!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_DeluigiPasianotValencia_2021_FeNiCrCoCu__MO_657255834688_000 Supported species : Co Cr Cu Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [20, 4, 58, 11, 1, 55, 24, 17, 26, 53, 34, 3, 19, 22, 52, 50, 28, 7, 23, 12, 0, 57, 13, 18, 6, 31, 8, 56, 16, 46, 39, 25, 51, 45, 10, 49, 40, 61, 54, 30, 36, 42, 41, 44, 43, 33, 29, 59, 63, 35, 15, 32, 14, 9, 38, 5, 27, 21, 2, 47, 62, 37, 60, 48] 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)) = 23.922738416908107 V(r_1,...,r_N) = 23.922738416908107 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 -2.87711932e+00 -2.71765056e+00 -4.13754239e+00 | -2.87711932e+00 -2.71765056e+00 -4.13754239e+00 1 -2.14267543e+00 -9.95173306e+00 1.34760784e+01 | -2.14267543e+00 -9.95173306e+00 1.34760784e+01 2 4.58717466e+00 1.43029193e+01 -7.46086852e+00 | 4.58717466e+00 1.43029193e+01 -7.46086852e+00 3 -5.50842973e+00 -1.10887328e-01 -9.83710199e+00 | -5.50842973e+00 -1.10887328e-01 -9.83710199e+00 4 -3.91147683e+01 -1.42342972e+01 -2.40537898e+01 | -3.91147683e+01 -1.42342972e+01 -2.40537898e+01 5 3.63563875e+01 2.01410133e+01 1.97652263e+01 | 3.63563875e+01 2.01410133e+01 1.97652263e+01 6 7.95187131e-01 -4.41122619e-01 -4.45504409e-01 | 7.95187131e-01 -4.41122619e-01 -4.45504409e-01 7 -2.52611453e+01 5.70136856e+01 -3.13585606e+01 | -2.52611453e+01 5.70136856e+01 -3.13585606e+01 8 -2.54233610e-01 4.92250633e-01 -6.37694463e-01 | -2.54233610e-01 4.92250633e-01 -6.37694463e-01 9 -3.02422059e+00 2.38703812e+00 -2.51659679e+00 | -3.02422059e+00 2.38703812e+00 -2.51659679e+00 10 -6.75218259e-01 -8.08738339e-02 6.99401905e-01 | -6.75218259e-01 -8.08738339e-02 6.99401905e-01 11 3.10119317e+00 -4.56367942e+00 -2.90259721e+00 | 3.10119317e+00 -4.56367942e+00 -2.90259721e+00 12 -3.95827178e+01 -1.74303819e+01 -1.31374584e+01 | -3.95827178e+01 -1.74303819e+01 -1.31374584e+01 13 4.35710670e+01 1.54902584e+01 1.57826184e+01 | 4.35710670e+01 1.54902584e+01 1.57826184e+01 14 2.16905875e+00 -7.58513673e+00 -1.46599355e+00 | 2.16905875e+00 -7.58513673e+00 -1.46599355e+00 15 6.16544981e+00 1.78789018e+00 8.24463466e+00 | 6.16544981e+00 1.78789018e+00 8.24463466e+00 16 -5.07552228e+00 -6.90834504e+00 -4.64386565e+00 | -5.07552228e+00 -6.90834504e+00 -4.64386565e+00 17 7.16105622e+00 5.30447477e+00 5.76588072e+00 | 7.16105622e+00 5.30447477e+00 5.76588072e+00 18 -5.32455846e-01 -9.59638181e-01 9.05219773e-01 | -5.32455846e-01 -9.59638181e-01 9.05219773e-01 19 -3.31621836e+01 1.97932042e+01 -2.14895559e+01 | -3.31621836e+01 1.97932042e+01 -2.14895559e+01 20 -5.58123448e+00 -1.32905060e+00 1.64628037e-01 | -5.58123448e+00 -1.32905060e+00 1.64628037e-01 21 6.30136446e+00 4.81435630e+00 4.20547567e+00 | 6.30136446e+00 4.81435630e+00 4.20547567e+00 22 1.49269454e+00 -5.35436390e+00 -2.51060409e+00 | 1.49269454e+00 -5.35436390e+00 -2.51060409e+00 23 8.93074307e-03 2.80211375e+00 4.00242996e+00 | 8.93074307e-03 2.80211375e+00 4.00242996e+00 24 6.96816061e-01 4.36659810e-02 1.58448861e+00 | 6.96816061e-01 4.36659810e-02 1.58448861e+00 25 -1.45359268e+01 3.70091651e+01 -2.94757300e+01 | -1.45359268e+01 3.70091651e+01 -2.94757300e+01 26 -1.78363575e+00 -1.43789087e-01 -1.50848153e+00 | -1.78363575e+00 -1.43789087e-01 -1.50848153e+00 27 3.92475222e-01 -1.24868557e+00 3.01310878e+00 | 3.92475222e-01 -1.24868557e+00 3.01310878e+00 28 6.78188040e+00 -3.48660322e+01 3.17128564e+01 | 6.78188040e+00 -3.48660322e+01 3.17128564e+01 29 5.40211264e+00 -1.13160117e+00 -8.65144320e-01 | 5.40211264e+00 -1.13160117e+00 -8.65144320e-01 30 3.51416219e+01 -1.80616905e+01 2.06350802e+01 | 3.51416219e+01 -1.80616905e+01 2.06350802e+01 31 -4.76943285e+00 2.34702019e+00 1.03393706e-01 | -4.76943285e+00 2.34702019e+00 1.03393706e-01 32 -4.49173816e-01 5.28458308e-01 -1.48988128e+00 | -4.49173816e-01 5.28458308e-01 -1.48988128e+00 33 -5.69574401e-01 5.41982599e+00 -5.53111159e+00 | -5.69574401e-01 5.41982599e+00 -5.53111159e+00 34 2.42073504e+01 -5.74334628e+01 3.24982618e+01 | 2.42073504e+01 -5.74334628e+01 3.24982618e+01 35 -3.52060428e+00 -4.76800963e+00 2.73775052e+00 | -3.52060428e+00 -4.76800963e+00 2.73775052e+00 36 -1.21487528e-01 -5.66687657e+00 2.28516567e+00 | -1.21487528e-01 -5.66687657e+00 2.28516567e+00 37 -7.95170218e-01 -1.07977659e+00 4.09147454e+00 | -7.95170218e-01 -1.07977659e+00 4.09147454e+00 38 -8.50886741e+00 -8.36284142e+00 -6.51460889e+00 | -8.50886741e+00 -8.36284142e+00 -6.51460889e+00 39 -1.14746026e+02 -4.01363468e+01 2.80595051e+01 | -1.14746026e+02 -4.01363468e+01 2.80595051e+01 40 1.49032641e+00 -2.05992147e+00 5.58396521e+00 | 1.49032641e+00 -2.05992147e+00 5.58396521e+00 41 -1.30602066e+01 2.43202434e+01 -1.32132792e+01 | -1.30602066e+01 2.43202434e+01 -1.32132792e+01 42 -4.55975281e+00 -1.30937439e+00 -2.72499266e+00 | -4.55975281e+00 -1.30937439e+00 -2.72499266e+00 43 2.80708465e+00 7.06791722e-01 3.54559656e+00 | 2.80708465e+00 7.06791722e-01 3.54559656e+00 44 1.34860892e+01 -2.32275207e+01 1.17964476e+01 | 1.34860892e+01 -2.32275207e+01 1.17964476e+01 45 -3.95636248e-01 5.22238584e-01 -4.60588077e-01 | -3.95636248e-01 5.22238584e-01 -4.60588077e-01 46 3.84085370e+00 3.67666647e+00 -2.16783981e+00 | 3.84085370e+00 3.67666647e+00 -2.16783981e+00 47 -3.81168617e+00 -2.52171630e+00 1.99289791e+00 | -3.81168617e+00 -2.52171630e+00 1.99289791e+00 48 -4.35269075e+00 -8.08816993e+00 -6.81851243e-01 | -4.35269075e+00 -8.08816993e+00 -6.81851243e-01 49 5.87744700e+00 5.45208276e+00 -3.27371700e+00 | 5.87744700e+00 5.45208276e+00 -3.27371700e+00 50 -8.98941637e-01 -8.96823588e-01 -1.40044303e+00 | -8.98941637e-01 -8.96823588e-01 -1.40044303e+00 51 -3.54964398e+00 3.18606312e+00 -2.28506765e+00 | -3.54964398e+00 3.18606312e+00 -2.28506765e+00 52 1.19431075e+02 4.63796229e+01 -2.41385418e+01 | 1.19431075e+02 4.63796229e+01 -2.41385418e+01 53 6.29424355e+00 2.39707706e+00 -1.33187888e+00 | 6.29424355e+00 2.39707706e+00 -1.33187888e+00 54 -4.96719768e-01 2.86615146e+00 4.06152274e+00 | -4.96719768e-01 2.86615146e+00 4.06152274e+00 55 -3.57039610e-01 -1.05893323e+00 -1.17637980e+00 | -3.57039610e-01 -1.05893323e+00 -1.17637980e+00 56 -2.25408226e+00 1.74956987e-01 -4.49583586e+00 | -2.25408226e+00 1.74956987e-01 -4.49583586e+00 57 1.67451489e+01 -1.87403929e+01 -2.95122945e+01 | 1.67451489e+01 -1.87403929e+01 -2.95122945e+01 58 -9.58082598e-04 -3.77547969e-01 2.75768745e+00 | -9.58082598e-04 -3.77547969e-01 2.75768745e+00 59 -1.46787261e+00 -1.50065887e+00 6.50517467e-01 | -1.46787261e+00 -1.50065887e+00 6.50517467e-01 60 2.63887095e+00 4.13045935e+00 -4.44350528e-01 | 2.63887095e+00 4.13045935e+00 -4.44350528e-01 61 -1.45062188e+00 1.07420221e+00 -1.13996161e+00 | -1.45062188e+00 1.07420221e+00 -1.13996161e+00 62 -8.82715370e+00 2.09582875e+01 3.17359670e+01 | -8.82715370e+00 2.09582875e+01 3.17359670e+01 63 1.13186942e+00 -1.17485156e+00 -1.42756783e+00 | 1.13186942e+00 -1.17485156e+00 -1.42756783e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [61, 6, 14, 41, 30, 37, 1, 36, 32, 40, 17, 12, 11, 33, 2, 27, 38, 10, 22, 20, 19, 29, 18, 46, 39, 35, 44, 15, 55, 21, 4, 47, 8, 13, 54, 25, 7, 5, 16, 24, 9, 3, 48, 57, 26, 56, 23, 31, 42, 62, 51, 50, 59, 63, 34, 28, 45, 43, 60, 52, 58, 0, 49, 53] 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)) = -46.90726475426005 V(r_1,...,r_N) = -46.90726475426004 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 -1.16662480e+01 -2.27844895e+01 -2.70413050e+01 | -1.16662480e+01 -2.27844895e+01 -2.70413050e+01 1 1.31504762e+01 2.33670072e+01 2.73240291e+01 | 1.31504762e+01 2.33670072e+01 2.73240291e+01 2 -2.24512079e+00 -1.64742411e+00 -1.05095519e+00 | -2.24512079e+00 -1.64742411e+00 -1.05095519e+00 3 -3.63411550e+00 -4.24958144e+00 1.00608648e+01 | -3.63411550e+00 -4.24958144e+00 1.00608648e+01 4 1.26605359e+00 -6.23121916e-01 1.37886104e+00 | 1.26605359e+00 -6.23121916e-01 1.37886104e+00 5 -6.20560477e+00 -1.16667408e+00 -1.87425423e+01 | -6.20560477e+00 -1.16667408e+00 -1.87425423e+01 6 -7.50241780e-01 2.77577642e+00 7.58297003e-01 | -7.50241780e-01 2.77577642e+00 7.58297003e-01 7 1.45085080e+00 -2.53403137e-01 -2.14469341e-01 | 1.45085080e+00 -2.53403137e-01 -2.14469341e-01 8 -7.86708562e+00 -4.41105733e+00 -2.36361802e+00 | -7.86708562e+00 -4.41105733e+00 -2.36361802e+00 9 6.70322601e+00 6.47000191e+00 3.49520374e+00 | 6.70322601e+00 6.47000191e+00 3.49520374e+00 10 -2.65300204e+01 -1.54948967e+01 -1.20889057e+01 | -2.65300204e+01 -1.54948967e+01 -1.20889057e+01 11 2.55175656e+01 1.37959425e+01 1.22720426e+01 | 2.55175656e+01 1.37959425e+01 1.22720426e+01 12 -2.23189647e+00 -2.79787362e+00 -1.54580769e+00 | -2.23189647e+00 -2.79787362e+00 -1.54580769e+00 13 9.89284452e-01 3.12420213e+00 1.46101691e-01 | 9.89284452e-01 3.12420213e+00 1.46101691e-01 14 -6.59953034e-01 -6.40128169e+00 -3.69880445e+00 | -6.59953034e-01 -6.40128169e+00 -3.69880445e+00 15 2.21378090e+00 6.10072346e+00 2.92708932e+00 | 2.21378090e+00 6.10072346e+00 2.92708932e+00 16 -9.38719106e-01 -7.93808520e+00 -2.07908194e+00 | -9.38719106e-01 -7.93808520e+00 -2.07908194e+00 17 -8.54637085e-01 8.76633968e+00 -3.87298291e-01 | -8.54637085e-01 8.76633968e+00 -3.87298291e-01 18 -5.88459216e+00 -2.92145874e+00 -4.57295659e+00 | -5.88459216e+00 -2.92145874e+00 -4.57295659e+00 19 1.51559975e+00 2.82853793e+00 2.04589399e+00 | 1.51559975e+00 2.82853793e+00 2.04589399e+00 20 3.80718362e+00 -1.70812887e+00 3.93471671e+00 | 3.80718362e+00 -1.70812887e+00 3.93471671e+00 21 -1.58395969e+00 7.38287961e-01 -1.66526161e+00 | -1.58395969e+00 7.38287961e-01 -1.66526161e+00 22 -2.75477661e+00 -5.26967801e+00 -1.73705296e-01 | -2.75477661e+00 -5.26967801e+00 -1.73705296e-01 23 3.91559368e+00 3.20321207e+00 -4.23759619e-01 | 3.91559368e+00 3.20321207e+00 -4.23759619e-01 24 6.74633065e+00 6.17275575e+00 -5.67339403e+00 | 6.74633065e+00 6.17275575e+00 -5.67339403e+00 25 -3.71475415e+00 -5.55727807e-01 1.39553704e+00 | -3.71475415e+00 -5.55727807e-01 1.39553704e+00 26 -2.03394148e+00 -6.44372296e-01 -4.08179065e+00 | -2.03394148e+00 -6.44372296e-01 -4.08179065e+00 27 2.24959546e+00 -2.00256711e-01 4.44458819e+00 | 2.24959546e+00 -2.00256711e-01 4.44458819e+00 28 -2.51693894e+00 -1.98456657e+00 -2.41169507e-01 | -2.51693894e+00 -1.98456657e+00 -2.41169507e-01 29 1.38772434e+00 3.98898501e+00 1.89353366e+00 | 1.38772434e+00 3.98898501e+00 1.89353366e+00 30 1.29919272e+00 -3.61631166e+00 3.19069284e+00 | 1.29919272e+00 -3.61631166e+00 3.19069284e+00 31 -2.22660501e+01 1.92217146e+01 -6.64047364e+00 | -2.22660501e+01 1.92217146e+01 -6.64047364e+00 32 3.38152645e-01 -2.89619011e+00 -7.09998549e+00 | 3.38152645e-01 -2.89619011e+00 -7.09998549e+00 33 3.11299958e+00 5.13305252e+00 6.38243732e+00 | 3.11299958e+00 5.13305252e+00 6.38243732e+00 34 4.09360308e+00 -8.66102094e-01 1.96120404e+01 | 4.09360308e+00 -8.66102094e-01 1.96120404e+01 35 -9.23259749e-01 -2.86686898e+00 -1.00915975e+01 | -9.23259749e-01 -2.86686898e+00 -1.00915975e+01 36 -5.72714997e+00 -8.21013171e+00 -6.21460497e+00 | -5.72714997e+00 -8.21013171e+00 -6.21460497e+00 37 4.29880299e+00 1.11664401e+01 3.24799537e+00 | 4.29880299e+00 1.11664401e+01 3.24799537e+00 38 -1.24188871e+00 -3.34862857e+00 -1.93589984e+00 | -1.24188871e+00 -3.34862857e+00 -1.93589984e+00 39 4.64774283e+00 2.83837821e+00 -4.06236030e-01 | 4.64774283e+00 2.83837821e+00 -4.06236030e-01 40 -9.84811844e-01 1.62786747e+00 -4.17950045e-01 | -9.84811844e-01 1.62786747e+00 -4.17950045e-01 41 -1.46578893e+00 -8.16921321e-01 1.94024644e+00 | -1.46578893e+00 -8.16921321e-01 1.94024644e+00 42 -4.96757360e+00 -1.92299120e+00 -4.62870850e+00 | -4.96757360e+00 -1.92299120e+00 -4.62870850e+00 43 3.77964033e+00 5.16972161e+00 5.24974475e+00 | 3.77964033e+00 5.16972161e+00 5.24974475e+00 44 -4.05286904e+00 -9.23339481e+00 -1.62518665e+01 | -4.05286904e+00 -9.23339481e+00 -1.62518665e+01 45 3.33416401e+00 1.02640041e+01 1.50440377e+01 | 3.33416401e+00 1.02640041e+01 1.50440377e+01 46 -1.97044484e+00 -1.47621550e+00 -1.93798778e+00 | -1.97044484e+00 -1.47621550e+00 -1.93798778e+00 47 -1.28869391e+01 -1.88581197e+01 2.52276562e+01 | -1.28869391e+01 -1.88581197e+01 2.52276562e+01 48 -2.42647732e+00 -3.09535354e+00 -3.97269677e+00 | -2.42647732e+00 -3.09535354e+00 -3.97269677e+00 49 8.51566193e+00 -2.30587492e+00 2.77891276e+00 | 8.51566193e+00 -2.30587492e+00 2.77891276e+00 50 -1.02739295e+01 -4.38476954e+00 -3.78255929e+00 | -1.02739295e+01 -4.38476954e+00 -3.78255929e+00 51 9.68021194e+00 3.05879200e+00 1.87171302e+00 | 9.68021194e+00 3.05879200e+00 1.87171302e+00 52 -1.19437388e+00 7.43263880e-01 5.08889732e+00 | -1.19437388e+00 7.43263880e-01 5.08889732e+00 53 1.32589417e+00 4.09668404e+00 2.83374349e+00 | 1.32589417e+00 4.09668404e+00 2.83374349e+00 54 -2.26961058e+00 5.47321114e+00 2.93286281e-02 | -2.26961058e+00 5.47321114e+00 2.93286281e-02 55 1.49015850e-01 -1.49348141e+00 -1.44530186e+00 | 1.49015850e-01 -1.49348141e+00 -1.44530186e+00 56 -3.93536835e+00 -4.49010749e+00 -3.50115250e+00 | -3.93536835e+00 -4.49010749e+00 -3.50115250e+00 57 1.08352231e+01 -8.27841767e-01 -7.92167336e-01 | 1.08352231e+01 -8.27841767e-01 -7.92167336e-01 58 2.42996748e+01 -1.93897078e+01 8.83354315e+00 | 2.42996748e+01 -1.93897078e+01 8.83354315e+00 59 -2.01865586e+00 -1.33662647e+00 4.94401575e-01 | -2.01865586e+00 -1.33662647e+00 4.94401575e-01 60 1.60978674e+01 1.80975010e+01 -2.43602206e+01 | 1.60978674e+01 1.80975010e+01 -2.43602206e+01 61 -1.47611111e+00 1.48944414e-01 -1.47164389e+00 | -1.47611111e+00 1.48944414e-01 -1.47164389e+00 62 -5.50090184e+00 5.15309457e+00 8.25410686e+00 | -5.50090184e+00 5.15309457e+00 8.25410686e+00 63 9.33697342e-01 -1.03672541e+00 -1.16037897e+00 | 9.33697342e-01 -1.03672541e+00 -1.16037897e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [31, 36, 17, 6, 22, 42, 3, 63, 20, 11, 60, 9, 29, 25, 46, 61, 45, 2, 57, 58, 8, 43, 4, 54, 56, 13, 49, 37, 51, 12, 41, 0, 38, 35, 47, 33, 1, 27, 32, 50, 44, 30, 5, 21, 40, 16, 14, 34, 52, 26, 39, 28, 48, 55, 23, 53, 24, 18, 19, 62, 10, 15, 59, 7] 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)) = 14.950732114300953 V(r_1,...,r_N) = 14.950732114300866 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 -8.28912657e+00 -1.80855019e+01 -1.74606880e+00 | -8.28912657e+00 -1.80855019e+01 -1.74606880e+00 1 5.88542920e+00 1.75905257e+01 2.13977316e+00 | 5.88542920e+00 1.75905257e+01 2.13977316e+00 2 1.21557671e-01 8.58373311e-01 -3.52650359e+00 | 1.21557671e-01 8.58373311e-01 -3.52650359e+00 3 5.87128812e+00 -4.47887511e+00 -6.15102798e+00 | 5.87128812e+00 -4.47887511e+00 -6.15102798e+00 4 -2.37683489e+00 -6.04795286e+00 -4.21702827e+00 | -2.37683489e+00 -6.04795286e+00 -4.21702827e+00 5 3.44761244e+00 6.10887862e+00 -6.70128648e-01 | 3.44761244e+00 6.10887862e+00 -6.70128648e-01 6 -4.35095701e+00 -6.13425484e+00 -5.41690692e+00 | -4.35095701e+00 -6.13425484e+00 -5.41690692e+00 7 3.01255458e+00 4.43064055e+00 4.81605299e+00 | 3.01255458e+00 4.43064055e+00 4.81605299e+00 8 -2.49559436e+00 -2.35268413e-01 -4.74993086e-01 | -2.49559436e+00 -2.35268413e-01 -4.74993086e-01 9 1.19883155e+01 -1.07005511e+01 -1.48283568e+01 | 1.19883155e+01 -1.07005511e+01 -1.48283568e+01 10 -5.42896550e-01 1.16399056e+00 -3.07084769e+00 | -5.42896550e-01 1.16399056e+00 -3.07084769e+00 11 3.79799753e+01 -1.09210496e+01 -2.79931331e+01 | 3.79799753e+01 -1.09210496e+01 -2.79931331e+01 12 -1.12158890e+00 -3.70871947e+00 3.43031511e-01 | -1.12158890e+00 -3.70871947e+00 3.43031511e-01 13 2.01520964e+00 2.60638635e+00 2.11586101e+00 | 2.01520964e+00 2.60638635e+00 2.11586101e+00 14 -1.39663837e+01 9.57876592e+00 1.35138500e+01 | -1.39663837e+01 9.57876592e+00 1.35138500e+01 15 6.88929325e+00 -1.18090916e+01 -2.81718401e+00 | 6.88929325e+00 -1.18090916e+01 -2.81718401e+00 16 -3.00029310e+00 -2.03435630e+00 -4.37788790e+00 | -3.00029310e+00 -2.03435630e+00 -4.37788790e+00 17 -1.58292533e+00 -8.24959132e+00 9.08686668e+00 | -1.58292533e+00 -8.24959132e+00 9.08686668e+00 18 -9.47545667e+00 -2.04118071e+01 -6.44242620e+00 | -9.47545667e+00 -2.04118071e+01 -6.44242620e+00 19 1.81546697e+01 2.57060764e+01 2.58295613e+00 | 1.81546697e+01 2.57060764e+01 2.58295613e+00 20 -2.83851760e-01 7.43339063e+00 7.85771090e+00 | -2.83851760e-01 7.43339063e+00 7.85771090e+00 21 -4.11446410e+01 -4.94131944e+01 4.28703279e+01 | -4.11446410e+01 -4.94131944e+01 4.28703279e+01 22 -1.82244347e+00 3.06678959e+00 2.49361345e+00 | -1.82244347e+00 3.06678959e+00 2.49361345e+00 23 2.80626848e-01 -1.11645205e+00 -4.73215565e-01 | 2.80626848e-01 -1.11645205e+00 -4.73215565e-01 24 -1.67499464e+00 -5.51557142e+00 -1.96801806e+00 | -1.67499464e+00 -5.51557142e+00 -1.96801806e+00 25 -6.16526225e+00 2.81658629e+00 8.55733404e+00 | -6.16526225e+00 2.81658629e+00 8.55733404e+00 26 8.02258532e+00 1.90351669e+00 -3.73794484e+00 | 8.02258532e+00 1.90351669e+00 -3.73794484e+00 27 -1.37134146e+00 -1.77321711e+00 4.08391381e-01 | -1.37134146e+00 -1.77321711e+00 4.08391381e-01 28 -3.82816911e+01 1.32501460e+01 2.94587117e+01 | -3.82816911e+01 1.32501460e+01 2.94587117e+01 29 1.13510558e+01 -1.11012926e+01 -4.63489554e+00 | 1.13510558e+01 -1.11012926e+01 -4.63489554e+00 30 4.23646165e+01 4.93624546e+01 -4.38782851e+01 | 4.23646165e+01 4.93624546e+01 -4.38782851e+01 31 -1.54885758e+01 7.13794214e+01 -6.90225502e+00 | -1.54885758e+01 7.13794214e+01 -6.90225502e+00 32 1.20842920e+00 1.00485624e+00 -6.67048716e-01 | 1.20842920e+00 1.00485624e+00 -6.67048716e-01 33 -1.01965262e+01 -9.44226296e-02 -5.85627844e+00 | -1.01965262e+01 -9.44226296e-02 -5.85627844e+00 34 -1.25735579e+00 4.79522571e+00 4.39861075e+00 | -1.25735579e+00 4.79522571e+00 4.39861075e+00 35 -2.15732101e+00 -1.01790740e+00 -1.53602641e+00 | -2.15732101e+00 -1.01790740e+00 -1.53602641e+00 36 6.41988373e+00 -3.94740605e+00 2.93609474e+00 | 6.41988373e+00 -3.94740605e+00 2.93609474e+00 37 6.46637320e-01 2.09117142e+00 3.48268225e+00 | 6.46637320e-01 2.09117142e+00 3.48268225e+00 38 -1.63717398e+01 -1.11089242e+01 -1.34941440e+01 | -1.63717398e+01 -1.11089242e+01 -1.34941440e+01 39 1.87269474e+01 1.20378847e+01 1.07816290e+01 | 1.87269474e+01 1.20378847e+01 1.07816290e+01 40 1.93435401e+00 -1.40354882e+00 2.18344310e+00 | 1.93435401e+00 -1.40354882e+00 2.18344310e+00 41 -1.27951051e+01 -2.86198902e+01 1.05541453e+01 | -1.27951051e+01 -2.86198902e+01 1.05541453e+01 42 1.52632100e+01 2.84619005e+01 -8.81652037e+00 | 1.52632100e+01 2.84619005e+01 -8.81652037e+00 43 1.01401202e+01 -5.19779685e+00 -1.47432641e+01 | 1.01401202e+01 -5.19779685e+00 -1.47432641e+01 44 -3.39512324e+00 -2.48819177e+00 -3.15487192e+00 | -3.39512324e+00 -2.48819177e+00 -3.15487192e+00 45 2.38829464e+00 3.27839412e+00 2.68317637e+00 | 2.38829464e+00 3.27839412e+00 2.68317637e+00 46 1.74680256e+00 -5.23678165e+00 -5.53283591e+00 | 1.74680256e+00 -5.23678165e+00 -5.53283591e+00 47 3.28550333e+00 4.57924292e+00 5.74832921e+00 | 3.28550333e+00 4.57924292e+00 5.74832921e+00 48 -1.58243783e-01 -2.08890055e+00 7.25869706e-01 | -1.58243783e-01 -2.08890055e+00 7.25869706e-01 49 1.75503288e+00 -6.53008295e-01 1.08692420e+00 | 1.75503288e+00 -6.53008295e-01 1.08692420e+00 50 -2.11302625e-01 2.62529622e-02 6.57415070e-01 | -2.11302625e-01 2.62529622e-02 6.57415070e-01 51 -3.71960852e+01 4.63083529e+01 -7.86187413e+01 | -3.71960852e+01 4.63083529e+01 -7.86187413e+01 52 -9.53660142e+00 -7.52158570e+00 3.88421980e-02 | -9.53660142e+00 -7.52158570e+00 3.88421980e-02 53 2.84980500e+00 3.02271691e+00 5.42070436e+00 | 2.84980500e+00 3.02271691e+00 5.42070436e+00 54 -2.70116053e+00 6.44349221e-02 1.54068750e-01 | -2.70116053e+00 6.44349221e-02 1.54068750e-01 55 3.72146125e+00 2.52528163e-01 -4.31112683e-01 | 3.72146125e+00 2.52528163e-01 -4.31112683e-01 56 -8.24672122e+00 1.64314164e+01 1.26159521e+00 | -8.24672122e+00 1.64314164e+01 1.26159521e+00 57 1.07849070e+00 -1.39871369e+01 6.23194270e+01 | 1.07849070e+00 -1.39871369e+01 6.23194270e+01 58 -3.11800901e+00 -4.87432576e+01 -5.19631122e+01 | -3.11800901e+00 -4.87432576e+01 -5.19631122e+01 59 3.42191578e+00 4.67389213e-01 2.12987350e+00 | 3.42191578e+00 4.67389213e-01 2.12987350e+00 60 -2.13080809e+01 -1.31510162e+01 2.14375392e+00 | -2.13080809e+01 -1.31510162e+01 2.14375392e+00 61 8.74196709e+00 1.95421349e+01 1.09063704e+01 | 8.74196709e+00 1.95421349e+01 1.09063704e+01 62 3.90471452e+01 -4.15866526e+01 7.17082785e+01 | 3.90471452e+01 -4.15866526e+01 7.17082785e+01 63 2.32344416e+00 -1.03667022e+00 5.75348549e-01 | 2.32344416e+00 -1.03667022e+00 5.75348549e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Fe (Configuration in file "config-Fe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [22, 4, 6, 34, 1, 49, 2, 21, 28, 33, 41, 23, 54, 46, 51, 37, 20, 36, 29, 30, 16, 7, 0, 11, 48, 44, 56, 61, 8, 18, 19, 35, 39, 9, 3, 31, 17, 15, 47, 32, 52, 10, 43, 42, 25, 59, 13, 38, 24, 5, 60, 14, 40, 63, 12, 57, 26, 55, 62, 45, 50, 27, 58, 53] 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)) = 64.75142347768411 V(r_1,...,r_N) = 64.75142347768411 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 2.84053006e+00 4.59198717e+00 3.31594128e+00 | 2.84053006e+00 4.59198717e+00 3.31594128e+00 1 -5.00486788e+00 5.36844436e+00 -7.43467458e+00 | -5.00486788e+00 5.36844436e+00 -7.43467458e+00 2 -6.36132517e+00 -4.66999303e-01 6.03451883e+00 | -6.36132517e+00 -4.66999303e-01 6.03451883e+00 3 -1.48147926e+00 -2.65926090e+00 3.11699090e+00 | -1.48147926e+00 -2.65926090e+00 3.11699090e+00 4 4.68400233e+00 1.87340016e-02 5.06580079e+00 | 4.68400233e+00 1.87340016e-02 5.06580079e+00 5 -2.91413616e+00 -8.32714315e+00 2.18825511e+00 | -2.91413616e+00 -8.32714315e+00 2.18825511e+00 6 4.84227602e+00 2.62293227e-01 -4.16256193e+00 | 4.84227602e+00 2.62293227e-01 -4.16256193e+00 7 -4.46212233e+00 9.23813187e-01 -1.93240116e+00 | -4.46212233e+00 9.23813187e-01 -1.93240116e+00 8 5.60985823e+00 5.44870350e+00 4.22054347e+00 | 5.60985823e+00 5.44870350e+00 4.22054347e+00 9 -9.79801900e+00 -4.37872862e-01 3.60862714e+01 | -9.79801900e+00 -4.37872862e-01 3.60862714e+01 10 7.74990641e+00 4.18552130e+00 -3.79856240e+01 | 7.74990641e+00 4.18552130e+00 -3.79856240e+01 11 -4.25434729e+00 -2.69383121e+00 2.86919637e+00 | -4.25434729e+00 -2.69383121e+00 2.86919637e+00 12 -2.27503401e+00 -5.46179992e+00 2.51766446e+00 | -2.27503401e+00 -5.46179992e+00 2.51766446e+00 13 5.02569647e+01 -6.01691585e+01 -9.51150190e+01 | 5.02569647e+01 -6.01691585e+01 -9.51150190e+01 14 5.10418293e+00 2.40559796e+00 -4.22121078e+00 | 5.10418293e+00 2.40559796e+00 -4.22121078e+00 15 5.64995310e-01 3.09926010e+00 1.98429108e+00 | 5.64995310e-01 3.09926010e+00 1.98429108e+00 16 8.40297802e+00 5.46718672e+00 9.09793956e+00 | 8.40297802e+00 5.46718672e+00 9.09793956e+00 17 -7.75216069e+01 4.96129042e+01 -6.93014703e+01 | -7.75216069e+01 4.96129042e+01 -6.93014703e+01 18 -3.65408117e+00 -5.99137645e+00 7.17811547e+00 | -3.65408117e+00 -5.99137645e+00 7.17811547e+00 19 5.03890137e+00 -8.99117512e+00 3.55317349e+00 | 5.03890137e+00 -8.99117512e+00 3.55317349e+00 20 7.17678356e+01 -4.49657645e+01 6.25659062e+01 | 7.17678356e+01 -4.49657645e+01 6.25659062e+01 21 -1.06108053e+00 2.14212699e+00 -7.80824626e-01 | -1.06108053e+00 2.14212699e+00 -7.80824626e-01 22 9.29472573e+00 -6.23989795e+00 -4.50752643e+00 | 9.29472573e+00 -6.23989795e+00 -4.50752643e+00 23 -5.65659638e+00 -6.45455237e+00 -3.57977928e+00 | -5.65659638e+00 -6.45455237e+00 -3.57977928e+00 24 -1.49102582e+00 5.99339053e+00 1.10369149e+00 | -1.49102582e+00 5.99339053e+00 1.10369149e+00 25 -6.52435121e+00 -1.23604737e+01 2.62358333e+00 | -6.52435121e+00 -1.23604737e+01 2.62358333e+00 26 3.34465467e+00 1.50938531e+01 -6.58537614e+00 | 3.34465467e+00 1.50938531e+01 -6.58537614e+00 27 -4.57732836e+00 -4.59836463e+00 5.32629424e+00 | -4.57732836e+00 -4.59836463e+00 5.32629424e+00 28 -7.28652596e-01 3.09097687e+00 -9.56395808e-01 | -7.28652596e-01 3.09097687e+00 -9.56395808e-01 29 3.05576402e+00 -4.37581343e+00 -4.40013062e-01 | 3.05576402e+00 -4.37581343e+00 -4.40013062e-01 30 -1.39526894e+01 -2.83795093e+01 -2.38074544e+01 | -1.39526894e+01 -2.83795093e+01 -2.38074544e+01 31 9.16302345e+00 3.34420729e+01 1.89568243e+01 | 9.16302345e+00 3.34420729e+01 1.89568243e+01 32 4.90624431e+00 3.13931755e+00 2.17689351e+00 | 4.90624431e+00 3.13931755e+00 2.17689351e+00 33 -7.12023760e-01 -5.46696045e+00 6.07322587e+00 | -7.12023760e-01 -5.46696045e+00 6.07322587e+00 34 1.23448126e+00 1.88026808e+00 2.70227128e+00 | 1.23448126e+00 1.88026808e+00 2.70227128e+00 35 1.39570412e+00 7.67234836e-01 -1.02156961e+00 | 1.39570412e+00 7.67234836e-01 -1.02156961e+00 36 -1.91976222e+00 9.05847383e+00 -4.36382813e+00 | -1.91976222e+00 9.05847383e+00 -4.36382813e+00 37 -3.96297093e+00 -6.06737928e-01 -4.57956087e+00 | -3.96297093e+00 -6.06737928e-01 -4.57956087e+00 38 6.16075329e+00 2.71641027e+00 -4.48407139e+00 | 6.16075329e+00 2.71641027e+00 -4.48407139e+00 39 -5.05172371e+00 -1.57312417e+00 2.72056945e+00 | -5.05172371e+00 -1.57312417e+00 2.72056945e+00 40 8.10849774e-01 2.99127187e+00 -3.05706708e+00 | 8.10849774e-01 2.99127187e+00 -3.05706708e+00 41 -7.48659111e-01 2.29263193e+00 -2.70711293e-01 | -7.48659111e-01 2.29263193e+00 -2.70711293e-01 42 -4.92377249e+01 5.61420147e+01 9.81547895e+01 | -4.92377249e+01 5.61420147e+01 9.81547895e+01 43 1.51953345e+01 -6.05411580e-01 -5.67392128e+00 | 1.51953345e+01 -6.05411580e-01 -5.67392128e+00 44 -6.15985771e-01 -2.02723975e+00 -1.03340766e+00 | -6.15985771e-01 -2.02723975e+00 -1.03340766e+00 45 4.49545630e-02 1.27106087e+00 1.65814267e-01 | 4.49545630e-02 1.27106087e+00 1.65814267e-01 46 -1.52539576e+00 -9.33283928e+00 1.91509435e+00 | -1.52539576e+00 -9.33283928e+00 1.91509435e+00 47 1.66056228e+00 3.97345180e+00 4.35911779e+00 | 1.66056228e+00 3.97345180e+00 4.35911779e+00 48 8.64518540e-01 -2.96177370e-01 -1.21074007e+00 | 8.64518540e-01 -2.96177370e-01 -1.21074007e+00 49 2.39307810e-01 -1.82425444e+00 -6.80424939e-01 | 2.39307810e-01 -1.82425444e+00 -6.80424939e-01 50 3.96137917e+00 -3.38669864e-02 -3.96614684e+00 | 3.96137917e+00 -3.38669864e-02 -3.96614684e+00 51 -2.24514155e+00 -6.82355020e-01 7.64438896e+00 | -2.24514155e+00 -6.82355020e-01 7.64438896e+00 52 -6.70688268e+00 3.10718853e-01 -8.27544352e+00 | -6.70688268e+00 3.10718853e-01 -8.27544352e+00 53 5.80886198e+00 3.36340893e+00 7.83434512e+00 | 5.80886198e+00 3.36340893e+00 7.83434512e+00 54 -6.98935722e+00 -9.02785538e+00 -4.86797112e+00 | -6.98935722e+00 -9.02785538e+00 -4.86797112e+00 55 1.27627431e+01 5.51375184e+00 2.27138986e+00 | 1.27627431e+01 5.51375184e+00 2.27138986e+00 56 4.28678246e+00 -8.44392037e-01 1.06177550e-01 | 4.28678246e+00 -8.44392037e-01 1.06177550e-01 57 5.02928337e+00 3.32123481e+00 4.08772751e+00 | 5.02928337e+00 3.32123481e+00 4.08772751e+00 58 1.89165649e+00 1.94966968e+00 -6.78354044e-01 | 1.89165649e+00 1.94966968e+00 -6.78354044e-01 59 -8.66429987e+00 -7.69518045e+00 3.97706824e+00 | -8.66429987e+00 -7.69518045e+00 3.97706824e+00 60 -1.50067763e+01 7.18413100e+00 -8.30984764e-01 | -1.50067763e+01 7.18413100e+00 -8.30984764e-01 61 -6.14744104e+00 3.23068097e-03 -1.17996896e+01 | -6.14744104e+00 3.23068097e-03 -1.17996896e+01 62 -1.51547474e+00 -2.91204012e-01 -9.03316500e-01 | -1.51547474e+00 -2.91204012e-01 -9.03316500e-01 63 4.79434713e+00 -4.14455559e+00 -3.48633470e+00 | 4.79434713e+00 -4.14455559e+00 -3.48633470e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [14, 4, 44, 39, 1, 27, 43, 32, 63, 58, 60, 57, 61, 15, 0, 13, 38, 53, 33, 40, 52, 41, 23, 22, 36, 45, 55, 5, 35, 50, 48, 34, 7, 18, 31, 28, 24, 46, 16, 3, 19, 21, 54, 6, 2, 25, 37, 59, 30, 62, 29, 56, 20, 17, 42, 26, 51, 11, 9, 47, 10, 12, 49, 8] 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)) = 56.722876675623745 V(r_1,...,r_N) = 56.7228766756238 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 -2.96250690e+00 -1.56911125e+00 1.28580924e-01 | -2.96250690e+00 -1.56911125e+00 1.28580924e-01 1 -1.07116803e+01 -2.24157828e+01 -3.43883297e+00 | -1.07116803e+01 -2.24157828e+01 -3.43883297e+00 2 1.29314448e+01 2.55398010e+01 3.10975246e+00 | 1.29314448e+01 2.55398010e+01 3.10975246e+00 3 -6.80623555e+00 -1.50949516e+00 -1.90480516e+00 | -6.80623555e+00 -1.50949516e+00 -1.90480516e+00 4 3.04719498e+00 7.61433745e-01 2.37749447e+00 | 3.04719498e+00 7.61433745e-01 2.37749447e+00 5 -6.15787616e+00 -4.25393656e+00 1.25365158e+01 | -6.15787616e+00 -4.25393656e+00 1.25365158e+01 6 -1.64858663e+00 -3.49910337e+00 -1.09256506e+00 | -1.64858663e+00 -3.49910337e+00 -1.09256506e+00 7 5.35262339e+00 5.01562654e+00 -5.23160061e+00 | 5.35262339e+00 5.01562654e+00 -5.23160061e+00 8 -5.20562068e-01 -1.81895071e+00 -1.27137441e-01 | -5.20562068e-01 -1.81895071e+00 -1.27137441e-01 9 1.09711482e+02 -1.66828705e+01 -4.56619030e+01 | 1.09711482e+02 -1.66828705e+01 -4.56619030e+01 10 8.16755587e-01 9.16203737e-01 1.63683932e+00 | 8.16755587e-01 9.16203737e-01 1.63683932e+00 11 6.96534282e+01 -7.36031525e+01 -9.82754609e+01 | 6.96534282e+01 -7.36031525e+01 -9.82754609e+01 12 -3.76389205e+00 -1.72290162e+00 -3.36752340e+00 | -3.76389205e+00 -1.72290162e+00 -3.36752340e+00 13 4.22498208e+00 -4.29636829e-02 -1.92223636e+00 | 4.22498208e+00 -4.29636829e-02 -1.92223636e+00 14 -1.05952722e+02 2.73497989e+01 3.16452936e+01 | -1.05952722e+02 2.73497989e+01 3.16452936e+01 15 3.14749627e-01 -2.49942775e+00 -1.26416145e+00 | 3.14749627e-01 -2.49942775e+00 -1.26416145e+00 16 -1.19344754e+01 -1.52421872e+01 -5.71352143e+00 | -1.19344754e+01 -1.52421872e+01 -5.71352143e+00 17 1.41102309e+01 1.22541792e+01 7.74543878e+00 | 1.41102309e+01 1.22541792e+01 7.74543878e+00 18 -7.83163879e+00 -6.21195080e+00 -5.30775762e+00 | -7.83163879e+00 -6.21195080e+00 -5.30775762e+00 19 5.63478478e+00 8.49653991e+00 7.83603000e+00 | 5.63478478e+00 8.49653991e+00 7.83603000e+00 20 5.35782017e-01 1.60833123e+00 2.35899271e+00 | 5.35782017e-01 1.60833123e+00 2.35899271e+00 21 -4.73639802e+00 5.58940228e+00 -6.82854108e-01 | -4.73639802e+00 5.58940228e+00 -6.82854108e-01 22 1.90711027e+00 1.03964390e-01 4.75968187e-01 | 1.90711027e+00 1.03964390e-01 4.75968187e-01 23 -4.50428718e+00 1.91802551e+01 -4.59080966e+01 | -4.50428718e+00 1.91802551e+01 -4.59080966e+01 24 4.59597927e+00 2.12589119e-01 3.03668521e-01 | 4.59597927e+00 2.12589119e-01 3.03668521e-01 25 -5.99440430e+01 -7.82028443e+01 7.60634640e+01 | -5.99440430e+01 -7.82028443e+01 7.60634640e+01 26 6.63028963e+01 7.46427368e+01 -7.48142742e+01 | 6.63028963e+01 7.46427368e+01 -7.48142742e+01 27 -2.27521872e+00 -1.48918892e+00 1.06551766e+00 | -2.27521872e+00 -1.48918892e+00 1.06551766e+00 28 -7.20787224e+01 7.41379245e+01 9.74597834e+01 | -7.20787224e+01 7.41379245e+01 9.74597834e+01 29 -2.75609917e+00 2.06176907e-01 -1.00174777e+00 | -2.75609917e+00 2.06176907e-01 -1.00174777e+00 30 -3.56188868e+00 -1.90506808e+00 2.42949069e+00 | -3.56188868e+00 -1.90506808e+00 2.42949069e+00 31 3.21199595e+00 3.81382811e-01 1.49667313e+00 | 3.21199595e+00 3.81382811e-01 1.49667313e+00 32 2.86526653e-01 6.33576230e-01 -1.04786213e+00 | 2.86526653e-01 6.33576230e-01 -1.04786213e+00 33 9.99778567e-01 -1.59095811e+00 -2.14464318e+00 | 9.99778567e-01 -1.59095811e+00 -2.14464318e+00 34 3.40104310e+00 -2.78474392e+00 2.43382327e+00 | 3.40104310e+00 -2.78474392e+00 2.43382327e+00 35 3.13092202e+00 7.60319149e+00 -2.90772022e+00 | 3.13092202e+00 7.60319149e+00 -2.90772022e+00 36 -3.54980125e+00 -2.83785203e+00 -3.16610422e+00 | -3.54980125e+00 -2.83785203e+00 -3.16610422e+00 37 4.47807696e+00 4.18474487e+00 1.77800670e-01 | 4.47807696e+00 4.18474487e+00 1.77800670e-01 38 -2.53115246e+01 -8.23219132e+00 -3.26926369e+01 | -2.53115246e+01 -8.23219132e+00 -3.26926369e+01 39 2.74099577e+01 1.21516365e+01 3.24454405e+01 | 2.74099577e+01 1.21516365e+01 3.24454405e+01 40 -9.32364170e-01 -9.48681418e-01 3.84704004e+00 | -9.32364170e-01 -9.48681418e-01 3.84704004e+00 41 -1.07317055e+01 1.56549504e+01 -1.15721178e+01 | -1.07317055e+01 1.56549504e+01 -1.15721178e+01 42 -3.25031654e+00 3.59661863e+00 4.01610613e+00 | -3.25031654e+00 3.59661863e+00 4.01610613e+00 43 1.05359380e+00 -2.33623308e+00 -5.67369086e+00 | 1.05359380e+00 -2.33623308e+00 -5.67369086e+00 44 9.56272656e+00 -1.50555163e+01 1.14069884e+01 | 9.56272656e+00 -1.50555163e+01 1.14069884e+01 45 3.64196632e-01 1.61354541e+00 2.56135007e-01 | 3.64196632e-01 1.61354541e+00 2.56135007e-01 46 2.93968301e+00 -1.18907177e+01 1.45949435e+00 | 2.93968301e+00 -1.18907177e+01 1.45949435e+00 47 -1.77149852e+00 4.54911902e-01 -1.24294862e+00 | -1.77149852e+00 4.54911902e-01 -1.24294862e+00 48 -2.42580306e+01 -3.08581543e+01 -1.14467423e+01 | -2.42580306e+01 -3.08581543e+01 -1.14467423e+01 49 2.03183763e+01 3.32071649e+01 1.56519780e+01 | 2.03183763e+01 3.32071649e+01 1.56519780e+01 50 5.80273987e+00 -2.10383894e+01 4.43728818e+01 | 5.80273987e+00 -2.10383894e+01 4.43728818e+01 51 -3.83115819e+00 4.87554805e-01 -3.38884333e+00 | -3.83115819e+00 4.87554805e-01 -3.38884333e+00 52 -6.18501862e+00 -1.85267729e+00 -1.85386642e-01 | -6.18501862e+00 -1.85267729e+00 -1.85386642e-01 53 -1.08055922e+00 -8.46353223e-01 3.33579753e+00 | -1.08055922e+00 -8.46353223e-01 3.33579753e+00 54 4.08323702e-01 -9.72922454e-01 -1.63033162e+00 | 4.08323702e-01 -9.72922454e-01 -1.63033162e+00 55 2.32952301e+00 -4.91345264e-01 -8.43071890e-01 | 2.32952301e+00 -4.91345264e-01 -8.43071890e-01 56 2.96594140e+00 -4.02529107e+00 1.43558113e+00 | 2.96594140e+00 -4.02529107e+00 1.43558113e+00 57 -6.13335669e+01 -4.48585694e+01 4.25528327e+01 | -6.13335669e+01 -4.48585694e+01 4.25528327e+01 58 6.28623853e+01 4.22510393e+01 -4.29488644e+01 | 6.28623853e+01 4.22510393e+01 -4.29488644e+01 59 -1.14359906e+00 -1.20506122e+00 -1.75816299e-01 | -1.14359906e+00 -1.20506122e+00 -1.75816299e-01 60 -1.49432140e+01 -8.85834333e+00 -1.45607635e+01 | -1.49432140e+01 -8.85834333e+00 -1.45607635e+01 61 1.06074265e+01 1.33980616e+01 1.72614565e+01 | 1.06074265e+01 1.33980616e+01 1.72614565e+01 62 2.45304329e+00 1.07859279e+00 1.44573644e+00 | 2.45304329e+00 1.07859279e+00 1.44573644e+00 63 2.74348503e+00 6.41000960e-01 5.73425908e-01 | 2.74348503e+00 6.41000960e-01 5.73425908e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Co Cr Cu Fe Ni (Configuration in file "config-CoCrCuFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [12, 8, 27, 35, 17, 44, 23, 43, 1, 19, 54, 61, 0, 39, 59, 49, 24, 4, 48, 9, 37, 50, 51, 6, 16, 33, 36, 2, 60, 34, 56, 58, 40, 25, 29, 3, 26, 20, 52, 13, 32, 57, 46, 7, 5, 45, 42, 63, 18, 15, 21, 22, 38, 53, 10, 55, 30, 41, 31, 14, 28, 11, 62, 47] 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)) = 9.663072634493682 V(r_1,...,r_N) = 9.663072634493705 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 -2.10089913e-01 5.69721320e-01 -2.44406292e-01 | -2.10089913e-01 5.69721320e-01 -2.44406292e-01 1 1.68151397e-01 1.31833340e+00 -7.47129890e+00 | 1.68151397e-01 1.31833340e+00 -7.47129890e+00 2 -1.26201742e+00 3.27179101e-01 2.08955009e+00 | -1.26201742e+00 3.27179101e-01 2.08955009e+00 3 -2.69602298e+00 -4.11533541e+00 -5.00517048e+00 | -2.69602298e+00 -4.11533541e+00 -5.00517048e+00 4 3.50198678e+00 -2.95738887e+00 5.64040338e+00 | 3.50198678e+00 -2.95738887e+00 5.64040338e+00 5 -1.38810343e+00 8.76598034e-01 -1.35748974e+00 | -1.38810343e+00 8.76598034e-01 -1.35748974e+00 6 -1.55244768e+00 1.15728872e+00 -5.53406558e-01 | -1.55244768e+00 1.15728872e+00 -5.53406558e-01 7 -1.00321410e+00 9.93235654e-01 2.08384528e+00 | -1.00321410e+00 9.93235654e-01 2.08384528e+00 8 1.49942002e+00 2.77469429e+00 5.50695209e-01 | 1.49942002e+00 2.77469429e+00 5.50695209e-01 9 1.69371689e+00 -1.90020255e+00 1.60388356e+01 | 1.69371689e+00 -1.90020255e+00 1.60388356e+01 10 -4.18793813e+00 3.34270298e+00 -1.02263254e+01 | -4.18793813e+00 3.34270298e+00 -1.02263254e+01 11 -4.08251556e-01 -3.84796738e+00 -3.41878219e+00 | -4.08251556e-01 -3.84796738e+00 -3.41878219e+00 12 -2.97343700e+00 -7.51878336e-01 -1.01935250e+00 | -2.97343700e+00 -7.51878336e-01 -1.01935250e+00 13 3.49916110e+00 -1.18743199e+00 1.07014220e-01 | 3.49916110e+00 -1.18743199e+00 1.07014220e-01 14 2.43504167e+00 -4.55038848e+00 -4.71586269e+00 | 2.43504167e+00 -4.55038848e+00 -4.71586269e+00 15 2.07889837e+00 -3.08825890e+00 2.57523638e+00 | 2.07889837e+00 -3.08825890e+00 2.57523638e+00 16 -2.19570332e+00 -4.46899319e+00 -8.37868132e-01 | -2.19570332e+00 -4.46899319e+00 -8.37868132e-01 17 2.65995138e+00 3.81207338e+00 4.05335938e+00 | 2.65995138e+00 3.81207338e+00 4.05335938e+00 18 -6.92199033e+00 -1.31545644e+01 -1.32011791e+01 | -6.92199033e+00 -1.31545644e+01 -1.32011791e+01 19 9.01460161e+00 1.13610632e+01 1.52575243e+01 | 9.01460161e+00 1.13610632e+01 1.52575243e+01 20 7.71455800e-01 2.07141577e+00 -5.16321978e-01 | 7.71455800e-01 2.07141577e+00 -5.16321978e-01 21 1.78779604e+00 2.15945466e+00 -1.73893724e+00 | 1.78779604e+00 2.15945466e+00 -1.73893724e+00 22 -3.41264624e+00 -7.26709545e+00 -2.94058270e+00 | -3.41264624e+00 -7.26709545e+00 -2.94058270e+00 23 6.76513406e+00 1.64365740e+00 5.18157369e+00 | 6.76513406e+00 1.64365740e+00 5.18157369e+00 24 -1.90861040e+01 -1.55199039e+01 -4.32832524e+01 | -1.90861040e+01 -1.55199039e+01 -4.32832524e+01 25 2.18598431e+01 1.89222235e+01 4.41582598e+01 | 2.18598431e+01 1.89222235e+01 4.41582598e+01 26 -7.45459962e+00 -1.27929278e+01 -8.20723967e-01 | -7.45459962e+00 -1.27929278e+01 -8.20723967e-01 27 5.23178753e+00 1.17202527e+01 2.52556202e+00 | 5.23178753e+00 1.17202527e+01 2.52556202e+00 28 -6.06063707e+00 1.06772754e+00 -6.35302267e-01 | -6.06063707e+00 1.06772754e+00 -6.35302267e-01 29 1.40949563e+00 6.19341362e-01 3.61691918e+00 | 1.40949563e+00 6.19341362e-01 3.61691918e+00 30 -5.15316544e+00 -1.92034868e+01 -2.51661713e+01 | -5.15316544e+00 -1.92034868e+01 -2.51661713e+01 31 -4.05401790e-01 1.64225549e+01 2.26076736e+01 | -4.05401790e-01 1.64225549e+01 2.26076736e+01 32 -5.72369709e+01 -2.26758057e+01 -6.71974059e+01 | -5.72369709e+01 -2.26758057e+01 -6.71974059e+01 33 5.74280859e+01 2.32822065e+01 6.96973336e+01 | 5.74280859e+01 2.32822065e+01 6.96973336e+01 34 -2.71965449e+01 -8.57170183e+00 -2.66957867e+01 | -2.71965449e+01 -8.57170183e+00 -2.66957867e+01 35 2.81869094e+01 1.13744039e+01 2.64444079e+01 | 2.81869094e+01 1.13744039e+01 2.64444079e+01 36 -3.66374197e+00 -2.21590323e+00 -3.45541907e+00 | -3.66374197e+00 -2.21590323e+00 -3.45541907e+00 37 2.68794663e+00 9.10354855e-01 1.58989134e+00 | 2.68794663e+00 9.10354855e-01 1.58989134e+00 38 -1.03073329e+01 -2.85147867e+01 -3.37321114e+01 | -1.03073329e+01 -2.85147867e+01 -3.37321114e+01 39 1.24755750e+01 2.84349661e+01 3.20490736e+01 | 1.24755750e+01 2.84349661e+01 3.20490736e+01 40 1.04091128e+00 -2.86002106e+00 -1.39135685e+00 | 1.04091128e+00 -2.86002106e+00 -1.39135685e+00 41 1.05121662e+00 2.19909163e+00 -7.29167202e+00 | 1.05121662e+00 2.19909163e+00 -7.29167202e+00 42 -5.55307509e+00 2.40193432e+00 -2.01201797e+00 | -5.55307509e+00 2.40193432e+00 -2.01201797e+00 43 4.46542281e-01 1.90396281e+00 3.86141365e+00 | 4.46542281e-01 1.90396281e+00 3.86141365e+00 44 4.19563748e-01 -2.67243043e+00 3.46171530e+00 | 4.19563748e-01 -2.67243043e+00 3.46171530e+00 45 -4.51831466e-01 3.56444132e-01 -4.75193928e-01 | -4.51831466e-01 3.56444132e-01 -4.75193928e-01 46 -2.23755772e-01 5.99049557e+00 3.24337216e+00 | -2.23755772e-01 5.99049557e+00 3.24337216e+00 47 -2.59087862e+00 -2.75943149e+01 1.45256509e+01 | -2.59087862e+00 -2.75943149e+01 1.45256509e+01 48 -2.46015837e+00 3.17257356e-02 -3.56900384e+00 | -2.46015837e+00 3.17257356e-02 -3.56900384e+00 49 -1.48640835e+01 -1.21277127e+01 2.48919799e+00 | -1.48640835e+01 -1.21277127e+01 2.48919799e+00 50 -2.09184879e+01 -4.47368666e+01 -4.52602136e+01 | -2.09184879e+01 -4.47368666e+01 -4.52602136e+01 51 3.79519309e+01 5.83752281e+01 4.15239631e+01 | 3.79519309e+01 5.83752281e+01 4.15239631e+01 52 -1.45895951e+00 -2.95657881e+00 -1.57659521e+00 | -1.45895951e+00 -2.95657881e+00 -1.57659521e+00 53 -2.06491997e+00 -3.43040343e+00 4.71718112e+00 | -2.06491997e+00 -3.43040343e+00 4.71718112e+00 54 -6.68286039e-01 -1.63448265e+00 3.83302956e-01 | -6.68286039e-01 -1.63448265e+00 3.83302956e-01 55 1.52155337e+00 2.64519608e+00 2.33938522e+00 | 1.52155337e+00 2.64519608e+00 2.33938522e+00 56 -5.34587327e+00 3.84197690e+00 -1.71812275e-01 | -5.34587327e+00 3.84197690e+00 -1.71812275e-01 57 6.46089226e+00 1.58832252e+00 2.72459901e+00 | 6.46089226e+00 1.58832252e+00 2.72459901e+00 58 5.87613039e-01 -2.79088656e+00 3.62823954e-01 | 5.87613039e-01 -2.79088656e+00 3.62823954e-01 59 1.41154649e+00 4.70763559e-01 8.86711319e-01 | 1.41154649e+00 4.70763559e-01 8.86711319e-01 60 -1.27802892e+00 2.71565289e+01 -1.66131994e+01 | -1.27802892e+00 2.71565289e+01 -1.66131994e+01 61 1.93794545e+00 1.96658124e+00 5.91409497e-01 | 1.93794545e+00 1.96658124e+00 5.91409497e-01 62 4.56299208e+00 4.54120565e+00 -4.16279148e+00 | 4.56299208e+00 4.54120565e+00 -4.16279148e+00 63 1.07033198e-01 -1.04318824e+00 -6.20871336e-01 | 1.07033198e-01 -1.04318824e+00 -6.20871336e-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.