!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_ADP_StarikovLopanitsynaSmirnova_2018_SiAu__SM_985135773293_000 Supported species : Au Si random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ 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)) = 2.47190788025 2^p V(r_1,...,r_N) = 2.47190788025 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 -1.38935508e+01 -2.12049459e+01 -2.47126822e+01 | -1.38935508e+01 -2.12049459e+01 -2.47126822e+01 1 9.32847489e+00 6.30840932e+00 -5.85826557e+00 | 9.32847489e+00 6.30840932e+00 -5.85826557e+00 2 1.22349118e+01 -8.95459482e+00 1.32861608e+01 | 1.22349118e+01 -8.95459482e+00 1.32861608e+01 3 -7.66983586e+00 2.38511314e+01 1.72847870e+01 | -7.66983586e+00 2.38511314e+01 1.72847870e+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)) = 7.68444120711 2^p V(r_1,...,r_N) = 7.68444120711 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 -2.17658204e+01 -1.47130732e+01 -1.36038875e+01 | -2.17658204e+01 -1.47130732e+01 -1.36038875e+01 1 1.56683253e+01 1.29215558e+01 -1.91734366e+01 | 1.56683253e+01 1.29215558e+01 -1.91734366e+01 2 2.39277034e+01 -2.48458409e+01 2.42394592e+01 | 2.39277034e+01 -2.48458409e+01 2.42394592e+01 3 -1.78302083e+01 2.66373582e+01 8.53786489e+00 | -1.78302083e+01 2.66373582e+01 8.53786489e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 14.9919997939 2^p V(r_1,...,r_N) = 14.9919997939 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 -2.28441647e+01 -2.74492052e+01 -3.53568007e+01 | -2.28441647e+01 -2.74492052e+01 -3.53568007e+01 1 3.00450010e+01 3.02021645e+01 -1.78265953e+01 | 3.00450010e+01 3.02021645e+01 -1.78265953e+01 2 1.90167162e+01 -2.57864951e+01 2.77454925e+01 | 1.90167162e+01 -2.57864951e+01 2.77454925e+01 3 -2.62175526e+01 2.30335357e+01 2.54379035e+01 | -2.62175526e+01 2.30335357e+01 2.54379035e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 33.1016614789 2^p V(r_1,...,r_N) = 33.1016614789 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 -3.29435560e+01 -3.11593774e+01 -4.41879936e+01 | -3.29435560e+01 -3.11593774e+01 -4.41879936e+01 1 2.47407220e+01 3.02805140e+01 -2.01728486e+01 | 2.47407220e+01 3.02805140e+01 -2.01728486e+01 2 3.88313754e+01 -3.19205527e+01 3.94513467e+01 | 3.88313754e+01 -3.19205527e+01 3.94513467e+01 3 -3.06285414e+01 3.27994162e+01 2.49094955e+01 | -3.06285414e+01 3.27994162e+01 2.49094955e+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)) = 14.0891483246 2^p V(r_1,...,r_N) = 14.0891483246 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 -3.05284633e+01 -2.22706928e+01 -2.93440716e+01 | -3.05284633e+01 -2.22706928e+01 -2.93440716e+01 1 2.12266571e+01 2.68852821e+01 -2.28133782e+01 | 2.12266571e+01 2.68852821e+01 -2.28133782e+01 2 2.90690705e+01 -3.06965823e+01 2.63196430e+01 | 2.90690705e+01 -3.06965823e+01 2.63196430e+01 3 -1.97672643e+01 2.60819929e+01 2.58378068e+01 | -1.97672643e+01 2.60819929e+01 2.58378068e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 2.55363716175 2^p V(r_1,...,r_N) = 2.55363716175 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 -2.53472939e+01 -1.95454188e+01 -1.38449672e+01 | -2.53472939e+01 -1.95454188e+01 -1.38449672e+01 1 1.56800904e+01 2.04028189e+01 -1.75074399e+01 | 1.56800904e+01 2.04028189e+01 -1.75074399e+01 2 1.67717503e+01 -8.86977987e+00 2.57492525e+01 | 1.67717503e+01 -8.86977987e+00 2.57492525e+01 3 -7.10454680e+00 8.01237974e+00 5.60315459e+00 | -7.10454680e+00 8.01237974e+00 5.60315459e+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)) = 27.4422824097 2^p V(r_1,...,r_N) = 27.4422824097 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 -2.50062949e+01 -2.27103238e+01 -3.08573190e+01 | -2.50062949e+01 -2.27103238e+01 -3.08573190e+01 1 3.13793675e+01 2.89168455e+01 -2.33434358e+01 | 3.13793675e+01 2.89168455e+01 -2.33434358e+01 2 3.29595255e+01 -4.01648485e+01 3.31957103e+01 | 3.29595255e+01 -4.01648485e+01 3.31957103e+01 3 -3.93325981e+01 3.39583269e+01 2.10050445e+01 | -3.93325981e+01 3.39583269e+01 2.10050445e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTT (Configuration in file "config-Si-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.16729031291 2^p V(r_1,...,r_N) = -6.16729031291 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 -7.37094049e+00 -4.95726980e+00 -8.65157707e+00 | -7.37094049e+00 -4.95726980e+00 -8.65157707e+00 1 4.58925089e+00 6.72943163e+00 -5.31230051e+00 | 4.58925089e+00 6.72943163e+00 -5.31230051e+00 2 9.29137702e+00 -8.25293119e+00 8.83052015e+00 | 9.29137702e+00 -8.25293119e+00 8.83052015e+00 3 -6.50968742e+00 6.48076936e+00 5.13335743e+00 | -6.50968742e+00 6.48076936e+00 5.13335743e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TTF (Configuration in file "config-Si-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)) = -5.5832557358 2^p V(r_1,...,r_N) = -5.5832557358 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 -7.35729270e+00 -5.49724360e+00 -6.33290243e+00 | -7.35729270e+00 -5.49724360e+00 -6.33290243e+00 1 5.52625357e+00 7.72201874e+00 -6.35987355e+00 | 5.52625357e+00 7.72201874e+00 -6.35987355e+00 2 9.30383962e+00 -8.47828128e+00 9.02212576e+00 | 9.30383962e+00 -8.47828128e+00 9.02212576e+00 3 -7.47280050e+00 6.25350615e+00 3.67065022e+00 | -7.47280050e+00 6.25350615e+00 3.67065022e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFT (Configuration in file "config-Si-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)) = -9.27520377785 2^p V(r_1,...,r_N) = -9.27520377785 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 -2.01722991e+00 -2.32875313e+00 -2.04329730e+00 | -2.01722991e+00 -2.32875313e+00 -2.04329730e+00 1 2.86120805e+00 3.63292766e+00 -6.58474012e+00 | 2.86120805e+00 3.63292766e+00 -6.58474012e+00 2 3.65070832e+00 -6.26373192e+00 6.61486633e+00 | 3.65070832e+00 -6.26373192e+00 6.61486633e+00 3 -4.49468646e+00 4.95955739e+00 2.01317110e+00 | -4.49468646e+00 4.95955739e+00 2.01317110e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = TFF (Configuration in file "config-Si-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.89766002152 2^p V(r_1,...,r_N) = -8.89766002152 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 -2.44911102e+00 -5.89730140e+00 -4.86198072e+00 | -2.44911102e+00 -5.89730140e+00 -4.86198072e+00 1 3.11170035e+00 3.14034498e+00 -4.11611156e+00 | 3.11170035e+00 3.14034498e+00 -4.11611156e+00 2 1.77412188e+00 -3.28567803e+00 2.96535184e+00 | 1.77412188e+00 -3.28567803e+00 2.96535184e+00 3 -2.43671121e+00 6.04263445e+00 6.01274044e+00 | -2.43671121e+00 6.04263445e+00 6.01274044e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTT (Configuration in file "config-Si-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)) = -11.225263845 2^p V(r_1,...,r_N) = -11.225263845 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 -1.84484867e+00 -1.84368862e+00 -8.23654657e-01 | -1.84484867e+00 -1.84368862e+00 -8.23654657e-01 1 3.78289994e+00 2.85500335e+00 -2.70589326e+00 | 3.78289994e+00 2.85500335e+00 -2.70589326e+00 2 2.14104488e-01 -1.81611513e+00 1.55385819e+00 | 2.14104488e-01 -1.81611513e+00 1.55385819e+00 3 -2.15215576e+00 8.04800401e-01 1.97568973e+00 | -2.15215576e+00 8.04800401e-01 1.97568973e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FTF (Configuration in file "config-Si-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)) = -9.48535750328 2^p V(r_1,...,r_N) = -9.48535750328 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 -2.33253025e+00 -2.72186278e+00 -4.36903926e+00 | -2.33253025e+00 -2.72186278e+00 -4.36903926e+00 1 3.42707322e+00 5.33710070e+00 -4.44337121e+00 | 3.42707322e+00 5.33710070e+00 -4.44337121e+00 2 2.40351697e+00 -6.55689597e+00 5.71821295e+00 | 2.40351697e+00 -6.55689597e+00 5.71821295e+00 3 -3.49805995e+00 3.94165805e+00 3.09419751e+00 | -3.49805995e+00 3.94165805e+00 3.09419751e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Si, PBC = FFT (Configuration in file "config-Si-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)) = 0.916088783369 2^p V(r_1,...,r_N) = 0.916088783369 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 -9.02379047e+00 -2.66772269e+01 -1.90099283e+01 | -9.02379047e+00 -2.66772269e+01 -1.90099283e+01 1 9.17659113e+00 6.98550923e+00 -8.81270938e+00 | 9.17659113e+00 6.98550923e+00 -8.81270938e+00 2 7.04282103e+00 -3.91758535e+00 4.09684903e+00 | 7.04282103e+00 -3.91758535e+00 4.09684903e+00 3 -7.19562168e+00 2.36093030e+01 2.37257886e+01 | -7.19562168e+00 2.36093030e+01 2.37257886e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = TTT (Configuration in file "config-AuSi-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.47715280275 2^p V(r_1,...,r_N) = -6.47715280275 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 -6.51960429e+00 -7.38676538e+00 -5.36998148e+00 | -6.51960429e+00 -7.38676538e+00 -5.36998148e+00 1 1.23044988e+01 6.51819458e+00 -9.19469946e+00 | 1.23044988e+01 6.51819458e+00 -9.19469946e+00 2 2.49913652e+00 -7.51150052e+00 6.48217895e+00 | 2.49913652e+00 -7.51150052e+00 6.48217895e+00 3 -8.28403098e+00 8.38007132e+00 8.08250199e+00 | -8.28403098e+00 8.38007132e+00 8.08250199e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = TTF (Configuration in file "config-AuSi-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)) = -6.98609095737 2^p V(r_1,...,r_N) = -6.98609095737 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 -1.16717364e+01 -9.41416989e+00 -2.08898319e+00 | -1.16717364e+01 -9.41416989e+00 -2.08898319e+00 1 1.09468273e+01 7.52902553e+00 -4.04920498e+00 | 1.09468273e+01 7.52902553e+00 -4.04920498e+00 2 1.19672254e+00 -1.70557161e+00 1.51643583e+00 | 1.19672254e+00 -1.70557161e+00 1.51643583e+00 3 -4.71813414e-01 3.59071598e+00 4.62175234e+00 | -4.71813414e-01 3.59071598e+00 4.62175234e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = TFT (Configuration in file "config-AuSi-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)) = 0.975565824075 2^p V(r_1,...,r_N) = 0.975565824075 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 -1.51602001e+01 -1.56889353e+01 -1.04917738e+01 | -1.51602001e+01 -1.56889353e+01 -1.04917738e+01 1 1.28661739e+01 9.39354885e+00 -1.43355973e+01 | 1.28661739e+01 9.39354885e+00 -1.43355973e+01 2 1.07075203e+01 -1.12038518e+01 9.57937276e+00 | 1.07075203e+01 -1.12038518e+01 9.57937276e+00 3 -8.41349408e+00 1.74992382e+01 1.52479983e+01 | -8.41349408e+00 1.74992382e+01 1.52479983e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = TFF (Configuration in file "config-AuSi-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 18.203896684 2^p V(r_1,...,r_N) = 18.203896684 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 -2.02366633e+01 -2.75848478e+01 -3.20129200e+01 | -2.02366633e+01 -2.75848478e+01 -3.20129200e+01 1 1.63003332e+01 1.37455592e+01 -1.48211011e+01 | 1.63003332e+01 1.37455592e+01 -1.48211011e+01 2 1.65463088e+01 -1.67726040e+01 1.18933733e+01 | 1.65463088e+01 -1.67726040e+01 1.18933733e+01 3 -1.26099787e+01 3.06118926e+01 3.49406479e+01 | -1.26099787e+01 3.06118926e+01 3.49406479e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = FTT (Configuration in file "config-AuSi-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)) = -10.9577828483 2^p V(r_1,...,r_N) = -10.9577828483 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 -1.34243096e+00 -3.92706871e+00 -2.38907820e+00 | -1.34243096e+00 -3.92706871e+00 -2.38907820e+00 1 2.52835793e+00 1.30107711e+00 -2.40999844e-01 | 2.52835793e+00 1.30107711e+00 -2.40999844e-01 2 2.81674330e-01 -1.86987394e-01 -1.62591836e-01 | 2.81674330e-01 -1.86987394e-01 -1.62591836e-01 3 -1.46760130e+00 2.81297899e+00 2.79266989e+00 | -1.46760130e+00 2.81297899e+00 2.79266989e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = FTF (Configuration in file "config-AuSi-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)) = -5.08245106369 2^p V(r_1,...,r_N) = -5.08245106369 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 -1.23682615e+01 -1.69050889e+01 -3.71253055e+00 | -1.23682615e+01 -1.69050889e+01 -3.71253055e+00 1 1.18952748e+01 2.02722844e+01 -8.30741297e+00 | 1.18952748e+01 2.02722844e+01 -8.30741297e+00 2 5.62492300e+00 -5.67443969e+00 5.16674438e+00 | 5.62492300e+00 -5.67443969e+00 5.16674438e+00 3 -5.15193631e+00 2.30724420e+00 6.85319913e+00 | -5.15193631e+00 2.30724420e+00 6.85319913e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Au Si, PBC = FFT (Configuration in file "config-AuSi-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.97874513074 2^p V(r_1,...,r_N) = -9.97874513074 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 -6.79975667e+00 -1.67712086e+00 -6.80786610e+00 | -6.79975667e+00 -1.67712086e+00 -6.80786610e+00 1 1.48208446e+00 1.26028898e+00 -1.13271145e+00 | 1.48208446e+00 1.26028898e+00 -1.13271145e+00 2 6.34640174e+00 -9.41487750e-01 6.32391753e+00 | 6.34640174e+00 -9.41487750e-01 6.32391753e+00 3 -1.02872953e+00 1.35831963e+00 1.61666002e+00 | -1.02872953e+00 1.35831963e+00 1.61666002e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.