!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KoGrabowskiNeugebauer_2015_NiTi__SM_770142935022_000 Supported species : Ni Ti 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)) = -7.76850653695 2^p V(r_1,...,r_N) = -7.76850653695 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 6.55053777e+00 5.20458048e+00 | -1.04325086e+00 6.55053777e+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)) = -8.27817576868 2^p V(r_1,...,r_N) = -8.27817576868 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)) = -6.61257874011 2^p V(r_1,...,r_N) = -6.61257874011 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)) = -7.9330965333 2^p V(r_1,...,r_N) = -7.9330965333 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)) = -2.97925224334 2^p V(r_1,...,r_N) = -2.97925224334 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)) = -4.95649577329 2^p V(r_1,...,r_N) = -4.95649577329 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)) = -9.16240977331 2^p V(r_1,...,r_N) = -9.16240977331 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)) = 2.75450393763 2^p V(r_1,...,r_N) = 2.75450393763 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)) = 8.75624162805 2^p V(r_1,...,r_N) = 8.75624162805 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)) = 6.9775894816 2^p V(r_1,...,r_N) = 6.9775894816 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)) = 4.49067304721 2^p V(r_1,...,r_N) = 4.49067304721 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 8.44838588e+00 1.12932892e+01 -6.16741005e+00 | 8.44838588e+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)) = 5.00039958096 2^p V(r_1,...,r_N) = 5.00039958096 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 -9.47630052e+00 -7.54978174e+00 -5.71675712e+00 | -9.47630052e+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)) = 10.8646348784 2^p V(r_1,...,r_N) = 10.8646348784 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)) = 1.97626806212 2^p V(r_1,...,r_N) = 1.97626806212 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 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = TTT (Configuration in file "config-NiTi-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.36972575956 2^p V(r_1,...,r_N) = -1.36972575956 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.91582423e+00 -3.47786969e+00 -1.07646705e+01 | -8.91582423e+00 -3.47786969e+00 -1.07646705e+01 1 3.58500799e+00 4.86145446e+00 -3.13784137e+00 | 3.58500799e+00 4.86145446e+00 -3.13784137e+00 2 9.47005692e+00 -8.53693923e+00 6.12167677e+00 | 9.47005692e+00 -8.53693923e+00 6.12167677e+00 3 -4.13924068e+00 7.15335446e+00 7.78083507e+00 | -4.13924068e+00 7.15335446e+00 7.78083507e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = TTF (Configuration in file "config-NiTi-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)) = -0.740278292472 2^p V(r_1,...,r_N) = -0.740278292472 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 -1.01942905e+01 -7.44423105e+00 -9.98805588e+00 | -1.01942905e+01 -7.44423105e+00 -9.98805588e+00 1 3.70103586e+00 4.94780805e+00 -3.35721533e+00 | 3.70103586e+00 4.94780805e+00 -3.35721533e+00 2 1.04443208e+01 -3.47892875e+00 9.63921279e+00 | 1.04443208e+01 -3.47892875e+00 9.63921279e+00 3 -3.95106612e+00 5.97535175e+00 3.70605843e+00 | -3.95106612e+00 5.97535175e+00 3.70605843e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = TFT (Configuration in file "config-NiTi-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.2523235024 2^p V(r_1,...,r_N) = -1.2523235024 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 -9.21681427e+00 -3.81703066e+00 -7.14189568e+00 | -9.21681427e+00 -3.81703066e+00 -7.14189568e+00 1 6.45190385e+00 8.04952981e+00 -8.01896902e+00 | 6.45190385e+00 8.04952981e+00 -8.01896902e+00 2 7.88973071e+00 -6.62169647e+00 1.12087841e+01 | 7.88973071e+00 -6.62169647e+00 1.12087841e+01 3 -5.12482029e+00 2.38919732e+00 3.95208061e+00 | -5.12482029e+00 2.38919732e+00 3.95208061e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = TFF (Configuration in file "config-NiTi-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)) = 1.28431266331 2^p V(r_1,...,r_N) = 1.28431266331 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 -6.73004016e+00 -6.37995166e+00 -4.26212659e+00 | -6.73004016e+00 -6.37995166e+00 -4.26212659e+00 1 7.39097900e+00 7.20442090e+00 -1.26903305e+01 | 7.39097900e+00 7.20442090e+00 -1.26903305e+01 2 9.54764889e+00 -9.53464348e+00 1.19545711e+01 | 9.54764889e+00 -9.53464348e+00 1.19545711e+01 3 -1.02085877e+01 8.71017424e+00 4.99788595e+00 | -1.02085877e+01 8.71017424e+00 4.99788595e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = FTT (Configuration in file "config-NiTi-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.67716786332 2^p V(r_1,...,r_N) = -3.67716786332 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 -2.17663460e+00 -3.03523295e+00 -2.74551274e+00 | -2.17663460e+00 -3.03523295e+00 -2.74551274e+00 1 4.04896945e+00 3.51469729e+00 -6.63752823e+00 | 4.04896945e+00 3.51469729e+00 -6.63752823e+00 2 3.15804506e+00 -6.07776579e+00 4.96162393e+00 | 3.15804506e+00 -6.07776579e+00 4.96162393e+00 3 -5.03037991e+00 5.59830145e+00 4.42141703e+00 | -5.03037991e+00 5.59830145e+00 4.42141703e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = FTF (Configuration in file "config-NiTi-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)) = -6.29359514199 2^p V(r_1,...,r_N) = -6.29359514199 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 -5.07953275e-01 -8.68103728e-01 -4.54252489e-01 | -5.07953275e-01 -8.68103728e-01 -4.54252489e-01 1 3.55166329e+00 5.46059197e-01 -3.59034136e+00 | 3.55166329e+00 5.46059197e-01 -3.59034136e+00 2 4.28063680e-01 -1.27396611e+00 4.30226919e-01 | 4.28063680e-01 -1.27396611e+00 4.30226919e-01 3 -3.47177370e+00 1.59601064e+00 3.61436693e+00 | -3.47177370e+00 1.59601064e+00 3.61436693e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ni Ti, PBC = FFT (Configuration in file "config-NiTi-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)) = -3.74666645385 2^p V(r_1,...,r_N) = -3.74666645385 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 -3.08844176e+00 -3.87941911e+00 -3.26584072e+00 | -3.08844176e+00 -3.87941911e+00 -3.26584072e+00 1 3.56548000e+00 3.56746832e+00 -6.00251556e+00 | 3.56548000e+00 3.56746832e+00 -6.00251556e+00 2 4.76516019e+00 -6.39534683e+00 4.28857427e+00 | 4.76516019e+00 -6.39534683e+00 4.28857427e+00 3 -5.24219842e+00 6.70729762e+00 4.97978201e+00 | -5.24219842e+00 6.70729762e+00 4.97978201e+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.