00 -5.41234038e+00 5.61748446e+00 3 -4.96016422e+00 4.98078866e+00 5.26758159e+00 | -4.96016422e+00 4.98078866e+00 5.26758159e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTF (Configuration in file "config-Mg-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 9.26645338132 2^p V(r_1,...,r_N) = 9.26645338132 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 -5.46986752e+00 -5.22484073e+00 -5.82195094e+00 | -5.46986752e+00 -5.22484073e+00 -5.82195094e+00 1 5.00477489e+00 5.53668191e+00 -4.96335074e+00 | 5.00477489e+00 5.53668191e+00 -4.96335074e+00 2 5.36001098e+00 -4.64401557e+00 6.23138205e+00 | 5.36001098e+00 -4.64401557e+00 6.23138205e+00 3 -4.89491835e+00 4.33217439e+00 4.55391963e+00 | -4.89491835e+00 4.33217439e+00 4.55391963e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFT (Configuration in file "config-Mg-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.95906611502 2^p V(r_1,...,r_N) = 5.95906611502 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 -4.23045790e+00 -4.26307772e+00 -3.73764653e+00 | -4.23045790e+00 -4.26307772e+00 -3.73764653e+00 1 4.72395270e+00 3.04679747e+00 -5.40137120e+00 | 4.72395270e+00 3.04679747e+00 -5.40137120e+00 2 4.31885637e+00 -4.60748068e+00 5.37875947e+00 | 4.31885637e+00 -4.60748068e+00 5.37875947e+00 3 -4.81235117e+00 5.82376094e+00 3.76025826e+00 | -4.81235117e+00 5.82376094e+00 3.76025826e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFF (Configuration in file "config-Mg-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.03856694981 2^p V(r_1,...,r_N) = 6.03856694981 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 -4.14168487e+00 -4.42761717e+00 -3.74854624e+00 | -4.14168487e+00 -4.42761717e+00 -3.74854624e+00 1 4.86438827e+00 4.42496047e+00 -5.37338755e+00 | 4.86438827e+00 4.42496047e+00 -5.37338755e+00 2 3.78560266e+00 -4.75766077e+00 4.32836469e+00 | 3.78560266e+00 -4.75766077e+00 4.32836469e+00 3 -4.50830605e+00 4.76031748e+00 4.79356910e+00 | -4.50830605e+00 4.76031748e+00 4.79356910e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTT (Configuration in file "config-Mg-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 3.30548391325 2^p V(r_1,...,r_N) = 3.30548391325 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 -3.61845584e+00 -3.73165702e+00 -3.15273784e+00 | -3.61845584e+00 -3.73165702e+00 -3.15273784e+00 1 5.66490995e+00 4.65744673e+00 -4.30476265e+00 | 5.66490995e+00 4.65744673e+00 -4.30476265e+00 2 1.99698262e+00 -3.85597716e+00 3.45082188e+00 | 1.99698262e+00 -3.85597716e+00 3.45082188e+00 3 -4.04343672e+00 2.93018745e+00 4.00667861e+00 | -4.04343672e+00 2.93018745e+00 4.00667861e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTF (Configuration in file "config-Mg-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.16137401727 2^p V(r_1,...,r_N) = 5.16137401727 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 -3.82062665e+00 -5.06447329e+00 -4.47677785e+00 | -3.82062665e+00 -5.06447329e+00 -4.47677785e+00 1 4.09363858e+00 4.20073379e+00 -4.25739275e+00 | 4.09363858e+00 4.20073379e+00 -4.25739275e+00 2 4.85557379e+00 -3.06501352e+00 2.81209954e+00 | 4.85557379e+00 -3.06501352e+00 2.81209954e+00 3 -5.12858572e+00 3.92875302e+00 5.92207106e+00 | -5.12858572e+00 3.92875302e+00 5.92207106e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FFT (Configuration in file "config-Mg-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 12.0424124014 2^p V(r_1,...,r_N) = 12.0424124014 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 -6.49200678e+00 -5.74668803e+00 -5.02802934e+00 | -6.49200678e+00 -5.74668803e+00 -5.02802934e+00 1 7.04671554e+00 3.53373697e+00 -6.35204742e+00 | 7.04671554e+00 3.53373697e+00 -6.35204742e+00 2 4.84761441e+00 -5.60600592e+00 6.56572346e+00 | 4.84761441e+00 -5.60600592e+00 6.56572346e+00 3 -5.40232318e+00 7.81895699e+00 4.81435330e+00 | -5.40232318e+00 7.81895699e+00 4.81435330e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TTT (Configuration in file "config-AlMg-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)) = 6.54853868528 2^p V(r_1,...,r_N) = 6.54853868528 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 -5.33243116e+00 -5.20364748e+00 -4.94382378e+00 | -5.33243116e+00 -5.20364748e+00 -4.94382378e+00 1 6.72460738e+00 4.63275456e+00 -6.57310879e+00 | 6.72460738e+00 4.63275456e+00 -6.57310879e+00 2 5.67493559e+00 -5.58095120e+00 5.28897004e+00 | 5.67493559e+00 -5.58095120e+00 5.28897004e+00 3 -7.06711181e+00 6.15184412e+00 6.22796253e+00 | -7.06711181e+00 6.15184412e+00 6.22796253e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TTF (Configuration in file "config-AlMg-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)) = 6.69371912774 2^p V(r_1,...,r_N) = 6.69371912774 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 -7.03859345e+00 -5.18660656e+00 -5.24858731e+00 | -7.03859345e+00 -5.18660656e+00 -5.24858731e+00 1 7.95289417e+00 8.32787105e+00 -6.11676927e+00 | 7.95289417e+00 8.32787105e+00 -6.11676927e+00 2 4.49101592e+00 -8.31171013e+00 6.58742655e+00 | 4.49101592e+00 -8.31171013e+00 6.58742655e+00 3 -5.40531664e+00 5.17044563e+00 4.77793003e+00 | -5.40531664e+00 5.17044563e+00 4.77793003e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TFT (Configuration in file "config-AlMg-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)) = 5.22777692923 2^p V(r_1,...,r_N) = 5.22777692923 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 -7.05306982e+00 -5.27517661e+00 -7.02951853e+00 | -7.05306982e+00 -5.27517661e+00 -7.02951853e+00 1 6.98076291e+00 5.44786527e+00 -5.23047200e+00 | 6.98076291e+00 5.44786527e+00 -5.23047200e+00 2 5.95537856e+00 -6.80721807e+00 6.99940456e+00 | 5.95537856e+00 -6.80721807e+00 6.99940456e+00 3 -5.88307165e+00 6.63452941e+00 5.26058596e+00 | -5.88307165e+00 6.63452941e+00 5.26058596e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TFF (Configuration in file "config-AlMg-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)) = -0.183276808564 2^p V(r_1,...,r_N) = -0.183276808564 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 -3.09993640e+00 -3.31705811e+00 -3.60814513e+00 | -3.09993640e+00 -3.31705811e+00 -3.60814513e+00 1 2.64772279e+00 5.04731394e+00 -3.77672475e+00 | 2.64772279e+00 5.04731394e+00 -3.77672475e+00 2 3.19551996e+00 -4.66315309e+00 3.85459261e+00 | 3.19551996e+00 -4.66315309e+00 3.85459261e+00 3 -2.74330636e+00 2.93289727e+00 3.53027727e+00 | -2.74330636e+00 2.93289727e+00 3.53027727e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FTT (Configuration in file "config-AlMg-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)) = -1.0951610289 2^p V(r_1,...,r_N) = -1.0951610289 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 -3.28231054e+00 -2.78956799e+00 -1.95854233e+00 | -3.28231054e+00 -2.78956799e+00 -1.95854233e+00 1 3.44488601e+00 2.68619975e+00 -2.00508012e+00 | 3.44488601e+00 2.68619975e+00 -2.00508012e+00 2 2.69294717e+00 -3.43129298e+00 1.89035736e+00 | 2.69294717e+00 -3.43129298e+00 1.89035736e+00 3 -2.85552264e+00 3.53466123e+00 2.07326508e+00 | -2.85552264e+00 3.53466123e+00 2.07326508e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FTF (Configuration in file "config-AlMg-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)) = 4.07270430835 2^p V(r_1,...,r_N) = 4.07270430835 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 -4.82253968e+00 -6.47245315e+00 -7.73563541e+00 | -4.82253968e+00 -6.47245315e+00 -7.73563541e+00 1 3.19364413e+00 3.63824992e+00 -3.47165017e+00 | 3.19364413e+00 3.63824992e+00 -3.47165017e+00 2 7.37829592e+00 -3.07220116e+00 7.60108722e+00 | 7.37829592e+00 -3.07220116e+00 7.60108722e+00 3 -5.74940036e+00 5.90640439e+00 3.60619836e+00 | -5.74940036e+00 5.90640439e+00 3.60619836e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FFT (Configuration in file "config-AlMg-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)) = 4.36424738387 2^p V(r_1,...,r_N) = 4.36424738387 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 -7.26071134e+00 -7.41127931e+00 -3.95679186e+00 | -7.26071134e+00 -7.41127931e+00 -3.95679186e+00 1 5.17900130e+00 9.67603805e+00 -7.20985250e+00 | 5.17900130e+00 9.67603805e+00 -7.20985250e+00 2 6.64484824e+00 -5.44506215e+00 5.57796399e+00 | 6.64484824e+00 -5.44506215e+00 5.57796399e+00 3 -4.56313820e+00 3.18030342e+00 5.58868037e+00 | -4.56313820e+00 3.18030342e+00 5.58868037e+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.