!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyGrigorev1Terentyev_2017_W__MO_234187151804_000 Supported species : Re W random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = TTT (Configuration in file "config-Re-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)) = -3.74998621175 2^p V(r_1,...,r_N) = -3.74998621175 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 -1.43436652e+01 -2.23675083e+01 -2.47380777e+01 | -1.43436652e+01 -2.23675083e+01 -2.47380777e+01 1 9.89541918e+00 7.05816300e+00 -5.98133717e+00 | 9.89541918e+00 7.05816300e+00 -5.98133717e+00 2 1.20189184e+01 -9.27150387e+00 1.32038568e+01 | 1.20189184e+01 -9.27150387e+00 1.32038568e+01 3 -7.57067243e+00 2.45808491e+01 1.75155581e+01 | -7.57067243e+00 2.45808491e+01 1.75155581e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = TTF (Configuration in file "config-Re-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)) = 1.49348524986 2^p V(r_1,...,r_N) = 1.49348524986 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 -2.02025015e+01 -1.40238817e+01 -1.28088241e+01 | -2.02025015e+01 -1.40238817e+01 -1.28088241e+01 1 1.48428180e+01 1.20334323e+01 -1.82792299e+01 | 1.48428180e+01 1.20334323e+01 -1.82792299e+01 2 2.46928124e+01 -2.66584471e+01 2.26559729e+01 | 2.46928124e+01 -2.66584471e+01 2.26559729e+01 3 -1.93331289e+01 2.86488965e+01 8.43208107e+00 | -1.93331289e+01 2.86488965e+01 8.43208107e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = TFT (Configuration in file "config-Re-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)) = 8.05215422779 2^p V(r_1,...,r_N) = 8.05215422779 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 -1.96671605e+01 -2.57861135e+01 -3.29654460e+01 | -1.96671605e+01 -2.57861135e+01 -3.29654460e+01 1 2.66147744e+01 2.63778700e+01 -1.56230406e+01 | 2.66147744e+01 2.63778700e+01 -1.56230406e+01 2 1.71684966e+01 -2.28639636e+01 2.42361700e+01 | 1.71684966e+01 -2.28639636e+01 2.42361700e+01 3 -2.41161106e+01 2.22722072e+01 2.43523166e+01 | -2.41161106e+01 2.22722072e+01 2.43523166e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = TFF (Configuration in file "config-Re-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)) = 30.9734532835 2^p V(r_1,...,r_N) = 30.9734532835 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 -5.56596793e+01 -3.93483654e+01 -8.68935421e+01 | -5.56596793e+01 -3.93483654e+01 -8.68935421e+01 1 2.23685763e+01 2.71486421e+01 -1.81123590e+01 | 2.23685763e+01 2.71486421e+01 -1.81123590e+01 2 6.61442211e+01 -3.11877955e+01 6.82329033e+01 | 6.61442211e+01 -3.11877955e+01 6.82329033e+01 3 -3.28531180e+01 4.33875188e+01 3.67729978e+01 | -3.28531180e+01 4.33875188e+01 3.67729978e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = FTT (Configuration in file "config-Re-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)) = 7.13715129429 2^p V(r_1,...,r_N) = 7.13715129429 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 -2.71741970e+01 -1.94921140e+01 -2.58766356e+01 | -2.71741970e+01 -1.94921140e+01 -2.58766356e+01 1 1.88695902e+01 2.39128938e+01 -2.03869113e+01 | 1.88695902e+01 2.39128938e+01 -2.03869113e+01 2 2.57477638e+01 -2.71632541e+01 2.35774070e+01 | 2.57477638e+01 -2.71632541e+01 2.35774070e+01 3 -1.74431569e+01 2.27424744e+01 2.26861398e+01 | -1.74431569e+01 2.27424744e+01 2.26861398e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = FTF (Configuration in file "config-Re-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)) = -3.21264765869 2^p V(r_1,...,r_N) = -3.21264765869 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 -2.16087937e+01 -1.82456439e+01 -1.33830652e+01 | -2.16087937e+01 -1.82456439e+01 -1.33830652e+01 1 1.25717732e+01 1.80487265e+01 -1.45584014e+01 | 1.25717732e+01 1.80487265e+01 -1.45584014e+01 2 1.59939127e+01 -8.86864722e+00 2.26609161e+01 | 1.59939127e+01 -8.86864722e+00 2.26609161e+01 3 -6.95689210e+00 9.06556456e+00 5.28055050e+00 | -6.95689210e+00 9.06556456e+00 5.28055050e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Re, PBC = FFT (Configuration in file "config-Re-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)) = 27.2127688772 2^p V(r_1,...,r_N) = 27.2127688772 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 -2.21382103e+01 -2.03839101e+01 -2.76995223e+01 | -2.21382103e+01 -2.03839101e+01 -2.76995223e+01 1 2.87696701e+01 2.76284862e+01 -2.33478312e+01 | 2.87696701e+01 2.76284862e+01 -2.33478312e+01 2 7.64421430e+01 -8.12075478e+01 3.15266435e+01 | 7.64421430e+01 -8.12075478e+01 3.15266435e+01 3 -8.30736028e+01 7.39629716e+01 1.95207100e+01 | -8.30736028e+01 7.39629716e+01 1.95207100e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TTT (Configuration in file "config-W-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)) = 1.71771433213 2^p V(r_1,...,r_N) = 1.71771433213 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 -2.51511532e+01 -1.69896786e+01 -2.93484236e+01 | -2.51511532e+01 -1.69896786e+01 -2.93484236e+01 1 1.48147023e+01 2.15234238e+01 -1.59812528e+01 | 1.48147023e+01 2.15234238e+01 -1.59812528e+01 2 3.09739583e+01 -2.59087686e+01 2.86111312e+01 | 3.09739583e+01 -2.59087686e+01 2.86111312e+01 3 -2.06375074e+01 2.13750234e+01 1.67185451e+01 | -2.06375074e+01 2.13750234e+01 1.67185451e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TTF (Configuration in file "config-W-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)) = 4.33952717714 2^p V(r_1,...,r_N) = 4.33952717714 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 -2.31461838e+01 -1.79129299e+01 -1.92546235e+01 | -2.31461838e+01 -1.79129299e+01 -1.92546235e+01 1 1.74927033e+01 2.45819493e+01 -1.89853318e+01 | 1.74927033e+01 2.45819493e+01 -1.89853318e+01 2 3.94272098e+01 -3.51143880e+01 2.47395615e+01 | 3.94272098e+01 -3.51143880e+01 2.47395615e+01 3 -3.37737294e+01 2.84453686e+01 1.35003937e+01 | -3.37737294e+01 2.84453686e+01 1.35003937e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TFT (Configuration in file "config-W-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)) = -8.75671224334 2^p V(r_1,...,r_N) = -8.75671224334 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 -7.14932391e+00 -8.80640042e+00 -7.43434404e+00 | -7.14932391e+00 -8.80640042e+00 -7.43434404e+00 1 1.01018237e+01 1.30672792e+01 -2.31714917e+01 | 1.01018237e+01 1.30672792e+01 -2.31714917e+01 2 1.22225595e+01 -2.18692538e+01 2.32010123e+01 | 1.22225595e+01 -2.18692538e+01 2.32010123e+01 3 -1.51750593e+01 1.76083750e+01 7.40482349e+00 | -1.51750593e+01 1.76083750e+01 7.40482349e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TFF (Configuration in file "config-W-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)) = -6.95459099198 2^p V(r_1,...,r_N) = -6.95459099198 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 -9.18751052e+00 -2.72055089e+01 -2.26664585e+01 | -9.18751052e+00 -2.72055089e+01 -2.26664585e+01 1 1.07218076e+01 1.13255776e+01 -1.50245889e+01 | 1.07218076e+01 1.13255776e+01 -1.50245889e+01 2 5.98107495e+00 -1.18819659e+01 1.08448290e+01 | 5.98107495e+00 -1.18819659e+01 1.08448290e+01 3 -7.51537206e+00 2.77618972e+01 2.68462183e+01 | -7.51537206e+00 2.77618972e+01 2.68462183e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FTT (Configuration in file "config-W-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)) = -16.2652850972 2^p V(r_1,...,r_N) = -16.2652850972 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 -8.29994320e+00 -7.77456868e+00 -4.94499934e+00 | -8.29994320e+00 -7.77456868e+00 -4.94499934e+00 1 1.44613825e+01 1.14196198e+01 -1.05977620e+01 | 1.44613825e+01 1.14196198e+01 -1.05977620e+01 2 2.74663141e+00 -7.85596120e+00 7.28177482e+00 | 2.74663141e+00 -7.85596120e+00 7.28177482e+00 3 -8.90807073e+00 4.21091012e+00 8.26098652e+00 | -8.90807073e+00 4.21091012e+00 8.26098652e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FTF (Configuration in file "config-W-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)) = -10.8966817258 2^p V(r_1,...,r_N) = -10.8966817258 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 -6.89931461e+00 -1.91828289e+01 -1.80965415e+01 | -6.89931461e+00 -1.91828289e+01 -1.80965415e+01 1 1.04547707e+01 8.13081916e+00 -1.08736316e+01 | 1.04547707e+01 8.13081916e+00 -1.08736316e+01 2 9.10689135e+00 -5.54307131e+00 4.72411326e+00 | 9.10689135e+00 -5.54307131e+00 4.72411326e+00 3 -1.26623475e+01 1.65950810e+01 2.42460598e+01 | -1.26623475e+01 1.65950810e+01 2.42460598e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FFT (Configuration in file "config-W-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)) = 15.3115711345 2^p V(r_1,...,r_N) = 15.3115711345 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 -2.94336536e+01 -2.34065106e+01 -2.90566416e+01 | -2.94336536e+01 -2.34065106e+01 -2.90566416e+01 1 2.52716396e+01 1.75665841e+01 -3.24313974e+01 | 2.52716396e+01 1.75665841e+01 -3.24313974e+01 2 3.96467822e+01 -4.77966571e+01 4.33265142e+01 | 3.96467822e+01 -4.77966571e+01 4.33265142e+01 3 -3.54847682e+01 5.36365836e+01 1.81615248e+01 | -3.54847682e+01 5.36365836e+01 1.81615248e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = TTT (Configuration in file "config-ReW-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)) = 0.0705118571454 2^p V(r_1,...,r_N) = 0.0705118571454 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 -7.43356712e+00 -8.95585117e+00 -8.69404373e+00 | -7.43356712e+00 -8.95585117e+00 -8.69404373e+00 1 1.14155773e+01 2.46121841e+01 -3.37446403e+01 | 1.14155773e+01 2.46121841e+01 -3.37446403e+01 2 1.57676935e+01 -3.45811670e+01 3.07530169e+01 | 1.57676935e+01 -3.45811670e+01 3.07530169e+01 3 -1.97497037e+01 1.89248340e+01 1.16856671e+01 | -1.97497037e+01 1.89248340e+01 1.16856671e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = TTF (Configuration in file "config-ReW-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)) = -2.19238075659 2^p V(r_1,...,r_N) = -2.19238075659 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 -1.22486066e+01 -1.75949632e+01 -1.64625532e+01 | -1.22486066e+01 -1.75949632e+01 -1.64625532e+01 1 1.23063550e+01 2.28486533e+01 -1.53048368e+01 | 1.23063550e+01 2.28486533e+01 -1.53048368e+01 2 7.87969364e+00 -2.30380612e+01 1.77138956e+01 | 7.87969364e+00 -2.30380612e+01 1.77138956e+01 3 -7.93744203e+00 1.77843710e+01 1.40534944e+01 | -7.93744203e+00 1.77843710e+01 1.40534944e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = TFT (Configuration in file "config-ReW-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)) = -6.74980834981 2^p V(r_1,...,r_N) = -6.74980834981 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 -9.98909997e+00 -1.55343004e+01 -1.94222697e+01 | -9.98909997e+00 -1.55343004e+01 -1.94222697e+01 1 9.96563339e+00 9.46750246e+00 -9.36233593e+00 | 9.96563339e+00 9.46750246e+00 -9.36233593e+00 2 9.40298849e+00 -1.31796384e+01 1.22171659e+01 | 9.40298849e+00 -1.31796384e+01 1.22171659e+01 3 -9.37952192e+00 1.92464363e+01 1.65674398e+01 | -9.37952192e+00 1.92464363e+01 1.65674398e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = TFF (Configuration in file "config-ReW-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)) = -15.6425626838 2^p V(r_1,...,r_N) = -15.6425626838 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 -3.22863958e+00 -4.79897426e+00 -5.33708534e+00 | -3.22863958e+00 -4.79897426e+00 -5.33708534e+00 1 2.38558529e+00 8.92563069e+00 -6.98285287e+00 | 2.38558529e+00 8.92563069e+00 -6.98285287e+00 2 3.47220981e+00 -8.47687264e+00 7.28845861e+00 | 3.47220981e+00 -8.47687264e+00 7.28845861e+00 3 -2.62915552e+00 4.35021621e+00 5.03147960e+00 | -2.62915552e+00 4.35021621e+00 5.03147960e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = FTT (Configuration in file "config-ReW-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)) = -17.213693846 2^p V(r_1,...,r_N) = -17.213693846 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 -3.05012726e+00 -2.77868455e+00 -6.45447161e-01 | -3.05012726e+00 -2.77868455e+00 -6.45447161e-01 1 3.61169672e+00 3.91648182e+00 -2.70212978e+00 | 3.61169672e+00 3.91648182e+00 -2.70212978e+00 2 2.36541814e+00 -4.66899790e+00 2.29500508e+00 | 2.36541814e+00 -4.66899790e+00 2.29500508e+00 3 -2.92698760e+00 3.53120062e+00 1.05257186e+00 | -2.92698760e+00 3.53120062e+00 1.05257186e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = FTF (Configuration in file "config-ReW-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)) = -7.38393555945 2^p V(r_1,...,r_N) = -7.38393555945 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 -1.71511416e+01 -9.21283179e+00 -2.76064290e+01 | -1.71511416e+01 -9.21283179e+00 -2.76064290e+01 1 4.48276094e+00 3.83992909e+00 -3.83593784e+00 | 4.48276094e+00 3.83992909e+00 -3.83593784e+00 2 1.97969790e+01 -1.98328769e+00 2.61722098e+01 | 1.97969790e+01 -1.98328769e+00 2.61722098e+01 3 -7.12859828e+00 7.35619039e+00 5.27015703e+00 | -7.12859828e+00 7.35619039e+00 5.27015703e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Re W, PBC = FFT (Configuration in file "config-ReW-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)) = -14.3777974986 2^p V(r_1,...,r_N) = -14.3777974986 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 -4.00576396e+00 -3.85104000e+00 -2.40723692e+00 | -4.00576396e+00 -3.85104000e+00 -2.40723692e+00 1 8.91642933e+00 7.73156137e+00 -1.01223150e+01 | 8.91642933e+00 7.73156137e+00 -1.01223150e+01 2 2.04896878e+00 -7.65328400e+00 5.65877268e+00 | 2.04896878e+00 -7.65328400e+00 5.65877268e+00 3 -6.95963415e+00 3.77276262e+00 6.87077923e+00 | -6.95963415e+00 3.77276262e+00 6.87077923e+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.