!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MendelevSordeletKramer_2007_CuZr__MO_120596890176_005 Supported species : Cu Zr random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.72759070817 2^p V(r_1,...,r_N) = -5.72759070817 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 -3.52819838e+00 -6.48382431e+00 -4.62339521e+00 | -3.52819838e+00 -6.48382431e+00 -4.62339521e+00 1 4.15847893e+00 2.48839850e+00 -2.97550102e+00 | 4.15847893e+00 2.48839850e+00 -2.97550102e+00 2 1.08259075e+00 -2.00282451e+00 2.27461486e+00 | 1.08259075e+00 -2.00282451e+00 2.27461486e+00 3 -1.71287130e+00 5.99825032e+00 5.32428137e+00 | -1.71287130e+00 5.99825032e+00 5.32428137e+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)) = -2.35030242088 2^p V(r_1,...,r_N) = -2.35030242088 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 -9.15699384e+00 -1.65780394e+01 -2.18823696e+01 | -9.15699384e+00 -1.65780394e+01 -2.18823696e+01 1 4.99049029e+00 1.20934241e+01 -1.13631658e+01 | 4.99049029e+00 1.20934241e+01 -1.13631658e+01 2 8.59963773e+00 -1.06862337e+01 1.96072463e+01 | 8.59963773e+00 -1.06862337e+01 1.96072463e+01 3 -4.43313418e+00 1.51708490e+01 1.36382891e+01 | -4.43313418e+00 1.51708490e+01 1.36382891e+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)) = -6.40095274291 2^p V(r_1,...,r_N) = -6.40095274291 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 -7.60193351e-01 -6.49808992e-01 -1.14657099e+00 | -7.60193351e-01 -6.49808992e-01 -1.14657099e+00 1 7.78073409e-01 7.41671350e-01 -1.35713785e+00 | 7.78073409e-01 7.41671350e-01 -1.35713785e+00 2 2.71144481e+00 -2.33930852e+00 1.21760315e+00 | 2.71144481e+00 -2.33930852e+00 1.21760315e+00 3 -2.72932487e+00 2.24744616e+00 1.28610569e+00 | -2.72932487e+00 2.24744616e+00 1.28610569e+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)) = -6.77810641812 2^p V(r_1,...,r_N) = -6.77810641812 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 -7.84621702e-01 -8.19907223e-01 -1.26847929e+00 | -7.84621702e-01 -8.19907223e-01 -1.26847929e+00 1 6.51896459e-01 7.74102944e-01 -7.37042302e-01 | 6.51896459e-01 7.74102944e-01 -7.37042302e-01 2 2.00868082e+00 -1.91639703e+00 8.94400546e-01 | 2.00868082e+00 -1.91639703e+00 8.94400546e-01 3 -1.87595558e+00 1.96220131e+00 1.11112105e+00 | -1.87595558e+00 1.96220131e+00 1.11112105e+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)) = 4.28766519413 2^p V(r_1,...,r_N) = 4.28766519413 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 -2.27901458e+01 -6.83613305e+00 -2.65851875e+01 | -2.27901458e+01 -6.83613305e+00 -2.65851875e+01 1 3.49552134e+01 -1.22238272e+00 -2.94518125e+01 | 3.49552134e+01 -1.22238272e+00 -2.94518125e+01 2 2.16296566e+01 -7.11650907e+00 2.18556926e+01 | 2.16296566e+01 -7.11650907e+00 2.18556926e+01 3 -3.37947242e+01 1.51750248e+01 3.41813074e+01 | -3.37947242e+01 1.51750248e+01 3.41813074e+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)) = 2.20278415895 2^p V(r_1,...,r_N) = 2.20278415895 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 -3.16117973e+01 -1.71310579e+01 -4.39645077e+01 | -3.16117973e+01 -1.71310579e+01 -4.39645077e+01 1 8.46710339e+00 9.02440144e+00 -3.78264546e+00 | 8.46710339e+00 9.02440144e+00 -3.78264546e+00 2 3.06266571e+01 -3.72372664e+00 3.53611393e+01 | 3.06266571e+01 -3.72372664e+00 3.53611393e+01 3 -7.48196311e+00 1.18303831e+01 1.23860138e+01 | -7.48196311e+00 1.18303831e+01 1.23860138e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.29709517035 2^p V(r_1,...,r_N) = -7.29709517035 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 -2.24687287e-01 -3.37309687e-01 -2.67579623e-01 | -2.24687287e-01 -3.37309687e-01 -2.67579623e-01 1 3.96013315e-01 -5.99197174e-02 4.22069813e-02 | 3.96013315e-01 -5.99197174e-02 4.22069813e-02 2 1.73308054e-01 2.19789567e-01 -1.57612082e-01 | 1.73308054e-01 2.19789567e-01 -1.57612082e-01 3 -3.44634082e-01 1.77439837e-01 3.82984724e-01 | -3.44634082e-01 1.77439837e-01 3.82984724e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TTT (Configuration in file "config-Zr-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -5.78368451716 2^p V(r_1,...,r_N) = -5.78368451716 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 -1.42592159e+01 -6.84154222e+00 -1.60909509e+01 | -1.42592159e+01 -6.84154222e+00 -1.60909509e+01 1 2.48605120e+00 1.23305533e+01 -9.30597310e+00 | 2.48605120e+00 1.23305533e+01 -9.30597310e+00 2 2.03949089e+01 -1.18076581e+01 2.19715329e+01 | 2.03949089e+01 -1.18076581e+01 2.19715329e+01 3 -8.62174423e+00 6.31864705e+00 3.42539111e+00 | -8.62174423e+00 6.31864705e+00 3.42539111e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TTF (Configuration in file "config-Zr-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 13.067848384 2^p V(r_1,...,r_N) = 13.067848384 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 -3.12462505e+01 -2.83407376e+01 -3.90798119e+01 | -3.12462505e+01 -2.83407376e+01 -3.90798119e+01 1 2.20106259e+01 2.31565462e+01 -1.88828763e+01 | 2.20106259e+01 2.31565462e+01 -1.88828763e+01 2 3.07267040e+01 -2.21745775e+01 3.88235458e+01 | 3.07267040e+01 -2.21745775e+01 3.88235458e+01 3 -2.14910794e+01 2.73587689e+01 1.91391424e+01 | -2.14910794e+01 2.73587689e+01 1.91391424e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TFT (Configuration in file "config-Zr-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 15.0582037853 2^p V(r_1,...,r_N) = 15.0582037853 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 -2.53861141e+01 -2.43496095e+01 -2.65159135e+01 | -2.53861141e+01 -2.43496095e+01 -2.65159135e+01 1 2.58632696e+01 2.78810177e+01 -3.24135129e+01 | 2.58632696e+01 2.78810177e+01 -3.24135129e+01 2 2.73586632e+01 -3.28730994e+01 3.98908466e+01 | 2.73586632e+01 -3.28730994e+01 3.98908466e+01 3 -2.78358187e+01 2.93416913e+01 1.90385798e+01 | -2.78358187e+01 2.93416913e+01 1.90385798e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = TFF (Configuration in file "config-Zr-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.96795461087 2^p V(r_1,...,r_N) = -7.96795461087 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 -1.68693845e+01 -7.50715105e+00 -1.25304711e+01 | -1.68693845e+01 -7.50715105e+00 -1.25304711e+01 1 1.24407933e+01 1.60296058e+01 -9.30645884e+00 | 1.24407933e+01 1.60296058e+01 -9.30645884e+00 2 8.38294046e+00 -1.63307363e+01 1.39790928e+01 | 8.38294046e+00 -1.63307363e+01 1.39790928e+01 3 -3.95434923e+00 7.80828154e+00 7.85783712e+00 | -3.95434923e+00 7.80828154e+00 7.85783712e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FTT (Configuration in file "config-Zr-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = -3.44128892697 2^p V(r_1,...,r_N) = -3.44128892697 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 -2.28894792e+01 -1.66855014e+01 -1.71626825e+01 | -2.28894792e+01 -1.66855014e+01 -1.71626825e+01 1 4.74531668e+00 2.01610657e+01 -1.01419615e+01 | 4.74531668e+00 2.01610657e+01 -1.01419615e+01 2 2.23852389e+01 -6.27036414e+00 2.28149548e+01 | 2.23852389e+01 -6.27036414e+00 2.28149548e+01 3 -4.24107641e+00 2.79479984e+00 4.48968920e+00 | -4.24107641e+00 2.79479984e+00 4.48968920e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FTF (Configuration in file "config-Zr-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -10.1949623581 2^p V(r_1,...,r_N) = -10.1949623581 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 -5.36563092e+00 -8.39472964e+00 -4.08051445e+00 | -5.36563092e+00 -8.39472964e+00 -4.08051445e+00 1 1.27722487e+01 4.83640581e+00 -1.18262223e+01 | 1.27722487e+01 4.83640581e+00 -1.18262223e+01 2 5.47116783e+00 -5.61485153e+00 2.83503128e+00 | 5.47116783e+00 -5.61485153e+00 2.83503128e+00 3 -1.28777857e+01 9.17317536e+00 1.30717055e+01 | -1.28777857e+01 9.17317536e+00 1.30717055e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Zr, PBC = FFT (Configuration in file "config-Zr-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=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)) = 2.8391244058 2^p V(r_1,...,r_N) = 2.8391244058 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 -2.68746702e+01 -2.35442321e+01 -2.08325529e+01 | -2.68746702e+01 -2.35442321e+01 -2.08325529e+01 1 1.52808514e+01 1.74197684e+01 -1.89949729e+01 | 1.52808514e+01 1.74197684e+01 -1.89949729e+01 2 2.09259658e+01 -1.44610137e+01 2.97886523e+01 | 2.09259658e+01 -1.44610137e+01 2.97886523e+01 3 -9.33214697e+00 2.05854774e+01 1.00388736e+01 | -9.33214697e+00 2.05854774e+01 1.00388736e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TTT (Configuration in file "config-CuZr-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)) = -8.18143871403 2^p V(r_1,...,r_N) = -8.18143871403 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 -1.48796859e+00 -8.99605011e+00 -6.30104651e+00 | -1.48796859e+00 -8.99605011e+00 -6.30104651e+00 1 5.59465532e+00 1.58394251e+00 -4.87465430e+00 | 5.59465532e+00 1.58394251e+00 -4.87465430e+00 2 1.67754177e+00 -2.38549077e+00 2.07488216e+00 | 1.67754177e+00 -2.38549077e+00 2.07488216e+00 3 -5.78422851e+00 9.79759837e+00 9.10081865e+00 | -5.78422851e+00 9.79759837e+00 9.10081865e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TTF (Configuration in file "config-CuZr-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)) = -6.90118881324 2^p V(r_1,...,r_N) = -6.90118881324 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 -1.08455726e+01 -1.42806254e+01 -4.02167826e+00 | -1.08455726e+01 -1.42806254e+01 -4.02167826e+00 1 1.31095431e+01 1.50847276e+01 -2.65556465e+00 | 1.31095431e+01 1.50847276e+01 -2.65556465e+00 2 7.64203686e+00 -8.50305371e+00 1.08128859e+00 | 7.64203686e+00 -8.50305371e+00 1.08128859e+00 3 -9.90600735e+00 7.69895155e+00 5.59595432e+00 | -9.90600735e+00 7.69895155e+00 5.59595432e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TFT (Configuration in file "config-CuZr-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)) = -9.711677518 2^p V(r_1,...,r_N) = -9.711677518 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 -8.94528028e+00 -2.05442507e+00 -5.93372660e+00 | -8.94528028e+00 -2.05442507e+00 -5.93372660e+00 1 1.40596112e+00 2.39716896e+00 -1.26700524e+00 | 1.40596112e+00 2.39716896e+00 -1.26700524e+00 2 8.45711145e+00 -2.17911892e+00 5.49508367e+00 | 8.45711145e+00 -2.17911892e+00 5.49508367e+00 3 -9.17792287e-01 1.83637504e+00 1.70564817e+00 | -9.17792287e-01 1.83637504e+00 1.70564817e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = TFF (Configuration in file "config-CuZr-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)) = 15.2393491625 2^p V(r_1,...,r_N) = 15.2393491625 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 -3.00095025e+01 -1.08050902e+01 -3.58413215e+01 | -3.00095025e+01 -1.08050902e+01 -3.58413215e+01 1 2.30497184e+01 3.81734926e+01 -3.59602307e+01 | 2.30497184e+01 3.81734926e+01 -3.59602307e+01 2 1.68539607e+01 -3.78450594e+01 6.53592744e+01 | 1.68539607e+01 -3.78450594e+01 6.53592744e+01 3 -9.89417652e+00 1.04766570e+01 6.44227775e+00 | -9.89417652e+00 1.04766570e+01 6.44227775e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = FTT (Configuration in file "config-CuZr-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)) = -6.87725919792 2^p V(r_1,...,r_N) = -6.87725919792 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 -1.10921444e+00 -1.30874330e+00 -9.06808281e-01 | -1.10921444e+00 -1.30874330e+00 -9.06808281e-01 1 1.52896569e+00 1.85559775e+00 -3.66453306e+00 | 1.52896569e+00 1.85559775e+00 -3.66453306e+00 2 1.30681436e+01 -1.24855207e+01 2.27471828e+00 | 1.30681436e+01 -1.24855207e+01 2.27471828e+00 3 -1.34878948e+01 1.19386662e+01 2.29662307e+00 | -1.34878948e+01 1.19386662e+01 2.29662307e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = FTF (Configuration in file "config-CuZr-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.95275317238 2^p V(r_1,...,r_N) = -1.95275317238 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 -2.33250065e+01 -1.03880318e+01 -2.55202888e+01 | -2.33250065e+01 -1.03880318e+01 -2.55202888e+01 1 7.81438848e+00 8.77463588e+00 -3.55845426e+00 | 7.81438848e+00 8.77463588e+00 -3.55845426e+00 2 2.60704553e+01 -1.38969563e+01 2.37308958e+01 | 2.60704553e+01 -1.38969563e+01 2.37308958e+01 3 -1.05598373e+01 1.55103522e+01 5.34784727e+00 | -1.05598373e+01 1.55103522e+01 5.34784727e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Cu Zr, PBC = FFT (Configuration in file "config-CuZr-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)) = -3.04889731348 2^p V(r_1,...,r_N) = -3.04889731348 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 -9.48976881e+00 -1.02260525e+01 -1.66203949e+01 | -9.48976881e+00 -1.02260525e+01 -1.66203949e+01 1 1.19551993e+01 7.12664726e+00 -1.12277182e+01 | 1.19551993e+01 7.12664726e+00 -1.12277182e+01 2 8.67533321e+00 -6.63355554e+00 4.38215435e+00 | 8.67533321e+00 -6.63355554e+00 4.38215435e+00 3 -1.11407637e+01 9.73296074e+00 2.34659588e+01 | -1.11407637e+01 9.73296074e+00 2.34659588e+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.