!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_GWZBL_Samolyuk_2016_SiC__SM_720598599889_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)) = -8.20670462491 2^p V(r_1,...,r_N) = -8.20670462491 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 4.14040062e+00 2.21022624e+00 1.25878387e+00 | 4.14040062e+00 2.21022624e+00 1.25878387e+00 1 -6.06514248e+00 -4.43818291e+00 5.44866693e+00 | -6.06514248e+00 -4.43818291e+00 5.44866693e+00 2 -3.31583578e+00 6.23357213e+00 -5.50079875e+00 | -3.31583578e+00 6.23357213e+00 -5.50079875e+00 3 5.24057765e+00 -4.00561546e+00 -1.20665205e+00 | 5.24057765e+00 -4.00561546e+00 -1.20665205e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -8.65476251603 2^p V(r_1,...,r_N) = -8.65476251603 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 2.24911475e+00 3.58876352e+00 3.69690543e+00 | 2.24911475e+00 3.58876352e+00 3.69690543e+00 1 -1.72177519e+00 -3.00419515e+00 6.44074968e+00 | -1.72177519e+00 -3.00419515e+00 6.44074968e+00 2 -2.87379260e+00 3.83582512e+00 -4.55672215e+00 | -2.87379260e+00 3.83582512e+00 -4.55672215e+00 3 2.34645304e+00 -4.42039349e+00 -5.58093297e+00 | 2.34645304e+00 -4.42039349e+00 -5.58093297e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -7.58933657692 2^p V(r_1,...,r_N) = -7.58933657692 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 4.19409474e+00 5.99482889e+00 5.54358512e+00 | 4.19409474e+00 5.99482889e+00 5.54358512e+00 1 -3.21406645e+00 -3.86985887e+00 1.34886916e+00 | -3.21406645e+00 -3.86985887e+00 1.34886916e+00 2 -3.09658828e+00 3.90211431e+00 -2.21196617e+00 | -3.09658828e+00 3.90211431e+00 -2.21196617e+00 3 2.11655999e+00 -6.02708432e+00 -4.68048810e+00 | 2.11655999e+00 -6.02708432e+00 -4.68048810e+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)) = -10.7219994214 2^p V(r_1,...,r_N) = -10.7219994214 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 -2.01716393e-01 3.51769211e-01 5.63105036e-01 | -2.01716393e-01 3.51769211e-01 5.63105036e-01 1 -7.83609173e-01 -4.08733154e-01 1.18576204e+00 | -7.83609173e-01 -4.08733154e-01 1.18576204e+00 2 -7.07556653e-01 1.35630422e+00 -4.59294128e-01 | -7.07556653e-01 1.35630422e+00 -4.59294128e-01 3 1.69288222e+00 -1.29934027e+00 -1.28957295e+00 | 1.69288222e+00 -1.29934027e+00 -1.28957295e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -8.89799958072 2^p V(r_1,...,r_N) = -8.89799958072 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 2.97995834e+00 2.73320098e+00 2.58308671e+00 | 2.97995834e+00 2.73320098e+00 2.58308671e+00 1 -2.34747861e+00 -1.96172176e+00 2.55498722e+00 | -2.34747861e+00 -1.96172176e+00 2.55498722e+00 2 -2.51741479e+00 2.22212391e+00 -2.07586113e+00 | -2.51741479e+00 2.22212391e+00 -2.07586113e+00 3 1.88493505e+00 -2.99360314e+00 -3.06221280e+00 | 1.88493505e+00 -2.99360314e+00 -3.06221280e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -7.64417781165 2^p V(r_1,...,r_N) = -7.64417781165 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 2.63990355e+00 1.67207777e+00 3.15322947e+00 | 2.63990355e+00 1.67207777e+00 3.15322947e+00 1 -3.17028313e+00 -1.94397901e+00 1.98077244e+00 | -3.17028313e+00 -1.94397901e+00 1.98077244e+00 2 -2.81994782e+00 2.28798992e+00 -3.96643603e+00 | -2.81994782e+00 2.28798992e+00 -3.96643603e+00 3 3.35032740e+00 -2.01608868e+00 -1.16756587e+00 | 3.35032740e+00 -2.01608868e+00 -1.16756587e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -9.18079670598 2^p V(r_1,...,r_N) = -9.18079670598 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 2.35178258e+00 2.63897528e+00 2.38736954e+00 | 2.35178258e+00 2.63897528e+00 2.38736954e+00 1 -1.88569704e+00 -1.48263566e+00 8.17378642e-01 | -1.88569704e+00 -1.48263566e+00 8.17378642e-01 2 -3.86044105e+00 2.39967495e+00 -1.55689752e+00 | -3.86044105e+00 2.39967495e+00 -1.55689752e+00 3 3.39435550e+00 -3.55601457e+00 -1.64785066e+00 | 3.39435550e+00 -3.55601457e+00 -1.64785066e+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)) = 0.520578464191 2^p V(r_1,...,r_N) = 0.520578464192 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 -6.48195695e+00 -1.08974940e+01 -9.16495505e+00 | -6.48195695e+00 -1.08974940e+01 -9.16495505e+00 1 1.10314872e+01 6.89217761e+00 -9.85120441e+00 | 1.10314872e+01 6.89217761e+00 -9.85120441e+00 2 6.36752130e+00 -5.77729740e+00 6.43763390e+00 | 6.36752130e+00 -5.77729740e+00 6.43763390e+00 3 -1.09170516e+01 9.78261382e+00 1.25785256e+01 | -1.09170516e+01 9.78261382e+00 1.25785256e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -4.65957519567 2^p V(r_1,...,r_N) = -4.65957519567 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 -1.08425897e+00 -7.28463972e+00 -5.94575472e+00 | -1.08425897e+00 -7.28463972e+00 -5.94575472e+00 1 3.04815675e+00 3.00535624e+00 -2.33779635e+00 | 3.04815675e+00 3.00535624e+00 -2.33779635e+00 2 1.40411584e+00 -1.46331550e+00 1.02329527e+00 | 1.40411584e+00 -1.46331550e+00 1.02329527e+00 3 -3.36801362e+00 5.74259898e+00 7.26025581e+00 | -3.36801362e+00 5.74259898e+00 7.26025581e+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)) = -3.75872317398 2^p V(r_1,...,r_N) = -3.75872317398 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 -5.94836860e+00 -4.78514989e+00 -5.30035452e+00 | -5.94836860e+00 -4.78514989e+00 -5.30035452e+00 1 2.86991375e+00 5.38479749e+00 -2.40902193e+00 | 2.86991375e+00 5.38479749e+00 -2.40902193e+00 2 4.68449165e+00 -1.31985926e+00 6.42322511e+00 | 4.68449165e+00 -1.31985926e+00 6.42322511e+00 3 -1.60603680e+00 7.20211656e-01 1.28615133e+00 | -1.60603680e+00 7.20211656e-01 1.28615133e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 4.27866550874 2^p V(r_1,...,r_N) = 4.27866550874 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 -1.43603947e+01 -1.68974162e+01 -1.64514050e+01 | -1.43603947e+01 -1.68974162e+01 -1.64514050e+01 1 2.40237066e+01 1.53129175e+01 -1.45633558e+01 | 2.40237066e+01 1.53129175e+01 -1.45633558e+01 2 1.40326944e+01 -1.64344944e+01 1.30608457e+01 | 1.40326944e+01 -1.64344944e+01 1.30608457e+01 3 -2.36960063e+01 1.80189931e+01 1.79539150e+01 | -2.36960063e+01 1.80189931e+01 1.79539150e+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)) = -0.297150943282 2^p V(r_1,...,r_N) = -0.297150943282 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 -9.59745815e+00 -9.86525363e+00 -1.29176159e+01 | -9.59745815e+00 -9.86525363e+00 -1.29176159e+01 1 1.42205308e+01 1.27152721e+01 -1.21924617e+01 | 1.42205308e+01 1.27152721e+01 -1.21924617e+01 2 5.93806169e+00 -1.00315341e+01 1.01637374e+01 | 5.93806169e+00 -1.00315341e+01 1.01637374e+01 3 -1.05611343e+01 7.18151564e+00 1.49463402e+01 | -1.05611343e+01 7.18151564e+00 1.49463402e+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)) = 2.18141993379 2^p V(r_1,...,r_N) = 2.18141993379 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 -1.35119810e+01 -8.85721066e+00 -9.06799389e+00 | -1.35119810e+01 -8.85721066e+00 -9.06799389e+00 1 1.53690498e+01 1.26326342e+01 -2.16363256e+01 | 1.53690498e+01 1.26326342e+01 -2.16363256e+01 2 7.15585750e+00 -1.52524895e+01 1.73811635e+01 | 7.15585750e+00 -1.52524895e+01 1.73811635e+01 3 -9.01292634e+00 1.14770660e+01 1.33231559e+01 | -9.01292634e+00 1.14770660e+01 1.33231559e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 6.83859690095 2^p V(r_1,...,r_N) = 6.83859690095 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 -2.67040382e+01 -1.80887970e+01 -2.15669503e+01 | -2.67040382e+01 -1.80887970e+01 -2.15669503e+01 1 1.48080543e+01 2.56710587e+01 -1.57432879e+01 | 1.48080543e+01 2.56710587e+01 -1.57432879e+01 2 2.37688717e+01 -2.31890786e+01 2.28480833e+01 | 2.37688717e+01 -2.31890786e+01 2.28480833e+01 3 -1.18728878e+01 1.56068169e+01 1.44621549e+01 | -1.18728878e+01 1.56068169e+01 1.44621549e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -5.68054072989 2^p V(r_1,...,r_N) = -5.68054072989 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 -1.02202886e+01 -1.20249681e+01 -1.82030497e+01 | -1.02202886e+01 -1.20249681e+01 -1.82030497e+01 1 2.06968831e+00 4.54858336e-01 -1.44536154e+00 | 2.06968831e+00 4.54858336e-01 -1.44536154e+00 2 1.22408557e+01 -4.61582035e+00 9.10748354e+00 | 1.22408557e+01 -4.61582035e+00 9.10748354e+00 3 -4.09025541e+00 1.61859302e+01 1.05409276e+01 | -4.09025541e+00 1.61859302e+01 1.05409276e+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)) = -8.61514066958 2^p V(r_1,...,r_N) = -8.61514066958 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 3.44432089e+00 2.45868716e+00 7.47179737e-01 | 3.44432089e+00 2.45868716e+00 7.47179737e-01 1 2.81857895e+00 -1.60480439e+00 -5.45688891e+00 | 2.81857895e+00 -1.60480439e+00 -5.45688891e+00 2 -2.39981675e+00 1.32221075e+00 -6.96338366e-01 | -2.39981675e+00 1.32221075e+00 -6.96338366e-01 3 -3.86308309e+00 -2.17609352e+00 5.40604754e+00 | -3.86308309e+00 -2.17609352e+00 5.40604754e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -8.51197906088 2^p V(r_1,...,r_N) = -8.51197906088 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 1.10213691e-01 3.40533242e-01 -6.14107253e-01 | 1.10213691e-01 3.40533242e-01 -6.14107253e-01 1 3.01207454e+00 7.46997186e+00 -1.04613857e+01 | 3.01207454e+00 7.46997186e+00 -1.04613857e+01 2 3.51743952e+00 -8.91288349e+00 8.34862373e+00 | 3.51743952e+00 -8.91288349e+00 8.34862373e+00 3 -6.63972775e+00 1.10237838e+00 2.72686925e+00 | -6.63972775e+00 1.10237838e+00 2.72686925e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -8.34117089596 2^p V(r_1,...,r_N) = -8.34117089596 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 1.64804432e+00 3.05762541e+00 2.43602067e+00 | 1.64804432e+00 3.05762541e+00 2.43602067e+00 1 -1.08712381e+00 -4.04177640e+00 3.48103012e+00 | -1.08712381e+00 -4.04177640e+00 3.48103012e+00 2 5.01513230e+00 -1.98107625e+00 -2.81855239e+00 | 5.01513230e+00 -1.98107625e+00 -2.81855239e+00 3 -5.57605281e+00 2.96522724e+00 -3.09849840e+00 | -5.57605281e+00 2.96522724e+00 -3.09849840e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -4.03107648765 2^p V(r_1,...,r_N) = -4.03107648765 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 -1.74584004e+01 -1.91966212e+01 -4.60628853e+00 | -1.74584004e+01 -1.91966212e+01 -4.60628853e+00 1 1.79450969e+01 1.66921572e+01 -9.63261028e+00 | 1.79450969e+01 1.66921572e+01 -9.63261028e+00 2 5.09271535e+00 -1.39784480e-01 5.67076692e+00 | 5.09271535e+00 -1.39784480e-01 5.67076692e+00 3 -5.57941183e+00 2.64424853e+00 8.56813189e+00 | -5.57941183e+00 2.64424853e+00 8.56813189e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -6.32457229461 2^p V(r_1,...,r_N) = -6.32457229461 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 -1.80724970e+01 -5.44850079e+00 -1.14623816e+01 | -1.80724970e+01 -5.44850079e+00 -1.14623816e+01 1 5.05603036e+00 7.71381853e+00 -4.16832199e+00 | 5.05603036e+00 7.71381853e+00 -4.16832199e+00 2 1.35464811e+01 -6.22756139e+00 1.24230952e+01 | 1.35464811e+01 -6.22756139e+00 1.24230952e+01 3 -5.30014414e-01 3.96224364e+00 3.20760842e+00 | -5.30014414e-01 3.96224364e+00 3.20760842e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -5.79207297863 2^p V(r_1,...,r_N) = -5.79207297863 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 -5.86047442e+00 -1.17292187e+01 -9.22849311e+00 | -5.86047442e+00 -1.17292187e+01 -9.22849311e+00 1 9.05536767e+00 5.35686349e+00 -3.66842922e+00 | 9.05536767e+00 5.35686349e+00 -3.66842922e+00 2 7.20718171e+00 -6.76753907e+00 6.34151090e-02 | 7.20718171e+00 -6.76753907e+00 6.34151090e-02 3 -1.04020750e+01 1.31398943e+01 1.28335072e+01 | -1.04020750e+01 1.31398943e+01 1.28335072e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.