!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-permutation-symmetry !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check whether a model is invariant with respect to atom permutations that preserve species, i.e. swapping any two atoms with the same species must not change the energy or forces. This must be true for all models. The check is performed for a randomly distorted non-periodic diamond 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. The energy and forces of each configuration are compared with one where each atom is randomly swapped with another atom of the same species. The energy and forces must remain unchanged. The verification check will pass if these conditions are satisfied for all configurations that the model is able to compute. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_ADP_StarikovGordeevLysogorskiy_2020_SiAuAl__SM_113843830602_000 Supported species : Al Au Si random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Al (Configuration in file "config-Al.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [52, 5, 63, 59, 33, 1, 40, 24, 30, 36, 60, 18, 27, 39, 46, 20, 57, 54, 11, 32, 15, 61, 62, 56, 7, 47, 45, 12, 50, 58, 8, 48, 19, 4, 55, 37, 9, 35, 44, 13, 6, 42, 41, 49, 38, 26, 14, 25, 31, 43, 28, 53, 0, 51, 17, 34, 23, 16, 29, 3, 10, 21, 22, 2] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 16.859687022683833 V(r_1,...,r_N) = 16.859687022683744 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -4.01964978e+00 -2.04920544e+00 -4.68699109e-01 | -4.01964978e+00 -2.04920544e+00 -4.68699109e-01 1 -4.14228096e+00 -1.09602489e+01 4.40256950e+00 | -4.14228096e+00 -1.09602489e+01 4.40256950e+00 2 -4.36025202e+00 8.95911184e+00 -1.71122650e+01 | -4.36025202e+00 8.95911184e+00 -1.71122650e+01 3 8.88767364e+00 7.87597320e+00 3.09255267e+00 | 8.88767364e+00 7.87597320e+00 3.09255267e+00 4 1.14912799e+00 -6.29918917e+00 5.50441100e+00 | 1.14912799e+00 -6.29918917e+00 5.50441100e+00 5 -1.94663677e+00 3.56077180e+00 -6.93469347e+00 | -1.94663677e+00 3.56077180e+00 -6.93469347e+00 6 -6.91554651e+00 -7.96372418e+00 -1.03069473e+01 | -6.91554651e+00 -7.96372418e+00 -1.03069473e+01 7 -5.94286818e+00 3.24345210e+01 -1.48201074e+01 | -5.94286818e+00 3.24345210e+01 -1.48201074e+01 8 -1.57690473e+00 -1.36087242e+00 -1.85285539e+00 | -1.57690473e+00 -1.36087242e+00 -1.85285539e+00 9 -1.22248942e+00 -3.36090840e+00 8.49224964e+00 | -1.22248942e+00 -3.36090840e+00 8.49224964e+00 10 -2.57138107e+00 -5.75455294e-01 -1.27423111e+01 | -2.57138107e+00 -5.75455294e-01 -1.27423111e+01 11 6.25447892e+00 4.87477581e+00 4.31775187e+00 | 6.25447892e+00 4.87477581e+00 4.31775187e+00 12 -2.55532810e+01 -1.50135985e+01 -1.20616330e+01 | -2.55532810e+01 -1.50135985e+01 -1.20616330e+01 13 2.80487326e+01 1.22707997e+01 9.68626102e+00 | 2.80487326e+01 1.22707997e+01 9.68626102e+00 14 -8.13656394e+00 -4.61613311e+00 -1.24253099e+01 | -8.13656394e+00 -4.61613311e+00 -1.24253099e+01 15 7.77935332e+00 5.17344218e+00 1.24971934e+01 | 7.77935332e+00 5.17344218e+00 1.24971934e+01 16 -1.89009563e+00 -2.46697252e+00 -1.80807596e+00 | -1.89009563e+00 -2.46697252e+00 -1.80807596e+00 17 -7.46381320e+00 -6.13035459e+00 1.18547633e+01 | -7.46381320e+00 -6.13035459e+00 1.18547633e+01 18 1.01679316e+01 4.91851133e+00 -1.18679967e+01 | 1.01679316e+01 4.91851133e+00 -1.18679967e+01 19 -2.20941795e+01 1.43022433e+01 -1.46803333e+01 | -2.20941795e+01 1.43022433e+01 -1.46803333e+01 20 -8.96937157e-01 -1.83048720e+00 -6.49785031e+00 | -8.96937157e-01 -1.83048720e+00 -6.49785031e+00 21 6.75655404e+00 5.07599132e+00 1.55503480e+00 | 6.75655404e+00 5.07599132e+00 1.55503480e+00 22 -5.04114813e+00 -3.99815329e+00 -9.16698330e+00 | -5.04114813e+00 -3.99815329e+00 -9.16698330e+00 23 2.42092344e+00 8.22007157e+00 1.04390962e+01 | 2.42092344e+00 8.22007157e+00 1.04390962e+01 24 -5.21869814e+00 -1.49311104e+00 -5.34303376e+00 | -5.21869814e+00 -1.49311104e+00 -5.34303376e+00 25 -4.30294578e+00 7.11452175e+00 -2.78939083e-01 | -4.30294578e+00 7.11452175e+00 -2.78939083e-01 26 -3.03477833e+00 1.32680703e+00 -5.51972207e+00 | -3.03477833e+00 1.32680703e+00 -5.51972207e+00 27 3.45154874e+00 9.65486334e-01 3.78544806e+00 | 3.45154874e+00 9.65486334e-01 3.78544806e+00 28 -1.44542575e+00 -1.70728101e+01 2.78158597e+00 | -1.44542575e+00 -1.70728101e+01 2.78158597e+00 29 9.53147250e+00 8.89342091e+00 6.08498138e+00 | 9.53147250e+00 8.89342091e+00 6.08498138e+00 30 2.10709453e+01 -1.24477439e+01 1.24071401e+01 | 2.10709453e+01 -1.24477439e+01 1.24071401e+01 31 -1.04520642e+01 5.14670687e+00 -5.15817316e+00 | -1.04520642e+01 5.14670687e+00 -5.15817316e+00 32 -1.70153289e+01 -1.53443220e+01 -1.95209705e+01 | -1.70153289e+01 -1.53443220e+01 -1.95209705e+01 33 1.58610665e+01 1.45860871e+01 1.91852187e+01 | 1.58610665e+01 1.45860871e+01 1.91852187e+01 34 1.44773892e+01 -3.25229538e+01 1.77514103e+01 | 1.44773892e+01 -3.25229538e+01 1.77514103e+01 35 -4.61395794e-01 -2.55646752e+00 1.69532139e+00 | -4.61395794e-01 -2.55646752e+00 1.69532139e+00 36 -9.86935168e-01 3.94392214e-04 -7.36908106e-01 | -9.86935168e-01 3.94392214e-04 -7.36908106e-01 37 -8.52383010e+00 -1.24013717e+01 9.34006642e+00 | -8.52383010e+00 -1.24013717e+01 9.34006642e+00 38 -5.28624493e+00 -4.87133562e+00 -5.91899570e+00 | -5.28624493e+00 -4.87133562e+00 -5.91899570e+00 39 -3.73715837e+00 -4.39216407e+00 1.09220627e+01 | -3.73715837e+00 -4.39216407e+00 1.09220627e+01 40 1.43613944e+00 -2.94630092e+00 8.29068414e+00 | 1.43613944e+00 -2.94630092e+00 8.29068414e+00 41 -1.22000798e+01 1.48009587e+01 -7.04610973e+00 | -1.22000798e+01 1.48009587e+01 -7.04610973e+00 42 -8.19074207e-01 -1.81759448e+00 -4.53898027e+00 | -8.19074207e-01 -1.81759448e+00 -4.53898027e+00 43 3.12924197e+00 7.92673174e+00 3.93993363e+00 | 3.12924197e+00 7.92673174e+00 3.93993363e+00 44 1.07406078e+01 -2.00681997e+01 9.13095384e+00 | 1.07406078e+01 -2.00681997e+01 9.13095384e+00 45 5.06713032e-01 1.21969271e+00 3.59651260e-01 | 5.06713032e-01 1.21969271e+00 3.59651260e-01 46 2.45164677e+00 8.32300114e+00 -8.67639268e+00 | 2.45164677e+00 8.32300114e+00 -8.67639268e+00 47 5.43071246e+00 5.66738353e+00 2.96150651e+00 | 5.43071246e+00 5.66738353e+00 2.96150651e+00 48 -7.96904923e+00 5.93969168e+00 1.12392569e+01 | -7.96904923e+00 5.93969168e+00 1.12392569e+01 49 -3.61355721e+00 -4.21518712e+00 2.35520605e+00 | -3.61355721e+00 -4.21518712e+00 2.35520605e+00 50 6.16630406e-01 -6.32360676e+00 -1.02600698e+01 | 6.16630406e-01 -6.32360676e+00 -1.02600698e+01 51 5.14825250e+00 8.69752631e+00 7.71271756e+00 | 5.14825250e+00 8.69752631e+00 7.71271756e+00 52 6.79539332e+00 9.16778062e+00 -6.06664985e+00 | 6.79539332e+00 9.16778062e+00 -6.06664985e+00 53 2.17481853e+00 -1.54320783e-02 1.41646316e+00 | 2.17481853e+00 -1.54320783e-02 1.41646316e+00 54 -2.85124116e+00 7.83600397e-03 -2.08514178e-01 | -2.85124116e+00 7.83600397e-03 -2.08514178e-01 55 1.73501007e+00 1.15331764e+00 9.26595434e-01 | 1.73501007e+00 1.15331764e+00 9.26595434e-01 56 -3.93063612e+00 -7.25778152e+00 -3.65310196e+00 | -3.93063612e+00 -7.25778152e+00 -3.65310196e+00 57 1.13603181e+01 -7.40194581e+00 -2.09381862e+01 | 1.13603181e+01 -7.40194581e+00 -2.09381862e+01 58 1.17216682e+01 -4.52826736e+00 6.10312584e+00 | 1.17216682e+01 -4.52826736e+00 6.10312584e+00 59 -3.25037214e-01 -6.38368605e-02 1.45114310e+00 | -3.25037214e-01 -6.38368605e-02 1.45114310e+00 60 3.70088177e+00 -6.05796904e+00 1.82671121e+00 | 3.70088177e+00 -6.05796904e+00 1.82671121e+00 61 2.74761883e+00 3.16703610e+00 3.47863366e+00 | 2.74761883e+00 3.16703610e+00 3.47863366e+00 62 -1.02280564e+01 1.97789468e+01 2.06139079e+01 | -1.02280564e+01 1.97789468e+01 2.06139079e+01 63 6.22713843e-01 -1.12583616e+00 -9.90800432e-01 | 6.22713843e-01 -1.12583616e+00 -9.90800432e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Au (Configuration in file "config-Au.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [40, 11, 5, 20, 21, 2, 27, 33, 52, 39, 50, 1, 60, 35, 29, 37, 22, 42, 31, 25, 3, 4, 16, 46, 47, 19, 53, 6, 45, 14, 51, 18, 63, 7, 54, 13, 38, 15, 36, 9, 0, 62, 17, 57, 56, 28, 23, 24, 61, 55, 10, 30, 8, 26, 34, 49, 44, 43, 59, 58, 12, 48, 41, 32] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 362.47766035282217 V(r_1,...,r_N) = 362.4776603528227 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -4.80212612e+01 -6.76329516e+01 -5.08289544e+01 | -4.80212612e+01 -6.76329516e+01 -5.08289544e+01 1 4.75500123e+01 6.69238511e+01 5.04152825e+01 | 4.75500123e+01 6.69238511e+01 5.04152825e+01 2 -2.01383093e+01 -1.85225006e+01 -2.67630143e+01 | -2.01383093e+01 -1.85225006e+01 -2.67630143e+01 3 3.22770294e+01 4.34505663e+01 -3.44330856e+01 | 3.22770294e+01 4.34505663e+01 -3.44330856e+01 4 -5.51116803e+01 -7.86491957e+01 -2.18609553e+01 | -5.51116803e+01 -7.86491957e+01 -2.18609553e+01 5 5.35054967e+01 7.01651260e+01 1.79979235e+01 | 5.35054967e+01 7.01651260e+01 1.79979235e+01 6 -2.75542310e+01 -1.17984000e+01 -1.39984558e+01 | -2.75542310e+01 -1.17984000e+01 -1.39984558e+01 7 -3.16999802e+01 1.35569081e+00 2.23406486e+01 | -3.16999802e+01 1.35569081e+00 2.23406486e+01 8 -8.12805346e+00 -3.39307485e+00 -1.16928108e+01 | -8.12805346e+00 -3.39307485e+00 -1.16928108e+01 9 -1.66566550e+01 1.12860004e+01 -1.69170861e+01 | -1.66566550e+01 1.12860004e+01 -1.69170861e+01 10 -1.27017277e+01 -1.06318930e+01 -1.90308772e+01 | -1.27017277e+01 -1.06318930e+01 -1.90308772e+01 11 1.48627753e+01 6.62306721e+00 1.59638336e+01 | 1.48627753e+01 6.62306721e+00 1.59638336e+01 12 2.08069719e+01 -1.56464725e+01 1.77411142e+01 | 2.08069719e+01 -1.56464725e+01 1.77411142e+01 13 2.35756959e+01 -1.13973103e+01 -2.56445545e+00 | 2.35756959e+01 -1.13973103e+01 -2.56445545e+00 14 3.13639243e+01 -7.34691243e+01 1.41325885e+00 | 3.13639243e+01 -7.34691243e+01 1.41325885e+00 15 4.49515617e+01 -1.54173624e+01 -9.06912870e+00 | 4.49515617e+01 -1.54173624e+01 -9.06912870e+00 16 -2.26298592e+01 -1.48520062e+01 -2.32823862e+01 | -2.26298592e+01 -1.48520062e+01 -2.32823862e+01 17 5.84033972e+01 -9.42224945e+01 -3.47596315e+01 | 5.84033972e+01 -9.42224945e+01 -3.47596315e+01 18 1.09008957e+01 9.88406761e+00 -1.29395554e+01 | 1.09008957e+01 9.88406761e+00 -1.29395554e+01 19 -2.82334005e+01 3.90670066e+01 -2.15679612e+01 | -2.82334005e+01 3.90670066e+01 -2.15679612e+01 20 -2.63328185e+01 5.33885620e+01 3.77415766e+01 | -2.63328185e+01 5.33885620e+01 3.77415766e+01 21 2.09294910e+01 -1.63040255e+01 8.25009917e+00 | 2.09294910e+01 -1.63040255e+01 8.25009917e+00 22 -5.02056148e+01 1.01772191e+02 6.73911383e+01 | -5.02056148e+01 1.01772191e+02 6.73911383e+01 23 -2.76080846e+01 6.61318355e+01 -3.36528388e+01 | -2.76080846e+01 6.61318355e+01 -3.36528388e+01 24 1.00547950e+01 1.11534108e+01 -3.26784191e+01 | 1.00547950e+01 1.11534108e+01 -3.26784191e+01 25 -9.92400683e+00 9.70675127e+00 -1.27242364e+01 | -9.92400683e+00 9.70675127e+00 -1.27242364e+01 26 -1.40927207e+01 -8.56637782e+00 -2.12478698e+01 | -1.40927207e+01 -8.56637782e+00 -2.12478698e+01 27 1.57094815e+01 1.01911340e+01 1.95686207e+01 | 1.57094815e+01 1.01911340e+01 1.95686207e+01 28 -5.90484228e+01 -2.28408285e+01 -7.25743842e+01 | -5.90484228e+01 -2.28408285e+01 -7.25743842e+01 29 7.46152964e+01 1.89357704e+01 9.05106138e+01 | 7.46152964e+01 1.89357704e+01 9.05106138e+01 30 3.27887750e+01 -3.07799950e+01 7.76072041e+00 | 3.27887750e+01 -3.07799950e+01 7.76072041e+00 31 -8.36488356e+01 8.08664001e+01 -3.68415217e+01 | -8.36488356e+01 8.08664001e+01 -3.68415217e+01 32 1.20077748e+00 6.42606112e-01 1.74281777e-01 | 1.20077748e+00 6.42606112e-01 1.74281777e-01 33 -3.37849653e+01 4.29767557e+01 -3.82621624e+01 | -3.37849653e+01 4.29767557e+01 -3.82621624e+01 34 5.28656395e+00 -1.20030053e+01 1.78245353e+01 | 5.28656395e+00 -1.20030053e+01 1.78245353e+01 35 1.44178323e+01 2.62573118e+01 -2.81493013e+01 | 1.44178323e+01 2.62573118e+01 -2.81493013e+01 36 3.46701903e+01 -4.92884067e+01 3.51445987e+01 | 3.46701903e+01 -4.92884067e+01 3.51445987e+01 37 1.95196498e+00 -1.92901330e+00 4.02340910e+00 | 1.95196498e+00 -1.92901330e+00 4.02340910e+00 38 -5.90269771e+00 3.34552681e+00 2.80792045e+00 | -5.90269771e+00 3.34552681e+00 2.80792045e+00 39 3.57298854e-02 8.95511122e-02 -3.53407885e-03 | 3.57298854e-02 8.95511122e-02 -3.53407885e-03 40 -7.10002485e-01 -8.04613738e+00 -4.77699489e+00 | -7.10002485e-01 -8.04613738e+00 -4.77699489e+00 41 -8.16347572e+00 -1.20518316e+01 1.01187957e+01 | -8.16347572e+00 -1.20518316e+01 1.01187957e+01 42 -3.41525041e+00 1.44664861e+01 -3.85346117e+00 | -3.41525041e+00 1.44664861e+01 -3.85346117e+00 43 7.92229717e+00 8.23628478e+00 3.14137098e+00 | 7.92229717e+00 8.23628478e+00 3.14137098e+00 44 1.33466368e+00 -4.43793707e-01 1.59472156e+00 | 1.33466368e+00 -4.43793707e-01 1.59472156e+00 45 -1.13479439e+00 -3.58920200e-01 -9.47757712e-01 | -1.13479439e+00 -3.58920200e-01 -9.47757712e-01 46 1.13292568e+01 -5.81331828e+01 2.22642343e+01 | 1.13292568e+01 -5.81331828e+01 2.22642343e+01 47 1.62746546e+01 1.12926728e+01 2.62816876e+01 | 1.62746546e+01 1.12926728e+01 2.62816876e+01 48 -2.56271952e+00 -2.02392758e+00 -1.21591567e+00 | -2.56271952e+00 -2.02392758e+00 -1.21591567e+00 49 1.73041525e+01 5.15848039e-01 -1.91303217e+01 | 1.73041525e+01 5.15848039e-01 -1.91303217e+01 50 -6.94935076e-01 -5.14174155e+01 3.74018169e+01 | -6.94935076e-01 -5.14174155e+01 3.74018169e+01 51 -1.06840380e+01 1.42729348e+01 -1.38803914e+01 | -1.06840380e+01 1.42729348e+01 -1.38803914e+01 52 -5.59074985e+01 2.75538700e+01 6.09470545e+00 | -5.59074985e+01 2.75538700e+01 6.09470545e+00 53 -3.09631036e+00 -1.75088182e+00 3.08496707e+00 | -3.09631036e+00 -1.75088182e+00 3.08496707e+00 54 -1.67509466e+01 1.42425698e+00 2.25726544e+01 | -1.67509466e+01 1.42425698e+00 2.25726544e+01 55 1.10583432e-01 -3.48433751e-01 -1.91887194e-01 | 1.10583432e-01 -3.48433751e-01 -1.91887194e-01 56 -2.33360590e+01 2.54423840e+01 1.88609398e+01 | -2.33360590e+01 2.54423840e+01 1.88609398e+01 57 -3.22479409e+01 2.55999836e+01 -9.42267632e+01 | -3.22479409e+01 2.55999836e+01 -9.42267632e+01 58 8.28936975e+01 -7.95860809e+01 3.52639161e+01 | 8.28936975e+01 -7.95860809e+01 3.52639161e+01 59 2.38955661e+00 9.37141317e-01 2.43362851e+00 | 2.38955661e+00 9.37141317e-01 2.43362851e+00 60 2.77048033e+01 -2.88051009e+01 8.46021675e+01 | 2.77048033e+01 -2.88051009e+01 8.46021675e+01 61 8.25758955e+00 5.99694861e+00 8.93945272e+00 | 8.25758955e+00 5.99694861e+00 8.93945272e+00 62 -2.05847265e-01 -2.39713799e+01 -2.80119070e+00 | -2.05847265e-01 -2.39713799e+01 -2.80119070e+00 63 1.49532294e+01 1.43295303e+01 1.71426751e+01 | 1.49532294e+01 1.43295303e+01 1.71426751e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Si (Configuration in file "config-Si.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [1, 0, 20, 6, 12, 23, 3, 19, 10, 42, 8, 24, 4, 38, 63, 21, 57, 27, 50, 7, 2, 15, 48, 5, 11, 40, 60, 17, 49, 41, 47, 36, 59, 34, 33, 53, 31, 46, 13, 62, 25, 29, 9, 51, 61, 56, 37, 30, 22, 28, 18, 43, 54, 35, 52, 58, 45, 16, 55, 32, 26, 44, 39, 14] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -19.335645487804946 V(r_1,...,r_N) = -19.33564548780485 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -2.50367599e+02 -9.24536952e+01 -1.24924463e+02 | -2.50367599e+02 -9.24536952e+01 -1.24924463e+02 1 2.49464201e+02 9.13026865e+01 1.23851930e+02 | 2.49464201e+02 9.13026865e+01 1.23851930e+02 2 -4.44114592e+00 1.01486891e-01 -4.00737193e+00 | -4.44114592e+00 1.01486891e-01 -4.00737193e+00 3 4.58139933e+00 2.16708200e+00 2.88831774e+00 | 4.58139933e+00 2.16708200e+00 2.88831774e+00 4 -5.31321586e+00 -6.67026926e+00 -6.63891182e+00 | -5.31321586e+00 -6.67026926e+00 -6.63891182e+00 5 9.01565627e+00 -9.30997152e+00 -1.80811083e-01 | 9.01565627e+00 -9.30997152e+00 -1.80811083e-01 6 -2.55431452e+00 -5.07799098e+00 1.18936087e+00 | -2.55431452e+00 -5.07799098e+00 1.18936087e+00 7 9.50612875e-01 2.63607727e+00 4.62390190e+00 | 9.50612875e-01 2.63607727e+00 4.62390190e+00 8 4.74419993e-01 -6.81830690e-02 1.11028639e+00 | 4.74419993e-01 -6.81830690e-02 1.11028639e+00 9 -9.96154751e+00 1.00820283e+00 -1.62803072e+01 | -9.96154751e+00 1.00820283e+00 -1.62803072e+01 10 2.98964836e+00 3.73790233e+00 -4.84303578e+00 | 2.98964836e+00 3.73790233e+00 -4.84303578e+00 11 1.68497237e+00 -1.76516847e+00 -1.58079842e+00 | 1.68497237e+00 -1.76516847e+00 -1.58079842e+00 12 3.58753362e+00 -1.02058272e+01 1.58472850e+01 | 3.58753362e+00 -1.02058272e+01 1.58472850e+01 13 5.46309407e+00 3.70949043e+00 3.34115106e+00 | 5.46309407e+00 3.70949043e+00 3.34115106e+00 14 -1.29321321e+01 -1.09753894e+01 -1.89526225e+01 | -1.29321321e+01 -1.09753894e+01 -1.89526225e+01 15 1.49840052e+01 1.22192193e+01 1.72199393e+01 | 1.49840052e+01 1.22192193e+01 1.72199393e+01 16 -6.15311964e+00 -4.78945632e+00 -5.72539183e+00 | -6.15311964e+00 -4.78945632e+00 -5.72539183e+00 17 -1.01111138e+02 6.04834668e+01 -4.07999071e+01 | -1.01111138e+02 6.04834668e+01 -4.07999071e+01 18 5.14157286e+00 6.99583162e+00 -4.14764558e+00 | 5.14157286e+00 6.99583162e+00 -4.14764558e+00 19 -1.53513303e+01 1.33903478e+01 -2.05618837e+01 | -1.53513303e+01 1.33903478e+01 -2.05618837e+01 20 9.99578447e+01 -6.43614328e+01 4.25113259e+01 | 9.99578447e+01 -6.43614328e+01 4.25113259e+01 21 8.14872144e+00 3.57198913e+00 5.95029404e+00 | 8.14872144e+00 3.57198913e+00 5.95029404e+00 22 -1.86423525e+00 -5.27734757e-01 -7.68406236e-01 | -1.86423525e+00 -5.27734757e-01 -7.68406236e-01 23 -1.18072774e+01 2.37949390e+01 -2.16981992e+01 | -1.18072774e+01 2.37949390e+01 -2.16981992e+01 24 -3.39036803e-01 -3.27690558e-01 -6.22781682e-01 | -3.39036803e-01 -3.27690558e-01 -6.22781682e-01 25 -8.48953109e-01 -3.37720974e+00 -2.20469331e-01 | -8.48953109e-01 -3.37720974e+00 -2.20469331e-01 26 1.58597370e+00 3.11677082e-01 -2.27592916e+00 | 1.58597370e+00 3.11677082e-01 -2.27592916e+00 27 1.57768735e+00 2.15051961e+00 1.45509622e-01 | 1.57768735e+00 2.15051961e+00 1.45509622e-01 28 1.53386385e-01 2.94299646e-02 3.62673793e-01 | 1.53386385e-01 2.94299646e-02 3.62673793e-01 29 4.90384435e+00 -2.13677973e+00 -2.06618234e+00 | 4.90384435e+00 -2.13677973e+00 -2.06618234e+00 30 -7.40748752e+00 -2.91864511e+01 -1.28787447e+00 | -7.40748752e+00 -2.91864511e+01 -1.28787447e+00 31 1.80834690e+01 1.67383419e+01 2.30850511e+01 | 1.80834690e+01 1.67383419e+01 2.30850511e+01 32 -5.38886025e-01 -3.48035087e-02 -2.10625581e+00 | -5.38886025e-01 -3.48035087e-02 -2.10625581e+00 33 -3.04735057e+00 3.54897291e+00 -4.54534570e+00 | -3.04735057e+00 3.54897291e+00 -4.54534570e+00 34 -8.63533854e+00 1.31266245e+01 1.04623346e+01 | -8.63533854e+00 1.31266245e+01 1.04623346e+01 35 5.43637351e+00 -3.32398182e+00 -4.01537697e+00 | 5.43637351e+00 -3.32398182e+00 -4.01537697e+00 36 7.18401850e-01 -7.11993771e+00 -3.10245432e+00 | 7.18401850e-01 -7.11993771e+00 -3.10245432e+00 37 3.76131044e+00 3.88364582e+00 7.24723169e+00 | 3.76131044e+00 3.88364582e+00 7.24723169e+00 38 -1.12979730e+01 -1.13709134e+01 -8.09232228e+00 | -1.12979730e+01 -1.13709134e+01 -8.09232228e+00 39 7.47773573e+00 7.19964369e+00 1.21682219e+01 | 7.47773573e+00 7.19964369e+00 1.21682219e+01 40 -3.89398677e+00 -2.98807257e+00 -2.62389080e+00 | -3.89398677e+00 -2.98807257e+00 -2.62389080e+00 41 5.30987014e+00 1.20152714e+00 4.19547241e+00 | 5.30987014e+00 1.20152714e+00 4.19547241e+00 42 -4.90092606e+00 -6.35263095e+00 -4.51771606e+00 | -4.90092606e+00 -6.35263095e+00 -4.51771606e+00 43 8.79397474e+00 2.45964908e+00 -5.23191335e+00 | 8.79397474e+00 2.45964908e+00 -5.23191335e+00 44 -2.59630291e+01 -7.25518741e+01 -4.63422036e+01 | -2.59630291e+01 -7.25518741e+01 -4.63422036e+01 45 2.57205686e+01 7.23521891e+01 4.63052331e+01 | 2.57205686e+01 7.23521891e+01 4.63052331e+01 46 -5.00344695e+00 -7.84229658e+00 -8.31918178e+00 | -5.00344695e+00 -7.84229658e+00 -8.31918178e+00 47 9.34070767e-01 7.88215786e+00 9.80512168e+00 | 9.34070767e-01 7.88215786e+00 9.80512168e+00 48 7.61552023e-01 9.30732293e-01 4.35999853e-01 | 7.61552023e-01 9.30732293e-01 4.35999853e-01 49 -3.66588692e+00 2.36907663e+00 -7.24230921e+00 | -3.66588692e+00 2.36907663e+00 -7.24230921e+00 50 1.13070744e+01 -2.31047968e+01 2.29361505e+01 | 1.13070744e+01 -2.31047968e+01 2.29361505e+01 51 2.67808089e+00 1.30585513e+00 2.12198770e+00 | 2.67808089e+00 1.30585513e+00 2.12198770e+00 52 3.32670829e+00 -3.20065412e-02 2.96642122e+00 | 3.32670829e+00 -3.20065412e-02 2.96642122e+00 53 -2.01363533e+00 -2.34276984e+00 3.64676157e+00 | -2.01363533e+00 -2.34276984e+00 3.64676157e+00 54 -3.94919345e+00 1.23624003e+00 -2.06387856e+00 | -3.94919345e+00 1.23624003e+00 -2.06387856e+00 55 2.16954384e+00 1.05019763e+00 4.27904025e+00 | 2.16954384e+00 1.05019763e+00 4.27904025e+00 56 -6.24349835e+00 1.91931409e+00 4.01675067e-01 | -6.24349835e+00 1.91931409e+00 4.01675067e-01 57 -2.16210942e+01 -2.73679313e+01 5.04047009e+01 | -2.16210942e+01 -2.73679313e+01 5.04047009e+01 58 2.63338648e+01 2.51463518e+01 -5.34698027e+01 | 2.63338648e+01 2.51463518e+01 -5.34698027e+01 59 1.86405658e+00 1.61578694e+00 5.95262624e-01 | 1.86405658e+00 1.61578694e+00 5.95262624e-01 60 -2.76069217e+00 3.93072792e+00 7.01849995e+00 | -2.76069217e+00 3.93072792e+00 7.01849995e+00 61 6.45315001e-01 7.70109154e-01 2.97537963e-01 | 6.45315001e-01 7.70109154e-01 2.97537963e-01 62 -7.12593613e+00 5.57150288e+00 -1.48922224e+00 | -7.12593613e+00 5.57150288e+00 -1.48922224e+00 63 1.12686222e+00 3.81627026e+00 3.33018656e+00 | 1.12686222e+00 3.81627026e+00 3.33018656e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Au Si (Configuration in file "config-AlAuSi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [37, 38, 24, 7, 20, 15, 35, 3, 21, 51, 33, 18, 29, 32, 25, 5, 17, 16, 11, 48, 4, 8, 45, 58, 2, 14, 56, 40, 46, 12, 36, 55, 13, 10, 63, 6, 30, 0, 1, 62, 27, 50, 54, 61, 47, 22, 28, 44, 19, 53, 41, 9, 52, 49, 42, 31, 26, 60, 23, 59, 57, 43, 39, 34] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -6.898562862951121 V(r_1,...,r_N) = -6.8985628629509925 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -2.75696603e+00 -1.91580642e+00 -2.53322299e+00 | -2.75696603e+00 -1.91580642e+00 -2.53322299e+00 1 -9.01812521e+00 -1.64576341e+01 1.92497140e+01 | -9.01812521e+00 -1.64576341e+01 1.92497140e+01 2 1.06605188e+01 1.73981598e+01 -1.80172581e+01 | 1.06605188e+01 1.73981598e+01 -1.80172581e+01 3 3.10964613e+00 -1.79093696e+00 5.54473590e-01 | 3.10964613e+00 -1.79093696e+00 5.54473590e-01 4 -4.65753866e+00 -6.55239951e-01 1.98260169e-01 | -4.65753866e+00 -6.55239951e-01 1.98260169e-01 5 -8.12580637e+00 -2.45579594e+00 -7.27628493e+00 | -8.12580637e+00 -2.45579594e+00 -7.27628493e+00 6 -2.18761068e+00 -1.79123299e+00 -2.00593966e+00 | -2.18761068e+00 -1.79123299e+00 -2.00593966e+00 7 -5.36541523e+01 4.36682687e+01 -4.98581263e+01 | -5.36541523e+01 4.36682687e+01 -4.98581263e+01 8 -1.25934632e+01 -2.16937971e+00 -7.10723094e+00 | -1.25934632e+01 -2.16937971e+00 -7.10723094e+00 9 1.28165588e+01 3.17577944e+00 7.84226223e+00 | 1.28165588e+01 3.17577944e+00 7.84226223e+00 10 -2.36809288e+00 -8.98038180e-01 -1.30812680e+00 | -2.36809288e+00 -8.98038180e-01 -1.30812680e+00 11 1.54095707e+01 -1.66735334e+01 -8.11849123e+00 | 1.54095707e+01 -1.66735334e+01 -8.11849123e+00 12 -5.15974379e+00 -5.67804083e+00 -6.49886742e+00 | -5.15974379e+00 -5.67804083e+00 -6.49886742e+00 13 3.89659614e+00 6.92547330e+00 6.15516826e+00 | 3.89659614e+00 6.92547330e+00 6.15516826e+00 14 2.61064175e+00 6.61638414e+00 -2.42000314e+00 | 2.61064175e+00 6.61638414e+00 -2.42000314e+00 15 1.77531856e+01 -2.04370511e+01 -1.83837938e+01 | 1.77531856e+01 -2.04370511e+01 -1.83837938e+01 16 -5.84219211e-01 -1.88524146e+00 -1.69522868e+00 | -5.84219211e-01 -1.88524146e+00 -1.69522868e+00 17 4.78081423e+00 -1.66342786e+01 -1.23746200e+01 | 4.78081423e+00 -1.66342786e+01 -1.23746200e+01 18 1.13325104e+00 5.98489414e-01 -3.05694614e-02 | 1.13325104e+00 5.98489414e-01 -3.05694614e-02 19 -1.44745310e+01 1.27080053e+01 -7.97345807e+00 | -1.44745310e+01 1.27080053e+01 -7.97345807e+00 20 -2.35008850e+00 1.39064117e+00 -9.71229463e-01 | -2.35008850e+00 1.39064117e+00 -9.71229463e-01 21 -2.06171089e+00 2.11833706e+00 -3.15495108e+00 | -2.06171089e+00 2.11833706e+00 -3.15495108e+00 22 -3.99925005e+00 1.74271436e+01 1.41068821e+01 | -3.99925005e+00 1.74271436e+01 1.41068821e+01 23 -2.71603573e-01 -2.93517090e-02 4.37604597e-01 | -2.71603573e-01 -2.93517090e-02 4.37604597e-01 24 1.06599221e-01 1.44941591e+00 -1.42012999e+00 | 1.06599221e-01 1.44941591e+00 -1.42012999e+00 25 2.36263380e+00 -1.06282215e+01 -3.85318072e-02 | 2.36263380e+00 -1.06282215e+01 -3.85318072e-02 26 7.65637914e+00 3.53992588e+00 -5.05457170e+00 | 7.65637914e+00 3.53992588e+00 -5.05457170e+00 27 -4.44057105e-01 -5.93139746e-01 3.47261586e-01 | -4.44057105e-01 -5.93139746e-01 3.47261586e-01 28 -1.41978173e+01 1.71695711e+01 1.05306261e+01 | -1.41978173e+01 1.71695711e+01 1.05306261e+01 29 1.21381929e+00 -2.18463970e-03 -2.53562665e+00 | 1.21381929e+00 -2.18463970e-03 -2.53562665e+00 30 3.30109937e+00 -7.25274294e+00 1.06840140e+01 | 3.30109937e+00 -7.25274294e+00 1.06840140e+01 31 1.64135932e+00 1.59775876e+00 3.40045263e+00 | 1.64135932e+00 1.59775876e+00 3.40045263e+00 32 -1.11232709e+00 -1.02925834e+00 -9.04083222e-01 | -1.11232709e+00 -1.02925834e+00 -9.04083222e-01 33 -9.20591503e+00 2.88052432e+01 -2.51590405e+01 | -9.20591503e+00 2.88052432e+01 -2.51590405e+01 34 5.66252874e+01 -4.37678614e+01 5.27439167e+01 | 5.66252874e+01 -4.37678614e+01 5.27439167e+01 35 -3.26404488e+00 4.31028430e-01 -1.41876357e+00 | -3.26404488e+00 4.31028430e-01 -1.41876357e+00 36 9.23361007e+00 -3.06722030e+01 2.41976734e+01 | 9.23361007e+00 -3.06722030e+01 2.41976734e+01 37 -1.16892146e+01 -5.21501633e+00 4.38912324e+00 | -1.16892146e+01 -5.21501633e+00 4.38912324e+00 38 -1.21416180e+01 -8.48228080e+00 -9.59897788e+00 | -1.21416180e+01 -8.48228080e+00 -9.59897788e+00 39 1.96441175e+00 -3.59861502e+00 1.63156995e+01 | 1.96441175e+00 -3.59861502e+00 1.63156995e+01 40 -9.23291846e+00 -6.48960850e+00 -9.24873904e+00 | -9.23291846e+00 -6.48960850e+00 -9.24873904e+00 41 1.65677196e+01 -1.00072906e-01 1.70614477e+01 | 1.65677196e+01 -1.00072906e-01 1.70614477e+01 42 3.57615345e+00 -2.71853517e+00 1.56913151e+00 | 3.57615345e+00 -2.71853517e+00 1.56913151e+00 43 2.24898597e+01 -3.46326482e+01 -2.05593006e+01 | 2.24898597e+01 -3.46326482e+01 -2.05593006e+01 44 -1.98716688e+00 4.07132187e-01 -1.75871408e+00 | -1.98716688e+00 4.07132187e-01 -1.75871408e+00 45 3.18271906e+00 1.02153548e+00 3.49595299e+00 | 3.18271906e+00 1.02153548e+00 3.49595299e+00 46 1.54679069e+01 6.22474857e+00 -4.43742709e-01 | 1.54679069e+01 6.22474857e+00 -4.43742709e-01 47 2.06369838e-01 -1.58761971e-01 -6.20206753e-01 | 2.06369838e-01 -1.58761971e-01 -6.20206753e-01 48 -3.40923455e+01 -6.51591338e+01 -4.70165473e+01 | -3.40923455e+01 -6.51591338e+01 -4.70165473e+01 49 1.07505882e+01 5.28514891e+01 2.33259343e+01 | 1.07505882e+01 5.28514891e+01 2.33259343e+01 50 2.84869704e+01 4.62466197e+00 -1.34410592e+01 | 2.84869704e+01 4.62466197e+00 -1.34410592e+01 51 -1.44285194e+00 2.96040114e+00 -3.49425851e+00 | -1.44285194e+00 2.96040114e+00 -3.49425851e+00 52 1.03348761e+01 7.35886552e+00 -5.19781793e+00 | 1.03348761e+01 7.35886552e+00 -5.19781793e+00 53 2.58100703e+00 9.22672248e-01 3.41009576e+00 | 2.58100703e+00 9.22672248e-01 3.41009576e+00 54 -1.12048938e+01 1.11892577e+01 3.28165979e+01 | -1.12048938e+01 1.11892577e+01 3.28165979e+01 55 3.68274899e-01 5.76197326e-01 6.75379624e-01 | 3.68274899e-01 5.76197326e-01 6.75379624e-01 56 -1.45396187e+01 2.44563452e+01 1.85817574e+01 | -1.45396187e+01 2.44563452e+01 1.85817574e+01 57 -9.86716484e+00 -3.34677522e+00 1.33880079e+01 | -9.86716484e+00 -3.34677522e+00 1.33880079e+01 58 5.15280139e+00 7.14801741e-01 -1.40010083e+01 | 5.15280139e+00 7.14801741e-01 -1.40010083e+01 59 3.03862871e+00 1.12188888e+00 1.46129935e+00 | 3.03862871e+00 1.12188888e+00 1.46129935e+00 60 -2.17968351e+01 3.51953746e+01 2.22358689e+01 | -2.17968351e+01 3.51953746e+01 2.22358689e+01 61 -5.93800418e-01 5.03693875e-02 -1.45408644e+00 | -5.93800418e-01 5.03693875e-02 -1.45408644e+00 62 -1.53266075e+01 -1.03595628e+01 -1.10416904e+01 | -1.53266075e+01 -1.03595628e+01 -1.10416904e+01 63 1.79222417e+01 8.98281736e+00 1.49596935e+01 | 1.79222417e+01 8.98281736e+00 1.49596935e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.