!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : EAM_Dynamo_ZhouWadleyJohnson_2001NISTretabulation_CuTa__MO_950828638160_000 Supported species : Cu Ta random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.73088440678 2^p V(r_1,...,r_N) = -3.73088440678 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 -2.95086890e+00 -5.91646097e+00 -6.08064560e+00 | -2.95086890e+00 -5.91646097e+00 -6.08064560e+00 1 2.38142154e+00 1.88605617e+00 -1.67981996e+00 | 2.38142154e+00 1.88605617e+00 -1.67981996e+00 2 1.72864266e+00 -2.07024250e+00 2.95967171e+00 | 1.72864266e+00 -2.07024250e+00 2.95967171e+00 3 -1.15919529e+00 6.10064730e+00 4.80079385e+00 | -1.15919529e+00 6.10064730e+00 4.80079385e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.21989172791 2^p V(r_1,...,r_N) = -4.21989172791 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 8.78391262e-01 5.93644672e-01 6.57869058e-01 | 8.78391262e-01 5.93644672e-01 6.57869058e-01 1 6.02910561e-01 1.02507510e+00 -2.29444729e+00 | 6.02910561e-01 1.02507510e+00 -2.29444729e+00 2 3.23621970e+00 -4.17172644e+00 8.93214317e-01 | 3.23621970e+00 -4.17172644e+00 8.93214317e-01 3 -4.71752153e+00 2.55300666e+00 7.43363919e-01 | -4.71752153e+00 2.55300666e+00 7.43363919e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.79510596694 2^p V(r_1,...,r_N) = -2.79510596694 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 -3.07502271e+00 -3.00992178e+00 -3.70310342e+00 | -3.07502271e+00 -3.00992178e+00 -3.70310342e+00 1 2.99919023e+00 3.16913841e+00 -4.27078356e+00 | 2.99919023e+00 3.16913841e+00 -4.27078356e+00 2 6.59222630e+00 -5.70109010e+00 3.92464894e+00 | 6.59222630e+00 -5.70109010e+00 3.92464894e+00 3 -6.51639382e+00 5.54187347e+00 4.04923804e+00 | -6.51639382e+00 5.54187347e+00 4.04923804e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.84968973552 2^p V(r_1,...,r_N) = -3.84968973552 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 -2.32592879e+00 -2.46869744e+00 -4.25083956e+00 | -2.32592879e+00 -2.46869744e+00 -4.25083956e+00 1 1.52011840e+00 2.14882126e+00 -2.08035548e+00 | 1.52011840e+00 2.14882126e+00 -2.08035548e+00 2 5.07405485e+00 -4.77622547e+00 2.99924075e+00 | 5.07405485e+00 -4.77622547e+00 2.99924075e+00 3 -4.26824446e+00 5.09610165e+00 3.33195429e+00 | -4.26824446e+00 5.09610165e+00 3.33195429e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.714965549826 2^p V(r_1,...,r_N) = 0.714965549826 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 -4.58611440e+00 -6.23223786e+00 -5.86268708e+00 | -4.58611440e+00 -6.23223786e+00 -5.86268708e+00 1 1.60722346e+01 1.27244476e+00 -1.32170656e+01 | 1.60722346e+01 1.27244476e+00 -1.32170656e+01 2 3.09375535e+00 -3.13667498e+00 2.75763225e+00 | 3.09375535e+00 -3.13667498e+00 2.75763225e+00 3 -1.45798755e+01 8.09646808e+00 1.63221204e+01 | -1.45798755e+01 8.09646808e+00 1.63221204e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.08425916598 2^p V(r_1,...,r_N) = -1.08425916598 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -5.76846174e+00 -1.22772321e+01 -7.12263335e+00 | -5.76846174e+00 -1.22772321e+01 -7.12263335e+00 1 8.76937654e+00 6.04024940e+00 -5.80441400e+00 | 8.76937654e+00 6.04024940e+00 -5.80441400e+00 2 2.60654815e+00 -9.11967228e-01 2.48926967e+00 | 2.60654815e+00 -9.11967228e-01 2.48926967e+00 3 -5.60746295e+00 7.14894990e+00 1.04377777e+01 | -5.60746295e+00 7.14894990e+00 1.04377777e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.01249974658 2^p V(r_1,...,r_N) = -5.01249974658 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 -1.87181944e+00 -3.07269888e+00 -1.33919594e+00 | -1.87181944e+00 -3.07269888e+00 -1.33919594e+00 1 1.62896473e+00 1.93287167e+00 -1.42155164e+00 | 1.62896473e+00 1.93287167e+00 -1.42155164e+00 2 8.92106078e-01 -4.72318673e-01 1.19274620e+00 | 8.92106078e-01 -4.72318673e-01 1.19274620e+00 3 -6.49251367e-01 1.61214588e+00 1.56800138e+00 | -6.49251367e-01 1.61214588e+00 1.56800138e+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=0 periodic directions, which means an increase by a factor n=2^0=1 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)) = -10.6494919806 2^p V(r_1,...,r_N) = -10.6494919806 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 -1.08986548e+01 -1.07003530e+01 -6.79208651e+00 | -1.08986548e+01 -1.07003530e+01 -6.79208651e+00 1 1.72167367e+01 3.29422269e+00 -1.83461273e+01 | 1.72167367e+01 3.29422269e+00 -1.83461273e+01 2 8.32812295e+00 -3.79146493e+00 7.79866105e+00 | 8.32812295e+00 -3.79146493e+00 7.79866105e+00 3 -1.46462049e+01 1.11975952e+01 1.73395528e+01 | -1.46462049e+01 1.11975952e+01 1.73395528e+01 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.14220672812 2^p V(r_1,...,r_N) = 1.14220672812 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 -2.51313671e+01 -1.70443020e+01 -2.19585474e+01 | -2.51313671e+01 -1.70443020e+01 -2.19585474e+01 1 3.13859467e+01 7.57613154e+00 -2.94228604e+01 | 3.13859467e+01 7.57613154e+00 -2.94228604e+01 2 1.92499790e+01 -1.42521435e+01 1.77081055e+01 | 1.92499790e+01 -1.42521435e+01 1.77081055e+01 3 -2.55045586e+01 2.37203140e+01 3.36733023e+01 | -2.55045586e+01 2.37203140e+01 3.36733023e+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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.53891334397 2^p V(r_1,...,r_N) = -2.53891334397 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 -2.40674199e+01 -2.92913114e+01 -2.86809145e+01 | -2.40674199e+01 -2.92913114e+01 -2.86809145e+01 1 2.45102568e+01 2.13109151e+01 -7.96516798e+00 | 2.45102568e+01 2.13109151e+01 -7.96516798e+00 2 1.20235251e+01 -1.09823838e+01 1.62273097e+01 | 1.20235251e+01 -1.09823838e+01 1.62273097e+01 3 -1.24663619e+01 1.89627801e+01 2.04187728e+01 | -1.24663619e+01 1.89627801e+01 2.04187728e+01 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.71235478187 2^p V(r_1,...,r_N) = -7.71235478187 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 -1.86145819e+01 -1.23047817e+01 -1.24324078e+01 | -1.86145819e+01 -1.23047817e+01 -1.24324078e+01 1 1.64410342e+01 2.36578940e+01 -1.17621313e+01 | 1.64410342e+01 2.36578940e+01 -1.17621313e+01 2 1.19730883e+01 -1.98395571e+01 1.74349109e+01 | 1.19730883e+01 -1.98395571e+01 1.74349109e+01 3 -9.79954060e+00 8.48644481e+00 6.75962815e+00 | -9.79954060e+00 8.48644481e+00 6.75962815e+00 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.96637043098 2^p V(r_1,...,r_N) = -6.96637043098 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 -1.76658996e+01 -1.45309645e+01 -9.59476655e+00 | -1.76658996e+01 -1.45309645e+01 -9.59476655e+00 1 2.43462705e+01 8.03875630e+00 -2.09596883e+01 | 2.43462705e+01 8.03875630e+00 -2.09596883e+01 2 8.40281013e+00 -1.16626623e+01 9.34077375e+00 | 8.40281013e+00 -1.16626623e+01 9.34077375e+00 3 -1.50831811e+01 1.81548705e+01 2.12136811e+01 | -1.50831811e+01 1.81548705e+01 2.12136811e+01 ------------------------------------------------------------------------------------------------------------------------ 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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.65005321525 2^p V(r_1,...,r_N) = 6.65005321525 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 -3.68056155e+01 -1.38258869e+01 -4.15339052e+01 | -3.68056155e+01 -1.38258869e+01 -4.15339052e+01 1 1.55136712e+01 1.07331742e+01 -1.85122881e+01 | 1.55136712e+01 1.07331742e+01 -1.85122881e+01 2 4.59900693e+01 -2.44228757e+01 3.07515979e+01 | 4.59900693e+01 -2.44228757e+01 3.07515979e+01 3 -2.46981249e+01 2.75155884e+01 2.92945955e+01 | -2.46981249e+01 2.75155884e+01 2.92945955e+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=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -12.1597950332 2^p V(r_1,...,r_N) = -12.1597950332 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 -6.20847354e+00 -1.23116902e+01 -7.21624156e+00 | -6.20847354e+00 -1.23116902e+01 -7.21624156e+00 1 1.43100324e+01 8.31382641e+00 -1.42591540e+01 | 1.43100324e+01 8.31382641e+00 -1.42591540e+01 2 4.92847519e+00 -4.44652381e+00 4.23205677e+00 | 4.92847519e+00 -4.44652381e+00 4.23205677e+00 3 -1.30300340e+01 8.44438763e+00 1.72433388e+01 | -1.30300340e+01 8.44438763e+00 1.72433388e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTT (Configuration in file "config-CuTa-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.26291949363 2^p V(r_1,...,r_N) = -1.26291949363 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 -1.93751791e+01 -2.60223986e+00 -1.94581839e+01 | -1.93751791e+01 -2.60223986e+00 -1.94581839e+01 1 6.08540967e+00 5.66575293e+00 -3.47316279e+00 | 6.08540967e+00 5.66575293e+00 -3.47316279e+00 2 2.18762703e+01 -1.51434566e+01 1.21808929e+01 | 2.18762703e+01 -1.51434566e+01 1.21808929e+01 3 -8.58650090e+00 1.20799435e+01 1.07504538e+01 | -8.58650090e+00 1.20799435e+01 1.07504538e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TTF (Configuration in file "config-CuTa-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.56923223857 2^p V(r_1,...,r_N) = -1.56923223857 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 -2.14058723e+01 -1.61372314e+01 -2.08155815e+01 | -2.14058723e+01 -1.61372314e+01 -2.08155815e+01 1 7.87882100e+00 1.05622458e+01 -6.73943274e+00 | 7.87882100e+00 1.05622458e+01 -6.73943274e+00 2 2.16446221e+01 -7.14921546e+00 1.97880984e+01 | 2.16446221e+01 -7.14921546e+00 1.97880984e+01 3 -8.11757077e+00 1.27242011e+01 7.76691589e+00 | -8.11757077e+00 1.27242011e+01 7.76691589e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFT (Configuration in file "config-CuTa-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.15746823734 2^p V(r_1,...,r_N) = -3.15746823734 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 -1.09929028e+01 -6.38817203e+00 -7.94188360e+00 | -1.09929028e+01 -6.38817203e+00 -7.94188360e+00 1 9.13565463e+00 1.89850758e+01 -1.51216499e+01 | 9.13565463e+00 1.89850758e+01 -1.51216499e+01 2 8.08856448e+00 -1.61502912e+01 1.80890057e+01 | 8.08856448e+00 -1.61502912e+01 1.80890057e+01 3 -6.23131631e+00 3.55338747e+00 4.97452779e+00 | -6.23131631e+00 3.55338747e+00 4.97452779e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = TFF (Configuration in file "config-CuTa-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.77454070354 2^p V(r_1,...,r_N) = 2.77454070354 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 -1.17840429e+01 -9.82209242e+00 -9.53310212e+00 | -1.17840429e+01 -9.82209242e+00 -9.53310212e+00 1 1.32551490e+01 1.32233737e+01 -2.94861992e+01 | 1.32551490e+01 1.32233737e+01 -2.94861992e+01 2 1.87362226e+01 -1.95631403e+01 2.77937546e+01 | 1.87362226e+01 -1.95631403e+01 2.77937546e+01 3 -2.02073288e+01 1.61618590e+01 1.12255468e+01 | -2.02073288e+01 1.61618590e+01 1.12255468e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTT (Configuration in file "config-CuTa-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.83199667236 2^p V(r_1,...,r_N) = -5.83199667236 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 -4.21607182e+00 -5.74896059e+00 -5.58502836e+00 | -4.21607182e+00 -5.74896059e+00 -5.58502836e+00 1 4.56586612e+00 7.63401389e+00 -1.06915869e+01 | 4.56586612e+00 7.63401389e+00 -1.06915869e+01 2 6.57965220e+00 -1.24953770e+01 1.06127288e+01 | 6.57965220e+00 -1.24953770e+01 1.06127288e+01 3 -6.92944650e+00 1.06103237e+01 5.66388650e+00 | -6.92944650e+00 1.06103237e+01 5.66388650e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FTF (Configuration in file "config-CuTa-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.1312567937 2^p V(r_1,...,r_N) = -8.1312567937 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 -1.53768794e+00 2.94856100e-01 -4.50446246e-01 | -1.53768794e+00 2.94856100e-01 -4.50446246e-01 1 6.95614887e+00 2.91960299e+00 -7.58956594e+00 | 6.95614887e+00 2.91960299e+00 -7.58956594e+00 2 4.85409185e+00 -6.76415410e+00 1.88145595e+00 | 4.85409185e+00 -6.76415410e+00 1.88145595e+00 3 -1.02725528e+01 3.54969502e+00 6.15855623e+00 | -1.02725528e+01 3.54969502e+00 6.15855623e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Ta, PBC = FFT (Configuration in file "config-CuTa-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.66727962155 2^p V(r_1,...,r_N) = -9.66727962155 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 -7.67100891e+00 -8.37311597e+00 -3.06387108e+00 | -7.67100891e+00 -8.37311597e+00 -3.06387108e+00 1 5.97572953e+00 7.45526937e+00 -2.61082414e+00 | 5.97572953e+00 7.45526937e+00 -2.61082414e+00 2 2.99708382e+00 -8.71614630e-01 3.46522500e+00 | 2.99708382e+00 -8.71614630e-01 3.46522500e+00 3 -1.30180444e+00 1.78946123e+00 2.20947022e+00 | -1.30180444e+00 1.78946123e+00 2.20947022e+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.