!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_FarkasJones_1996_NbTiAl__MO_042691367780_000 Supported species : Al Nb Ti random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.87085342804 2^p V(r_1,...,r_N) = 1.87085342804 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.49017136e+00 -1.68246388e+01 -1.81313043e+01 | -7.49017136e+00 -1.68246388e+01 -1.81313043e+01 1 4.58881882e+00 3.25398403e+00 -2.47603461e+00 | 4.58881882e+00 3.25398403e+00 -2.47603461e+00 2 6.58266349e+00 -4.28832113e+00 6.96786359e+00 | 6.58266349e+00 -4.28832113e+00 6.96786359e+00 3 -3.68131094e+00 1.78589759e+01 1.36394753e+01 | -3.68131094e+00 1.78589759e+01 1.36394753e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 4.75252959524 2^p V(r_1,...,r_N) = 4.75252959524 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 -1.20343499e+01 -7.56274212e+00 -7.51644969e+00 | -1.20343499e+01 -7.56274212e+00 -7.51644969e+00 1 8.08901365e+00 7.25581635e+00 -1.03349037e+01 | 8.08901365e+00 7.25581635e+00 -1.03349037e+01 2 1.86060063e+01 -2.06355509e+01 1.41862996e+01 | 1.86060063e+01 -2.06355509e+01 1.41862996e+01 3 -1.46606701e+01 2.09424766e+01 3.66505375e+00 | -1.46606701e+01 2.09424766e+01 3.66505375e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.44088945154 2^p V(r_1,...,r_N) = 8.44088945154 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 -1.36008354e+01 -1.99197950e+01 -2.45462591e+01 | -1.36008354e+01 -1.99197950e+01 -2.45462591e+01 1 1.81706502e+01 1.88841691e+01 -1.03289100e+01 | 1.81706502e+01 1.88841691e+01 -1.03289100e+01 2 1.06712711e+01 -1.50400956e+01 1.66320854e+01 | 1.06712711e+01 -1.50400956e+01 1.66320854e+01 3 -1.52410859e+01 1.60757215e+01 1.82430838e+01 | -1.52410859e+01 1.60757215e+01 1.82430838e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 26.6800826065 2^p V(r_1,...,r_N) = 26.6800826065 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 -3.83994207e+01 -3.16183023e+01 -6.39832459e+01 | -3.83994207e+01 -3.16183023e+01 -6.39832459e+01 1 1.54710816e+01 2.03701877e+01 -1.25574216e+01 | 1.54710816e+01 2.03701877e+01 -1.25574216e+01 2 4.77429366e+01 -2.40915688e+01 4.81007984e+01 | 4.77429366e+01 -2.40915688e+01 4.81007984e+01 3 -2.48145975e+01 3.53396834e+01 2.84398691e+01 | -2.48145975e+01 3.53396834e+01 2.84398691e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.79569125138 2^p V(r_1,...,r_N) = 7.79569125138 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 -1.92180838e+01 -1.32589562e+01 -1.90290111e+01 | -1.92180838e+01 -1.32589562e+01 -1.90290111e+01 1 1.14954987e+01 1.68798426e+01 -1.36456708e+01 | 1.14954987e+01 1.68798426e+01 -1.36456708e+01 2 1.86143013e+01 -1.95958159e+01 1.78137807e+01 | 1.86143013e+01 -1.95958159e+01 1.78137807e+01 3 -1.08917161e+01 1.59749295e+01 1.48609012e+01 | -1.08917161e+01 1.59749295e+01 1.48609012e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.56688539059 2^p V(r_1,...,r_N) = 1.56688539059 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 -1.48870880e+01 -1.14189669e+01 -7.62560947e+00 | -1.48870880e+01 -1.14189669e+01 -7.62560947e+00 1 8.95351869e+00 1.19681743e+01 -9.47923377e+00 | 8.95351869e+00 1.19681743e+01 -9.47923377e+00 2 9.29755017e+00 -4.81440591e+00 1.44623847e+01 | 9.29755017e+00 -4.81440591e+00 1.44623847e+01 3 -3.36398084e+00 4.26519849e+00 2.64245852e+00 | -3.36398084e+00 4.26519849e+00 2.64245852e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 22.7598544686 2^p V(r_1,...,r_N) = 22.7598544686 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 -1.61342063e+01 -1.43243824e+01 -1.86441410e+01 | -1.61342063e+01 -1.43243824e+01 -1.86441410e+01 1 2.05899592e+01 2.16431186e+01 -1.76416327e+01 | 2.05899592e+01 2.16431186e+01 -1.76416327e+01 2 4.69583930e+01 -5.33759183e+01 2.42407222e+01 | 4.69583930e+01 -5.33759183e+01 2.42407222e+01 3 -5.14141458e+01 4.60571821e+01 1.20450515e+01 | -5.14141458e+01 4.60571821e+01 1.20450515e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTT (Configuration in file "config-Nb-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)) = -5.28867117648 2^p V(r_1,...,r_N) = -5.28867117648 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 -2.64774162e+01 -1.44880181e+01 -3.07719239e+01 | -2.64774162e+01 -1.44880181e+01 -3.07719239e+01 1 1.30365341e+01 1.98636516e+01 -1.56925362e+01 | 1.30365341e+01 1.98636516e+01 -1.56925362e+01 2 3.50782070e+01 -2.65253312e+01 3.11596744e+01 | 3.50782070e+01 -2.65253312e+01 3.11596744e+01 3 -2.16373249e+01 2.11496977e+01 1.53047857e+01 | -2.16373249e+01 2.11496977e+01 1.53047857e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TTF (Configuration in file "config-Nb-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)) = -2.35738802413 2^p V(r_1,...,r_N) = -2.35738802413 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 -2.12601627e+01 -1.60111683e+01 -1.97389552e+01 | -2.12601627e+01 -1.60111683e+01 -1.97389552e+01 1 1.61532830e+01 2.39492162e+01 -2.15460812e+01 | 1.61532830e+01 2.39492162e+01 -2.15460812e+01 2 4.38181844e+01 -4.00603898e+01 2.61231788e+01 | 4.38181844e+01 -4.00603898e+01 2.61231788e+01 3 -3.87113048e+01 3.21223419e+01 1.51618576e+01 | -3.87113048e+01 3.21223419e+01 1.51618576e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFT (Configuration in file "config-Nb-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)) = -14.1228926499 2^p V(r_1,...,r_N) = -14.1228926499 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 -4.92298962e+00 -5.02682656e+00 -4.42743632e+00 | -4.92298962e+00 -5.02682656e+00 -4.42743632e+00 1 7.94198555e+00 1.14134910e+01 -2.09269122e+01 | 7.94198555e+00 1.14134910e+01 -2.09269122e+01 2 8.53288166e+00 -1.79959857e+01 2.07700154e+01 | 8.53288166e+00 -1.79959857e+01 2.07700154e+01 3 -1.15518776e+01 1.16093213e+01 4.58433317e+00 | -1.15518776e+01 1.16093213e+01 4.58433317e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = TFF (Configuration in file "config-Nb-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)) = -12.4500049804 2^p V(r_1,...,r_N) = -12.4500049804 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 -8.74230394e+00 -2.71475499e+01 -2.25265277e+01 | -8.74230394e+00 -2.71475499e+01 -2.25265277e+01 1 8.82721001e+00 6.62113520e+00 -9.20451927e+00 | 8.82721001e+00 6.62113520e+00 -9.20451927e+00 2 5.11308507e+00 -6.96701535e+00 6.22005382e+00 | 5.11308507e+00 -6.96701535e+00 6.22005382e+00 3 -5.19799114e+00 2.74934301e+01 2.55109931e+01 | -5.19799114e+00 2.74934301e+01 2.55109931e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTT (Configuration in file "config-Nb-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)) = -18.6074062958 2^p V(r_1,...,r_N) = -18.6074062958 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 -3.59889759e+00 -3.38010753e+00 -1.86065914e+00 | -3.59889759e+00 -3.38010753e+00 -1.86065914e+00 1 6.95726088e+00 5.12941845e+00 -4.94276750e+00 | 6.95726088e+00 5.12941845e+00 -4.94276750e+00 2 7.36848363e-01 -3.39523633e+00 3.08014491e+00 | 7.36848363e-01 -3.39523633e+00 3.08014491e+00 3 -4.09521165e+00 1.64592541e+00 3.72328173e+00 | -4.09521165e+00 1.64592541e+00 3.72328173e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FTF (Configuration in file "config-Nb-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)) = -14.8502589374 2^p V(r_1,...,r_N) = -14.8502589374 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 -6.11141420e+00 -5.91126432e+00 -9.86506521e+00 | -6.11141420e+00 -5.91126432e+00 -9.86506521e+00 1 9.19572075e+00 1.50013551e+01 -1.25829018e+01 | 9.19572075e+00 1.50013551e+01 -1.25829018e+01 2 5.63705819e+00 -1.79877982e+01 1.58273068e+01 | 5.63705819e+00 -1.79877982e+01 1.58273068e+01 3 -8.72136474e+00 8.89770745e+00 6.62066017e+00 | -8.72136474e+00 8.89770745e+00 6.62066017e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Nb, PBC = FFT (Configuration in file "config-Nb-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)) = 46.5374496233 2^p V(r_1,...,r_N) = 46.5374496233 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 -4.50364992e+01 -2.21959831e+02 -1.78701572e+02 | -4.50364992e+01 -2.21959831e+02 -1.78701572e+02 1 3.85766337e+01 2.84810751e+01 -3.53736911e+01 | 3.85766337e+01 2.84810751e+01 -3.53736911e+01 2 3.45055422e+01 -1.89932068e+01 2.05103486e+01 | 3.45055422e+01 -1.89932068e+01 2.05103486e+01 3 -2.80456768e+01 2.12471963e+02 1.93564914e+02 | -2.80456768e+01 2.12471963e+02 1.93564914e+02 ------------------------------------------------------------------------------------------------------------------------ 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)) = -11.3580567696 2^p V(r_1,...,r_N) = -11.3580567696 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 -2.11714049e+00 -3.41953476e+00 -2.14573898e+00 | -2.11714049e+00 -3.41953476e+00 -2.14573898e+00 1 3.16183376e+00 2.59234067e+00 -3.27939167e+00 | 3.16183376e+00 2.59234067e+00 -3.27939167e+00 2 2.00418436e+00 -1.67321611e+00 1.68892086e+00 | 2.00418436e+00 -1.67321611e+00 1.68892086e+00 3 -3.04887763e+00 2.50041021e+00 3.73620979e+00 | -3.04887763e+00 2.50041021e+00 3.73620979e+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)) = -5.67505872883 2^p V(r_1,...,r_N) = -5.67505872883 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 -5.42517681e+00 -1.13034461e+01 -1.01594549e+01 | -5.42517681e+00 -1.13034461e+01 -1.01594549e+01 1 1.27236268e+01 1.00984567e+01 -4.54422994e+00 | 1.27236268e+01 1.00984567e+01 -4.54422994e+00 2 3.21768546e+00 -3.65801350e+00 3.70902707e+00 | 3.21768546e+00 -3.65801350e+00 3.70902707e+00 3 -1.05161354e+01 4.86300290e+00 1.09946578e+01 | -1.05161354e+01 4.86300290e+00 1.09946578e+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)) = -10.7068018933 2^p V(r_1,...,r_N) = -10.7068018933 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 -1.14763492e+00 -1.64028956e+00 -1.59284608e+00 | -1.14763492e+00 -1.64028956e+00 -1.59284608e+00 1 5.27390208e+00 2.70175072e+00 -4.78298318e+00 | 5.27390208e+00 2.70175072e+00 -4.78298318e+00 2 1.65691592e+00 -3.52646335e+00 1.73818038e+00 | 1.65691592e+00 -3.52646335e+00 1.73818038e+00 3 -5.78318308e+00 2.46500219e+00 4.63764888e+00 | -5.78318308e+00 2.46500219e+00 4.63764888e+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)) = -11.3206017465 2^p V(r_1,...,r_N) = -11.3206017465 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 -3.07138447e+00 -2.51023690e+00 -3.17450970e+00 | -3.07138447e+00 -2.51023690e+00 -3.17450970e+00 1 1.63358773e+00 3.32160942e+00 -2.35802221e+00 | 1.63358773e+00 3.32160942e+00 -2.35802221e+00 2 3.19689774e+00 -2.63326208e+00 3.99727361e+00 | 3.19689774e+00 -2.63326208e+00 3.99727361e+00 3 -1.75910099e+00 1.82188955e+00 1.53525830e+00 | -1.75910099e+00 1.82188955e+00 1.53525830e+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)) = -8.38520086256 2^p V(r_1,...,r_N) = -8.38520086256 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.05455018e+00 -4.47781201e+00 -5.38472233e+00 | -7.05455018e+00 -4.47781201e+00 -5.38472233e+00 1 4.69687463e+00 7.68348939e+00 -5.59510558e+00 | 4.69687463e+00 7.68348939e+00 -5.59510558e+00 2 6.00018147e+00 -6.29375305e+00 8.18486921e+00 | 6.00018147e+00 -6.29375305e+00 8.18486921e+00 3 -3.64250592e+00 3.08807567e+00 2.79495870e+00 | -3.64250592e+00 3.08807567e+00 2.79495870e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -12.1365833165 2^p V(r_1,...,r_N) = -12.1365833165 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 -2.77236591e+00 -2.25859077e+00 -1.90969587e+00 | -2.77236591e+00 -2.25859077e+00 -1.90969587e+00 1 1.66862602e+00 2.38856773e+00 -2.09290951e+00 | 1.66862602e+00 2.38856773e+00 -2.09290951e+00 2 2.54248992e+00 -1.98022431e+00 1.51121935e+00 | 2.54248992e+00 -1.98022431e+00 1.51121935e+00 3 -1.43875002e+00 1.85024735e+00 2.49138602e+00 | -1.43875002e+00 1.85024735e+00 2.49138602e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.19714109875 2^p V(r_1,...,r_N) = -2.19714109875 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 -1.03902015e+01 -8.18760777e+00 -9.06651443e+00 | -1.03902015e+01 -8.18760777e+00 -9.06651443e+00 1 5.10707477e+00 1.12702398e+01 -1.05303618e+01 | 5.10707477e+00 1.12702398e+01 -1.05303618e+01 2 1.66466809e+01 -1.29592663e+01 7.19502586e+00 | 1.66466809e+01 -1.29592663e+01 7.19502586e+00 3 -1.13635542e+01 9.87663426e+00 1.24018503e+01 | -1.13635542e+01 9.87663426e+00 1.24018503e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TTT (Configuration in file "config-AlNbTi-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)) = -2.29294212495 2^p V(r_1,...,r_N) = -2.29294212495 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.77860752e+00 -9.15474557e+00 -1.45822302e+01 | -7.77860752e+00 -9.15474557e+00 -1.45822302e+01 1 2.17364021e+00 2.30315192e+00 -2.91141950e+00 | 2.17364021e+00 2.30315192e+00 -2.91141950e+00 2 1.69607210e+01 -6.87097228e+00 5.49600478e+00 | 1.69607210e+01 -6.87097228e+00 5.49600478e+00 3 -1.13557537e+01 1.37225659e+01 1.19976449e+01 | -1.13557537e+01 1.37225659e+01 1.19976449e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TTF (Configuration in file "config-AlNbTi-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.90140548979 2^p V(r_1,...,r_N) = 1.90140548979 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 -1.93939794e+01 -6.42012894e+00 -5.44912275e+00 | -1.93939794e+01 -6.42012894e+00 -5.44912275e+00 1 1.19754310e+01 1.89154871e+01 -8.46256259e+00 | 1.19754310e+01 1.89154871e+01 -8.46256259e+00 2 9.85166644e+00 -1.23548128e+01 1.47711869e+01 | 9.85166644e+00 -1.23548128e+01 1.47711869e+01 3 -2.43311797e+00 -1.40545371e-01 -8.59501516e-01 | -2.43311797e+00 -1.40545371e-01 -8.59501516e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TFT (Configuration in file "config-AlNbTi-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)) = -8.7549597659 2^p V(r_1,...,r_N) = -8.7549597659 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 -4.19384880e+00 -5.58064428e+00 -7.10233442e+00 | -4.19384880e+00 -5.58064428e+00 -7.10233442e+00 1 2.33514746e+00 1.27243404e+00 -1.27310853e+00 | 2.33514746e+00 1.27243404e+00 -1.27310853e+00 2 6.06811176e+00 -1.40571225e+00 3.66533275e+00 | 6.06811176e+00 -1.40571225e+00 3.66533275e+00 3 -4.20941041e+00 5.71392250e+00 4.71011020e+00 | -4.20941041e+00 5.71392250e+00 4.71011020e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = TFF (Configuration in file "config-AlNbTi-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)) = -3.59691054733 2^p V(r_1,...,r_N) = -3.59691054733 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 -2.24116831e+01 3.13698040e+01 1.55738882e+01 | -2.24116831e+01 3.13698040e+01 1.55738882e+01 1 9.52381108e+00 8.81757289e+00 -1.10975552e+01 | 9.52381108e+00 8.81757289e+00 -1.10975552e+01 2 1.21405565e+01 -1.04537205e+01 1.25004273e+01 | 1.21405565e+01 -1.04537205e+01 1.25004273e+01 3 7.47315481e-01 -2.97336564e+01 -1.69767603e+01 | 7.47315481e-01 -2.97336564e+01 -1.69767603e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = FTT (Configuration in file "config-AlNbTi-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)) = -8.89623968882 2^p V(r_1,...,r_N) = -8.89623968882 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 -2.11367618e+00 -2.88285672e+00 -6.35814249e-01 | -2.11367618e+00 -2.88285672e+00 -6.35814249e-01 1 5.51039571e+00 4.04253241e+00 -6.03294458e+00 | 5.51039571e+00 4.04253241e+00 -6.03294458e+00 2 3.16784263e+00 -4.70367332e+00 2.03468336e+00 | 3.16784263e+00 -4.70367332e+00 2.03468336e+00 3 -6.56456216e+00 3.54399764e+00 4.63407547e+00 | -6.56456216e+00 3.54399764e+00 4.63407547e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = FTF (Configuration in file "config-AlNbTi-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)) = -7.94670836972 2^p V(r_1,...,r_N) = -7.94670836972 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 -5.53756632e+00 -5.98547348e+00 -3.31744158e+00 | -5.53756632e+00 -5.98547348e+00 -3.31744158e+00 1 7.69264490e+00 8.78156716e+00 -4.92794522e+00 | 7.69264490e+00 8.78156716e+00 -4.92794522e+00 2 1.64791744e+00 -3.05987942e+00 4.63931669e+00 | 1.64791744e+00 -3.05987942e+00 4.63931669e+00 3 -3.80299603e+00 2.63785737e-01 3.60607010e+00 | -3.80299603e+00 2.63785737e-01 3.60607010e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Nb Ti, PBC = FFT (Configuration in file "config-AlNbTi-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.26351591828 2^p V(r_1,...,r_N) = 6.26351591828 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 -2.27859508e+01 -1.26605416e+01 -3.09911652e+01 | -2.27859508e+01 -1.26605416e+01 -3.09911652e+01 1 7.92873733e+00 5.84711358e+00 -7.39448271e+00 | 7.92873733e+00 5.84711358e+00 -7.39448271e+00 2 3.26069039e+01 -6.90894622e+00 2.42524925e+01 | 3.26069039e+01 -6.90894622e+00 2.42524925e+01 3 -1.77496905e+01 1.37223743e+01 1.41331554e+01 | -1.77496905e+01 1.37223743e+01 1.41331554e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.