Model Extended KIM ID = === Verification check vc-periodicity-support start (2023-05-09 20:57:40) === !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_002 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) = 76.0554515884495 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) = 99.2155066343101 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) = 70.63175057174644 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) = 343.3815407376026 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) = 69.49336570760204 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) = 44.12127346631123 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) = 70.0460068803362 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) = -10.393497627254058 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) = -10.78424933578216 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) = 74.2374189029163 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) = 24.50042654126649 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) = 188.94921660707982 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)) = 94.23866396440422 2^p V(r_1,...,r_N) = 94.23866396440427 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) = 48.97827984784152 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) = 172.70040306786848 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) = 152.72617356153992 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) = 39.74002106912711 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) = 5233.611604290416 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) = 1971.5602456454733 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) = 2596.390257869388 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) = 2432.46697878585 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. === Verification check vc-periodicity-support end (2023-05-09 20:59:49) ===