!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_TehranchiCurtin_2010_NiH__MO_535504325462_003 Supported species : H Ni random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTT (Configuration in file "config-H-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)) = -1.22140815753 2^p V(r_1,...,r_N) = -1.22140815753 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 1.28447352e+00 1.93533111e+00 2.15394657e+00 | 1.28447352e+00 1.93533111e+00 2.15394657e+00 1 -8.69715374e-01 -6.42666390e-01 5.32802249e-01 | -8.69715374e-01 -6.42666390e-01 5.32802249e-01 2 -1.05003979e+00 8.15769727e-01 -1.18642459e+00 | -1.05003979e+00 8.15769727e-01 -1.18642459e+00 3 6.35281642e-01 -2.10843445e+00 -1.50032423e+00 | 6.35281642e-01 -2.10843445e+00 -1.50032423e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTF (Configuration in file "config-H-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)) = -1.6785693943 2^p V(r_1,...,r_N) = -1.6785693943 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 1.76102424e+00 1.20233204e+00 1.04188512e+00 | 1.76102424e+00 1.20233204e+00 1.04188512e+00 1 -1.29368151e+00 -1.06676355e+00 1.52026430e+00 | -1.29368151e+00 -1.06676355e+00 1.52026430e+00 2 -2.01261630e+00 2.15393023e+00 -1.89947797e+00 | -2.01261630e+00 2.15393023e+00 -1.89947797e+00 3 1.54527357e+00 -2.28949872e+00 -6.62671448e-01 | 1.54527357e+00 -2.28949872e+00 -6.62671448e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFT (Configuration in file "config-H-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)) = -2.21817855801 2^p V(r_1,...,r_N) = -2.21817855801 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 1.55831969e+00 2.03449859e+00 2.60305588e+00 | 1.55831969e+00 2.03449859e+00 2.60305588e+00 1 -2.10555044e+00 -2.14853733e+00 1.28280506e+00 | -2.10555044e+00 -2.14853733e+00 1.28280506e+00 2 -1.34245739e+00 1.86219779e+00 -1.96900134e+00 | -1.34245739e+00 1.86219779e+00 -1.96900134e+00 3 1.88968814e+00 -1.74815905e+00 -1.91685960e+00 | 1.88968814e+00 -1.74815905e+00 -1.91685960e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFF (Configuration in file "config-H-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)) = -3.54739354089 2^p V(r_1,...,r_N) = -3.54739354089 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 2.12639488e+00 2.18256761e+00 3.27153641e+00 | 2.12639488e+00 2.18256761e+00 3.27153641e+00 1 -1.49491106e+00 -1.86582043e+00 1.24760189e+00 | -1.49491106e+00 -1.86582043e+00 1.24760189e+00 2 -2.54254633e+00 1.95115318e+00 -2.68255034e+00 | -2.54254633e+00 1.95115318e+00 -2.68255034e+00 3 1.91106251e+00 -2.26790036e+00 -1.83658796e+00 | 1.91106251e+00 -2.26790036e+00 -1.83658796e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTT (Configuration in file "config-H-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)) = -2.14541628893 2^p V(r_1,...,r_N) = -2.14541628893 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 2.16900805e+00 1.60464026e+00 2.10403513e+00 | 2.16900805e+00 1.60464026e+00 2.10403513e+00 1 -1.50210844e+00 -1.95572843e+00 1.64767307e+00 | -1.50210844e+00 -1.95572843e+00 1.64767307e+00 2 -2.05388320e+00 2.21952717e+00 -1.90665084e+00 | -2.05388320e+00 2.21952717e+00 -1.90665084e+00 3 1.38698358e+00 -1.86843900e+00 -1.84505736e+00 | 1.38698358e+00 -1.86843900e+00 -1.84505736e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTF (Configuration in file "config-H-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)) = -1.26186255799 2^p V(r_1,...,r_N) = -1.26186255799 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 1.95683305e+00 1.66468919e+00 1.19401900e+00 | 1.95683305e+00 1.66468919e+00 1.19401900e+00 1 -1.21165787e+00 -1.64108868e+00 1.37743263e+00 | -1.21165787e+00 -1.64108868e+00 1.37743263e+00 2 -1.43969520e+00 8.09796805e-01 -2.03460986e+00 | -1.43969520e+00 8.09796805e-01 -2.03460986e+00 3 6.94520019e-01 -8.33397310e-01 -5.36841776e-01 | 6.94520019e-01 -8.33397310e-01 -5.36841776e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FFT (Configuration in file "config-H-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.23143733322 2^p V(r_1,...,r_N) = -3.23143733322 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 1.68011391e+00 1.54067718e+00 1.89031892e+00 | 1.68011391e+00 1.54067718e+00 1.89031892e+00 1 -2.08431487e+00 -1.98669726e+00 1.44586344e+00 | -2.08431487e+00 -1.98669726e+00 1.44586344e+00 2 -2.43684907e+00 2.96179186e+00 -2.07481496e+00 | -2.43684907e+00 2.96179186e+00 -2.07481496e+00 3 2.84105002e+00 -2.51577178e+00 -1.26136740e+00 | 2.84105002e+00 -2.51577178e+00 -1.26136740e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.2051534357 2^p V(r_1,...,r_N) = -4.2051534357 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 -4.06996432e+00 -2.26083007e+00 -4.75208300e+00 | -4.06996432e+00 -2.26083007e+00 -4.75208300e+00 1 1.61112391e+00 3.19254358e+00 -2.16663785e+00 | 1.61112391e+00 3.19254358e+00 -2.16663785e+00 2 5.48064326e+00 -4.35608846e+00 4.93005738e+00 | 5.48064326e+00 -4.35608846e+00 4.93005738e+00 3 -3.02180285e+00 3.42437496e+00 1.98866346e+00 | -3.02180285e+00 3.42437496e+00 1.98866346e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.79968826084 2^p V(r_1,...,r_N) = -3.79968826084 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 -3.54894926e+00 -2.40926879e+00 -2.79664208e+00 | -3.54894926e+00 -2.40926879e+00 -2.79664208e+00 1 2.29812257e+00 3.89823773e+00 -2.94676221e+00 | 2.29812257e+00 3.89823773e+00 -2.94676221e+00 2 5.91451636e+00 -5.48550984e+00 4.37047633e+00 | 5.91451636e+00 -5.48550984e+00 4.37047633e+00 3 -4.66368967e+00 3.99654089e+00 1.37292795e+00 | -4.66368967e+00 3.99654089e+00 1.37292795e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.40595704532 2^p V(r_1,...,r_N) = -5.40595704532 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 -7.99837667e-01 -1.58621850e+00 -1.42458344e+00 | -7.99837667e-01 -1.58621850e+00 -1.42458344e+00 1 7.22166472e-01 1.87582242e+00 -3.42494197e+00 | 7.22166472e-01 1.87582242e+00 -3.42494197e+00 2 1.74692768e+00 -3.23329335e+00 3.74848749e+00 | 1.74692768e+00 -3.23329335e+00 3.74848749e+00 3 -1.66925648e+00 2.94368943e+00 1.10103791e+00 | -1.66925648e+00 2.94368943e+00 1.10103791e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.73996858393 2^p V(r_1,...,r_N) = -4.73996858393 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 -3.80695159e+00 -3.12918643e+00 -5.24308922e+00 | -3.80695159e+00 -3.12918643e+00 -5.24308922e+00 1 1.57461543e+00 2.26754193e+00 -1.71281540e+00 | 1.57461543e+00 2.26754193e+00 -1.71281540e+00 2 3.70802246e+00 -2.03654598e+00 4.94084113e+00 | 3.70802246e+00 -2.03654598e+00 4.94084113e+00 3 -1.47568630e+00 2.89819048e+00 2.01506349e+00 | -1.47568630e+00 2.89819048e+00 2.01506349e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.67561878023 2^p V(r_1,...,r_N) = -4.67561878023 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 -2.73994415e+00 -2.27952274e+00 -3.05090146e+00 | -2.73994415e+00 -2.27952274e+00 -3.05090146e+00 1 2.43797652e+00 3.36288783e+00 -4.04273001e+00 | 2.43797652e+00 3.36288783e+00 -4.04273001e+00 2 3.38082987e+00 -4.34901145e+00 5.29521262e+00 | 3.38082987e+00 -4.34901145e+00 5.29521262e+00 3 -3.07886224e+00 3.26564636e+00 1.79841884e+00 | -3.07886224e+00 3.26564636e+00 1.79841884e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.22689856683 2^p V(r_1,...,r_N) = -6.22689856683 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 -1.03414856e+00 -7.41567912e-01 -3.40183989e-01 | -1.03414856e+00 -7.41567912e-01 -3.40183989e-01 1 8.37034770e-01 1.12314118e+00 -1.80175947e-02 | 8.37034770e-01 1.12314118e+00 -1.80175947e-02 2 -4.30268434e-01 -3.11178976e-01 4.47953291e-01 | -4.30268434e-01 -3.11178976e-01 4.47953291e-01 3 6.27382223e-01 -7.03942929e-02 -8.97517076e-02 | 6.27382223e-01 -7.03942929e-02 -8.97517076e-02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.98077578176 2^p V(r_1,...,r_N) = -5.98077578176 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 4.21161827e-01 -1.00621798e+00 -1.23357277e+00 | 4.21161827e-01 -1.00621798e+00 -1.23357277e+00 1 -9.27616201e-01 -7.08317995e-01 9.87721829e-01 | -9.27616201e-01 -7.08317995e-01 9.87721829e-01 2 2.81477419e-01 2.25119855e-01 -6.85730450e-01 | 2.81477419e-01 2.25119855e-01 -6.85730450e-01 3 2.24976954e-01 1.48941612e+00 9.31581393e-01 | 2.24976954e-01 1.48941612e+00 9.31581393e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = TTT (Configuration in file "config-HNi-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)) = -6.06299210759 2^p V(r_1,...,r_N) = -6.06299210759 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 8.07844853e-02 2.27191455e-01 6.15734361e-01 | 8.07844853e-02 2.27191455e-01 6.15734361e-01 1 -2.98420904e-01 -4.98611512e-01 8.16922555e-01 | -2.98420904e-01 -4.98611512e-01 8.16922555e-01 2 1.98406669e-01 2.88719267e-01 -8.68298745e-01 | 1.98406669e-01 2.88719267e-01 -8.68298745e-01 3 1.92297504e-02 -1.72992098e-02 -5.64358171e-01 | 1.92297504e-02 -1.72992098e-02 -5.64358171e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = TTF (Configuration in file "config-HNi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.83106381911 2^p V(r_1,...,r_N) = -5.83106381911 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 5.38965133e-01 5.30538389e-01 6.46907439e-01 | 5.38965133e-01 5.30538389e-01 6.46907439e-01 1 -9.71393698e-02 -1.74847669e-01 4.23112769e-01 | -9.71393698e-02 -1.74847669e-01 4.23112769e-01 2 -8.49767186e-01 3.56456479e-01 -4.64484526e-01 | -8.49767186e-01 3.56456479e-01 -4.64484526e-01 3 4.07941423e-01 -7.12147199e-01 -6.05535682e-01 | 4.07941423e-01 -7.12147199e-01 -6.05535682e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = TFT (Configuration in file "config-HNi-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)) = -5.47643412068 2^p V(r_1,...,r_N) = -5.47643412068 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 2.16726263e-01 1.25503600e-01 5.39424958e-01 | 2.16726263e-01 1.25503600e-01 5.39424958e-01 1 -4.72942634e-01 -4.72296372e-01 8.74820435e-01 | -4.72942634e-01 -4.72296372e-01 8.74820435e-01 2 1.45263476e+00 -1.90062858e+00 -1.14519642e+00 | 1.45263476e+00 -1.90062858e+00 -1.14519642e+00 3 -1.19641839e+00 2.24742135e+00 -2.69048977e-01 | -1.19641839e+00 2.24742135e+00 -2.69048977e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = TFF (Configuration in file "config-HNi-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)) = -6.20930628446 2^p V(r_1,...,r_N) = -6.20930628446 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 1.76710966e-01 -2.27204999e-01 -2.10500809e-01 | 1.76710966e-01 -2.27204999e-01 -2.10500809e-01 1 -1.85550036e-01 1.62710659e+00 -1.48020584e+00 | -1.85550036e-01 1.62710659e+00 -1.48020584e+00 2 -2.38211634e-01 -1.58481225e+00 1.46536390e+00 | -2.38211634e-01 -1.58481225e+00 1.46536390e+00 3 2.47050704e-01 1.84910666e-01 2.25342744e-01 | 2.47050704e-01 1.84910666e-01 2.25342744e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = FTT (Configuration in file "config-HNi-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)) = -6.18956042985 2^p V(r_1,...,r_N) = -6.18956042985 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 4.72951274e-01 6.75609756e-01 4.65151704e-01 | 4.72951274e-01 6.75609756e-01 4.65151704e-01 1 -8.40579045e-01 -3.74420116e-01 6.83259914e-01 | -8.40579045e-01 -3.74420116e-01 6.83259914e-01 2 -1.88709176e-01 4.42939651e-01 -2.80260377e-01 | -1.88709176e-01 4.42939651e-01 -2.80260377e-01 3 5.56336947e-01 -7.44129291e-01 -8.68151242e-01 | 5.56336947e-01 -7.44129291e-01 -8.68151242e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = FTF (Configuration in file "config-HNi-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)) = -5.32787745793 2^p V(r_1,...,r_N) = -5.32787745793 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 4.68950887e-01 6.03126202e-01 8.38443764e-01 | 4.68950887e-01 6.03126202e-01 8.38443764e-01 1 -6.88650974e-01 -6.81416793e-02 5.49106236e-01 | -6.88650974e-01 -6.81416793e-02 5.49106236e-01 2 -7.49214409e-01 6.98645807e-01 -2.96838710e-01 | -7.49214409e-01 6.98645807e-01 -2.96838710e-01 3 9.68914496e-01 -1.23363033e+00 -1.09071129e+00 | 9.68914496e-01 -1.23363033e+00 -1.09071129e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Ni, PBC = FFT (Configuration in file "config-HNi-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)) = -6.0384502813 2^p V(r_1,...,r_N) = -6.0384502813 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 6.17525394e-01 2.15195468e-01 2.47980483e-01 | 6.17525394e-01 2.15195468e-01 2.47980483e-01 1 -5.90371940e-01 -2.44754855e-01 3.07574208e-01 | -5.90371940e-01 -2.44754855e-01 3.07574208e-01 2 -9.04664364e-01 5.27264819e-01 -3.64556744e-01 | -9.04664364e-01 5.27264819e-01 -3.64556744e-01 3 8.77510910e-01 -4.97705433e-01 -1.90997948e-01 | 8.77510910e-01 -4.97705433e-01 -1.90997948e-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.