!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BOP_ZhouWardFoster_2016_AlCu__SM_566399258279_000 Supported species : Al Cu random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-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)) = -5.97156105881 2^p V(r_1,...,r_N) = -5.97156105881 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 -7.83734634e-01 -7.85321977e-01 -9.57268340e-01 | -7.83734634e-01 -7.85321977e-01 -9.57268340e-01 1 5.85248978e-01 3.78482005e-01 -2.89176608e-01 | 5.85248978e-01 3.78482005e-01 -2.89176608e-01 2 5.10977262e-01 -3.98077288e-01 6.31052197e-01 | 5.10977262e-01 -3.98077288e-01 6.31052197e-01 3 -3.12491605e-01 8.04917260e-01 6.15392751e-01 | -3.12491605e-01 8.04917260e-01 6.15392751e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-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)) = -6.02122072755 2^p V(r_1,...,r_N) = -6.02122072755 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 6.07068899e-01 7.48373471e-02 1.46553466e-01 | 6.07068899e-01 7.48373471e-02 1.46553466e-01 1 1.61105915e-02 -1.80145848e-02 -5.44360904e-01 | 1.61105915e-02 -1.80145848e-02 -5.44360904e-01 2 2.27212328e-01 -7.30834563e-01 -1.78814063e-01 | 2.27212328e-01 -7.30834563e-01 -1.78814063e-01 3 -8.50391818e-01 6.74011801e-01 5.76621501e-01 | -8.50391818e-01 6.74011801e-01 5.76621501e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-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)) = -5.83155726048 2^p V(r_1,...,r_N) = -5.83155726048 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 -2.25848929e-01 -5.82156376e-01 -3.95645109e-01 | -2.25848929e-01 -5.82156376e-01 -3.95645109e-01 1 6.20758854e-01 8.89910759e-01 -9.36886201e-01 | 6.20758854e-01 8.89910759e-01 -9.36886201e-01 2 5.93736269e-01 -7.68921326e-01 2.04148080e-01 | 5.93736269e-01 -7.68921326e-01 2.04148080e-01 3 -9.88646194e-01 4.61166943e-01 1.12838323e+00 | -9.88646194e-01 4.61166943e-01 1.12838323e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.00240356354 2^p V(r_1,...,r_N) = -6.00240356354 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 -9.50355498e-01 -5.25744107e-01 -5.20642033e-01 | -9.50355498e-01 -5.25744107e-01 -5.20642033e-01 1 7.41718449e-01 7.85296281e-01 -5.12427524e-01 | 7.41718449e-01 7.85296281e-01 -5.12427524e-01 2 5.85210354e-01 -5.03679307e-01 6.28901678e-01 | 5.85210354e-01 -5.03679307e-01 6.28901678e-01 3 -3.76573304e-01 2.44127133e-01 4.04167879e-01 | -3.76573304e-01 2.44127133e-01 4.04167879e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-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)) = -5.91314696326 2^p V(r_1,...,r_N) = -5.91314696326 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 1.60265526e-01 -1.78089130e-01 -4.74907706e-01 | 1.60265526e-01 -1.78089130e-01 -4.74907706e-01 1 -2.53945725e-01 -5.86779860e-03 -2.85092176e-01 | -2.53945725e-01 -5.86779860e-03 -2.85092176e-01 2 7.64093392e-01 -9.53335853e-01 3.74086350e-01 | 7.64093392e-01 -9.53335853e-01 3.74086350e-01 3 -6.70413193e-01 1.13729278e+00 3.85913533e-01 | -6.70413193e-01 1.13729278e+00 3.85913533e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-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)) = -6.15389195777 2^p V(r_1,...,r_N) = -6.15389195777 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 -5.40001555e-01 -6.08075840e-01 -6.52406516e-01 | -5.40001555e-01 -6.08075840e-01 -6.52406516e-01 1 2.10216346e-01 2.36248871e-01 -2.76258474e-01 | 2.10216346e-01 2.36248871e-01 -2.76258474e-01 2 6.48023031e-01 -1.73463398e-01 5.83806503e-01 | 6.48023031e-01 -1.73463398e-01 5.83806503e-01 3 -3.18237822e-01 5.45290366e-01 3.44858487e-01 | -3.18237822e-01 5.45290366e-01 3.44858487e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-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)) = -6.16294520059 2^p V(r_1,...,r_N) = -6.16294520059 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 -5.94640626e-01 -8.12436326e-01 -4.35563228e-01 | -5.94640626e-01 -8.12436326e-01 -4.35563228e-01 1 4.65208878e-01 5.33398368e-01 -4.70406081e-01 | 4.65208878e-01 5.33398368e-01 -4.70406081e-01 2 3.90001819e-01 -1.74960751e-01 4.48924439e-01 | 3.90001819e-01 -1.74960751e-01 4.48924439e-01 3 -2.60570071e-01 4.53998709e-01 4.57044870e-01 | -2.60570071e-01 4.53998709e-01 4.57044870e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.44762718062 2^p V(r_1,...,r_N) = -4.44762718062 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 -9.77020231e-01 -1.04174125e+00 -5.63714570e-01 | -9.77020231e-01 -1.04174125e+00 -5.63714570e-01 1 1.54519967e+00 2.74794498e-01 -1.48878314e+00 | 1.54519967e+00 2.74794498e-01 -1.48878314e+00 2 5.38750009e-01 -8.43454606e-02 5.38140725e-01 | 5.38750009e-01 -8.43454606e-02 5.38140725e-01 3 -1.10692945e+00 8.51292211e-01 1.51435699e+00 | -1.10692945e+00 8.51292211e-01 1.51435699e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.19609613713 2^p V(r_1,...,r_N) = -4.19609613713 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 -2.07967752e+00 -1.81334641e+00 -1.21281810e+00 | -2.07967752e+00 -1.81334641e+00 -1.21281810e+00 1 1.18447065e+00 1.61012116e+00 -5.41524555e-01 | 1.18447065e+00 1.61012116e+00 -5.41524555e-01 2 1.46148526e+00 -5.94897130e-01 1.62729179e+00 | 1.46148526e+00 -5.94897130e-01 1.62729179e+00 3 -5.66278390e-01 7.98122388e-01 1.27050862e-01 | -5.66278390e-01 7.98122388e-01 1.27050862e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.33405128287 2^p V(r_1,...,r_N) = -2.33405128287 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 -2.91678761e+00 -2.14082857e+00 -2.46566566e+00 | -2.91678761e+00 -2.14082857e+00 -2.46566566e+00 1 3.31041673e+00 2.53033792e+00 -3.26798392e+00 | 3.31041673e+00 2.53033792e+00 -3.26798392e+00 2 2.40126203e+00 -2.97414370e+00 3.29986971e+00 | 2.40126203e+00 -2.97414370e+00 3.29986971e+00 3 -2.79489115e+00 2.58463434e+00 2.43377987e+00 | -2.79489115e+00 2.58463434e+00 2.43377987e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.4068236607 2^p V(r_1,...,r_N) = -4.4068236607 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 -1.11236096e+00 -1.76072107e+00 -1.39266039e+00 | -1.11236096e+00 -1.76072107e+00 -1.39266039e+00 1 1.39151514e+00 8.12578775e-01 -6.91554442e-01 | 1.39151514e+00 8.12578775e-01 -6.91554442e-01 2 8.36134954e-01 -3.82399276e-01 7.44305774e-01 | 8.36134954e-01 -3.82399276e-01 7.44305774e-01 3 -1.11528913e+00 1.33054157e+00 1.33990906e+00 | -1.11528913e+00 1.33054157e+00 1.33990906e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.91736326784 2^p V(r_1,...,r_N) = -2.91736326784 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 -2.37525518e+00 -1.09749226e+00 -3.12056903e+00 | -2.37525518e+00 -1.09749226e+00 -3.12056903e+00 1 1.21670505e+00 5.05640037e-01 -1.54147528e+00 | 1.21670505e+00 5.05640037e-01 -1.54147528e+00 2 3.47796962e+00 -2.08333073e+00 1.92143878e+00 | 3.47796962e+00 -2.08333073e+00 1.92143878e+00 3 -2.31941949e+00 2.67518295e+00 2.74060553e+00 | -2.31941949e+00 2.67518295e+00 2.74060553e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.25926629623 2^p V(r_1,...,r_N) = -4.25926629623 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 -1.17299951e+00 -1.24976450e+00 -1.20496920e+00 | -1.17299951e+00 -1.24976450e+00 -1.20496920e+00 1 1.31823520e+00 1.16103792e+00 -1.62095851e+00 | 1.31823520e+00 1.16103792e+00 -1.62095851e+00 2 1.39099034e+00 -1.10549171e+00 1.14902958e+00 | 1.39099034e+00 -1.10549171e+00 1.14902958e+00 3 -1.53622603e+00 1.19421828e+00 1.67689813e+00 | -1.53622603e+00 1.19421828e+00 1.67689813e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.22486762999 2^p V(r_1,...,r_N) = -3.22486762999 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 -2.89866838e+00 -1.34889333e+00 -3.49436558e+00 | -2.89866838e+00 -1.34889333e+00 -3.49436558e+00 1 1.11675119e+00 1.11824800e+00 -5.28859403e-01 | 1.11675119e+00 1.11824800e+00 -5.28859403e-01 2 2.93571573e+00 -2.10878691e+00 1.57266775e+00 | 2.93571573e+00 -2.10878691e+00 1.57266775e+00 3 -1.15379853e+00 2.33943223e+00 2.45055723e+00 | -1.15379853e+00 2.33943223e+00 2.45055723e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TTT (Configuration in file "config-AlCu-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)) = -5.3195578801 2^p V(r_1,...,r_N) = -5.3195578801 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 -1.34082844e+00 -1.44554432e+00 -1.26388306e+00 | -1.34082844e+00 -1.44554432e+00 -1.26388306e+00 1 8.59314200e-01 9.46959650e-01 -7.31070560e-01 | 8.59314200e-01 9.46959650e-01 -7.31070560e-01 2 1.32119468e+00 -6.42640023e-01 1.13136287e+00 | 1.32119468e+00 -6.42640023e-01 1.13136287e+00 3 -8.39680446e-01 1.14122470e+00 8.63590751e-01 | -8.39680446e-01 1.14122470e+00 8.63590751e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TTF (Configuration in file "config-AlCu-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)) = -5.29290365626 2^p V(r_1,...,r_N) = -5.29290365626 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 -1.14726025e+00 -6.99430918e-01 -6.29625692e-01 | -1.14726025e+00 -6.99430918e-01 -6.29625692e-01 1 6.84168475e-01 1.50516063e+00 -7.87758852e-01 | 6.84168475e-01 1.50516063e+00 -7.87758852e-01 2 6.66611676e-01 -9.56470379e-01 1.25159884e+00 | 6.66611676e-01 -9.56470379e-01 1.25159884e+00 3 -2.03519904e-01 1.50740668e-01 1.65785704e-01 | -2.03519904e-01 1.50740668e-01 1.65785704e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TFT (Configuration in file "config-AlCu-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)) = -4.84725718165 2^p V(r_1,...,r_N) = -4.84725718165 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 -1.12475072e+00 -9.97821079e-01 -7.77211613e-01 | -1.12475072e+00 -9.97821079e-01 -7.77211613e-01 1 1.07918687e+00 1.04721511e+00 -1.86516824e+00 | 1.07918687e+00 1.04721511e+00 -1.86516824e+00 2 1.12305599e+00 -8.90697401e-01 1.84468810e+00 | 1.12305599e+00 -8.90697401e-01 1.84468810e+00 3 -1.07749214e+00 8.41303365e-01 7.97691761e-01 | -1.07749214e+00 8.41303365e-01 7.97691761e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = TFF (Configuration in file "config-AlCu-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)) = -5.32961315575 2^p V(r_1,...,r_N) = -5.32961315575 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 -1.00614635e+00 -8.83366028e-01 -6.56113139e-01 | -1.00614635e+00 -8.83366028e-01 -6.56113139e-01 1 6.63376953e-01 9.87122758e-01 -8.63666493e-01 | 6.63376953e-01 9.87122758e-01 -8.63666493e-01 2 8.85134690e-01 -1.08027544e+00 1.02610542e+00 | 8.85134690e-01 -1.08027544e+00 1.02610542e+00 3 -5.42365290e-01 9.76518707e-01 4.93674212e-01 | -5.42365290e-01 9.76518707e-01 4.93674212e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = FTT (Configuration in file "config-AlCu-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)) = -5.95313207279 2^p V(r_1,...,r_N) = -5.95313207279 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 -6.05562797e-02 -4.53053698e-01 -1.27171192e-01 | -6.05562797e-02 -4.53053698e-01 -1.27171192e-01 1 3.36908209e-01 2.72140390e-01 -5.04670292e-01 | 3.36908209e-01 2.72140390e-01 -5.04670292e-01 2 1.85277042e-01 -5.26729976e-01 8.02281979e-02 | 1.85277042e-01 -5.26729976e-01 8.02281979e-02 3 -4.61628972e-01 7.07643285e-01 5.51613286e-01 | -4.61628972e-01 7.07643285e-01 5.51613286e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = FTF (Configuration in file "config-AlCu-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)) = -5.15045019519 2^p V(r_1,...,r_N) = -5.15045019519 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 -1.02327426e+00 -6.98282647e-01 -9.08395757e-01 | -1.02327426e+00 -6.98282647e-01 -9.08395757e-01 1 4.90900371e-01 1.12447432e+00 -6.74720360e-01 | 4.90900371e-01 1.12447432e+00 -6.74720360e-01 2 1.12399808e+00 -1.53963933e+00 1.06217967e+00 | 1.12399808e+00 -1.53963933e+00 1.06217967e+00 3 -5.91624198e-01 1.11344766e+00 5.20936447e-01 | -5.91624198e-01 1.11344766e+00 5.20936447e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Cu, PBC = FFT (Configuration in file "config-AlCu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.52002542239 2^p V(r_1,...,r_N) = -5.52002542239 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 -4.86214521e-01 -4.04047961e-01 -4.03506818e-01 | -4.86214521e-01 -4.04047961e-01 -4.03506818e-01 1 1.06050120e+00 7.17881402e-01 -9.43039612e-01 | 1.06050120e+00 7.17881402e-01 -9.43039612e-01 2 6.79504494e-01 -5.13784196e-01 5.71947562e-01 | 6.79504494e-01 -5.13784196e-01 5.71947562e-01 3 -1.25379117e+00 1.99950755e-01 7.74598868e-01 | -1.25379117e+00 1.99950755e-01 7.74598868e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.