!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ZopeMishin_2003_TiAl__MO_117656786760_005 Supported species : Al 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)) = -1.53941023721 2^p V(r_1,...,r_N) = -1.53941023721 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 -2.45779588e+00 -2.93621260e+00 -3.25758359e+00 | -2.45779588e+00 -2.93621260e+00 -3.25758359e+00 1 2.13581951e+00 1.42803509e+00 -1.52465568e+00 | 2.13581951e+00 1.42803509e+00 -1.52465568e+00 2 2.00609010e+00 -1.91511143e+00 2.40606111e+00 | 2.00609010e+00 -1.91511143e+00 2.40606111e+00 3 -1.68411373e+00 3.42328894e+00 2.37617816e+00 | -1.68411373e+00 3.42328894e+00 2.37617816e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -0.620002960863 2^p V(r_1,...,r_N) = -0.620002960863 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 -3.13778384e+00 -2.40950891e+00 -2.09191892e+00 | -3.13778384e+00 -2.40950891e+00 -2.09191892e+00 1 2.52418012e+00 1.80084210e+00 -3.05106137e+00 | 2.52418012e+00 1.80084210e+00 -3.05106137e+00 2 3.14152346e+00 -3.29083838e+00 3.37806141e+00 | 3.14152346e+00 -3.29083838e+00 3.37806141e+00 3 -2.52791974e+00 3.89950519e+00 1.76491888e+00 | -2.52791974e+00 3.89950519e+00 1.76491888e+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)) = 0.45678138938 2^p V(r_1,...,r_N) = 0.45678138938 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 -2.80344972e+00 -3.35193545e+00 -4.38724241e+00 | -2.80344972e+00 -3.35193545e+00 -4.38724241e+00 1 3.80432433e+00 3.66803816e+00 -2.26883073e+00 | 3.80432433e+00 3.66803816e+00 -2.26883073e+00 2 2.59639955e+00 -3.35528281e+00 3.44616640e+00 | 2.59639955e+00 -3.35528281e+00 3.44616640e+00 3 -3.59727416e+00 3.03918010e+00 3.20990675e+00 | -3.59727416e+00 3.03918010e+00 3.20990675e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.81172413702 2^p V(r_1,...,r_N) = 2.81172413702 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 -4.35726421e+00 -4.25641013e+00 -6.42172104e+00 | -4.35726421e+00 -4.25641013e+00 -6.42172104e+00 1 3.36871879e+00 3.74101628e+00 -2.71325102e+00 | 3.36871879e+00 3.74101628e+00 -2.71325102e+00 2 5.19267292e+00 -3.89576929e+00 5.33328679e+00 | 5.19267292e+00 -3.89576929e+00 5.33328679e+00 3 -4.20412750e+00 4.41116314e+00 3.80168527e+00 | -4.20412750e+00 4.41116314e+00 3.80168527e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 0.326373722373 2^p V(r_1,...,r_N) = 0.326373722373 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 -3.79300063e+00 -2.78535169e+00 -3.53672296e+00 | -3.79300063e+00 -2.78535169e+00 -3.53672296e+00 1 2.92208612e+00 3.34383969e+00 -3.01789041e+00 | 2.92208612e+00 3.34383969e+00 -3.01789041e+00 2 3.54841316e+00 -3.74914539e+00 3.16353626e+00 | 3.54841316e+00 -3.74914539e+00 3.16353626e+00 3 -2.67749865e+00 3.19065738e+00 3.39107711e+00 | -2.67749865e+00 3.19065738e+00 3.39107711e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.45383062195 2^p V(r_1,...,r_N) = -1.45383062195 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 -3.02567803e+00 -2.83907974e+00 -2.19890263e+00 | -3.02567803e+00 -2.83907974e+00 -2.19890263e+00 1 1.93941043e+00 2.59692321e+00 -2.31684053e+00 | 1.93941043e+00 2.59692321e+00 -2.31684053e+00 2 2.62620181e+00 -1.51875739e+00 3.33275670e+00 | 2.62620181e+00 -1.51875739e+00 3.33275670e+00 3 -1.53993422e+00 1.76091392e+00 1.18298647e+00 | -1.53993422e+00 1.76091392e+00 1.18298647e+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)) = 2.15494561423 2^p V(r_1,...,r_N) = 2.15494561423 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 -3.05236480e+00 -2.88078542e+00 -4.03090051e+00 | -3.05236480e+00 -2.88078542e+00 -4.03090051e+00 1 4.02718807e+00 3.57989540e+00 -3.12265404e+00 | 4.02718807e+00 3.57989540e+00 -3.12265404e+00 2 4.57468130e+00 -5.44702883e+00 4.19924133e+00 | 4.57468130e+00 -5.44702883e+00 4.19924133e+00 3 -5.54950457e+00 4.74791885e+00 2.95431321e+00 | -5.54950457e+00 4.74791885e+00 2.95431321e+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)) = 4.49952340007 2^p V(r_1,...,r_N) = 4.49952340007 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 -1.53918978e+01 -8.98220453e+00 -1.78039197e+01 | -1.53918978e+01 -8.98220453e+00 -1.78039197e+01 1 8.13855027e+00 1.24428888e+01 -9.72876914e+00 | 8.13855027e+00 1.24428888e+01 -9.72876914e+00 2 2.03152474e+01 -1.63191039e+01 1.82104042e+01 | 2.03152474e+01 -1.63191039e+01 1.82104042e+01 3 -1.30618999e+01 1.28584197e+01 9.32228456e+00 | -1.30618999e+01 1.28584197e+01 9.32228456e+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)) = 6.23624255315 2^p V(r_1,...,r_N) = 6.23624255315 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 -1.31578902e+01 -1.00361000e+01 -1.11873743e+01 | -1.31578902e+01 -1.00361000e+01 -1.11873743e+01 1 1.01202026e+01 1.46530170e+01 -1.21634340e+01 | 1.01202026e+01 1.46530170e+01 -1.21634340e+01 2 2.32622706e+01 -2.14691891e+01 1.53104806e+01 | 2.32622706e+01 -2.14691891e+01 1.53104806e+01 3 -2.02245830e+01 1.68522721e+01 8.04032776e+00 | -2.02245830e+01 1.68522721e+01 8.04032776e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.32081505061 2^p V(r_1,...,r_N) = -1.32081505061 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 -4.35658717e+00 -4.90037434e+00 -4.21445853e+00 | -4.35658717e+00 -4.90037434e+00 -4.21445853e+00 1 6.11746550e+00 8.41705396e+00 -1.48309792e+01 | 6.11746550e+00 8.41705396e+00 -1.48309792e+01 2 6.49099213e+00 -1.29235360e+01 1.49477463e+01 | 6.49099213e+00 -1.29235360e+01 1.49477463e+01 3 -8.25187046e+00 9.40685638e+00 4.09769142e+00 | -8.25187046e+00 9.40685638e+00 4.09769142e+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)) = -0.0702156891663 2^p V(r_1,...,r_N) = -0.0702156891663 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 -5.92812545e+00 -1.72124485e+01 -1.44074236e+01 | -5.92812545e+00 -1.72124485e+01 -1.44074236e+01 1 5.92528696e+00 6.14090239e+00 -7.84975538e+00 | 5.92528696e+00 6.14090239e+00 -7.84975538e+00 2 3.81363942e+00 -6.47294087e+00 5.93761659e+00 | 3.81363942e+00 -6.47294087e+00 5.93761659e+00 3 -3.81080093e+00 1.75444869e+01 1.63195624e+01 | -3.81080093e+00 1.75444869e+01 1.63195624e+01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -5.65602928458 2^p V(r_1,...,r_N) = -5.65602928458 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 -4.31946115e+00 -4.48546133e+00 -2.99178764e+00 | -4.31946115e+00 -4.48546133e+00 -2.99178764e+00 1 7.59289812e+00 6.06411529e+00 -5.61227870e+00 | 7.59289812e+00 6.06411529e+00 -5.61227870e+00 2 1.59881315e+00 -4.38145641e+00 3.84172112e+00 | 1.59881315e+00 -4.38145641e+00 3.84172112e+00 3 -4.87225012e+00 2.80280245e+00 4.76234522e+00 | -4.87225012e+00 2.80280245e+00 4.76234522e+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)) = -2.55080289562 2^p V(r_1,...,r_N) = -2.55080289562 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 -4.17122309e+00 -1.22104195e+01 -1.14882671e+01 | -4.17122309e+00 -1.22104195e+01 -1.14882671e+01 1 5.67504904e+00 4.63547973e+00 -5.77430739e+00 | 5.67504904e+00 4.63547973e+00 -5.77430739e+00 2 5.23745798e+00 -3.11902636e+00 2.77070116e+00 | 5.23745798e+00 -3.11902636e+00 2.77070116e+00 3 -6.74128393e+00 1.06939661e+01 1.44918734e+01 | -6.74128393e+00 1.06939661e+01 1.44918734e+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)) = 12.8881184277 2^p V(r_1,...,r_N) = 12.8881184277 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 -1.87282632e+01 -1.46045398e+01 -1.88077561e+01 | -1.87282632e+01 -1.46045398e+01 -1.88077561e+01 1 1.45628634e+01 1.14454356e+01 -1.99329753e+01 | 1.45628634e+01 1.14454356e+01 -1.99329753e+01 2 2.40895413e+01 -2.88182767e+01 2.81168464e+01 | 2.40895413e+01 -2.88182767e+01 2.81168464e+01 3 -1.99241415e+01 3.19773809e+01 1.06238849e+01 | -1.99241415e+01 3.19773809e+01 1.06238849e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = TTT (Configuration in file "config-AlTi-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)) = 29.7033770327 2^p V(r_1,...,r_N) = 29.7033770327 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 -1.85985569e+01 -1.14702247e+01 -9.53387038e+00 | -1.85985569e+01 -1.14702247e+01 -9.53387038e+00 1 3.63980286e+01 2.01734107e+01 -4.14638058e+01 | 3.63980286e+01 2.01734107e+01 -4.14638058e+01 2 7.95335906e+01 -7.70479614e+01 2.36273017e+01 | 7.95335906e+01 -7.70479614e+01 2.36273017e+01 3 -9.73330622e+01 6.83447753e+01 2.73703745e+01 | -9.73330622e+01 6.83447753e+01 2.73703745e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = TTF (Configuration in file "config-AlTi-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)) = 32.6379313996 2^p V(r_1,...,r_N) = 32.6379313996 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 -8.96546150e+01 -8.78305195e+00 -5.09716841e+01 | -8.96546150e+01 -8.78305195e+00 -5.09716841e+01 1 4.39088588e+01 4.09218338e+01 -1.53940436e+01 | 4.39088588e+01 4.09218338e+01 -1.53940436e+01 2 8.20549279e+01 -7.02033675e+01 4.20223931e+01 | 8.20549279e+01 -7.02033675e+01 4.20223931e+01 3 -3.63091716e+01 3.80645856e+01 2.43433346e+01 | -3.63091716e+01 3.80645856e+01 2.43433346e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = TFT (Configuration in file "config-AlTi-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)) = 24.7636408688 2^p V(r_1,...,r_N) = 24.7636408688 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 -7.35287793e+01 -4.98872973e+01 -1.27778462e+01 | -7.35287793e+01 -4.98872973e+01 -1.27778462e+01 1 9.02042680e+01 5.20043599e+01 -3.28952620e+01 | 9.02042680e+01 5.20043599e+01 -3.28952620e+01 2 2.16708917e+01 -1.71863630e+01 1.93808495e+01 | 2.16708917e+01 -1.71863630e+01 1.93808495e+01 3 -3.83463804e+01 1.50693004e+01 2.62922587e+01 | -3.83463804e+01 1.50693004e+01 2.62922587e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = TFF (Configuration in file "config-AlTi-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)) = 33.2117157255 2^p V(r_1,...,r_N) = 33.2117157255 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 -3.65593146e+01 -1.01496219e+02 -8.03311632e+01 | -3.65593146e+01 -1.01496219e+02 -8.03311632e+01 1 2.58118094e+01 1.87014333e+01 -2.21290112e+01 | 2.58118094e+01 1.87014333e+01 -2.21290112e+01 2 1.63216145e+01 -2.64560264e+01 6.72601434e+00 | 1.63216145e+01 -2.64560264e+01 6.72601434e+00 3 -5.57410925e+00 1.09250812e+02 9.57341601e+01 | -5.57410925e+00 1.09250812e+02 9.57341601e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = FTT (Configuration in file "config-AlTi-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)) = 16.8505493042 2^p V(r_1,...,r_N) = 16.8505493042 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 -1.40218707e+01 -9.47325830e+00 -1.38106831e+01 | -1.40218707e+01 -9.47325830e+00 -1.38106831e+01 1 3.44645534e+01 2.87738507e+01 -6.36038477e+01 | 3.44645534e+01 2.87738507e+01 -6.36038477e+01 2 2.24567251e+01 -2.89197781e+01 2.96639877e+01 | 2.24567251e+01 -2.89197781e+01 2.96639877e+01 3 -4.28994079e+01 9.61918573e+00 4.77505431e+01 | -4.28994079e+01 9.61918573e+00 4.77505431e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = FTF (Configuration in file "config-AlTi-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)) = 4.60162346907 2^p V(r_1,...,r_N) = 4.60162346907 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 -1.58335788e+01 -1.22172359e+01 -2.81571049e+01 | -1.58335788e+01 -1.22172359e+01 -2.81571049e+01 1 8.18121349e+00 1.25404261e+01 -1.44923847e+01 | 8.18121349e+00 1.25404261e+01 -1.44923847e+01 2 1.78756039e+01 -6.67426964e+00 2.63268801e+01 | 1.78756039e+01 -6.67426964e+00 2.63268801e+01 3 -1.02232386e+01 6.35107939e+00 1.63226094e+01 | -1.02232386e+01 6.35107939e+00 1.63226094e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Ti, PBC = FFT (Configuration in file "config-AlTi-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)) = 15.1172022084 2^p V(r_1,...,r_N) = 15.1172022084 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 -3.81696008e+01 -2.65707788e+01 -1.03756578e+01 | -3.81696008e+01 -2.65707788e+01 -1.03756578e+01 1 4.53283237e+01 3.02276906e+01 -3.15813094e+01 | 4.53283237e+01 3.02276906e+01 -3.15813094e+01 2 2.26085088e+01 -1.91548949e+01 2.49435333e+01 | 2.26085088e+01 -1.91548949e+01 2.49435333e+01 3 -2.97672317e+01 1.54979832e+01 1.70134338e+01 | -2.97672317e+01 1.54979832e+01 1.70134338e+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.