!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_FarkasCaro_2020_FeNiCrCoAl__MO_820335782779_000 Supported species : Al Co Cr Fe Ni 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)) = 5.236117169850618 2^p V(r_1,...,r_N) = 5.2361171698510365 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 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 1 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 2 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 3 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 4 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 5 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 6 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 7 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 8 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 9 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 10 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 11 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 12 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 13 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 14 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 15 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 16 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 17 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 18 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 19 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 20 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 21 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 22 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 23 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 24 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 25 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 26 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 27 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-01 28 3.90625723e+00 -7.00698018e+00 4.05475101e-01 | 3.90625723e+00 -7.00698018e+00 4.05475101e-01 29 -6.48768452e+00 6.78018553e+00 1.71204291e+00 | -6.48768452e+00 6.78018553e+00 1.71204291e+00 30 -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 | -2.94380770e+00 -8.65960248e+00 -1.72712392e+00 31 5.52523499e+00 8.88639713e+00 -3.90394092e-01 | 5.52523499e+00 8.88639713e+00 -3.90394092e-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)) = 70.70840122416882 2^p V(r_1,...,r_N) = 70.70840122416887 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 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 | 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 1 -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 | -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 2 -2.77713785e+00 1.03681768e+00 1.49402399e+01 | -2.77713785e+00 1.03681768e+00 1.49402399e+01 3 2.02287419e+00 5.51262035e-01 1.17646990e+01 | 2.02287419e+00 5.51262035e-01 1.17646990e+01 4 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 | 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 5 -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 | -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 6 -2.77713785e+00 1.03681768e+00 1.49402399e+01 | -2.77713785e+00 1.03681768e+00 1.49402399e+01 7 2.02287419e+00 5.51262035e-01 1.17646990e+01 | 2.02287419e+00 5.51262035e-01 1.17646990e+01 8 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 | 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 9 -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 | -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 10 -2.77713785e+00 1.03681768e+00 1.49402399e+01 | -2.77713785e+00 1.03681768e+00 1.49402399e+01 11 2.02287419e+00 5.51262035e-01 1.17646990e+01 | 2.02287419e+00 5.51262035e-01 1.17646990e+01 12 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 | 2.79767625e+00 -3.42754265e-01 -1.28490679e+01 13 -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 | -2.04341260e+00 -1.24532545e+00 -1.38558711e+01 14 -2.77713785e+00 1.03681768e+00 1.49402399e+01 | -2.77713785e+00 1.03681768e+00 1.49402399e+01 15 2.02287419e+00 5.51262035e-01 1.17646990e+01 | 2.02287419e+00 5.51262035e-01 1.17646990e+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)) = 78.928729488987 2^p V(r_1,...,r_N) = 78.9287294889869 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 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 | 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 1 -3.03976751e+00 1.53177272e+01 -2.32139534e+00 | -3.03976751e+00 1.53177272e+01 -2.32139534e+00 2 -2.37291547e+00 -1.39550450e+01 2.83347700e+00 | -2.37291547e+00 -1.39550450e+01 2.83347700e+00 3 2.34513914e+00 1.05462294e+01 7.10383648e-01 | 2.34513914e+00 1.05462294e+01 7.10383648e-01 4 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 | 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 5 -3.03976751e+00 1.53177272e+01 -2.32139534e+00 | -3.03976751e+00 1.53177272e+01 -2.32139534e+00 6 -2.37291547e+00 -1.39550450e+01 2.83347700e+00 | -2.37291547e+00 -1.39550450e+01 2.83347700e+00 7 2.34513914e+00 1.05462294e+01 7.10383648e-01 | 2.34513914e+00 1.05462294e+01 7.10383648e-01 8 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 | 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 9 -3.03976751e+00 1.53177272e+01 -2.32139534e+00 | -3.03976751e+00 1.53177272e+01 -2.32139534e+00 10 -2.37291547e+00 -1.39550450e+01 2.83347700e+00 | -2.37291547e+00 -1.39550450e+01 2.83347700e+00 11 2.34513914e+00 1.05462294e+01 7.10383648e-01 | 2.34513914e+00 1.05462294e+01 7.10383648e-01 12 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 | 3.06754384e+00 -1.19089117e+01 -1.22246531e+00 13 -3.03976751e+00 1.53177272e+01 -2.32139534e+00 | -3.03976751e+00 1.53177272e+01 -2.32139534e+00 14 -2.37291547e+00 -1.39550450e+01 2.83347700e+00 | -2.37291547e+00 -1.39550450e+01 2.83347700e+00 15 2.34513914e+00 1.05462294e+01 7.10383648e-01 | 2.34513914e+00 1.05462294e+01 7.10383648e-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)) = 29.944744298670635 2^p V(r_1,...,r_N) = 29.944744298670642 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 -3.59007348e+00 -1.05375719e+01 -1.00071187e+01 | -3.59007348e+00 -1.05375719e+01 -1.00071187e+01 1 2.85971503e+00 1.16303896e+01 -1.02959146e+01 | 2.85971503e+00 1.16303896e+01 -1.02959146e+01 2 2.57716663e+00 -9.75417016e+00 1.12573615e+01 | 2.57716663e+00 -9.75417016e+00 1.12573615e+01 3 -1.84680818e+00 8.66135247e+00 9.04567186e+00 | -1.84680818e+00 8.66135247e+00 9.04567186e+00 4 -3.59007348e+00 -1.05375719e+01 -1.00071187e+01 | -3.59007348e+00 -1.05375719e+01 -1.00071187e+01 5 2.85971503e+00 1.16303896e+01 -1.02959146e+01 | 2.85971503e+00 1.16303896e+01 -1.02959146e+01 6 2.57716663e+00 -9.75417016e+00 1.12573615e+01 | 2.57716663e+00 -9.75417016e+00 1.12573615e+01 7 -1.84680818e+00 8.66135247e+00 9.04567186e+00 | -1.84680818e+00 8.66135247e+00 9.04567186e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 88.50788766244864 2^p V(r_1,...,r_N) = 88.50788766244854 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 -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 | -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 1 1.01114859e+01 1.14926810e+00 -2.92291102e+00 | 1.01114859e+01 1.14926810e+00 -2.92291102e+00 2 1.51313784e+01 -2.55772461e+00 4.05330708e+00 | 1.51313784e+01 -2.55772461e+00 4.05330708e+00 3 -1.39019923e+01 2.27878479e+00 2.61462525e+00 | -1.39019923e+01 2.27878479e+00 2.61462525e+00 4 -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 | -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 5 1.01114859e+01 1.14926810e+00 -2.92291102e+00 | 1.01114859e+01 1.14926810e+00 -2.92291102e+00 6 1.51313784e+01 -2.55772461e+00 4.05330708e+00 | 1.51313784e+01 -2.55772461e+00 4.05330708e+00 7 -1.39019923e+01 2.27878479e+00 2.61462525e+00 | -1.39019923e+01 2.27878479e+00 2.61462525e+00 8 -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 | -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 9 1.01114859e+01 1.14926810e+00 -2.92291102e+00 | 1.01114859e+01 1.14926810e+00 -2.92291102e+00 10 1.51313784e+01 -2.55772461e+00 4.05330708e+00 | 1.51313784e+01 -2.55772461e+00 4.05330708e+00 11 -1.39019923e+01 2.27878479e+00 2.61462525e+00 | -1.39019923e+01 2.27878479e+00 2.61462525e+00 12 -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 | -1.13408719e+01 -8.70328271e-01 -3.74502131e+00 13 1.01114859e+01 1.14926810e+00 -2.92291102e+00 | 1.01114859e+01 1.14926810e+00 -2.92291102e+00 14 1.51313784e+01 -2.55772461e+00 4.05330708e+00 | 1.51313784e+01 -2.55772461e+00 4.05330708e+00 15 -1.39019923e+01 2.27878479e+00 2.61462525e+00 | -1.39019923e+01 2.27878479e+00 2.61462525e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 36.621231705063074 2^p V(r_1,...,r_N) = 36.621231705063074 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 -1.14458427e+01 -3.81265779e-01 -9.90142166e+00 | -1.14458427e+01 -3.81265779e-01 -9.90142166e+00 1 1.18865513e+01 -1.91777377e-01 -1.23469242e+01 | 1.18865513e+01 -1.91777377e-01 -1.23469242e+01 2 1.01608276e+01 5.26407947e-01 1.23885786e+01 | 1.01608276e+01 5.26407947e-01 1.23885786e+01 3 -1.06015361e+01 4.66352087e-02 9.85976732e+00 | -1.06015361e+01 4.66352087e-02 9.85976732e+00 4 -1.14458427e+01 -3.81265779e-01 -9.90142166e+00 | -1.14458427e+01 -3.81265779e-01 -9.90142166e+00 5 1.18865513e+01 -1.91777377e-01 -1.23469242e+01 | 1.18865513e+01 -1.91777377e-01 -1.23469242e+01 6 1.01608276e+01 5.26407947e-01 1.23885786e+01 | 1.01608276e+01 5.26407947e-01 1.23885786e+01 7 -1.06015361e+01 4.66352087e-02 9.85976732e+00 | -1.06015361e+01 4.66352087e-02 9.85976732e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 29.398115888006668 2^p V(r_1,...,r_N) = 29.398115888006675 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 -1.11822396e+01 -1.06132740e+01 1.32841486e-01 | -1.11822396e+01 -1.06132740e+01 1.32841486e-01 1 8.42606359e+00 1.33199715e+01 1.27564523e+00 | 8.42606359e+00 1.33199715e+01 1.27564523e+00 2 1.19774567e+01 -1.09158854e+01 -3.76414278e-01 | 1.19774567e+01 -1.09158854e+01 -3.76414278e-01 3 -9.22128072e+00 8.20918791e+00 -1.03207244e+00 | -9.22128072e+00 8.20918791e+00 -1.03207244e+00 4 -1.11822396e+01 -1.06132740e+01 1.32841486e-01 | -1.11822396e+01 -1.06132740e+01 1.32841486e-01 5 8.42606359e+00 1.33199715e+01 1.27564523e+00 | 8.42606359e+00 1.33199715e+01 1.27564523e+00 6 1.19774567e+01 -1.09158854e+01 -3.76414278e-01 | 1.19774567e+01 -1.09158854e+01 -3.76414278e-01 7 -9.22128072e+00 8.20918791e+00 -1.03207244e+00 | -9.22128072e+00 8.20918791e+00 -1.03207244e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TTT (Configuration in file "config-Co-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)) = -12.744025775376516 2^p V(r_1,...,r_N) = -12.744025775376922 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 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 1 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 2 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 3 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 4 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 5 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 6 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 7 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 8 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 9 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 10 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 11 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 12 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 13 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 14 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 15 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 16 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 17 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 18 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 19 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 20 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 21 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 22 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 23 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 24 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 25 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 26 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 27 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 28 1.40795017e+00 4.12160272e+00 -3.57713077e+00 | 1.40795017e+00 4.12160272e+00 -3.57713077e+00 29 3.75474483e+00 -1.87412031e+00 1.36783697e+00 | 3.75474483e+00 -1.87412031e+00 1.36783697e+00 30 1.35276112e+00 9.80532062e-01 -2.80250598e+00 | 1.35276112e+00 9.80532062e-01 -2.80250598e+00 31 -6.51545613e+00 -3.22801446e+00 5.01179978e+00 | -6.51545613e+00 -3.22801446e+00 5.01179978e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TTF (Configuration in file "config-Co-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)) = -17.4393341286293 2^p V(r_1,...,r_N) = -17.43933412862931 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 3.13490091e+00 2.70183752e+00 -1.01977557e+01 | 3.13490091e+00 2.70183752e+00 -1.01977557e+01 1 -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 | -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 2 -4.33438137e+00 2.28852750e+00 8.91427552e+00 | -4.33438137e+00 2.28852750e+00 8.91427552e+00 3 3.42805496e+00 -1.81327313e+00 1.14754611e+01 | 3.42805496e+00 -1.81327313e+00 1.14754611e+01 4 3.13490091e+00 2.70183752e+00 -1.01977557e+01 | 3.13490091e+00 2.70183752e+00 -1.01977557e+01 5 -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 | -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 6 -4.33438137e+00 2.28852750e+00 8.91427552e+00 | -4.33438137e+00 2.28852750e+00 8.91427552e+00 7 3.42805496e+00 -1.81327313e+00 1.14754611e+01 | 3.42805496e+00 -1.81327313e+00 1.14754611e+01 8 3.13490091e+00 2.70183752e+00 -1.01977557e+01 | 3.13490091e+00 2.70183752e+00 -1.01977557e+01 9 -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 | -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 10 -4.33438137e+00 2.28852750e+00 8.91427552e+00 | -4.33438137e+00 2.28852750e+00 8.91427552e+00 11 3.42805496e+00 -1.81327313e+00 1.14754611e+01 | 3.42805496e+00 -1.81327313e+00 1.14754611e+01 12 3.13490091e+00 2.70183752e+00 -1.01977557e+01 | 3.13490091e+00 2.70183752e+00 -1.01977557e+01 13 -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 | -2.22857450e+00 -3.17709190e+00 -1.01919809e+01 14 -4.33438137e+00 2.28852750e+00 8.91427552e+00 | -4.33438137e+00 2.28852750e+00 8.91427552e+00 15 3.42805496e+00 -1.81327313e+00 1.14754611e+01 | 3.42805496e+00 -1.81327313e+00 1.14754611e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TFT (Configuration in file "config-Co-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)) = -13.189113744396582 2^p V(r_1,...,r_N) = -13.189113744396614 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 -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 | -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 1 1.32021827e+00 1.02582022e+01 -7.48814380e+00 | 1.32021827e+00 1.02582022e+01 -7.48814380e+00 2 3.35687435e+00 -1.10479877e+01 7.40427091e+00 | 3.35687435e+00 -1.10479877e+01 7.40427091e+00 3 -2.83333855e+00 8.54957217e+00 4.71668767e+00 | -2.83333855e+00 8.54957217e+00 4.71668767e+00 4 -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 | -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 5 1.32021827e+00 1.02582022e+01 -7.48814380e+00 | 1.32021827e+00 1.02582022e+01 -7.48814380e+00 6 3.35687435e+00 -1.10479877e+01 7.40427091e+00 | 3.35687435e+00 -1.10479877e+01 7.40427091e+00 7 -2.83333855e+00 8.54957217e+00 4.71668767e+00 | -2.83333855e+00 8.54957217e+00 4.71668767e+00 8 -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 | -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 9 1.32021827e+00 1.02582022e+01 -7.48814380e+00 | 1.32021827e+00 1.02582022e+01 -7.48814380e+00 10 3.35687435e+00 -1.10479877e+01 7.40427091e+00 | 3.35687435e+00 -1.10479877e+01 7.40427091e+00 11 -2.83333855e+00 8.54957217e+00 4.71668767e+00 | -2.83333855e+00 8.54957217e+00 4.71668767e+00 12 -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 | -1.84375408e+00 -7.75978666e+00 -4.63281478e+00 13 1.32021827e+00 1.02582022e+01 -7.48814380e+00 | 1.32021827e+00 1.02582022e+01 -7.48814380e+00 14 3.35687435e+00 -1.10479877e+01 7.40427091e+00 | 3.35687435e+00 -1.10479877e+01 7.40427091e+00 15 -2.83333855e+00 8.54957217e+00 4.71668767e+00 | -2.83333855e+00 8.54957217e+00 4.71668767e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = TFF (Configuration in file "config-Co-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)) = 7.327284248564281 2^p V(r_1,...,r_N) = 7.327284248564271 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 -9.52265429e-02 -7.65163654e+00 -9.49909379e+00 | -9.52265429e-02 -7.65163654e+00 -9.49909379e+00 1 3.03969194e+00 1.17797530e+01 -6.25364187e+00 | 3.03969194e+00 1.17797530e+01 -6.25364187e+00 2 2.87609626e+00 -8.01301482e+00 1.04302455e+01 | 2.87609626e+00 -8.01301482e+00 1.04302455e+01 3 -5.82056165e+00 3.88489841e+00 5.32249020e+00 | -5.82056165e+00 3.88489841e+00 5.32249020e+00 4 -9.52265429e-02 -7.65163654e+00 -9.49909379e+00 | -9.52265429e-02 -7.65163654e+00 -9.49909379e+00 5 3.03969194e+00 1.17797530e+01 -6.25364187e+00 | 3.03969194e+00 1.17797530e+01 -6.25364187e+00 6 2.87609626e+00 -8.01301482e+00 1.04302455e+01 | 2.87609626e+00 -8.01301482e+00 1.04302455e+01 7 -5.82056165e+00 3.88489841e+00 5.32249020e+00 | -5.82056165e+00 3.88489841e+00 5.32249020e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FTT (Configuration in file "config-Co-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)) = -1.8391202845844963 2^p V(r_1,...,r_N) = -1.8391202845844528 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 -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 | -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 1 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 | 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 2 9.78246970e+00 1.45670052e+00 5.63982719e+00 | 9.78246970e+00 1.45670052e+00 5.63982719e+00 3 -9.25651363e+00 2.30931689e+00 4.26039819e+00 | -9.25651363e+00 2.30931689e+00 4.26039819e+00 4 -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 | -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 5 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 | 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 6 9.78246970e+00 1.45670052e+00 5.63982719e+00 | 9.78246970e+00 1.45670052e+00 5.63982719e+00 7 -9.25651363e+00 2.30931689e+00 4.26039819e+00 | -9.25651363e+00 2.30931689e+00 4.26039819e+00 8 -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 | -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 9 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 | 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 10 9.78246970e+00 1.45670052e+00 5.63982719e+00 | 9.78246970e+00 1.45670052e+00 5.63982719e+00 11 -9.25651363e+00 2.30931689e+00 4.26039819e+00 | -9.25651363e+00 2.30931689e+00 4.26039819e+00 12 -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 | -9.45536471e+00 -2.10385713e+00 -4.53760419e+00 13 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 | 8.92940864e+00 -1.66216028e+00 -5.36262119e+00 14 9.78246970e+00 1.45670052e+00 5.63982719e+00 | 9.78246970e+00 1.45670052e+00 5.63982719e+00 15 -9.25651363e+00 2.30931689e+00 4.26039819e+00 | -9.25651363e+00 2.30931689e+00 4.26039819e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FTF (Configuration in file "config-Co-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)) = 4.44790739084081 2^p V(r_1,...,r_N) = 4.447907390840811 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 -9.93276080e+00 -3.04066217e+00 -6.04525555e+00 | -9.93276080e+00 -3.04066217e+00 -6.04525555e+00 1 9.35026394e+00 5.47820257e-01 -7.54362428e+00 | 9.35026394e+00 5.47820257e-01 -7.54362428e+00 2 1.05464209e+01 -6.41988243e-01 8.09161224e+00 | 1.05464209e+01 -6.41988243e-01 8.09161224e+00 3 -9.96392408e+00 3.13483016e+00 5.49726760e+00 | -9.96392408e+00 3.13483016e+00 5.49726760e+00 4 -9.93276080e+00 -3.04066217e+00 -6.04525555e+00 | -9.93276080e+00 -3.04066217e+00 -6.04525555e+00 5 9.35026394e+00 5.47820257e-01 -7.54362428e+00 | 9.35026394e+00 5.47820257e-01 -7.54362428e+00 6 1.05464209e+01 -6.41988243e-01 8.09161224e+00 | 1.05464209e+01 -6.41988243e-01 8.09161224e+00 7 -9.96392408e+00 3.13483016e+00 5.49726760e+00 | -9.96392408e+00 3.13483016e+00 5.49726760e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Co, PBC = FFT (Configuration in file "config-Co-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)) = 8.496495570542722 2^p V(r_1,...,r_N) = 8.496495570542733 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.71139597e+00 -6.84963380e+00 -3.06965348e+00 | -7.71139597e+00 -6.84963380e+00 -3.06965348e+00 1 7.50556398e+00 6.04242400e+00 1.61343729e+00 | 7.50556398e+00 6.04242400e+00 1.61343729e+00 2 7.97578071e+00 -6.17104401e+00 -3.29693763e-01 | 7.97578071e+00 -6.17104401e+00 -3.29693763e-01 3 -7.76994872e+00 6.97825381e+00 1.78590996e+00 | -7.76994872e+00 6.97825381e+00 1.78590996e+00 4 -7.71139597e+00 -6.84963380e+00 -3.06965348e+00 | -7.71139597e+00 -6.84963380e+00 -3.06965348e+00 5 7.50556398e+00 6.04242400e+00 1.61343729e+00 | 7.50556398e+00 6.04242400e+00 1.61343729e+00 6 7.97578071e+00 -6.17104401e+00 -3.29693763e-01 | 7.97578071e+00 -6.17104401e+00 -3.29693763e-01 7 -7.76994872e+00 6.97825381e+00 1.78590996e+00 | -7.76994872e+00 6.97825381e+00 1.78590996e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTT (Configuration in file "config-Cr-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)) = -60.281520009734336 2^p V(r_1,...,r_N) = -60.28152000973302 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 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 1 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 2 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 3 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 4 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 5 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 6 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 7 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 8 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 9 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 10 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 11 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 12 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 13 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 14 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 15 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 16 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 17 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 18 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 19 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 20 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 21 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 22 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 23 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 24 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 25 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 26 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 27 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 28 -4.99986785e+00 1.93308974e+00 2.30440010e+00 | -4.99986785e+00 1.93308974e+00 2.30440010e+00 29 6.24763777e+00 -2.11348453e+00 1.70036416e+00 | 6.24763777e+00 -2.11348453e+00 1.70036416e+00 30 2.15639197e+00 4.67854475e+00 -2.94045242e+00 | 2.15639197e+00 4.67854475e+00 -2.94045242e+00 31 -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 | -3.40416190e+00 -4.49814995e+00 -1.06431184e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTF (Configuration in file "config-Cr-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)) = -28.707495258869127 2^p V(r_1,...,r_N) = -28.707495258869297 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 -1.71960100e+00 1.17355042e+00 -6.10550235e+00 | -1.71960100e+00 1.17355042e+00 -6.10550235e+00 1 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 | 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 2 1.80461290e+00 2.28774133e+00 7.19598730e+00 | 1.80461290e+00 2.28774133e+00 7.19598730e+00 3 -9.67991619e-01 -1.91498957e+00 7.08982445e+00 | -9.67991619e-01 -1.91498957e+00 7.08982445e+00 4 -1.71960100e+00 1.17355042e+00 -6.10550235e+00 | -1.71960100e+00 1.17355042e+00 -6.10550235e+00 5 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 | 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 6 1.80461290e+00 2.28774133e+00 7.19598730e+00 | 1.80461290e+00 2.28774133e+00 7.19598730e+00 7 -9.67991619e-01 -1.91498957e+00 7.08982445e+00 | -9.67991619e-01 -1.91498957e+00 7.08982445e+00 8 -1.71960100e+00 1.17355042e+00 -6.10550235e+00 | -1.71960100e+00 1.17355042e+00 -6.10550235e+00 9 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 | 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 10 1.80461290e+00 2.28774133e+00 7.19598730e+00 | 1.80461290e+00 2.28774133e+00 7.19598730e+00 11 -9.67991619e-01 -1.91498957e+00 7.08982445e+00 | -9.67991619e-01 -1.91498957e+00 7.08982445e+00 12 -1.71960100e+00 1.17355042e+00 -6.10550235e+00 | -1.71960100e+00 1.17355042e+00 -6.10550235e+00 13 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 | 8.82979719e-01 -1.54630218e+00 -8.18030940e+00 14 1.80461290e+00 2.28774133e+00 7.19598730e+00 | 1.80461290e+00 2.28774133e+00 7.19598730e+00 15 -9.67991619e-01 -1.91498957e+00 7.08982445e+00 | -9.67991619e-01 -1.91498957e+00 7.08982445e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFT (Configuration in file "config-Cr-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)) = -9.455032747876054 2^p V(r_1,...,r_N) = -9.455032747876077 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 -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 | -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 1 -3.59017756e-01 5.72781573e+00 2.09963617e+00 | -3.59017756e-01 5.72781573e+00 2.09963617e+00 2 -3.12019413e-01 -4.79939854e+00 7.20729775e-01 | -3.12019413e-01 -4.79939854e+00 7.20729775e-01 3 1.63598837e+00 4.50820817e+00 -2.42786184e+00 | 1.63598837e+00 4.50820817e+00 -2.42786184e+00 4 -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 | -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 5 -3.59017756e-01 5.72781573e+00 2.09963617e+00 | -3.59017756e-01 5.72781573e+00 2.09963617e+00 6 -3.12019413e-01 -4.79939854e+00 7.20729775e-01 | -3.12019413e-01 -4.79939854e+00 7.20729775e-01 7 1.63598837e+00 4.50820817e+00 -2.42786184e+00 | 1.63598837e+00 4.50820817e+00 -2.42786184e+00 8 -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 | -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 9 -3.59017756e-01 5.72781573e+00 2.09963617e+00 | -3.59017756e-01 5.72781573e+00 2.09963617e+00 10 -3.12019413e-01 -4.79939854e+00 7.20729775e-01 | -3.12019413e-01 -4.79939854e+00 7.20729775e-01 11 1.63598837e+00 4.50820817e+00 -2.42786184e+00 | 1.63598837e+00 4.50820817e+00 -2.42786184e+00 12 -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 | -9.64951198e-01 -5.43662537e+00 -3.92504097e-01 13 -3.59017756e-01 5.72781573e+00 2.09963617e+00 | -3.59017756e-01 5.72781573e+00 2.09963617e+00 14 -3.12019413e-01 -4.79939854e+00 7.20729775e-01 | -3.12019413e-01 -4.79939854e+00 7.20729775e-01 15 1.63598837e+00 4.50820817e+00 -2.42786184e+00 | 1.63598837e+00 4.50820817e+00 -2.42786184e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFF (Configuration in file "config-Cr-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)) = -7.3213921015618855 2^p V(r_1,...,r_N) = -7.3213921015618855 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 -3.10144963e+00 -5.58450460e+00 -8.43941931e+00 | -3.10144963e+00 -5.58450460e+00 -8.43941931e+00 1 1.93936744e+00 6.79291402e+00 -6.31051662e+00 | 1.93936744e+00 6.79291402e+00 -6.31051662e+00 2 2.34384964e+00 -7.06471635e+00 6.00058918e+00 | 2.34384964e+00 -7.06471635e+00 6.00058918e+00 3 -1.18176745e+00 5.85630693e+00 8.74934675e+00 | -1.18176745e+00 5.85630693e+00 8.74934675e+00 4 -3.10144963e+00 -5.58450460e+00 -8.43941931e+00 | -3.10144963e+00 -5.58450460e+00 -8.43941931e+00 5 1.93936744e+00 6.79291402e+00 -6.31051662e+00 | 1.93936744e+00 6.79291402e+00 -6.31051662e+00 6 2.34384964e+00 -7.06471635e+00 6.00058918e+00 | 2.34384964e+00 -7.06471635e+00 6.00058918e+00 7 -1.18176745e+00 5.85630693e+00 8.74934675e+00 | -1.18176745e+00 5.85630693e+00 8.74934675e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTT (Configuration in file "config-Cr-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)) = -22.146148214956586 2^p V(r_1,...,r_N) = -22.146148214956703 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 -6.08778099e+00 5.34291489e-01 -9.17378810e-01 | -6.08778099e+00 5.34291489e-01 -9.17378810e-01 1 7.53945271e+00 -7.14691138e-01 2.30629160e+00 | 7.53945271e+00 -7.14691138e-01 2.30629160e+00 2 5.56669919e+00 8.32052006e-01 -3.41930539e+00 | 5.56669919e+00 8.32052006e-01 -3.41930539e+00 3 -7.01837092e+00 -6.51652357e-01 2.03039259e+00 | -7.01837092e+00 -6.51652357e-01 2.03039259e+00 4 -6.08778099e+00 5.34291489e-01 -9.17378810e-01 | -6.08778099e+00 5.34291489e-01 -9.17378810e-01 5 7.53945271e+00 -7.14691138e-01 2.30629160e+00 | 7.53945271e+00 -7.14691138e-01 2.30629160e+00 6 5.56669919e+00 8.32052006e-01 -3.41930539e+00 | 5.56669919e+00 8.32052006e-01 -3.41930539e+00 7 -7.01837092e+00 -6.51652357e-01 2.03039259e+00 | -7.01837092e+00 -6.51652357e-01 2.03039259e+00 8 -6.08778099e+00 5.34291489e-01 -9.17378810e-01 | -6.08778099e+00 5.34291489e-01 -9.17378810e-01 9 7.53945271e+00 -7.14691138e-01 2.30629160e+00 | 7.53945271e+00 -7.14691138e-01 2.30629160e+00 10 5.56669919e+00 8.32052006e-01 -3.41930539e+00 | 5.56669919e+00 8.32052006e-01 -3.41930539e+00 11 -7.01837092e+00 -6.51652357e-01 2.03039259e+00 | -7.01837092e+00 -6.51652357e-01 2.03039259e+00 12 -6.08778099e+00 5.34291489e-01 -9.17378810e-01 | -6.08778099e+00 5.34291489e-01 -9.17378810e-01 13 7.53945271e+00 -7.14691138e-01 2.30629160e+00 | 7.53945271e+00 -7.14691138e-01 2.30629160e+00 14 5.56669919e+00 8.32052006e-01 -3.41930539e+00 | 5.56669919e+00 8.32052006e-01 -3.41930539e+00 15 -7.01837092e+00 -6.51652357e-01 2.03039259e+00 | -7.01837092e+00 -6.51652357e-01 2.03039259e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTF (Configuration in file "config-Cr-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)) = -5.153554421018367 2^p V(r_1,...,r_N) = -5.153554421018369 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.29972055e+00 1.51687719e+00 -5.14085604e+00 | -7.29972055e+00 1.51687719e+00 -5.14085604e+00 1 5.99667050e+00 1.18936171e+00 -4.30203534e+00 | 5.99667050e+00 1.18936171e+00 -4.30203534e+00 2 4.67202311e+00 7.57766751e-01 6.11830923e+00 | 4.67202311e+00 7.57766751e-01 6.11830923e+00 3 -3.36897306e+00 -3.46400565e+00 3.32458215e+00 | -3.36897306e+00 -3.46400565e+00 3.32458215e+00 4 -7.29972055e+00 1.51687719e+00 -5.14085604e+00 | -7.29972055e+00 1.51687719e+00 -5.14085604e+00 5 5.99667050e+00 1.18936171e+00 -4.30203534e+00 | 5.99667050e+00 1.18936171e+00 -4.30203534e+00 6 4.67202311e+00 7.57766751e-01 6.11830923e+00 | 4.67202311e+00 7.57766751e-01 6.11830923e+00 7 -3.36897306e+00 -3.46400565e+00 3.32458215e+00 | -3.36897306e+00 -3.46400565e+00 3.32458215e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cr, PBC = FFT (Configuration in file "config-Cr-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)) = -6.838769074867655 2^p V(r_1,...,r_N) = -6.8387690748676455 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.10666989e+00 -6.03352857e+00 -1.00542483e+00 | -7.10666989e+00 -6.03352857e+00 -1.00542483e+00 1 7.36641514e+00 4.55424764e+00 8.10252077e-01 | 7.36641514e+00 4.55424764e+00 8.10252077e-01 2 5.83397397e+00 -5.10792965e+00 -2.08278624e+00 | 5.83397397e+00 -5.10792965e+00 -2.08278624e+00 3 -6.09371922e+00 6.58721059e+00 2.27795899e+00 | -6.09371922e+00 6.58721059e+00 2.27795899e+00 4 -7.10666989e+00 -6.03352857e+00 -1.00542483e+00 | -7.10666989e+00 -6.03352857e+00 -1.00542483e+00 5 7.36641514e+00 4.55424764e+00 8.10252077e-01 | 7.36641514e+00 4.55424764e+00 8.10252077e-01 6 5.83397397e+00 -5.10792965e+00 -2.08278624e+00 | 5.83397397e+00 -5.10792965e+00 -2.08278624e+00 7 -6.09371922e+00 6.58721059e+00 2.27795899e+00 | -6.09371922e+00 6.58721059e+00 2.27795899e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTT (Configuration in file "config-Fe-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)) = -135.23885569524128 2^p V(r_1,...,r_N) = -135.23885569524296 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 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 1 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 2 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 3 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 4 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 5 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 6 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 7 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 8 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 9 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 10 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 11 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 12 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 13 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 14 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 15 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 16 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 17 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 18 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 19 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 20 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 21 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 22 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 23 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 24 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 25 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 26 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 27 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 28 -2.09675296e+00 1.31902912e+00 8.43498276e+00 | -2.09675296e+00 1.31902912e+00 8.43498276e+00 29 -3.80469449e+00 2.37371494e+00 3.05655633e+00 | -3.80469449e+00 2.37371494e+00 3.05655633e+00 30 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 | 1.24287740e+00 -6.14383481e-01 -7.84195233e-01 31 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 | 4.65857005e+00 -3.07836058e+00 -1.07073439e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTF (Configuration in file "config-Fe-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)) = 3.625558560260368 2^p V(r_1,...,r_N) = 3.6255585602603904 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 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 | 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 1 2.32644286e-01 2.53730341e+00 -1.18216831e+01 | 2.32644286e-01 2.53730341e+00 -1.18216831e+01 2 -3.54765737e+00 -3.30291878e+00 1.60904379e+01 | -3.54765737e+00 -3.30291878e+00 1.60904379e+01 3 2.13099346e+00 2.92758310e+00 1.10219867e+01 | 2.13099346e+00 2.92758310e+00 1.10219867e+01 4 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 | 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 5 2.32644286e-01 2.53730341e+00 -1.18216831e+01 | 2.32644286e-01 2.53730341e+00 -1.18216831e+01 6 -3.54765737e+00 -3.30291878e+00 1.60904379e+01 | -3.54765737e+00 -3.30291878e+00 1.60904379e+01 7 2.13099346e+00 2.92758310e+00 1.10219867e+01 | 2.13099346e+00 2.92758310e+00 1.10219867e+01 8 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 | 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 9 2.32644286e-01 2.53730341e+00 -1.18216831e+01 | 2.32644286e-01 2.53730341e+00 -1.18216831e+01 10 -3.54765737e+00 -3.30291878e+00 1.60904379e+01 | -3.54765737e+00 -3.30291878e+00 1.60904379e+01 11 2.13099346e+00 2.92758310e+00 1.10219867e+01 | 2.13099346e+00 2.92758310e+00 1.10219867e+01 12 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 | 1.18401962e+00 -2.16196773e+00 -1.52907416e+01 13 2.32644286e-01 2.53730341e+00 -1.18216831e+01 | 2.32644286e-01 2.53730341e+00 -1.18216831e+01 14 -3.54765737e+00 -3.30291878e+00 1.60904379e+01 | -3.54765737e+00 -3.30291878e+00 1.60904379e+01 15 2.13099346e+00 2.92758310e+00 1.10219867e+01 | 2.13099346e+00 2.92758310e+00 1.10219867e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFT (Configuration in file "config-Fe-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)) = -17.47118541830707 2^p V(r_1,...,r_N) = -17.47118541830697 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 -2.40666736e+00 -1.36172049e+01 1.79082706e+00 | -2.40666736e+00 -1.36172049e+01 1.79082706e+00 1 2.44892419e+00 1.29688083e+01 3.19505368e+00 | 2.44892419e+00 1.29688083e+01 3.19505368e+00 2 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 | 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 3 -4.80286090e+00 1.25057845e+01 -1.50502552e+00 | -4.80286090e+00 1.25057845e+01 -1.50502552e+00 4 -2.40666736e+00 -1.36172049e+01 1.79082706e+00 | -2.40666736e+00 -1.36172049e+01 1.79082706e+00 5 2.44892419e+00 1.29688083e+01 3.19505368e+00 | 2.44892419e+00 1.29688083e+01 3.19505368e+00 6 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 | 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 7 -4.80286090e+00 1.25057845e+01 -1.50502552e+00 | -4.80286090e+00 1.25057845e+01 -1.50502552e+00 8 -2.40666736e+00 -1.36172049e+01 1.79082706e+00 | -2.40666736e+00 -1.36172049e+01 1.79082706e+00 9 2.44892419e+00 1.29688083e+01 3.19505368e+00 | 2.44892419e+00 1.29688083e+01 3.19505368e+00 10 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 | 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 11 -4.80286090e+00 1.25057845e+01 -1.50502552e+00 | -4.80286090e+00 1.25057845e+01 -1.50502552e+00 12 -2.40666736e+00 -1.36172049e+01 1.79082706e+00 | -2.40666736e+00 -1.36172049e+01 1.79082706e+00 13 2.44892419e+00 1.29688083e+01 3.19505368e+00 | 2.44892419e+00 1.29688083e+01 3.19505368e+00 14 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 | 4.76060408e+00 -1.18573880e+01 -3.48085522e+00 15 -4.80286090e+00 1.25057845e+01 -1.50502552e+00 | -4.80286090e+00 1.25057845e+01 -1.50502552e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFF (Configuration in file "config-Fe-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)) = -4.638636851623982 2^p V(r_1,...,r_N) = -4.6386368516239695 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 -1.59338341e+00 -1.00770148e+01 -9.47942194e+00 | -1.59338341e+00 -1.00770148e+01 -9.47942194e+00 1 -1.16602620e+00 1.23109702e+01 -1.09606541e+01 | -1.16602620e+00 1.23109702e+01 -1.09606541e+01 2 2.71279472e+00 -9.85079185e+00 7.60312720e+00 | 2.71279472e+00 -9.85079185e+00 7.60312720e+00 3 4.66148919e-02 7.61683646e+00 1.28369489e+01 | 4.66148919e-02 7.61683646e+00 1.28369489e+01 4 -1.59338341e+00 -1.00770148e+01 -9.47942194e+00 | -1.59338341e+00 -1.00770148e+01 -9.47942194e+00 5 -1.16602620e+00 1.23109702e+01 -1.09606541e+01 | -1.16602620e+00 1.23109702e+01 -1.09606541e+01 6 2.71279472e+00 -9.85079185e+00 7.60312720e+00 | 2.71279472e+00 -9.85079185e+00 7.60312720e+00 7 4.66148919e-02 7.61683646e+00 1.28369489e+01 | 4.66148919e-02 7.61683646e+00 1.28369489e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTT (Configuration in file "config-Fe-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)) = 14.537359246347723 2^p V(r_1,...,r_N) = 14.537359246347775 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 -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 | -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 1 1.22352871e+01 4.60656974e-01 -2.10517463e+00 | 1.22352871e+01 4.60656974e-01 -2.10517463e+00 2 6.28533597e+00 5.09620368e+00 8.20072923e-01 | 6.28533597e+00 5.09620368e+00 8.20072923e-01 3 -8.04423478e+00 -7.12329521e-01 2.42430787e+00 | -8.04423478e+00 -7.12329521e-01 2.42430787e+00 4 -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 | -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 5 1.22352871e+01 4.60656974e-01 -2.10517463e+00 | 1.22352871e+01 4.60656974e-01 -2.10517463e+00 6 6.28533597e+00 5.09620368e+00 8.20072923e-01 | 6.28533597e+00 5.09620368e+00 8.20072923e-01 7 -8.04423478e+00 -7.12329521e-01 2.42430787e+00 | -8.04423478e+00 -7.12329521e-01 2.42430787e+00 8 -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 | -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 9 1.22352871e+01 4.60656974e-01 -2.10517463e+00 | 1.22352871e+01 4.60656974e-01 -2.10517463e+00 10 6.28533597e+00 5.09620368e+00 8.20072923e-01 | 6.28533597e+00 5.09620368e+00 8.20072923e-01 11 -8.04423478e+00 -7.12329521e-01 2.42430787e+00 | -8.04423478e+00 -7.12329521e-01 2.42430787e+00 12 -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 | -1.04763883e+01 -4.84453114e+00 -1.13920617e+00 13 1.22352871e+01 4.60656974e-01 -2.10517463e+00 | 1.22352871e+01 4.60656974e-01 -2.10517463e+00 14 6.28533597e+00 5.09620368e+00 8.20072923e-01 | 6.28533597e+00 5.09620368e+00 8.20072923e-01 15 -8.04423478e+00 -7.12329521e-01 2.42430787e+00 | -8.04423478e+00 -7.12329521e-01 2.42430787e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTF (Configuration in file "config-Fe-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)) = 9.039411674601109 2^p V(r_1,...,r_N) = 9.039411674601112 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.48774032e+00 -2.66878374e+00 -1.90643519e+00 | -7.48774032e+00 -2.66878374e+00 -1.90643519e+00 1 1.14503374e+01 3.62589818e+00 -8.48319559e+00 | 1.14503374e+01 3.62589818e+00 -8.48319559e+00 2 2.57457672e+01 -1.87105003e+01 1.12922901e+00 | 2.57457672e+01 -1.87105003e+01 1.12922901e+00 3 -2.97083642e+01 1.77533859e+01 9.26040178e+00 | -2.97083642e+01 1.77533859e+01 9.26040178e+00 4 -7.48774032e+00 -2.66878374e+00 -1.90643519e+00 | -7.48774032e+00 -2.66878374e+00 -1.90643519e+00 5 1.14503374e+01 3.62589818e+00 -8.48319559e+00 | 1.14503374e+01 3.62589818e+00 -8.48319559e+00 6 2.57457672e+01 -1.87105003e+01 1.12922901e+00 | 2.57457672e+01 -1.87105003e+01 1.12922901e+00 7 -2.97083642e+01 1.77533859e+01 9.26040178e+00 | -2.97083642e+01 1.77533859e+01 9.26040178e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FFT (Configuration in file "config-Fe-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)) = 0.4387289425931906 2^p V(r_1,...,r_N) = 0.43872894259319783 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 -5.86149302e+00 -8.17877528e+00 2.74036674e+00 | -5.86149302e+00 -8.17877528e+00 2.74036674e+00 1 1.08287494e+01 8.76460719e+00 -2.26028839e+00 | 1.08287494e+01 8.76460719e+00 -2.26028839e+00 2 3.68345409e+00 -6.75042404e+00 1.16301703e+00 | 3.68345409e+00 -6.75042404e+00 1.16301703e+00 3 -8.65071051e+00 6.16459214e+00 -1.64309539e+00 | -8.65071051e+00 6.16459214e+00 -1.64309539e+00 4 -5.86149302e+00 -8.17877528e+00 2.74036674e+00 | -5.86149302e+00 -8.17877528e+00 2.74036674e+00 5 1.08287494e+01 8.76460719e+00 -2.26028839e+00 | 1.08287494e+01 8.76460719e+00 -2.26028839e+00 6 3.68345409e+00 -6.75042404e+00 1.16301703e+00 | 3.68345409e+00 -6.75042404e+00 1.16301703e+00 7 -8.65071051e+00 6.16459214e+00 -1.64309539e+00 | -8.65071051e+00 6.16459214e+00 -1.64309539e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -43.735689695572795 2^p V(r_1,...,r_N) = -43.735689695574045 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 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 1 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 2 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 3 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 4 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 5 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 6 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 7 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 8 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 9 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 10 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 11 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 12 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 13 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 14 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 15 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 16 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 17 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 18 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 19 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 20 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 21 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 22 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 23 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 24 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 25 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 26 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 27 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 28 6.17732398e+00 8.01661075e+00 -3.97404700e+00 | 6.17732398e+00 8.01661075e+00 -3.97404700e+00 29 -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 | -7.59750386e+00 -8.27661005e+00 -3.18349605e+00 30 -4.65517664e+00 3.97328356e+00 2.36268063e+00 | -4.65517664e+00 3.97328356e+00 2.36268063e+00 31 6.07535651e+00 -3.71328426e+00 4.79486241e+00 | 6.07535651e+00 -3.71328426e+00 4.79486241e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -18.752336533021584 2^p V(r_1,...,r_N) = -18.752336533021595 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 1.92560313e+00 1.35834598e+00 -8.87107162e+00 | 1.92560313e+00 1.35834598e+00 -8.87107162e+00 1 -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 | -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 2 -3.05528410e+00 -7.11100450e-02 1.00346881e+01 | -3.05528410e+00 -7.11100450e-02 1.00346881e+01 3 2.05402510e+00 -9.30726284e-01 7.18382409e+00 | 2.05402510e+00 -9.30726284e-01 7.18382409e+00 4 1.92560313e+00 1.35834598e+00 -8.87107162e+00 | 1.92560313e+00 1.35834598e+00 -8.87107162e+00 5 -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 | -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 6 -3.05528410e+00 -7.11100450e-02 1.00346881e+01 | -3.05528410e+00 -7.11100450e-02 1.00346881e+01 7 2.05402510e+00 -9.30726284e-01 7.18382409e+00 | 2.05402510e+00 -9.30726284e-01 7.18382409e+00 8 1.92560313e+00 1.35834598e+00 -8.87107162e+00 | 1.92560313e+00 1.35834598e+00 -8.87107162e+00 9 -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 | -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 10 -3.05528410e+00 -7.11100450e-02 1.00346881e+01 | -3.05528410e+00 -7.11100450e-02 1.00346881e+01 11 2.05402510e+00 -9.30726284e-01 7.18382409e+00 | 2.05402510e+00 -9.30726284e-01 7.18382409e+00 12 1.92560313e+00 1.35834598e+00 -8.87107162e+00 | 1.92560313e+00 1.35834598e+00 -8.87107162e+00 13 -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 | -9.24344139e-01 -3.56509650e-01 -8.34744061e+00 14 -3.05528410e+00 -7.11100450e-02 1.00346881e+01 | -3.05528410e+00 -7.11100450e-02 1.00346881e+01 15 2.05402510e+00 -9.30726284e-01 7.18382409e+00 | 2.05402510e+00 -9.30726284e-01 7.18382409e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -19.948114027952375 2^p V(r_1,...,r_N) = -19.94811402795246 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 -3.74027518e+00 -7.34354341e+00 1.02585796e+00 | -3.74027518e+00 -7.34354341e+00 1.02585796e+00 1 2.71809869e+00 9.56690119e+00 3.05365254e+00 | 2.71809869e+00 9.56690119e+00 3.05365254e+00 2 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 | 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 3 8.18538962e-01 4.45667646e+00 -2.43082893e+00 | 8.18538962e-01 4.45667646e+00 -2.43082893e+00 4 -3.74027518e+00 -7.34354341e+00 1.02585796e+00 | -3.74027518e+00 -7.34354341e+00 1.02585796e+00 5 2.71809869e+00 9.56690119e+00 3.05365254e+00 | 2.71809869e+00 9.56690119e+00 3.05365254e+00 6 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 | 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 7 8.18538962e-01 4.45667646e+00 -2.43082893e+00 | 8.18538962e-01 4.45667646e+00 -2.43082893e+00 8 -3.74027518e+00 -7.34354341e+00 1.02585796e+00 | -3.74027518e+00 -7.34354341e+00 1.02585796e+00 9 2.71809869e+00 9.56690119e+00 3.05365254e+00 | 2.71809869e+00 9.56690119e+00 3.05365254e+00 10 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 | 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 11 8.18538962e-01 4.45667646e+00 -2.43082893e+00 | 8.18538962e-01 4.45667646e+00 -2.43082893e+00 12 -3.74027518e+00 -7.34354341e+00 1.02585796e+00 | -3.74027518e+00 -7.34354341e+00 1.02585796e+00 13 2.71809869e+00 9.56690119e+00 3.05365254e+00 | 2.71809869e+00 9.56690119e+00 3.05365254e+00 14 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 | 2.03637525e-01 -6.68003424e+00 -1.64868157e+00 15 8.18538962e-01 4.45667646e+00 -2.43082893e+00 | 8.18538962e-01 4.45667646e+00 -2.43082893e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -2.385656101444399 2^p V(r_1,...,r_N) = -2.3856561014443987 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 2.59299569e+00 -6.41252110e+00 -5.66787514e+00 | 2.59299569e+00 -6.41252110e+00 -5.66787514e+00 1 -1.41751259e+00 3.13998703e+00 -5.96508514e+00 | -1.41751259e+00 3.13998703e+00 -5.96508514e+00 2 -5.41628165e-01 -5.70730674e+00 3.88475815e+00 | -5.41628165e-01 -5.70730674e+00 3.88475815e+00 3 -6.33854930e-01 8.97984081e+00 7.74820213e+00 | -6.33854930e-01 8.97984081e+00 7.74820213e+00 4 2.59299569e+00 -6.41252110e+00 -5.66787514e+00 | 2.59299569e+00 -6.41252110e+00 -5.66787514e+00 5 -1.41751259e+00 3.13998703e+00 -5.96508514e+00 | -1.41751259e+00 3.13998703e+00 -5.96508514e+00 6 -5.41628165e-01 -5.70730674e+00 3.88475815e+00 | -5.41628165e-01 -5.70730674e+00 3.88475815e+00 7 -6.33854930e-01 8.97984081e+00 7.74820213e+00 | -6.33854930e-01 8.97984081e+00 7.74820213e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -26.5614643342999 2^p V(r_1,...,r_N) = -26.56146433429973 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 -5.87996069e+00 -4.37479397e+00 7.34108151e-01 | -5.87996069e+00 -4.37479397e+00 7.34108151e-01 1 5.81623852e+00 4.95613534e+00 -1.02549281e+00 | 5.81623852e+00 4.95613534e+00 -1.02549281e+00 2 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 | 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 3 -6.22208338e+00 4.62865735e+00 9.94000202e-01 | -6.22208338e+00 4.62865735e+00 9.94000202e-01 4 -5.87996069e+00 -4.37479397e+00 7.34108151e-01 | -5.87996069e+00 -4.37479397e+00 7.34108151e-01 5 5.81623852e+00 4.95613534e+00 -1.02549281e+00 | 5.81623852e+00 4.95613534e+00 -1.02549281e+00 6 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 | 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 7 -6.22208338e+00 4.62865735e+00 9.94000202e-01 | -6.22208338e+00 4.62865735e+00 9.94000202e-01 8 -5.87996069e+00 -4.37479397e+00 7.34108151e-01 | -5.87996069e+00 -4.37479397e+00 7.34108151e-01 9 5.81623852e+00 4.95613534e+00 -1.02549281e+00 | 5.81623852e+00 4.95613534e+00 -1.02549281e+00 10 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 | 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 11 -6.22208338e+00 4.62865735e+00 9.94000202e-01 | -6.22208338e+00 4.62865735e+00 9.94000202e-01 12 -5.87996069e+00 -4.37479397e+00 7.34108151e-01 | -5.87996069e+00 -4.37479397e+00 7.34108151e-01 13 5.81623852e+00 4.95613534e+00 -1.02549281e+00 | 5.81623852e+00 4.95613534e+00 -1.02549281e+00 14 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 | 6.28580555e+00 -5.20999872e+00 -7.02615546e-01 15 -6.22208338e+00 4.62865735e+00 9.94000202e-01 | -6.22208338e+00 4.62865735e+00 9.94000202e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -4.52693044065456 2^p V(r_1,...,r_N) = -4.5269304406545565 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 -4.34346049e+00 -1.20282139e-01 -6.97714476e+00 | -4.34346049e+00 -1.20282139e-01 -6.97714476e+00 1 3.52203981e+00 -6.47766032e-01 -7.84687353e+00 | 3.52203981e+00 -6.47766032e-01 -7.84687353e+00 2 5.11508243e+00 -2.92965211e+00 6.13063292e+00 | 5.11508243e+00 -2.92965211e+00 6.13063292e+00 3 -4.29366175e+00 3.69770028e+00 8.69338537e+00 | -4.29366175e+00 3.69770028e+00 8.69338537e+00 4 -4.34346049e+00 -1.20282139e-01 -6.97714476e+00 | -4.34346049e+00 -1.20282139e-01 -6.97714476e+00 5 3.52203981e+00 -6.47766032e-01 -7.84687353e+00 | 3.52203981e+00 -6.47766032e-01 -7.84687353e+00 6 5.11508243e+00 -2.92965211e+00 6.13063292e+00 | 5.11508243e+00 -2.92965211e+00 6.13063292e+00 7 -4.29366175e+00 3.69770028e+00 8.69338537e+00 | -4.29366175e+00 3.69770028e+00 8.69338537e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -2.36991036225575 2^p V(r_1,...,r_N) = -2.369910362255763 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 -5.42344044e+00 -6.07993601e+00 -2.75749102e-01 | -5.42344044e+00 -6.07993601e+00 -2.75749102e-01 1 1.15164619e+01 9.11017713e+00 8.88464132e+00 | 1.15164619e+01 9.11017713e+00 8.88464132e+00 2 4.11504511e+00 -3.73627099e+00 -9.17035350e-01 | 4.11504511e+00 -3.73627099e+00 -9.17035350e-01 3 -1.02080666e+01 7.06029867e-01 -7.69185687e+00 | -1.02080666e+01 7.06029867e-01 -7.69185687e+00 4 -5.42344044e+00 -6.07993601e+00 -2.75749102e-01 | -5.42344044e+00 -6.07993601e+00 -2.75749102e-01 5 1.15164619e+01 9.11017713e+00 8.88464132e+00 | 1.15164619e+01 9.11017713e+00 8.88464132e+00 6 4.11504511e+00 -3.73627099e+00 -9.17035350e-01 | 4.11504511e+00 -3.73627099e+00 -9.17035350e-01 7 -1.02080666e+01 7.06029867e-01 -7.69185687e+00 | -1.02080666e+01 7.06029867e-01 -7.69185687e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = TTT (Configuration in file "config-AlCoCrFeNi-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)) = -614.0880828250538 2^p V(r_1,...,r_N) = -614.0880828250715 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 -5.99191651e+00 -1.26463978e+00 1.05682071e+00 | -5.99191651e+00 -1.26463978e+00 1.05682071e+00 1 3.67253482e+00 4.12667669e+00 -1.29065772e+00 | 3.67253482e+00 4.12667669e+00 -1.29065772e+00 2 -3.85785199e+00 8.01407890e+00 1.40186596e+00 | -3.85785199e+00 8.01407890e+00 1.40186596e+00 3 -7.58566069e+00 -4.25647716e+00 1.11428347e+01 | -7.58566069e+00 -4.25647716e+00 1.11428347e+01 4 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 | 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 5 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 | 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 6 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 | 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 7 4.18233829e+00 4.14945397e+00 5.74485957e+00 | 4.18233829e+00 4.14945397e+00 5.74485957e+00 8 -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 | -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 9 4.34110155e+00 2.13108967e+00 -3.29266361e+00 | 4.34110155e+00 2.13108967e+00 -3.29266361e+00 10 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 | 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 11 -9.85550421e-01 3.21240020e+00 2.74998437e+00 | -9.85550421e-01 3.21240020e+00 2.74998437e+00 12 4.71899923e-01 4.89266117e+00 2.50070485e+00 | 4.71899923e-01 4.89266117e+00 2.50070485e+00 13 -7.32348004e+00 4.57933441e-01 -6.87784248e+00 | -7.32348004e+00 4.57933441e-01 -6.87784248e+00 14 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 | 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 15 -5.61102778e-03 -1.18430681e+00 2.69286140e+00 | -5.61102778e-03 -1.18430681e+00 2.69286140e+00 16 2.00901792e+00 2.06827365e+00 -1.61790446e+00 | 2.00901792e+00 2.06827365e+00 -1.61790446e+00 17 -1.59244834e-01 1.82020071e+00 -2.93595063e+00 | -1.59244834e-01 1.82020071e+00 -2.93595063e+00 18 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 | 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 19 -1.28985530e+00 6.12157720e-01 5.73926307e+00 | -1.28985530e+00 6.12157720e-01 5.73926307e+00 20 3.32028667e+00 5.91425215e+00 5.70225550e+00 | 3.32028667e+00 5.91425215e+00 5.70225550e+00 21 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 | 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 22 -5.70771704e+00 7.63463573e+00 -1.74289517e+00 | -5.70771704e+00 7.63463573e+00 -1.74289517e+00 23 -1.95284608e+00 -9.81461975e+00 3.85111180e+00 | -1.95284608e+00 -9.81461975e+00 3.85111180e+00 24 -2.44345840e+00 2.09061729e+00 1.76661280e+00 | -2.44345840e+00 2.09061729e+00 1.76661280e+00 25 1.20203809e-02 -4.82714977e+00 2.31404906e-01 | 1.20203809e-02 -4.82714977e+00 2.31404906e-01 26 -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 | -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 27 -4.24587020e-02 -5.60871797e-01 3.68083196e+00 | -4.24587020e-02 -5.60871797e-01 3.68083196e+00 28 2.53638469e+00 1.97597300e+00 -4.02519474e+00 | 2.53638469e+00 1.97597300e+00 -4.02519474e+00 29 -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 | -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 30 -4.13288650e-01 3.43536371e+00 8.31069749e+00 | -4.13288650e-01 3.43536371e+00 8.31069749e+00 31 -2.13552260e+00 1.71209288e-01 7.46899013e+00 | -2.13552260e+00 1.71209288e-01 7.46899013e+00 32 -5.99191651e+00 -1.26463978e+00 1.05682071e+00 | -5.99191651e+00 -1.26463978e+00 1.05682071e+00 33 3.67253482e+00 4.12667669e+00 -1.29065772e+00 | 3.67253482e+00 4.12667669e+00 -1.29065772e+00 34 -3.85785199e+00 8.01407890e+00 1.40186596e+00 | -3.85785199e+00 8.01407890e+00 1.40186596e+00 35 -7.58566069e+00 -4.25647716e+00 1.11428347e+01 | -7.58566069e+00 -4.25647716e+00 1.11428347e+01 36 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 | 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 37 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 | 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 38 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 | 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 39 4.18233829e+00 4.14945397e+00 5.74485957e+00 | 4.18233829e+00 4.14945397e+00 5.74485957e+00 40 -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 | -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 41 4.34110155e+00 2.13108967e+00 -3.29266361e+00 | 4.34110155e+00 2.13108967e+00 -3.29266361e+00 42 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 | 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 43 -9.85550421e-01 3.21240020e+00 2.74998437e+00 | -9.85550421e-01 3.21240020e+00 2.74998437e+00 44 4.71899923e-01 4.89266117e+00 2.50070485e+00 | 4.71899923e-01 4.89266117e+00 2.50070485e+00 45 -7.32348004e+00 4.57933441e-01 -6.87784248e+00 | -7.32348004e+00 4.57933441e-01 -6.87784248e+00 46 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 | 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 47 -5.61102778e-03 -1.18430681e+00 2.69286140e+00 | -5.61102778e-03 -1.18430681e+00 2.69286140e+00 48 2.00901792e+00 2.06827365e+00 -1.61790446e+00 | 2.00901792e+00 2.06827365e+00 -1.61790446e+00 49 -1.59244834e-01 1.82020071e+00 -2.93595063e+00 | -1.59244834e-01 1.82020071e+00 -2.93595063e+00 50 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 | 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 51 -1.28985530e+00 6.12157720e-01 5.73926307e+00 | -1.28985530e+00 6.12157720e-01 5.73926307e+00 52 3.32028667e+00 5.91425215e+00 5.70225550e+00 | 3.32028667e+00 5.91425215e+00 5.70225550e+00 53 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 | 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 54 -5.70771704e+00 7.63463573e+00 -1.74289517e+00 | -5.70771704e+00 7.63463573e+00 -1.74289517e+00 55 -1.95284608e+00 -9.81461975e+00 3.85111180e+00 | -1.95284608e+00 -9.81461975e+00 3.85111180e+00 56 -2.44345840e+00 2.09061729e+00 1.76661280e+00 | -2.44345840e+00 2.09061729e+00 1.76661280e+00 57 1.20203809e-02 -4.82714977e+00 2.31404906e-01 | 1.20203809e-02 -4.82714977e+00 2.31404906e-01 58 -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 | -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 59 -4.24587020e-02 -5.60871797e-01 3.68083196e+00 | -4.24587020e-02 -5.60871797e-01 3.68083196e+00 60 2.53638469e+00 1.97597300e+00 -4.02519474e+00 | 2.53638469e+00 1.97597300e+00 -4.02519474e+00 61 -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 | -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 62 -4.13288650e-01 3.43536371e+00 8.31069749e+00 | -4.13288650e-01 3.43536371e+00 8.31069749e+00 63 -2.13552260e+00 1.71209288e-01 7.46899013e+00 | -2.13552260e+00 1.71209288e-01 7.46899013e+00 64 -5.99191651e+00 -1.26463978e+00 1.05682071e+00 | -5.99191651e+00 -1.26463978e+00 1.05682071e+00 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-7.58566069e+00 -4.25647716e+00 1.11428347e+01 196 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 | 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 197 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 | 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 198 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 | 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 199 4.18233829e+00 4.14945397e+00 5.74485957e+00 | 4.18233829e+00 4.14945397e+00 5.74485957e+00 200 -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 | -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 201 4.34110155e+00 2.13108967e+00 -3.29266361e+00 | 4.34110155e+00 2.13108967e+00 -3.29266361e+00 202 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 | 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 203 -9.85550421e-01 3.21240020e+00 2.74998437e+00 | -9.85550421e-01 3.21240020e+00 2.74998437e+00 204 4.71899923e-01 4.89266117e+00 2.50070485e+00 | 4.71899923e-01 4.89266117e+00 2.50070485e+00 205 -7.32348004e+00 4.57933441e-01 -6.87784248e+00 | -7.32348004e+00 4.57933441e-01 -6.87784248e+00 206 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 | 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 207 -5.61102778e-03 -1.18430681e+00 2.69286140e+00 | -5.61102778e-03 -1.18430681e+00 2.69286140e+00 208 2.00901792e+00 2.06827365e+00 -1.61790446e+00 | 2.00901792e+00 2.06827365e+00 -1.61790446e+00 209 -1.59244834e-01 1.82020071e+00 -2.93595063e+00 | -1.59244834e-01 1.82020071e+00 -2.93595063e+00 210 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 | 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 211 -1.28985530e+00 6.12157720e-01 5.73926307e+00 | -1.28985530e+00 6.12157720e-01 5.73926307e+00 212 3.32028667e+00 5.91425215e+00 5.70225550e+00 | 3.32028667e+00 5.91425215e+00 5.70225550e+00 213 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 | 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 214 -5.70771704e+00 7.63463573e+00 -1.74289517e+00 | -5.70771704e+00 7.63463573e+00 -1.74289517e+00 215 -1.95284608e+00 -9.81461975e+00 3.85111180e+00 | -1.95284608e+00 -9.81461975e+00 3.85111180e+00 216 -2.44345840e+00 2.09061729e+00 1.76661280e+00 | -2.44345840e+00 2.09061729e+00 1.76661280e+00 217 1.20203809e-02 -4.82714977e+00 2.31404906e-01 | 1.20203809e-02 -4.82714977e+00 2.31404906e-01 218 -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 | -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 219 -4.24587020e-02 -5.60871797e-01 3.68083196e+00 | -4.24587020e-02 -5.60871797e-01 3.68083196e+00 220 2.53638469e+00 1.97597300e+00 -4.02519474e+00 | 2.53638469e+00 1.97597300e+00 -4.02519474e+00 221 -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 | -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 222 -4.13288650e-01 3.43536371e+00 8.31069749e+00 | -4.13288650e-01 3.43536371e+00 8.31069749e+00 223 -2.13552260e+00 1.71209288e-01 7.46899013e+00 | -2.13552260e+00 1.71209288e-01 7.46899013e+00 224 -5.99191651e+00 -1.26463978e+00 1.05682071e+00 | -5.99191651e+00 -1.26463978e+00 1.05682071e+00 225 3.67253482e+00 4.12667669e+00 -1.29065772e+00 | 3.67253482e+00 4.12667669e+00 -1.29065772e+00 226 -3.85785199e+00 8.01407890e+00 1.40186596e+00 | -3.85785199e+00 8.01407890e+00 1.40186596e+00 227 -7.58566069e+00 -4.25647716e+00 1.11428347e+01 | -7.58566069e+00 -4.25647716e+00 1.11428347e+01 228 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 | 7.95209540e+00 -1.65343169e+00 -1.00306652e+01 229 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 | 8.13634668e+00 -3.05559550e+00 -3.25492356e+00 230 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 | 2.81075865e+00 -3.97110576e-02 -3.25533128e+00 231 4.18233829e+00 4.14945397e+00 5.74485957e+00 | 4.18233829e+00 4.14945397e+00 5.74485957e+00 232 -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 | -2.91570135e+00 -3.27309427e+00 -3.82280742e+00 233 4.34110155e+00 2.13108967e+00 -3.29266361e+00 | 4.34110155e+00 2.13108967e+00 -3.29266361e+00 234 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 | 1.51389558e+00 -4.21930112e+00 -2.81217419e+00 235 -9.85550421e-01 3.21240020e+00 2.74998437e+00 | -9.85550421e-01 3.21240020e+00 2.74998437e+00 236 4.71899923e-01 4.89266117e+00 2.50070485e+00 | 4.71899923e-01 4.89266117e+00 2.50070485e+00 237 -7.32348004e+00 4.57933441e-01 -6.87784248e+00 | -7.32348004e+00 4.57933441e-01 -6.87784248e+00 238 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 | 3.33132939e+00 -5.16156335e+00 -5.60871068e+00 239 -5.61102778e-03 -1.18430681e+00 2.69286140e+00 | -5.61102778e-03 -1.18430681e+00 2.69286140e+00 240 2.00901792e+00 2.06827365e+00 -1.61790446e+00 | 2.00901792e+00 2.06827365e+00 -1.61790446e+00 241 -1.59244834e-01 1.82020071e+00 -2.93595063e+00 | -1.59244834e-01 1.82020071e+00 -2.93595063e+00 242 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 | 3.70500485e+00 -8.89734424e-02 -5.06061357e+00 243 -1.28985530e+00 6.12157720e-01 5.73926307e+00 | -1.28985530e+00 6.12157720e-01 5.73926307e+00 244 3.32028667e+00 5.91425215e+00 5.70225550e+00 | 3.32028667e+00 5.91425215e+00 5.70225550e+00 245 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 | 1.91549296e+00 -4.24710683e+00 -6.95363959e+00 246 -5.70771704e+00 7.63463573e+00 -1.74289517e+00 | -5.70771704e+00 7.63463573e+00 -1.74289517e+00 247 -1.95284608e+00 -9.81461975e+00 3.85111180e+00 | -1.95284608e+00 -9.81461975e+00 3.85111180e+00 248 -2.44345840e+00 2.09061729e+00 1.76661280e+00 | -2.44345840e+00 2.09061729e+00 1.76661280e+00 249 1.20203809e-02 -4.82714977e+00 2.31404906e-01 | 1.20203809e-02 -4.82714977e+00 2.31404906e-01 250 -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 | -4.10289925e+00 -7.00577318e+00 -1.17804029e-01 251 -4.24587020e-02 -5.60871797e-01 3.68083196e+00 | -4.24587020e-02 -5.60871797e-01 3.68083196e+00 252 2.53638469e+00 1.97597300e+00 -4.02519474e+00 | 2.53638469e+00 1.97597300e+00 -4.02519474e+00 253 -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 | -2.99744487e+00 -2.05436180e+00 -1.34132094e+00 254 -4.13288650e-01 3.43536371e+00 8.31069749e+00 | -4.13288650e-01 3.43536371e+00 8.31069749e+00 255 -2.13552260e+00 1.71209288e-01 7.46899013e+00 | -2.13552260e+00 1.71209288e-01 7.46899013e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = TTF (Configuration in file "config-AlCoCrFeNi-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)) = -107.40070515688144 2^p V(r_1,...,r_N) = -107.40070515687886 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 | 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 1 -2.30188022e+00 1.90590727e+00 -9.42578481e+00 | -2.30188022e+00 1.90590727e+00 -9.42578481e+00 2 -2.97341783e+00 -8.36524659e+00 4.73651525e+00 | -2.97341783e+00 -8.36524659e+00 4.73651525e+00 3 -2.36270474e+00 1.87074440e+00 6.97642647e+00 | -2.36270474e+00 1.87074440e+00 6.97642647e+00 4 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 | 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 5 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 | 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 6 2.00706972e+00 3.44714953e+00 5.17954817e+00 | 2.00706972e+00 3.44714953e+00 5.17954817e+00 7 3.89010581e+00 6.73261807e+00 3.84864311e+00 | 3.89010581e+00 6.73261807e+00 3.84864311e+00 8 -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 | -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 9 -4.19043341e+00 2.64891446e+00 1.05676926e+00 | -4.19043341e+00 2.64891446e+00 1.05676926e+00 10 -3.26211931e+00 -1.28082546e+00 2.03794786e+00 | -3.26211931e+00 -1.28082546e+00 2.03794786e+00 11 4.94933082e+00 1.02709979e+01 -1.64203403e+00 | 4.94933082e+00 1.02709979e+01 -1.64203403e+00 12 -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 | -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 13 2.28465552e+00 3.86273937e+00 -5.26430676e+00 | 2.28465552e+00 3.86273937e+00 -5.26430676e+00 14 -5.08684132e+00 -1.22542212e+00 2.52025824e+00 | -5.08684132e+00 -1.22542212e+00 2.52025824e+00 15 -1.31101705e+00 3.18834491e+00 4.02794518e+00 | -1.31101705e+00 3.18834491e+00 4.02794518e+00 16 -2.49310851e+00 1.37601019e+00 -6.65210187e+00 | -2.49310851e+00 1.37601019e+00 -6.65210187e+00 17 -4.71879782e-01 -1.56077287e+00 5.44874730e+00 | -4.71879782e-01 -1.56077287e+00 5.44874730e+00 18 1.27325372e+00 7.57668516e+00 1.94821848e+00 | 1.27325372e+00 7.57668516e+00 1.94821848e+00 19 3.51402381e+00 4.70249532e-01 1.32393897e-01 | 3.51402381e+00 4.70249532e-01 1.32393897e-01 20 -8.82760366e-01 -1.67079591e+00 2.53932442e+00 | -8.82760366e-01 -1.67079591e+00 2.53932442e+00 21 -8.11921767e-01 1.46019569e+00 -7.09967607e+00 | -8.11921767e-01 1.46019569e+00 -7.09967607e+00 22 -1.22450795e+00 -3.18307315e+00 4.61330453e+00 | -1.22450795e+00 -3.18307315e+00 4.61330453e+00 23 -5.18894040e+00 -3.43054564e+00 4.39730154e+00 | -5.18894040e+00 -3.43054564e+00 4.39730154e+00 24 -1.74169372e+00 -9.59797825e+00 5.09602192e+00 | -1.74169372e+00 -9.59797825e+00 5.09602192e+00 25 4.15977169e+00 5.22500910e+00 -6.99139962e+00 | 4.15977169e+00 5.22500910e+00 -6.99139962e+00 26 -4.17444473e+00 -5.19694281e+00 3.43235516e+00 | -4.17444473e+00 -5.19694281e+00 3.43235516e+00 27 -5.56218847e+00 -2.26337756e-01 5.34395732e+00 | -5.56218847e+00 -2.26337756e-01 5.34395732e+00 28 1.87090170e+00 9.16623932e-01 -2.96636806e+00 | 1.87090170e+00 9.16623932e-01 -2.96636806e+00 29 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 | 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 30 3.04257522e+00 -4.01826073e-01 6.04297828e+00 | 3.04257522e+00 -4.01826073e-01 6.04297828e+00 31 7.12903139e+00 4.93600112e+00 2.14977718e+00 | 7.12903139e+00 4.93600112e+00 2.14977718e+00 32 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 | 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 33 -2.30188022e+00 1.90590727e+00 -9.42578481e+00 | -2.30188022e+00 1.90590727e+00 -9.42578481e+00 34 -2.97341783e+00 -8.36524659e+00 4.73651525e+00 | -2.97341783e+00 -8.36524659e+00 4.73651525e+00 35 -2.36270474e+00 1.87074440e+00 6.97642647e+00 | -2.36270474e+00 1.87074440e+00 6.97642647e+00 36 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 | 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 37 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 | 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 38 2.00706972e+00 3.44714953e+00 5.17954817e+00 | 2.00706972e+00 3.44714953e+00 5.17954817e+00 39 3.89010581e+00 6.73261807e+00 3.84864311e+00 | 3.89010581e+00 6.73261807e+00 3.84864311e+00 40 -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 | -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 41 -4.19043341e+00 2.64891446e+00 1.05676926e+00 | -4.19043341e+00 2.64891446e+00 1.05676926e+00 42 -3.26211931e+00 -1.28082546e+00 2.03794786e+00 | -3.26211931e+00 -1.28082546e+00 2.03794786e+00 43 4.94933082e+00 1.02709979e+01 -1.64203403e+00 | 4.94933082e+00 1.02709979e+01 -1.64203403e+00 44 -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 | -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 45 2.28465552e+00 3.86273937e+00 -5.26430676e+00 | 2.28465552e+00 3.86273937e+00 -5.26430676e+00 46 -5.08684132e+00 -1.22542212e+00 2.52025824e+00 | -5.08684132e+00 -1.22542212e+00 2.52025824e+00 47 -1.31101705e+00 3.18834491e+00 4.02794518e+00 | -1.31101705e+00 3.18834491e+00 4.02794518e+00 48 -2.49310851e+00 1.37601019e+00 -6.65210187e+00 | -2.49310851e+00 1.37601019e+00 -6.65210187e+00 49 -4.71879782e-01 -1.56077287e+00 5.44874730e+00 | -4.71879782e-01 -1.56077287e+00 5.44874730e+00 50 1.27325372e+00 7.57668516e+00 1.94821848e+00 | 1.27325372e+00 7.57668516e+00 1.94821848e+00 51 3.51402381e+00 4.70249532e-01 1.32393897e-01 | 3.51402381e+00 4.70249532e-01 1.32393897e-01 52 -8.82760366e-01 -1.67079591e+00 2.53932442e+00 | -8.82760366e-01 -1.67079591e+00 2.53932442e+00 53 -8.11921767e-01 1.46019569e+00 -7.09967607e+00 | -8.11921767e-01 1.46019569e+00 -7.09967607e+00 54 -1.22450795e+00 -3.18307315e+00 4.61330453e+00 | -1.22450795e+00 -3.18307315e+00 4.61330453e+00 55 -5.18894040e+00 -3.43054564e+00 4.39730154e+00 | -5.18894040e+00 -3.43054564e+00 4.39730154e+00 56 -1.74169372e+00 -9.59797825e+00 5.09602192e+00 | -1.74169372e+00 -9.59797825e+00 5.09602192e+00 57 4.15977169e+00 5.22500910e+00 -6.99139962e+00 | 4.15977169e+00 5.22500910e+00 -6.99139962e+00 58 -4.17444473e+00 -5.19694281e+00 3.43235516e+00 | -4.17444473e+00 -5.19694281e+00 3.43235516e+00 59 -5.56218847e+00 -2.26337756e-01 5.34395732e+00 | -5.56218847e+00 -2.26337756e-01 5.34395732e+00 60 1.87090170e+00 9.16623932e-01 -2.96636806e+00 | 1.87090170e+00 9.16623932e-01 -2.96636806e+00 61 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 | 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 62 3.04257522e+00 -4.01826073e-01 6.04297828e+00 | 3.04257522e+00 -4.01826073e-01 6.04297828e+00 63 7.12903139e+00 4.93600112e+00 2.14977718e+00 | 7.12903139e+00 4.93600112e+00 2.14977718e+00 64 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 | 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 65 -2.30188022e+00 1.90590727e+00 -9.42578481e+00 | -2.30188022e+00 1.90590727e+00 -9.42578481e+00 66 -2.97341783e+00 -8.36524659e+00 4.73651525e+00 | -2.97341783e+00 -8.36524659e+00 4.73651525e+00 67 -2.36270474e+00 1.87074440e+00 6.97642647e+00 | -2.36270474e+00 1.87074440e+00 6.97642647e+00 68 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 | 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 69 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 | 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 70 2.00706972e+00 3.44714953e+00 5.17954817e+00 | 2.00706972e+00 3.44714953e+00 5.17954817e+00 71 3.89010581e+00 6.73261807e+00 3.84864311e+00 | 3.89010581e+00 6.73261807e+00 3.84864311e+00 72 -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 | -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 73 -4.19043341e+00 2.64891446e+00 1.05676926e+00 | -4.19043341e+00 2.64891446e+00 1.05676926e+00 74 -3.26211931e+00 -1.28082546e+00 2.03794786e+00 | -3.26211931e+00 -1.28082546e+00 2.03794786e+00 75 4.94933082e+00 1.02709979e+01 -1.64203403e+00 | 4.94933082e+00 1.02709979e+01 -1.64203403e+00 76 -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 | -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 77 2.28465552e+00 3.86273937e+00 -5.26430676e+00 | 2.28465552e+00 3.86273937e+00 -5.26430676e+00 78 -5.08684132e+00 -1.22542212e+00 2.52025824e+00 | -5.08684132e+00 -1.22542212e+00 2.52025824e+00 79 -1.31101705e+00 3.18834491e+00 4.02794518e+00 | -1.31101705e+00 3.18834491e+00 4.02794518e+00 80 -2.49310851e+00 1.37601019e+00 -6.65210187e+00 | -2.49310851e+00 1.37601019e+00 -6.65210187e+00 81 -4.71879782e-01 -1.56077287e+00 5.44874730e+00 | -4.71879782e-01 -1.56077287e+00 5.44874730e+00 82 1.27325372e+00 7.57668516e+00 1.94821848e+00 | 1.27325372e+00 7.57668516e+00 1.94821848e+00 83 3.51402381e+00 4.70249532e-01 1.32393897e-01 | 3.51402381e+00 4.70249532e-01 1.32393897e-01 84 -8.82760366e-01 -1.67079591e+00 2.53932442e+00 | -8.82760366e-01 -1.67079591e+00 2.53932442e+00 85 -8.11921767e-01 1.46019569e+00 -7.09967607e+00 | -8.11921767e-01 1.46019569e+00 -7.09967607e+00 86 -1.22450795e+00 -3.18307315e+00 4.61330453e+00 | -1.22450795e+00 -3.18307315e+00 4.61330453e+00 87 -5.18894040e+00 -3.43054564e+00 4.39730154e+00 | -5.18894040e+00 -3.43054564e+00 4.39730154e+00 88 -1.74169372e+00 -9.59797825e+00 5.09602192e+00 | -1.74169372e+00 -9.59797825e+00 5.09602192e+00 89 4.15977169e+00 5.22500910e+00 -6.99139962e+00 | 4.15977169e+00 5.22500910e+00 -6.99139962e+00 90 -4.17444473e+00 -5.19694281e+00 3.43235516e+00 | -4.17444473e+00 -5.19694281e+00 3.43235516e+00 91 -5.56218847e+00 -2.26337756e-01 5.34395732e+00 | -5.56218847e+00 -2.26337756e-01 5.34395732e+00 92 1.87090170e+00 9.16623932e-01 -2.96636806e+00 | 1.87090170e+00 9.16623932e-01 -2.96636806e+00 93 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 | 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 94 3.04257522e+00 -4.01826073e-01 6.04297828e+00 | 3.04257522e+00 -4.01826073e-01 6.04297828e+00 95 7.12903139e+00 4.93600112e+00 2.14977718e+00 | 7.12903139e+00 4.93600112e+00 2.14977718e+00 96 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 | 7.02347910e+00 -2.18144208e+00 -1.24572410e+00 97 -2.30188022e+00 1.90590727e+00 -9.42578481e+00 | -2.30188022e+00 1.90590727e+00 -9.42578481e+00 98 -2.97341783e+00 -8.36524659e+00 4.73651525e+00 | -2.97341783e+00 -8.36524659e+00 4.73651525e+00 99 -2.36270474e+00 1.87074440e+00 6.97642647e+00 | -2.36270474e+00 1.87074440e+00 6.97642647e+00 100 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 | 4.41923224e-01 -3.54483620e+00 -9.30007382e+00 101 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 | 1.70977822e+00 -4.82142492e+00 -2.44563220e+00 102 2.00706972e+00 3.44714953e+00 5.17954817e+00 | 2.00706972e+00 3.44714953e+00 5.17954817e+00 103 3.89010581e+00 6.73261807e+00 3.84864311e+00 | 3.89010581e+00 6.73261807e+00 3.84864311e+00 104 -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 | -1.37995618e+00 -1.62827410e+00 -4.10597558e+00 105 -4.19043341e+00 2.64891446e+00 1.05676926e+00 | -4.19043341e+00 2.64891446e+00 1.05676926e+00 106 -3.26211931e+00 -1.28082546e+00 2.03794786e+00 | -3.26211931e+00 -1.28082546e+00 2.03794786e+00 107 4.94933082e+00 1.02709979e+01 -1.64203403e+00 | 4.94933082e+00 1.02709979e+01 -1.64203403e+00 108 -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 | -2.18906541e+00 -2.35054957e+00 -8.53122017e+00 109 2.28465552e+00 3.86273937e+00 -5.26430676e+00 | 2.28465552e+00 3.86273937e+00 -5.26430676e+00 110 -5.08684132e+00 -1.22542212e+00 2.52025824e+00 | -5.08684132e+00 -1.22542212e+00 2.52025824e+00 111 -1.31101705e+00 3.18834491e+00 4.02794518e+00 | -1.31101705e+00 3.18834491e+00 4.02794518e+00 112 -2.49310851e+00 1.37601019e+00 -6.65210187e+00 | -2.49310851e+00 1.37601019e+00 -6.65210187e+00 113 -4.71879782e-01 -1.56077287e+00 5.44874730e+00 | -4.71879782e-01 -1.56077287e+00 5.44874730e+00 114 1.27325372e+00 7.57668516e+00 1.94821848e+00 | 1.27325372e+00 7.57668516e+00 1.94821848e+00 115 3.51402381e+00 4.70249532e-01 1.32393897e-01 | 3.51402381e+00 4.70249532e-01 1.32393897e-01 116 -8.82760366e-01 -1.67079591e+00 2.53932442e+00 | -8.82760366e-01 -1.67079591e+00 2.53932442e+00 117 -8.11921767e-01 1.46019569e+00 -7.09967607e+00 | -8.11921767e-01 1.46019569e+00 -7.09967607e+00 118 -1.22450795e+00 -3.18307315e+00 4.61330453e+00 | -1.22450795e+00 -3.18307315e+00 4.61330453e+00 119 -5.18894040e+00 -3.43054564e+00 4.39730154e+00 | -5.18894040e+00 -3.43054564e+00 4.39730154e+00 120 -1.74169372e+00 -9.59797825e+00 5.09602192e+00 | -1.74169372e+00 -9.59797825e+00 5.09602192e+00 121 4.15977169e+00 5.22500910e+00 -6.99139962e+00 | 4.15977169e+00 5.22500910e+00 -6.99139962e+00 122 -4.17444473e+00 -5.19694281e+00 3.43235516e+00 | -4.17444473e+00 -5.19694281e+00 3.43235516e+00 123 -5.56218847e+00 -2.26337756e-01 5.34395732e+00 | -5.56218847e+00 -2.26337756e-01 5.34395732e+00 124 1.87090170e+00 9.16623932e-01 -2.96636806e+00 | 1.87090170e+00 9.16623932e-01 -2.96636806e+00 125 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 | 4.31298121e+00 -5.22189712e+00 -5.85813647e+00 126 3.04257522e+00 -4.01826073e-01 6.04297828e+00 | 3.04257522e+00 -4.01826073e-01 6.04297828e+00 127 7.12903139e+00 4.93600112e+00 2.14977718e+00 | 7.12903139e+00 4.93600112e+00 2.14977718e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = TFT (Configuration in file "config-AlCoCrFeNi-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)) = -70.64213075124684 2^p V(r_1,...,r_N) = -70.64213075125113 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 -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 | -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 1 7.20625843e+00 1.20675414e+01 2.80910412e+00 | 7.20625843e+00 1.20675414e+01 2.80910412e+00 2 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 | 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 3 -3.48715295e+00 6.18188738e+00 1.66663621e+00 | -3.48715295e+00 6.18188738e+00 1.66663621e+00 4 8.52990460e-01 5.06887476e-01 2.90632096e+00 | 8.52990460e-01 5.06887476e-01 2.90632096e+00 5 -9.97415456e+00 5.62542285e+00 2.04507240e+00 | -9.97415456e+00 5.62542285e+00 2.04507240e+00 6 -5.03393537e+00 -7.08498270e+00 2.41545308e+00 | -5.03393537e+00 -7.08498270e+00 2.41545308e+00 7 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 | 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 8 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 | 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 9 -1.30210454e+00 -5.16988341e-01 6.23173018e+00 | -1.30210454e+00 -5.16988341e-01 6.23173018e+00 10 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 | 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 11 -5.43560560e+00 1.37120194e+00 -6.82875516e+00 | -5.43560560e+00 1.37120194e+00 -6.82875516e+00 12 -4.28701100e+00 -8.93987232e+00 1.97337822e+00 | -4.28701100e+00 -8.93987232e+00 1.97337822e+00 13 7.12862145e+00 4.38669562e+00 -1.84599697e-01 | 7.12862145e+00 4.38669562e+00 -1.84599697e-01 14 -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 | -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 15 -4.75868539e+00 2.86175012e+00 3.06536225e+00 | -4.75868539e+00 2.86175012e+00 3.06536225e+00 16 -1.47915618e+00 -5.08097959e+00 3.22125091e+00 | -1.47915618e+00 -5.08097959e+00 3.22125091e+00 17 2.73047840e-01 8.52644133e+00 3.98257390e+00 | 2.73047840e-01 8.52644133e+00 3.98257390e+00 18 -5.93476097e-01 -8.66712291e+00 1.85971949e+00 | -5.93476097e-01 -8.66712291e+00 1.85971949e+00 19 -9.08861010e-01 6.70760102e+00 1.64999505e+00 | -9.08861010e-01 6.70760102e+00 1.64999505e+00 20 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 | 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 21 3.65246968e-01 4.93712465e+00 -2.93932739e+00 | 3.65246968e-01 4.93712465e+00 -2.93932739e+00 22 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 | 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 23 3.55164062e+00 4.65276386e+00 4.45178279e+00 | 3.55164062e+00 4.65276386e+00 4.45178279e+00 24 -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 | -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 25 1.30471369e+01 8.96315215e+00 3.22368538e+00 | 1.30471369e+01 8.96315215e+00 3.22368538e+00 26 1.48622198e+00 -9.45132301e+00 2.26147309e+00 | 1.48622198e+00 -9.45132301e+00 2.26147309e+00 27 -5.22486333e+00 3.44011731e+00 5.07721474e+00 | -5.22486333e+00 3.44011731e+00 5.07721474e+00 28 -7.12994341e-01 4.57734265e+00 -7.95548386e+00 | -7.12994341e-01 4.57734265e+00 -7.95548386e+00 29 -7.35005418e+00 2.95006432e+00 4.43879727e+00 | -7.35005418e+00 2.95006432e+00 4.43879727e+00 30 1.29535332e+00 5.22177963e+00 -3.49754093e+00 | 1.29535332e+00 5.22177963e+00 -3.49754093e+00 31 1.43617792e+00 9.06400824e-01 -9.77599300e+00 | 1.43617792e+00 9.06400824e-01 -9.77599300e+00 32 -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 | -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 33 7.20625843e+00 1.20675414e+01 2.80910412e+00 | 7.20625843e+00 1.20675414e+01 2.80910412e+00 34 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 | 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 35 -3.48715295e+00 6.18188738e+00 1.66663621e+00 | -3.48715295e+00 6.18188738e+00 1.66663621e+00 36 8.52990460e-01 5.06887476e-01 2.90632096e+00 | 8.52990460e-01 5.06887476e-01 2.90632096e+00 37 -9.97415456e+00 5.62542285e+00 2.04507240e+00 | -9.97415456e+00 5.62542285e+00 2.04507240e+00 38 -5.03393537e+00 -7.08498270e+00 2.41545308e+00 | -5.03393537e+00 -7.08498270e+00 2.41545308e+00 39 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 | 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 40 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 | 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 41 -1.30210454e+00 -5.16988341e-01 6.23173018e+00 | -1.30210454e+00 -5.16988341e-01 6.23173018e+00 42 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 | 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 43 -5.43560560e+00 1.37120194e+00 -6.82875516e+00 | -5.43560560e+00 1.37120194e+00 -6.82875516e+00 44 -4.28701100e+00 -8.93987232e+00 1.97337822e+00 | -4.28701100e+00 -8.93987232e+00 1.97337822e+00 45 7.12862145e+00 4.38669562e+00 -1.84599697e-01 | 7.12862145e+00 4.38669562e+00 -1.84599697e-01 46 -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 | -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 47 -4.75868539e+00 2.86175012e+00 3.06536225e+00 | -4.75868539e+00 2.86175012e+00 3.06536225e+00 48 -1.47915618e+00 -5.08097959e+00 3.22125091e+00 | -1.47915618e+00 -5.08097959e+00 3.22125091e+00 49 2.73047840e-01 8.52644133e+00 3.98257390e+00 | 2.73047840e-01 8.52644133e+00 3.98257390e+00 50 -5.93476097e-01 -8.66712291e+00 1.85971949e+00 | -5.93476097e-01 -8.66712291e+00 1.85971949e+00 51 -9.08861010e-01 6.70760102e+00 1.64999505e+00 | -9.08861010e-01 6.70760102e+00 1.64999505e+00 52 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 | 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 53 3.65246968e-01 4.93712465e+00 -2.93932739e+00 | 3.65246968e-01 4.93712465e+00 -2.93932739e+00 54 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 | 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 55 3.55164062e+00 4.65276386e+00 4.45178279e+00 | 3.55164062e+00 4.65276386e+00 4.45178279e+00 56 -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 | -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 57 1.30471369e+01 8.96315215e+00 3.22368538e+00 | 1.30471369e+01 8.96315215e+00 3.22368538e+00 58 1.48622198e+00 -9.45132301e+00 2.26147309e+00 | 1.48622198e+00 -9.45132301e+00 2.26147309e+00 59 -5.22486333e+00 3.44011731e+00 5.07721474e+00 | -5.22486333e+00 3.44011731e+00 5.07721474e+00 60 -7.12994341e-01 4.57734265e+00 -7.95548386e+00 | -7.12994341e-01 4.57734265e+00 -7.95548386e+00 61 -7.35005418e+00 2.95006432e+00 4.43879727e+00 | -7.35005418e+00 2.95006432e+00 4.43879727e+00 62 1.29535332e+00 5.22177963e+00 -3.49754093e+00 | 1.29535332e+00 5.22177963e+00 -3.49754093e+00 63 1.43617792e+00 9.06400824e-01 -9.77599300e+00 | 1.43617792e+00 9.06400824e-01 -9.77599300e+00 64 -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 | -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 65 7.20625843e+00 1.20675414e+01 2.80910412e+00 | 7.20625843e+00 1.20675414e+01 2.80910412e+00 66 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 | 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 67 -3.48715295e+00 6.18188738e+00 1.66663621e+00 | -3.48715295e+00 6.18188738e+00 1.66663621e+00 68 8.52990460e-01 5.06887476e-01 2.90632096e+00 | 8.52990460e-01 5.06887476e-01 2.90632096e+00 69 -9.97415456e+00 5.62542285e+00 2.04507240e+00 | -9.97415456e+00 5.62542285e+00 2.04507240e+00 70 -5.03393537e+00 -7.08498270e+00 2.41545308e+00 | -5.03393537e+00 -7.08498270e+00 2.41545308e+00 71 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 | 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 72 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 | 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 73 -1.30210454e+00 -5.16988341e-01 6.23173018e+00 | -1.30210454e+00 -5.16988341e-01 6.23173018e+00 74 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 | 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 75 -5.43560560e+00 1.37120194e+00 -6.82875516e+00 | -5.43560560e+00 1.37120194e+00 -6.82875516e+00 76 -4.28701100e+00 -8.93987232e+00 1.97337822e+00 | -4.28701100e+00 -8.93987232e+00 1.97337822e+00 77 7.12862145e+00 4.38669562e+00 -1.84599697e-01 | 7.12862145e+00 4.38669562e+00 -1.84599697e-01 78 -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 | -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 79 -4.75868539e+00 2.86175012e+00 3.06536225e+00 | -4.75868539e+00 2.86175012e+00 3.06536225e+00 80 -1.47915618e+00 -5.08097959e+00 3.22125091e+00 | -1.47915618e+00 -5.08097959e+00 3.22125091e+00 81 2.73047840e-01 8.52644133e+00 3.98257390e+00 | 2.73047840e-01 8.52644133e+00 3.98257390e+00 82 -5.93476097e-01 -8.66712291e+00 1.85971949e+00 | -5.93476097e-01 -8.66712291e+00 1.85971949e+00 83 -9.08861010e-01 6.70760102e+00 1.64999505e+00 | -9.08861010e-01 6.70760102e+00 1.64999505e+00 84 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 | 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 85 3.65246968e-01 4.93712465e+00 -2.93932739e+00 | 3.65246968e-01 4.93712465e+00 -2.93932739e+00 86 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 | 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 87 3.55164062e+00 4.65276386e+00 4.45178279e+00 | 3.55164062e+00 4.65276386e+00 4.45178279e+00 88 -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 | -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 89 1.30471369e+01 8.96315215e+00 3.22368538e+00 | 1.30471369e+01 8.96315215e+00 3.22368538e+00 90 1.48622198e+00 -9.45132301e+00 2.26147309e+00 | 1.48622198e+00 -9.45132301e+00 2.26147309e+00 91 -5.22486333e+00 3.44011731e+00 5.07721474e+00 | -5.22486333e+00 3.44011731e+00 5.07721474e+00 92 -7.12994341e-01 4.57734265e+00 -7.95548386e+00 | -7.12994341e-01 4.57734265e+00 -7.95548386e+00 93 -7.35005418e+00 2.95006432e+00 4.43879727e+00 | -7.35005418e+00 2.95006432e+00 4.43879727e+00 94 1.29535332e+00 5.22177963e+00 -3.49754093e+00 | 1.29535332e+00 5.22177963e+00 -3.49754093e+00 95 1.43617792e+00 9.06400824e-01 -9.77599300e+00 | 1.43617792e+00 9.06400824e-01 -9.77599300e+00 96 -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 | -9.17042887e-01 -6.50147304e+00 -5.83912367e+00 97 7.20625843e+00 1.20675414e+01 2.80910412e+00 | 7.20625843e+00 1.20675414e+01 2.80910412e+00 98 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 | 4.09948544e+00 -7.26311996e+00 -1.04791910e+00 99 -3.48715295e+00 6.18188738e+00 1.66663621e+00 | -3.48715295e+00 6.18188738e+00 1.66663621e+00 100 8.52990460e-01 5.06887476e-01 2.90632096e+00 | 8.52990460e-01 5.06887476e-01 2.90632096e+00 101 -9.97415456e+00 5.62542285e+00 2.04507240e+00 | -9.97415456e+00 5.62542285e+00 2.04507240e+00 102 -5.03393537e+00 -7.08498270e+00 2.41545308e+00 | -5.03393537e+00 -7.08498270e+00 2.41545308e+00 103 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 | 4.48828333e-02 -6.51127201e-01 -2.95344758e+00 104 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 | 3.03910353e+00 -6.77635702e-01 -2.37724448e+00 105 -1.30210454e+00 -5.16988341e-01 6.23173018e+00 | -1.30210454e+00 -5.16988341e-01 6.23173018e+00 106 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 | 9.18744929e+00 -1.83346049e+00 -4.25956854e+00 107 -5.43560560e+00 1.37120194e+00 -6.82875516e+00 | -5.43560560e+00 1.37120194e+00 -6.82875516e+00 108 -4.28701100e+00 -8.93987232e+00 1.97337822e+00 | -4.28701100e+00 -8.93987232e+00 1.97337822e+00 109 7.12862145e+00 4.38669562e+00 -1.84599697e-01 | 7.12862145e+00 4.38669562e+00 -1.84599697e-01 110 -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 | -1.26326959e+00 -7.71265241e+00 -1.01681325e+00 111 -4.75868539e+00 2.86175012e+00 3.06536225e+00 | -4.75868539e+00 2.86175012e+00 3.06536225e+00 112 -1.47915618e+00 -5.08097959e+00 3.22125091e+00 | -1.47915618e+00 -5.08097959e+00 3.22125091e+00 113 2.73047840e-01 8.52644133e+00 3.98257390e+00 | 2.73047840e-01 8.52644133e+00 3.98257390e+00 114 -5.93476097e-01 -8.66712291e+00 1.85971949e+00 | -5.93476097e-01 -8.66712291e+00 1.85971949e+00 115 -9.08861010e-01 6.70760102e+00 1.64999505e+00 | -9.08861010e-01 6.70760102e+00 1.64999505e+00 116 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 | 9.04004296e-01 -4.27790942e+00 -2.79805493e+00 117 3.65246968e-01 4.93712465e+00 -2.93932739e+00 | 3.65246968e-01 4.93712465e+00 -2.93932739e+00 118 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 | 1.82606999e-03 -3.58600641e+00 -2.79125188e-01 119 3.55164062e+00 4.65276386e+00 4.45178279e+00 | 3.55164062e+00 4.65276386e+00 4.45178279e+00 120 -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 | -1.19108029e+00 -1.16395210e+01 -1.52655327e+00 121 1.30471369e+01 8.96315215e+00 3.22368538e+00 | 1.30471369e+01 8.96315215e+00 3.22368538e+00 122 1.48622198e+00 -9.45132301e+00 2.26147309e+00 | 1.48622198e+00 -9.45132301e+00 2.26147309e+00 123 -5.22486333e+00 3.44011731e+00 5.07721474e+00 | -5.22486333e+00 3.44011731e+00 5.07721474e+00 124 -7.12994341e-01 4.57734265e+00 -7.95548386e+00 | -7.12994341e-01 4.57734265e+00 -7.95548386e+00 125 -7.35005418e+00 2.95006432e+00 4.43879727e+00 | -7.35005418e+00 2.95006432e+00 4.43879727e+00 126 1.29535332e+00 5.22177963e+00 -3.49754093e+00 | 1.29535332e+00 5.22177963e+00 -3.49754093e+00 127 1.43617792e+00 9.06400824e-01 -9.77599300e+00 | 1.43617792e+00 9.06400824e-01 -9.77599300e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = TFF (Configuration in file "config-AlCoCrFeNi-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)) = -17.753498915775484 2^p V(r_1,...,r_N) = -17.753498915774983 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 1.82881053e+00 -4.23814169e+00 -7.64660394e+00 | 1.82881053e+00 -4.23814169e+00 -7.64660394e+00 1 -3.04483755e+00 -7.98607740e-01 -8.16688488e+00 | -3.04483755e+00 -7.98607740e-01 -8.16688488e+00 2 -1.61591092e-01 -6.60713094e+00 -2.17611819e+00 | -1.61591092e-01 -6.60713094e+00 -2.17611819e+00 3 1.10526747e-01 5.48239230e+00 2.08841753e+00 | 1.10526747e-01 5.48239230e+00 2.08841753e+00 4 3.04236253e+00 -4.04232535e+00 -3.40547901e+00 | 3.04236253e+00 -4.04232535e+00 -3.40547901e+00 5 4.02251998e-01 -1.75242043e+00 -8.27208269e+00 | 4.02251998e-01 -1.75242043e+00 -8.27208269e+00 6 -2.38325262e+00 -7.37923930e+00 8.53551224e-01 | -2.38325262e+00 -7.37923930e+00 8.53551224e-01 7 -5.26023308e+00 2.59335467e+00 -5.22578645e-01 | -5.26023308e+00 2.59335467e+00 -5.22578645e-01 8 -3.78932968e+00 -4.93027541e+00 -5.82972146e+00 | -3.78932968e+00 -4.93027541e+00 -5.82972146e+00 9 3.61764758e+00 8.57445247e+00 -5.88045198e+00 | 3.61764758e+00 8.57445247e+00 -5.88045198e+00 10 4.35197522e+00 -7.42068060e+00 6.23737571e+00 | 4.35197522e+00 -7.42068060e+00 6.23737571e+00 11 -1.05353990e+00 4.19193914e+00 3.37854563e+00 | -1.05353990e+00 4.19193914e+00 3.37854563e+00 12 -6.29729992e+00 -2.55993328e+00 -8.49816963e+00 | -6.29729992e+00 -2.55993328e+00 -8.49816963e+00 13 -9.75074627e-01 5.48246682e+00 -3.88296804e+00 | -9.75074627e-01 5.48246682e+00 -3.88296804e+00 14 4.75862536e+00 4.92436825e-01 9.97137246e-01 | 4.75862536e+00 4.92436825e-01 9.97137246e-01 15 2.64958212e-01 1.15436421e+01 -2.85932674e+00 | 2.64958212e-01 1.15436421e+01 -2.85932674e+00 16 -4.37296167e+00 -5.01051549e+00 2.32589050e+00 | -4.37296167e+00 -5.01051549e+00 2.32589050e+00 17 4.02752163e+00 4.39314227e+00 -6.79922527e+00 | 4.02752163e+00 4.39314227e+00 -6.79922527e+00 18 3.79123908e+00 -6.80263067e+00 9.23624528e+00 | 3.79123908e+00 -6.80263067e+00 9.23624528e+00 19 -3.09672429e+00 -1.65356945e+00 7.23107161e+00 | -3.09672429e+00 -1.65356945e+00 7.23107161e+00 20 -1.11610781e+00 -6.74902219e+00 -4.06855913e+00 | -1.11610781e+00 -6.74902219e+00 -4.06855913e+00 21 -8.29641779e-01 -5.34218384e+00 6.16745429e-01 | -8.29641779e-01 -5.34218384e+00 6.16745429e-01 22 1.57109205e+00 -2.66045931e+00 3.75408714e+00 | 1.57109205e+00 -2.66045931e+00 3.75408714e+00 23 7.91776593e-01 1.92976804e+00 6.64357200e+00 | 7.91776593e-01 1.92976804e+00 6.64357200e+00 24 2.95767710e+00 4.15135604e+00 -1.95446454e+00 | 2.95767710e+00 4.15135604e+00 -1.95446454e+00 25 -1.58795123e+00 1.59411186e+00 8.54715919e-01 | -1.58795123e+00 1.59411186e+00 8.54715919e-01 26 -1.67551035e+00 1.91277287e+00 5.74260350e+00 | -1.67551035e+00 1.91277287e+00 5.74260350e+00 27 2.38518238e+00 4.89109122e+00 6.87005165e+00 | 2.38518238e+00 4.89109122e+00 6.87005165e+00 28 -2.99508169e+00 -1.88923358e+00 1.63963697e+00 | -2.99508169e+00 -1.88923358e+00 1.63963697e+00 29 3.39593585e+00 9.29635451e+00 -4.65412467e+00 | 3.39593585e+00 9.29635451e+00 -4.65412467e+00 30 4.86047483e+00 -4.22011683e+00 9.88232025e+00 | 4.86047483e+00 -4.22011683e+00 9.88232025e+00 31 -3.51892041e+00 7.52720500e+00 6.26479123e+00 | -3.51892041e+00 7.52720500e+00 6.26479123e+00 32 1.82881053e+00 -4.23814169e+00 -7.64660394e+00 | 1.82881053e+00 -4.23814169e+00 -7.64660394e+00 33 -3.04483755e+00 -7.98607740e-01 -8.16688488e+00 | -3.04483755e+00 -7.98607740e-01 -8.16688488e+00 34 -1.61591092e-01 -6.60713094e+00 -2.17611819e+00 | -1.61591092e-01 -6.60713094e+00 -2.17611819e+00 35 1.10526747e-01 5.48239230e+00 2.08841753e+00 | 1.10526747e-01 5.48239230e+00 2.08841753e+00 36 3.04236253e+00 -4.04232535e+00 -3.40547901e+00 | 3.04236253e+00 -4.04232535e+00 -3.40547901e+00 37 4.02251998e-01 -1.75242043e+00 -8.27208269e+00 | 4.02251998e-01 -1.75242043e+00 -8.27208269e+00 38 -2.38325262e+00 -7.37923930e+00 8.53551224e-01 | -2.38325262e+00 -7.37923930e+00 8.53551224e-01 39 -5.26023308e+00 2.59335467e+00 -5.22578645e-01 | -5.26023308e+00 2.59335467e+00 -5.22578645e-01 40 -3.78932968e+00 -4.93027541e+00 -5.82972146e+00 | -3.78932968e+00 -4.93027541e+00 -5.82972146e+00 41 3.61764758e+00 8.57445247e+00 -5.88045198e+00 | 3.61764758e+00 8.57445247e+00 -5.88045198e+00 42 4.35197522e+00 -7.42068060e+00 6.23737571e+00 | 4.35197522e+00 -7.42068060e+00 6.23737571e+00 43 -1.05353990e+00 4.19193914e+00 3.37854563e+00 | -1.05353990e+00 4.19193914e+00 3.37854563e+00 44 -6.29729992e+00 -2.55993328e+00 -8.49816963e+00 | -6.29729992e+00 -2.55993328e+00 -8.49816963e+00 45 -9.75074627e-01 5.48246682e+00 -3.88296804e+00 | -9.75074627e-01 5.48246682e+00 -3.88296804e+00 46 4.75862536e+00 4.92436825e-01 9.97137246e-01 | 4.75862536e+00 4.92436825e-01 9.97137246e-01 47 2.64958212e-01 1.15436421e+01 -2.85932674e+00 | 2.64958212e-01 1.15436421e+01 -2.85932674e+00 48 -4.37296167e+00 -5.01051549e+00 2.32589050e+00 | -4.37296167e+00 -5.01051549e+00 2.32589050e+00 49 4.02752163e+00 4.39314227e+00 -6.79922527e+00 | 4.02752163e+00 4.39314227e+00 -6.79922527e+00 50 3.79123908e+00 -6.80263067e+00 9.23624528e+00 | 3.79123908e+00 -6.80263067e+00 9.23624528e+00 51 -3.09672429e+00 -1.65356945e+00 7.23107161e+00 | -3.09672429e+00 -1.65356945e+00 7.23107161e+00 52 -1.11610781e+00 -6.74902219e+00 -4.06855913e+00 | -1.11610781e+00 -6.74902219e+00 -4.06855913e+00 53 -8.29641779e-01 -5.34218384e+00 6.16745429e-01 | -8.29641779e-01 -5.34218384e+00 6.16745429e-01 54 1.57109205e+00 -2.66045931e+00 3.75408714e+00 | 1.57109205e+00 -2.66045931e+00 3.75408714e+00 55 7.91776593e-01 1.92976804e+00 6.64357200e+00 | 7.91776593e-01 1.92976804e+00 6.64357200e+00 56 2.95767710e+00 4.15135604e+00 -1.95446454e+00 | 2.95767710e+00 4.15135604e+00 -1.95446454e+00 57 -1.58795123e+00 1.59411186e+00 8.54715919e-01 | -1.58795123e+00 1.59411186e+00 8.54715919e-01 58 -1.67551035e+00 1.91277287e+00 5.74260350e+00 | -1.67551035e+00 1.91277287e+00 5.74260350e+00 59 2.38518238e+00 4.89109122e+00 6.87005165e+00 | 2.38518238e+00 4.89109122e+00 6.87005165e+00 60 -2.99508169e+00 -1.88923358e+00 1.63963697e+00 | -2.99508169e+00 -1.88923358e+00 1.63963697e+00 61 3.39593585e+00 9.29635451e+00 -4.65412467e+00 | 3.39593585e+00 9.29635451e+00 -4.65412467e+00 62 4.86047483e+00 -4.22011683e+00 9.88232025e+00 | 4.86047483e+00 -4.22011683e+00 9.88232025e+00 63 -3.51892041e+00 7.52720500e+00 6.26479123e+00 | -3.51892041e+00 7.52720500e+00 6.26479123e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = FTT (Configuration in file "config-AlCoCrFeNi-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)) = -83.46848922611666 2^p V(r_1,...,r_N) = -83.46848922611493 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 -3.75680919e+00 -2.44465646e+00 1.57348885e+00 | -3.75680919e+00 -2.44465646e+00 1.57348885e+00 1 -5.31527910e+00 -1.98480987e+01 2.79501055e+00 | -5.31527910e+00 -1.98480987e+01 2.79501055e+00 2 5.71256558e+00 6.15820275e-01 -6.64282481e+00 | 5.71256558e+00 6.15820275e-01 -6.64282481e+00 3 1.82270241e+00 4.79152370e-01 -2.25865366e+00 | 1.82270241e+00 4.79152370e-01 -2.25865366e+00 4 -1.94683954e+01 1.51839512e+01 5.77431091e+00 | -1.94683954e+01 1.51839512e+01 5.77431091e+00 5 4.66305608e+00 1.24658812e+00 -3.55105406e+00 | 4.66305608e+00 1.24658812e+00 -3.55105406e+00 6 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 | 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 7 -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 | -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 8 -8.65957453e+00 -1.47877376e+00 3.02071913e+00 | -8.65957453e+00 -1.47877376e+00 3.02071913e+00 9 6.18439966e-01 3.81238351e+00 3.46318347e+00 | 6.18439966e-01 3.81238351e+00 3.46318347e+00 10 1.92513634e+00 -1.29671801e+00 2.84676909e+00 | 1.92513634e+00 -1.29671801e+00 2.84676909e+00 11 -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 | -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 12 1.11891662e+01 5.82126324e+00 -6.89520662e-01 | 1.11891662e+01 5.82126324e+00 -6.89520662e-01 13 6.21075139e+00 -8.70916407e+00 6.09672832e+00 | 6.21075139e+00 -8.70916407e+00 6.09672832e+00 14 1.28164593e+00 7.21739108e+00 1.63298361e+00 | 1.28164593e+00 7.21739108e+00 1.63298361e+00 15 -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 | -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 16 -4.79820629e+00 -2.43822416e+00 2.13415818e+00 | -4.79820629e+00 -2.43822416e+00 2.13415818e+00 17 7.30558467e+00 6.79742040e+00 2.83877482e+00 | 7.30558467e+00 6.79742040e+00 2.83877482e+00 18 1.12138286e+01 2.08247494e+00 2.16553439e+00 | 1.12138286e+01 2.08247494e+00 2.16553439e+00 19 -2.51461279e+00 3.53684490e+00 1.47840642e+00 | -2.51461279e+00 3.53684490e+00 1.47840642e+00 20 -7.37316531e+00 7.93137974e-02 2.82628619e+00 | -7.37316531e+00 7.93137974e-02 2.82628619e+00 21 1.90989968e-01 2.50634454e+00 5.89391509e+00 | 1.90989968e-01 2.50634454e+00 5.89391509e+00 22 4.37219763e+00 6.36852974e+00 -7.17326773e+00 | 4.37219763e+00 6.36852974e+00 -7.17326773e+00 23 -2.17545623e+00 -1.34807532e+00 2.05893730e+00 | -2.17545623e+00 -1.34807532e+00 2.05893730e+00 24 -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 | -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 25 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 | 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 26 1.09358103e+00 3.47559209e+00 -5.86497936e+00 | 1.09358103e+00 3.47559209e+00 -5.86497936e+00 27 -1.03749558e+01 3.19926006e+00 4.94156012e+00 | -1.03749558e+01 3.19926006e+00 4.94156012e+00 28 -5.26503458e+00 -7.28903433e+00 2.84742460e-02 | -5.26503458e+00 -7.28903433e+00 2.84742460e-02 29 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 | 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 30 5.29316792e+00 6.96702460e-01 -1.69666131e+00 | 5.29316792e+00 6.96702460e-01 -1.69666131e+00 31 -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 | -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 32 -3.75680919e+00 -2.44465646e+00 1.57348885e+00 | -3.75680919e+00 -2.44465646e+00 1.57348885e+00 33 -5.31527910e+00 -1.98480987e+01 2.79501055e+00 | -5.31527910e+00 -1.98480987e+01 2.79501055e+00 34 5.71256558e+00 6.15820275e-01 -6.64282481e+00 | 5.71256558e+00 6.15820275e-01 -6.64282481e+00 35 1.82270241e+00 4.79152370e-01 -2.25865366e+00 | 1.82270241e+00 4.79152370e-01 -2.25865366e+00 36 -1.94683954e+01 1.51839512e+01 5.77431091e+00 | -1.94683954e+01 1.51839512e+01 5.77431091e+00 37 4.66305608e+00 1.24658812e+00 -3.55105406e+00 | 4.66305608e+00 1.24658812e+00 -3.55105406e+00 38 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 | 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 39 -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 | -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 40 -8.65957453e+00 -1.47877376e+00 3.02071913e+00 | -8.65957453e+00 -1.47877376e+00 3.02071913e+00 41 6.18439966e-01 3.81238351e+00 3.46318347e+00 | 6.18439966e-01 3.81238351e+00 3.46318347e+00 42 1.92513634e+00 -1.29671801e+00 2.84676909e+00 | 1.92513634e+00 -1.29671801e+00 2.84676909e+00 43 -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 | -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 44 1.11891662e+01 5.82126324e+00 -6.89520662e-01 | 1.11891662e+01 5.82126324e+00 -6.89520662e-01 45 6.21075139e+00 -8.70916407e+00 6.09672832e+00 | 6.21075139e+00 -8.70916407e+00 6.09672832e+00 46 1.28164593e+00 7.21739108e+00 1.63298361e+00 | 1.28164593e+00 7.21739108e+00 1.63298361e+00 47 -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 | -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 48 -4.79820629e+00 -2.43822416e+00 2.13415818e+00 | -4.79820629e+00 -2.43822416e+00 2.13415818e+00 49 7.30558467e+00 6.79742040e+00 2.83877482e+00 | 7.30558467e+00 6.79742040e+00 2.83877482e+00 50 1.12138286e+01 2.08247494e+00 2.16553439e+00 | 1.12138286e+01 2.08247494e+00 2.16553439e+00 51 -2.51461279e+00 3.53684490e+00 1.47840642e+00 | -2.51461279e+00 3.53684490e+00 1.47840642e+00 52 -7.37316531e+00 7.93137974e-02 2.82628619e+00 | -7.37316531e+00 7.93137974e-02 2.82628619e+00 53 1.90989968e-01 2.50634454e+00 5.89391509e+00 | 1.90989968e-01 2.50634454e+00 5.89391509e+00 54 4.37219763e+00 6.36852974e+00 -7.17326773e+00 | 4.37219763e+00 6.36852974e+00 -7.17326773e+00 55 -2.17545623e+00 -1.34807532e+00 2.05893730e+00 | -2.17545623e+00 -1.34807532e+00 2.05893730e+00 56 -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 | -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 57 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 | 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 58 1.09358103e+00 3.47559209e+00 -5.86497936e+00 | 1.09358103e+00 3.47559209e+00 -5.86497936e+00 59 -1.03749558e+01 3.19926006e+00 4.94156012e+00 | -1.03749558e+01 3.19926006e+00 4.94156012e+00 60 -5.26503458e+00 -7.28903433e+00 2.84742460e-02 | -5.26503458e+00 -7.28903433e+00 2.84742460e-02 61 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 | 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 62 5.29316792e+00 6.96702460e-01 -1.69666131e+00 | 5.29316792e+00 6.96702460e-01 -1.69666131e+00 63 -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 | -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 64 -3.75680919e+00 -2.44465646e+00 1.57348885e+00 | -3.75680919e+00 -2.44465646e+00 1.57348885e+00 65 -5.31527910e+00 -1.98480987e+01 2.79501055e+00 | -5.31527910e+00 -1.98480987e+01 2.79501055e+00 66 5.71256558e+00 6.15820275e-01 -6.64282481e+00 | 5.71256558e+00 6.15820275e-01 -6.64282481e+00 67 1.82270241e+00 4.79152370e-01 -2.25865366e+00 | 1.82270241e+00 4.79152370e-01 -2.25865366e+00 68 -1.94683954e+01 1.51839512e+01 5.77431091e+00 | -1.94683954e+01 1.51839512e+01 5.77431091e+00 69 4.66305608e+00 1.24658812e+00 -3.55105406e+00 | 4.66305608e+00 1.24658812e+00 -3.55105406e+00 70 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 | 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 71 -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 | -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 72 -8.65957453e+00 -1.47877376e+00 3.02071913e+00 | -8.65957453e+00 -1.47877376e+00 3.02071913e+00 73 6.18439966e-01 3.81238351e+00 3.46318347e+00 | 6.18439966e-01 3.81238351e+00 3.46318347e+00 74 1.92513634e+00 -1.29671801e+00 2.84676909e+00 | 1.92513634e+00 -1.29671801e+00 2.84676909e+00 75 -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 | -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 76 1.11891662e+01 5.82126324e+00 -6.89520662e-01 | 1.11891662e+01 5.82126324e+00 -6.89520662e-01 77 6.21075139e+00 -8.70916407e+00 6.09672832e+00 | 6.21075139e+00 -8.70916407e+00 6.09672832e+00 78 1.28164593e+00 7.21739108e+00 1.63298361e+00 | 1.28164593e+00 7.21739108e+00 1.63298361e+00 79 -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 | -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 80 -4.79820629e+00 -2.43822416e+00 2.13415818e+00 | -4.79820629e+00 -2.43822416e+00 2.13415818e+00 81 7.30558467e+00 6.79742040e+00 2.83877482e+00 | 7.30558467e+00 6.79742040e+00 2.83877482e+00 82 1.12138286e+01 2.08247494e+00 2.16553439e+00 | 1.12138286e+01 2.08247494e+00 2.16553439e+00 83 -2.51461279e+00 3.53684490e+00 1.47840642e+00 | -2.51461279e+00 3.53684490e+00 1.47840642e+00 84 -7.37316531e+00 7.93137974e-02 2.82628619e+00 | -7.37316531e+00 7.93137974e-02 2.82628619e+00 85 1.90989968e-01 2.50634454e+00 5.89391509e+00 | 1.90989968e-01 2.50634454e+00 5.89391509e+00 86 4.37219763e+00 6.36852974e+00 -7.17326773e+00 | 4.37219763e+00 6.36852974e+00 -7.17326773e+00 87 -2.17545623e+00 -1.34807532e+00 2.05893730e+00 | -2.17545623e+00 -1.34807532e+00 2.05893730e+00 88 -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 | -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 89 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 | 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 90 1.09358103e+00 3.47559209e+00 -5.86497936e+00 | 1.09358103e+00 3.47559209e+00 -5.86497936e+00 91 -1.03749558e+01 3.19926006e+00 4.94156012e+00 | -1.03749558e+01 3.19926006e+00 4.94156012e+00 92 -5.26503458e+00 -7.28903433e+00 2.84742460e-02 | -5.26503458e+00 -7.28903433e+00 2.84742460e-02 93 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 | 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 94 5.29316792e+00 6.96702460e-01 -1.69666131e+00 | 5.29316792e+00 6.96702460e-01 -1.69666131e+00 95 -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 | -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 96 -3.75680919e+00 -2.44465646e+00 1.57348885e+00 | -3.75680919e+00 -2.44465646e+00 1.57348885e+00 97 -5.31527910e+00 -1.98480987e+01 2.79501055e+00 | -5.31527910e+00 -1.98480987e+01 2.79501055e+00 98 5.71256558e+00 6.15820275e-01 -6.64282481e+00 | 5.71256558e+00 6.15820275e-01 -6.64282481e+00 99 1.82270241e+00 4.79152370e-01 -2.25865366e+00 | 1.82270241e+00 4.79152370e-01 -2.25865366e+00 100 -1.94683954e+01 1.51839512e+01 5.77431091e+00 | -1.94683954e+01 1.51839512e+01 5.77431091e+00 101 4.66305608e+00 1.24658812e+00 -3.55105406e+00 | 4.66305608e+00 1.24658812e+00 -3.55105406e+00 102 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 | 5.48944722e+00 -2.66505931e+00 -3.61668895e-01 103 -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 | -8.65861902e+00 -7.21416102e+00 -7.87303132e-01 104 -8.65957453e+00 -1.47877376e+00 3.02071913e+00 | -8.65957453e+00 -1.47877376e+00 3.02071913e+00 105 6.18439966e-01 3.81238351e+00 3.46318347e+00 | 6.18439966e-01 3.81238351e+00 3.46318347e+00 106 1.92513634e+00 -1.29671801e+00 2.84676909e+00 | 1.92513634e+00 -1.29671801e+00 2.84676909e+00 107 -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 | -2.16185545e+00 -1.31813524e+00 -5.47407394e+00 108 1.11891662e+01 5.82126324e+00 -6.89520662e-01 | 1.11891662e+01 5.82126324e+00 -6.89520662e-01 109 6.21075139e+00 -8.70916407e+00 6.09672832e+00 | 6.21075139e+00 -8.70916407e+00 6.09672832e+00 110 1.28164593e+00 7.21739108e+00 1.63298361e+00 | 1.28164593e+00 7.21739108e+00 1.63298361e+00 111 -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 | -4.65662278e-01 -1.68425688e+00 -3.66338357e+00 112 -4.79820629e+00 -2.43822416e+00 2.13415818e+00 | -4.79820629e+00 -2.43822416e+00 2.13415818e+00 113 7.30558467e+00 6.79742040e+00 2.83877482e+00 | 7.30558467e+00 6.79742040e+00 2.83877482e+00 114 1.12138286e+01 2.08247494e+00 2.16553439e+00 | 1.12138286e+01 2.08247494e+00 2.16553439e+00 115 -2.51461279e+00 3.53684490e+00 1.47840642e+00 | -2.51461279e+00 3.53684490e+00 1.47840642e+00 116 -7.37316531e+00 7.93137974e-02 2.82628619e+00 | -7.37316531e+00 7.93137974e-02 2.82628619e+00 117 1.90989968e-01 2.50634454e+00 5.89391509e+00 | 1.90989968e-01 2.50634454e+00 5.89391509e+00 118 4.37219763e+00 6.36852974e+00 -7.17326773e+00 | 4.37219763e+00 6.36852974e+00 -7.17326773e+00 119 -2.17545623e+00 -1.34807532e+00 2.05893730e+00 | -2.17545623e+00 -1.34807532e+00 2.05893730e+00 120 -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 | -2.26497577e-01 -1.39847720e-01 -4.88188943e+00 121 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 | 1.06854623e+01 -2.80842457e+00 -5.99866654e+00 122 1.09358103e+00 3.47559209e+00 -5.86497936e+00 | 1.09358103e+00 3.47559209e+00 -5.86497936e+00 123 -1.03749558e+01 3.19926006e+00 4.94156012e+00 | -1.03749558e+01 3.19926006e+00 4.94156012e+00 124 -5.26503458e+00 -7.28903433e+00 2.84742460e-02 | -5.26503458e+00 -7.28903433e+00 2.84742460e-02 125 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 | 6.77835819e+00 -1.95583182e+00 -3.91875898e-01 126 5.29316792e+00 6.96702460e-01 -1.69666131e+00 | 5.29316792e+00 6.96702460e-01 -1.69666131e+00 127 -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 | -4.63195794e+00 -4.80571356e-01 -2.13341770e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = FTF (Configuration in file "config-AlCoCrFeNi-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)) = -4.3403761165935775 2^p V(r_1,...,r_N) = -4.340376116593029 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 -8.92380186e+00 -4.27690778e-01 -1.00480956e+01 | -8.92380186e+00 -4.27690778e-01 -1.00480956e+01 1 1.02178142e+01 -1.21620315e+01 -5.67724175e+00 | 1.02178142e+01 -1.21620315e+01 -5.67724175e+00 2 9.90975798e+00 5.99062418e+00 3.18169928e+00 | 9.90975798e+00 5.99062418e+00 3.18169928e+00 3 -5.48361342e+00 1.92262803e+00 3.71683501e+00 | -5.48361342e+00 1.92262803e+00 3.71683501e+00 4 -1.53888331e+00 3.24681344e+00 -3.18767034e+00 | -1.53888331e+00 3.24681344e+00 -3.18767034e+00 5 3.46637926e+00 3.89772320e-01 -5.71172245e+00 | 3.46637926e+00 3.89772320e-01 -5.71172245e+00 6 7.38405854e+00 4.12443030e+00 -4.43793629e-01 | 7.38405854e+00 4.12443030e+00 -4.43793629e-01 7 -6.46779992e+00 -1.66984227e-01 3.57516770e+00 | -6.46779992e+00 -1.66984227e-01 3.57516770e+00 8 -9.80614185e+00 9.26345762e+00 -2.07034323e+00 | -9.80614185e+00 9.26345762e+00 -2.07034323e+00 9 -3.28859237e+00 -3.68805708e+00 -8.94939660e+00 | -3.28859237e+00 -3.68805708e+00 -8.94939660e+00 10 7.84239777e+00 -2.37038129e+00 5.27139174e+00 | 7.84239777e+00 -2.37038129e+00 5.27139174e+00 11 -8.44809762e+00 -2.41904735e+00 -3.63002969e+00 | -8.44809762e+00 -2.41904735e+00 -3.63002969e+00 12 -1.54036060e+00 -2.67813715e+00 -4.15379604e+00 | -1.54036060e+00 -2.67813715e+00 -4.15379604e+00 13 7.00596744e+00 -5.66817291e+00 -7.37287615e+00 | 7.00596744e+00 -5.66817291e+00 -7.37287615e+00 14 6.86501634e+00 -1.62990468e+00 -5.00199238e-01 | 6.86501634e+00 -1.62990468e+00 -5.00199238e-01 15 -9.99762828e+00 1.42090397e+00 6.42740009e+00 | -9.99762828e+00 1.42090397e+00 6.42740009e+00 16 -6.77939014e+00 2.90053611e+00 6.15611762e-01 | -6.77939014e+00 2.90053611e+00 6.15611762e-01 17 -4.95393692e+00 -1.07223007e+00 -5.27154772e+00 | -4.95393692e+00 -1.07223007e+00 -5.27154772e+00 18 8.55281768e-01 6.09886159e-01 4.78990014e+00 | 8.55281768e-01 6.09886159e-01 4.78990014e+00 19 -4.03858172e+00 1.22872403e-01 5.58207772e+00 | -4.03858172e+00 1.22872403e-01 5.58207772e+00 20 -2.87096114e+00 8.23324888e-01 6.63312593e-01 | -2.87096114e+00 8.23324888e-01 6.63312593e-01 21 4.73958407e+00 -4.26599321e+00 -2.10054068e+00 | 4.73958407e+00 -4.26599321e+00 -2.10054068e+00 22 4.95222808e+00 3.74746007e+00 1.04991933e+00 | 4.95222808e+00 3.74746007e+00 1.04991933e+00 23 5.96129750e+00 2.35227371e+00 8.70515633e+00 | 5.96129750e+00 2.35227371e+00 8.70515633e+00 24 -6.57296128e+00 -4.48522435e+00 -2.21606338e+00 | -6.57296128e+00 -4.48522435e+00 -2.21606338e+00 25 8.21233163e+00 1.48125364e+00 -4.06291284e+00 | 8.21233163e+00 1.48125364e+00 -4.06291284e+00 26 2.02275324e+00 3.44194863e+00 8.56584451e+00 | 2.02275324e+00 3.44194863e+00 8.56584451e+00 27 -4.55380293e+00 -1.76398036e+00 4.40676985e+00 | -4.55380293e+00 -1.76398036e+00 4.40676985e+00 28 1.98289453e+00 6.43346340e+00 -4.30315197e+00 | 1.98289453e+00 6.43346340e+00 -4.30315197e+00 29 6.85983401e+00 -2.23048493e+00 3.15753634e+00 | 6.85983401e+00 -2.23048493e+00 3.15753634e+00 30 1.32075975e+00 -1.16056145e+00 6.07500896e+00 | 1.32075975e+00 -1.16056145e+00 6.07500896e+00 31 -4.33380269e+00 -2.08276756e+00 3.91574998e+00 | -4.33380269e+00 -2.08276756e+00 3.91574998e+00 32 -8.92380186e+00 -4.27690778e-01 -1.00480956e+01 | -8.92380186e+00 -4.27690778e-01 -1.00480956e+01 33 1.02178142e+01 -1.21620315e+01 -5.67724175e+00 | 1.02178142e+01 -1.21620315e+01 -5.67724175e+00 34 9.90975798e+00 5.99062418e+00 3.18169928e+00 | 9.90975798e+00 5.99062418e+00 3.18169928e+00 35 -5.48361342e+00 1.92262803e+00 3.71683501e+00 | -5.48361342e+00 1.92262803e+00 3.71683501e+00 36 -1.53888331e+00 3.24681344e+00 -3.18767034e+00 | -1.53888331e+00 3.24681344e+00 -3.18767034e+00 37 3.46637926e+00 3.89772320e-01 -5.71172245e+00 | 3.46637926e+00 3.89772320e-01 -5.71172245e+00 38 7.38405854e+00 4.12443030e+00 -4.43793629e-01 | 7.38405854e+00 4.12443030e+00 -4.43793629e-01 39 -6.46779992e+00 -1.66984227e-01 3.57516770e+00 | -6.46779992e+00 -1.66984227e-01 3.57516770e+00 40 -9.80614185e+00 9.26345762e+00 -2.07034323e+00 | -9.80614185e+00 9.26345762e+00 -2.07034323e+00 41 -3.28859237e+00 -3.68805708e+00 -8.94939660e+00 | -3.28859237e+00 -3.68805708e+00 -8.94939660e+00 42 7.84239777e+00 -2.37038129e+00 5.27139174e+00 | 7.84239777e+00 -2.37038129e+00 5.27139174e+00 43 -8.44809762e+00 -2.41904735e+00 -3.63002969e+00 | -8.44809762e+00 -2.41904735e+00 -3.63002969e+00 44 -1.54036060e+00 -2.67813715e+00 -4.15379604e+00 | -1.54036060e+00 -2.67813715e+00 -4.15379604e+00 45 7.00596744e+00 -5.66817291e+00 -7.37287615e+00 | 7.00596744e+00 -5.66817291e+00 -7.37287615e+00 46 6.86501634e+00 -1.62990468e+00 -5.00199238e-01 | 6.86501634e+00 -1.62990468e+00 -5.00199238e-01 47 -9.99762828e+00 1.42090397e+00 6.42740009e+00 | -9.99762828e+00 1.42090397e+00 6.42740009e+00 48 -6.77939014e+00 2.90053611e+00 6.15611762e-01 | -6.77939014e+00 2.90053611e+00 6.15611762e-01 49 -4.95393692e+00 -1.07223007e+00 -5.27154772e+00 | -4.95393692e+00 -1.07223007e+00 -5.27154772e+00 50 8.55281768e-01 6.09886159e-01 4.78990014e+00 | 8.55281768e-01 6.09886159e-01 4.78990014e+00 51 -4.03858172e+00 1.22872403e-01 5.58207772e+00 | -4.03858172e+00 1.22872403e-01 5.58207772e+00 52 -2.87096114e+00 8.23324888e-01 6.63312593e-01 | -2.87096114e+00 8.23324888e-01 6.63312593e-01 53 4.73958407e+00 -4.26599321e+00 -2.10054068e+00 | 4.73958407e+00 -4.26599321e+00 -2.10054068e+00 54 4.95222808e+00 3.74746007e+00 1.04991933e+00 | 4.95222808e+00 3.74746007e+00 1.04991933e+00 55 5.96129750e+00 2.35227371e+00 8.70515633e+00 | 5.96129750e+00 2.35227371e+00 8.70515633e+00 56 -6.57296128e+00 -4.48522435e+00 -2.21606338e+00 | -6.57296128e+00 -4.48522435e+00 -2.21606338e+00 57 8.21233163e+00 1.48125364e+00 -4.06291284e+00 | 8.21233163e+00 1.48125364e+00 -4.06291284e+00 58 2.02275324e+00 3.44194863e+00 8.56584451e+00 | 2.02275324e+00 3.44194863e+00 8.56584451e+00 59 -4.55380293e+00 -1.76398036e+00 4.40676985e+00 | -4.55380293e+00 -1.76398036e+00 4.40676985e+00 60 1.98289453e+00 6.43346340e+00 -4.30315197e+00 | 1.98289453e+00 6.43346340e+00 -4.30315197e+00 61 6.85983401e+00 -2.23048493e+00 3.15753634e+00 | 6.85983401e+00 -2.23048493e+00 3.15753634e+00 62 1.32075975e+00 -1.16056145e+00 6.07500896e+00 | 1.32075975e+00 -1.16056145e+00 6.07500896e+00 63 -4.33380269e+00 -2.08276756e+00 3.91574998e+00 | -4.33380269e+00 -2.08276756e+00 3.91574998e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Co Cr Fe Ni, PBC = FFT (Configuration in file "config-AlCoCrFeNi-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)) = -34.09864621662636 2^p V(r_1,...,r_N) = -34.09864621662637 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 -9.14322739e+00 -6.51366826e+00 -3.92523865e+00 | -9.14322739e+00 -6.51366826e+00 -3.92523865e+00 1 3.26217054e+00 3.09226249e+00 3.59144907e+00 | 3.26217054e+00 3.09226249e+00 3.59144907e+00 2 -2.60884628e-01 -2.44502053e+00 2.75886946e+00 | -2.60884628e-01 -2.44502053e+00 2.75886946e+00 3 -9.54129057e-01 7.04653805e-01 5.42777170e+00 | -9.54129057e-01 7.04653805e-01 5.42777170e+00 4 1.88251400e+00 -5.52483857e+00 -6.36864272e-01 | 1.88251400e+00 -5.52483857e+00 -6.36864272e-01 5 6.66968020e+00 9.68652787e-01 -1.75429318e+00 | 6.66968020e+00 9.68652787e-01 -1.75429318e+00 6 8.97347063e+00 -6.47567488e+00 -5.70702918e-01 | 8.97347063e+00 -6.47567488e+00 -5.70702918e-01 7 -6.14863569e+00 2.76223285e+00 -5.72678319e-01 | -6.14863569e+00 2.76223285e+00 -5.72678319e-01 8 -3.43188225e+00 3.91152357e+00 1.62531101e-01 | -3.43188225e+00 3.91152357e+00 1.62531101e-01 9 -3.58843567e+00 6.79050925e+00 2.71739315e+00 | -3.58843567e+00 6.79050925e+00 2.71739315e+00 10 2.71368335e+00 -2.68037376e+00 -8.18518295e+00 | 2.71368335e+00 -2.68037376e+00 -8.18518295e+00 11 -5.16148008e+00 4.90990239e+00 -3.02143292e+00 | -5.16148008e+00 4.90990239e+00 -3.02143292e+00 12 -5.47984810e+00 -5.57196569e+00 2.55033628e-01 | -5.47984810e+00 -5.57196569e+00 2.55033628e-01 13 5.61334761e+00 8.12463782e+00 7.86751942e-01 | 5.61334761e+00 8.12463782e+00 7.86751942e-01 14 5.80656164e+00 2.41314807e+00 6.03516459e+00 | 5.80656164e+00 2.41314807e+00 6.03516459e+00 15 1.50497108e+00 3.81630314e+00 3.90147316e+00 | 1.50497108e+00 3.81630314e+00 3.90147316e+00 16 -4.96318309e+00 -3.74367764e+00 1.45624888e+00 | -4.96318309e+00 -3.74367764e+00 1.45624888e+00 17 -2.18967198e+00 9.32802429e-01 -5.95493075e-01 | -2.18967198e+00 9.32802429e-01 -5.95493075e-01 18 1.34292925e+00 -4.51506170e+00 -3.06430440e+00 | 1.34292925e+00 -4.51506170e+00 -3.06430440e+00 19 -5.83023536e+00 -4.35010977e+00 -1.75086278e+00 | -5.83023536e+00 -4.35010977e+00 -1.75086278e+00 20 -2.09373239e+00 -5.18087860e+00 2.90107554e+00 | -2.09373239e+00 -5.18087860e+00 2.90107554e+00 21 3.54550460e+00 3.60394764e+00 2.43215068e+00 | 3.54550460e+00 3.60394764e+00 2.43215068e+00 22 2.31272183e+00 -5.85092952e+00 -1.09313227e+00 | 2.31272183e+00 -5.85092952e+00 -1.09313227e+00 23 2.67201495e+00 -8.75887022e-01 -6.21178724e-01 | 2.67201495e+00 -8.75887022e-01 -6.21178724e-01 24 -7.86174370e+00 -1.67473782e+00 -7.90146466e+00 | -7.86174370e+00 -1.67473782e+00 -7.90146466e+00 25 2.62771188e+00 9.33496667e+00 3.70434704e+00 | 2.62771188e+00 9.33496667e+00 3.70434704e+00 26 5.36464286e+00 -4.07360677e+00 8.88974157e-01 | 5.36464286e+00 -4.07360677e+00 8.88974157e-01 27 -9.69166815e+00 4.91370103e+00 2.04586090e+00 | -9.69166815e+00 4.91370103e+00 2.04586090e+00 28 5.14598182e+00 -2.79817542e-01 4.12176578e+00 | 5.14598182e+00 -2.79817542e-01 4.12176578e+00 29 9.59348465e-02 3.55597894e+00 -3.96635820e+00 | 9.59348465e-02 3.55597894e+00 -3.96635820e+00 30 6.20018926e+00 -4.70726252e+00 -4.29004374e+00 | 6.20018926e+00 -4.70726252e+00 -4.29004374e+00 31 1.06472718e+00 4.62828774e+00 -1.23762972e+00 | 1.06472718e+00 4.62828774e+00 -1.23762972e+00 32 -9.14322739e+00 -6.51366826e+00 -3.92523865e+00 | -9.14322739e+00 -6.51366826e+00 -3.92523865e+00 33 3.26217054e+00 3.09226249e+00 3.59144907e+00 | 3.26217054e+00 3.09226249e+00 3.59144907e+00 34 -2.60884628e-01 -2.44502053e+00 2.75886946e+00 | -2.60884628e-01 -2.44502053e+00 2.75886946e+00 35 -9.54129057e-01 7.04653805e-01 5.42777170e+00 | -9.54129057e-01 7.04653805e-01 5.42777170e+00 36 1.88251400e+00 -5.52483857e+00 -6.36864272e-01 | 1.88251400e+00 -5.52483857e+00 -6.36864272e-01 37 6.66968020e+00 9.68652787e-01 -1.75429318e+00 | 6.66968020e+00 9.68652787e-01 -1.75429318e+00 38 8.97347063e+00 -6.47567488e+00 -5.70702918e-01 | 8.97347063e+00 -6.47567488e+00 -5.70702918e-01 39 -6.14863569e+00 2.76223285e+00 -5.72678319e-01 | -6.14863569e+00 2.76223285e+00 -5.72678319e-01 40 -3.43188225e+00 3.91152357e+00 1.62531101e-01 | -3.43188225e+00 3.91152357e+00 1.62531101e-01 41 -3.58843567e+00 6.79050925e+00 2.71739315e+00 | -3.58843567e+00 6.79050925e+00 2.71739315e+00 42 2.71368335e+00 -2.68037376e+00 -8.18518295e+00 | 2.71368335e+00 -2.68037376e+00 -8.18518295e+00 43 -5.16148008e+00 4.90990239e+00 -3.02143292e+00 | -5.16148008e+00 4.90990239e+00 -3.02143292e+00 44 -5.47984810e+00 -5.57196569e+00 2.55033628e-01 | -5.47984810e+00 -5.57196569e+00 2.55033628e-01 45 5.61334761e+00 8.12463782e+00 7.86751942e-01 | 5.61334761e+00 8.12463782e+00 7.86751942e-01 46 5.80656164e+00 2.41314807e+00 6.03516459e+00 | 5.80656164e+00 2.41314807e+00 6.03516459e+00 47 1.50497108e+00 3.81630314e+00 3.90147316e+00 | 1.50497108e+00 3.81630314e+00 3.90147316e+00 48 -4.96318309e+00 -3.74367764e+00 1.45624888e+00 | -4.96318309e+00 -3.74367764e+00 1.45624888e+00 49 -2.18967198e+00 9.32802429e-01 -5.95493075e-01 | -2.18967198e+00 9.32802429e-01 -5.95493075e-01 50 1.34292925e+00 -4.51506170e+00 -3.06430440e+00 | 1.34292925e+00 -4.51506170e+00 -3.06430440e+00 51 -5.83023536e+00 -4.35010977e+00 -1.75086278e+00 | -5.83023536e+00 -4.35010977e+00 -1.75086278e+00 52 -2.09373239e+00 -5.18087860e+00 2.90107554e+00 | -2.09373239e+00 -5.18087860e+00 2.90107554e+00 53 3.54550460e+00 3.60394764e+00 2.43215068e+00 | 3.54550460e+00 3.60394764e+00 2.43215068e+00 54 2.31272183e+00 -5.85092952e+00 -1.09313227e+00 | 2.31272183e+00 -5.85092952e+00 -1.09313227e+00 55 2.67201495e+00 -8.75887022e-01 -6.21178724e-01 | 2.67201495e+00 -8.75887022e-01 -6.21178724e-01 56 -7.86174370e+00 -1.67473782e+00 -7.90146466e+00 | -7.86174370e+00 -1.67473782e+00 -7.90146466e+00 57 2.62771188e+00 9.33496667e+00 3.70434704e+00 | 2.62771188e+00 9.33496667e+00 3.70434704e+00 58 5.36464286e+00 -4.07360677e+00 8.88974157e-01 | 5.36464286e+00 -4.07360677e+00 8.88974157e-01 59 -9.69166815e+00 4.91370103e+00 2.04586090e+00 | -9.69166815e+00 4.91370103e+00 2.04586090e+00 60 5.14598182e+00 -2.79817542e-01 4.12176578e+00 | 5.14598182e+00 -2.79817542e-01 4.12176578e+00 61 9.59348465e-02 3.55597894e+00 -3.96635820e+00 | 9.59348465e-02 3.55597894e+00 -3.96635820e+00 62 6.20018926e+00 -4.70726252e+00 -4.29004374e+00 | 6.20018926e+00 -4.70726252e+00 -4.29004374e+00 63 1.06472718e+00 4.62828774e+00 -1.23762972e+00 | 1.06472718e+00 4.62828774e+00 -1.23762972e+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.