!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MEAM_MaiselKoZhang_2017_VNiTi__SM_971529344487_000 Supported species : Ni Ti V random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-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)) = -7.76850653698 2^p V(r_1,...,r_N) = -7.76850653698 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 -2.98795354e+00 -6.43555481e+00 -6.55478124e+00 | -2.98795354e+00 -6.43555481e+00 -6.55478124e+00 1 2.35033255e+00 2.00296328e+00 -1.74053573e+00 | 2.35033255e+00 2.00296328e+00 -1.74053573e+00 2 1.68087184e+00 -2.11794623e+00 3.09073649e+00 | 1.68087184e+00 -2.11794623e+00 3.09073649e+00 3 -1.04325086e+00 6.55053776e+00 5.20458048e+00 | -1.04325086e+00 6.55053776e+00 5.20458048e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-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)) = -8.2781757687 2^p V(r_1,...,r_N) = -8.2781757687 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 1.00955583e+00 6.25286184e-01 7.38757059e-01 | 1.00955583e+00 6.25286184e-01 7.38757059e-01 1 6.44074339e-01 1.14778158e+00 -2.51955737e+00 | 6.44074339e-01 1.14778158e+00 -2.51955737e+00 2 3.60574092e+00 -4.70043092e+00 9.48490783e-01 | 3.60574092e+00 -4.70043092e+00 9.48490783e-01 3 -5.25937109e+00 2.92736316e+00 8.32309529e-01 | -5.25937109e+00 2.92736316e+00 8.32309529e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.61257874015 2^p V(r_1,...,r_N) = -6.61257874015 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 -2.66986157e+00 -2.44476258e+00 -4.54982779e+00 | -2.66986157e+00 -2.44476258e+00 -4.54982779e+00 1 2.50636077e+00 2.63148121e+00 -5.09886083e+00 | 2.50636077e+00 2.63148121e+00 -5.09886083e+00 2 7.31069852e+00 -6.27931330e+00 4.79095469e+00 | 7.31069852e+00 -6.27931330e+00 4.79095469e+00 3 -7.14719772e+00 6.09259467e+00 4.85773393e+00 | -7.14719772e+00 6.09259467e+00 4.85773393e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-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)) = -7.93309653333 2^p V(r_1,...,r_N) = -7.93309653333 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 -2.34365519e+00 -2.55260223e+00 -4.43268953e+00 | -2.34365519e+00 -2.55260223e+00 -4.43268953e+00 1 1.46635038e+00 2.18748044e+00 -2.11699306e+00 | 1.46635038e+00 2.18748044e+00 -2.11699306e+00 2 5.34159159e+00 -5.06064833e+00 3.09856923e+00 | 5.34159159e+00 -5.06064833e+00 3.09856923e+00 3 -4.46428678e+00 5.42577013e+00 3.45111336e+00 | -4.46428678e+00 5.42577013e+00 3.45111336e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-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)) = -2.97925224345 2^p V(r_1,...,r_N) = -2.97925224345 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 -4.32029871e+00 -6.20233866e+00 -6.24613912e+00 | -4.32029871e+00 -6.20233866e+00 -6.24613912e+00 1 1.69470163e+01 6.61197729e-01 -1.42411860e+01 | 1.69470163e+01 6.61197729e-01 -1.42411860e+01 2 3.15368455e+00 -2.88442978e+00 2.68866754e+00 | 3.15368455e+00 -2.88442978e+00 2.68866754e+00 3 -1.57804021e+01 8.42557071e+00 1.77986576e+01 | -1.57804021e+01 8.42557071e+00 1.77986576e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-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)) = -4.95649577337 2^p V(r_1,...,r_N) = -4.95649577337 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 -6.50485592e+00 -1.30683073e+01 -7.74384928e+00 | -6.50485592e+00 -1.30683073e+01 -7.74384928e+00 1 9.45231236e+00 6.08175216e+00 -5.64771873e+00 | 9.45231236e+00 6.08175216e+00 -5.64771873e+00 2 2.82732018e+00 -3.85608967e-01 2.39930894e+00 | 2.82732018e+00 -3.85608967e-01 2.39930894e+00 3 -5.77477663e+00 7.37216408e+00 1.09922591e+01 | -5.77477663e+00 7.37216408e+00 1.09922591e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.16240977332 2^p V(r_1,...,r_N) = -9.16240977332 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 -2.01382868e+00 -3.36946999e+00 -1.45796741e+00 | -2.01382868e+00 -3.36946999e+00 -1.45796741e+00 1 1.74698875e+00 2.11419668e+00 -1.52703511e+00 | 1.74698875e+00 2.11419668e+00 -1.52703511e+00 2 9.31380151e-01 -5.09450811e-01 1.28583006e+00 | 9.31380151e-01 -5.09450811e-01 1.28583006e+00 3 -6.64540218e-01 1.76472412e+00 1.69917246e+00 | -6.64540218e-01 1.76472412e+00 1.69917246e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTT (Configuration in file "config-Ti-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.75450393749 2^p V(r_1,...,r_N) = 2.75450393749 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 -6.83512659e+00 -6.64297779e+00 -4.09032853e+00 | -6.83512659e+00 -6.64297779e+00 -4.09032853e+00 1 8.49181570e+00 3.02253855e+00 -9.47718069e+00 | 8.49181570e+00 3.02253855e+00 -9.47718069e+00 2 5.50707517e+00 -3.04969223e+00 5.16979288e+00 | 5.50707517e+00 -3.04969223e+00 5.16979288e+00 3 -7.16376428e+00 6.67013146e+00 8.39771634e+00 | -7.16376428e+00 6.67013146e+00 8.39771634e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TTF (Configuration in file "config-Ti-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)) = 8.75624162776 2^p V(r_1,...,r_N) = 8.75624162776 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 -1.20267833e+01 -8.44644119e+00 -9.99677416e+00 | -1.20267833e+01 -8.44644119e+00 -9.99677416e+00 1 1.33769979e+01 4.87442019e+00 -1.24695348e+01 | 1.33769979e+01 4.87442019e+00 -1.24695348e+01 2 9.09836222e+00 -7.87982024e+00 8.63630958e+00 | 9.09836222e+00 -7.87982024e+00 8.63630958e+00 3 -1.04485768e+01 1.14518412e+01 1.38299994e+01 | -1.04485768e+01 1.14518412e+01 1.38299994e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFT (Configuration in file "config-Ti-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.97758948135 2^p V(r_1,...,r_N) = 6.97758948135 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 -1.07769229e+01 -1.24133851e+01 -1.30842808e+01 | -1.07769229e+01 -1.24133851e+01 -1.30842808e+01 1 1.13615410e+01 9.90059158e+00 -4.87445953e+00 | 1.13615410e+01 9.90059158e+00 -4.87445953e+00 2 6.39501447e+00 -6.47655232e+00 8.54180348e+00 | 6.39501447e+00 -6.47655232e+00 8.54180348e+00 3 -6.97963259e+00 8.98934584e+00 9.41693688e+00 | -6.97963259e+00 8.98934584e+00 9.41693688e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = TFF (Configuration in file "config-Ti-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)) = 4.49067304703 2^p V(r_1,...,r_N) = 4.49067304703 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 -9.30359112e+00 -6.32761028e+00 -7.31592624e+00 | -9.30359112e+00 -6.32761028e+00 -7.31592624e+00 1 8.44838587e+00 1.12932892e+01 -6.16741005e+00 | 8.44838587e+00 1.12932892e+01 -6.16741005e+00 2 6.83875796e+00 -1.00654698e+01 8.72115702e+00 | 6.83875796e+00 -1.00654698e+01 8.72115702e+00 3 -5.98355272e+00 5.09979090e+00 4.76217927e+00 | -5.98355272e+00 5.09979090e+00 4.76217927e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTT (Configuration in file "config-Ti-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)) = 5.00039958077 2^p V(r_1,...,r_N) = 5.00039958077 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 -9.47630051e+00 -7.54978174e+00 -5.71675712e+00 | -9.47630051e+00 -7.54978174e+00 -5.71675712e+00 1 1.16008091e+01 4.69674991e+00 -1.02636768e+01 | 1.16008091e+01 4.69674991e+00 -1.02636768e+01 2 5.01443850e+00 -6.97685689e+00 5.89028764e+00 | 5.01443850e+00 -6.97685689e+00 5.89028764e+00 3 -7.13894708e+00 9.82988872e+00 1.00901463e+01 | -7.13894708e+00 9.82988872e+00 1.00901463e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FTF (Configuration in file "config-Ti-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.8646348781 2^p V(r_1,...,r_N) = 10.8646348781 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 -1.42487674e+01 -7.17481933e+00 -1.61905138e+01 | -1.42487674e+01 -7.17481933e+00 -1.61905138e+01 1 7.43953115e+00 6.04449264e+00 -8.73955783e+00 | 7.43953115e+00 6.04449264e+00 -8.73955783e+00 2 1.75794016e+01 -1.09566318e+01 1.16776650e+01 | 1.75794016e+01 -1.09566318e+01 1.16776650e+01 3 -1.07701654e+01 1.20869585e+01 1.32524066e+01 | -1.07701654e+01 1.20869585e+01 1.32524066e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ti, PBC = FFT (Configuration in file "config-Ti-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)) = 1.97626806199 2^p V(r_1,...,r_N) = 1.97626806199 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 -4.44904271e+00 -7.40391938e+00 -4.71772240e+00 | -4.44904271e+00 -7.40391938e+00 -4.71772240e+00 1 7.46360121e+00 5.53517249e+00 -7.85829710e+00 | 7.46360121e+00 5.53517249e+00 -7.85829710e+00 2 4.22048737e+00 -3.55543763e+00 3.60787437e+00 | 4.22048737e+00 -3.55543763e+00 3.60787437e+00 3 -7.23504587e+00 5.42418452e+00 8.96814514e+00 | -7.23504587e+00 5.42418452e+00 8.96814514e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = TTT (Configuration in file "config-V-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)) = -5.5160218483 2^p V(r_1,...,r_N) = -5.5160218483 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 -3.52526819e+00 -7.96327955e+00 -6.73947871e+00 | -3.52526819e+00 -7.96327955e+00 -6.73947871e+00 1 8.93903729e+00 6.60247117e+00 -2.75763711e+00 | 8.93903729e+00 6.60247117e+00 -2.75763711e+00 2 1.38790950e+00 -1.59175934e+00 1.60990569e+00 | 1.38790950e+00 -1.59175934e+00 1.60990569e+00 3 -6.80167860e+00 2.95256772e+00 7.88721013e+00 | -6.80167860e+00 2.95256772e+00 7.88721013e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = TTF (Configuration in file "config-V-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.89575752928 2^p V(r_1,...,r_N) = -7.89575752928 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 -1.59738362e+00 -2.26492388e+00 -2.25695619e+00 | -1.59738362e+00 -2.26492388e+00 -2.25695619e+00 1 4.24829786e+00 1.94348908e+00 -3.62694912e+00 | 4.24829786e+00 1.94348908e+00 -3.62694912e+00 2 1.34993870e+00 -2.46081787e+00 1.16513648e+00 | 1.34993870e+00 -2.46081787e+00 1.16513648e+00 3 -4.00085294e+00 2.78225267e+00 4.71876884e+00 | -4.00085294e+00 2.78225267e+00 4.71876884e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = TFT (Configuration in file "config-V-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)) = -7.96461517027 2^p V(r_1,...,r_N) = -7.96461517027 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 -3.40407790e+00 -4.54198296e+00 -1.50500174e+00 | -3.40407790e+00 -4.54198296e+00 -1.50500174e+00 1 3.50027041e+00 4.62633267e+00 -2.34228941e+00 | 3.50027041e+00 4.62633267e+00 -2.34228941e+00 2 2.53155388e+00 -2.00733310e+00 1.35300336e+00 | 2.53155388e+00 -2.00733310e+00 1.35300336e+00 3 -2.62774639e+00 1.92298339e+00 2.49428780e+00 | -2.62774639e+00 1.92298339e+00 2.49428780e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = TFF (Configuration in file "config-V-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.97688323041 2^p V(r_1,...,r_N) = -8.97688323041 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 -1.85810865e+00 -1.07082633e+00 -1.18317174e+00 | -1.85810865e+00 -1.07082633e+00 -1.18317174e+00 1 2.21398384e+00 2.26126188e+00 -1.61177150e+00 | 2.21398384e+00 2.26126188e+00 -1.61177150e+00 2 4.88338900e-01 -1.79735502e+00 2.10024360e+00 | 4.88338900e-01 -1.79735502e+00 2.10024360e+00 3 -8.44214092e-01 6.06919469e-01 6.94699630e-01 | -8.44214092e-01 6.06919469e-01 6.94699630e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = FTT (Configuration in file "config-V-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)) = -8.73793548961 2^p V(r_1,...,r_N) = -8.73793548961 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 1.75797602e-01 -2.37353522e+00 -1.08094810e+00 | 1.75797602e-01 -2.37353522e+00 -1.08094810e+00 1 1.41229855e+00 -1.91829052e-01 5.34133887e-01 | 1.41229855e+00 -1.91829052e-01 5.34133887e-01 2 -1.54462632e+00 1.78727781e+00 -1.78361725e+00 | -1.54462632e+00 1.78727781e+00 -1.78361725e+00 3 -4.34698260e-02 7.78086467e-01 2.33043147e+00 | -4.34698260e-02 7.78086467e-01 2.33043147e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = FTF (Configuration in file "config-V-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)) = -7.97362652441 2^p V(r_1,...,r_N) = -7.97362652441 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 -2.94756417e+00 -3.93718281e+00 -3.62498454e+00 | -2.94756417e+00 -3.93718281e+00 -3.62498454e+00 1 3.82607292e+00 2.33944848e+00 -2.27502435e+00 | 3.82607292e+00 2.33944848e+00 -2.27502435e+00 2 1.28755716e+00 -1.41191419e+00 9.71132124e-01 | 1.28755716e+00 -1.41191419e+00 9.71132124e-01 3 -2.16606590e+00 3.00964851e+00 4.92887677e+00 | -2.16606590e+00 3.00964851e+00 4.92887677e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = V, PBC = FFT (Configuration in file "config-V-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -9.31849694054 2^p V(r_1,...,r_N) = -9.31849694054 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 9.18876190e-01 4.33919168e-01 3.37205014e-01 | 9.18876190e-01 4.33919168e-01 3.37205014e-01 1 -5.61554800e-01 -4.83121517e-01 2.70498358e-01 | -5.61554800e-01 -4.83121517e-01 2.70498358e-01 2 4.37762479e-01 -6.62455600e-01 -4.67729403e-01 | 4.37762479e-01 -6.62455600e-01 -4.67729403e-01 3 -7.95083869e-01 7.11657948e-01 -1.39973969e-01 | -7.95083869e-01 7.11657948e-01 -1.39973969e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = TTT (Configuration in file "config-NiTiV-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)) = -4.04900695073 2^p V(r_1,...,r_N) = -4.04900695073 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 -5.54730027e+00 -5.52246014e+00 -3.17059376e+00 | -5.54730027e+00 -5.52246014e+00 -3.17059376e+00 1 6.66908218e+00 8.50569284e+00 -6.04300545e+00 | 6.66908218e+00 8.50569284e+00 -6.04300545e+00 2 5.49022441e+00 -7.26297595e+00 5.03441116e+00 | 5.49022441e+00 -7.26297595e+00 5.03441116e+00 3 -6.61200633e+00 4.27974324e+00 4.17918805e+00 | -6.61200633e+00 4.27974324e+00 4.17918805e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = TTF (Configuration in file "config-NiTiV-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)) = -5.91283954474 2^p V(r_1,...,r_N) = -5.91283954474 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 -5.85749514e+00 -6.38659267e+00 -5.68992377e+00 | -5.85749514e+00 -6.38659267e+00 -5.68992377e+00 1 3.14789068e+00 1.38553971e+00 -1.85670867e+00 | 3.14789068e+00 1.38553971e+00 -1.85670867e+00 2 3.88715622e+00 -1.62030933e+00 2.83792237e+00 | 3.88715622e+00 -1.62030933e+00 2.83792237e+00 3 -1.17755176e+00 6.62136230e+00 4.70871007e+00 | -1.17755176e+00 6.62136230e+00 4.70871007e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = TFT (Configuration in file "config-NiTiV-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)) = -2.75647205838 2^p V(r_1,...,r_N) = -2.75647205838 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 -2.71223992e+00 -4.49459846e+00 -5.05603467e+00 | -2.71223992e+00 -4.49459846e+00 -5.05603467e+00 1 7.06744357e+00 4.61583322e+00 -1.04294622e+01 | 7.06744357e+00 4.61583322e+00 -1.04294622e+01 2 7.41668147e+00 -6.51229182e+00 9.47890419e-01 | 7.41668147e+00 -6.51229182e+00 9.47890419e-01 3 -1.17718851e+01 6.39105706e+00 1.45376065e+01 | -1.17718851e+01 6.39105706e+00 1.45376065e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = TFF (Configuration in file "config-NiTiV-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)) = 4.80950375113 2^p V(r_1,...,r_N) = 4.80950375113 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 -3.61763325e+00 -3.55071902e+00 -2.12489307e+00 | -3.61763325e+00 -3.55071902e+00 -2.12489307e+00 1 3.01515093e+01 5.42028886e+00 -3.06967164e+01 | 3.01515093e+01 5.42028886e+00 -3.06967164e+01 2 3.21473077e+00 -1.00493450e+01 7.69077052e+00 | 3.21473077e+00 -1.00493450e+01 7.69077052e+00 3 -2.97486068e+01 8.17977513e+00 2.51308389e+01 | -2.97486068e+01 8.17977513e+00 2.51308389e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = FTT (Configuration in file "config-NiTiV-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)) = -0.892910218125 2^p V(r_1,...,r_N) = -0.892910218125 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 -1.27729472e+01 -4.66134735e+00 -1.06272507e+01 | -1.27729472e+01 -4.66134735e+00 -1.06272507e+01 1 8.84363493e+00 7.31158550e+00 -8.56295320e+00 | 8.84363493e+00 7.31158550e+00 -8.56295320e+00 2 9.65328367e+00 -1.01602762e+01 1.43026814e+01 | 9.65328367e+00 -1.01602762e+01 1.43026814e+01 3 -5.72397139e+00 7.51003803e+00 4.88752249e+00 | -5.72397139e+00 7.51003803e+00 4.88752249e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = FTF (Configuration in file "config-NiTiV-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)) = -4.7444411341 2^p V(r_1,...,r_N) = -4.7444411341 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 -6.64326156e+00 -4.06375388e+00 -5.24774306e+00 | -6.64326156e+00 -4.06375388e+00 -5.24774306e+00 1 5.60028661e+00 7.09645572e+00 -6.11610983e+00 | 5.60028661e+00 7.09645572e+00 -6.11610983e+00 2 4.04633684e+00 -4.83082865e+00 8.86518771e+00 | 4.04633684e+00 -4.83082865e+00 8.86518771e+00 3 -3.00336188e+00 1.79812681e+00 2.49866518e+00 | -3.00336188e+00 1.79812681e+00 2.49866518e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti V, PBC = FFT (Configuration in file "config-NiTiV-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.34835239421 2^p V(r_1,...,r_N) = -7.34835239421 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 -9.22770875e-01 -1.37147723e+00 -4.33828933e-01 | -9.22770875e-01 -1.37147723e+00 -4.33828933e-01 1 3.60135236e+00 1.23627068e+00 -4.00148626e+00 | 3.60135236e+00 1.23627068e+00 -4.00148626e+00 2 8.36575752e-01 -1.84678434e+00 1.02081872e+00 | 8.36575752e-01 -1.84678434e+00 1.02081872e+00 3 -3.51515723e+00 1.98199089e+00 3.41449647e+00 | -3.51515723e+00 1.98199089e+00 3.41449647e+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.