!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_KinaciHaskinsSevik_2012_BNC__MO_105008013807_000 Supported species : B C N random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = TTT (Configuration in file "config-B-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)) = 515.6829376552696 2^p V(r_1,...,r_N) = 515.6829376552674 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 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 1 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 2 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 3 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 4 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 5 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 6 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 7 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 8 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 9 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 10 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 11 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 12 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 13 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 14 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 15 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 16 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 17 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 18 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 19 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 20 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 21 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 22 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 23 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 24 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 25 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 26 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 27 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 28 1.62430623e+01 2.92362454e+00 1.13523918e+01 | 1.62430623e+01 2.92362454e+00 1.13523918e+01 29 -2.69265959e+01 2.13588287e+01 -2.61316268e+00 | -2.69265959e+01 2.13588287e+01 -2.61316268e+00 30 1.40477422e+01 -2.85405099e+01 5.93072399e+00 | 1.40477422e+01 -2.85405099e+01 5.93072399e+00 31 -3.36420867e+00 4.25805665e+00 -1.46699531e+01 | -3.36420867e+00 4.25805665e+00 -1.46699531e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = TTF (Configuration in file "config-B-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)) = 108.33776981785738 2^p V(r_1,...,r_N) = 108.33776981785725 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 4.29394930e+01 8.30745772e+01 -5.20098509e+01 | 4.29394930e+01 8.30745772e+01 -5.20098509e+01 1 1.40409987e+01 -4.44714469e+01 5.86872290e+01 | 1.40409987e+01 -4.44714469e+01 5.86872290e+01 2 -8.30532014e+00 4.07740885e+00 1.48929117e+01 | -8.30532014e+00 4.07740885e+00 1.48929117e+01 3 -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 | -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 4 4.29394930e+01 8.30745772e+01 -5.20098509e+01 | 4.29394930e+01 8.30745772e+01 -5.20098509e+01 5 1.40409987e+01 -4.44714469e+01 5.86872290e+01 | 1.40409987e+01 -4.44714469e+01 5.86872290e+01 6 -8.30532014e+00 4.07740885e+00 1.48929117e+01 | -8.30532014e+00 4.07740885e+00 1.48929117e+01 7 -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 | -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 8 4.29394930e+01 8.30745772e+01 -5.20098509e+01 | 4.29394930e+01 8.30745772e+01 -5.20098509e+01 9 1.40409987e+01 -4.44714469e+01 5.86872290e+01 | 1.40409987e+01 -4.44714469e+01 5.86872290e+01 10 -8.30532014e+00 4.07740885e+00 1.48929117e+01 | -8.30532014e+00 4.07740885e+00 1.48929117e+01 11 -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 | -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 12 4.29394930e+01 8.30745772e+01 -5.20098509e+01 | 4.29394930e+01 8.30745772e+01 -5.20098509e+01 13 1.40409987e+01 -4.44714469e+01 5.86872290e+01 | 1.40409987e+01 -4.44714469e+01 5.86872290e+01 14 -8.30532014e+00 4.07740885e+00 1.48929117e+01 | -8.30532014e+00 4.07740885e+00 1.48929117e+01 15 -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 | -4.86751716e+01 -4.26805391e+01 -2.15702898e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = TFT (Configuration in file "config-B-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)) = 133.93600299823456 2^p V(r_1,...,r_N) = 133.93600299823476 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 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 | 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 1 -3.36617654e+00 2.35566690e+01 -3.29430678e+00 | -3.36617654e+00 2.35566690e+01 -3.29430678e+00 2 -2.52356162e+01 -2.15850358e+01 1.66235662e+01 | -2.52356162e+01 -2.15850358e+01 1.66235662e+01 3 1.94176079e+01 1.70614870e+01 4.83421755e+00 | 1.94176079e+01 1.70614870e+01 4.83421755e+00 4 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 | 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 5 -3.36617654e+00 2.35566690e+01 -3.29430678e+00 | -3.36617654e+00 2.35566690e+01 -3.29430678e+00 6 -2.52356162e+01 -2.15850358e+01 1.66235662e+01 | -2.52356162e+01 -2.15850358e+01 1.66235662e+01 7 1.94176079e+01 1.70614870e+01 4.83421755e+00 | 1.94176079e+01 1.70614870e+01 4.83421755e+00 8 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 | 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 9 -3.36617654e+00 2.35566690e+01 -3.29430678e+00 | -3.36617654e+00 2.35566690e+01 -3.29430678e+00 10 -2.52356162e+01 -2.15850358e+01 1.66235662e+01 | -2.52356162e+01 -2.15850358e+01 1.66235662e+01 11 1.94176079e+01 1.70614870e+01 4.83421755e+00 | 1.94176079e+01 1.70614870e+01 4.83421755e+00 12 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 | 9.18418487e+00 -1.90331202e+01 -1.81634769e+01 13 -3.36617654e+00 2.35566690e+01 -3.29430678e+00 | -3.36617654e+00 2.35566690e+01 -3.29430678e+00 14 -2.52356162e+01 -2.15850358e+01 1.66235662e+01 | -2.52356162e+01 -2.15850358e+01 1.66235662e+01 15 1.94176079e+01 1.70614870e+01 4.83421755e+00 | 1.94176079e+01 1.70614870e+01 4.83421755e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = TFF (Configuration in file "config-B-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)) = 4.682939289552548 2^p V(r_1,...,r_N) = 4.682939289552545 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 4.67644394e-01 -3.04082154e+00 -3.81531290e+00 | 4.67644394e-01 -3.04082154e+00 -3.81531290e+00 1 1.81699038e+01 8.20433645e+00 -8.86994756e+00 | 1.81699038e+01 8.20433645e+00 -8.86994756e+00 2 -5.16596045e+00 -1.01461436e+01 7.56638316e+00 | -5.16596045e+00 -1.01461436e+01 7.56638316e+00 3 -1.34715878e+01 4.98262873e+00 5.11887730e+00 | -1.34715878e+01 4.98262873e+00 5.11887730e+00 4 4.67644394e-01 -3.04082154e+00 -3.81531290e+00 | 4.67644394e-01 -3.04082154e+00 -3.81531290e+00 5 1.81699038e+01 8.20433645e+00 -8.86994756e+00 | 1.81699038e+01 8.20433645e+00 -8.86994756e+00 6 -5.16596045e+00 -1.01461436e+01 7.56638316e+00 | -5.16596045e+00 -1.01461436e+01 7.56638316e+00 7 -1.34715878e+01 4.98262873e+00 5.11887730e+00 | -1.34715878e+01 4.98262873e+00 5.11887730e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = FTT (Configuration in file "config-B-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)) = 111.13087022901678 2^p V(r_1,...,r_N) = 111.13087022901709 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 -9.34430792e+00 2.40250510e+01 -5.55537647e+00 | -9.34430792e+00 2.40250510e+01 -5.55537647e+00 1 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 | 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 2 1.69971073e+01 4.85501776e+00 8.95839267e+00 | 1.69971073e+01 4.85501776e+00 8.95839267e+00 3 -1.99169103e+01 -1.63659999e+01 7.89162611e+00 | -1.99169103e+01 -1.63659999e+01 7.89162611e+00 4 -9.34430792e+00 2.40250510e+01 -5.55537647e+00 | -9.34430792e+00 2.40250510e+01 -5.55537647e+00 5 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 | 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 6 1.69971073e+01 4.85501776e+00 8.95839267e+00 | 1.69971073e+01 4.85501776e+00 8.95839267e+00 7 -1.99169103e+01 -1.63659999e+01 7.89162611e+00 | -1.99169103e+01 -1.63659999e+01 7.89162611e+00 8 -9.34430792e+00 2.40250510e+01 -5.55537647e+00 | -9.34430792e+00 2.40250510e+01 -5.55537647e+00 9 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 | 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 10 1.69971073e+01 4.85501776e+00 8.95839267e+00 | 1.69971073e+01 4.85501776e+00 8.95839267e+00 11 -1.99169103e+01 -1.63659999e+01 7.89162611e+00 | -1.99169103e+01 -1.63659999e+01 7.89162611e+00 12 -9.34430792e+00 2.40250510e+01 -5.55537647e+00 | -9.34430792e+00 2.40250510e+01 -5.55537647e+00 13 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 | 1.22641109e+01 -1.25140688e+01 -1.12946423e+01 14 1.69971073e+01 4.85501776e+00 8.95839267e+00 | 1.69971073e+01 4.85501776e+00 8.95839267e+00 15 -1.99169103e+01 -1.63659999e+01 7.89162611e+00 | -1.99169103e+01 -1.63659999e+01 7.89162611e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = FTF (Configuration in file "config-B-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)) = -0.7633239075392979 2^p V(r_1,...,r_N) = -0.7633239075393277 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 -5.06380245e+01 -1.33148566e+02 -4.67296904e-01 | -5.06380245e+01 -1.33148566e+02 -4.67296904e-01 1 7.27255687e+01 2.31107039e+01 4.34914785e+01 | 7.27255687e+01 2.31107039e+01 4.34914785e+01 2 -2.21952115e+01 9.84003804e+01 -5.00921872e+01 | -2.21952115e+01 9.84003804e+01 -5.00921872e+01 3 1.07667290e-01 1.16374821e+01 7.06800562e+00 | 1.07667290e-01 1.16374821e+01 7.06800562e+00 4 -5.06380245e+01 -1.33148566e+02 -4.67296904e-01 | -5.06380245e+01 -1.33148566e+02 -4.67296904e-01 5 7.27255687e+01 2.31107039e+01 4.34914785e+01 | 7.27255687e+01 2.31107039e+01 4.34914785e+01 6 -2.21952115e+01 9.84003804e+01 -5.00921872e+01 | -2.21952115e+01 9.84003804e+01 -5.00921872e+01 7 1.07667290e-01 1.16374821e+01 7.06800562e+00 | 1.07667290e-01 1.16374821e+01 7.06800562e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = B, PBC = FFT (Configuration in file "config-B-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)) = -2.5764490125438595 2^p V(r_1,...,r_N) = -2.576449012543847 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 -4.02792055e+00 -2.45220872e+00 -7.45065091e+00 | -4.02792055e+00 -2.45220872e+00 -7.45065091e+00 1 5.39726072e+00 6.24663705e-01 -9.11216764e+00 | 5.39726072e+00 6.24663705e-01 -9.11216764e+00 2 1.51443422e+01 -1.15888363e+01 4.72880371e+00 | 1.51443422e+01 -1.15888363e+01 4.72880371e+00 3 -1.65136823e+01 1.34163813e+01 1.18340148e+01 | -1.65136823e+01 1.34163813e+01 1.18340148e+01 4 -4.02792055e+00 -2.45220872e+00 -7.45065091e+00 | -4.02792055e+00 -2.45220872e+00 -7.45065091e+00 5 5.39726072e+00 6.24663705e-01 -9.11216764e+00 | 5.39726072e+00 6.24663705e-01 -9.11216764e+00 6 1.51443422e+01 -1.15888363e+01 4.72880371e+00 | 1.51443422e+01 -1.15888363e+01 4.72880371e+00 7 -1.65136823e+01 1.34163813e+01 1.18340148e+01 | -1.65136823e+01 1.34163813e+01 1.18340148e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTT (Configuration in file "config-C-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)) = 6849.227431496395 2^p V(r_1,...,r_N) = 6849.227431496375 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 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 1 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 2 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 3 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 4 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 5 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 6 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 7 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 8 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 9 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 10 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 11 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 12 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 13 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 14 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 15 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 16 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 17 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 18 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 19 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 20 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 21 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 22 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 23 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 24 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 25 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 26 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 27 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 28 -2.58285891e+02 2.91250164e+02 -2.54076740e+02 | -2.58285891e+02 2.91250164e+02 -2.54076740e+02 29 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 | 3.07077897e+02 -4.18711935e+02 -9.61524698e+01 30 -3.56533870e+01 4.33253419e+00 2.07808212e+02 | -3.56533870e+01 4.33253419e+00 2.07808212e+02 31 -1.31386189e+01 1.23129237e+02 1.42420998e+02 | -1.31386189e+01 1.23129237e+02 1.42420998e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TTF (Configuration in file "config-C-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 2986.8615076811575 2^p V(r_1,...,r_N) = 2986.8615076811634 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 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 | 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 1 -3.39635681e+02 3.24077989e+02 -4.21921347e+02 | -3.39635681e+02 3.24077989e+02 -4.21921347e+02 2 -5.66897810e+01 -1.58770591e+02 4.79910821e+02 | -5.66897810e+01 -1.58770591e+02 4.79910821e+02 3 9.05519638e+01 8.16204160e+01 3.17922113e+02 | 9.05519638e+01 8.16204160e+01 3.17922113e+02 4 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 | 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 5 -3.39635681e+02 3.24077989e+02 -4.21921347e+02 | -3.39635681e+02 3.24077989e+02 -4.21921347e+02 6 -5.66897810e+01 -1.58770591e+02 4.79910821e+02 | -5.66897810e+01 -1.58770591e+02 4.79910821e+02 7 9.05519638e+01 8.16204160e+01 3.17922113e+02 | 9.05519638e+01 8.16204160e+01 3.17922113e+02 8 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 | 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 9 -3.39635681e+02 3.24077989e+02 -4.21921347e+02 | -3.39635681e+02 3.24077989e+02 -4.21921347e+02 10 -5.66897810e+01 -1.58770591e+02 4.79910821e+02 | -5.66897810e+01 -1.58770591e+02 4.79910821e+02 11 9.05519638e+01 8.16204160e+01 3.17922113e+02 | 9.05519638e+01 8.16204160e+01 3.17922113e+02 12 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 | 3.05773498e+02 -2.46927814e+02 -3.75911588e+02 13 -3.39635681e+02 3.24077989e+02 -4.21921347e+02 | -3.39635681e+02 3.24077989e+02 -4.21921347e+02 14 -5.66897810e+01 -1.58770591e+02 4.79910821e+02 | -5.66897810e+01 -1.58770591e+02 4.79910821e+02 15 9.05519638e+01 8.16204160e+01 3.17922113e+02 | 9.05519638e+01 8.16204160e+01 3.17922113e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFT (Configuration in file "config-C-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 2057.761063725071 2^p V(r_1,...,r_N) = 2057.7610637250696 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 -6.33014299e+01 -3.41309284e+02 1.10099265e+02 | -6.33014299e+01 -3.41309284e+02 1.10099265e+02 1 -1.46975882e+01 4.09143468e+02 2.78440697e+02 | -1.46975882e+01 4.09143468e+02 2.78440697e+02 2 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 | 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 3 3.56889296e+01 3.42648266e+02 -4.66462774e+01 | 3.56889296e+01 3.42648266e+02 -4.66462774e+01 4 -6.33014299e+01 -3.41309284e+02 1.10099265e+02 | -6.33014299e+01 -3.41309284e+02 1.10099265e+02 5 -1.46975882e+01 4.09143468e+02 2.78440697e+02 | -1.46975882e+01 4.09143468e+02 2.78440697e+02 6 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 | 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 7 3.56889296e+01 3.42648266e+02 -4.66462774e+01 | 3.56889296e+01 3.42648266e+02 -4.66462774e+01 8 -6.33014299e+01 -3.41309284e+02 1.10099265e+02 | -6.33014299e+01 -3.41309284e+02 1.10099265e+02 9 -1.46975882e+01 4.09143468e+02 2.78440697e+02 | -1.46975882e+01 4.09143468e+02 2.78440697e+02 10 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 | 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 11 3.56889296e+01 3.42648266e+02 -4.66462774e+01 | 3.56889296e+01 3.42648266e+02 -4.66462774e+01 12 -6.33014299e+01 -3.41309284e+02 1.10099265e+02 | -6.33014299e+01 -3.41309284e+02 1.10099265e+02 13 -1.46975882e+01 4.09143468e+02 2.78440697e+02 | -1.46975882e+01 4.09143468e+02 2.78440697e+02 14 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 | 4.23100884e+01 -4.10482450e+02 -3.41893685e+02 15 3.56889296e+01 3.42648266e+02 -4.66462774e+01 | 3.56889296e+01 3.42648266e+02 -4.66462774e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = TFF (Configuration in file "config-C-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 446.6473589664347 2^p V(r_1,...,r_N) = 446.64735896643487 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 5.48694477e+01 -1.98236646e+02 -2.31169152e+02 | 5.48694477e+01 -1.98236646e+02 -2.31169152e+02 1 -5.66216830e+01 2.36229459e+02 -1.07289550e+02 | -5.66216830e+01 2.36229459e+02 -1.07289550e+02 2 6.13287142e+01 -2.49372845e+02 1.70959438e+02 | 6.13287142e+01 -2.49372845e+02 1.70959438e+02 3 -5.95764788e+01 2.11380032e+02 1.67499264e+02 | -5.95764788e+01 2.11380032e+02 1.67499264e+02 4 5.48694477e+01 -1.98236646e+02 -2.31169152e+02 | 5.48694477e+01 -1.98236646e+02 -2.31169152e+02 5 -5.66216830e+01 2.36229459e+02 -1.07289550e+02 | -5.66216830e+01 2.36229459e+02 -1.07289550e+02 6 6.13287142e+01 -2.49372845e+02 1.70959438e+02 | 6.13287142e+01 -2.49372845e+02 1.70959438e+02 7 -5.95764788e+01 2.11380032e+02 1.67499264e+02 | -5.95764788e+01 2.11380032e+02 1.67499264e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTT (Configuration in file "config-C-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 2996.7215217498037 2^p V(r_1,...,r_N) = 2996.7215217498056 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 -2.82906586e+02 -2.99755172e+02 3.17842936e+02 | -2.82906586e+02 -2.99755172e+02 3.17842936e+02 1 6.97951766e+02 1.30064867e+02 1.26347877e+02 | 6.97951766e+02 1.30064867e+02 1.26347877e+02 2 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 | 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 3 -6.16803384e+02 5.35301562e+02 -1.91405836e+00 | -6.16803384e+02 5.35301562e+02 -1.91405836e+00 4 -2.82906586e+02 -2.99755172e+02 3.17842936e+02 | -2.82906586e+02 -2.99755172e+02 3.17842936e+02 5 6.97951766e+02 1.30064867e+02 1.26347877e+02 | 6.97951766e+02 1.30064867e+02 1.26347877e+02 6 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 | 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 7 -6.16803384e+02 5.35301562e+02 -1.91405836e+00 | -6.16803384e+02 5.35301562e+02 -1.91405836e+00 8 -2.82906586e+02 -2.99755172e+02 3.17842936e+02 | -2.82906586e+02 -2.99755172e+02 3.17842936e+02 9 6.97951766e+02 1.30064867e+02 1.26347877e+02 | 6.97951766e+02 1.30064867e+02 1.26347877e+02 10 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 | 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 11 -6.16803384e+02 5.35301562e+02 -1.91405836e+00 | -6.16803384e+02 5.35301562e+02 -1.91405836e+00 12 -2.82906586e+02 -2.99755172e+02 3.17842936e+02 | -2.82906586e+02 -2.99755172e+02 3.17842936e+02 13 6.97951766e+02 1.30064867e+02 1.26347877e+02 | 6.97951766e+02 1.30064867e+02 1.26347877e+02 14 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 | 2.01758204e+02 -3.65611256e+02 -4.42276754e+02 15 -6.16803384e+02 5.35301562e+02 -1.91405836e+00 | -6.16803384e+02 5.35301562e+02 -1.91405836e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FTF (Configuration in file "config-C-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 1031.8973849706067 2^p V(r_1,...,r_N) = 1031.897384970607 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 -6.52336011e+02 -3.91202626e+02 -5.79202641e+02 | -6.52336011e+02 -3.91202626e+02 -5.79202641e+02 1 3.89568743e+02 2.43326268e+02 -4.01168328e+02 | 3.89568743e+02 2.43326268e+02 -4.01168328e+02 2 5.22549564e+02 -4.90964002e+01 5.85864505e+02 | 5.22549564e+02 -4.90964002e+01 5.85864505e+02 3 -2.59782296e+02 1.96972758e+02 3.94506464e+02 | -2.59782296e+02 1.96972758e+02 3.94506464e+02 4 -6.52336011e+02 -3.91202626e+02 -5.79202641e+02 | -6.52336011e+02 -3.91202626e+02 -5.79202641e+02 5 3.89568743e+02 2.43326268e+02 -4.01168328e+02 | 3.89568743e+02 2.43326268e+02 -4.01168328e+02 6 5.22549564e+02 -4.90964002e+01 5.85864505e+02 | 5.22549564e+02 -4.90964002e+01 5.85864505e+02 7 -2.59782296e+02 1.96972758e+02 3.94506464e+02 | -2.59782296e+02 1.96972758e+02 3.94506464e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = C, PBC = FFT (Configuration in file "config-C-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 600.50537106728 2^p V(r_1,...,r_N) = 600.5053710672797 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 -2.46515851e+02 -2.33859833e+02 -1.36678306e+02 | -2.46515851e+02 -2.33859833e+02 -1.36678306e+02 1 1.83499298e+02 2.93624492e+02 -9.32014732e+01 | 1.83499298e+02 2.93624492e+02 -9.32014732e+01 2 2.72449571e+02 -2.41004545e+02 8.39316939e+01 | 2.72449571e+02 -2.41004545e+02 8.39316939e+01 3 -2.09433019e+02 1.81239886e+02 1.45948085e+02 | -2.09433019e+02 1.81239886e+02 1.45948085e+02 4 -2.46515851e+02 -2.33859833e+02 -1.36678306e+02 | -2.46515851e+02 -2.33859833e+02 -1.36678306e+02 5 1.83499298e+02 2.93624492e+02 -9.32014732e+01 | 1.83499298e+02 2.93624492e+02 -9.32014732e+01 6 2.72449571e+02 -2.41004545e+02 8.39316939e+01 | 2.72449571e+02 -2.41004545e+02 8.39316939e+01 7 -2.09433019e+02 1.81239886e+02 1.45948085e+02 | -2.09433019e+02 1.81239886e+02 1.45948085e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TTT (Configuration in file "config-N-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)) = 278.59951327178595 2^p V(r_1,...,r_N) = 278.5995132717868 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 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 1 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 2 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 3 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 4 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 5 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 6 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 7 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 8 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 9 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 10 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 11 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 12 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 13 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 14 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 15 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 16 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 17 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 18 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 19 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 20 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 21 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 22 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 23 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 24 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 25 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 26 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 27 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 28 -1.32788537e+01 -4.14270097e+00 3.63407724e-01 | -1.32788537e+01 -4.14270097e+00 3.63407724e-01 29 5.03742479e-01 -8.31991594e+00 1.89151764e+00 | 5.03742479e-01 -8.31991594e+00 1.89151764e+00 30 1.84880925e+01 1.58938024e+01 -1.82054847e+00 | 1.84880925e+01 1.58938024e+01 -1.82054847e+00 31 -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 | -5.71298127e+00 -3.43118544e+00 -4.34376899e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TTF (Configuration in file "config-N-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)) = 61.7729012042849 2^p V(r_1,...,r_N) = 61.77290120428501 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 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 | 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 1 -1.10562778e+01 1.72415464e+01 -1.69624013e+01 | -1.10562778e+01 1.72415464e+01 -1.69624013e+01 2 -2.40633118e+01 -1.83751641e+01 1.50145460e+01 | -2.40633118e+01 -1.83751641e+01 1.50145460e+01 3 1.54929533e+01 1.31609785e+01 1.90140537e+01 | 1.54929533e+01 1.31609785e+01 1.90140537e+01 4 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 | 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 5 -1.10562778e+01 1.72415464e+01 -1.69624013e+01 | -1.10562778e+01 1.72415464e+01 -1.69624013e+01 6 -2.40633118e+01 -1.83751641e+01 1.50145460e+01 | -2.40633118e+01 -1.83751641e+01 1.50145460e+01 7 1.54929533e+01 1.31609785e+01 1.90140537e+01 | 1.54929533e+01 1.31609785e+01 1.90140537e+01 8 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 | 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 9 -1.10562778e+01 1.72415464e+01 -1.69624013e+01 | -1.10562778e+01 1.72415464e+01 -1.69624013e+01 10 -2.40633118e+01 -1.83751641e+01 1.50145460e+01 | -2.40633118e+01 -1.83751641e+01 1.50145460e+01 11 1.54929533e+01 1.31609785e+01 1.90140537e+01 | 1.54929533e+01 1.31609785e+01 1.90140537e+01 12 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 | 1.96266363e+01 -1.20273608e+01 -1.70661985e+01 13 -1.10562778e+01 1.72415464e+01 -1.69624013e+01 | -1.10562778e+01 1.72415464e+01 -1.69624013e+01 14 -2.40633118e+01 -1.83751641e+01 1.50145460e+01 | -2.40633118e+01 -1.83751641e+01 1.50145460e+01 15 1.54929533e+01 1.31609785e+01 1.90140537e+01 | 1.54929533e+01 1.31609785e+01 1.90140537e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TFT (Configuration in file "config-N-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)) = 16.003811393774388 2^p V(r_1,...,r_N) = 16.003811393774505 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 -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 | -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 1 -2.95782708e+00 1.15011224e+01 5.69403746e+00 | -2.95782708e+00 1.15011224e+01 5.69403746e+00 2 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 | 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 3 -1.37521448e+00 6.73871815e+00 -9.54774353e-01 | -1.37521448e+00 6.73871815e+00 -9.54774353e-01 4 -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 | -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 5 -2.95782708e+00 1.15011224e+01 5.69403746e+00 | -2.95782708e+00 1.15011224e+01 5.69403746e+00 6 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 | 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 7 -1.37521448e+00 6.73871815e+00 -9.54774353e-01 | -1.37521448e+00 6.73871815e+00 -9.54774353e-01 8 -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 | -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 9 -2.95782708e+00 1.15011224e+01 5.69403746e+00 | -2.95782708e+00 1.15011224e+01 5.69403746e+00 10 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 | 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 11 -1.37521448e+00 6.73871815e+00 -9.54774353e-01 | -1.37521448e+00 6.73871815e+00 -9.54774353e-01 12 -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 | -1.43698181e+00 -9.30847169e+00 -2.36528318e+00 13 -2.95782708e+00 1.15011224e+01 5.69403746e+00 | -2.95782708e+00 1.15011224e+01 5.69403746e+00 14 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 | 5.77002337e+00 -8.93136886e+00 -2.37397993e+00 15 -1.37521448e+00 6.73871815e+00 -9.54774353e-01 | -1.37521448e+00 6.73871815e+00 -9.54774353e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TFF (Configuration in file "config-N-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)) = -6.2377773769769105 2^p V(r_1,...,r_N) = -6.23777737697692 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 -1.89774186e+00 -5.22247965e+00 -5.52521098e+00 | -1.89774186e+00 -5.22247965e+00 -5.52521098e+00 1 2.53617604e+00 4.81433292e+00 -4.95031972e+00 | 2.53617604e+00 4.81433292e+00 -4.95031972e+00 2 7.98488029e+00 -4.16156260e+00 3.97610896e+00 | 7.98488029e+00 -4.16156260e+00 3.97610896e+00 3 -8.62331447e+00 4.56970933e+00 6.49942175e+00 | -8.62331447e+00 4.56970933e+00 6.49942175e+00 4 -1.89774186e+00 -5.22247965e+00 -5.52521098e+00 | -1.89774186e+00 -5.22247965e+00 -5.52521098e+00 5 2.53617604e+00 4.81433292e+00 -4.95031972e+00 | 2.53617604e+00 4.81433292e+00 -4.95031972e+00 6 7.98488029e+00 -4.16156260e+00 3.97610896e+00 | 7.98488029e+00 -4.16156260e+00 3.97610896e+00 7 -8.62331447e+00 4.56970933e+00 6.49942175e+00 | -8.62331447e+00 4.56970933e+00 6.49942175e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FTT (Configuration in file "config-N-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)) = 19.817441749893717 2^p V(r_1,...,r_N) = 19.817441749893902 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 -1.42088553e+01 8.73523031e-02 -5.77724070e-01 | -1.42088553e+01 8.73523031e-02 -5.77724070e-01 1 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 | 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 2 1.04596441e+01 4.48056349e+00 -3.13672132e+00 | 1.04596441e+01 4.48056349e+00 -3.13672132e+00 3 -1.00318573e+01 -3.55582451e+00 7.05492248e+00 | -1.00318573e+01 -3.55582451e+00 7.05492248e+00 4 -1.42088553e+01 8.73523031e-02 -5.77724070e-01 | -1.42088553e+01 8.73523031e-02 -5.77724070e-01 5 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 | 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 6 1.04596441e+01 4.48056349e+00 -3.13672132e+00 | 1.04596441e+01 4.48056349e+00 -3.13672132e+00 7 -1.00318573e+01 -3.55582451e+00 7.05492248e+00 | -1.00318573e+01 -3.55582451e+00 7.05492248e+00 8 -1.42088553e+01 8.73523031e-02 -5.77724070e-01 | -1.42088553e+01 8.73523031e-02 -5.77724070e-01 9 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 | 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 10 1.04596441e+01 4.48056349e+00 -3.13672132e+00 | 1.04596441e+01 4.48056349e+00 -3.13672132e+00 11 -1.00318573e+01 -3.55582451e+00 7.05492248e+00 | -1.00318573e+01 -3.55582451e+00 7.05492248e+00 12 -1.42088553e+01 8.73523031e-02 -5.77724070e-01 | -1.42088553e+01 8.73523031e-02 -5.77724070e-01 13 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 | 1.37810685e+01 -1.01209128e+00 -3.34047709e+00 14 1.04596441e+01 4.48056349e+00 -3.13672132e+00 | 1.04596441e+01 4.48056349e+00 -3.13672132e+00 15 -1.00318573e+01 -3.55582451e+00 7.05492248e+00 | -1.00318573e+01 -3.55582451e+00 7.05492248e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FTF (Configuration in file "config-N-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)) = -7.306635029821497 2^p V(r_1,...,r_N) = -7.306635029821493 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 -4.92825848e+00 -5.27757668e+00 -4.94531082e+00 | -4.92825848e+00 -5.27757668e+00 -4.94531082e+00 1 1.30038322e+00 1.31683125e-01 -1.89311107e+00 | 1.30038322e+00 1.31683125e-01 -1.89311107e+00 2 7.23762161e+00 2.48576748e+00 1.35710307e+00 | 7.23762161e+00 2.48576748e+00 1.35710307e+00 3 -3.60974636e+00 2.66012608e+00 5.48131883e+00 | -3.60974636e+00 2.66012608e+00 5.48131883e+00 4 -4.92825848e+00 -5.27757668e+00 -4.94531082e+00 | -4.92825848e+00 -5.27757668e+00 -4.94531082e+00 5 1.30038322e+00 1.31683125e-01 -1.89311107e+00 | 1.30038322e+00 1.31683125e-01 -1.89311107e+00 6 7.23762161e+00 2.48576748e+00 1.35710307e+00 | 7.23762161e+00 2.48576748e+00 1.35710307e+00 7 -3.60974636e+00 2.66012608e+00 5.48131883e+00 | -3.60974636e+00 2.66012608e+00 5.48131883e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FFT (Configuration in file "config-N-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)) = -4.9935824774743125 2^p V(r_1,...,r_N) = -4.993582477474303 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 -5.25252614e+00 -1.50897625e+00 6.91911989e+00 | -5.25252614e+00 -1.50897625e+00 6.91911989e+00 1 3.61743007e+00 2.25104722e+00 1.11159137e+00 | 3.61743007e+00 2.25104722e+00 1.11159137e+00 2 6.16160580e+00 -7.67899767e+00 -5.89960177e+00 | 6.16160580e+00 -7.67899767e+00 -5.89960177e+00 3 -4.52650973e+00 6.93692670e+00 -2.13110949e+00 | -4.52650973e+00 6.93692670e+00 -2.13110949e+00 4 -5.25252614e+00 -1.50897625e+00 6.91911989e+00 | -5.25252614e+00 -1.50897625e+00 6.91911989e+00 5 3.61743007e+00 2.25104722e+00 1.11159137e+00 | 3.61743007e+00 2.25104722e+00 1.11159137e+00 6 6.16160580e+00 -7.67899767e+00 -5.89960177e+00 | 6.16160580e+00 -7.67899767e+00 -5.89960177e+00 7 -4.52650973e+00 6.93692670e+00 -2.13110949e+00 | -4.52650973e+00 6.93692670e+00 -2.13110949e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = TTT (Configuration in file "config-BCN-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)) = 5285.237661803365 2^p V(r_1,...,r_N) = 5285.23766180334 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 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 1 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 2 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 3 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 4 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 5 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 6 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 7 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 8 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 9 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 10 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 11 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 12 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 13 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 14 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 15 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 16 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 17 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 18 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 19 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 20 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 21 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 22 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 23 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 24 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 25 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 26 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 27 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 28 1.82045165e+02 2.85908713e+02 -6.92359127e+00 | 1.82045165e+02 2.85908713e+02 -6.92359127e+00 29 -3.64785691e+02 -2.29289740e+02 2.39102409e+01 | -3.64785691e+02 -2.29289740e+02 2.39102409e+01 30 -1.59487220e+02 8.57841137e+01 2.87694629e+02 | -1.59487220e+02 8.57841137e+01 2.87694629e+02 31 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 | 3.42227747e+02 -1.42403087e+02 -3.04681278e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = TTF (Configuration in file "config-BCN-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)) = 1443.2831343042665 2^p V(r_1,...,r_N) = 1443.2831343042642 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 1.13673234e+02 1.14458536e+02 -1.92287421e+02 | 1.13673234e+02 1.14458536e+02 -1.92287421e+02 1 -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 | -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 2 4.69925347e+00 7.86809992e+01 1.92437271e+02 | 4.69925347e+00 7.86809992e+01 1.92437271e+02 3 1.72410453e+01 -4.20429801e+01 2.79279498e+02 | 1.72410453e+01 -4.20429801e+01 2.79279498e+02 4 1.13673234e+02 1.14458536e+02 -1.92287421e+02 | 1.13673234e+02 1.14458536e+02 -1.92287421e+02 5 -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 | -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 6 4.69925347e+00 7.86809992e+01 1.92437271e+02 | 4.69925347e+00 7.86809992e+01 1.92437271e+02 7 1.72410453e+01 -4.20429801e+01 2.79279498e+02 | 1.72410453e+01 -4.20429801e+01 2.79279498e+02 8 1.13673234e+02 1.14458536e+02 -1.92287421e+02 | 1.13673234e+02 1.14458536e+02 -1.92287421e+02 9 -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 | -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 10 4.69925347e+00 7.86809992e+01 1.92437271e+02 | 4.69925347e+00 7.86809992e+01 1.92437271e+02 11 1.72410453e+01 -4.20429801e+01 2.79279498e+02 | 1.72410453e+01 -4.20429801e+01 2.79279498e+02 12 1.13673234e+02 1.14458536e+02 -1.92287421e+02 | 1.13673234e+02 1.14458536e+02 -1.92287421e+02 13 -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 | -1.35613533e+02 -1.51096555e+02 -2.79429347e+02 14 4.69925347e+00 7.86809992e+01 1.92437271e+02 | 4.69925347e+00 7.86809992e+01 1.92437271e+02 15 1.72410453e+01 -4.20429801e+01 2.79279498e+02 | 1.72410453e+01 -4.20429801e+01 2.79279498e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = TFT (Configuration in file "config-BCN-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)) = 1137.8432883618175 2^p V(r_1,...,r_N) = 1137.8432883618173 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 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 | 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 1 -3.00323842e+01 9.52418936e+01 -8.53835979e+00 | -3.00323842e+01 9.52418936e+01 -8.53835979e+00 2 5.03778186e+01 -3.62204952e+02 4.02543878e+01 | 5.03778186e+01 -3.62204952e+02 4.02543878e+01 3 -3.34601729e+01 3.60470968e+02 8.08316969e+01 | -3.34601729e+01 3.60470968e+02 8.08316969e+01 4 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 | 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 5 -3.00323842e+01 9.52418936e+01 -8.53835979e+00 | -3.00323842e+01 9.52418936e+01 -8.53835979e+00 6 5.03778186e+01 -3.62204952e+02 4.02543878e+01 | 5.03778186e+01 -3.62204952e+02 4.02543878e+01 7 -3.34601729e+01 3.60470968e+02 8.08316969e+01 | -3.34601729e+01 3.60470968e+02 8.08316969e+01 8 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 | 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 9 -3.00323842e+01 9.52418936e+01 -8.53835979e+00 | -3.00323842e+01 9.52418936e+01 -8.53835979e+00 10 5.03778186e+01 -3.62204952e+02 4.02543878e+01 | 5.03778186e+01 -3.62204952e+02 4.02543878e+01 11 -3.34601729e+01 3.60470968e+02 8.08316969e+01 | -3.34601729e+01 3.60470968e+02 8.08316969e+01 12 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 | 1.31147385e+01 -9.35079100e+01 -1.12547725e+02 13 -3.00323842e+01 9.52418936e+01 -8.53835979e+00 | -3.00323842e+01 9.52418936e+01 -8.53835979e+00 14 5.03778186e+01 -3.62204952e+02 4.02543878e+01 | 5.03778186e+01 -3.62204952e+02 4.02543878e+01 15 -3.34601729e+01 3.60470968e+02 8.08316969e+01 | -3.34601729e+01 3.60470968e+02 8.08316969e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = TFF (Configuration in file "config-BCN-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)) = 286.5931161609085 2^p V(r_1,...,r_N) = 286.5931161609085 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 -5.85942022e+01 -1.93391242e+02 -7.91570548e+01 | -5.85942022e+01 -1.93391242e+02 -7.91570548e+01 1 9.69009895e+01 2.28675776e+02 -1.68953329e+02 | 9.69009895e+01 2.28675776e+02 -1.68953329e+02 2 2.44045679e+01 -1.84994226e+02 2.14442569e+01 | 2.44045679e+01 -1.84994226e+02 2.14442569e+01 3 -6.27113552e+01 1.49709692e+02 2.26666127e+02 | -6.27113552e+01 1.49709692e+02 2.26666127e+02 4 -5.85942022e+01 -1.93391242e+02 -7.91570548e+01 | -5.85942022e+01 -1.93391242e+02 -7.91570548e+01 5 9.69009895e+01 2.28675776e+02 -1.68953329e+02 | 9.69009895e+01 2.28675776e+02 -1.68953329e+02 6 2.44045679e+01 -1.84994226e+02 2.14442569e+01 | 2.44045679e+01 -1.84994226e+02 2.14442569e+01 7 -6.27113552e+01 1.49709692e+02 2.26666127e+02 | -6.27113552e+01 1.49709692e+02 2.26666127e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = FTT (Configuration in file "config-BCN-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)) = 1547.144130170464 2^p V(r_1,...,r_N) = 1547.1441301704642 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 -3.82143962e+02 -5.12555947e+01 1.74536611e+02 | -3.82143962e+02 -5.12555947e+01 1.74536611e+02 1 4.89676830e+02 1.15024433e+02 -2.00437963e+01 | 4.89676830e+02 1.15024433e+02 -2.00437963e+01 2 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 | 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 3 -1.25546504e+02 4.51305176e+01 2.13580981e+01 | -1.25546504e+02 4.51305176e+01 2.13580981e+01 4 -3.82143962e+02 -5.12555947e+01 1.74536611e+02 | -3.82143962e+02 -5.12555947e+01 1.74536611e+02 5 4.89676830e+02 1.15024433e+02 -2.00437963e+01 | 4.89676830e+02 1.15024433e+02 -2.00437963e+01 6 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 | 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 7 -1.25546504e+02 4.51305176e+01 2.13580981e+01 | -1.25546504e+02 4.51305176e+01 2.13580981e+01 8 -3.82143962e+02 -5.12555947e+01 1.74536611e+02 | -3.82143962e+02 -5.12555947e+01 1.74536611e+02 9 4.89676830e+02 1.15024433e+02 -2.00437963e+01 | 4.89676830e+02 1.15024433e+02 -2.00437963e+01 10 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 | 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 11 -1.25546504e+02 4.51305176e+01 2.13580981e+01 | -1.25546504e+02 4.51305176e+01 2.13580981e+01 12 -3.82143962e+02 -5.12555947e+01 1.74536611e+02 | -3.82143962e+02 -5.12555947e+01 1.74536611e+02 13 4.89676830e+02 1.15024433e+02 -2.00437963e+01 | 4.89676830e+02 1.15024433e+02 -2.00437963e+01 14 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 | 1.80136363e+01 -1.08899356e+02 -1.75850913e+02 15 -1.25546504e+02 4.51305176e+01 2.13580981e+01 | -1.25546504e+02 4.51305176e+01 2.13580981e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = FTF (Configuration in file "config-BCN-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)) = 1370.6119677209756 2^p V(r_1,...,r_N) = 1370.611967720975 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 -8.79241238e+02 1.02814587e+03 -3.45553537e+02 | -8.79241238e+02 1.02814587e+03 -3.45553537e+02 1 6.76072544e+02 -1.00876429e+03 -4.25870022e+02 | 6.76072544e+02 -1.00876429e+03 -4.25870022e+02 2 4.01120313e+02 2.16371604e+02 3.12712948e+02 | 4.01120313e+02 2.16371604e+02 3.12712948e+02 3 -1.97951619e+02 -2.35753181e+02 4.58710611e+02 | -1.97951619e+02 -2.35753181e+02 4.58710611e+02 4 -8.79241238e+02 1.02814587e+03 -3.45553537e+02 | -8.79241238e+02 1.02814587e+03 -3.45553537e+02 5 6.76072544e+02 -1.00876429e+03 -4.25870022e+02 | 6.76072544e+02 -1.00876429e+03 -4.25870022e+02 6 4.01120313e+02 2.16371604e+02 3.12712948e+02 | 4.01120313e+02 2.16371604e+02 3.12712948e+02 7 -1.97951619e+02 -2.35753181e+02 4.58710611e+02 | -1.97951619e+02 -2.35753181e+02 4.58710611e+02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = B C N, PBC = FFT (Configuration in file "config-BCN-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)) = 493.6611782118217 2^p V(r_1,...,r_N) = 493.6611782118217 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 -9.77525381e+01 -1.48652993e+02 -2.00272549e+01 | -9.77525381e+01 -1.48652993e+02 -2.00272549e+01 1 5.58480003e+01 -4.01371204e+01 -2.00532579e+02 | 5.58480003e+01 -4.01371204e+01 -2.00532579e+02 2 3.05564950e+02 -1.73038313e+02 8.26505025e+01 | 3.05564950e+02 -1.73038313e+02 8.26505025e+01 3 -2.63660412e+02 3.61828426e+02 1.37909331e+02 | -2.63660412e+02 3.61828426e+02 1.37909331e+02 4 -9.77525381e+01 -1.48652993e+02 -2.00272549e+01 | -9.77525381e+01 -1.48652993e+02 -2.00272549e+01 5 5.58480003e+01 -4.01371204e+01 -2.00532579e+02 | 5.58480003e+01 -4.01371204e+01 -2.00532579e+02 6 3.05564950e+02 -1.73038313e+02 8.26505025e+01 | 3.05564950e+02 -1.73038313e+02 8.26505025e+01 7 -2.63660412e+02 3.61828426e+02 1.37909331e+02 | -2.63660412e+02 3.61828426e+02 1.37909331e+02 ------------------------------------------------------------------------------------------------------------------------ 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.