!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_FarkasJones_1996_NbTiAl__MO_042691367780_000 Supported species : Al Nb Ti random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 296.90895140745357 2^p V(r_1,...,r_N) = 296.9089514074557 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 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 1 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 2 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 3 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 4 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 5 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 6 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 7 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 8 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 9 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 10 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 11 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 12 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 13 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 14 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 15 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 16 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 17 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 18 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 19 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 20 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 21 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 22 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 23 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 24 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 25 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 26 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 27 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 28 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 | 1.81290851e+01 -3.20277293e+01 -7.78546493e+00 29 -4.27662039e+01 2.26931798e+01 3.54184542e+00 | -4.27662039e+01 2.26931798e+01 3.54184542e+00 30 8.99765688e+00 2.32023068e+00 -9.93347011e+00 | 8.99765688e+00 2.32023068e+00 -9.93347011e+00 31 1.56394619e+01 7.01431883e+00 1.41770896e+01 | 1.56394619e+01 7.01431883e+00 1.41770896e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 110.22930499890097 2^p V(r_1,...,r_N) = 110.22930499890101 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 -1.20204718e+01 1.10171821e+01 -3.02224656e+01 | -1.20204718e+01 1.10171821e+01 -3.02224656e+01 1 -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 | -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 2 -1.10885979e+01 -9.13950140e+00 3.15084169e+01 | -1.10885979e+01 -9.13950140e+00 3.15084169e+01 3 3.07480632e+01 3.18849896e+00 4.00383915e+01 | 3.07480632e+01 3.18849896e+00 4.00383915e+01 4 -1.20204718e+01 1.10171821e+01 -3.02224656e+01 | -1.20204718e+01 1.10171821e+01 -3.02224656e+01 5 -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 | -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 6 -1.10885979e+01 -9.13950140e+00 3.15084169e+01 | -1.10885979e+01 -9.13950140e+00 3.15084169e+01 7 3.07480632e+01 3.18849896e+00 4.00383915e+01 | 3.07480632e+01 3.18849896e+00 4.00383915e+01 8 -1.20204718e+01 1.10171821e+01 -3.02224656e+01 | -1.20204718e+01 1.10171821e+01 -3.02224656e+01 9 -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 | -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 10 -1.10885979e+01 -9.13950140e+00 3.15084169e+01 | -1.10885979e+01 -9.13950140e+00 3.15084169e+01 11 3.07480632e+01 3.18849896e+00 4.00383915e+01 | 3.07480632e+01 3.18849896e+00 4.00383915e+01 12 -1.20204718e+01 1.10171821e+01 -3.02224656e+01 | -1.20204718e+01 1.10171821e+01 -3.02224656e+01 13 -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 | -7.63899350e+00 -5.06617962e+00 -4.13243429e+01 14 -1.10885979e+01 -9.13950140e+00 3.15084169e+01 | -1.10885979e+01 -9.13950140e+00 3.15084169e+01 15 3.07480632e+01 3.18849896e+00 4.00383915e+01 | 3.07480632e+01 3.18849896e+00 4.00383915e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 171.69393779533002 2^p V(r_1,...,r_N) = 171.6939377953298 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 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 | 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 1 -3.84245120e+01 4.18100967e+01 -6.35811022e+00 | -3.84245120e+01 4.18100967e+01 -6.35811022e+00 2 -4.24316752e+01 -4.70603804e+01 1.66054802e+01 | -4.24316752e+01 -4.70603804e+01 1.66054802e+01 3 4.73019715e+01 5.39454201e+01 1.84187389e+01 | 4.73019715e+01 5.39454201e+01 1.84187389e+01 4 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 | 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 5 -3.84245120e+01 4.18100967e+01 -6.35811022e+00 | -3.84245120e+01 4.18100967e+01 -6.35811022e+00 6 -4.24316752e+01 -4.70603804e+01 1.66054802e+01 | -4.24316752e+01 -4.70603804e+01 1.66054802e+01 7 4.73019715e+01 5.39454201e+01 1.84187389e+01 | 4.73019715e+01 5.39454201e+01 1.84187389e+01 8 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 | 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 9 -3.84245120e+01 4.18100967e+01 -6.35811022e+00 | -3.84245120e+01 4.18100967e+01 -6.35811022e+00 10 -4.24316752e+01 -4.70603804e+01 1.66054802e+01 | -4.24316752e+01 -4.70603804e+01 1.66054802e+01 11 4.73019715e+01 5.39454201e+01 1.84187389e+01 | 4.73019715e+01 5.39454201e+01 1.84187389e+01 12 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 | 3.35542158e+01 -4.86951364e+01 -2.86661089e+01 13 -3.84245120e+01 4.18100967e+01 -6.35811022e+00 | -3.84245120e+01 4.18100967e+01 -6.35811022e+00 14 -4.24316752e+01 -4.70603804e+01 1.66054802e+01 | -4.24316752e+01 -4.70603804e+01 1.66054802e+01 15 4.73019715e+01 5.39454201e+01 1.84187389e+01 | 4.73019715e+01 5.39454201e+01 1.84187389e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 56.5443505668297 2^p V(r_1,...,r_N) = 56.54435056682972 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 2.38666435e+01 -4.54172443e+01 -3.26386732e+01 | 2.38666435e+01 -4.54172443e+01 -3.26386732e+01 1 -2.88195000e+01 3.86455375e+01 -2.97657052e+01 | -2.88195000e+01 3.86455375e+01 -2.97657052e+01 2 -2.38324051e+01 -3.51898586e+01 3.08653777e+01 | -2.38324051e+01 -3.51898586e+01 3.08653777e+01 3 2.87852616e+01 4.19615653e+01 3.15390007e+01 | 2.87852616e+01 4.19615653e+01 3.15390007e+01 4 2.38666435e+01 -4.54172443e+01 -3.26386732e+01 | 2.38666435e+01 -4.54172443e+01 -3.26386732e+01 5 -2.88195000e+01 3.86455375e+01 -2.97657052e+01 | -2.88195000e+01 3.86455375e+01 -2.97657052e+01 6 -2.38324051e+01 -3.51898586e+01 3.08653777e+01 | -2.38324051e+01 -3.51898586e+01 3.08653777e+01 7 2.87852616e+01 4.19615653e+01 3.15390007e+01 | 2.87852616e+01 4.19615653e+01 3.15390007e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 158.76907419858176 2^p V(r_1,...,r_N) = 158.76907419858154 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 -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 | -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 1 3.36673112e+01 -3.45909168e+01 2.38223978e+01 | 3.36673112e+01 -3.45909168e+01 2.38223978e+01 2 3.80751095e+01 4.05364949e+01 -3.53483047e+01 | 3.80751095e+01 4.05364949e+01 -3.53483047e+01 3 -3.83472679e+01 -5.30451517e+00 2.31527726e+01 | -3.83472679e+01 -5.30451517e+00 2.31527726e+01 4 -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 | -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 5 3.36673112e+01 -3.45909168e+01 2.38223978e+01 | 3.36673112e+01 -3.45909168e+01 2.38223978e+01 6 3.80751095e+01 4.05364949e+01 -3.53483047e+01 | 3.80751095e+01 4.05364949e+01 -3.53483047e+01 7 -3.83472679e+01 -5.30451517e+00 2.31527726e+01 | -3.83472679e+01 -5.30451517e+00 2.31527726e+01 8 -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 | -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 9 3.36673112e+01 -3.45909168e+01 2.38223978e+01 | 3.36673112e+01 -3.45909168e+01 2.38223978e+01 10 3.80751095e+01 4.05364949e+01 -3.53483047e+01 | 3.80751095e+01 4.05364949e+01 -3.53483047e+01 11 -3.83472679e+01 -5.30451517e+00 2.31527726e+01 | -3.83472679e+01 -5.30451517e+00 2.31527726e+01 12 -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 | -3.33951527e+01 -6.41062916e-01 -1.16268657e+01 13 3.36673112e+01 -3.45909168e+01 2.38223978e+01 | 3.36673112e+01 -3.45909168e+01 2.38223978e+01 14 3.80751095e+01 4.05364949e+01 -3.53483047e+01 | 3.80751095e+01 4.05364949e+01 -3.53483047e+01 15 -3.83472679e+01 -5.30451517e+00 2.31527726e+01 | -3.83472679e+01 -5.30451517e+00 2.31527726e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 71.23462866844005 2^p V(r_1,...,r_N) = 71.23462866844002 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 -5.51308534e+01 -5.60110937e+00 -4.57752987e+01 | -5.51308534e+01 -5.60110937e+00 -4.57752987e+01 1 3.47199346e+01 1.40176570e+01 -3.77628416e+01 | 3.47199346e+01 1.40176570e+01 -3.77628416e+01 2 5.64851706e+01 4.73335565e+00 5.03328027e+01 | 5.64851706e+01 4.73335565e+00 5.03328027e+01 3 -3.60742517e+01 -1.31499033e+01 3.32053376e+01 | -3.60742517e+01 -1.31499033e+01 3.32053376e+01 4 -5.51308534e+01 -5.60110937e+00 -4.57752987e+01 | -5.51308534e+01 -5.60110937e+00 -4.57752987e+01 5 3.47199346e+01 1.40176570e+01 -3.77628416e+01 | 3.47199346e+01 1.40176570e+01 -3.77628416e+01 6 5.64851706e+01 4.73335565e+00 5.03328027e+01 | 5.64851706e+01 4.73335565e+00 5.03328027e+01 7 -3.60742517e+01 -1.31499033e+01 3.32053376e+01 | -3.60742517e+01 -1.31499033e+01 3.32053376e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 115.75077016500504 2^p V(r_1,...,r_N) = 115.75077016500511 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 -5.59854812e+01 -4.49887744e+01 3.24048948e+01 | -5.59854812e+01 -4.49887744e+01 3.24048948e+01 1 5.30590111e+01 4.50626407e+01 -3.09489871e+01 | 5.30590111e+01 4.50626407e+01 -3.09489871e+01 2 7.80200046e+01 -5.69437385e+01 -1.29178257e+01 | 7.80200046e+01 -5.69437385e+01 -1.29178257e+01 3 -7.50935346e+01 5.68698722e+01 1.14619180e+01 | -7.50935346e+01 5.68698722e+01 1.14619180e+01 4 -5.59854812e+01 -4.49887744e+01 3.24048948e+01 | -5.59854812e+01 -4.49887744e+01 3.24048948e+01 5 5.30590111e+01 4.50626407e+01 -3.09489871e+01 | 5.30590111e+01 4.50626407e+01 -3.09489871e+01 6 7.80200046e+01 -5.69437385e+01 -1.29178257e+01 | 7.80200046e+01 -5.69437385e+01 -1.29178257e+01 7 -7.50935346e+01 5.68698722e+01 1.14619180e+01 | -7.50935346e+01 5.68698722e+01 1.14619180e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTT (Configuration in file "config-Nb-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 594.1879137481994 2^p V(r_1,...,r_N) = 594.1879137482023 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 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 1 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 2 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 3 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 4 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 5 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 6 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 7 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 8 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 9 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 10 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 11 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 12 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 13 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 14 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 15 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 16 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 17 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 18 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 19 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 20 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 21 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 22 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 23 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 24 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 25 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 26 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 27 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 28 -2.08257728e+01 1.98334442e+02 2.02665735e+02 | -2.08257728e+01 1.98334442e+02 2.02665735e+02 29 -9.15170730e+00 -3.02386319e+01 2.88350589e+01 | -9.15170730e+00 -3.02386319e+01 2.88350589e+01 30 -9.45054744e+00 3.77475477e+01 1.44291073e+01 | -9.45054744e+00 3.77475477e+01 1.44291073e+01 31 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 | 3.94280275e+01 -2.05843358e+02 -2.45929902e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTF (Configuration in file "config-Nb-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 169.01515828820283 2^p V(r_1,...,r_N) = 169.0151582882023 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 -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 | -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 1 3.32342577e+01 1.37344293e+01 -5.54398153e+01 | 3.32342577e+01 1.37344293e+01 -5.54398153e+01 2 9.93903896e+00 -3.87196152e+01 4.84993192e+01 | 9.93903896e+00 -3.87196152e+01 4.84993192e+01 3 -2.42095608e+01 5.79320749e+01 8.14637607e+01 | -2.42095608e+01 5.79320749e+01 8.14637607e+01 4 -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 | -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 5 3.32342577e+01 1.37344293e+01 -5.54398153e+01 | 3.32342577e+01 1.37344293e+01 -5.54398153e+01 6 9.93903896e+00 -3.87196152e+01 4.84993192e+01 | 9.93903896e+00 -3.87196152e+01 4.84993192e+01 7 -2.42095608e+01 5.79320749e+01 8.14637607e+01 | -2.42095608e+01 5.79320749e+01 8.14637607e+01 8 -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 | -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 9 3.32342577e+01 1.37344293e+01 -5.54398153e+01 | 3.32342577e+01 1.37344293e+01 -5.54398153e+01 10 9.93903896e+00 -3.87196152e+01 4.84993192e+01 | 9.93903896e+00 -3.87196152e+01 4.84993192e+01 11 -2.42095608e+01 5.79320749e+01 8.14637607e+01 | -2.42095608e+01 5.79320749e+01 8.14637607e+01 12 -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 | -1.89637359e+01 -3.29468890e+01 -7.45232647e+01 13 3.32342577e+01 1.37344293e+01 -5.54398153e+01 | 3.32342577e+01 1.37344293e+01 -5.54398153e+01 14 9.93903896e+00 -3.87196152e+01 4.84993192e+01 | 9.93903896e+00 -3.87196152e+01 4.84993192e+01 15 -2.42095608e+01 5.79320749e+01 8.14637607e+01 | -2.42095608e+01 5.79320749e+01 8.14637607e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFT (Configuration in file "config-Nb-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 98.47049562174502 2^p V(r_1,...,r_N) = 98.47049562174502 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 1.04554499e+01 -4.65798007e+01 1.47424760e+00 | 1.04554499e+01 -4.65798007e+01 1.47424760e+00 1 -1.97214634e+01 3.97342482e+01 2.57755089e+01 | -1.97214634e+01 3.97342482e+01 2.57755089e+01 2 -1.30458483e+01 -3.96024778e+01 8.23708521e+00 | -1.30458483e+01 -3.96024778e+01 8.23708521e+00 3 2.23118618e+01 4.64480303e+01 -3.54868417e+01 | 2.23118618e+01 4.64480303e+01 -3.54868417e+01 4 1.04554499e+01 -4.65798007e+01 1.47424760e+00 | 1.04554499e+01 -4.65798007e+01 1.47424760e+00 5 -1.97214634e+01 3.97342482e+01 2.57755089e+01 | -1.97214634e+01 3.97342482e+01 2.57755089e+01 6 -1.30458483e+01 -3.96024778e+01 8.23708521e+00 | -1.30458483e+01 -3.96024778e+01 8.23708521e+00 7 2.23118618e+01 4.64480303e+01 -3.54868417e+01 | 2.23118618e+01 4.64480303e+01 -3.54868417e+01 8 1.04554499e+01 -4.65798007e+01 1.47424760e+00 | 1.04554499e+01 -4.65798007e+01 1.47424760e+00 9 -1.97214634e+01 3.97342482e+01 2.57755089e+01 | -1.97214634e+01 3.97342482e+01 2.57755089e+01 10 -1.30458483e+01 -3.96024778e+01 8.23708521e+00 | -1.30458483e+01 -3.96024778e+01 8.23708521e+00 11 2.23118618e+01 4.64480303e+01 -3.54868417e+01 | 2.23118618e+01 4.64480303e+01 -3.54868417e+01 12 1.04554499e+01 -4.65798007e+01 1.47424760e+00 | 1.04554499e+01 -4.65798007e+01 1.47424760e+00 13 -1.97214634e+01 3.97342482e+01 2.57755089e+01 | -1.97214634e+01 3.97342482e+01 2.57755089e+01 14 -1.30458483e+01 -3.96024778e+01 8.23708521e+00 | -1.30458483e+01 -3.96024778e+01 8.23708521e+00 15 2.23118618e+01 4.64480303e+01 -3.54868417e+01 | 2.23118618e+01 4.64480303e+01 -3.54868417e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFF (Configuration in file "config-Nb-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 49.23337062895673 2^p V(r_1,...,r_N) = 49.233370628956784 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 -1.26638168e+01 -4.35323182e+01 -3.85644477e+01 | -1.26638168e+01 -4.35323182e+01 -3.85644477e+01 1 1.23544273e+01 6.08538655e+01 -5.17487109e+01 | 1.23544273e+01 6.08538655e+01 -5.17487109e+01 2 3.96134333e+01 -8.35983340e+01 5.87547526e+01 | 3.96134333e+01 -8.35983340e+01 5.87547526e+01 3 -3.93040438e+01 6.62767867e+01 3.15584060e+01 | -3.93040438e+01 6.62767867e+01 3.15584060e+01 4 -1.26638168e+01 -4.35323182e+01 -3.85644477e+01 | -1.26638168e+01 -4.35323182e+01 -3.85644477e+01 5 1.23544273e+01 6.08538655e+01 -5.17487109e+01 | 1.23544273e+01 6.08538655e+01 -5.17487109e+01 6 3.96134333e+01 -8.35983340e+01 5.87547526e+01 | 3.96134333e+01 -8.35983340e+01 5.87547526e+01 7 -3.93040438e+01 6.62767867e+01 3.15584060e+01 | -3.93040438e+01 6.62767867e+01 3.15584060e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTT (Configuration in file "config-Nb-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 152.7448191246904 2^p V(r_1,...,r_N) = 152.74481912468988 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 -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 | -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 1 6.23518619e+01 3.64087943e+01 -1.97947810e+01 | 6.23518619e+01 3.64087943e+01 -1.97947810e+01 2 5.81272166e+01 -3.79022659e+01 1.07353421e+01 | 5.81272166e+01 -3.79022659e+01 1.07353421e+01 3 -6.21499554e+01 3.50291281e+01 3.10010122e+01 | -6.21499554e+01 3.50291281e+01 3.10010122e+01 4 -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 | -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 5 6.23518619e+01 3.64087943e+01 -1.97947810e+01 | 6.23518619e+01 3.64087943e+01 -1.97947810e+01 6 5.81272166e+01 -3.79022659e+01 1.07353421e+01 | 5.81272166e+01 -3.79022659e+01 1.07353421e+01 7 -6.21499554e+01 3.50291281e+01 3.10010122e+01 | -6.21499554e+01 3.50291281e+01 3.10010122e+01 8 -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 | -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 9 6.23518619e+01 3.64087943e+01 -1.97947810e+01 | 6.23518619e+01 3.64087943e+01 -1.97947810e+01 10 5.81272166e+01 -3.79022659e+01 1.07353421e+01 | 5.81272166e+01 -3.79022659e+01 1.07353421e+01 11 -6.21499554e+01 3.50291281e+01 3.10010122e+01 | -6.21499554e+01 3.50291281e+01 3.10010122e+01 12 -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 | -5.83291231e+01 -3.35356565e+01 -2.19415732e+01 13 6.23518619e+01 3.64087943e+01 -1.97947810e+01 | 6.23518619e+01 3.64087943e+01 -1.97947810e+01 14 5.81272166e+01 -3.79022659e+01 1.07353421e+01 | 5.81272166e+01 -3.79022659e+01 1.07353421e+01 15 -6.21499554e+01 3.50291281e+01 3.10010122e+01 | -6.21499554e+01 3.50291281e+01 3.10010122e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTF (Configuration in file "config-Nb-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 50.238962841214395 2^p V(r_1,...,r_N) = 50.2389628412144 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 -4.29822505e+01 1.90215976e+01 -7.11245879e+01 | -4.29822505e+01 1.90215976e+01 -7.11245879e+01 1 4.25078925e+01 1.01983414e+00 -4.02876400e+01 | 4.25078925e+01 1.01983414e+00 -4.02876400e+01 2 5.72306103e+01 1.19152035e+01 6.25413617e+01 | 5.72306103e+01 1.19152035e+01 6.25413617e+01 3 -5.67562524e+01 -3.19566353e+01 4.88708661e+01 | -5.67562524e+01 -3.19566353e+01 4.88708661e+01 4 -4.29822505e+01 1.90215976e+01 -7.11245879e+01 | -4.29822505e+01 1.90215976e+01 -7.11245879e+01 5 4.25078925e+01 1.01983414e+00 -4.02876400e+01 | 4.25078925e+01 1.01983414e+00 -4.02876400e+01 6 5.72306103e+01 1.19152035e+01 6.25413617e+01 | 5.72306103e+01 1.19152035e+01 6.25413617e+01 7 -5.67562524e+01 -3.19566353e+01 4.88708661e+01 | -5.67562524e+01 -3.19566353e+01 4.88708661e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FFT (Configuration in file "config-Nb-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 79.0620467051181 2^p V(r_1,...,r_N) = 79.06204670511808 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 -6.68760335e+01 -7.85349424e+01 3.28956444e+01 | -6.68760335e+01 -7.85349424e+01 3.28956444e+01 1 8.17629868e+01 6.04162491e+01 3.11380480e+01 | 8.17629868e+01 6.04162491e+01 3.11380480e+01 2 5.52092605e+01 -6.15645416e+01 -9.76506357e+00 | 5.52092605e+01 -6.15645416e+01 -9.76506357e+00 3 -7.00962138e+01 7.96832349e+01 -5.42686288e+01 | -7.00962138e+01 7.96832349e+01 -5.42686288e+01 4 -6.68760335e+01 -7.85349424e+01 3.28956444e+01 | -6.68760335e+01 -7.85349424e+01 3.28956444e+01 5 8.17629868e+01 6.04162491e+01 3.11380480e+01 | 8.17629868e+01 6.04162491e+01 3.11380480e+01 6 5.52092605e+01 -6.15645416e+01 -9.76506357e+00 | 5.52092605e+01 -6.15645416e+01 -9.76506357e+00 7 -7.00962138e+01 7.96832349e+01 -5.42686288e+01 | -7.00962138e+01 7.96832349e+01 -5.42686288e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTT (Configuration in file "config-Ti-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 202.1506737002289 2^p V(r_1,...,r_N) = 202.150673700227 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 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 1 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 2 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 3 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 4 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 5 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 6 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 7 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 8 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 9 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 10 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 11 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 12 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 13 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 14 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 15 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 16 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 17 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 18 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 19 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 20 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 21 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 22 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 23 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 24 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 25 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 26 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 27 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 28 1.22263517e+00 4.82003750e+00 9.35205037e-01 | 1.22263517e+00 4.82003750e+00 9.35205037e-01 29 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 | 1.18868223e+00 -5.55761899e+00 -5.59255152e+00 30 -1.56831316e+00 9.78515230e+00 5.15439901e+00 | -1.56831316e+00 9.78515230e+00 5.15439901e+00 31 -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 | -8.43004249e-01 -9.04757080e+00 -4.97052531e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTF (Configuration in file "config-Ti-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 28.951351560750712 2^p V(r_1,...,r_N) = 28.95135156075069 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 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 | 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 1 -3.22948137e+00 2.87113631e+00 -1.70264050e+01 | -3.22948137e+00 2.87113631e+00 -1.70264050e+01 2 3.41978082e+00 -2.00991733e+00 1.70300996e+01 | 3.41978082e+00 -2.00991733e+00 1.70300996e+01 3 -1.49542428e+00 4.07565165e+00 1.71119161e+01 | -1.49542428e+00 4.07565165e+00 1.71119161e+01 4 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 | 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 5 -3.22948137e+00 2.87113631e+00 -1.70264050e+01 | -3.22948137e+00 2.87113631e+00 -1.70264050e+01 6 3.41978082e+00 -2.00991733e+00 1.70300996e+01 | 3.41978082e+00 -2.00991733e+00 1.70300996e+01 7 -1.49542428e+00 4.07565165e+00 1.71119161e+01 | -1.49542428e+00 4.07565165e+00 1.71119161e+01 8 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 | 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 9 -3.22948137e+00 2.87113631e+00 -1.70264050e+01 | -3.22948137e+00 2.87113631e+00 -1.70264050e+01 10 3.41978082e+00 -2.00991733e+00 1.70300996e+01 | 3.41978082e+00 -2.00991733e+00 1.70300996e+01 11 -1.49542428e+00 4.07565165e+00 1.71119161e+01 | -1.49542428e+00 4.07565165e+00 1.71119161e+01 12 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 | 1.30512483e+00 -4.93687063e+00 -1.71156107e+01 13 -3.22948137e+00 2.87113631e+00 -1.70264050e+01 | -3.22948137e+00 2.87113631e+00 -1.70264050e+01 14 3.41978082e+00 -2.00991733e+00 1.70300996e+01 | 3.41978082e+00 -2.00991733e+00 1.70300996e+01 15 -1.49542428e+00 4.07565165e+00 1.71119161e+01 | -1.49542428e+00 4.07565165e+00 1.71119161e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFT (Configuration in file "config-Ti-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 77.58946300428956 2^p V(r_1,...,r_N) = 77.58946300428985 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 -1.17359396e+01 -2.31048197e+01 5.00782331e+00 | -1.17359396e+01 -2.31048197e+01 5.00782331e+00 1 6.96087353e+00 2.65311360e+01 2.31552399e+00 | 6.96087353e+00 2.65311360e+01 2.31552399e+00 2 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 | 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 3 -2.78803655e+00 2.02948913e+01 2.03944659e+00 | -2.78803655e+00 2.02948913e+01 2.03944659e+00 4 -1.17359396e+01 -2.31048197e+01 5.00782331e+00 | -1.17359396e+01 -2.31048197e+01 5.00782331e+00 5 6.96087353e+00 2.65311360e+01 2.31552399e+00 | 6.96087353e+00 2.65311360e+01 2.31552399e+00 6 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 | 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 7 -2.78803655e+00 2.02948913e+01 2.03944659e+00 | -2.78803655e+00 2.02948913e+01 2.03944659e+00 8 -1.17359396e+01 -2.31048197e+01 5.00782331e+00 | -1.17359396e+01 -2.31048197e+01 5.00782331e+00 9 6.96087353e+00 2.65311360e+01 2.31552399e+00 | 6.96087353e+00 2.65311360e+01 2.31552399e+00 10 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 | 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 11 -2.78803655e+00 2.02948913e+01 2.03944659e+00 | -2.78803655e+00 2.02948913e+01 2.03944659e+00 12 -1.17359396e+01 -2.31048197e+01 5.00782331e+00 | -1.17359396e+01 -2.31048197e+01 5.00782331e+00 13 6.96087353e+00 2.65311360e+01 2.31552399e+00 | 6.96087353e+00 2.65311360e+01 2.31552399e+00 14 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 | 7.56310261e+00 -2.37212075e+01 -9.36279388e+00 15 -2.78803655e+00 2.02948913e+01 2.03944659e+00 | -2.78803655e+00 2.02948913e+01 2.03944659e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFF (Configuration in file "config-Ti-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -0.49294084596902116 2^p V(r_1,...,r_N) = -0.4929408459690248 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 -3.60146476e+00 -1.32240428e+01 -1.76888598e+01 | -3.60146476e+00 -1.32240428e+01 -1.76888598e+01 1 -9.40213195e-02 1.09615390e+01 -1.06666602e+01 | -9.40213195e-02 1.09615390e+01 -1.06666602e+01 2 5.91348639e+00 -1.28945643e+01 1.33997571e+01 | 5.91348639e+00 -1.28945643e+01 1.33997571e+01 3 -2.21800031e+00 1.51570681e+01 1.49557629e+01 | -2.21800031e+00 1.51570681e+01 1.49557629e+01 4 -3.60146476e+00 -1.32240428e+01 -1.76888598e+01 | -3.60146476e+00 -1.32240428e+01 -1.76888598e+01 5 -9.40213195e-02 1.09615390e+01 -1.06666602e+01 | -9.40213195e-02 1.09615390e+01 -1.06666602e+01 6 5.91348639e+00 -1.28945643e+01 1.33997571e+01 | 5.91348639e+00 -1.28945643e+01 1.33997571e+01 7 -2.21800031e+00 1.51570681e+01 1.49557629e+01 | -2.21800031e+00 1.51570681e+01 1.49557629e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTT (Configuration in file "config-Ti-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 63.2279602391297 2^p V(r_1,...,r_N) = 63.227960239129665 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 -2.21518892e+01 5.65489702e+00 3.95616548e+00 | -2.21518892e+01 5.65489702e+00 3.95616548e+00 1 2.20937425e+01 -7.74143907e+00 2.43247075e+00 | 2.20937425e+01 -7.74143907e+00 2.43247075e+00 2 2.15984923e+01 6.76935930e+00 -2.72651726e+00 | 2.15984923e+01 6.76935930e+00 -2.72651726e+00 3 -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 | -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 4 -2.21518892e+01 5.65489702e+00 3.95616548e+00 | -2.21518892e+01 5.65489702e+00 3.95616548e+00 5 2.20937425e+01 -7.74143907e+00 2.43247075e+00 | 2.20937425e+01 -7.74143907e+00 2.43247075e+00 6 2.15984923e+01 6.76935930e+00 -2.72651726e+00 | 2.15984923e+01 6.76935930e+00 -2.72651726e+00 7 -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 | -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 8 -2.21518892e+01 5.65489702e+00 3.95616548e+00 | -2.21518892e+01 5.65489702e+00 3.95616548e+00 9 2.20937425e+01 -7.74143907e+00 2.43247075e+00 | 2.20937425e+01 -7.74143907e+00 2.43247075e+00 10 2.15984923e+01 6.76935930e+00 -2.72651726e+00 | 2.15984923e+01 6.76935930e+00 -2.72651726e+00 11 -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 | -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 12 -2.21518892e+01 5.65489702e+00 3.95616548e+00 | -2.21518892e+01 5.65489702e+00 3.95616548e+00 13 2.20937425e+01 -7.74143907e+00 2.43247075e+00 | 2.20937425e+01 -7.74143907e+00 2.43247075e+00 14 2.15984923e+01 6.76935930e+00 -2.72651726e+00 | 2.15984923e+01 6.76935930e+00 -2.72651726e+00 15 -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 | -2.15403455e+01 -4.68281725e+00 -3.66211897e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTF (Configuration in file "config-Ti-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 2.349173424374949 2^p V(r_1,...,r_N) = 2.3491734243749547 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 -1.41727603e+01 -2.15993533e+00 -1.11481097e+01 | -1.41727603e+01 -2.15993533e+00 -1.11481097e+01 1 1.11952354e+01 6.95846767e+00 -1.94944978e+01 | 1.11952354e+01 6.95846767e+00 -1.94944978e+01 2 1.52633360e+01 -7.56155994e+00 1.50430365e+01 | 1.52633360e+01 -7.56155994e+00 1.50430365e+01 3 -1.22858111e+01 2.76302760e+00 1.55995710e+01 | -1.22858111e+01 2.76302760e+00 1.55995710e+01 4 -1.41727603e+01 -2.15993533e+00 -1.11481097e+01 | -1.41727603e+01 -2.15993533e+00 -1.11481097e+01 5 1.11952354e+01 6.95846767e+00 -1.94944978e+01 | 1.11952354e+01 6.95846767e+00 -1.94944978e+01 6 1.52633360e+01 -7.56155994e+00 1.50430365e+01 | 1.52633360e+01 -7.56155994e+00 1.50430365e+01 7 -1.22858111e+01 2.76302760e+00 1.55995710e+01 | -1.22858111e+01 2.76302760e+00 1.55995710e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FFT (Configuration in file "config-Ti-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -0.5458265567525291 2^p V(r_1,...,r_N) = -0.5458265567525354 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 -1.29543315e+01 -1.48843285e+01 -6.20673780e+00 | -1.29543315e+01 -1.48843285e+01 -6.20673780e+00 1 1.26041191e+01 1.33965464e+01 -4.87041915e+00 | 1.26041191e+01 1.33965464e+01 -4.87041915e+00 2 1.10637344e+01 -1.37674348e+01 4.36805002e+00 | 1.10637344e+01 -1.37674348e+01 4.36805002e+00 3 -1.07135220e+01 1.52552169e+01 6.70910693e+00 | -1.07135220e+01 1.52552169e+01 6.70910693e+00 4 -1.29543315e+01 -1.48843285e+01 -6.20673780e+00 | -1.29543315e+01 -1.48843285e+01 -6.20673780e+00 5 1.26041191e+01 1.33965464e+01 -4.87041915e+00 | 1.26041191e+01 1.33965464e+01 -4.87041915e+00 6 1.10637344e+01 -1.37674348e+01 4.36805002e+00 | 1.10637344e+01 -1.37674348e+01 4.36805002e+00 7 -1.07135220e+01 1.52552169e+01 6.70910693e+00 | -1.07135220e+01 1.52552169e+01 6.70910693e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TTT (Configuration in file "config-AlNbTi-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 271.2155022715049 2^p V(r_1,...,r_N) = 271.21550227150885 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 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 1 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 2 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 3 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 4 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 5 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 6 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 7 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 8 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 9 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 10 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 11 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 12 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 13 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 14 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 15 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 16 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 17 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 18 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 19 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 20 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 21 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 22 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 23 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 24 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 25 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 26 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 27 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 28 -2.58974282e+02 8.78199932e+02 1.12785876e+02 | -2.58974282e+02 8.78199932e+02 1.12785876e+02 29 1.72179027e+02 -7.51494199e+02 2.36458371e+02 | 1.72179027e+02 -7.51494199e+02 2.36458371e+02 30 1.13302332e+02 7.06033565e+01 -1.35550108e+02 | 1.13302332e+02 7.06033565e+01 -1.35550108e+02 31 -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 | -2.65070778e+01 -1.97309090e+02 -2.13694139e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TTF (Configuration in file "config-AlNbTi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 48.561939214192606 2^p V(r_1,...,r_N) = 48.56193921419254 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 -4.71477604e+00 1.42965696e+01 -8.55162341e+00 | -4.71477604e+00 1.42965696e+01 -8.55162341e+00 1 4.75776885e+00 4.66287785e+01 1.95869220e+01 | 4.75776885e+00 4.66287785e+01 1.95869220e+01 2 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 | 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 3 -7.79096046e+00 7.94615423e+00 1.84391011e+01 | -7.79096046e+00 7.94615423e+00 1.84391011e+01 4 -4.71477604e+00 1.42965696e+01 -8.55162341e+00 | -4.71477604e+00 1.42965696e+01 -8.55162341e+00 5 4.75776885e+00 4.66287785e+01 1.95869220e+01 | 4.75776885e+00 4.66287785e+01 1.95869220e+01 6 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 | 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 7 -7.79096046e+00 7.94615423e+00 1.84391011e+01 | -7.79096046e+00 7.94615423e+00 1.84391011e+01 8 -4.71477604e+00 1.42965696e+01 -8.55162341e+00 | -4.71477604e+00 1.42965696e+01 -8.55162341e+00 9 4.75776885e+00 4.66287785e+01 1.95869220e+01 | 4.75776885e+00 4.66287785e+01 1.95869220e+01 10 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 | 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 11 -7.79096046e+00 7.94615423e+00 1.84391011e+01 | -7.79096046e+00 7.94615423e+00 1.84391011e+01 12 -4.71477604e+00 1.42965696e+01 -8.55162341e+00 | -4.71477604e+00 1.42965696e+01 -8.55162341e+00 13 4.75776885e+00 4.66287785e+01 1.95869220e+01 | 4.75776885e+00 4.66287785e+01 1.95869220e+01 14 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 | 7.74796764e+00 -6.88715023e+01 -2.94743997e+01 15 -7.79096046e+00 7.94615423e+00 1.84391011e+01 | -7.79096046e+00 7.94615423e+00 1.84391011e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TFT (Configuration in file "config-AlNbTi-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 15.564190411738672 2^p V(r_1,...,r_N) = 15.564190411738679 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 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 | 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 1 -1.94334788e+01 1.02449975e+02 -3.05334745e+01 | -1.94334788e+01 1.02449975e+02 -3.05334745e+01 2 -2.56698098e+02 4.72058818e+01 2.77238526e+02 | -2.56698098e+02 4.72058818e+01 2.77238526e+02 3 8.94160035e+00 1.49729651e+01 2.37653881e+01 | 8.94160035e+00 1.49729651e+01 2.37653881e+01 4 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 | 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 5 -1.94334788e+01 1.02449975e+02 -3.05334745e+01 | -1.94334788e+01 1.02449975e+02 -3.05334745e+01 6 -2.56698098e+02 4.72058818e+01 2.77238526e+02 | -2.56698098e+02 4.72058818e+01 2.77238526e+02 7 8.94160035e+00 1.49729651e+01 2.37653881e+01 | 8.94160035e+00 1.49729651e+01 2.37653881e+01 8 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 | 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 9 -1.94334788e+01 1.02449975e+02 -3.05334745e+01 | -1.94334788e+01 1.02449975e+02 -3.05334745e+01 10 -2.56698098e+02 4.72058818e+01 2.77238526e+02 | -2.56698098e+02 4.72058818e+01 2.77238526e+02 11 8.94160035e+00 1.49729651e+01 2.37653881e+01 | 8.94160035e+00 1.49729651e+01 2.37653881e+01 12 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 | 2.67189977e+02 -1.64628822e+02 -2.70470440e+02 13 -1.94334788e+01 1.02449975e+02 -3.05334745e+01 | -1.94334788e+01 1.02449975e+02 -3.05334745e+01 14 -2.56698098e+02 4.72058818e+01 2.77238526e+02 | -2.56698098e+02 4.72058818e+01 2.77238526e+02 15 8.94160035e+00 1.49729651e+01 2.37653881e+01 | 8.94160035e+00 1.49729651e+01 2.37653881e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TFF (Configuration in file "config-AlNbTi-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -5.855128659031246 2^p V(r_1,...,r_N) = -5.855128659031239 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 -5.29427427e+00 -6.55181225e+00 -1.42175442e+01 | -5.29427427e+00 -6.55181225e+00 -1.42175442e+01 1 1.83982043e+00 3.33959707e+00 -1.11959197e+01 | 1.83982043e+00 3.33959707e+00 -1.11959197e+01 2 9.32170859e+00 -1.31797696e+01 1.09177527e+01 | 9.32170859e+00 -1.31797696e+01 1.09177527e+01 3 -5.86725475e+00 1.63919848e+01 1.44957112e+01 | -5.86725475e+00 1.63919848e+01 1.44957112e+01 4 -5.29427427e+00 -6.55181225e+00 -1.42175442e+01 | -5.29427427e+00 -6.55181225e+00 -1.42175442e+01 5 1.83982043e+00 3.33959707e+00 -1.11959197e+01 | 1.83982043e+00 3.33959707e+00 -1.11959197e+01 6 9.32170859e+00 -1.31797696e+01 1.09177527e+01 | 9.32170859e+00 -1.31797696e+01 1.09177527e+01 7 -5.86725475e+00 1.63919848e+01 1.44957112e+01 | -5.86725475e+00 1.63919848e+01 1.44957112e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = FTT (Configuration in file "config-AlNbTi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.802432707584336 2^p V(r_1,...,r_N) = 10.80243270758425 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 8.40933629e+00 1.50460547e+01 9.32036096e+00 | 8.40933629e+00 1.50460547e+01 9.32036096e+00 1 -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 | -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 2 2.02127321e+01 -4.98388658e+00 3.79800607e+00 | 2.02127321e+01 -4.98388658e+00 3.79800607e+00 3 -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 | -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 4 8.40933629e+00 1.50460547e+01 9.32036096e+00 | 8.40933629e+00 1.50460547e+01 9.32036096e+00 5 -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 | -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 6 2.02127321e+01 -4.98388658e+00 3.79800607e+00 | 2.02127321e+01 -4.98388658e+00 3.79800607e+00 7 -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 | -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 8 8.40933629e+00 1.50460547e+01 9.32036096e+00 | 8.40933629e+00 1.50460547e+01 9.32036096e+00 9 -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 | -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 10 2.02127321e+01 -4.98388658e+00 3.79800607e+00 | 2.02127321e+01 -4.98388658e+00 3.79800607e+00 11 -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 | -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 12 8.40933629e+00 1.50460547e+01 9.32036096e+00 | 8.40933629e+00 1.50460547e+01 9.32036096e+00 13 -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 | -2.30272795e+01 -1.28339239e+00 -6.02515061e+00 14 2.02127321e+01 -4.98388658e+00 3.79800607e+00 | 2.02127321e+01 -4.98388658e+00 3.79800607e+00 15 -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 | -5.59478897e+00 -8.77877570e+00 -7.09321642e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = FTF (Configuration in file "config-AlNbTi-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -0.5916337118826768 2^p V(r_1,...,r_N) = -0.5916337118826679 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 -1.29987635e+01 -1.81657037e+01 -2.12115034e+01 | -1.29987635e+01 -1.81657037e+01 -2.12115034e+01 1 1.70181629e+01 7.13462706e+00 -1.67258953e+01 | 1.70181629e+01 7.13462706e+00 -1.67258953e+01 2 -4.76935605e+01 3.63577461e+01 6.36457524e+00 | -4.76935605e+01 3.63577461e+01 6.36457524e+00 3 4.36741611e+01 -2.53266695e+01 3.15728235e+01 | 4.36741611e+01 -2.53266695e+01 3.15728235e+01 4 -1.29987635e+01 -1.81657037e+01 -2.12115034e+01 | -1.29987635e+01 -1.81657037e+01 -2.12115034e+01 5 1.70181629e+01 7.13462706e+00 -1.67258953e+01 | 1.70181629e+01 7.13462706e+00 -1.67258953e+01 6 -4.76935605e+01 3.63577461e+01 6.36457524e+00 | -4.76935605e+01 3.63577461e+01 6.36457524e+00 7 4.36741611e+01 -2.53266695e+01 3.15728235e+01 | 4.36741611e+01 -2.53266695e+01 3.15728235e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = FFT (Configuration in file "config-AlNbTi-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -1.0067480735973624 2^p V(r_1,...,r_N) = -1.006748073597365 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 -3.35631601e-01 7.23744809e+00 1.26730939e+01 | -3.35631601e-01 7.23744809e+00 1.26730939e+01 1 4.65219094e+00 1.42096430e+01 -3.46977545e+00 | 4.65219094e+00 1.42096430e+01 -3.46977545e+00 2 -1.21768516e+00 -1.56684720e+01 -1.63872316e+00 | -1.21768516e+00 -1.56684720e+01 -1.63872316e+00 3 -3.09887418e+00 -5.77861914e+00 -7.56459529e+00 | -3.09887418e+00 -5.77861914e+00 -7.56459529e+00 4 -3.35631601e-01 7.23744809e+00 1.26730939e+01 | -3.35631601e-01 7.23744809e+00 1.26730939e+01 5 4.65219094e+00 1.42096430e+01 -3.46977545e+00 | 4.65219094e+00 1.42096430e+01 -3.46977545e+00 6 -1.21768516e+00 -1.56684720e+01 -1.63872316e+00 | -1.21768516e+00 -1.56684720e+01 -1.63872316e+00 7 -3.09887418e+00 -5.77861914e+00 -7.56459529e+00 | -3.09887418e+00 -5.77861914e+00 -7.56459529e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.