!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_HuangLiuDuan_2021_HfNbTaTiZr__MO_893505888031_000 Supported species : Hf Nb Ta Ti Zr random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = TTT (Configuration in file "config-Hf-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 202.4299182232628 2^p V(r_1,...,r_N) = 202.4299182232625 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 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 1 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 2 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 3 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 4 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 5 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 6 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 7 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 8 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 9 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 10 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 11 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 12 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 13 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 14 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 15 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 16 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 17 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 18 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 19 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 20 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 21 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 22 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 23 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 24 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 25 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 26 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 27 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 28 -1.70112518e+00 5.02581770e+00 3.83146337e+00 | -1.70112518e+00 5.02581770e+00 3.83146337e+00 29 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 | 9.44174694e+00 -5.99461446e+00 -5.84194234e+00 30 -3.20987747e+00 -3.43959899e+00 5.15940808e+00 | -3.20987747e+00 -3.43959899e+00 5.15940808e+00 31 -4.53074429e+00 4.40839574e+00 -3.14892911e+00 | -4.53074429e+00 4.40839574e+00 -3.14892911e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = TTF (Configuration in file "config-Hf-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)) = 76.05545158844957 2^p V(r_1,...,r_N) = 76.05545158844951 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 -2.37149539e+00 8.02021994e-01 -1.70430351e+01 | -2.37149539e+00 8.02021994e-01 -1.70430351e+01 1 -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 | -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 2 6.09188127e-01 -9.97520019e-01 1.63159373e+01 | 6.09188127e-01 -9.97520019e-01 1.63159373e+01 3 1.89916749e+00 3.96247643e+00 1.51284481e+01 | 1.89916749e+00 3.96247643e+00 1.51284481e+01 4 -2.37149539e+00 8.02021994e-01 -1.70430351e+01 | -2.37149539e+00 8.02021994e-01 -1.70430351e+01 5 -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 | -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 6 6.09188127e-01 -9.97520019e-01 1.63159373e+01 | 6.09188127e-01 -9.97520019e-01 1.63159373e+01 7 1.89916749e+00 3.96247643e+00 1.51284481e+01 | 1.89916749e+00 3.96247643e+00 1.51284481e+01 8 -2.37149539e+00 8.02021994e-01 -1.70430351e+01 | -2.37149539e+00 8.02021994e-01 -1.70430351e+01 9 -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 | -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 10 6.09188127e-01 -9.97520019e-01 1.63159373e+01 | 6.09188127e-01 -9.97520019e-01 1.63159373e+01 11 1.89916749e+00 3.96247643e+00 1.51284481e+01 | 1.89916749e+00 3.96247643e+00 1.51284481e+01 12 -2.37149539e+00 8.02021994e-01 -1.70430351e+01 | -2.37149539e+00 8.02021994e-01 -1.70430351e+01 13 -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 | -1.36860228e-01 -3.76697841e+00 -1.44013503e+01 14 6.09188127e-01 -9.97520019e-01 1.63159373e+01 | 6.09188127e-01 -9.97520019e-01 1.63159373e+01 15 1.89916749e+00 3.96247643e+00 1.51284481e+01 | 1.89916749e+00 3.96247643e+00 1.51284481e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = TFT (Configuration in file "config-Hf-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)) = 99.2155066343102 2^p V(r_1,...,r_N) = 99.21550663431017 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 3.86199482e+00 -1.48834872e+01 1.16263272e+00 | 3.86199482e+00 -1.48834872e+01 1.16263272e+00 1 5.66476805e-01 2.07563129e+01 -3.69173019e-01 | 5.66476805e-01 2.07563129e+01 -3.69173019e-01 2 -1.33540801e+00 -1.80443364e+01 4.10315106e-02 | -1.33540801e+00 -1.80443364e+01 4.10315106e-02 3 -3.09306362e+00 1.21715107e+01 -8.34491207e-01 | -3.09306362e+00 1.21715107e+01 -8.34491207e-01 4 3.86199482e+00 -1.48834872e+01 1.16263272e+00 | 3.86199482e+00 -1.48834872e+01 1.16263272e+00 5 5.66476805e-01 2.07563129e+01 -3.69173019e-01 | 5.66476805e-01 2.07563129e+01 -3.69173019e-01 6 -1.33540801e+00 -1.80443364e+01 4.10315106e-02 | -1.33540801e+00 -1.80443364e+01 4.10315106e-02 7 -3.09306362e+00 1.21715107e+01 -8.34491207e-01 | -3.09306362e+00 1.21715107e+01 -8.34491207e-01 8 3.86199482e+00 -1.48834872e+01 1.16263272e+00 | 3.86199482e+00 -1.48834872e+01 1.16263272e+00 9 5.66476805e-01 2.07563129e+01 -3.69173019e-01 | 5.66476805e-01 2.07563129e+01 -3.69173019e-01 10 -1.33540801e+00 -1.80443364e+01 4.10315106e-02 | -1.33540801e+00 -1.80443364e+01 4.10315106e-02 11 -3.09306362e+00 1.21715107e+01 -8.34491207e-01 | -3.09306362e+00 1.21715107e+01 -8.34491207e-01 12 3.86199482e+00 -1.48834872e+01 1.16263272e+00 | 3.86199482e+00 -1.48834872e+01 1.16263272e+00 13 5.66476805e-01 2.07563129e+01 -3.69173019e-01 | 5.66476805e-01 2.07563129e+01 -3.69173019e-01 14 -1.33540801e+00 -1.80443364e+01 4.10315106e-02 | -1.33540801e+00 -1.80443364e+01 4.10315106e-02 15 -3.09306362e+00 1.21715107e+01 -8.34491207e-01 | -3.09306362e+00 1.21715107e+01 -8.34491207e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = TFF (Configuration in file "config-Hf-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)) = 40.61417582196251 2^p V(r_1,...,r_N) = 40.614175821962526 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 1.85469184e+00 -1.07400884e+01 -1.88531999e+01 | 1.85469184e+00 -1.07400884e+01 -1.88531999e+01 1 -7.71174621e+00 6.75933334e+00 -9.34736364e+00 | -7.71174621e+00 6.75933334e+00 -9.34736364e+00 2 8.23275959e+00 -1.15508509e+01 9.79655323e+00 | 8.23275959e+00 -1.15508509e+01 9.79655323e+00 3 -2.37570522e+00 1.55316059e+01 1.84040103e+01 | -2.37570522e+00 1.55316059e+01 1.84040103e+01 4 1.85469184e+00 -1.07400884e+01 -1.88531999e+01 | 1.85469184e+00 -1.07400884e+01 -1.88531999e+01 5 -7.71174621e+00 6.75933334e+00 -9.34736364e+00 | -7.71174621e+00 6.75933334e+00 -9.34736364e+00 6 8.23275959e+00 -1.15508509e+01 9.79655323e+00 | 8.23275959e+00 -1.15508509e+01 9.79655323e+00 7 -2.37570522e+00 1.55316059e+01 1.84040103e+01 | -2.37570522e+00 1.55316059e+01 1.84040103e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = FTT (Configuration in file "config-Hf-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)) = 70.63175057174644 2^p V(r_1,...,r_N) = 70.63175057174641 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 -2.12730138e+01 1.92206940e+00 4.70468265e+00 | -2.12730138e+01 1.92206940e+00 4.70468265e+00 1 1.27489320e+01 8.47936340e+00 5.33602026e+00 | 1.27489320e+01 8.47936340e+00 5.33602026e+00 2 1.94866742e+01 -4.46942650e-01 4.75435055e-01 | 1.94866742e+01 -4.46942650e-01 4.75435055e-01 3 -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 | -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 4 -2.12730138e+01 1.92206940e+00 4.70468265e+00 | -2.12730138e+01 1.92206940e+00 4.70468265e+00 5 1.27489320e+01 8.47936340e+00 5.33602026e+00 | 1.27489320e+01 8.47936340e+00 5.33602026e+00 6 1.94866742e+01 -4.46942650e-01 4.75435055e-01 | 1.94866742e+01 -4.46942650e-01 4.75435055e-01 7 -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 | -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 8 -2.12730138e+01 1.92206940e+00 4.70468265e+00 | -2.12730138e+01 1.92206940e+00 4.70468265e+00 9 1.27489320e+01 8.47936340e+00 5.33602026e+00 | 1.27489320e+01 8.47936340e+00 5.33602026e+00 10 1.94866742e+01 -4.46942650e-01 4.75435055e-01 | 1.94866742e+01 -4.46942650e-01 4.75435055e-01 11 -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 | -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 12 -2.12730138e+01 1.92206940e+00 4.70468265e+00 | -2.12730138e+01 1.92206940e+00 4.70468265e+00 13 1.27489320e+01 8.47936340e+00 5.33602026e+00 | 1.27489320e+01 8.47936340e+00 5.33602026e+00 14 1.94866742e+01 -4.46942650e-01 4.75435055e-01 | 1.94866742e+01 -4.46942650e-01 4.75435055e-01 15 -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 | -1.09625924e+01 -9.95449015e+00 -1.05161380e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = FTF (Configuration in file "config-Hf-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)) = 54.36305987173931 2^p V(r_1,...,r_N) = 54.363059871739324 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 -6.40876653e+00 -4.73235305e+00 -2.28159901e+01 | -6.40876653e+00 -4.73235305e+00 -2.28159901e+01 1 5.12893609e+00 6.95582003e+00 -1.44663108e+01 | 5.12893609e+00 6.95582003e+00 -1.44663108e+01 2 6.23396701e+00 4.05153955e+00 1.84230700e+01 | 6.23396701e+00 4.05153955e+00 1.84230700e+01 3 -4.95413657e+00 -6.27500654e+00 1.88592309e+01 | -4.95413657e+00 -6.27500654e+00 1.88592309e+01 4 -6.40876653e+00 -4.73235305e+00 -2.28159901e+01 | -6.40876653e+00 -4.73235305e+00 -2.28159901e+01 5 5.12893609e+00 6.95582003e+00 -1.44663108e+01 | 5.12893609e+00 6.95582003e+00 -1.44663108e+01 6 6.23396701e+00 4.05153955e+00 1.84230700e+01 | 6.23396701e+00 4.05153955e+00 1.84230700e+01 7 -4.95413657e+00 -6.27500654e+00 1.88592309e+01 | -4.95413657e+00 -6.27500654e+00 1.88592309e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Hf, PBC = FFT (Configuration in file "config-Hf-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)) = 34.81229008952661 2^p V(r_1,...,r_N) = 34.812290089526584 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 -1.81936094e+01 -1.30979426e+01 -2.46835595e+00 | -1.81936094e+01 -1.30979426e+01 -2.46835595e+00 1 9.97872672e+00 1.98438862e+01 3.30524000e+00 | 9.97872672e+00 1.98438862e+01 3.30524000e+00 2 1.27492798e+01 -1.71985795e+01 5.13535703e+00 | 1.27492798e+01 -1.71985795e+01 5.13535703e+00 3 -4.53439720e+00 1.04526360e+01 -5.97224108e+00 | -4.53439720e+00 1.04526360e+01 -5.97224108e+00 4 -1.81936094e+01 -1.30979426e+01 -2.46835595e+00 | -1.81936094e+01 -1.30979426e+01 -2.46835595e+00 5 9.97872672e+00 1.98438862e+01 3.30524000e+00 | 9.97872672e+00 1.98438862e+01 3.30524000e+00 6 1.27492798e+01 -1.71985795e+01 5.13535703e+00 | 1.27492798e+01 -1.71985795e+01 5.13535703e+00 7 -4.53439720e+00 1.04526360e+01 -5.97224108e+00 | -4.53439720e+00 1.04526360e+01 -5.97224108e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTT (Configuration in file "config-Nb-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 343.3815407376002 2^p V(r_1,...,r_N) = 343.38154073760245 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 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 1 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 2 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 3 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 4 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 5 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 6 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 7 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 8 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 9 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 10 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 11 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 12 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 13 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 14 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 15 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 16 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 17 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 18 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 19 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 20 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 21 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 22 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 23 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 24 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 25 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 26 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 27 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 28 -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 | -8.67895570e+00 -8.20052909e+00 -3.38982258e+00 29 7.32157129e+00 8.59648840e+00 -8.62439177e+00 | 7.32157129e+00 8.59648840e+00 -8.62439177e+00 30 7.66491002e+00 -1.02908577e+01 1.82922272e+00 | 7.66491002e+00 -1.02908577e+01 1.82922272e+00 31 -6.30752561e+00 9.89489838e+00 1.01849916e+01 | -6.30752561e+00 9.89489838e+00 1.01849916e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTF (Configuration in file "config-Nb-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 69.4933657076021 2^p V(r_1,...,r_N) = 69.49336570760201 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 -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 | -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 1 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 | 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 2 4.84755803e+00 -3.03426465e+00 2.43350404e+01 | 4.84755803e+00 -3.03426465e+00 2.43350404e+01 3 -2.85000969e+00 9.21364622e+00 2.19387242e+01 | -2.85000969e+00 9.21364622e+00 2.19387242e+01 4 -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 | -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 5 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 | 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 6 4.84755803e+00 -3.03426465e+00 2.43350404e+01 | 4.84755803e+00 -3.03426465e+00 2.43350404e+01 7 -2.85000969e+00 9.21364622e+00 2.19387242e+01 | -2.85000969e+00 9.21364622e+00 2.19387242e+01 8 -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 | -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 9 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 | 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 10 4.84755803e+00 -3.03426465e+00 2.43350404e+01 | 4.84755803e+00 -3.03426465e+00 2.43350404e+01 11 -2.85000969e+00 9.21364622e+00 2.19387242e+01 | -2.85000969e+00 9.21364622e+00 2.19387242e+01 12 -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 | -1.12159427e+01 -6.08273633e+00 -1.87887679e+01 13 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 | 9.21839439e+00 -9.66452470e-02 -2.74849967e+01 14 4.84755803e+00 -3.03426465e+00 2.43350404e+01 | 4.84755803e+00 -3.03426465e+00 2.43350404e+01 15 -2.85000969e+00 9.21364622e+00 2.19387242e+01 | -2.85000969e+00 9.21364622e+00 2.19387242e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFT (Configuration in file "config-Nb-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 44.121273466311436 2^p V(r_1,...,r_N) = 44.12127346631125 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 -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 | -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 1 8.29261431e-01 2.40389730e+01 -3.88141425e+00 | 8.29261431e-01 2.40389730e+01 -3.88141425e+00 2 6.72503769e-01 -3.09974892e+01 6.78742857e-01 | 6.72503769e-01 -3.09974892e+01 6.78742857e-01 3 -1.13797801e+00 2.73090521e+01 6.55346882e+00 | -1.13797801e+00 2.73090521e+01 6.55346882e+00 4 -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 | -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 5 8.29261431e-01 2.40389730e+01 -3.88141425e+00 | 8.29261431e-01 2.40389730e+01 -3.88141425e+00 6 6.72503769e-01 -3.09974892e+01 6.78742857e-01 | 6.72503769e-01 -3.09974892e+01 6.78742857e-01 7 -1.13797801e+00 2.73090521e+01 6.55346882e+00 | -1.13797801e+00 2.73090521e+01 6.55346882e+00 8 -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 | -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 9 8.29261431e-01 2.40389730e+01 -3.88141425e+00 | 8.29261431e-01 2.40389730e+01 -3.88141425e+00 10 6.72503769e-01 -3.09974892e+01 6.78742857e-01 | 6.72503769e-01 -3.09974892e+01 6.78742857e-01 11 -1.13797801e+00 2.73090521e+01 6.55346882e+00 | -1.13797801e+00 2.73090521e+01 6.55346882e+00 12 -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 | -3.63787187e-01 -2.03505358e+01 -3.35079743e+00 13 8.29261431e-01 2.40389730e+01 -3.88141425e+00 | 8.29261431e-01 2.40389730e+01 -3.88141425e+00 14 6.72503769e-01 -3.09974892e+01 6.78742857e-01 | 6.72503769e-01 -3.09974892e+01 6.78742857e-01 15 -1.13797801e+00 2.73090521e+01 6.55346882e+00 | -1.13797801e+00 2.73090521e+01 6.55346882e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFF (Configuration in file "config-Nb-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -28.632420994240903 2^p V(r_1,...,r_N) = -28.632420994240903 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 -8.04338302e-01 -7.87391566e+00 -1.05460573e+01 | -8.04338302e-01 -7.87391566e+00 -1.05460573e+01 1 -3.21319514e-01 8.54424826e+00 -7.40719102e+00 | -3.21319514e-01 8.54424826e+00 -7.40719102e+00 2 1.84002711e+00 -1.08269387e+01 8.38979520e+00 | 1.84002711e+00 -1.08269387e+01 8.38979520e+00 3 -7.14369291e-01 1.01566061e+01 9.56345311e+00 | -7.14369291e-01 1.01566061e+01 9.56345311e+00 4 -8.04338302e-01 -7.87391566e+00 -1.05460573e+01 | -8.04338302e-01 -7.87391566e+00 -1.05460573e+01 5 -3.21319514e-01 8.54424826e+00 -7.40719102e+00 | -3.21319514e-01 8.54424826e+00 -7.40719102e+00 6 1.84002711e+00 -1.08269387e+01 8.38979520e+00 | 1.84002711e+00 -1.08269387e+01 8.38979520e+00 7 -7.14369291e-01 1.01566061e+01 9.56345311e+00 | -7.14369291e-01 1.01566061e+01 9.56345311e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTT (Configuration in file "config-Nb-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 70.04600688033631 2^p V(r_1,...,r_N) = 70.04600688033615 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 -2.90708248e+01 -1.01552234e+01 3.81332750e+00 | -2.90708248e+01 -1.01552234e+01 3.81332750e+00 1 2.74582873e+01 1.68559901e+00 1.49489832e+01 | 2.74582873e+01 1.68559901e+00 1.49489832e+01 2 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 | 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 3 -3.14172936e+01 1.25973253e+01 -1.46556118e+01 | -3.14172936e+01 1.25973253e+01 -1.46556118e+01 4 -2.90708248e+01 -1.01552234e+01 3.81332750e+00 | -2.90708248e+01 -1.01552234e+01 3.81332750e+00 5 2.74582873e+01 1.68559901e+00 1.49489832e+01 | 2.74582873e+01 1.68559901e+00 1.49489832e+01 6 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 | 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 7 -3.14172936e+01 1.25973253e+01 -1.46556118e+01 | -3.14172936e+01 1.25973253e+01 -1.46556118e+01 8 -2.90708248e+01 -1.01552234e+01 3.81332750e+00 | -2.90708248e+01 -1.01552234e+01 3.81332750e+00 9 2.74582873e+01 1.68559901e+00 1.49489832e+01 | 2.74582873e+01 1.68559901e+00 1.49489832e+01 10 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 | 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 11 -3.14172936e+01 1.25973253e+01 -1.46556118e+01 | -3.14172936e+01 1.25973253e+01 -1.46556118e+01 12 -2.90708248e+01 -1.01552234e+01 3.81332750e+00 | -2.90708248e+01 -1.01552234e+01 3.81332750e+00 13 2.74582873e+01 1.68559901e+00 1.49489832e+01 | 2.74582873e+01 1.68559901e+00 1.49489832e+01 14 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 | 3.30298311e+01 -4.12770093e+00 -4.10669890e+00 15 -3.14172936e+01 1.25973253e+01 -1.46556118e+01 | -3.14172936e+01 1.25973253e+01 -1.46556118e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTF (Configuration in file "config-Nb-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -10.39349762725409 2^p V(r_1,...,r_N) = -10.393497627254076 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 -1.44885744e+01 4.73464811e+00 -1.50113018e+01 | -1.44885744e+01 4.73464811e+00 -1.50113018e+01 1 1.84624036e+01 -3.51512518e+00 -1.71327695e+01 | 1.84624036e+01 -3.51512518e+00 -1.71327695e+01 2 1.22428021e+01 5.52076959e-01 1.31063239e+01 | 1.22428021e+01 5.52076959e-01 1.31063239e+01 3 -1.62166313e+01 -1.77159989e+00 1.90377475e+01 | -1.62166313e+01 -1.77159989e+00 1.90377475e+01 4 -1.44885744e+01 4.73464811e+00 -1.50113018e+01 | -1.44885744e+01 4.73464811e+00 -1.50113018e+01 5 1.84624036e+01 -3.51512518e+00 -1.71327695e+01 | 1.84624036e+01 -3.51512518e+00 -1.71327695e+01 6 1.22428021e+01 5.52076959e-01 1.31063239e+01 | 1.22428021e+01 5.52076959e-01 1.31063239e+01 7 -1.62166313e+01 -1.77159989e+00 1.90377475e+01 | -1.62166313e+01 -1.77159989e+00 1.90377475e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FFT (Configuration in file "config-Nb-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -10.784249335782153 2^p V(r_1,...,r_N) = -10.784249335782174 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 -1.51334638e+01 -1.12522757e+01 3.16827829e+00 | -1.51334638e+01 -1.12522757e+01 3.16827829e+00 1 1.46398263e+01 9.61982685e+00 7.37862121e-01 | 1.46398263e+01 9.61982685e+00 7.37862121e-01 2 1.55777364e+01 -1.73237087e+01 -1.26570018e+00 | 1.55777364e+01 -1.73237087e+01 -1.26570018e+00 3 -1.50840989e+01 1.89561576e+01 -2.64044023e+00 | -1.50840989e+01 1.89561576e+01 -2.64044023e+00 4 -1.51334638e+01 -1.12522757e+01 3.16827829e+00 | -1.51334638e+01 -1.12522757e+01 3.16827829e+00 5 1.46398263e+01 9.61982685e+00 7.37862121e-01 | 1.46398263e+01 9.61982685e+00 7.37862121e-01 6 1.55777364e+01 -1.73237087e+01 -1.26570018e+00 | 1.55777364e+01 -1.73237087e+01 -1.26570018e+00 7 -1.50840989e+01 1.89561576e+01 -2.64044023e+00 | -1.50840989e+01 1.89561576e+01 -2.64044023e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTT (Configuration in file "config-Ta-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)) = 448.4637383403098 2^p V(r_1,...,r_N) = 448.4637383403108 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 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 1 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 2 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 3 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 4 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 5 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 6 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 7 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 8 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 9 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 10 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 11 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 12 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 13 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 14 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 15 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 16 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 17 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 18 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 19 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 20 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 21 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 22 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 23 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 24 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 25 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 26 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 27 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 28 -1.79675869e+01 -1.35841706e+01 1.25007319e+01 | -1.79675869e+01 -1.35841706e+01 1.25007319e+01 29 1.49414754e+01 1.76801852e+01 1.30600836e+01 | 1.49414754e+01 1.76801852e+01 1.30600836e+01 30 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 | 1.22288538e+01 -9.71172646e+00 -1.64377060e+01 31 -9.20274231e+00 5.61571180e+00 -9.12310952e+00 | -9.20274231e+00 5.61571180e+00 -9.12310952e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TTF (Configuration in file "config-Ta-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)) = 74.23741890291656 2^p V(r_1,...,r_N) = 74.23741890291627 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 3.32254724e+00 1.40586893e+01 -3.30851345e+01 | 3.32254724e+00 1.40586893e+01 -3.30851345e+01 1 -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 | -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 2 -7.54175469e+00 6.19930702e+00 3.02356248e+01 | -7.54175469e+00 6.19930702e+00 3.02356248e+01 3 7.93150772e+00 -1.00447351e+01 3.20292442e+01 | 7.93150772e+00 -1.00447351e+01 3.20292442e+01 4 3.32254724e+00 1.40586893e+01 -3.30851345e+01 | 3.32254724e+00 1.40586893e+01 -3.30851345e+01 5 -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 | -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 6 -7.54175469e+00 6.19930702e+00 3.02356248e+01 | -7.54175469e+00 6.19930702e+00 3.02356248e+01 7 7.93150772e+00 -1.00447351e+01 3.20292442e+01 | 7.93150772e+00 -1.00447351e+01 3.20292442e+01 8 3.32254724e+00 1.40586893e+01 -3.30851345e+01 | 3.32254724e+00 1.40586893e+01 -3.30851345e+01 9 -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 | -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 10 -7.54175469e+00 6.19930702e+00 3.02356248e+01 | -7.54175469e+00 6.19930702e+00 3.02356248e+01 11 7.93150772e+00 -1.00447351e+01 3.20292442e+01 | 7.93150772e+00 -1.00447351e+01 3.20292442e+01 12 3.32254724e+00 1.40586893e+01 -3.30851345e+01 | 3.32254724e+00 1.40586893e+01 -3.30851345e+01 13 -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 | -3.71230027e+00 -1.02132612e+01 -2.91797344e+01 14 -7.54175469e+00 6.19930702e+00 3.02356248e+01 | -7.54175469e+00 6.19930702e+00 3.02356248e+01 15 7.93150772e+00 -1.00447351e+01 3.20292442e+01 | 7.93150772e+00 -1.00447351e+01 3.20292442e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFT (Configuration in file "config-Ta-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)) = 101.77194916224505 2^p V(r_1,...,r_N) = 101.77194916224478 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 -1.60827944e+01 -3.22639223e+01 1.58555416e+01 | -1.60827944e+01 -3.22639223e+01 1.58555416e+01 1 8.92724535e+00 3.23408527e+01 1.50615189e+00 | 8.92724535e+00 3.23408527e+01 1.50615189e+00 2 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 | 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 3 -1.42137215e+01 3.81310481e+01 -7.21642575e+00 | -1.42137215e+01 3.81310481e+01 -7.21642575e+00 4 -1.60827944e+01 -3.22639223e+01 1.58555416e+01 | -1.60827944e+01 -3.22639223e+01 1.58555416e+01 5 8.92724535e+00 3.23408527e+01 1.50615189e+00 | 8.92724535e+00 3.23408527e+01 1.50615189e+00 6 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 | 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 7 -1.42137215e+01 3.81310481e+01 -7.21642575e+00 | -1.42137215e+01 3.81310481e+01 -7.21642575e+00 8 -1.60827944e+01 -3.22639223e+01 1.58555416e+01 | -1.60827944e+01 -3.22639223e+01 1.58555416e+01 9 8.92724535e+00 3.23408527e+01 1.50615189e+00 | 8.92724535e+00 3.23408527e+01 1.50615189e+00 10 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 | 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 11 -1.42137215e+01 3.81310481e+01 -7.21642575e+00 | -1.42137215e+01 3.81310481e+01 -7.21642575e+00 12 -1.60827944e+01 -3.22639223e+01 1.58555416e+01 | -1.60827944e+01 -3.22639223e+01 1.58555416e+01 13 8.92724535e+00 3.23408527e+01 1.50615189e+00 | 8.92724535e+00 3.23408527e+01 1.50615189e+00 14 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 | 2.13692706e+01 -3.82079785e+01 -1.01452677e+01 15 -1.42137215e+01 3.81310481e+01 -7.21642575e+00 | -1.42137215e+01 3.81310481e+01 -7.21642575e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = TFF (Configuration in file "config-Ta-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 49.36925300820854 2^p V(r_1,...,r_N) = 49.36925300820851 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 -2.02318452e+01 -2.58064241e+01 -3.52763810e+01 | -2.02318452e+01 -2.58064241e+01 -3.52763810e+01 1 1.55168472e+01 4.46794787e+01 -3.34615632e+01 | 1.55168472e+01 4.46794787e+01 -3.34615632e+01 2 1.31176860e+01 -4.39524877e+01 3.96367254e+01 | 1.31176860e+01 -4.39524877e+01 3.96367254e+01 3 -8.40268804e+00 2.50794331e+01 2.91012188e+01 | -8.40268804e+00 2.50794331e+01 2.91012188e+01 4 -2.02318452e+01 -2.58064241e+01 -3.52763810e+01 | -2.02318452e+01 -2.58064241e+01 -3.52763810e+01 5 1.55168472e+01 4.46794787e+01 -3.34615632e+01 | 1.55168472e+01 4.46794787e+01 -3.34615632e+01 6 1.31176860e+01 -4.39524877e+01 3.96367254e+01 | 1.31176860e+01 -4.39524877e+01 3.96367254e+01 7 -8.40268804e+00 2.50794331e+01 2.91012188e+01 | -8.40268804e+00 2.50794331e+01 2.91012188e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTT (Configuration in file "config-Ta-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)) = 96.09061463521722 2^p V(r_1,...,r_N) = 96.09061463521724 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 -3.37989848e+01 5.90843402e+00 2.46418294e+00 | -3.37989848e+01 5.90843402e+00 2.46418294e+00 1 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 | 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 2 3.21700017e+01 1.11090418e+01 7.08960805e+00 | 3.21700017e+01 1.11090418e+01 7.08960805e+00 3 -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 | -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 4 -3.37989848e+01 5.90843402e+00 2.46418294e+00 | -3.37989848e+01 5.90843402e+00 2.46418294e+00 5 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 | 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 6 3.21700017e+01 1.11090418e+01 7.08960805e+00 | 3.21700017e+01 1.11090418e+01 7.08960805e+00 7 -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 | -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 8 -3.37989848e+01 5.90843402e+00 2.46418294e+00 | -3.37989848e+01 5.90843402e+00 2.46418294e+00 9 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 | 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 10 3.21700017e+01 1.11090418e+01 7.08960805e+00 | 3.21700017e+01 1.11090418e+01 7.08960805e+00 11 -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 | -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 12 -3.37989848e+01 5.90843402e+00 2.46418294e+00 | -3.37989848e+01 5.90843402e+00 2.46418294e+00 13 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 | 3.35125341e+01 -1.13425913e+01 -2.63746447e+00 14 3.21700017e+01 1.11090418e+01 7.08960805e+00 | 3.21700017e+01 1.11090418e+01 7.08960805e+00 15 -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 | -3.18835511e+01 -5.67488444e+00 -6.91632652e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FTF (Configuration in file "config-Ta-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)) = 24.50042654126647 2^p V(r_1,...,r_N) = 24.500426541266496 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 -3.07193573e+01 7.76052489e+00 -3.41856611e+01 | -3.07193573e+01 7.76052489e+00 -3.41856611e+01 1 2.44879787e+01 -5.22716048e+00 -2.02802643e+01 | 2.44879787e+01 -5.22716048e+00 -2.02802643e+01 2 3.10008476e+01 9.30837779e+00 2.77971510e+01 | 3.10008476e+01 9.30837779e+00 2.77971510e+01 3 -2.47694690e+01 -1.18417422e+01 2.66687743e+01 | -2.47694690e+01 -1.18417422e+01 2.66687743e+01 4 -3.07193573e+01 7.76052489e+00 -3.41856611e+01 | -3.07193573e+01 7.76052489e+00 -3.41856611e+01 5 2.44879787e+01 -5.22716048e+00 -2.02802643e+01 | 2.44879787e+01 -5.22716048e+00 -2.02802643e+01 6 3.10008476e+01 9.30837779e+00 2.77971510e+01 | 3.10008476e+01 9.30837779e+00 2.77971510e+01 7 -2.47694690e+01 -1.18417422e+01 2.66687743e+01 | -2.47694690e+01 -1.18417422e+01 2.66687743e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ta, PBC = FFT (Configuration in file "config-Ta-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)) = 64.44715403206604 2^p V(r_1,...,r_N) = 64.447154032066 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 -3.90277762e+01 -3.22593045e+01 -2.85186682e+01 | -3.90277762e+01 -3.22593045e+01 -2.85186682e+01 1 2.97936463e+01 3.12054181e+01 -7.11789295e+00 | 2.97936463e+01 3.12054181e+01 -7.11789295e+00 2 4.58603337e+01 -4.81485481e+01 1.83895778e+01 | 4.58603337e+01 -4.81485481e+01 1.83895778e+01 3 -3.66262038e+01 4.92024345e+01 1.72469834e+01 | -3.66262038e+01 4.92024345e+01 1.72469834e+01 4 -3.90277762e+01 -3.22593045e+01 -2.85186682e+01 | -3.90277762e+01 -3.22593045e+01 -2.85186682e+01 5 2.97936463e+01 3.12054181e+01 -7.11789295e+00 | 2.97936463e+01 3.12054181e+01 -7.11789295e+00 6 4.58603337e+01 -4.81485481e+01 1.83895778e+01 | 4.58603337e+01 -4.81485481e+01 1.83895778e+01 7 -3.66262038e+01 4.92024345e+01 1.72469834e+01 | -3.66262038e+01 4.92024345e+01 1.72469834e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTT (Configuration in file "config-Ti-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 188.94921660707956 2^p V(r_1,...,r_N) = 188.94921660707968 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 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 1 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 2 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 3 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 4 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 5 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 6 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 7 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 8 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 9 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 10 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 11 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 12 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 13 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 14 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 15 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 16 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 17 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 18 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 19 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 20 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 21 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 22 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 23 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 24 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 25 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 26 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 27 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 28 -1.40330639e+00 1.19838524e+01 -4.64342158e+00 | -1.40330639e+00 1.19838524e+01 -4.64342158e+00 29 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 | 1.29830631e+00 -7.66855422e+00 -5.62700084e+00 30 -4.05647231e+00 1.68265162e+00 4.09231131e+00 | -4.05647231e+00 1.68265162e+00 4.09231131e+00 31 4.16147238e+00 -5.99794977e+00 6.17811111e+00 | 4.16147238e+00 -5.99794977e+00 6.17811111e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTF (Configuration in file "config-Ti-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 69.65036152049777 2^p V(r_1,...,r_N) = 69.65036152049775 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 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 | 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 1 -9.84791812e+00 1.42330008e+01 -1.83175901e+01 | -9.84791812e+00 1.42330008e+01 -1.83175901e+01 2 -1.32262445e+01 -1.54469540e+01 1.95055240e+01 | -1.32262445e+01 -1.54469540e+01 1.95055240e+01 3 1.13529779e+01 1.26857430e+01 1.63839691e+01 | 1.13529779e+01 1.26857430e+01 1.63839691e+01 4 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 | 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 5 -9.84791812e+00 1.42330008e+01 -1.83175901e+01 | -9.84791812e+00 1.42330008e+01 -1.83175901e+01 6 -1.32262445e+01 -1.54469540e+01 1.95055240e+01 | -1.32262445e+01 -1.54469540e+01 1.95055240e+01 7 1.13529779e+01 1.26857430e+01 1.63839691e+01 | 1.13529779e+01 1.26857430e+01 1.63839691e+01 8 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 | 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 9 -9.84791812e+00 1.42330008e+01 -1.83175901e+01 | -9.84791812e+00 1.42330008e+01 -1.83175901e+01 10 -1.32262445e+01 -1.54469540e+01 1.95055240e+01 | -1.32262445e+01 -1.54469540e+01 1.95055240e+01 11 1.13529779e+01 1.26857430e+01 1.63839691e+01 | 1.13529779e+01 1.26857430e+01 1.63839691e+01 12 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 | 1.17211848e+01 -1.14717898e+01 -1.75719030e+01 13 -9.84791812e+00 1.42330008e+01 -1.83175901e+01 | -9.84791812e+00 1.42330008e+01 -1.83175901e+01 14 -1.32262445e+01 -1.54469540e+01 1.95055240e+01 | -1.32262445e+01 -1.54469540e+01 1.95055240e+01 15 1.13529779e+01 1.26857430e+01 1.63839691e+01 | 1.13529779e+01 1.26857430e+01 1.63839691e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFT (Configuration in file "config-Ti-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 94.23866396440421 2^p V(r_1,...,r_N) = 94.23866396440425 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 -1.22093093e+01 -1.94172068e+01 8.53317550e+00 | -1.22093093e+01 -1.94172068e+01 8.53317550e+00 1 3.41963964e-01 1.85074624e+01 -3.41639334e+00 | 3.41963964e-01 1.85074624e+01 -3.41639334e+00 2 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 | 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 3 -3.96213822e+00 2.07741111e+01 5.58450244e+00 | -3.96213822e+00 2.07741111e+01 5.58450244e+00 4 -1.22093093e+01 -1.94172068e+01 8.53317550e+00 | -1.22093093e+01 -1.94172068e+01 8.53317550e+00 5 3.41963964e-01 1.85074624e+01 -3.41639334e+00 | 3.41963964e-01 1.85074624e+01 -3.41639334e+00 6 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 | 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 7 -3.96213822e+00 2.07741111e+01 5.58450244e+00 | -3.96213822e+00 2.07741111e+01 5.58450244e+00 8 -1.22093093e+01 -1.94172068e+01 8.53317550e+00 | -1.22093093e+01 -1.94172068e+01 8.53317550e+00 9 3.41963964e-01 1.85074624e+01 -3.41639334e+00 | 3.41963964e-01 1.85074624e+01 -3.41639334e+00 10 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 | 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 11 -3.96213822e+00 2.07741111e+01 5.58450244e+00 | -3.96213822e+00 2.07741111e+01 5.58450244e+00 12 -1.22093093e+01 -1.94172068e+01 8.53317550e+00 | -1.22093093e+01 -1.94172068e+01 8.53317550e+00 13 3.41963964e-01 1.85074624e+01 -3.41639334e+00 | 3.41963964e-01 1.85074624e+01 -3.41639334e+00 14 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 | 1.58294835e+01 -1.98643667e+01 -1.07012846e+01 15 -3.96213822e+00 2.07741111e+01 5.58450244e+00 | -3.96213822e+00 2.07741111e+01 5.58450244e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFF (Configuration in file "config-Ti-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 34.09437733920449 2^p V(r_1,...,r_N) = 34.09437733920449 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 -8.76270954e+00 -1.43566967e+01 -1.90302724e+01 | -8.76270954e+00 -1.43566967e+01 -1.90302724e+01 1 7.12527095e+00 1.77835170e+01 -1.78270077e+01 | 7.12527095e+00 1.77835170e+01 -1.78270077e+01 2 2.12464563e+01 -2.35042534e+01 1.29026009e+01 | 2.12464563e+01 -2.35042534e+01 1.29026009e+01 3 -1.96090177e+01 2.00774331e+01 2.39546792e+01 | -1.96090177e+01 2.00774331e+01 2.39546792e+01 4 -8.76270954e+00 -1.43566967e+01 -1.90302724e+01 | -8.76270954e+00 -1.43566967e+01 -1.90302724e+01 5 7.12527095e+00 1.77835170e+01 -1.78270077e+01 | 7.12527095e+00 1.77835170e+01 -1.78270077e+01 6 2.12464563e+01 -2.35042534e+01 1.29026009e+01 | 2.12464563e+01 -2.35042534e+01 1.29026009e+01 7 -1.96090177e+01 2.00774331e+01 2.39546792e+01 | -1.96090177e+01 2.00774331e+01 2.39546792e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTT (Configuration in file "config-Ti-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 77.66072476994778 2^p V(r_1,...,r_N) = 77.66072476994776 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 -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 | -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 1 2.00555437e+01 1.45226824e+01 -1.62214921e+01 | 2.00555437e+01 1.45226824e+01 -1.62214921e+01 2 1.61705631e+01 -1.50177366e+01 1.47105676e+01 | 1.61705631e+01 -1.50177366e+01 1.47105676e+01 3 -1.94220220e+01 2.20554398e+00 7.26372300e+00 | -1.94220220e+01 2.20554398e+00 7.26372300e+00 4 -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 | -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 5 2.00555437e+01 1.45226824e+01 -1.62214921e+01 | 2.00555437e+01 1.45226824e+01 -1.62214921e+01 6 1.61705631e+01 -1.50177366e+01 1.47105676e+01 | 1.61705631e+01 -1.50177366e+01 1.47105676e+01 7 -1.94220220e+01 2.20554398e+00 7.26372300e+00 | -1.94220220e+01 2.20554398e+00 7.26372300e+00 8 -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 | -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 9 2.00555437e+01 1.45226824e+01 -1.62214921e+01 | 2.00555437e+01 1.45226824e+01 -1.62214921e+01 10 1.61705631e+01 -1.50177366e+01 1.47105676e+01 | 1.61705631e+01 -1.50177366e+01 1.47105676e+01 11 -1.94220220e+01 2.20554398e+00 7.26372300e+00 | -1.94220220e+01 2.20554398e+00 7.26372300e+00 12 -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 | -1.68040848e+01 -1.71048981e+00 -5.75279854e+00 13 2.00555437e+01 1.45226824e+01 -1.62214921e+01 | 2.00555437e+01 1.45226824e+01 -1.62214921e+01 14 1.61705631e+01 -1.50177366e+01 1.47105676e+01 | 1.61705631e+01 -1.50177366e+01 1.47105676e+01 15 -1.94220220e+01 2.20554398e+00 7.26372300e+00 | -1.94220220e+01 2.20554398e+00 7.26372300e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTF (Configuration in file "config-Ti-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 38.04277540127684 2^p V(r_1,...,r_N) = 38.042775401276835 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 -1.83180129e+01 1.08327284e+01 -1.75860624e+01 | -1.83180129e+01 1.08327284e+01 -1.75860624e+01 1 1.62462911e+01 -9.53584265e+00 -1.65207067e+01 | 1.62462911e+01 -9.53584265e+00 -1.65207067e+01 2 2.75625292e+01 1.92237140e+01 1.60873109e+01 | 2.75625292e+01 1.92237140e+01 1.60873109e+01 3 -2.54908074e+01 -2.05205998e+01 1.80194582e+01 | -2.54908074e+01 -2.05205998e+01 1.80194582e+01 4 -1.83180129e+01 1.08327284e+01 -1.75860624e+01 | -1.83180129e+01 1.08327284e+01 -1.75860624e+01 5 1.62462911e+01 -9.53584265e+00 -1.65207067e+01 | 1.62462911e+01 -9.53584265e+00 -1.65207067e+01 6 2.75625292e+01 1.92237140e+01 1.60873109e+01 | 2.75625292e+01 1.92237140e+01 1.60873109e+01 7 -2.54908074e+01 -2.05205998e+01 1.80194582e+01 | -2.54908074e+01 -2.05205998e+01 1.80194582e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FFT (Configuration in file "config-Ti-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 48.978279847841534 2^p V(r_1,...,r_N) = 48.97827984784153 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 -2.18282259e+01 -2.73928333e+01 6.46178648e+00 | -2.18282259e+01 -2.73928333e+01 6.46178648e+00 1 2.31596922e+01 3.02750506e+01 1.18777593e+01 | 2.31596922e+01 3.02750506e+01 1.18777593e+01 2 2.29439174e+01 -2.00579997e+01 -1.01724485e+01 | 2.29439174e+01 -2.00579997e+01 -1.01724485e+01 3 -2.42753837e+01 1.71757824e+01 -8.16709729e+00 | -2.42753837e+01 1.71757824e+01 -8.16709729e+00 4 -2.18282259e+01 -2.73928333e+01 6.46178648e+00 | -2.18282259e+01 -2.73928333e+01 6.46178648e+00 5 2.31596922e+01 3.02750506e+01 1.18777593e+01 | 2.31596922e+01 3.02750506e+01 1.18777593e+01 6 2.29439174e+01 -2.00579997e+01 -1.01724485e+01 | 2.29439174e+01 -2.00579997e+01 -1.01724485e+01 7 -2.42753837e+01 1.71757824e+01 -8.16709729e+00 | -2.42753837e+01 1.71757824e+01 -8.16709729e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TTT (Configuration in file "config-Zr-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)) = 506.56863464806196 2^p V(r_1,...,r_N) = 506.56863464806185 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 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 1 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 2 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 3 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 4 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 5 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 6 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 7 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 8 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 9 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 10 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 11 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 12 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 13 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 14 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 15 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 16 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 17 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 18 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 19 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 20 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 21 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 22 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 23 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 24 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 25 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 26 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 27 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 28 -1.72706112e+00 1.08376037e+01 5.94091047e+00 | -1.72706112e+00 1.08376037e+01 5.94091047e+00 29 7.07601308e+00 -8.24587075e+00 7.26252053e+00 | 7.07601308e+00 -8.24587075e+00 7.26252053e+00 30 -9.92954381e+00 1.30026450e+01 -5.18496084e+00 | -9.92954381e+00 1.30026450e+01 -5.18496084e+00 31 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 | 4.58059186e+00 -1.55943780e+01 -8.01847017e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TTF (Configuration in file "config-Zr-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)) = 190.9464183487457 2^p V(r_1,...,r_N) = 190.94641834874565 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 7.89217202e+00 1.20118294e+01 -3.04188408e+01 | 7.89217202e+00 1.20118294e+01 -3.04188408e+01 1 -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 | -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 2 -5.91094661e+00 9.07134588e+00 2.78115001e+01 | -5.91094661e+00 9.07134588e+00 2.78115001e+01 3 9.43222652e+00 -1.02809808e+01 3.13552052e+01 | 9.43222652e+00 -1.02809808e+01 3.13552052e+01 4 7.89217202e+00 1.20118294e+01 -3.04188408e+01 | 7.89217202e+00 1.20118294e+01 -3.04188408e+01 5 -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 | -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 6 -5.91094661e+00 9.07134588e+00 2.78115001e+01 | -5.91094661e+00 9.07134588e+00 2.78115001e+01 7 9.43222652e+00 -1.02809808e+01 3.13552052e+01 | 9.43222652e+00 -1.02809808e+01 3.13552052e+01 8 7.89217202e+00 1.20118294e+01 -3.04188408e+01 | 7.89217202e+00 1.20118294e+01 -3.04188408e+01 9 -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 | -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 10 -5.91094661e+00 9.07134588e+00 2.78115001e+01 | -5.91094661e+00 9.07134588e+00 2.78115001e+01 11 9.43222652e+00 -1.02809808e+01 3.13552052e+01 | 9.43222652e+00 -1.02809808e+01 3.13552052e+01 12 7.89217202e+00 1.20118294e+01 -3.04188408e+01 | 7.89217202e+00 1.20118294e+01 -3.04188408e+01 13 -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 | -1.14134519e+01 -1.08021945e+01 -2.87478644e+01 14 -5.91094661e+00 9.07134588e+00 2.78115001e+01 | -5.91094661e+00 9.07134588e+00 2.78115001e+01 15 9.43222652e+00 -1.02809808e+01 3.13552052e+01 | 9.43222652e+00 -1.02809808e+01 3.13552052e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TFT (Configuration in file "config-Zr-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)) = 172.7004030678684 2^p V(r_1,...,r_N) = 172.70040306786845 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 -3.08776914e+00 -2.26129097e+01 7.40376548e+00 | -3.08776914e+00 -2.26129097e+01 7.40376548e+00 1 1.13075486e+01 2.93489581e+01 1.22658317e+01 | 1.13075486e+01 2.93489581e+01 1.22658317e+01 2 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 | 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 3 -1.50836927e+01 2.34379479e+01 -1.35678878e+01 | -1.50836927e+01 2.34379479e+01 -1.35678878e+01 4 -3.08776914e+00 -2.26129097e+01 7.40376548e+00 | -3.08776914e+00 -2.26129097e+01 7.40376548e+00 5 1.13075486e+01 2.93489581e+01 1.22658317e+01 | 1.13075486e+01 2.93489581e+01 1.22658317e+01 6 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 | 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 7 -1.50836927e+01 2.34379479e+01 -1.35678878e+01 | -1.50836927e+01 2.34379479e+01 -1.35678878e+01 8 -3.08776914e+00 -2.26129097e+01 7.40376548e+00 | -3.08776914e+00 -2.26129097e+01 7.40376548e+00 9 1.13075486e+01 2.93489581e+01 1.22658317e+01 | 1.13075486e+01 2.93489581e+01 1.22658317e+01 10 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 | 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 11 -1.50836927e+01 2.34379479e+01 -1.35678878e+01 | -1.50836927e+01 2.34379479e+01 -1.35678878e+01 12 -3.08776914e+00 -2.26129097e+01 7.40376548e+00 | -3.08776914e+00 -2.26129097e+01 7.40376548e+00 13 1.13075486e+01 2.93489581e+01 1.22658317e+01 | 1.13075486e+01 2.93489581e+01 1.22658317e+01 14 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 | 6.86391324e+00 -3.01739963e+01 -6.10170933e+00 15 -1.50836927e+01 2.34379479e+01 -1.35678878e+01 | -1.50836927e+01 2.34379479e+01 -1.35678878e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TFF (Configuration in file "config-Zr-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)) = 42.30596208326645 2^p V(r_1,...,r_N) = 42.30596208326644 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 -8.83285786e+00 -2.06350770e+01 -1.83085978e+01 | -8.83285786e+00 -2.06350770e+01 -1.83085978e+01 1 8.38580211e+00 1.88779819e+01 -2.18004811e+01 | 8.38580211e+00 1.88779819e+01 -2.18004811e+01 2 7.93839245e+00 -2.02984375e+01 2.38043946e+01 | 7.93839245e+00 -2.02984375e+01 2.38043946e+01 3 -7.49133669e+00 2.20555326e+01 1.63046842e+01 | -7.49133669e+00 2.20555326e+01 1.63046842e+01 4 -8.83285786e+00 -2.06350770e+01 -1.83085978e+01 | -8.83285786e+00 -2.06350770e+01 -1.83085978e+01 5 8.38580211e+00 1.88779819e+01 -2.18004811e+01 | 8.38580211e+00 1.88779819e+01 -2.18004811e+01 6 7.93839245e+00 -2.02984375e+01 2.38043946e+01 | 7.93839245e+00 -2.02984375e+01 2.38043946e+01 7 -7.49133669e+00 2.20555326e+01 1.63046842e+01 | -7.49133669e+00 2.20555326e+01 1.63046842e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FTT (Configuration in file "config-Zr-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 152.72617356153995 2^p V(r_1,...,r_N) = 152.72617356153987 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 -2.49568602e+01 7.25274974e+00 -1.37825673e+01 | -2.49568602e+01 7.25274974e+00 -1.37825673e+01 1 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 | 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 2 2.43770583e+01 4.95612013e+00 1.36453710e+01 | 2.43770583e+01 4.95612013e+00 1.36453710e+01 3 -2.70761779e+01 -7.87669849e+00 1.33924649e+01 | -2.70761779e+01 -7.87669849e+00 1.33924649e+01 4 -2.49568602e+01 7.25274974e+00 -1.37825673e+01 | -2.49568602e+01 7.25274974e+00 -1.37825673e+01 5 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 | 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 6 2.43770583e+01 4.95612013e+00 1.36453710e+01 | 2.43770583e+01 4.95612013e+00 1.36453710e+01 7 -2.70761779e+01 -7.87669849e+00 1.33924649e+01 | -2.70761779e+01 -7.87669849e+00 1.33924649e+01 8 -2.49568602e+01 7.25274974e+00 -1.37825673e+01 | -2.49568602e+01 7.25274974e+00 -1.37825673e+01 9 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 | 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 10 2.43770583e+01 4.95612013e+00 1.36453710e+01 | 2.43770583e+01 4.95612013e+00 1.36453710e+01 11 -2.70761779e+01 -7.87669849e+00 1.33924649e+01 | -2.70761779e+01 -7.87669849e+00 1.33924649e+01 12 -2.49568602e+01 7.25274974e+00 -1.37825673e+01 | -2.49568602e+01 7.25274974e+00 -1.37825673e+01 13 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 | 2.76559798e+01 -4.33217138e+00 -1.32552686e+01 14 2.43770583e+01 4.95612013e+00 1.36453710e+01 | 2.43770583e+01 4.95612013e+00 1.36453710e+01 15 -2.70761779e+01 -7.87669849e+00 1.33924649e+01 | -2.70761779e+01 -7.87669849e+00 1.33924649e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FTF (Configuration in file "config-Zr-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)) = 48.38025816051434 2^p V(r_1,...,r_N) = 48.38025816051433 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 -2.30197553e+01 -8.33094454e+00 -2.33624810e+01 | -2.30197553e+01 -8.33094454e+00 -2.33624810e+01 1 2.07423198e+01 8.73719419e+00 -1.82780900e+01 | 2.07423198e+01 8.73719419e+00 -1.82780900e+01 2 2.06686834e+01 -5.21857279e+00 2.26805984e+01 | 2.06686834e+01 -5.21857279e+00 2.26805984e+01 3 -1.83912479e+01 4.81232315e+00 1.89599727e+01 | -1.83912479e+01 4.81232315e+00 1.89599727e+01 4 -2.30197553e+01 -8.33094454e+00 -2.33624810e+01 | -2.30197553e+01 -8.33094454e+00 -2.33624810e+01 5 2.07423198e+01 8.73719419e+00 -1.82780900e+01 | 2.07423198e+01 8.73719419e+00 -1.82780900e+01 6 2.06686834e+01 -5.21857279e+00 2.26805984e+01 | 2.06686834e+01 -5.21857279e+00 2.26805984e+01 7 -1.83912479e+01 4.81232315e+00 1.89599727e+01 | -1.83912479e+01 4.81232315e+00 1.89599727e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FFT (Configuration in file "config-Zr-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)) = 39.74002106912712 2^p V(r_1,...,r_N) = 39.740021069127124 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 -1.82766147e+01 -2.06736133e+01 4.56673983e+00 | -1.82766147e+01 -2.06736133e+01 4.56673983e+00 1 1.85354319e+01 2.29633219e+01 1.02058012e+01 | 1.85354319e+01 2.29633219e+01 1.02058012e+01 2 2.39238253e+01 -1.72474911e+01 -4.95487889e+00 | 2.39238253e+01 -1.72474911e+01 -4.95487889e+00 3 -2.41826424e+01 1.49577825e+01 -9.81766211e+00 | -2.41826424e+01 1.49577825e+01 -9.81766211e+00 4 -1.82766147e+01 -2.06736133e+01 4.56673983e+00 | -1.82766147e+01 -2.06736133e+01 4.56673983e+00 5 1.85354319e+01 2.29633219e+01 1.02058012e+01 | 1.85354319e+01 2.29633219e+01 1.02058012e+01 6 2.39238253e+01 -1.72474911e+01 -4.95487889e+00 | 2.39238253e+01 -1.72474911e+01 -4.95487889e+00 7 -2.41826424e+01 1.49577825e+01 -9.81766211e+00 | -2.41826424e+01 1.49577825e+01 -9.81766211e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = TTT (Configuration in file "config-HfNbTaTiZr-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)) = 5233.611604290427 2^p V(r_1,...,r_N) = 5233.611604290417 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 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 | 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 1 -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 | -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 2 4.53428966e+01 9.30542051e+01 -2.45553853e+01 | 4.53428966e+01 9.30542051e+01 -2.45553853e+01 3 7.90560103e+00 2.08236749e+01 1.99787054e+01 | 7.90560103e+00 2.08236749e+01 1.99787054e+01 4 -4.57716580e+00 -5.99480942e+00 5.48972922e-01 | -4.57716580e+00 -5.99480942e+00 5.48972922e-01 5 8.75971868e+01 1.10107461e+01 -8.19756415e+01 | 8.75971868e+01 1.10107461e+01 -8.19756415e+01 6 -1.80156021e+01 1.49842019e+01 3.12180927e+01 | -1.80156021e+01 1.49842019e+01 3.12180927e+01 7 -4.93527361e+01 -3.11800037e+01 9.00170161e+01 | -4.93527361e+01 -3.11800037e+01 9.00170161e+01 8 -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 | -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 9 -2.24006188e+00 2.33549972e+01 -3.13821809e+01 | -2.24006188e+00 2.33549972e+01 -3.13821809e+01 10 1.11737106e+01 -2.85507817e+01 3.50304223e+00 | 1.11737106e+01 -2.85507817e+01 3.50304223e+00 11 -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 | -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 12 -1.76658196e+01 2.45422755e+01 -4.63293866e+01 | -1.76658196e+01 2.45422755e+01 -4.63293866e+01 13 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 | 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 14 -3.35071483e+00 -1.64093719e+01 6.08250673e+00 | -3.35071483e+00 -1.64093719e+01 6.08250673e+00 15 3.89017041e+01 1.70714450e+01 -1.37578327e+01 | 3.89017041e+01 1.70714450e+01 -1.37578327e+01 16 -3.63907849e+00 1.24201793e+01 2.02970706e+01 | -3.63907849e+00 1.24201793e+01 2.02970706e+01 17 -2.12520100e+01 7.32047642e+00 -2.29832308e+01 | -2.12520100e+01 7.32047642e+00 -2.29832308e+01 18 -2.89734005e+01 -4.48736739e+01 1.04176479e+01 | -2.89734005e+01 -4.48736739e+01 1.04176479e+01 19 -1.50055679e+01 -2.86610594e+01 3.36537598e+00 | -1.50055679e+01 -2.86610594e+01 3.36537598e+00 20 -4.83468391e+01 3.78480379e+01 -3.42392875e+01 | -4.83468391e+01 3.78480379e+01 -3.42392875e+01 21 -3.49239969e+00 3.03583115e+01 -6.86200675e+00 | -3.49239969e+00 3.03583115e+01 -6.86200675e+00 22 8.94590793e+01 -1.27103229e+01 8.74444755e+01 | 8.94590793e+01 -1.27103229e+01 8.74444755e+01 23 2.72072451e+01 5.76452374e+01 4.11125692e+01 | 2.72072451e+01 5.76452374e+01 4.11125692e+01 24 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 | 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 25 2.09696629e+01 -4.12888661e+01 1.04460375e+02 | 2.09696629e+01 -4.12888661e+01 1.04460375e+02 26 2.86457634e+01 2.27781065e+01 -1.50650199e+01 | 2.86457634e+01 2.27781065e+01 -1.50650199e+01 27 -5.23913120e+00 6.52423229e+00 1.74356235e+01 | -5.23913120e+00 6.52423229e+00 1.74356235e+01 28 3.68109599e+00 2.54913694e+00 -4.82724186e+00 | 3.68109599e+00 2.54913694e+00 -4.82724186e+00 29 -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 | -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 30 -3.01945382e+01 -1.34740226e+01 2.77466682e+01 | -3.01945382e+01 -1.34740226e+01 2.77466682e+01 31 -3.49242558e+01 -3.69933825e+01 4.59311398e+00 | -3.49242558e+01 -3.69933825e+01 4.59311398e+00 32 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 | 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 33 -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 | -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 34 4.53428966e+01 9.30542051e+01 -2.45553853e+01 | 4.53428966e+01 9.30542051e+01 -2.45553853e+01 35 7.90560103e+00 2.08236749e+01 1.99787054e+01 | 7.90560103e+00 2.08236749e+01 1.99787054e+01 36 -4.57716580e+00 -5.99480942e+00 5.48972922e-01 | -4.57716580e+00 -5.99480942e+00 5.48972922e-01 37 8.75971868e+01 1.10107461e+01 -8.19756415e+01 | 8.75971868e+01 1.10107461e+01 -8.19756415e+01 38 -1.80156021e+01 1.49842019e+01 3.12180927e+01 | -1.80156021e+01 1.49842019e+01 3.12180927e+01 39 -4.93527361e+01 -3.11800037e+01 9.00170161e+01 | -4.93527361e+01 -3.11800037e+01 9.00170161e+01 40 -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 | -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 41 -2.24006188e+00 2.33549972e+01 -3.13821809e+01 | -2.24006188e+00 2.33549972e+01 -3.13821809e+01 42 1.11737106e+01 -2.85507817e+01 3.50304223e+00 | 1.11737106e+01 -2.85507817e+01 3.50304223e+00 43 -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 | -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 44 -1.76658196e+01 2.45422755e+01 -4.63293866e+01 | -1.76658196e+01 2.45422755e+01 -4.63293866e+01 45 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 | 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 46 -3.35071483e+00 -1.64093719e+01 6.08250673e+00 | -3.35071483e+00 -1.64093719e+01 6.08250673e+00 47 3.89017041e+01 1.70714450e+01 -1.37578327e+01 | 3.89017041e+01 1.70714450e+01 -1.37578327e+01 48 -3.63907849e+00 1.24201793e+01 2.02970706e+01 | -3.63907849e+00 1.24201793e+01 2.02970706e+01 49 -2.12520100e+01 7.32047642e+00 -2.29832308e+01 | -2.12520100e+01 7.32047642e+00 -2.29832308e+01 50 -2.89734005e+01 -4.48736739e+01 1.04176479e+01 | -2.89734005e+01 -4.48736739e+01 1.04176479e+01 51 -1.50055679e+01 -2.86610594e+01 3.36537598e+00 | -1.50055679e+01 -2.86610594e+01 3.36537598e+00 52 -4.83468391e+01 3.78480379e+01 -3.42392875e+01 | -4.83468391e+01 3.78480379e+01 -3.42392875e+01 53 -3.49239969e+00 3.03583115e+01 -6.86200675e+00 | -3.49239969e+00 3.03583115e+01 -6.86200675e+00 54 8.94590793e+01 -1.27103229e+01 8.74444755e+01 | 8.94590793e+01 -1.27103229e+01 8.74444755e+01 55 2.72072451e+01 5.76452374e+01 4.11125692e+01 | 2.72072451e+01 5.76452374e+01 4.11125692e+01 56 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 | 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 57 2.09696629e+01 -4.12888661e+01 1.04460375e+02 | 2.09696629e+01 -4.12888661e+01 1.04460375e+02 58 2.86457634e+01 2.27781065e+01 -1.50650199e+01 | 2.86457634e+01 2.27781065e+01 -1.50650199e+01 59 -5.23913120e+00 6.52423229e+00 1.74356235e+01 | -5.23913120e+00 6.52423229e+00 1.74356235e+01 60 3.68109599e+00 2.54913694e+00 -4.82724186e+00 | 3.68109599e+00 2.54913694e+00 -4.82724186e+00 61 -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 | -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 62 -3.01945382e+01 -1.34740226e+01 2.77466682e+01 | -3.01945382e+01 -1.34740226e+01 2.77466682e+01 63 -3.49242558e+01 -3.69933825e+01 4.59311398e+00 | -3.49242558e+01 -3.69933825e+01 4.59311398e+00 64 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 | 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 65 -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 | -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 66 4.53428966e+01 9.30542051e+01 -2.45553853e+01 | 4.53428966e+01 9.30542051e+01 -2.45553853e+01 67 7.90560103e+00 2.08236749e+01 1.99787054e+01 | 7.90560103e+00 2.08236749e+01 1.99787054e+01 68 -4.57716580e+00 -5.99480942e+00 5.48972922e-01 | -4.57716580e+00 -5.99480942e+00 5.48972922e-01 69 8.75971868e+01 1.10107461e+01 -8.19756415e+01 | 8.75971868e+01 1.10107461e+01 -8.19756415e+01 70 -1.80156021e+01 1.49842019e+01 3.12180927e+01 | -1.80156021e+01 1.49842019e+01 3.12180927e+01 71 -4.93527361e+01 -3.11800037e+01 9.00170161e+01 | -4.93527361e+01 -3.11800037e+01 9.00170161e+01 72 -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 | -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 73 -2.24006188e+00 2.33549972e+01 -3.13821809e+01 | -2.24006188e+00 2.33549972e+01 -3.13821809e+01 74 1.11737106e+01 -2.85507817e+01 3.50304223e+00 | 1.11737106e+01 -2.85507817e+01 3.50304223e+00 75 -5.37884468e+01 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1.99787054e+01 | 7.90560103e+00 2.08236749e+01 1.99787054e+01 196 -4.57716580e+00 -5.99480942e+00 5.48972922e-01 | -4.57716580e+00 -5.99480942e+00 5.48972922e-01 197 8.75971868e+01 1.10107461e+01 -8.19756415e+01 | 8.75971868e+01 1.10107461e+01 -8.19756415e+01 198 -1.80156021e+01 1.49842019e+01 3.12180927e+01 | -1.80156021e+01 1.49842019e+01 3.12180927e+01 199 -4.93527361e+01 -3.11800037e+01 9.00170161e+01 | -4.93527361e+01 -3.11800037e+01 9.00170161e+01 200 -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 | -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 201 -2.24006188e+00 2.33549972e+01 -3.13821809e+01 | -2.24006188e+00 2.33549972e+01 -3.13821809e+01 202 1.11737106e+01 -2.85507817e+01 3.50304223e+00 | 1.11737106e+01 -2.85507817e+01 3.50304223e+00 203 -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 | -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 204 -1.76658196e+01 2.45422755e+01 -4.63293866e+01 | -1.76658196e+01 2.45422755e+01 -4.63293866e+01 205 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 | 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 206 -3.35071483e+00 -1.64093719e+01 6.08250673e+00 | -3.35071483e+00 -1.64093719e+01 6.08250673e+00 207 3.89017041e+01 1.70714450e+01 -1.37578327e+01 | 3.89017041e+01 1.70714450e+01 -1.37578327e+01 208 -3.63907849e+00 1.24201793e+01 2.02970706e+01 | -3.63907849e+00 1.24201793e+01 2.02970706e+01 209 -2.12520100e+01 7.32047642e+00 -2.29832308e+01 | -2.12520100e+01 7.32047642e+00 -2.29832308e+01 210 -2.89734005e+01 -4.48736739e+01 1.04176479e+01 | -2.89734005e+01 -4.48736739e+01 1.04176479e+01 211 -1.50055679e+01 -2.86610594e+01 3.36537598e+00 | -1.50055679e+01 -2.86610594e+01 3.36537598e+00 212 -4.83468391e+01 3.78480379e+01 -3.42392875e+01 | -4.83468391e+01 3.78480379e+01 -3.42392875e+01 213 -3.49239969e+00 3.03583115e+01 -6.86200675e+00 | -3.49239969e+00 3.03583115e+01 -6.86200675e+00 214 8.94590793e+01 -1.27103229e+01 8.74444755e+01 | 8.94590793e+01 -1.27103229e+01 8.74444755e+01 215 2.72072451e+01 5.76452374e+01 4.11125692e+01 | 2.72072451e+01 5.76452374e+01 4.11125692e+01 216 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 | 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 217 2.09696629e+01 -4.12888661e+01 1.04460375e+02 | 2.09696629e+01 -4.12888661e+01 1.04460375e+02 218 2.86457634e+01 2.27781065e+01 -1.50650199e+01 | 2.86457634e+01 2.27781065e+01 -1.50650199e+01 219 -5.23913120e+00 6.52423229e+00 1.74356235e+01 | -5.23913120e+00 6.52423229e+00 1.74356235e+01 220 3.68109599e+00 2.54913694e+00 -4.82724186e+00 | 3.68109599e+00 2.54913694e+00 -4.82724186e+00 221 -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 | -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 222 -3.01945382e+01 -1.34740226e+01 2.77466682e+01 | -3.01945382e+01 -1.34740226e+01 2.77466682e+01 223 -3.49242558e+01 -3.69933825e+01 4.59311398e+00 | -3.49242558e+01 -3.69933825e+01 4.59311398e+00 224 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 | 4.74755495e+00 -2.04953432e+00 -1.09836117e+02 225 -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 | -2.84675596e+01 -7.09384808e+00 -2.50086355e+01 226 4.53428966e+01 9.30542051e+01 -2.45553853e+01 | 4.53428966e+01 9.30542051e+01 -2.45553853e+01 227 7.90560103e+00 2.08236749e+01 1.99787054e+01 | 7.90560103e+00 2.08236749e+01 1.99787054e+01 228 -4.57716580e+00 -5.99480942e+00 5.48972922e-01 | -4.57716580e+00 -5.99480942e+00 5.48972922e-01 229 8.75971868e+01 1.10107461e+01 -8.19756415e+01 | 8.75971868e+01 1.10107461e+01 -8.19756415e+01 230 -1.80156021e+01 1.49842019e+01 3.12180927e+01 | -1.80156021e+01 1.49842019e+01 3.12180927e+01 231 -4.93527361e+01 -3.11800037e+01 9.00170161e+01 | -4.93527361e+01 -3.11800037e+01 9.00170161e+01 232 -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 | -4.06794975e+01 -2.75435069e+01 -1.83534630e+00 233 -2.24006188e+00 2.33549972e+01 -3.13821809e+01 | -2.24006188e+00 2.33549972e+01 -3.13821809e+01 234 1.11737106e+01 -2.85507817e+01 3.50304223e+00 | 1.11737106e+01 -2.85507817e+01 3.50304223e+00 235 -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 | -5.37884468e+01 -2.97440787e+01 -4.26506710e+00 236 -1.76658196e+01 2.45422755e+01 -4.63293866e+01 | -1.76658196e+01 2.45422755e+01 -4.63293866e+01 237 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 | 9.19513459e+00 -1.70285085e+01 -9.73160479e+00 238 -3.35071483e+00 -1.64093719e+01 6.08250673e+00 | -3.35071483e+00 -1.64093719e+01 6.08250673e+00 239 3.89017041e+01 1.70714450e+01 -1.37578327e+01 | 3.89017041e+01 1.70714450e+01 -1.37578327e+01 240 -3.63907849e+00 1.24201793e+01 2.02970706e+01 | -3.63907849e+00 1.24201793e+01 2.02970706e+01 241 -2.12520100e+01 7.32047642e+00 -2.29832308e+01 | -2.12520100e+01 7.32047642e+00 -2.29832308e+01 242 -2.89734005e+01 -4.48736739e+01 1.04176479e+01 | -2.89734005e+01 -4.48736739e+01 1.04176479e+01 243 -1.50055679e+01 -2.86610594e+01 3.36537598e+00 | -1.50055679e+01 -2.86610594e+01 3.36537598e+00 244 -4.83468391e+01 3.78480379e+01 -3.42392875e+01 | -4.83468391e+01 3.78480379e+01 -3.42392875e+01 245 -3.49239969e+00 3.03583115e+01 -6.86200675e+00 | -3.49239969e+00 3.03583115e+01 -6.86200675e+00 246 8.94590793e+01 -1.27103229e+01 8.74444755e+01 | 8.94590793e+01 -1.27103229e+01 8.74444755e+01 247 2.72072451e+01 5.76452374e+01 4.11125692e+01 | 2.72072451e+01 5.76452374e+01 4.11125692e+01 248 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 | 5.32539912e+01 -1.14465210e+01 -1.86094506e+01 249 2.09696629e+01 -4.12888661e+01 1.04460375e+02 | 2.09696629e+01 -4.12888661e+01 1.04460375e+02 250 2.86457634e+01 2.27781065e+01 -1.50650199e+01 | 2.86457634e+01 2.27781065e+01 -1.50650199e+01 251 -5.23913120e+00 6.52423229e+00 1.74356235e+01 | -5.23913120e+00 6.52423229e+00 1.74356235e+01 252 3.68109599e+00 2.54913694e+00 -4.82724186e+00 | 3.68109599e+00 2.54913694e+00 -4.82724186e+00 253 -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 | -1.88758016e+01 -2.72429725e+01 -1.69578207e+01 254 -3.01945382e+01 -1.34740226e+01 2.77466682e+01 | -3.01945382e+01 -1.34740226e+01 2.77466682e+01 255 -3.49242558e+01 -3.69933825e+01 4.59311398e+00 | -3.49242558e+01 -3.69933825e+01 4.59311398e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = TTF (Configuration in file "config-HfNbTaTiZr-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)) = 1971.5602456454706 2^p V(r_1,...,r_N) = 1971.5602456454728 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 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 | 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 1 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 | 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 2 -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 | -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 3 4.99516712e-01 5.43353892e+01 -6.66990741e+01 | 4.99516712e-01 5.43353892e+01 -6.66990741e+01 4 -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 | -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 5 -3.67303722e+01 7.60954696e+01 -5.05130602e+01 | -3.67303722e+01 7.60954696e+01 -5.05130602e+01 6 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 | 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 7 -1.63158304e+01 1.92105840e+01 -1.53121971e+01 | -1.63158304e+01 1.92105840e+01 -1.53121971e+01 8 -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 | -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 9 2.48478516e+01 6.10559701e+01 -7.32949736e+01 | 2.48478516e+01 6.10559701e+01 -7.32949736e+01 10 1.50768716e+01 -1.60799106e+01 6.82966000e+01 | 1.50768716e+01 -1.60799106e+01 6.82966000e+01 11 2.68886420e+01 3.74863084e+01 4.37726462e+01 | 2.68886420e+01 3.74863084e+01 4.37726462e+01 12 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 | 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 13 -1.77667516e+01 2.36068707e+01 -4.08201350e+01 | -1.77667516e+01 2.36068707e+01 -4.08201350e+01 14 -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 | -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 15 1.47346705e+00 4.59718976e+00 7.04701980e+00 | 1.47346705e+00 4.59718976e+00 7.04701980e+00 16 2.61592403e+01 -5.72331257e+01 5.97886834e+01 | 2.61592403e+01 -5.72331257e+01 5.97886834e+01 17 -1.47549423e+01 3.83954339e+01 2.87715368e+01 | -1.47549423e+01 3.83954339e+01 2.87715368e+01 18 -1.39913249e+01 7.38870798e+01 5.54249427e+01 | -1.39913249e+01 7.38870798e+01 5.54249427e+01 19 1.91320209e+01 -5.68186881e+01 5.81735391e+01 | 1.91320209e+01 -5.68186881e+01 5.81735391e+01 20 5.61551513e+01 -3.31727409e+01 8.34655006e+00 | 5.61551513e+01 -3.31727409e+01 8.34655006e+00 21 -3.37088711e+01 -3.48334501e+01 1.13268413e+01 | -3.37088711e+01 -3.48334501e+01 1.13268413e+01 22 -4.84404373e-01 -3.35666221e+00 7.50658196e+00 | -4.84404373e-01 -3.35666221e+00 7.50658196e+00 23 -2.20217540e+00 -2.03274324e+00 2.25640569e+01 | -2.20217540e+00 -2.03274324e+00 2.25640569e+01 24 4.07558348e+01 2.37756499e+01 -1.96564466e+01 | 4.07558348e+01 2.37756499e+01 -1.96564466e+01 25 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 | 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 26 1.50555190e+01 8.12634977e-01 2.24882693e+01 | 1.50555190e+01 8.12634977e-01 2.24882693e+01 27 -4.97144071e+01 -1.03142587e+01 4.48301085e+01 | -4.97144071e+01 -1.03142587e+01 4.48301085e+01 28 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 | 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 29 -4.80576848e+01 -1.54417271e+01 4.09241815e+01 | -4.80576848e+01 -1.54417271e+01 4.09241815e+01 30 -4.91826970e+01 2.98748206e+01 3.14806337e+01 | -4.91826970e+01 2.98748206e+01 3.14806337e+01 31 4.95613116e+01 -2.20944448e+01 5.19912914e+01 | 4.95613116e+01 -2.20944448e+01 5.19912914e+01 32 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 | 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 33 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 | 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 34 -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 | -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 35 4.99516712e-01 5.43353892e+01 -6.66990741e+01 | 4.99516712e-01 5.43353892e+01 -6.66990741e+01 36 -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 | -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 37 -3.67303722e+01 7.60954696e+01 -5.05130602e+01 | -3.67303722e+01 7.60954696e+01 -5.05130602e+01 38 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 | 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 39 -1.63158304e+01 1.92105840e+01 -1.53121971e+01 | -1.63158304e+01 1.92105840e+01 -1.53121971e+01 40 -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 | -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 41 2.48478516e+01 6.10559701e+01 -7.32949736e+01 | 2.48478516e+01 6.10559701e+01 -7.32949736e+01 42 1.50768716e+01 -1.60799106e+01 6.82966000e+01 | 1.50768716e+01 -1.60799106e+01 6.82966000e+01 43 2.68886420e+01 3.74863084e+01 4.37726462e+01 | 2.68886420e+01 3.74863084e+01 4.37726462e+01 44 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 | 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 45 -1.77667516e+01 2.36068707e+01 -4.08201350e+01 | -1.77667516e+01 2.36068707e+01 -4.08201350e+01 46 -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 | -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 47 1.47346705e+00 4.59718976e+00 7.04701980e+00 | 1.47346705e+00 4.59718976e+00 7.04701980e+00 48 2.61592403e+01 -5.72331257e+01 5.97886834e+01 | 2.61592403e+01 -5.72331257e+01 5.97886834e+01 49 -1.47549423e+01 3.83954339e+01 2.87715368e+01 | -1.47549423e+01 3.83954339e+01 2.87715368e+01 50 -1.39913249e+01 7.38870798e+01 5.54249427e+01 | -1.39913249e+01 7.38870798e+01 5.54249427e+01 51 1.91320209e+01 -5.68186881e+01 5.81735391e+01 | 1.91320209e+01 -5.68186881e+01 5.81735391e+01 52 5.61551513e+01 -3.31727409e+01 8.34655006e+00 | 5.61551513e+01 -3.31727409e+01 8.34655006e+00 53 -3.37088711e+01 -3.48334501e+01 1.13268413e+01 | -3.37088711e+01 -3.48334501e+01 1.13268413e+01 54 -4.84404373e-01 -3.35666221e+00 7.50658196e+00 | -4.84404373e-01 -3.35666221e+00 7.50658196e+00 55 -2.20217540e+00 -2.03274324e+00 2.25640569e+01 | -2.20217540e+00 -2.03274324e+00 2.25640569e+01 56 4.07558348e+01 2.37756499e+01 -1.96564466e+01 | 4.07558348e+01 2.37756499e+01 -1.96564466e+01 57 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 | 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 58 1.50555190e+01 8.12634977e-01 2.24882693e+01 | 1.50555190e+01 8.12634977e-01 2.24882693e+01 59 -4.97144071e+01 -1.03142587e+01 4.48301085e+01 | -4.97144071e+01 -1.03142587e+01 4.48301085e+01 60 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 | 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 61 -4.80576848e+01 -1.54417271e+01 4.09241815e+01 | -4.80576848e+01 -1.54417271e+01 4.09241815e+01 62 -4.91826970e+01 2.98748206e+01 3.14806337e+01 | -4.91826970e+01 2.98748206e+01 3.14806337e+01 63 4.95613116e+01 -2.20944448e+01 5.19912914e+01 | 4.95613116e+01 -2.20944448e+01 5.19912914e+01 64 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 | 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 65 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 | 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 66 -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 | -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 67 4.99516712e-01 5.43353892e+01 -6.66990741e+01 | 4.99516712e-01 5.43353892e+01 -6.66990741e+01 68 -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 | -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 69 -3.67303722e+01 7.60954696e+01 -5.05130602e+01 | -3.67303722e+01 7.60954696e+01 -5.05130602e+01 70 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 | 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 71 -1.63158304e+01 1.92105840e+01 -1.53121971e+01 | -1.63158304e+01 1.92105840e+01 -1.53121971e+01 72 -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 | -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 73 2.48478516e+01 6.10559701e+01 -7.32949736e+01 | 2.48478516e+01 6.10559701e+01 -7.32949736e+01 74 1.50768716e+01 -1.60799106e+01 6.82966000e+01 | 1.50768716e+01 -1.60799106e+01 6.82966000e+01 75 2.68886420e+01 3.74863084e+01 4.37726462e+01 | 2.68886420e+01 3.74863084e+01 4.37726462e+01 76 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 | 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 77 -1.77667516e+01 2.36068707e+01 -4.08201350e+01 | -1.77667516e+01 2.36068707e+01 -4.08201350e+01 78 -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 | -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 79 1.47346705e+00 4.59718976e+00 7.04701980e+00 | 1.47346705e+00 4.59718976e+00 7.04701980e+00 80 2.61592403e+01 -5.72331257e+01 5.97886834e+01 | 2.61592403e+01 -5.72331257e+01 5.97886834e+01 81 -1.47549423e+01 3.83954339e+01 2.87715368e+01 | -1.47549423e+01 3.83954339e+01 2.87715368e+01 82 -1.39913249e+01 7.38870798e+01 5.54249427e+01 | -1.39913249e+01 7.38870798e+01 5.54249427e+01 83 1.91320209e+01 -5.68186881e+01 5.81735391e+01 | 1.91320209e+01 -5.68186881e+01 5.81735391e+01 84 5.61551513e+01 -3.31727409e+01 8.34655006e+00 | 5.61551513e+01 -3.31727409e+01 8.34655006e+00 85 -3.37088711e+01 -3.48334501e+01 1.13268413e+01 | -3.37088711e+01 -3.48334501e+01 1.13268413e+01 86 -4.84404373e-01 -3.35666221e+00 7.50658196e+00 | -4.84404373e-01 -3.35666221e+00 7.50658196e+00 87 -2.20217540e+00 -2.03274324e+00 2.25640569e+01 | -2.20217540e+00 -2.03274324e+00 2.25640569e+01 88 4.07558348e+01 2.37756499e+01 -1.96564466e+01 | 4.07558348e+01 2.37756499e+01 -1.96564466e+01 89 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 | 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 90 1.50555190e+01 8.12634977e-01 2.24882693e+01 | 1.50555190e+01 8.12634977e-01 2.24882693e+01 91 -4.97144071e+01 -1.03142587e+01 4.48301085e+01 | -4.97144071e+01 -1.03142587e+01 4.48301085e+01 92 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 | 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 93 -4.80576848e+01 -1.54417271e+01 4.09241815e+01 | -4.80576848e+01 -1.54417271e+01 4.09241815e+01 94 -4.91826970e+01 2.98748206e+01 3.14806337e+01 | -4.91826970e+01 2.98748206e+01 3.14806337e+01 95 4.95613116e+01 -2.20944448e+01 5.19912914e+01 | 4.95613116e+01 -2.20944448e+01 5.19912914e+01 96 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 | 2.84984888e+01 -2.10910932e+01 -2.66174448e+01 97 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 | 4.18489192e+00 -1.88822477e+01 -1.66213037e+01 98 -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 | -1.20071700e+01 -1.12910873e+01 -2.75896635e+01 99 4.99516712e-01 5.43353892e+01 -6.66990741e+01 | 4.99516712e-01 5.43353892e+01 -6.66990741e+01 100 -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 | -2.63211349e+01 -4.82831608e+00 -2.21119139e+01 101 -3.67303722e+01 7.60954696e+01 -5.05130602e+01 | -3.67303722e+01 7.60954696e+01 -5.05130602e+01 102 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 | 5.08904143e+00 -2.66391676e+01 -1.50983933e+01 103 -1.63158304e+01 1.92105840e+01 -1.53121971e+01 | -1.63158304e+01 1.92105840e+01 -1.53121971e+01 104 -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 | -4.01582979e+01 -3.79152796e+01 -7.46821818e+01 105 2.48478516e+01 6.10559701e+01 -7.32949736e+01 | 2.48478516e+01 6.10559701e+01 -7.32949736e+01 106 1.50768716e+01 -1.60799106e+01 6.82966000e+01 | 1.50768716e+01 -1.60799106e+01 6.82966000e+01 107 2.68886420e+01 3.74863084e+01 4.37726462e+01 | 2.68886420e+01 3.74863084e+01 4.37726462e+01 108 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 | 4.96346753e+01 -1.80679340e+01 -4.91629598e+01 109 -1.77667516e+01 2.36068707e+01 -4.08201350e+01 | -1.77667516e+01 2.36068707e+01 -4.08201350e+01 110 -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 | -1.53836108e+01 -2.21934235e+01 -1.23151409e+01 111 1.47346705e+00 4.59718976e+00 7.04701980e+00 | 1.47346705e+00 4.59718976e+00 7.04701980e+00 112 2.61592403e+01 -5.72331257e+01 5.97886834e+01 | 2.61592403e+01 -5.72331257e+01 5.97886834e+01 113 -1.47549423e+01 3.83954339e+01 2.87715368e+01 | -1.47549423e+01 3.83954339e+01 2.87715368e+01 114 -1.39913249e+01 7.38870798e+01 5.54249427e+01 | -1.39913249e+01 7.38870798e+01 5.54249427e+01 115 1.91320209e+01 -5.68186881e+01 5.81735391e+01 | 1.91320209e+01 -5.68186881e+01 5.81735391e+01 116 5.61551513e+01 -3.31727409e+01 8.34655006e+00 | 5.61551513e+01 -3.31727409e+01 8.34655006e+00 117 -3.37088711e+01 -3.48334501e+01 1.13268413e+01 | -3.37088711e+01 -3.48334501e+01 1.13268413e+01 118 -4.84404373e-01 -3.35666221e+00 7.50658196e+00 | -4.84404373e-01 -3.35666221e+00 7.50658196e+00 119 -2.20217540e+00 -2.03274324e+00 2.25640569e+01 | -2.20217540e+00 -2.03274324e+00 2.25640569e+01 120 4.07558348e+01 2.37756499e+01 -1.96564466e+01 | 4.07558348e+01 2.37756499e+01 -1.96564466e+01 121 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 | 1.15258095e+01 -2.94179173e+01 -5.21755965e+01 122 1.50555190e+01 8.12634977e-01 2.24882693e+01 | 1.50555190e+01 8.12634977e-01 2.24882693e+01 123 -4.97144071e+01 -1.03142587e+01 4.48301085e+01 | -4.97144071e+01 -1.03142587e+01 4.48301085e+01 124 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 | 2.24134078e+00 -1.42918299e+00 -6.29977007e-02 125 -4.80576848e+01 -1.54417271e+01 4.09241815e+01 | -4.80576848e+01 -1.54417271e+01 4.09241815e+01 126 -4.91826970e+01 2.98748206e+01 3.14806337e+01 | -4.91826970e+01 2.98748206e+01 3.14806337e+01 127 4.95613116e+01 -2.20944448e+01 5.19912914e+01 | 4.95613116e+01 -2.20944448e+01 5.19912914e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = TFT (Configuration in file "config-HfNbTaTiZr-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)) = 2596.390257869386 2^p V(r_1,...,r_N) = 2596.3902578693887 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 -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 | -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 1 -3.80838833e+00 -1.62293946e+01 2.71538256e+00 | -3.80838833e+00 -1.62293946e+01 2.71538256e+00 2 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 | 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 3 -6.30359282e+00 4.04049051e+01 -2.96275319e+01 | -6.30359282e+00 4.04049051e+01 -2.96275319e+01 4 -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 | -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 5 7.99765680e+01 4.35192291e+01 -1.52754276e+01 | 7.99765680e+01 4.35192291e+01 -1.52754276e+01 6 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 | 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 7 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 | 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 8 -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 | -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 9 6.53158537e-01 2.66316412e+01 -8.76703547e+00 | 6.53158537e-01 2.66316412e+01 -8.76703547e+00 10 -6.62746898e+01 5.15165103e+01 3.33577080e+01 | -6.62746898e+01 5.15165103e+01 3.33577080e+01 11 1.36388494e+01 5.39996870e+01 6.03315240e+01 | 1.36388494e+01 5.39996870e+01 6.03315240e+01 12 2.52737740e+01 3.51859487e+01 1.40653576e+01 | 2.52737740e+01 3.51859487e+01 1.40653576e+01 13 -2.30480715e+01 2.29863388e+01 -2.75119954e+01 | -2.30480715e+01 2.29863388e+01 -2.75119954e+01 14 -8.58895541e+00 -6.89881970e+00 1.01892020e+01 | -8.58895541e+00 -6.89881970e+00 1.01892020e+01 15 2.68269769e+01 3.71277230e+01 -1.51048263e+00 | 2.68269769e+01 3.71277230e+01 -1.51048263e+00 16 2.41908241e+01 -9.91670694e+01 1.96967984e+01 | 2.41908241e+01 -9.91670694e+01 1.96967984e+01 17 -6.84064918e+01 -7.23888396e+01 -1.04384076e+02 | -6.84064918e+01 -7.23888396e+01 -1.04384076e+02 18 -1.79106484e+01 -7.39945141e+01 -1.42657912e+01 | -1.79106484e+01 -7.39945141e+01 -1.42657912e+01 19 2.64375152e+01 -1.29456096e+01 3.35307436e+01 | 2.64375152e+01 -1.29456096e+01 3.35307436e+01 20 -3.18579328e+01 -3.37394445e+01 3.08827249e+01 | -3.18579328e+01 -3.37394445e+01 3.08827249e+01 21 -6.25860578e+01 1.64182085e+01 -4.03916810e+01 | -6.25860578e+01 1.64182085e+01 -4.03916810e+01 22 -3.82451274e+00 -2.64013242e+01 3.18209277e+01 | -3.82451274e+00 -2.64013242e+01 3.18209277e+01 23 5.93636101e+01 -7.26864972e+01 4.60124969e+01 | 5.93636101e+01 -7.26864972e+01 4.60124969e+01 24 5.63928431e+01 1.95297623e+00 -2.05333411e+01 | 5.63928431e+01 1.95297623e+00 -2.05333411e+01 25 -1.78328140e+01 4.12157812e+01 -1.59104999e+01 | -1.78328140e+01 4.12157812e+01 -1.59104999e+01 26 -1.66042783e+02 9.43350724e+01 1.90593596e+02 | -1.66042783e+02 9.43350724e+01 1.90593596e+02 27 -1.54982293e+01 1.43846004e+01 2.30083767e-02 | -1.54982293e+01 1.43846004e+01 2.30083767e-02 28 1.40111050e+02 7.76571939e+01 -8.77014124e+01 | 1.40111050e+02 7.76571939e+01 -8.77014124e+01 29 8.54115449e+00 2.10973360e+01 -1.34327467e+01 | 8.54115449e+00 2.10973360e+01 -1.34327467e+01 30 -4.53491921e+01 5.18908806e+01 2.55700606e+01 | -4.53491921e+01 5.18908806e+01 2.55700606e+01 31 2.82448885e+01 5.06673704e+01 1.50844677e+00 | 2.82448885e+01 5.06673704e+01 1.50844677e+00 32 -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 | -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 33 -3.80838833e+00 -1.62293946e+01 2.71538256e+00 | -3.80838833e+00 -1.62293946e+01 2.71538256e+00 34 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 | 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 35 -6.30359282e+00 4.04049051e+01 -2.96275319e+01 | -6.30359282e+00 4.04049051e+01 -2.96275319e+01 36 -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 | -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 37 7.99765680e+01 4.35192291e+01 -1.52754276e+01 | 7.99765680e+01 4.35192291e+01 -1.52754276e+01 38 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 | 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 39 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 | 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 40 -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 | -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 41 6.53158537e-01 2.66316412e+01 -8.76703547e+00 | 6.53158537e-01 2.66316412e+01 -8.76703547e+00 42 -6.62746898e+01 5.15165103e+01 3.33577080e+01 | -6.62746898e+01 5.15165103e+01 3.33577080e+01 43 1.36388494e+01 5.39996870e+01 6.03315240e+01 | 1.36388494e+01 5.39996870e+01 6.03315240e+01 44 2.52737740e+01 3.51859487e+01 1.40653576e+01 | 2.52737740e+01 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-2.64013242e+01 3.18209277e+01 55 5.93636101e+01 -7.26864972e+01 4.60124969e+01 | 5.93636101e+01 -7.26864972e+01 4.60124969e+01 56 5.63928431e+01 1.95297623e+00 -2.05333411e+01 | 5.63928431e+01 1.95297623e+00 -2.05333411e+01 57 -1.78328140e+01 4.12157812e+01 -1.59104999e+01 | -1.78328140e+01 4.12157812e+01 -1.59104999e+01 58 -1.66042783e+02 9.43350724e+01 1.90593596e+02 | -1.66042783e+02 9.43350724e+01 1.90593596e+02 59 -1.54982293e+01 1.43846004e+01 2.30083767e-02 | -1.54982293e+01 1.43846004e+01 2.30083767e-02 60 1.40111050e+02 7.76571939e+01 -8.77014124e+01 | 1.40111050e+02 7.76571939e+01 -8.77014124e+01 61 8.54115449e+00 2.10973360e+01 -1.34327467e+01 | 8.54115449e+00 2.10973360e+01 -1.34327467e+01 62 -4.53491921e+01 5.18908806e+01 2.55700606e+01 | -4.53491921e+01 5.18908806e+01 2.55700606e+01 63 2.82448885e+01 5.06673704e+01 1.50844677e+00 | 2.82448885e+01 5.06673704e+01 1.50844677e+00 64 -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 | -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 65 -3.80838833e+00 -1.62293946e+01 2.71538256e+00 | -3.80838833e+00 -1.62293946e+01 2.71538256e+00 66 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 | 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 67 -6.30359282e+00 4.04049051e+01 -2.96275319e+01 | -6.30359282e+00 4.04049051e+01 -2.96275319e+01 68 -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 | -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 69 7.99765680e+01 4.35192291e+01 -1.52754276e+01 | 7.99765680e+01 4.35192291e+01 -1.52754276e+01 70 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 | 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 71 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 | 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 72 -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 | -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 73 6.53158537e-01 2.66316412e+01 -8.76703547e+00 | 6.53158537e-01 2.66316412e+01 -8.76703547e+00 74 -6.62746898e+01 5.15165103e+01 3.33577080e+01 | -6.62746898e+01 5.15165103e+01 3.33577080e+01 75 1.36388494e+01 5.39996870e+01 6.03315240e+01 | 1.36388494e+01 5.39996870e+01 6.03315240e+01 76 2.52737740e+01 3.51859487e+01 1.40653576e+01 | 2.52737740e+01 3.51859487e+01 1.40653576e+01 77 -2.30480715e+01 2.29863388e+01 -2.75119954e+01 | -2.30480715e+01 2.29863388e+01 -2.75119954e+01 78 -8.58895541e+00 -6.89881970e+00 1.01892020e+01 | -8.58895541e+00 -6.89881970e+00 1.01892020e+01 79 2.68269769e+01 3.71277230e+01 -1.51048263e+00 | 2.68269769e+01 3.71277230e+01 -1.51048263e+00 80 2.41908241e+01 -9.91670694e+01 1.96967984e+01 | 2.41908241e+01 -9.91670694e+01 1.96967984e+01 81 -6.84064918e+01 -7.23888396e+01 -1.04384076e+02 | -6.84064918e+01 -7.23888396e+01 -1.04384076e+02 82 -1.79106484e+01 -7.39945141e+01 -1.42657912e+01 | -1.79106484e+01 -7.39945141e+01 -1.42657912e+01 83 2.64375152e+01 -1.29456096e+01 3.35307436e+01 | 2.64375152e+01 -1.29456096e+01 3.35307436e+01 84 -3.18579328e+01 -3.37394445e+01 3.08827249e+01 | -3.18579328e+01 -3.37394445e+01 3.08827249e+01 85 -6.25860578e+01 1.64182085e+01 -4.03916810e+01 | -6.25860578e+01 1.64182085e+01 -4.03916810e+01 86 -3.82451274e+00 -2.64013242e+01 3.18209277e+01 | -3.82451274e+00 -2.64013242e+01 3.18209277e+01 87 5.93636101e+01 -7.26864972e+01 4.60124969e+01 | 5.93636101e+01 -7.26864972e+01 4.60124969e+01 88 5.63928431e+01 1.95297623e+00 -2.05333411e+01 | 5.63928431e+01 1.95297623e+00 -2.05333411e+01 89 -1.78328140e+01 4.12157812e+01 -1.59104999e+01 | -1.78328140e+01 4.12157812e+01 -1.59104999e+01 90 -1.66042783e+02 9.43350724e+01 1.90593596e+02 | -1.66042783e+02 9.43350724e+01 1.90593596e+02 91 -1.54982293e+01 1.43846004e+01 2.30083767e-02 | -1.54982293e+01 1.43846004e+01 2.30083767e-02 92 1.40111050e+02 7.76571939e+01 -8.77014124e+01 | 1.40111050e+02 7.76571939e+01 -8.77014124e+01 93 8.54115449e+00 2.10973360e+01 -1.34327467e+01 | 8.54115449e+00 2.10973360e+01 -1.34327467e+01 94 -4.53491921e+01 5.18908806e+01 2.55700606e+01 | -4.53491921e+01 5.18908806e+01 2.55700606e+01 95 2.82448885e+01 5.06673704e+01 1.50844677e+00 | 2.82448885e+01 5.06673704e+01 1.50844677e+00 96 -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 | -1.07001044e+01 -3.62836667e+01 -5.75277488e+00 97 -3.80838833e+00 -1.62293946e+01 2.71538256e+00 | -3.80838833e+00 -1.62293946e+01 2.71538256e+00 98 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 | 1.82966727e+00 -1.12561778e+01 -6.78022062e+00 99 -6.30359282e+00 4.04049051e+01 -2.96275319e+01 | -6.30359282e+00 4.04049051e+01 -2.96275319e+01 100 -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 | -2.31833193e+01 -1.18872706e+02 -2.58615091e+01 101 7.99765680e+01 4.35192291e+01 -1.52754276e+01 | 7.99765680e+01 4.35192291e+01 -1.52754276e+01 102 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 | 4.53292874e+01 -4.98347311e+01 -2.91669796e+01 103 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 | 6.92250675e+01 -4.62220447e+01 -5.66978311e-01 104 -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 | -3.48194504e+01 -4.07056309e+00 -5.28574941e+01 105 6.53158537e-01 2.66316412e+01 -8.76703547e+00 | 6.53158537e-01 2.66316412e+01 -8.76703547e+00 106 -6.62746898e+01 5.15165103e+01 3.33577080e+01 | -6.62746898e+01 5.15165103e+01 3.33577080e+01 107 1.36388494e+01 5.39996870e+01 6.03315240e+01 | 1.36388494e+01 5.39996870e+01 6.03315240e+01 108 2.52737740e+01 3.51859487e+01 1.40653576e+01 | 2.52737740e+01 3.51859487e+01 1.40653576e+01 109 -2.30480715e+01 2.29863388e+01 -2.75119954e+01 | -2.30480715e+01 2.29863388e+01 -2.75119954e+01 110 -8.58895541e+00 -6.89881970e+00 1.01892020e+01 | -8.58895541e+00 -6.89881970e+00 1.01892020e+01 111 2.68269769e+01 3.71277230e+01 -1.51048263e+00 | 2.68269769e+01 3.71277230e+01 -1.51048263e+00 112 2.41908241e+01 -9.91670694e+01 1.96967984e+01 | 2.41908241e+01 -9.91670694e+01 1.96967984e+01 113 -6.84064918e+01 -7.23888396e+01 -1.04384076e+02 | -6.84064918e+01 -7.23888396e+01 -1.04384076e+02 114 -1.79106484e+01 -7.39945141e+01 -1.42657912e+01 | -1.79106484e+01 -7.39945141e+01 -1.42657912e+01 115 2.64375152e+01 -1.29456096e+01 3.35307436e+01 | 2.64375152e+01 -1.29456096e+01 3.35307436e+01 116 -3.18579328e+01 -3.37394445e+01 3.08827249e+01 | -3.18579328e+01 -3.37394445e+01 3.08827249e+01 117 -6.25860578e+01 1.64182085e+01 -4.03916810e+01 | -6.25860578e+01 1.64182085e+01 -4.03916810e+01 118 -3.82451274e+00 -2.64013242e+01 3.18209277e+01 | -3.82451274e+00 -2.64013242e+01 3.18209277e+01 119 5.93636101e+01 -7.26864972e+01 4.60124969e+01 | 5.93636101e+01 -7.26864972e+01 4.60124969e+01 120 5.63928431e+01 1.95297623e+00 -2.05333411e+01 | 5.63928431e+01 1.95297623e+00 -2.05333411e+01 121 -1.78328140e+01 4.12157812e+01 -1.59104999e+01 | -1.78328140e+01 4.12157812e+01 -1.59104999e+01 122 -1.66042783e+02 9.43350724e+01 1.90593596e+02 | -1.66042783e+02 9.43350724e+01 1.90593596e+02 123 -1.54982293e+01 1.43846004e+01 2.30083767e-02 | -1.54982293e+01 1.43846004e+01 2.30083767e-02 124 1.40111050e+02 7.76571939e+01 -8.77014124e+01 | 1.40111050e+02 7.76571939e+01 -8.77014124e+01 125 8.54115449e+00 2.10973360e+01 -1.34327467e+01 | 8.54115449e+00 2.10973360e+01 -1.34327467e+01 126 -4.53491921e+01 5.18908806e+01 2.55700606e+01 | -4.53491921e+01 5.18908806e+01 2.55700606e+01 127 2.82448885e+01 5.06673704e+01 1.50844677e+00 | 2.82448885e+01 5.06673704e+01 1.50844677e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = TFF (Configuration in file "config-HfNbTaTiZr-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)) = 1089.9079271070755 2^p V(r_1,...,r_N) = 1089.9079271070764 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 1.26981082e+01 -5.04275106e+01 -4.34688139e+01 | 1.26981082e+01 -5.04275106e+01 -4.34688139e+01 1 3.34512502e+01 -3.18581702e+01 -4.34346348e+01 | 3.34512502e+01 -3.18581702e+01 -4.34346348e+01 2 -7.31342250e+01 -5.14851488e+01 -4.89911372e+00 | -7.31342250e+01 -5.14851488e+01 -4.89911372e+00 3 7.97186720e+01 5.32929751e+01 5.74552340e+01 | 7.97186720e+01 5.32929751e+01 5.74552340e+01 4 -6.16839943e+00 -1.11404431e+02 -1.09432468e+02 | -6.16839943e+00 -1.11404431e+02 -1.09432468e+02 5 -1.95647689e+01 7.78706993e+01 -9.15431697e+01 | -1.95647689e+01 7.78706993e+01 -9.15431697e+01 6 7.01937208e+00 -2.06842581e+02 -5.96117352e+01 | 7.01937208e+00 -2.06842581e+02 -5.96117352e+01 7 1.71812546e+01 9.22670621e+01 4.85276044e+01 | 1.71812546e+01 9.22670621e+01 4.85276044e+01 8 -3.29545859e+01 5.02758359e+01 -1.99039442e+01 | -3.29545859e+01 5.02758359e+01 -1.99039442e+01 9 -4.06067793e+01 6.20714027e+01 -2.38703822e+01 | -4.06067793e+01 6.20714027e+01 -2.38703822e+01 10 -2.99626060e+01 -7.61266308e+01 -1.35519398e+00 | -2.99626060e+01 -7.61266308e+01 -1.35519398e+00 11 4.35629972e+00 1.89497464e+01 -2.64328534e+01 | 4.35629972e+00 1.89497464e+01 -2.64328534e+01 12 1.68835609e+01 -3.81273161e+01 -5.59134031e+01 | 1.68835609e+01 -3.81273161e+01 -5.59134031e+01 13 1.79401338e+01 1.42095915e+01 2.04265309e+00 | 1.79401338e+01 1.42095915e+01 2.04265309e+00 14 -3.81871747e+00 1.26206845e+01 -1.43503559e+01 | -3.81871747e+00 1.26206845e+01 -1.43503559e+01 15 3.94623819e+01 4.55345191e+01 3.54500483e+00 | 3.94623819e+01 4.55345191e+01 3.54500483e+00 16 8.14559633e+00 -2.83057986e+01 -6.29245545e+00 | 8.14559633e+00 -2.83057986e+01 -6.29245545e+00 17 1.96484814e+01 1.83875063e+01 -5.62598539e+01 | 1.96484814e+01 1.83875063e+01 -5.62598539e+01 18 -2.27467569e+01 -9.28792588e+01 8.35948191e+01 | -2.27467569e+01 -9.28792588e+01 8.35948191e+01 19 -6.77722846e+01 -5.35366124e+00 5.39949469e+01 | -6.77722846e+01 -5.35366124e+00 5.39949469e+01 20 -3.99636996e+01 -7.95722423e+01 -1.39738930e+01 | -3.99636996e+01 -7.95722423e+01 -1.39738930e+01 21 6.81833950e+01 8.33755671e+01 7.53175369e+01 | 6.81833950e+01 8.33755671e+01 7.53175369e+01 22 1.99467520e+01 -3.34133345e+01 1.20504465e+01 | 1.99467520e+01 -3.34133345e+01 1.20504465e+01 23 2.07547149e+01 3.71791247e+01 8.63173926e+01 | 2.07547149e+01 3.71791247e+01 8.63173926e+01 24 3.00973369e+00 2.81586684e+00 7.80364821e-02 | 3.00973369e+00 2.81586684e+00 7.80364821e-02 25 -3.15467060e+01 7.66989450e+01 4.85383003e+01 | -3.15467060e+01 7.66989450e+01 4.85383003e+01 26 2.10514257e+01 2.83955891e+01 4.76831735e+01 | 2.10514257e+01 2.83955891e+01 4.76831735e+01 27 -6.85673486e+00 2.43498805e+01 -2.77254950e+00 | -6.85673486e+00 2.43498805e+01 -2.77254950e+00 28 -4.65293089e+01 7.11677677e+01 -2.04469956e+01 | -4.65293089e+01 7.11677677e+01 -2.04469956e+01 29 2.02482301e+01 1.50563990e+01 -5.34002126e+00 | 2.02482301e+01 1.50563990e+01 -5.34002126e+00 30 1.85797519e+01 5.21979657e+00 6.10698476e+01 | 1.85797519e+01 5.21979657e+00 6.10698476e+01 31 -6.65354144e+00 1.60571238e+01 1.90868406e+01 | -6.65354144e+00 1.60571238e+01 1.90868406e+01 32 1.26981082e+01 -5.04275106e+01 -4.34688139e+01 | 1.26981082e+01 -5.04275106e+01 -4.34688139e+01 33 3.34512502e+01 -3.18581702e+01 -4.34346348e+01 | 3.34512502e+01 -3.18581702e+01 -4.34346348e+01 34 -7.31342250e+01 -5.14851488e+01 -4.89911372e+00 | -7.31342250e+01 -5.14851488e+01 -4.89911372e+00 35 7.97186720e+01 5.32929751e+01 5.74552340e+01 | 7.97186720e+01 5.32929751e+01 5.74552340e+01 36 -6.16839943e+00 -1.11404431e+02 -1.09432468e+02 | -6.16839943e+00 -1.11404431e+02 -1.09432468e+02 37 -1.95647689e+01 7.78706993e+01 -9.15431697e+01 | -1.95647689e+01 7.78706993e+01 -9.15431697e+01 38 7.01937208e+00 -2.06842581e+02 -5.96117352e+01 | 7.01937208e+00 -2.06842581e+02 -5.96117352e+01 39 1.71812546e+01 9.22670621e+01 4.85276044e+01 | 1.71812546e+01 9.22670621e+01 4.85276044e+01 40 -3.29545859e+01 5.02758359e+01 -1.99039442e+01 | -3.29545859e+01 5.02758359e+01 -1.99039442e+01 41 -4.06067793e+01 6.20714027e+01 -2.38703822e+01 | -4.06067793e+01 6.20714027e+01 -2.38703822e+01 42 -2.99626060e+01 -7.61266308e+01 -1.35519398e+00 | -2.99626060e+01 -7.61266308e+01 -1.35519398e+00 43 4.35629972e+00 1.89497464e+01 -2.64328534e+01 | 4.35629972e+00 1.89497464e+01 -2.64328534e+01 44 1.68835609e+01 -3.81273161e+01 -5.59134031e+01 | 1.68835609e+01 -3.81273161e+01 -5.59134031e+01 45 1.79401338e+01 1.42095915e+01 2.04265309e+00 | 1.79401338e+01 1.42095915e+01 2.04265309e+00 46 -3.81871747e+00 1.26206845e+01 -1.43503559e+01 | -3.81871747e+00 1.26206845e+01 -1.43503559e+01 47 3.94623819e+01 4.55345191e+01 3.54500483e+00 | 3.94623819e+01 4.55345191e+01 3.54500483e+00 48 8.14559633e+00 -2.83057986e+01 -6.29245545e+00 | 8.14559633e+00 -2.83057986e+01 -6.29245545e+00 49 1.96484814e+01 1.83875063e+01 -5.62598539e+01 | 1.96484814e+01 1.83875063e+01 -5.62598539e+01 50 -2.27467569e+01 -9.28792588e+01 8.35948191e+01 | -2.27467569e+01 -9.28792588e+01 8.35948191e+01 51 -6.77722846e+01 -5.35366124e+00 5.39949469e+01 | -6.77722846e+01 -5.35366124e+00 5.39949469e+01 52 -3.99636996e+01 -7.95722423e+01 -1.39738930e+01 | -3.99636996e+01 -7.95722423e+01 -1.39738930e+01 53 6.81833950e+01 8.33755671e+01 7.53175369e+01 | 6.81833950e+01 8.33755671e+01 7.53175369e+01 54 1.99467520e+01 -3.34133345e+01 1.20504465e+01 | 1.99467520e+01 -3.34133345e+01 1.20504465e+01 55 2.07547149e+01 3.71791247e+01 8.63173926e+01 | 2.07547149e+01 3.71791247e+01 8.63173926e+01 56 3.00973369e+00 2.81586684e+00 7.80364821e-02 | 3.00973369e+00 2.81586684e+00 7.80364821e-02 57 -3.15467060e+01 7.66989450e+01 4.85383003e+01 | -3.15467060e+01 7.66989450e+01 4.85383003e+01 58 2.10514257e+01 2.83955891e+01 4.76831735e+01 | 2.10514257e+01 2.83955891e+01 4.76831735e+01 59 -6.85673486e+00 2.43498805e+01 -2.77254950e+00 | -6.85673486e+00 2.43498805e+01 -2.77254950e+00 60 -4.65293089e+01 7.11677677e+01 -2.04469956e+01 | -4.65293089e+01 7.11677677e+01 -2.04469956e+01 61 2.02482301e+01 1.50563990e+01 -5.34002126e+00 | 2.02482301e+01 1.50563990e+01 -5.34002126e+00 62 1.85797519e+01 5.21979657e+00 6.10698476e+01 | 1.85797519e+01 5.21979657e+00 6.10698476e+01 63 -6.65354144e+00 1.60571238e+01 1.90868406e+01 | -6.65354144e+00 1.60571238e+01 1.90868406e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = FTT (Configuration in file "config-HfNbTaTiZr-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)) = 2432.4669787858575 2^p V(r_1,...,r_N) = 2432.4669787858493 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 -2.05061611e+01 7.87792135e+00 -1.93731116e+01 | -2.05061611e+01 7.87792135e+00 -1.93731116e+01 1 -5.12869508e+01 4.97605953e+01 9.89714446e+00 | -5.12869508e+01 4.97605953e+01 9.89714446e+00 2 6.35575595e+01 3.12984374e+01 -6.12979848e+01 | 6.35575595e+01 3.12984374e+01 -6.12979848e+01 3 -5.91858452e+01 3.58159444e+01 -3.29587150e+01 | -5.91858452e+01 3.58159444e+01 -3.29587150e+01 4 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 | 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 5 9.57194644e+01 -1.32321271e+01 4.19727144e+01 | 9.57194644e+01 -1.32321271e+01 4.19727144e+01 6 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 | 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 7 -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 | -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 8 -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 | -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 9 1.10180820e+01 2.04013856e+00 -2.16499589e+01 | 1.10180820e+01 2.04013856e+00 -2.16499589e+01 10 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 | 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 11 -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 | -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 12 -2.73156345e+01 6.56890408e+01 5.16880417e+01 | -2.73156345e+01 6.56890408e+01 5.16880417e+01 13 1.11676847e+01 5.59510788e+00 -3.72766964e+00 | 1.11676847e+01 5.59510788e+00 -3.72766964e+00 14 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 | 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 15 -9.72853360e+00 2.16810053e+01 4.30264230e+00 | -9.72853360e+00 2.16810053e+01 4.30264230e+00 16 -1.27947995e+02 4.40629491e+01 3.53869510e+01 | -1.27947995e+02 4.40629491e+01 3.53869510e+01 17 3.78209930e+01 4.62206620e+01 1.07336951e+01 | 3.78209930e+01 4.62206620e+01 1.07336951e+01 18 -1.71199927e+01 -1.32142380e+01 3.00293705e+01 | -1.71199927e+01 -1.32142380e+01 3.00293705e+01 19 -3.60023463e+01 -1.29976064e+00 3.48314943e+01 | -3.60023463e+01 -1.29976064e+00 3.48314943e+01 20 -2.08120307e+00 8.72388078e+00 -4.86204652e+01 | -2.08120307e+00 8.72388078e+00 -4.86204652e+01 21 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 | 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 22 5.37711303e+01 -2.73349976e+01 3.27762187e+01 | 5.37711303e+01 -2.73349976e+01 3.27762187e+01 23 -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 | -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 24 -8.43141883e+01 3.58086819e+01 1.68558147e+01 | -8.43141883e+01 3.58086819e+01 1.68558147e+01 25 5.75908353e+01 -1.25721059e+02 1.01431337e+02 | 5.75908353e+01 -1.25721059e+02 1.01431337e+02 26 2.42133745e+01 -1.11191738e+01 5.65191714e+01 | 2.42133745e+01 -1.11191738e+01 5.65191714e+01 27 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 | 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 28 -5.21448190e+01 6.95833224e+01 5.38462574e+01 | -5.21448190e+01 6.95833224e+01 5.38462574e+01 29 4.87702976e+01 4.95304619e+01 2.81294279e+01 | 4.87702976e+01 4.95304619e+01 2.81294279e+01 30 4.41600913e+01 3.14541365e+01 6.09278896e+00 | 4.41600913e+01 3.14541365e+01 6.09278896e+00 31 2.62439922e+00 -5.80150293e+00 3.62331499e+00 | 2.62439922e+00 -5.80150293e+00 3.62331499e+00 32 -2.05061611e+01 7.87792135e+00 -1.93731116e+01 | -2.05061611e+01 7.87792135e+00 -1.93731116e+01 33 -5.12869508e+01 4.97605953e+01 9.89714446e+00 | -5.12869508e+01 4.97605953e+01 9.89714446e+00 34 6.35575595e+01 3.12984374e+01 -6.12979848e+01 | 6.35575595e+01 3.12984374e+01 -6.12979848e+01 35 -5.91858452e+01 3.58159444e+01 -3.29587150e+01 | -5.91858452e+01 3.58159444e+01 -3.29587150e+01 36 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 | 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 37 9.57194644e+01 -1.32321271e+01 4.19727144e+01 | 9.57194644e+01 -1.32321271e+01 4.19727144e+01 38 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 | 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 39 -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 | -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 40 -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 | -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 41 1.10180820e+01 2.04013856e+00 -2.16499589e+01 | 1.10180820e+01 2.04013856e+00 -2.16499589e+01 42 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 | 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 43 -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 | -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 44 -2.73156345e+01 6.56890408e+01 5.16880417e+01 | -2.73156345e+01 6.56890408e+01 5.16880417e+01 45 1.11676847e+01 5.59510788e+00 -3.72766964e+00 | 1.11676847e+01 5.59510788e+00 -3.72766964e+00 46 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 | 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 47 -9.72853360e+00 2.16810053e+01 4.30264230e+00 | -9.72853360e+00 2.16810053e+01 4.30264230e+00 48 -1.27947995e+02 4.40629491e+01 3.53869510e+01 | -1.27947995e+02 4.40629491e+01 3.53869510e+01 49 3.78209930e+01 4.62206620e+01 1.07336951e+01 | 3.78209930e+01 4.62206620e+01 1.07336951e+01 50 -1.71199927e+01 -1.32142380e+01 3.00293705e+01 | -1.71199927e+01 -1.32142380e+01 3.00293705e+01 51 -3.60023463e+01 -1.29976064e+00 3.48314943e+01 | -3.60023463e+01 -1.29976064e+00 3.48314943e+01 52 -2.08120307e+00 8.72388078e+00 -4.86204652e+01 | -2.08120307e+00 8.72388078e+00 -4.86204652e+01 53 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 | 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 54 5.37711303e+01 -2.73349976e+01 3.27762187e+01 | 5.37711303e+01 -2.73349976e+01 3.27762187e+01 55 -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 | -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 56 -8.43141883e+01 3.58086819e+01 1.68558147e+01 | -8.43141883e+01 3.58086819e+01 1.68558147e+01 57 5.75908353e+01 -1.25721059e+02 1.01431337e+02 | 5.75908353e+01 -1.25721059e+02 1.01431337e+02 58 2.42133745e+01 -1.11191738e+01 5.65191714e+01 | 2.42133745e+01 -1.11191738e+01 5.65191714e+01 59 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 | 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 60 -5.21448190e+01 6.95833224e+01 5.38462574e+01 | -5.21448190e+01 6.95833224e+01 5.38462574e+01 61 4.87702976e+01 4.95304619e+01 2.81294279e+01 | 4.87702976e+01 4.95304619e+01 2.81294279e+01 62 4.41600913e+01 3.14541365e+01 6.09278896e+00 | 4.41600913e+01 3.14541365e+01 6.09278896e+00 63 2.62439922e+00 -5.80150293e+00 3.62331499e+00 | 2.62439922e+00 -5.80150293e+00 3.62331499e+00 64 -2.05061611e+01 7.87792135e+00 -1.93731116e+01 | -2.05061611e+01 7.87792135e+00 -1.93731116e+01 65 -5.12869508e+01 4.97605953e+01 9.89714446e+00 | -5.12869508e+01 4.97605953e+01 9.89714446e+00 66 6.35575595e+01 3.12984374e+01 -6.12979848e+01 | 6.35575595e+01 3.12984374e+01 -6.12979848e+01 67 -5.91858452e+01 3.58159444e+01 -3.29587150e+01 | -5.91858452e+01 3.58159444e+01 -3.29587150e+01 68 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 | 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 69 9.57194644e+01 -1.32321271e+01 4.19727144e+01 | 9.57194644e+01 -1.32321271e+01 4.19727144e+01 70 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 | 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 71 -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 | -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 72 -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 | -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 73 1.10180820e+01 2.04013856e+00 -2.16499589e+01 | 1.10180820e+01 2.04013856e+00 -2.16499589e+01 74 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 | 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 75 -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 | -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 76 -2.73156345e+01 6.56890408e+01 5.16880417e+01 | -2.73156345e+01 6.56890408e+01 5.16880417e+01 77 1.11676847e+01 5.59510788e+00 -3.72766964e+00 | 1.11676847e+01 5.59510788e+00 -3.72766964e+00 78 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 | 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 79 -9.72853360e+00 2.16810053e+01 4.30264230e+00 | -9.72853360e+00 2.16810053e+01 4.30264230e+00 80 -1.27947995e+02 4.40629491e+01 3.53869510e+01 | -1.27947995e+02 4.40629491e+01 3.53869510e+01 81 3.78209930e+01 4.62206620e+01 1.07336951e+01 | 3.78209930e+01 4.62206620e+01 1.07336951e+01 82 -1.71199927e+01 -1.32142380e+01 3.00293705e+01 | -1.71199927e+01 -1.32142380e+01 3.00293705e+01 83 -3.60023463e+01 -1.29976064e+00 3.48314943e+01 | -3.60023463e+01 -1.29976064e+00 3.48314943e+01 84 -2.08120307e+00 8.72388078e+00 -4.86204652e+01 | -2.08120307e+00 8.72388078e+00 -4.86204652e+01 85 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 | 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 86 5.37711303e+01 -2.73349976e+01 3.27762187e+01 | 5.37711303e+01 -2.73349976e+01 3.27762187e+01 87 -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 | -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 88 -8.43141883e+01 3.58086819e+01 1.68558147e+01 | -8.43141883e+01 3.58086819e+01 1.68558147e+01 89 5.75908353e+01 -1.25721059e+02 1.01431337e+02 | 5.75908353e+01 -1.25721059e+02 1.01431337e+02 90 2.42133745e+01 -1.11191738e+01 5.65191714e+01 | 2.42133745e+01 -1.11191738e+01 5.65191714e+01 91 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 | 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 92 -5.21448190e+01 6.95833224e+01 5.38462574e+01 | -5.21448190e+01 6.95833224e+01 5.38462574e+01 93 4.87702976e+01 4.95304619e+01 2.81294279e+01 | 4.87702976e+01 4.95304619e+01 2.81294279e+01 94 4.41600913e+01 3.14541365e+01 6.09278896e+00 | 4.41600913e+01 3.14541365e+01 6.09278896e+00 95 2.62439922e+00 -5.80150293e+00 3.62331499e+00 | 2.62439922e+00 -5.80150293e+00 3.62331499e+00 96 -2.05061611e+01 7.87792135e+00 -1.93731116e+01 | -2.05061611e+01 7.87792135e+00 -1.93731116e+01 97 -5.12869508e+01 4.97605953e+01 9.89714446e+00 | -5.12869508e+01 4.97605953e+01 9.89714446e+00 98 6.35575595e+01 3.12984374e+01 -6.12979848e+01 | 6.35575595e+01 3.12984374e+01 -6.12979848e+01 99 -5.91858452e+01 3.58159444e+01 -3.29587150e+01 | -5.91858452e+01 3.58159444e+01 -3.29587150e+01 100 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 | 4.48097977e+01 -7.48776768e+01 -3.36852947e+01 101 9.57194644e+01 -1.32321271e+01 4.19727144e+01 | 9.57194644e+01 -1.32321271e+01 4.19727144e+01 102 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 | 3.71851648e+01 -1.84180842e+01 -3.00803429e+01 103 -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 | -1.50780965e+01 -6.66961365e+00 -1.38857646e+01 104 -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 | -5.14281225e+01 -6.96759862e+00 -5.38445933e+01 105 1.10180820e+01 2.04013856e+00 -2.16499589e+01 | 1.10180820e+01 2.04013856e+00 -2.16499589e+01 106 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 | 2.85223280e+01 -3.88807959e+01 -2.04794982e+01 107 -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 | -5.14879140e+01 -1.32232740e+01 -8.82802218e+00 108 -2.73156345e+01 6.56890408e+01 5.16880417e+01 | -2.73156345e+01 6.56890408e+01 5.16880417e+01 109 1.11676847e+01 5.59510788e+00 -3.72766964e+00 | 1.11676847e+01 5.59510788e+00 -3.72766964e+00 110 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 | 4.08525402e+01 -7.70905746e+00 -5.34278354e+01 111 -9.72853360e+00 2.16810053e+01 4.30264230e+00 | -9.72853360e+00 2.16810053e+01 4.30264230e+00 112 -1.27947995e+02 4.40629491e+01 3.53869510e+01 | -1.27947995e+02 4.40629491e+01 3.53869510e+01 113 3.78209930e+01 4.62206620e+01 1.07336951e+01 | 3.78209930e+01 4.62206620e+01 1.07336951e+01 114 -1.71199927e+01 -1.32142380e+01 3.00293705e+01 | -1.71199927e+01 -1.32142380e+01 3.00293705e+01 115 -3.60023463e+01 -1.29976064e+00 3.48314943e+01 | -3.60023463e+01 -1.29976064e+00 3.48314943e+01 116 -2.08120307e+00 8.72388078e+00 -4.86204652e+01 | -2.08120307e+00 8.72388078e+00 -4.86204652e+01 117 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 | 6.26387732e+01 -1.00827374e+02 -1.71209700e+01 118 5.37711303e+01 -2.73349976e+01 3.27762187e+01 | 5.37711303e+01 -2.73349976e+01 3.27762187e+01 119 -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 | -6.00439034e+01 -2.11625339e+01 -4.68250199e+01 120 -8.43141883e+01 3.58086819e+01 1.68558147e+01 | -8.43141883e+01 3.58086819e+01 1.68558147e+01 121 5.75908353e+01 -1.25721059e+02 1.01431337e+02 | 5.75908353e+01 -1.25721059e+02 1.01431337e+02 122 2.42133745e+01 -1.11191738e+01 5.65191714e+01 | 2.42133745e+01 -1.11191738e+01 5.65191714e+01 123 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 | 1.24919032e+00 -1.86834179e+01 -5.23111388e+01 124 -5.21448190e+01 6.95833224e+01 5.38462574e+01 | -5.21448190e+01 6.95833224e+01 5.38462574e+01 125 4.87702976e+01 4.95304619e+01 2.81294279e+01 | 4.87702976e+01 4.95304619e+01 2.81294279e+01 126 4.41600913e+01 3.14541365e+01 6.09278896e+00 | 4.41600913e+01 3.14541365e+01 6.09278896e+00 127 2.62439922e+00 -5.80150293e+00 3.62331499e+00 | 2.62439922e+00 -5.80150293e+00 3.62331499e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = FTF (Configuration in file "config-HfNbTaTiZr-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)) = 955.2746957938202 2^p V(r_1,...,r_N) = 955.27469579382 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 -4.00838564e+01 1.83729465e+01 6.51073681e+00 | -4.00838564e+01 1.83729465e+01 6.51073681e+00 1 -2.67218980e+01 -7.74555542e+01 -9.20235760e+01 | -2.67218980e+01 -7.74555542e+01 -9.20235760e+01 2 -1.64621251e+01 1.31006784e+01 -1.28634883e+01 | -1.64621251e+01 1.31006784e+01 -1.28634883e+01 3 -6.44927405e+01 -6.23955863e+00 -1.25820701e+01 | -6.44927405e+01 -6.23955863e+00 -1.25820701e+01 4 -8.88169295e-01 1.14165041e+00 -2.44387646e+01 | -8.88169295e-01 1.14165041e+00 -2.44387646e+01 5 1.15860167e+02 -1.13436628e+02 -5.11639544e+01 | 1.15860167e+02 -1.13436628e+02 -5.11639544e+01 6 4.72838794e+01 3.24740821e+01 -1.10834210e+01 | 4.72838794e+01 3.24740821e+01 -1.10834210e+01 7 1.65246534e+01 -2.30282301e+01 1.15671857e+01 | 1.65246534e+01 -2.30282301e+01 1.15671857e+01 8 -6.95613340e+01 -1.90660587e+01 -3.23656697e+01 | -6.95613340e+01 -1.90660587e+01 -3.23656697e+01 9 8.86980609e+01 -2.78795588e+01 -6.52498715e+01 | 8.86980609e+01 -2.78795588e+01 -6.52498715e+01 10 -4.25763752e+01 4.93190173e+01 9.30706869e+00 | -4.25763752e+01 4.93190173e+01 9.30706869e+00 11 -6.51590751e+01 2.32266428e+01 1.78399814e+01 | -6.51590751e+01 2.32266428e+01 1.78399814e+01 12 -5.25930985e+01 8.49219276e+01 -7.61352532e+01 | -5.25930985e+01 8.49219276e+01 -7.61352532e+01 13 1.01931952e+01 5.65556717e+00 -2.01211481e+01 | 1.01931952e+01 5.65556717e+00 -2.01211481e+01 14 5.84842967e+01 4.77368370e+01 5.88086573e+01 | 5.84842967e+01 4.77368370e+01 5.88086573e+01 15 4.20993586e+01 -3.68331974e+01 -8.46234742e+00 | 4.20993586e+01 -3.68331974e+01 -8.46234742e+00 16 -8.55505952e+01 7.40445501e+00 3.21176859e+01 | -8.55505952e+01 7.40445501e+00 3.21176859e+01 17 4.99265287e+01 4.64220387e+01 -3.10530665e+00 | 4.99265287e+01 4.64220387e+01 -3.10530665e+00 18 4.49413923e+00 8.05665575e+00 2.60303697e+01 | 4.49413923e+00 8.05665575e+00 2.60303697e+01 19 -4.57791988e+01 -2.05587173e+01 3.48093125e+01 | -4.57791988e+01 -2.05587173e+01 3.48093125e+01 20 1.54109331e+01 3.37758339e+00 1.33030253e+01 | 1.54109331e+01 3.37758339e+00 1.33030253e+01 21 1.67388430e+01 1.49384582e+01 -2.03340034e+01 | 1.67388430e+01 1.49384582e+01 -2.03340034e+01 22 2.39037181e+01 -2.24842871e+01 3.06578803e+01 | 2.39037181e+01 -2.24842871e+01 3.06578803e+01 23 1.40354691e+01 -1.12349683e+01 4.04436221e+01 | 1.40354691e+01 -1.12349683e+01 4.04436221e+01 24 -2.29707358e+01 2.23661078e+01 1.42596131e+01 | -2.29707358e+01 2.23661078e+01 1.42596131e+01 25 -3.65373087e+01 -1.93995327e+01 -1.42217922e+01 | -3.65373087e+01 -1.93995327e+01 -1.42217922e+01 26 -2.47683639e+01 6.56889623e+01 3.06458392e+01 | -2.47683639e+01 6.56889623e+01 3.06458392e+01 27 -1.91943068e+01 -4.19384768e+01 3.54806026e+01 | -1.91943068e+01 -4.19384768e+01 3.54806026e+01 28 7.34877197e+01 -2.45904636e+01 4.75712371e+01 | 7.34877197e+01 -2.45904636e+01 4.75712371e+01 29 2.48852278e+01 1.09685254e+01 -1.75401870e+00 | 2.48852278e+01 1.09685254e+01 -1.75401870e+00 30 1.55482443e+01 -9.56113788e+00 1.90445480e+01 | 1.55482443e+01 -9.56113788e+00 1.90445480e+01 31 -4.23525235e+00 -1.46576621e+00 1.75073194e+01 | -4.23525235e+00 -1.46576621e+00 1.75073194e+01 32 -4.00838564e+01 1.83729465e+01 6.51073681e+00 | -4.00838564e+01 1.83729465e+01 6.51073681e+00 33 -2.67218980e+01 -7.74555542e+01 -9.20235760e+01 | -2.67218980e+01 -7.74555542e+01 -9.20235760e+01 34 -1.64621251e+01 1.31006784e+01 -1.28634883e+01 | -1.64621251e+01 1.31006784e+01 -1.28634883e+01 35 -6.44927405e+01 -6.23955863e+00 -1.25820701e+01 | -6.44927405e+01 -6.23955863e+00 -1.25820701e+01 36 -8.88169295e-01 1.14165041e+00 -2.44387646e+01 | -8.88169295e-01 1.14165041e+00 -2.44387646e+01 37 1.15860167e+02 -1.13436628e+02 -5.11639544e+01 | 1.15860167e+02 -1.13436628e+02 -5.11639544e+01 38 4.72838794e+01 3.24740821e+01 -1.10834210e+01 | 4.72838794e+01 3.24740821e+01 -1.10834210e+01 39 1.65246534e+01 -2.30282301e+01 1.15671857e+01 | 1.65246534e+01 -2.30282301e+01 1.15671857e+01 40 -6.95613340e+01 -1.90660587e+01 -3.23656697e+01 | -6.95613340e+01 -1.90660587e+01 -3.23656697e+01 41 8.86980609e+01 -2.78795588e+01 -6.52498715e+01 | 8.86980609e+01 -2.78795588e+01 -6.52498715e+01 42 -4.25763752e+01 4.93190173e+01 9.30706869e+00 | -4.25763752e+01 4.93190173e+01 9.30706869e+00 43 -6.51590751e+01 2.32266428e+01 1.78399814e+01 | -6.51590751e+01 2.32266428e+01 1.78399814e+01 44 -5.25930985e+01 8.49219276e+01 -7.61352532e+01 | -5.25930985e+01 8.49219276e+01 -7.61352532e+01 45 1.01931952e+01 5.65556717e+00 -2.01211481e+01 | 1.01931952e+01 5.65556717e+00 -2.01211481e+01 46 5.84842967e+01 4.77368370e+01 5.88086573e+01 | 5.84842967e+01 4.77368370e+01 5.88086573e+01 47 4.20993586e+01 -3.68331974e+01 -8.46234742e+00 | 4.20993586e+01 -3.68331974e+01 -8.46234742e+00 48 -8.55505952e+01 7.40445501e+00 3.21176859e+01 | -8.55505952e+01 7.40445501e+00 3.21176859e+01 49 4.99265287e+01 4.64220387e+01 -3.10530665e+00 | 4.99265287e+01 4.64220387e+01 -3.10530665e+00 50 4.49413923e+00 8.05665575e+00 2.60303697e+01 | 4.49413923e+00 8.05665575e+00 2.60303697e+01 51 -4.57791988e+01 -2.05587173e+01 3.48093125e+01 | -4.57791988e+01 -2.05587173e+01 3.48093125e+01 52 1.54109331e+01 3.37758339e+00 1.33030253e+01 | 1.54109331e+01 3.37758339e+00 1.33030253e+01 53 1.67388430e+01 1.49384582e+01 -2.03340034e+01 | 1.67388430e+01 1.49384582e+01 -2.03340034e+01 54 2.39037181e+01 -2.24842871e+01 3.06578803e+01 | 2.39037181e+01 -2.24842871e+01 3.06578803e+01 55 1.40354691e+01 -1.12349683e+01 4.04436221e+01 | 1.40354691e+01 -1.12349683e+01 4.04436221e+01 56 -2.29707358e+01 2.23661078e+01 1.42596131e+01 | -2.29707358e+01 2.23661078e+01 1.42596131e+01 57 -3.65373087e+01 -1.93995327e+01 -1.42217922e+01 | -3.65373087e+01 -1.93995327e+01 -1.42217922e+01 58 -2.47683639e+01 6.56889623e+01 3.06458392e+01 | -2.47683639e+01 6.56889623e+01 3.06458392e+01 59 -1.91943068e+01 -4.19384768e+01 3.54806026e+01 | -1.91943068e+01 -4.19384768e+01 3.54806026e+01 60 7.34877197e+01 -2.45904636e+01 4.75712371e+01 | 7.34877197e+01 -2.45904636e+01 4.75712371e+01 61 2.48852278e+01 1.09685254e+01 -1.75401870e+00 | 2.48852278e+01 1.09685254e+01 -1.75401870e+00 62 1.55482443e+01 -9.56113788e+00 1.90445480e+01 | 1.55482443e+01 -9.56113788e+00 1.90445480e+01 63 -4.23525235e+00 -1.46576621e+00 1.75073194e+01 | -4.23525235e+00 -1.46576621e+00 1.75073194e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr, PBC = FFT (Configuration in file "config-HfNbTaTiZr-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)) = 825.9460107034168 2^p V(r_1,...,r_N) = 825.9460107034186 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 -3.82657870e+01 -6.57581289e+01 -1.53749459e+01 | -3.82657870e+01 -6.57581289e+01 -1.53749459e+01 1 -1.98493775e+00 5.43817604e+01 -3.43433766e+01 | -1.98493775e+00 5.43817604e+01 -3.43433766e+01 2 3.34343427e+01 -7.88163712e+01 -2.22490744e+01 | 3.34343427e+01 -7.88163712e+01 -2.22490744e+01 3 -5.63842509e+01 5.81921567e+01 1.18861911e+01 | -5.63842509e+01 5.81921567e+01 1.18861911e+01 4 1.48874836e+01 -6.10601079e+00 -3.15966435e+00 | 1.48874836e+01 -6.10601079e+00 -3.15966435e+00 5 -1.73589011e+01 -1.88642679e+01 -3.57159331e+01 | -1.73589011e+01 -1.88642679e+01 -3.57159331e+01 6 1.45690898e+01 -1.26862049e+01 -2.61555925e+00 | 1.45690898e+01 -1.26862049e+01 -2.61555925e+00 7 4.62448954e+01 -4.74592962e+00 6.35788675e+00 | 4.62448954e+01 -4.74592962e+00 6.35788675e+00 8 -1.15176023e+02 -2.57919081e+01 -4.44754040e+01 | -1.15176023e+02 -2.57919081e+01 -4.44754040e+01 9 2.00871125e+01 5.77536508e+01 -1.72970118e+01 | 2.00871125e+01 5.77536508e+01 -1.72970118e+01 10 5.22194097e+01 -1.73662938e+01 2.54068091e+01 | 5.22194097e+01 -1.73662938e+01 2.54068091e+01 11 -3.50308661e+01 1.97861737e+01 -5.51186932e+00 | -3.50308661e+01 1.97861737e+01 -5.51186932e+00 12 1.70178858e+01 -1.19671522e+01 7.29537165e-01 | 1.70178858e+01 -1.19671522e+01 7.29537165e-01 13 3.39656199e+01 1.19334624e+01 -2.29308279e+01 | 3.39656199e+01 1.19334624e+01 -2.29308279e+01 14 4.38426534e+01 9.83056584e+00 -3.42589730e+01 | 4.38426534e+01 9.83056584e+00 -3.42589730e+01 15 2.24747592e+01 3.62788024e+01 3.16389546e+01 | 2.24747592e+01 3.62788024e+01 3.16389546e+01 16 -9.71483785e+01 -1.38381392e+02 -5.01208274e+01 | -9.71483785e+01 -1.38381392e+02 -5.01208274e+01 17 1.09964840e+01 2.11790235e+01 -1.98901638e+01 | 1.09964840e+01 2.11790235e+01 -1.98901638e+01 18 4.69121473e+01 -3.72467257e+01 3.83098968e+01 | 4.69121473e+01 -3.72467257e+01 3.83098968e+01 19 -8.94886970e+01 7.60493169e+01 7.07338961e+01 | -8.94886970e+01 7.60493169e+01 7.07338961e+01 20 2.24349813e+01 -4.21874522e+01 -1.26539184e+01 | 2.24349813e+01 -4.21874522e+01 -1.26539184e+01 21 5.41866810e+01 -3.78955514e+01 2.55600169e+01 | 5.41866810e+01 -3.78955514e+01 2.55600169e+01 22 9.65593737e+00 -1.35474292e+01 1.30632648e+01 | 9.65593737e+00 -1.35474292e+01 1.30632648e+01 23 3.31120791e+01 1.61775621e+01 1.33821710e+01 | 3.31120791e+01 1.61775621e+01 1.33821710e+01 24 -6.22910435e+01 -2.78730617e+01 -1.84093279e+01 | -6.22910435e+01 -2.78730617e+01 -1.84093279e+01 25 4.62018755e+01 6.13453029e+01 -1.03303905e+01 | 4.62018755e+01 6.13453029e+01 -1.03303905e+01 26 8.95724427e+00 1.59313083e+01 2.37964817e+01 | 8.95724427e+00 1.59313083e+01 2.37964817e+01 27 -4.02067536e+01 2.72999041e+01 2.44687983e+01 | -4.02067536e+01 2.72999041e+01 2.44687983e+01 28 -2.95284745e+01 -3.15033562e+00 2.45478701e+01 | -2.95284745e+01 -3.15033562e+00 2.45478701e+01 29 3.46102731e+01 6.70401733e+01 2.86891373e+01 | 3.46102731e+01 6.70401733e+01 2.86891373e+01 30 1.10518230e+01 5.99764121e-01 6.02238937e+00 | 1.10518230e+01 5.99764121e-01 6.02238937e+00 31 6.00133516e+00 8.60528765e+00 4.74396645e+00 | 6.00133516e+00 8.60528765e+00 4.74396645e+00 32 -3.82657870e+01 -6.57581289e+01 -1.53749459e+01 | -3.82657870e+01 -6.57581289e+01 -1.53749459e+01 33 -1.98493775e+00 5.43817604e+01 -3.43433766e+01 | -1.98493775e+00 5.43817604e+01 -3.43433766e+01 34 3.34343427e+01 -7.88163712e+01 -2.22490744e+01 | 3.34343427e+01 -7.88163712e+01 -2.22490744e+01 35 -5.63842509e+01 5.81921567e+01 1.18861911e+01 | -5.63842509e+01 5.81921567e+01 1.18861911e+01 36 1.48874836e+01 -6.10601079e+00 -3.15966435e+00 | 1.48874836e+01 -6.10601079e+00 -3.15966435e+00 37 -1.73589011e+01 -1.88642679e+01 -3.57159331e+01 | -1.73589011e+01 -1.88642679e+01 -3.57159331e+01 38 1.45690898e+01 -1.26862049e+01 -2.61555925e+00 | 1.45690898e+01 -1.26862049e+01 -2.61555925e+00 39 4.62448954e+01 -4.74592962e+00 6.35788675e+00 | 4.62448954e+01 -4.74592962e+00 6.35788675e+00 40 -1.15176023e+02 -2.57919081e+01 -4.44754040e+01 | -1.15176023e+02 -2.57919081e+01 -4.44754040e+01 41 2.00871125e+01 5.77536508e+01 -1.72970118e+01 | 2.00871125e+01 5.77536508e+01 -1.72970118e+01 42 5.22194097e+01 -1.73662938e+01 2.54068091e+01 | 5.22194097e+01 -1.73662938e+01 2.54068091e+01 43 -3.50308661e+01 1.97861737e+01 -5.51186932e+00 | -3.50308661e+01 1.97861737e+01 -5.51186932e+00 44 1.70178858e+01 -1.19671522e+01 7.29537165e-01 | 1.70178858e+01 -1.19671522e+01 7.29537165e-01 45 3.39656199e+01 1.19334624e+01 -2.29308279e+01 | 3.39656199e+01 1.19334624e+01 -2.29308279e+01 46 4.38426534e+01 9.83056584e+00 -3.42589730e+01 | 4.38426534e+01 9.83056584e+00 -3.42589730e+01 47 2.24747592e+01 3.62788024e+01 3.16389546e+01 | 2.24747592e+01 3.62788024e+01 3.16389546e+01 48 -9.71483785e+01 -1.38381392e+02 -5.01208274e+01 | -9.71483785e+01 -1.38381392e+02 -5.01208274e+01 49 1.09964840e+01 2.11790235e+01 -1.98901638e+01 | 1.09964840e+01 2.11790235e+01 -1.98901638e+01 50 4.69121473e+01 -3.72467257e+01 3.83098968e+01 | 4.69121473e+01 -3.72467257e+01 3.83098968e+01 51 -8.94886970e+01 7.60493169e+01 7.07338961e+01 | -8.94886970e+01 7.60493169e+01 7.07338961e+01 52 2.24349813e+01 -4.21874522e+01 -1.26539184e+01 | 2.24349813e+01 -4.21874522e+01 -1.26539184e+01 53 5.41866810e+01 -3.78955514e+01 2.55600169e+01 | 5.41866810e+01 -3.78955514e+01 2.55600169e+01 54 9.65593737e+00 -1.35474292e+01 1.30632648e+01 | 9.65593737e+00 -1.35474292e+01 1.30632648e+01 55 3.31120791e+01 1.61775621e+01 1.33821710e+01 | 3.31120791e+01 1.61775621e+01 1.33821710e+01 56 -6.22910435e+01 -2.78730617e+01 -1.84093279e+01 | -6.22910435e+01 -2.78730617e+01 -1.84093279e+01 57 4.62018755e+01 6.13453029e+01 -1.03303905e+01 | 4.62018755e+01 6.13453029e+01 -1.03303905e+01 58 8.95724427e+00 1.59313083e+01 2.37964817e+01 | 8.95724427e+00 1.59313083e+01 2.37964817e+01 59 -4.02067536e+01 2.72999041e+01 2.44687983e+01 | -4.02067536e+01 2.72999041e+01 2.44687983e+01 60 -2.95284745e+01 -3.15033562e+00 2.45478701e+01 | -2.95284745e+01 -3.15033562e+00 2.45478701e+01 61 3.46102731e+01 6.70401733e+01 2.86891373e+01 | 3.46102731e+01 6.70401733e+01 2.86891373e+01 62 1.10518230e+01 5.99764121e-01 6.02238937e+00 | 1.10518230e+01 5.99764121e-01 6.02238937e+00 63 6.00133516e+00 8.60528765e+00 4.74396645e+00 | 6.00133516e+00 8.60528765e+00 4.74396645e+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.