!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Polymorphic_NordAlbeErhart_2003_GaN__SM_333071728528_000 Supported species : Ga N random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = TTT (Configuration in file "config-Ga-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)) = -4.26497008806 2^p V(r_1,...,r_N) = -4.26497008806 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 -1.95723744e+00 -3.61626563e+00 -4.01357998e+00 | -1.95723744e+00 -3.61626563e+00 -4.01357998e+00 1 1.23858244e+00 8.76512914e-01 -7.09859903e-01 | 1.23858244e+00 8.76512914e-01 -7.09859903e-01 2 1.73924807e+00 -1.22080081e+00 1.82907576e+00 | 1.73924807e+00 -1.22080081e+00 1.82907576e+00 3 -1.02059307e+00 3.96055353e+00 2.89436413e+00 | -1.02059307e+00 3.96055353e+00 2.89436413e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = TTF (Configuration in file "config-Ga-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)) = -3.52178125769 2^p V(r_1,...,r_N) = -3.52178125769 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 -3.02753181e+00 -2.03936645e+00 -1.90278629e+00 | -3.02753181e+00 -2.03936645e+00 -1.90278629e+00 1 2.16328519e+00 1.80293299e+00 -2.67032339e+00 | 2.16328519e+00 1.80293299e+00 -2.67032339e+00 2 3.98891382e+00 -4.33506611e+00 3.42221759e+00 | 3.98891382e+00 -4.33506611e+00 3.42221759e+00 3 -3.12466719e+00 4.57149958e+00 1.15089208e+00 | -3.12466719e+00 4.57149958e+00 1.15089208e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = TFT (Configuration in file "config-Ga-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)) = -2.53905016509 2^p V(r_1,...,r_N) = -2.53905016509 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 -3.20126720e+00 -4.32690444e+00 -5.44245410e+00 | -3.20126720e+00 -4.32690444e+00 -5.44245410e+00 1 4.30202385e+00 4.34346257e+00 -2.49420763e+00 | 4.30202385e+00 4.34346257e+00 -2.49420763e+00 2 2.67045731e+00 -3.64100638e+00 3.91566431e+00 | 2.67045731e+00 -3.64100638e+00 3.91566431e+00 3 -3.77121397e+00 3.62444824e+00 4.02099742e+00 | -3.77121397e+00 3.62444824e+00 4.02099742e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = TFF (Configuration in file "config-Ga-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)) = 0.957054643419 2^p V(r_1,...,r_N) = 0.957054643419 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 -6.76988379e+00 -5.96765917e+00 -1.08864304e+01 | -6.76988379e+00 -5.96765917e+00 -1.08864304e+01 1 3.61300053e+00 4.39791176e+00 -2.95133377e+00 | 3.61300053e+00 4.39791176e+00 -2.95133377e+00 2 8.47414277e+00 -5.05389835e+00 8.46045747e+00 | 8.47414277e+00 -5.05389835e+00 8.46045747e+00 3 -5.31725951e+00 6.62364575e+00 5.37730667e+00 | -5.31725951e+00 6.62364575e+00 5.37730667e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = FTT (Configuration in file "config-Ga-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)) = -2.68650365775 2^p V(r_1,...,r_N) = -2.68650365775 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 -4.44647911e+00 -3.13502561e+00 -4.30864177e+00 | -4.44647911e+00 -3.13502561e+00 -4.30864177e+00 1 2.91784377e+00 3.89422043e+00 -3.26443381e+00 | 2.91784377e+00 3.89422043e+00 -3.26443381e+00 2 4.25061761e+00 -4.46338011e+00 3.96150258e+00 | 4.25061761e+00 -4.46338011e+00 3.96150258e+00 3 -2.72198227e+00 3.70418529e+00 3.61157300e+00 | -2.72198227e+00 3.70418529e+00 3.61157300e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = FTF (Configuration in file "config-Ga-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)) = -4.09389735296 2^p V(r_1,...,r_N) = -4.09389735296 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 -3.32976321e+00 -3.25460642e+00 -2.37448210e+00 | -3.32976321e+00 -3.25460642e+00 -2.37448210e+00 1 2.10118885e+00 2.80554891e+00 -2.33879895e+00 | 2.10118885e+00 2.80554891e+00 -2.33879895e+00 2 2.37033189e+00 -1.23729432e+00 3.61645144e+00 | 2.37033189e+00 -1.23729432e+00 3.61645144e+00 3 -1.14175753e+00 1.68635183e+00 1.09682960e+00 | -1.14175753e+00 1.68635183e+00 1.09682960e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ga, PBC = FFT (Configuration in file "config-Ga-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)) = -3.60302296538 2^p V(r_1,...,r_N) = -3.60302296538 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 -2.38901822e+00 -2.88199441e+00 -2.99950923e+00 | -2.38901822e+00 -2.88199441e+00 -2.99950923e+00 1 3.81698867e+00 2.13379422e+00 -3.53881689e+00 | 3.81698867e+00 2.13379422e+00 -3.53881689e+00 2 2.17109046e+00 -7.23905519e-01 1.95436151e+00 | 2.17109046e+00 -7.23905519e-01 1.95436151e+00 3 -3.59906091e+00 1.47210571e+00 4.58396461e+00 | -3.59906091e+00 1.47210571e+00 4.58396461e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TTT (Configuration in file "config-N-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)) = -5.21746576978 2^p V(r_1,...,r_N) = -5.21746576978 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 4.62856243e+00 3.99971256e+00 5.53354863e+00 | 4.62856243e+00 3.99971256e+00 5.53354863e+00 1 -3.66248777e+00 -2.58125757e+00 2.17218815e+00 | -3.66248777e+00 -2.58125757e+00 2.17218815e+00 2 -3.24599185e+00 6.40040844e-01 -4.14338858e+00 | -3.24599185e+00 6.40040844e-01 -4.14338858e+00 3 2.27991720e+00 -2.05849583e+00 -3.56234820e+00 | 2.27991720e+00 -2.05849583e+00 -3.56234820e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TTF (Configuration in file "config-N-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.45402672988 2^p V(r_1,...,r_N) = -1.45402672988 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 4.23826804e+00 4.91539980e+00 4.42545711e+00 | 4.23826804e+00 4.91539980e+00 4.42545711e+00 1 -6.38342378e+00 -4.34343009e+00 4.62152776e+00 | -6.38342378e+00 -4.34343009e+00 4.62152776e+00 2 -4.07214114e+00 1.92720021e+00 -2.93119590e+00 | -4.07214114e+00 1.92720021e+00 -2.93119590e+00 3 6.21729688e+00 -2.49916991e+00 -6.11578897e+00 | 6.21729688e+00 -2.49916991e+00 -6.11578897e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TFT (Configuration in file "config-N-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.51024515596 2^p V(r_1,...,r_N) = -3.51024515596 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 2.49706323e+00 3.33275511e-01 3.13213345e+00 | 2.49706323e+00 3.33275511e-01 3.13213345e+00 1 -9.47730565e-01 -3.86507239e+00 4.86777812e+00 | -9.47730565e-01 -3.86507239e+00 4.86777812e+00 2 -5.06011353e+00 4.80303236e+00 -6.26993085e+00 | -5.06011353e+00 4.80303236e+00 -6.26993085e+00 3 3.51078087e+00 -1.27123547e+00 -1.72998073e+00 | 3.51078087e+00 -1.27123547e+00 -1.72998073e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = TFF (Configuration in file "config-N-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)) = -7.00753678744 2^p V(r_1,...,r_N) = -7.00753678744 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 2.12487361e+00 1.25208017e+00 1.24096209e+00 | 2.12487361e+00 1.25208017e+00 1.24096209e+00 1 -2.22264709e+00 -2.06582996e+00 1.97248853e+00 | -2.22264709e+00 -2.06582996e+00 1.97248853e+00 2 -1.78140146e+00 2.39757434e+00 -2.22173830e+00 | -1.78140146e+00 2.39757434e+00 -2.22173830e+00 3 1.87917494e+00 -1.58382455e+00 -9.91712325e-01 | 1.87917494e+00 -1.58382455e+00 -9.91712325e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FTT (Configuration in file "config-N-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)) = -3.56323453013 2^p V(r_1,...,r_N) = -3.56323453013 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 5.41068113e+00 8.38365432e+00 6.16851108e+00 | 5.41068113e+00 8.38365432e+00 6.16851108e+00 1 -3.95639487e+00 -4.45270403e+00 6.31649897e-01 | -3.95639487e+00 -4.45270403e+00 6.31649897e-01 2 -4.44575301e+00 1.30011530e+00 -4.00554636e+00 | -4.44575301e+00 1.30011530e+00 -4.00554636e+00 3 2.99146675e+00 -5.23106559e+00 -2.79461462e+00 | 2.99146675e+00 -5.23106559e+00 -2.79461462e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FTF (Configuration in file "config-N-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)) = -7.30269807417 2^p V(r_1,...,r_N) = -7.30269807417 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 6.18797538e-01 -9.32653789e-01 3.48023352e+00 | 6.18797538e-01 -9.32653789e-01 3.48023352e+00 1 -6.50146495e-01 3.27121247e+00 1.70878437e+00 | -6.50146495e-01 3.27121247e+00 1.70878437e+00 2 -3.53499840e+00 3.89965483e-01 -6.42460284e-01 | -3.53499840e+00 3.89965483e-01 -6.42460284e-01 3 3.56634735e+00 -2.72852416e+00 -4.54655760e+00 | 3.56634735e+00 -2.72852416e+00 -4.54655760e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = N, PBC = FFT (Configuration in file "config-N-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)) = -4.8659412237 2^p V(r_1,...,r_N) = -4.8659412237 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 1.38017724e+00 1.03003004e+00 8.41761913e-01 | 1.38017724e+00 1.03003004e+00 8.41761913e-01 1 -2.45113378e+00 -3.10252419e+00 2.86545683e+00 | -2.45113378e+00 -3.10252419e+00 2.86545683e+00 2 -2.24546192e+00 4.11543829e+00 -2.00768353e+00 | -2.24546192e+00 4.11543829e+00 -2.00768353e+00 3 3.31641846e+00 -2.04294414e+00 -1.69953522e+00 | 3.31641846e+00 -2.04294414e+00 -1.69953522e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = TTT (Configuration in file "config-GaN-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.74265054789 2^p V(r_1,...,r_N) = -1.74265054789 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 -3.44828806e+00 -4.38640997e+00 -5.39788707e-02 | -3.44828806e+00 -4.38640997e+00 -5.39788707e-02 1 5.53864729e+00 4.64449057e+00 -1.55297983e+00 | 5.53864729e+00 4.64449057e+00 -1.55297983e+00 2 1.03797305e-01 -2.71775483e+00 -3.95396434e-02 | 1.03797305e-01 -2.71775483e+00 -3.95396434e-02 3 -2.19415654e+00 2.45967423e+00 1.64649834e+00 | -2.19415654e+00 2.45967423e+00 1.64649834e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = TTF (Configuration in file "config-GaN-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.28357314413 2^p V(r_1,...,r_N) = 1.28357314413 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 -4.21426250e+01 -1.04056422e+01 -5.26567322e+01 | -4.21426250e+01 -1.04056422e+01 -5.26567322e+01 1 5.51601230e+00 9.98851309e+00 -1.10853016e+01 | 5.51601230e+00 9.98851309e+00 -1.10853016e+01 2 4.88122853e+01 -4.64180083e+00 5.59435597e+01 | 4.88122853e+01 -4.64180083e+00 5.59435597e+01 3 -1.21856727e+01 5.05892990e+00 7.79847413e+00 | -1.21856727e+01 5.05892990e+00 7.79847413e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = TFT (Configuration in file "config-GaN-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)) = -1.85123251824 2^p V(r_1,...,r_N) = -1.85123251824 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 -2.80120433e+00 -1.04366350e+01 -7.77312226e+00 | -2.80120433e+00 -1.04366350e+01 -7.77312226e+00 1 3.06981271e+00 3.67762799e+00 -2.67655970e+00 | 3.06981271e+00 3.67762799e+00 -2.67655970e+00 2 1.05381543e+00 -1.99975108e+00 3.09995819e+00 | 1.05381543e+00 -1.99975108e+00 3.09995819e+00 3 -1.32242381e+00 8.75875810e+00 7.34972377e+00 | -1.32242381e+00 8.75875810e+00 7.34972377e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = TFF (Configuration in file "config-GaN-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)) = 27.1294884544 2^p V(r_1,...,r_N) = 27.1294884544 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 -3.36541218e+01 -3.24968415e+01 -4.67773295e+01 | -3.36541218e+01 -3.24968415e+01 -4.67773295e+01 1 3.79362566e+01 3.51963404e+01 -4.05030385e+01 | 3.79362566e+01 3.51963404e+01 -4.05030385e+01 2 1.69085622e+01 -1.14256800e+01 5.65796663e+01 | 1.69085622e+01 -1.14256800e+01 5.65796663e+01 3 -2.11906970e+01 8.72618104e+00 3.07007018e+01 | -2.11906970e+01 8.72618104e+00 3.07007018e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = FTT (Configuration in file "config-GaN-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)) = 3.87060602857 2^p V(r_1,...,r_N) = 3.87060602857 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 -9.83312617e+00 -7.13945490e+00 -8.83693778e+00 | -9.83312617e+00 -7.13945490e+00 -8.83693778e+00 1 -2.14108148e+00 2.07232594e+01 -6.49854375e-01 | -2.14108148e+00 2.07232594e+01 -6.49854375e-01 2 1.25369065e+01 -2.62739906e+01 1.10593730e+01 | 1.25369065e+01 -2.62739906e+01 1.10593730e+01 3 -5.62698824e-01 1.26901861e+01 -1.57258087e+00 | -5.62698824e-01 1.26901861e+01 -1.57258087e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = FTF (Configuration in file "config-GaN-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.70728705027 2^p V(r_1,...,r_N) = -3.70728705027 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 -2.36247384e+00 -1.82605021e+00 -4.17386872e+00 | -2.36247384e+00 -1.82605021e+00 -4.17386872e+00 1 2.06728303e+01 4.80683259e-01 -1.75979471e+01 | 2.06728303e+01 4.80683259e-01 -1.75979471e+01 2 1.43280016e+00 8.47822316e-01 1.46165840e+00 | 1.43280016e+00 8.47822316e-01 1.46165840e+00 3 -1.97431566e+01 4.97544635e-01 2.03101574e+01 | -1.97431566e+01 4.97544635e-01 2.03101574e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ga N, PBC = FFT (Configuration in file "config-GaN-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)) = 2.41425067221 2^p V(r_1,...,r_N) = 2.41425067221 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 -4.67329503e-01 5.21382176e+00 1.88224010e+00 | -4.67329503e-01 5.21382176e+00 1.88224010e+00 1 1.58807893e+01 6.90815691e+00 -1.10514007e+01 | 1.58807893e+01 6.90815691e+00 -1.10514007e+01 2 1.06798375e+01 -1.14700219e+01 7.36259178e+00 | 1.06798375e+01 -1.14700219e+01 7.36259178e+00 3 -2.60932973e+01 -6.51956791e-01 1.80656880e+00 | -2.60932973e+01 -6.51956791e-01 1.80656880e+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.