!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyTerentyev_2014EAM1_W__MO_292520929154_000 Supported species : H He W 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)) = 0.349575358175 2^p V(r_1,...,r_N) = 0.349575358175 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 -2.97732168e-01 -3.86835484e-01 -4.27314109e-01 | -2.97732168e-01 -3.86835484e-01 -4.27314109e-01 1 2.47944091e-01 1.67280070e-01 -1.72161751e-01 | 2.47944091e-01 1.67280070e-01 -1.72161751e-01 2 2.44616183e-01 -2.23402889e-01 2.88082159e-01 | 2.44616183e-01 -2.23402889e-01 2.88082159e-01 3 -1.94828106e-01 4.42958304e-01 3.11393702e-01 | -1.94828106e-01 4.42958304e-01 3.11393702e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.460746689752 2^p V(r_1,...,r_N) = 0.460746689752 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 -3.89014060e-01 -2.91774913e-01 -2.55892125e-01 | -3.89014060e-01 -2.91774913e-01 -2.55892125e-01 1 3.06491221e-01 2.25490848e-01 -3.71755005e-01 | 3.06491221e-01 2.25490848e-01 -3.71755005e-01 2 4.17283279e-01 -4.43086524e-01 4.23009335e-01 | 4.17283279e-01 -4.43086524e-01 4.23009335e-01 3 -3.34760440e-01 5.09370589e-01 2.04637795e-01 | -3.34760440e-01 5.09370589e-01 2.04637795e-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)) = 0.591872355017 2^p V(r_1,...,r_N) = 0.591872355017 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 -3.52184659e-01 -4.36823501e-01 -5.68117800e-01 | -3.52184659e-01 -4.36823501e-01 -5.68117800e-01 1 4.79666572e-01 4.64878229e-01 -2.85028510e-01 | 4.79666572e-01 4.64878229e-01 -2.85028510e-01 2 3.23439703e-01 -4.20338434e-01 4.34787759e-01 | 3.23439703e-01 -4.20338434e-01 4.34787759e-01 3 -4.50921616e-01 3.92283706e-01 4.18358551e-01 | -4.50921616e-01 3.92283706e-01 4.18358551e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.927350172754 2^p V(r_1,...,r_N) = 0.927350172754 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 -6.57129476e-01 -5.99345952e-01 -1.02226368e+00 | -6.57129476e-01 -5.99345952e-01 -1.02226368e+00 1 4.18507505e-01 4.75015881e-01 -3.37533788e-01 | 4.18507505e-01 4.75015881e-01 -3.37533788e-01 2 7.93410092e-01 -5.10605409e-01 8.13033236e-01 | 7.93410092e-01 -5.10605409e-01 8.13033236e-01 3 -5.54788120e-01 6.34935481e-01 5.46764234e-01 | -5.54788120e-01 6.34935481e-01 5.46764234e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.575203140596 2^p V(r_1,...,r_N) = 0.575203140596 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 -4.81596526e-01 -3.51065144e-01 -4.50643446e-01 | -4.81596526e-01 -3.51065144e-01 -4.50643446e-01 1 3.61951012e-01 4.24306673e-01 -3.77587294e-01 | 3.61951012e-01 4.24306673e-01 -3.77587294e-01 2 4.51603155e-01 -4.76894794e-01 4.05601581e-01 | 4.51603155e-01 -4.76894794e-01 4.05601581e-01 3 -3.31957641e-01 4.03653264e-01 4.22629159e-01 | -3.31957641e-01 4.03653264e-01 4.22629159e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.35809562663 2^p V(r_1,...,r_N) = 0.35809562663 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 -3.83667397e-01 -3.51012971e-01 -2.68981327e-01 | -3.83667397e-01 -3.51012971e-01 -2.68981327e-01 1 2.48525233e-01 3.26334958e-01 -2.93904147e-01 | 2.48525233e-01 3.26334958e-01 -2.93904147e-01 2 3.21081250e-01 -1.84205366e-01 4.18448269e-01 | 3.21081250e-01 -1.84205366e-01 4.18448269e-01 3 -1.85939087e-01 2.08883380e-01 1.44437206e-01 | -1.85939087e-01 2.08883380e-01 1.44437206e-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)) = 0.844152628465 2^p V(r_1,...,r_N) = 0.844152628465 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 -3.88274969e-01 -3.64494759e-01 -5.06318344e-01 | -3.88274969e-01 -3.64494759e-01 -5.06318344e-01 1 5.12390736e-01 4.67432124e-01 -4.06347953e-01 | 5.12390736e-01 4.67432124e-01 -4.06347953e-01 2 7.45040450e-01 -8.57912674e-01 5.44850855e-01 | 7.45040450e-01 -8.57912674e-01 5.44850855e-01 3 -8.69156218e-01 7.54975309e-01 3.67815441e-01 | -8.69156218e-01 7.54975309e-01 3.67815441e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TTT (Configuration in file "config-He-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)) = -1.30158781566 2^p V(r_1,...,r_N) = -1.30158781566 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 8.62143484e-01 7.21585482e-01 1.00510063e+00 | 8.62143484e-01 7.21585482e-01 1.00510063e+00 1 -6.78685843e-01 -8.62841675e-01 6.56700215e-01 | -6.78685843e-01 -8.62841675e-01 6.56700215e-01 2 -9.49991382e-01 9.16319665e-01 -9.39454056e-01 | -9.49991382e-01 9.16319665e-01 -9.39454056e-01 3 7.66533741e-01 -7.75063472e-01 -7.22346790e-01 | 7.66533741e-01 -7.75063472e-01 -7.22346790e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TTF (Configuration in file "config-He-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)) = -1.3274915928 2^p V(r_1,...,r_N) = -1.3274915928 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 8.89625686e-01 7.77127094e-01 8.54740762e-01 | 8.89625686e-01 7.77127094e-01 8.54740762e-01 1 -7.50890970e-01 -9.10698798e-01 7.63225321e-01 | -7.50890970e-01 -9.10698798e-01 7.63225321e-01 2 -7.76100406e-01 7.01111415e-01 -1.05685001e+00 | -7.76100406e-01 7.01111415e-01 -1.05685001e+00 3 6.37365690e-01 -5.67539711e-01 -5.61116077e-01 | 6.37365690e-01 -5.67539711e-01 -5.61116077e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TFT (Configuration in file "config-He-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)) = -0.851901105727 2^p V(r_1,...,r_N) = -0.851901105727 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 5.05042575e-01 5.22935975e-01 4.54098343e-01 | 5.05042575e-01 5.22935975e-01 4.54098343e-01 1 -5.97404985e-01 -4.80394598e-01 8.52711187e-01 | -5.97404985e-01 -4.80394598e-01 8.52711187e-01 2 -5.92484965e-01 7.60402101e-01 -8.50688145e-01 | -5.92484965e-01 7.60402101e-01 -8.50688145e-01 3 6.84847375e-01 -8.02943478e-01 -4.56121385e-01 | 6.84847375e-01 -8.02943478e-01 -4.56121385e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TFF (Configuration in file "config-He-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.875972391559 2^p V(r_1,...,r_N) = -0.875972391559 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 5.07816195e-01 6.50798463e-01 5.46840489e-01 | 5.07816195e-01 6.50798463e-01 5.46840489e-01 1 -6.03334612e-01 -5.64112916e-01 6.93594264e-01 | -6.03334612e-01 -5.64112916e-01 6.93594264e-01 2 -4.48820521e-01 6.03015639e-01 -5.48348120e-01 | -4.48820521e-01 6.03015639e-01 -5.48348120e-01 3 5.44338938e-01 -6.89701186e-01 -6.92086633e-01 | 5.44338938e-01 -6.89701186e-01 -6.92086633e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = FTT (Configuration in file "config-He-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)) = -0.494718571493 2^p V(r_1,...,r_N) = -0.494718571493 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 4.32189101e-01 4.53487261e-01 3.51629837e-01 | 4.32189101e-01 4.53487261e-01 3.51629837e-01 1 -7.11391186e-01 -5.81198115e-01 5.37869588e-01 | -7.11391186e-01 -5.81198115e-01 5.37869588e-01 2 -2.07553494e-01 4.56729890e-01 -4.04331143e-01 | -2.07553494e-01 4.56729890e-01 -4.04331143e-01 3 4.86755580e-01 -3.29019035e-01 -4.85168282e-01 | 4.86755580e-01 -3.29019035e-01 -4.85168282e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = FTF (Configuration in file "config-He-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.747091710589 2^p V(r_1,...,r_N) = -0.747091710589 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 4.64067900e-01 7.75620377e-01 7.01947630e-01 | 4.64067900e-01 7.75620377e-01 7.01947630e-01 1 -5.22498497e-01 -4.99231670e-01 5.28707228e-01 | -5.22498497e-01 -4.99231670e-01 5.28707228e-01 2 -5.85781412e-01 3.56591432e-01 -3.25554179e-01 | -5.85781412e-01 3.56591432e-01 -3.25554179e-01 3 6.44212008e-01 -6.32980139e-01 -9.05100680e-01 | 6.44212008e-01 -6.32980139e-01 -9.05100680e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = FFT (Configuration in file "config-He-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)) = -1.73480012504 2^p V(r_1,...,r_N) = -1.73480012504 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 9.51795931e-01 8.87184669e-01 8.34348796e-01 | 9.51795931e-01 8.87184669e-01 8.34348796e-01 1 -9.84088118e-01 -5.10963078e-01 9.63627421e-01 | -9.84088118e-01 -5.10963078e-01 9.63627421e-01 2 -6.79534245e-01 7.70511587e-01 -1.03671315e+00 | -6.79534245e-01 7.70511587e-01 -1.03671315e+00 3 7.11826432e-01 -1.14673318e+00 -7.61263071e-01 | 7.11826432e-01 -1.14673318e+00 -7.61263071e-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)) = -6.68117284377 2^p V(r_1,...,r_N) = -6.68117284377 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 -1.54954027e+01 -8.20131663e+00 -9.09308322e+00 | -1.54954027e+01 -8.20131663e+00 -9.09308322e+00 1 6.80063160e+00 1.60661684e+01 -2.20645799e+01 | 6.80063160e+00 1.60661684e+01 -2.20645799e+01 2 2.46453037e+01 -2.40833492e+01 1.75350395e+01 | 2.46453037e+01 -2.40833492e+01 1.75350395e+01 3 -1.59505326e+01 1.62184974e+01 1.36226236e+01 | -1.59505326e+01 1.62184974e+01 1.36226236e+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)) = -9.8905792159 2^p V(r_1,...,r_N) = -9.8905792159 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 -1.68284423e+01 -1.59084345e+01 -1.40854971e+01 | -1.68284423e+01 -1.59084345e+01 -1.40854971e+01 1 2.26344979e+01 1.87038410e+01 -1.46728465e+01 | 2.26344979e+01 1.87038410e+01 -1.46728465e+01 2 7.82758362e+00 -1.28618087e+01 9.75630033e+00 | 7.82758362e+00 -1.28618087e+01 9.75630033e+00 3 -1.36336392e+01 1.00664022e+01 1.90020433e+01 | -1.36336392e+01 1.00664022e+01 1.90020433e+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)) = -9.53593353011 2^p V(r_1,...,r_N) = -9.53593353011 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 -2.38761677e+01 -1.66020188e+01 -1.22906167e+00 | -2.38761677e+01 -1.66020188e+01 -1.22906167e+00 1 2.40654908e+01 1.55911769e+01 -7.55660392e+00 | 2.40654908e+01 1.55911769e+01 -7.55660392e+00 2 2.59494591e+00 -3.07124361e+00 2.90757174e+00 | 2.59494591e+00 -3.07124361e+00 2.90757174e+00 3 -2.78426900e+00 4.08208548e+00 5.87809385e+00 | -2.78426900e+00 4.08208548e+00 5.87809385e+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)) = -3.11362291397 2^p V(r_1,...,r_N) = -3.11362291397 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 -2.37022368e+01 -2.63996821e+01 -2.27715550e+01 | -2.37022368e+01 -2.63996821e+01 -2.27715550e+01 1 1.49998848e+01 1.78890218e+01 -1.37341798e+01 | 1.49998848e+01 1.78890218e+01 -1.37341798e+01 2 2.48041605e+01 -1.36868256e+01 2.10893971e+01 | 2.48041605e+01 -1.36868256e+01 2.10893971e+01 3 -1.61018085e+01 2.21974860e+01 1.54163377e+01 | -1.61018085e+01 2.21974860e+01 1.54163377e+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)) = -12.863215119 2^p V(r_1,...,r_N) = -12.863215119 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 -3.35633957e+00 -3.62829702e+00 -2.92095568e+00 | -3.35633957e+00 -3.62829702e+00 -2.92095568e+00 1 1.01138426e+01 6.71426478e+00 -1.89712405e+01 | 1.01138426e+01 6.71426478e+00 -1.89712405e+01 2 1.39146211e+01 -1.50571794e+01 5.70418823e+00 | 1.39146211e+01 -1.50571794e+01 5.70418823e+00 3 -2.06721241e+01 1.19712116e+01 1.61880080e+01 | -2.06721241e+01 1.19712116e+01 1.61880080e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -11.3554853801 2^p V(r_1,...,r_N) = -11.3554853801 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 -1.25130570e+01 -1.29539015e+01 -6.92039708e+00 | -1.25130570e+01 -1.29539015e+01 -6.92039708e+00 1 1.64326236e+01 1.39377087e+01 -1.42790548e+01 | 1.64326236e+01 1.39377087e+01 -1.42790548e+01 2 1.29716967e+01 -1.33040346e+01 2.70495594e+00 | 1.29716967e+01 -1.33040346e+01 2.70495594e+00 3 -1.68912634e+01 1.23202274e+01 1.84944959e+01 | -1.68912634e+01 1.23202274e+01 1.84944959e+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)) = -7.70732822996 2^p V(r_1,...,r_N) = -7.70732822996 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 -2.21726653e+01 -1.66680140e+01 -1.42265719e+01 | -2.21726653e+01 -1.66680140e+01 -1.42265719e+01 1 1.55118140e+01 9.63220700e+00 -1.75113313e+01 | 1.55118140e+01 9.63220700e+00 -1.75113313e+01 2 1.90753361e+01 -4.90988566e+00 1.16022086e+01 | 1.90753361e+01 -4.90988566e+00 1.16022086e+01 3 -1.24144848e+01 1.19456926e+01 2.01356946e+01 | -1.24144848e+01 1.19456926e+01 2.01356946e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TTT (Configuration in file "config-HHeW-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)) = 0.408283546132 2^p V(r_1,...,r_N) = 0.408283546132 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 -8.94710806e-01 -3.36868486e-01 -7.33455945e-01 | -8.94710806e-01 -3.36868486e-01 -7.33455945e-01 1 2.47556255e-01 1.26728955e-01 -1.11880219e-01 | 2.47556255e-01 1.26728955e-01 -1.11880219e-01 2 5.36256447e-01 1.12421852e-01 5.04461352e-01 | 5.36256447e-01 1.12421852e-01 5.04461352e-01 3 1.10898104e-01 9.77176800e-02 3.40874813e-01 | 1.10898104e-01 9.77176800e-02 3.40874813e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TTF (Configuration in file "config-HHeW-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)) = 1.56836721697 2^p V(r_1,...,r_N) = 1.56836721697 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 -2.96089803e+00 -3.20135437e+00 2.40366367e-01 | -2.96089803e+00 -3.20135437e+00 2.40366367e-01 1 3.47845843e+00 3.98511161e+00 -2.17198669e+00 | 3.47845843e+00 3.98511161e+00 -2.17198669e+00 2 -6.39136755e-02 -1.04225180e+00 9.76813591e-01 | -6.39136755e-02 -1.04225180e+00 9.76813591e-01 3 -4.53646728e-01 2.58494559e-01 9.54806729e-01 | -4.53646728e-01 2.58494559e-01 9.54806729e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TFT (Configuration in file "config-HHeW-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)) = 0.708563538968 2^p V(r_1,...,r_N) = 0.708563538968 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 -3.62128210e-01 -5.48631159e-02 -6.75762213e-01 | -3.62128210e-01 -5.48631159e-02 -6.75762213e-01 1 5.34899085e-01 -1.31611907e-01 -6.68244569e-01 | 5.34899085e-01 -1.31611907e-01 -6.68244569e-01 2 6.30613130e-01 -2.43889557e-01 4.67400860e-01 | 6.30613130e-01 -2.43889557e-01 4.67400860e-01 3 -8.03384006e-01 4.30364580e-01 8.76605922e-01 | -8.03384006e-01 4.30364580e-01 8.76605922e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TFF (Configuration in file "config-HHeW-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.593254505391 2^p V(r_1,...,r_N) = 0.593254505391 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 -4.84904965e-01 -7.75936498e-01 2.33887907e-01 | -4.84904965e-01 -7.75936498e-01 2.33887907e-01 1 8.32188598e-01 1.14873887e+00 -5.91023150e-01 | 8.32188598e-01 1.14873887e+00 -5.91023150e-01 2 2.44962844e-01 -5.49117582e-01 1.65461828e-01 | 2.44962844e-01 -5.49117582e-01 1.65461828e-01 3 -5.92246477e-01 1.76315208e-01 1.91673415e-01 | -5.92246477e-01 1.76315208e-01 1.91673415e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = FTT (Configuration in file "config-HHeW-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)) = 0.871751542782 2^p V(r_1,...,r_N) = 0.871751542782 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 -4.49875629e-02 -1.65399941e-01 -2.47874774e-01 | -4.49875629e-02 -1.65399941e-01 -2.47874774e-01 1 -1.36855097e-01 1.00757982e+00 -1.12349805e+00 | -1.36855097e-01 1.00757982e+00 -1.12349805e+00 2 3.87881090e-01 -1.18170607e+00 1.23944162e+00 | 3.87881090e-01 -1.18170607e+00 1.23944162e+00 3 -2.06038430e-01 3.39526197e-01 1.31931199e-01 | -2.06038430e-01 3.39526197e-01 1.31931199e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = FTF (Configuration in file "config-HHeW-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.787696456323 2^p V(r_1,...,r_N) = 0.787696456323 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 -1.70618293e+00 -1.05277303e+00 -8.63017675e-01 | -1.70618293e+00 -1.05277303e+00 -8.63017675e-01 1 1.05609525e+00 1.10434209e+00 -3.06301830e-01 | 1.05609525e+00 1.10434209e+00 -3.06301830e-01 2 7.51654070e-01 -5.53488864e-01 1.07044987e+00 | 7.51654070e-01 -5.53488864e-01 1.07044987e+00 3 -1.01566389e-01 5.01919808e-01 9.88696334e-02 | -1.01566389e-01 5.01919808e-01 9.88696334e-02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = FFT (Configuration in file "config-HHeW-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)) = 1.71450615644 2^p V(r_1,...,r_N) = 1.71450615644 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 -1.26522212e+00 -8.10239327e-01 -1.06315888e+00 | -1.26522212e+00 -8.10239327e-01 -1.06315888e+00 1 8.73581735e-01 2.84660730e+00 -3.05528607e+00 | 8.73581735e-01 2.84660730e+00 -3.05528607e+00 2 4.81368147e-01 -2.13520742e+00 3.80638566e+00 | 4.81368147e-01 -2.13520742e+00 3.80638566e+00 3 -8.97277589e-02 9.88394505e-02 3.12059287e-01 | -8.97277589e-02 9.88394505e-02 3.12059287e-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.