!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BereSerra_2006_GaN__SM_518345582208_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)) = 1.00808459431 2^p V(r_1,...,r_N) = 1.00808459431 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 -4.57458498e+00 -6.59487353e+00 -7.44169794e+00 | -4.57458498e+00 -6.59487353e+00 -7.44169794e+00 1 4.27106046e+00 2.44436980e+00 -3.10915775e+00 | 4.27106046e+00 2.44436980e+00 -3.10915775e+00 2 4.32306125e+00 -3.93107459e+00 4.72587986e+00 | 4.32306125e+00 -3.93107459e+00 4.72587986e+00 3 -4.01953673e+00 8.08157832e+00 5.82497583e+00 | -4.01953673e+00 8.08157832e+00 5.82497583e+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)) = 3.04242684779 2^p V(r_1,...,r_N) = 3.04242684779 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 -7.29132577e+00 -5.98026857e+00 -5.46509153e+00 | -7.29132577e+00 -5.98026857e+00 -5.46509153e+00 1 6.10358612e+00 3.92894884e+00 -7.71823739e+00 | 6.10358612e+00 3.92894884e+00 -7.71823739e+00 2 7.92173821e+00 -8.36734928e+00 8.10579812e+00 | 7.92173821e+00 -8.36734928e+00 8.10579812e+00 3 -6.73399856e+00 1.04186690e+01 5.07753080e+00 | -6.73399856e+00 1.04186690e+01 5.07753080e+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)) = 5.96878551236 2^p V(r_1,...,r_N) = 5.96878551236 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 -7.96071641e+00 -9.38205588e+00 -1.22622838e+01 | -7.96071641e+00 -9.38205588e+00 -1.22622838e+01 1 1.08581633e+01 1.00948108e+01 -6.24064967e+00 | 1.08581633e+01 1.00948108e+01 -6.24064967e+00 2 7.57124055e+00 -9.37471605e+00 9.50277469e+00 | 7.57124055e+00 -9.37471605e+00 9.50277469e+00 3 -1.04686875e+01 8.66196109e+00 9.00015882e+00 | -1.04686875e+01 8.66196109e+00 9.00015882e+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)) = 13.4506255722 2^p V(r_1,...,r_N) = 13.4506255722 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 -1.60124607e+01 -1.36865285e+01 -2.40716641e+01 | -1.60124607e+01 -1.36865285e+01 -2.40716641e+01 1 1.13888095e+01 1.12826103e+01 -9.03873984e+00 | 1.13888095e+01 1.12826103e+01 -9.03873984e+00 2 1.94770708e+01 -1.22720108e+01 1.94838148e+01 | 1.94770708e+01 -1.22720108e+01 1.94838148e+01 3 -1.48534196e+01 1.46759290e+01 1.36265892e+01 | -1.48534196e+01 1.46759290e+01 1.36265892e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = 5.59053326935 2^p V(r_1,...,r_N) = 5.59053326935 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 -1.06320352e+01 -7.51098045e+00 -9.72313667e+00 | -1.06320352e+01 -7.51098045e+00 -9.72313667e+00 1 8.45976858e+00 9.05973970e+00 -8.60260751e+00 | 8.45976858e+00 9.05973970e+00 -8.60260751e+00 2 9.93721801e+00 -1.01448502e+01 8.72938806e+00 | 9.93721801e+00 -1.01448502e+01 8.72938806e+00 3 -7.76495140e+00 8.59609093e+00 9.59635611e+00 | -7.76495140e+00 8.59609093e+00 9.59635611e+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)) = 0.837605338281 2^p V(r_1,...,r_N) = 0.837605338281 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 -6.88175424e+00 -5.24367064e+00 -4.31246606e+00 | -6.88175424e+00 -5.24367064e+00 -4.31246606e+00 1 4.76143894e+00 5.15797623e+00 -5.41871029e+00 | 4.76143894e+00 5.15797623e+00 -5.41871029e+00 2 5.12292683e+00 -2.46220536e+00 7.26422729e+00 | 5.12292683e+00 -2.46220536e+00 7.26422729e+00 3 -3.00261154e+00 2.54789977e+00 2.46694907e+00 | -3.00261154e+00 2.54789977e+00 2.46694907e+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)) = 11.5038974059 2^p V(r_1,...,r_N) = 11.5038974059 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 -8.87910725e+00 -8.37119525e+00 -1.26001949e+01 | -8.87910725e+00 -8.37119525e+00 -1.26001949e+01 1 1.24282703e+01 1.03532878e+01 -1.02495886e+01 | 1.24282703e+01 1.03532878e+01 -1.02495886e+01 2 1.84818127e+01 -2.04064205e+01 1.29605961e+01 | 1.84818127e+01 -2.04064205e+01 1.29605961e+01 3 -2.20309757e+01 1.84243279e+01 9.88918736e+00 | -2.20309757e+01 1.84243279e+01 9.88918736e+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)) = -1.45568855446 2^p V(r_1,...,r_N) = -1.45568855446 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 2.20028410e+00 1.27769900e+00 2.64085605e+00 | 2.20028410e+00 1.27769900e+00 2.64085605e+00 1 -1.05996234e+00 -2.09937803e+00 1.64142597e+00 | -1.05996234e+00 -2.09937803e+00 1.64142597e+00 2 -3.13756175e+00 2.92046291e+00 -2.99567705e+00 | -3.13756175e+00 2.92046291e+00 -2.99567705e+00 3 1.99724000e+00 -2.09878389e+00 -1.28660497e+00 | 1.99724000e+00 -2.09878389e+00 -1.28660497e+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)) = -1.81408054876 2^p V(r_1,...,r_N) = -1.81408054876 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 2.38399151e+00 2.14625539e+00 2.16469994e+00 | 2.38399151e+00 2.14625539e+00 2.16469994e+00 1 -1.62737159e+00 -2.63248806e+00 1.73736370e+00 | -1.62737159e+00 -2.63248806e+00 1.73736370e+00 2 -2.37090744e+00 2.34872339e+00 -3.22077708e+00 | -2.37090744e+00 2.34872339e+00 -3.22077708e+00 3 1.61428752e+00 -1.86249073e+00 -6.81286567e-01 | 1.61428752e+00 -1.86249073e+00 -6.81286567e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.91582511125 2^p V(r_1,...,r_N) = -1.91582511125 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 9.65422297e-01 2.52189704e+00 9.43573387e-01 | 9.65422297e-01 2.52189704e+00 9.43573387e-01 1 -1.54278862e+00 -1.40074816e+00 1.52944767e+00 | -1.54278862e+00 -1.40074816e+00 1.52944767e+00 2 -2.58851374e-01 4.50258231e-01 -4.40411772e-01 | -2.58851374e-01 4.50258231e-01 -4.40411772e-01 3 8.36217692e-01 -1.57140710e+00 -2.03260928e+00 | 8.36217692e-01 -1.57140710e+00 -2.03260928e+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)) = -2.44347366062 2^p V(r_1,...,r_N) = -2.44347366062 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 2.28622636e+00 1.60319320e+00 2.20283913e+00 | 2.28622636e+00 1.60319320e+00 2.20283913e+00 1 -2.38977677e+00 -2.62545976e+00 2.06541262e+00 | -2.38977677e+00 -2.62545976e+00 2.06541262e+00 2 -2.21211617e+00 2.31254087e+00 -2.44828728e+00 | -2.21211617e+00 2.31254087e+00 -2.44828728e+00 3 2.31566658e+00 -1.29027431e+00 -1.81996447e+00 | 2.31566658e+00 -1.29027431e+00 -1.81996447e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.66735181723 2^p V(r_1,...,r_N) = -1.66735181723 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 1.53508154e+00 4.96050027e-01 1.62410760e+00 | 1.53508154e+00 4.96050027e-01 1.62410760e+00 1 -1.62228840e+00 -1.53438029e+00 2.84861772e+00 | -1.62228840e+00 -1.53438029e+00 2.84861772e+00 2 -3.00182372e+00 2.56088900e+00 -2.70653662e+00 | -3.00182372e+00 2.56088900e+00 -2.70653662e+00 3 3.08903057e+00 -1.52255874e+00 -1.76618870e+00 | 3.08903057e+00 -1.52255874e+00 -1.76618870e+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)) = -0.546122972828 2^p V(r_1,...,r_N) = -0.546122972828 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 -4.65044103e-02 5.15325174e-01 6.40020552e-01 | -4.65044103e-02 5.15325174e-01 6.40020552e-01 1 -2.35057500e-01 -2.01843000e+00 1.80532249e+00 | -2.35057500e-01 -2.01843000e+00 1.80532249e+00 2 2.35057500e-01 2.01843000e+00 -1.80532249e+00 | 2.35057500e-01 2.01843000e+00 -1.80532249e+00 3 4.65044103e-02 -5.15325174e-01 -6.40020552e-01 | 4.65044103e-02 -5.15325174e-01 -6.40020552e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.492585533638 2^p V(r_1,...,r_N) = -0.492585533638 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 2.17513275e+00 1.22574505e+00 1.62384746e+00 | 2.17513275e+00 1.22574505e+00 1.62384746e+00 1 -1.14902709e+00 -1.30969851e+00 1.41883473e+00 | -1.14902709e+00 -1.30969851e+00 1.41883473e+00 2 -1.96226974e+00 -8.38290161e-02 -1.82047646e+00 | -1.96226974e+00 -8.38290161e-02 -1.82047646e+00 3 9.36164081e-01 1.67782477e-01 -1.22220574e+00 | 9.36164081e-01 1.67782477e-01 -1.22220574e+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)) = -4.78864144029 2^p V(r_1,...,r_N) = -4.78864144029 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 1.17254150e+00 9.80737092e-01 2.15462494e+00 | 1.17254150e+00 9.80737092e-01 2.15462494e+00 1 -5.50737033e-01 -1.35111986e+00 1.94585186e+00 | -5.50737033e-01 -1.35111986e+00 1.94585186e+00 2 -9.37869416e-01 9.83520234e-01 -2.17777433e+00 | -9.37869416e-01 9.83520234e-01 -2.17777433e+00 3 3.16064944e-01 -6.13137464e-01 -1.92270247e+00 | 3.16064944e-01 -6.13137464e-01 -1.92270247e+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)) = -1.60220799048 2^p V(r_1,...,r_N) = -1.60220799048 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 -9.14408867e+00 -5.17663510e+00 -7.53772965e+00 | -9.14408867e+00 -5.17663510e+00 -7.53772965e+00 1 5.71854607e+00 5.98318510e+00 -4.51344651e+00 | 5.71854607e+00 5.98318510e+00 -4.51344651e+00 2 7.80804522e+00 -6.68526707e+00 7.58402530e+00 | 7.80804522e+00 -6.68526707e+00 7.58402530e+00 3 -4.38250263e+00 5.87871706e+00 4.46715086e+00 | -4.38250263e+00 5.87871706e+00 4.46715086e+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)) = 0.887262823731 2^p V(r_1,...,r_N) = 0.887262823731 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 -1.14435122e+01 -8.39610319e+00 -1.20462652e+01 | -1.14435122e+01 -8.39610319e+00 -1.20462652e+01 1 9.11043699e+00 1.22552474e+01 -4.99987996e+00 | 9.11043699e+00 1.22552474e+01 -4.99987996e+00 2 9.27704598e+00 -8.70598920e+00 1.00263654e+01 | 9.27704598e+00 -8.70598920e+00 1.00263654e+01 3 -6.94397076e+00 4.84684501e+00 7.01977973e+00 | -6.94397076e+00 4.84684501e+00 7.01977973e+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)) = -2.50277884912 2^p V(r_1,...,r_N) = -2.50277884912 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 -7.64381379e+00 -7.92865769e+00 -4.01300610e+00 | -7.64381379e+00 -7.92865769e+00 -4.01300610e+00 1 8.49050122e+00 7.14041797e+00 -4.67346170e+00 | 8.49050122e+00 7.14041797e+00 -4.67346170e+00 2 4.35750299e+00 -3.72680372e+00 5.93376910e+00 | 4.35750299e+00 -3.72680372e+00 5.93376910e+00 3 -5.20419042e+00 4.51504344e+00 2.75269870e+00 | -5.20419042e+00 4.51504344e+00 2.75269870e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.07582412683 2^p V(r_1,...,r_N) = -2.07582412683 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 -6.02518706e+00 -4.34451146e+00 -3.33568637e+00 | -6.02518706e+00 -4.34451146e+00 -3.33568637e+00 1 4.95485849e+00 5.22670992e+00 -5.57095048e+00 | 4.95485849e+00 5.22670992e+00 -5.57095048e+00 2 8.67625643e+00 -9.67367928e+00 3.98622398e+00 | 8.67625643e+00 -9.67367928e+00 3.98622398e+00 3 -7.60592786e+00 8.79148082e+00 4.92041288e+00 | -7.60592786e+00 8.79148082e+00 4.92041288e+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)) = -3.53040084791 2^p V(r_1,...,r_N) = -3.53040084791 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 -1.20561831e+00 -4.90748621e+00 -6.40481965e+00 | -1.20561831e+00 -4.90748621e+00 -6.40481965e+00 1 2.78437134e+00 2.67145881e+00 -1.95304159e+00 | 2.78437134e+00 2.67145881e+00 -1.95304159e+00 2 2.62962794e+00 -3.40867530e+00 3.19843652e+00 | 2.62962794e+00 -3.40867530e+00 3.19843652e+00 3 -4.20838097e+00 5.64470270e+00 5.15942472e+00 | -4.20838097e+00 5.64470270e+00 5.15942472e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.63963855315 2^p V(r_1,...,r_N) = -1.63963855315 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 -1.02683452e+01 -5.35664515e+00 -7.61397153e+00 | -1.02683452e+01 -5.35664515e+00 -7.61397153e+00 1 4.03278569e+00 6.36415975e+00 -3.34806834e+00 | 4.03278569e+00 6.36415975e+00 -3.34806834e+00 2 1.34272461e+01 -7.49403291e+00 5.92981134e+00 | 1.34272461e+01 -7.49403291e+00 5.92981134e+00 3 -7.19168658e+00 6.48651830e+00 5.03222854e+00 | -7.19168658e+00 6.48651830e+00 5.03222854e+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.