!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_WilliamsMishinHamilton_2006_CuAg__MO_128703483589_005 Supported species : Ag Cu random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTT (Configuration in file "config-Ag-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)) = 2.21982963164 2^p V(r_1,...,r_N) = 2.21982963164 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 -8.08720626e+00 -1.13150633e+01 -1.26083074e+01 | -8.08720626e+00 -1.13150633e+01 -1.26083074e+01 1 6.19160517e+00 4.22633108e+00 -4.06045473e+00 | 6.19160517e+00 4.22633108e+00 -4.06045473e+00 2 6.71145927e+00 -5.62103256e+00 7.63839589e+00 | 6.71145927e+00 -5.62103256e+00 7.63839589e+00 3 -4.81585819e+00 1.27097647e+01 9.03036619e+00 | -4.81585819e+00 1.27097647e+01 9.03036619e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTF (Configuration in file "config-Ag-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)) = 5.20903281517 2^p V(r_1,...,r_N) = 5.20903281517 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 -1.10645647e+01 -7.96342138e+00 -7.16116460e+00 | -1.10645647e+01 -7.96342138e+00 -7.16116460e+00 1 8.39954679e+00 6.49293560e+00 -1.02889988e+01 | 8.39954679e+00 6.49293560e+00 -1.02889988e+01 2 1.23568502e+01 -1.31196472e+01 1.22378506e+01 | 1.23568502e+01 -1.31196472e+01 1.22378506e+01 3 -9.69183231e+00 1.45901330e+01 5.21231281e+00 | -9.69183231e+00 1.45901330e+01 5.21231281e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFT (Configuration in file "config-Ag-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)) = 8.8988873241 2^p V(r_1,...,r_N) = 8.8988873241 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 -1.05850122e+01 -1.32868929e+01 -1.71022845e+01 | -1.05850122e+01 -1.32868929e+01 -1.71022845e+01 1 1.42564421e+01 1.40497988e+01 -8.41052197e+00 | 1.42564421e+01 1.40497988e+01 -8.41052197e+00 2 9.33820320e+00 -1.23524090e+01 1.29773277e+01 | 9.33820320e+00 -1.23524090e+01 1.29773277e+01 3 -1.30096331e+01 1.15895031e+01 1.25354788e+01 | -1.30096331e+01 1.15895031e+01 1.25354788e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFF (Configuration in file "config-Ag-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)) = 18.7121857745 2^p V(r_1,...,r_N) = 18.7121857745 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 -1.81422949e+01 -1.74449895e+01 -2.77610622e+01 | -1.81422949e+01 -1.74449895e+01 -2.77610622e+01 1 1.22132894e+01 1.43914381e+01 -9.87490183e+00 | 1.22132894e+01 1.43914381e+01 -9.87490183e+00 2 2.19881459e+01 -1.54024268e+01 2.23952874e+01 | 2.19881459e+01 -1.54024268e+01 2.23952874e+01 3 -1.60591404e+01 1.84559782e+01 1.52406767e+01 | -1.60591404e+01 1.84559782e+01 1.52406767e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTT (Configuration in file "config-Ag-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)) = 8.41636353123 2^p V(r_1,...,r_N) = 8.41636353123 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 -1.44390433e+01 -1.04508162e+01 -1.36990425e+01 | -1.44390433e+01 -1.04508162e+01 -1.36990425e+01 1 1.03522424e+01 1.27207752e+01 -1.10432711e+01 | 1.03522424e+01 1.27207752e+01 -1.10432711e+01 2 1.36442334e+01 -1.44090267e+01 1.23963827e+01 | 1.36442334e+01 -1.44090267e+01 1.23963827e+01 3 -9.55743244e+00 1.21390677e+01 1.23459309e+01 | -9.55743244e+00 1.21390677e+01 1.23459309e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTF (Configuration in file "config-Ag-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)) = 2.41966543267 2^p V(r_1,...,r_N) = 2.41966543267 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 -1.15234527e+01 -9.99369878e+00 -7.43343560e+00 | -1.15234527e+01 -9.99369878e+00 -7.43343560e+00 1 7.13779996e+00 9.64687169e+00 -8.25909668e+00 | 7.13779996e+00 9.64687169e+00 -8.25909668e+00 2 8.89285721e+00 -4.97660730e+00 1.22036745e+01 | 8.89285721e+00 -4.97660730e+00 1.22036745e+01 3 -4.50720444e+00 5.32343439e+00 3.48885782e+00 | -4.50720444e+00 5.32343439e+00 3.48885782e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FFT (Configuration in file "config-Ag-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)) = 16.0385006668 2^p V(r_1,...,r_N) = 16.0385006668 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 -1.17283317e+01 -1.08653195e+01 -1.48685519e+01 | -1.17283317e+01 -1.08653195e+01 -1.48685519e+01 1 1.52174684e+01 1.41794816e+01 -1.19800470e+01 | 1.52174684e+01 1.41794816e+01 -1.19800470e+01 2 1.94464763e+01 -2.32508344e+01 1.63651703e+01 | 1.94464763e+01 -2.32508344e+01 1.63651703e+01 3 -2.29356129e+01 1.99366723e+01 1.04834286e+01 | -2.29356129e+01 1.99366723e+01 1.04834286e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.15026782927 2^p V(r_1,...,r_N) = -2.15026782927 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 -8.90093779e+00 -4.35164302e+00 -1.02889979e+01 | -8.90093779e+00 -4.35164302e+00 -1.02889979e+01 1 3.48179330e+00 6.52035854e+00 -4.86200217e+00 | 3.48179330e+00 6.52035854e+00 -4.86200217e+00 2 1.24462387e+01 -9.40508649e+00 1.08674486e+01 | 1.24462387e+01 -9.40508649e+00 1.08674486e+01 3 -7.02709421e+00 7.23637098e+00 4.28355142e+00 | -7.02709421e+00 7.23637098e+00 4.28355142e+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)) = -0.889267416374 2^p V(r_1,...,r_N) = -0.889267416374 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 -7.11433774e+00 -4.87812704e+00 -5.51134578e+00 | -7.11433774e+00 -4.87812704e+00 -5.51134578e+00 1 4.89415326e+00 8.14481404e+00 -6.43795931e+00 | 4.89415326e+00 8.14481404e+00 -6.43795931e+00 2 1.59686552e+01 -1.46851283e+01 8.10555511e+00 | 1.59686552e+01 -1.46851283e+01 8.10555511e+00 3 -1.37484707e+01 1.14184413e+01 3.84374998e+00 | -1.37484707e+01 1.14184413e+01 3.84374998e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -5.01093560595 2^p V(r_1,...,r_N) = -5.01093560595 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 -7.50125696e-01 -1.36766130e+00 -1.06640974e+00 | -7.50125696e-01 -1.36766130e+00 -1.06640974e+00 1 1.92926481e+00 4.57542818e+00 -8.11952968e+00 | 1.92926481e+00 4.57542818e+00 -8.11952968e+00 2 2.48042566e+00 -7.27088024e+00 8.09634340e+00 | 2.48042566e+00 -7.27088024e+00 8.09634340e+00 3 -3.65956478e+00 4.06311336e+00 1.08959601e+00 | -3.65956478e+00 4.06311336e+00 1.08959601e+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)) = -5.29365565556 2^p V(r_1,...,r_N) = -5.29365565556 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 -4.21318007e+00 -4.72712556e+00 -7.77081159e+00 | -4.21318007e+00 -4.72712556e+00 -7.77081159e+00 1 2.69646869e+00 3.31054800e+00 -9.54191446e-01 | 2.69646869e+00 3.31054800e+00 -9.54191446e-01 2 4.31448444e+00 -2.41200393e+00 4.20423423e+00 | 4.31448444e+00 -2.41200393e+00 4.20423423e+00 3 -2.79777306e+00 3.82858148e+00 4.52076880e+00 | -2.79777306e+00 3.82858148e+00 4.52076880e+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)) = -4.52881054017 2^p V(r_1,...,r_N) = -4.52881054017 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 -6.26532523e+00 -3.33406509e+00 -5.35691509e+00 | -6.26532523e+00 -3.33406509e+00 -5.35691509e+00 1 4.74729433e+00 3.89096371e+00 -6.41611467e+00 | 4.74729433e+00 3.89096371e+00 -6.41611467e+00 2 5.94364468e+00 -2.04395465e+00 8.35793249e+00 | 5.94364468e+00 -2.04395465e+00 8.35793249e+00 3 -4.42561378e+00 1.48705603e+00 3.41509726e+00 | -4.42561378e+00 1.48705603e+00 3.41509726e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -5.46678081818 2^p V(r_1,...,r_N) = -5.46678081818 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 -3.59776887e+00 -5.69547377e+00 -1.32021487e+00 | -3.59776887e+00 -5.69547377e+00 -1.32021487e+00 1 6.55267653e+00 4.26702669e+00 -4.24680453e+00 | 6.55267653e+00 4.26702669e+00 -4.24680453e+00 2 9.27285635e-01 -1.54165084e+00 1.65658518e+00 | 9.27285635e-01 -1.54165084e+00 1.65658518e+00 3 -3.88219330e+00 2.97009793e+00 3.91043423e+00 | -3.88219330e+00 2.97009793e+00 3.91043423e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 3.80387588154 2^p V(r_1,...,r_N) = 3.80387588154 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 -2.36912783e+01 -1.45696293e+01 -2.17630147e+01 | -2.36912783e+01 -1.45696293e+01 -2.17630147e+01 1 4.50757330e+00 7.41273056e+00 -8.01116537e+00 | 4.50757330e+00 7.41273056e+00 -8.01116537e+00 2 2.88474157e+01 -5.64654427e+00 2.44323125e+01 | 2.88474157e+01 -5.64654427e+00 2.44323125e+01 3 -9.66371065e+00 1.28034430e+01 5.34186755e+00 | -9.66371065e+00 1.28034430e+01 5.34186755e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TTT (Configuration in file "config-AgCu-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)) = 6.46354296517 2^p V(r_1,...,r_N) = 6.46354296517 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 -1.98415884e+01 -1.12029956e+01 -1.57407363e+01 | -1.98415884e+01 -1.12029956e+01 -1.57407363e+01 1 2.16175503e+00 2.00425976e+01 -1.60530289e+01 | 2.16175503e+00 2.00425976e+01 -1.60530289e+01 2 2.28698435e+01 -1.46162068e+01 2.61689806e+01 | 2.28698435e+01 -1.46162068e+01 2.61689806e+01 3 -5.19001015e+00 5.77660475e+00 5.62478462e+00 | -5.19001015e+00 5.77660475e+00 5.62478462e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TTF (Configuration in file "config-AgCu-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)) = 2.73827237113 2^p V(r_1,...,r_N) = 2.73827237113 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 -7.84566419e+00 -1.00069890e+01 -5.29911584e+00 | -7.84566419e+00 -1.00069890e+01 -5.29911584e+00 1 1.24914203e+01 1.28035507e+01 -2.05070358e+01 | 1.24914203e+01 1.28035507e+01 -2.05070358e+01 2 6.68439370e+00 -8.42663304e+00 8.71174021e+00 | 6.68439370e+00 -8.42663304e+00 8.71174021e+00 3 -1.13301498e+01 5.63007133e+00 1.70944115e+01 | -1.13301498e+01 5.63007133e+00 1.70944115e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TFT (Configuration in file "config-AgCu-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)) = 4.1929141645 2^p V(r_1,...,r_N) = 4.1929141645 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 -1.41734117e+01 -6.61029650e+00 -1.03851730e+01 | -1.41734117e+01 -6.61029650e+00 -1.03851730e+01 1 5.80903465e+00 1.95755838e+01 -1.26989407e+01 | 5.80903465e+00 1.95755838e+01 -1.26989407e+01 2 1.10023449e+01 -1.55984937e+01 2.06262233e+01 | 1.10023449e+01 -1.55984937e+01 2.06262233e+01 3 -2.63796786e+00 2.63320643e+00 2.45789032e+00 | -2.63796786e+00 2.63320643e+00 2.45789032e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TFF (Configuration in file "config-AgCu-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)) = 8.65421887034 2^p V(r_1,...,r_N) = 8.65421887034 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 -1.44681511e+01 -1.28416057e+01 -9.16312593e+00 | -1.44681511e+01 -1.28416057e+01 -9.16312593e+00 1 1.60715663e+01 1.60956526e+01 -2.95267612e+01 | 1.60715663e+01 1.60956526e+01 -2.95267612e+01 2 1.26565221e+01 -1.27175208e+01 2.66761174e+01 | 1.26565221e+01 -1.27175208e+01 2.66761174e+01 3 -1.42599373e+01 9.46347390e+00 1.20137698e+01 | -1.42599373e+01 9.46347390e+00 1.20137698e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = FTT (Configuration in file "config-AgCu-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)) = 0.14578536858 2^p V(r_1,...,r_N) = 0.14578536858 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 -5.69891277e+00 -6.15771149e+00 -7.21597275e+00 | -5.69891277e+00 -6.15771149e+00 -7.21597275e+00 1 4.19977759e+00 8.15579494e+00 -1.09139630e+01 | 4.19977759e+00 8.15579494e+00 -1.09139630e+01 2 8.43418224e+00 -1.33819892e+01 1.24992350e+01 | 8.43418224e+00 -1.33819892e+01 1.24992350e+01 3 -6.93504706e+00 1.13839057e+01 5.63070075e+00 | -6.93504706e+00 1.13839057e+01 5.63070075e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = FTF (Configuration in file "config-AgCu-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)) = -3.01133921351 2^p V(r_1,...,r_N) = -3.01133921351 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 -2.91747283e+00 -2.07972086e+00 -9.89028485e-01 | -2.91747283e+00 -2.07972086e+00 -9.89028485e-01 1 9.44025861e+00 4.23423391e+00 -9.18178472e+00 | 9.44025861e+00 4.23423391e+00 -9.18178472e+00 2 1.48215561e+00 -5.09119306e+00 3.29711127e+00 | 1.48215561e+00 -5.09119306e+00 3.29711127e+00 3 -8.00494139e+00 2.93668001e+00 6.87370194e+00 | -8.00494139e+00 2.93668001e+00 6.87370194e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = FFT (Configuration in file "config-AgCu-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)) = -4.61909744137 2^p V(r_1,...,r_N) = -4.61909744137 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 -4.85228070e+00 -4.11502869e+00 -5.33134332e+00 | -4.85228070e+00 -4.11502869e+00 -5.33134332e+00 1 2.05493079e+00 2.74820156e+00 -1.39260310e+00 | 2.05493079e+00 2.74820156e+00 -1.39260310e+00 2 3.75036180e+00 -1.49846577e+00 4.21071860e+00 | 3.75036180e+00 -1.49846577e+00 4.21071860e+00 3 -9.53011891e-01 2.86529289e+00 2.51322782e+00 | -9.53011891e-01 2.86529289e+00 2.51322782e+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.