!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ZhouJohnsonWadley_2004NISTretabulation_CuAgAu__MO_318213562153_000 Supported species : Ag Au 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)) = 2.23941499193 2^p V(r_1,...,r_N) = 2.23941499193 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 -7.85992963e+00 -1.52618765e+01 -1.65399208e+01 | -7.85992963e+00 -1.52618765e+01 -1.65399208e+01 1 5.44696525e+00 3.70592235e+00 -3.26313834e+00 | 5.44696525e+00 3.70592235e+00 -3.26313834e+00 2 6.81835378e+00 -4.98225631e+00 7.39332944e+00 | 6.81835378e+00 -4.98225631e+00 7.39332944e+00 3 -4.40538941e+00 1.65382105e+01 1.24097297e+01 | -4.40538941e+00 1.65382105e+01 1.24097297e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 5.26447470684 2^p V(r_1,...,r_N) = 5.26447470684 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 -1.20000111e+01 -8.03988774e+00 -7.74766220e+00 | -1.20000111e+01 -8.03988774e+00 -7.74766220e+00 1 8.50938884e+00 7.10461182e+00 -1.07848313e+01 | 8.50938884e+00 7.10461182e+00 -1.07848313e+01 2 1.69368024e+01 -1.85920327e+01 1.39029554e+01 | 1.69368024e+01 -1.85920327e+01 1.39029554e+01 3 -1.34461801e+01 1.95273086e+01 4.62953807e+00 | -1.34461801e+01 1.95273086e+01 4.62953807e+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)) = 9.12792290953 2^p V(r_1,...,r_N) = 9.12792290953 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 -1.29992479e+01 -1.82058267e+01 -2.27172631e+01 | -1.29992479e+01 -1.82058267e+01 -2.27172631e+01 1 1.74598933e+01 1.77725340e+01 -1.00210715e+01 | 1.74598933e+01 1.77725340e+01 -1.00210715e+01 2 1.06805753e+01 -1.46622619e+01 1.58944180e+01 | 1.06805753e+01 -1.46622619e+01 1.58944180e+01 3 -1.51412207e+01 1.50955546e+01 1.68439167e+01 | -1.51412207e+01 1.50955546e+01 1.68439167e+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)) = 25.0767615371 2^p V(r_1,...,r_N) = 25.0767615371 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 -3.36033082e+01 -2.76647644e+01 -5.49808408e+01 | -3.36033082e+01 -2.76647644e+01 -5.49808408e+01 1 1.49017917e+01 1.86911712e+01 -1.20727810e+01 | 1.49017917e+01 1.86911712e+01 -1.20727810e+01 2 4.13874879e+01 -2.16263494e+01 4.19091024e+01 | 4.13874879e+01 -2.16263494e+01 4.19091024e+01 3 -2.26859713e+01 3.05999425e+01 2.51445194e+01 | -2.26859713e+01 3.05999425e+01 2.51445194e+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)) = 8.51209732689 2^p V(r_1,...,r_N) = 8.51209732689 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 -1.81826438e+01 -1.26996404e+01 -1.77301840e+01 | -1.81826438e+01 -1.26996404e+01 -1.77301840e+01 1 1.16393339e+01 1.59461471e+01 -1.32834456e+01 | 1.16393339e+01 1.59461471e+01 -1.32834456e+01 2 1.74646978e+01 -1.83582773e+01 1.64365110e+01 | 1.74646978e+01 -1.83582773e+01 1.64365110e+01 3 -1.09213878e+01 1.51117706e+01 1.45771186e+01 | -1.09213878e+01 1.51117706e+01 1.45771186e+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)) = 2.05891588362 2^p V(r_1,...,r_N) = 2.05891588362 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 -1.39049855e+01 -1.10646765e+01 -7.74415811e+00 | -1.39049855e+01 -1.10646765e+01 -7.74415811e+00 1 8.55274659e+00 1.12435539e+01 -9.30237418e+00 | 8.55274659e+00 1.12435539e+01 -9.30237418e+00 2 9.35891128e+00 -4.93105282e+00 1.38878439e+01 | 9.35891128e+00 -4.93105282e+00 1.38878439e+01 3 -4.00667234e+00 4.75217539e+00 3.15868835e+00 | -4.00667234e+00 4.75217539e+00 3.15868835e+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)) = 21.6826683182 2^p V(r_1,...,r_N) = 21.6826683182 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 -1.50468176e+01 -1.35694470e+01 -1.78886012e+01 | -1.50468176e+01 -1.35694470e+01 -1.78886012e+01 1 1.93955250e+01 1.95859709e+01 -1.61650447e+01 | 1.93955250e+01 1.95859709e+01 -1.61650447e+01 2 4.14338815e+01 -4.67762630e+01 2.20290681e+01 | 4.14338815e+01 -4.67762630e+01 2.20290681e+01 3 -4.57825888e+01 4.07597392e+01 1.20245779e+01 | -4.57825888e+01 4.07597392e+01 1.20245779e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = TTT (Configuration in file "config-Au-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)) = 4.84604564297 2^p V(r_1,...,r_N) = 4.84604564297 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 -1.92679126e+01 -1.09245473e+01 -2.23124976e+01 | -1.92679126e+01 -1.09245473e+01 -2.23124976e+01 1 9.63284724e+00 1.51106970e+01 -1.16507160e+01 | 9.63284724e+00 1.51106970e+01 -1.16507160e+01 2 2.54956274e+01 -2.00139269e+01 2.27842229e+01 | 2.54956274e+01 -2.00139269e+01 2.27842229e+01 3 -1.58605620e+01 1.58277772e+01 1.11789907e+01 | -1.58605620e+01 1.58277772e+01 1.11789907e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = TTF (Configuration in file "config-Au-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)) = 6.99323063938 2^p V(r_1,...,r_N) = 6.99323063938 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 -1.61163566e+01 -1.21263001e+01 -1.39867593e+01 | -1.61163566e+01 -1.21263001e+01 -1.39867593e+01 1 1.21337339e+01 1.79586086e+01 -1.51090258e+01 | 1.21337339e+01 1.79586086e+01 -1.51090258e+01 2 3.01090027e+01 -2.76379097e+01 1.90464934e+01 | 3.01090027e+01 -2.76379097e+01 1.90464934e+01 3 -2.61263800e+01 2.18056013e+01 1.00492918e+01 | -2.61263800e+01 2.18056013e+01 1.00492918e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = TFT (Configuration in file "config-Au-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)) = -2.12348190659 2^p V(r_1,...,r_N) = -2.12348190659 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 -4.10816998e+00 -4.80242995e+00 -4.10246869e+00 | -4.10816998e+00 -4.80242995e+00 -4.10246869e+00 1 6.44798325e+00 9.64435382e+00 -1.73082082e+01 | 6.44798325e+00 9.64435382e+00 -1.73082082e+01 2 7.09717511e+00 -1.51813674e+01 1.72655015e+01 | 7.09717511e+00 -1.51813674e+01 1.72655015e+01 3 -9.43698838e+00 1.03394435e+01 4.14517537e+00 | -9.43698838e+00 1.03394435e+01 4.14517537e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = TFF (Configuration in file "config-Au-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)) = -0.633583948246 2^p V(r_1,...,r_N) = -0.633583948246 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 -6.34102572e+00 -2.08775682e+01 -1.73410109e+01 | -6.34102572e+00 -2.08775682e+01 -1.73410109e+01 1 6.63778033e+00 6.35327835e+00 -8.52400047e+00 | 6.63778033e+00 6.35327835e+00 -8.52400047e+00 2 3.70466728e+00 -6.67073973e+00 6.01691691e+00 | 3.70466728e+00 -6.67073973e+00 6.01691691e+00 3 -4.00142189e+00 2.11950296e+01 1.98480945e+01 | -4.00142189e+00 2.11950296e+01 1.98480945e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = FTT (Configuration in file "config-Au-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)) = -6.36873258454 2^p V(r_1,...,r_N) = -6.36873258454 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 -3.97070684e+00 -3.90717065e+00 -1.99833651e+00 | -3.97070684e+00 -3.90717065e+00 -1.99833651e+00 1 7.78895374e+00 5.95231663e+00 -5.58776825e+00 | 7.78895374e+00 5.95231663e+00 -5.58776825e+00 2 7.31724922e-01 -3.96238924e+00 3.42966738e+00 | 7.31724922e-01 -3.96238924e+00 3.42966738e+00 3 -4.54997182e+00 1.91724326e+00 4.15643737e+00 | -4.54997182e+00 1.91724326e+00 4.15643737e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = FTF (Configuration in file "config-Au-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)) = -2.68865714347 2^p V(r_1,...,r_N) = -2.68865714347 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 -4.92143313e+00 -5.55831908e+00 -9.04359854e+00 | -4.92143313e+00 -5.55831908e+00 -9.04359854e+00 1 7.55014102e+00 1.29958142e+01 -1.08804043e+01 | 7.55014102e+00 1.29958142e+01 -1.08804043e+01 2 4.62260455e+00 -1.56175543e+01 1.36684385e+01 | 4.62260455e+00 -1.56175543e+01 1.36684385e+01 3 -7.25131245e+00 8.18005922e+00 6.25556433e+00 | -7.25131245e+00 8.18005922e+00 6.25556433e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Au, PBC = FFT (Configuration in file "config-Au-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)) = 32.324753581 2^p V(r_1,...,r_N) = 32.324753581 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 -2.72572826e+01 -9.08620301e+01 -7.04574374e+01 | -2.72572826e+01 -9.08620301e+01 -7.04574374e+01 1 2.44577588e+01 1.82122156e+01 -2.30009543e+01 | 2.44577588e+01 1.82122156e+01 -2.30009543e+01 2 2.28799541e+01 -1.29175373e+01 1.36306177e+01 | 2.28799541e+01 -1.29175373e+01 1.36306177e+01 3 -2.00804304e+01 8.55673519e+01 7.98277740e+01 | -2.00804304e+01 8.55673519e+01 7.98277740e+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)) = -0.795964921355 2^p V(r_1,...,r_N) = -0.795964921355 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 -1.88041942e+00 -1.82162461e+00 -1.65154547e+00 | -1.88041942e+00 -1.82162461e+00 -1.65154547e+00 1 4.29841548e+00 7.73986095e+00 -1.19337215e+01 | 4.29841548e+00 7.73986095e+00 -1.19337215e+01 2 7.12488653e+00 -1.32077454e+01 9.83462263e+00 | 7.12488653e+00 -1.32077454e+01 9.83462263e+00 3 -9.54288259e+00 7.28950911e+00 3.75064430e+00 | -9.54288259e+00 7.28950911e+00 3.75064430e+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)) = 3.29971956153 2^p V(r_1,...,r_N) = 3.29971956153 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 -8.11472554e+00 -1.48587028e+01 -1.38631523e+01 | -8.11472554e+00 -1.48587028e+01 -1.38631523e+01 1 1.72632194e+01 1.44030966e+01 -6.11124351e+00 | 1.72632194e+01 1.44030966e+01 -6.11124351e+00 2 7.11801560e+00 -8.33337810e+00 6.71967747e+00 | 7.11801560e+00 -8.33337810e+00 6.71967747e+00 3 -1.62665094e+01 8.78898430e+00 1.32547183e+01 | -1.62665094e+01 8.78898430e+00 1.32547183e+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)) = 6.00053954787 2^p V(r_1,...,r_N) = 6.00053954787 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.59240919e+00 -2.28548684e+01 -2.44355583e+01 | -9.59240919e+00 -2.28548684e+01 -2.44355583e+01 1 6.53386051e+00 8.66914574e+00 -8.55619983e+00 | 6.53386051e+00 8.66914574e+00 -8.55619983e+00 2 1.07766300e+01 -9.62818584e+00 9.15692634e+00 | 1.07766300e+01 -9.62818584e+00 9.15692634e+00 3 -7.71808130e+00 2.38139085e+01 2.38348318e+01 | -7.71808130e+00 2.38139085e+01 2.38348318e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.49966882452 2^p V(r_1,...,r_N) = -1.49966882452 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 -7.16403884e+00 -2.24164985e+00 -8.89454996e+00 | -7.16403884e+00 -2.24164985e+00 -8.89454996e+00 1 2.92776331e+00 3.32464300e+00 -1.20137293e+00 | 2.92776331e+00 3.32464300e+00 -1.20137293e+00 2 9.61275379e+00 -9.22869299e+00 7.33839684e+00 | 9.61275379e+00 -9.22869299e+00 7.33839684e+00 3 -5.37647826e+00 8.14569985e+00 2.75752605e+00 | -5.37647826e+00 8.14569985e+00 2.75752605e+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)) = 0.634703997277 2^p V(r_1,...,r_N) = 0.634703997277 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 -7.29333354e+00 -1.55052743e+01 -1.18252526e+01 | -7.29333354e+00 -1.55052743e+01 -1.18252526e+01 1 7.49497514e+00 7.96560280e+00 -6.91366769e+00 | 7.49497514e+00 7.96560280e+00 -6.91366769e+00 2 2.94590004e+00 -4.78523293e+00 5.24707164e+00 | 2.94590004e+00 -4.78523293e+00 5.24707164e+00 3 -3.14754165e+00 1.23249044e+01 1.34918486e+01 | -3.14754165e+00 1.23249044e+01 1.34918486e+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)) = -0.332981396089 2^p V(r_1,...,r_N) = -0.332981396089 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 -6.33549937e+00 -5.38746542e+00 -3.71950238e+00 | -6.33549937e+00 -5.38746542e+00 -3.71950238e+00 1 7.19458448e+00 7.75690339e+00 -1.39196066e+01 | 7.19458448e+00 7.75690339e+00 -1.39196066e+01 2 6.77203735e+00 -7.61111962e+00 1.26151599e+01 | 6.77203735e+00 -7.61111962e+00 1.26151599e+01 3 -7.63112247e+00 5.24168165e+00 5.02394914e+00 | -7.63112247e+00 5.24168165e+00 5.02394914e+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)) = 5.95771751363 2^p V(r_1,...,r_N) = 5.95771751363 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 -1.27703244e+01 -6.48273117e+00 -1.72184261e+01 | -1.27703244e+01 -6.48273117e+00 -1.72184261e+01 1 1.24394394e+01 1.54520562e+01 -1.35905611e+01 | 1.24394394e+01 1.54520562e+01 -1.35905611e+01 2 1.01087031e+01 -1.89501901e+01 2.60124376e+01 | 1.01087031e+01 -1.89501901e+01 2.60124376e+01 3 -9.77781808e+00 9.98086509e+00 4.79654952e+00 | -9.77781808e+00 9.98086509e+00 4.79654952e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = TTT (Configuration in file "config-AgAuCu-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)) = -3.96496784564 2^p V(r_1,...,r_N) = -3.96496784564 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 -4.83432755e-01 -6.04134658e-01 -2.08988805e-01 | -4.83432755e-01 -6.04134658e-01 -2.08988805e-01 1 1.22836004e+00 1.66845927e+00 -2.67321124e+00 | 1.22836004e+00 1.66845927e+00 -2.67321124e+00 2 6.19962068e+00 -6.73577331e+00 1.93858624e+00 | 6.19962068e+00 -6.73577331e+00 1.93858624e+00 3 -6.94454796e+00 5.67144869e+00 9.43613806e-01 | -6.94454796e+00 5.67144869e+00 9.43613806e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = TTF (Configuration in file "config-AgAuCu-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)) = -4.1650973879 2^p V(r_1,...,r_N) = -4.1650973879 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 -3.84988415e+00 -5.07743250e+00 -3.97122394e+00 | -3.84988415e+00 -5.07743250e+00 -3.97122394e+00 1 4.15092536e+00 3.17312850e+00 -2.55408076e+00 | 4.15092536e+00 3.17312850e+00 -2.55408076e+00 2 1.69624110e+00 -7.81006586e-01 2.46640762e+00 | 1.69624110e+00 -7.81006586e-01 2.46640762e+00 3 -1.99728231e+00 2.68531059e+00 4.05889708e+00 | -1.99728231e+00 2.68531059e+00 4.05889708e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = TFT (Configuration in file "config-AgAuCu-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)) = 1.32967470998 2^p V(r_1,...,r_N) = 1.32967470998 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 -5.95781399e+00 -6.58994774e+00 -3.83469481e+00 | -5.95781399e+00 -6.58994774e+00 -3.83469481e+00 1 7.90005078e+00 1.80753220e+01 -1.74557960e+01 | 7.90005078e+00 1.80753220e+01 -1.74557960e+01 2 6.67082634e+00 -1.51857390e+01 1.51410924e+01 | 6.67082634e+00 -1.51857390e+01 1.51410924e+01 3 -8.61306313e+00 3.70036467e+00 6.14939835e+00 | -8.61306313e+00 3.70036467e+00 6.14939835e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = TFF (Configuration in file "config-AgAuCu-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)) = -0.565648023592 2^p V(r_1,...,r_N) = -0.565648023592 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 -4.98975305e+00 -1.11632351e+01 -1.60333829e+01 | -4.98975305e+00 -1.11632351e+01 -1.60333829e+01 1 5.19468332e+00 4.32000158e+00 -1.81221693e+00 | 5.19468332e+00 4.32000158e+00 -1.81221693e+00 2 2.19340002e+00 -2.82525761e+00 2.47404601e+00 | 2.19340002e+00 -2.82525761e+00 2.47404601e+00 3 -2.39833029e+00 9.66849115e+00 1.53715538e+01 | -2.39833029e+00 9.66849115e+00 1.53715538e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = FTT (Configuration in file "config-AgAuCu-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)) = 1.56278259221 2^p V(r_1,...,r_N) = 1.56278259221 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 -7.27964429e+00 -7.29130517e+00 -7.78625956e+00 | -7.27964429e+00 -7.29130517e+00 -7.78625956e+00 1 1.58856854e+00 1.75127380e+01 -1.39713217e+01 | 1.58856854e+00 1.75127380e+01 -1.39713217e+01 2 7.92567144e+00 -1.62467522e+01 1.66628027e+01 | 7.92567144e+00 -1.62467522e+01 1.66628027e+01 3 -2.23459569e+00 6.02531927e+00 5.09477853e+00 | -2.23459569e+00 6.02531927e+00 5.09477853e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = FTF (Configuration in file "config-AgAuCu-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)) = 5.56536900026 2^p V(r_1,...,r_N) = 5.56536900026 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 -6.51346096e+00 -4.28983973e+00 -6.93009208e+00 | -6.51346096e+00 -4.28983973e+00 -6.93009208e+00 1 9.66806599e+00 1.85959489e+01 -1.70124235e+01 | 9.66806599e+00 1.85959489e+01 -1.70124235e+01 2 1.44055020e+01 -2.56558899e+01 1.17824549e+01 | 1.44055020e+01 -2.56558899e+01 1.17824549e+01 3 -1.75601071e+01 1.13497807e+01 1.21600607e+01 | -1.75601071e+01 1.13497807e+01 1.21600607e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Au Cu, PBC = FFT (Configuration in file "config-AgAuCu-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)) = 4.89396086526 2^p V(r_1,...,r_N) = 4.89396086526 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 -4.71235314e+00 -1.02025673e+01 -7.84378960e+00 | -4.71235314e+00 -1.02025673e+01 -7.84378960e+00 1 1.88006111e+01 1.10372013e+01 -2.00072967e+01 | 1.88006111e+01 1.10372013e+01 -2.00072967e+01 2 8.81866270e+00 -9.63084918e+00 8.03322810e+00 | 8.81866270e+00 -9.63084918e+00 8.03322810e+00 3 -2.29069206e+01 8.79621510e+00 1.98178582e+01 | -2.29069206e+01 8.79621510e+00 1.98178582e+01 ------------------------------------------------------------------------------------------------------------------------ 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.