!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : IMD_EAM_Schopf_AlNiCo_A__MO_122703700223_002 Supported species : Al Co Ni 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 = [27, 28, 16, 20, 40, 38, 59, 23, 49, 13, 46, 19, 57, 9, 62, 30, 2, 54, 31, 11, 3, 35, 25, 7, 43, 22, 32, 0, 1, 53, 15, 18, 26, 50, 45, 21, 56, 42, 5, 47, 4, 51, 37, 24, 63, 34, 10, 39, 60, 8, 33, 41, 61, 29, 17, 58, 36, 12, 55, 6, 48, 52, 14, 44] 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)) = 137.250857917 V(r_1,...,r_N) = 137.250857917 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 -2.21503385e+01 -1.12382253e+01 -2.86903144e+01 | -2.21503385e+01 -1.12382253e+01 -2.86903144e+01 1 1.86262630e+01 7.04055381e+00 2.96485143e+01 | 1.86262630e+01 7.04055381e+00 2.96485143e+01 2 1.73647018e+00 2.07685535e+00 -3.02029122e+00 | 1.73647018e+00 2.07685535e+00 -3.02029122e+00 3 3.58861317e+00 -2.41395129e+00 -9.47197372e+00 | 3.58861317e+00 -2.41395129e+00 -9.47197372e+00 4 -3.53400792e+01 -1.78914898e+01 -2.89794606e+01 | -3.53400792e+01 -1.78914898e+01 -2.89794606e+01 5 3.47395813e+01 2.12398870e+01 2.55034122e+01 | 3.47395813e+01 2.12398870e+01 2.55034122e+01 6 -1.47133523e+00 -1.06220910e+00 -1.35323377e+00 | -1.47133523e+00 -1.06220910e+00 -1.35323377e+00 7 -4.61237369e+01 2.05767219e+01 -5.20344330e+01 | -4.61237369e+01 2.05767219e+01 -5.20344330e+01 8 -5.77496129e+00 -2.96756470e+00 -2.21593915e+00 | -5.77496129e+00 -2.96756470e+00 -2.21593915e+00 9 -3.46841835e-02 -4.29647636e+00 1.24081861e+01 | -3.46841835e-02 -4.29647636e+00 1.24081861e+01 10 6.51207652e+00 4.64015024e+00 -1.11241811e+01 | 6.51207652e+00 4.64015024e+00 -1.11241811e+01 11 1.79657654e+00 -2.79097757e-01 -7.71688748e-01 | 1.79657654e+00 -2.79097757e-01 -7.71688748e-01 12 -6.92925620e+00 -1.56609404e+01 -5.37996806e+00 | -6.92925620e+00 -1.56609404e+01 -5.37996806e+00 13 1.46369773e+01 9.46942131e+00 -2.66237303e+00 | 1.46369773e+01 9.46942131e+00 -2.66237303e+00 14 -6.47287092e+00 3.83949071e-01 -9.28747382e+00 | -6.47287092e+00 3.83949071e-01 -9.28747382e+00 15 4.06758445e+00 2.07665592e+00 1.03929509e+01 | 4.06758445e+00 2.07665592e+00 1.03929509e+01 16 -3.14731136e+00 -2.51438312e+00 -3.23734315e+00 | -3.14731136e+00 -2.51438312e+00 -3.23734315e+00 17 1.67491835e+00 2.79501230e+00 3.76549221e+00 | 1.67491835e+00 2.79501230e+00 3.76549221e+00 18 1.35101056e-01 4.20773591e-01 -8.50815017e-01 | 1.35101056e-01 4.20773591e-01 -8.50815017e-01 19 -3.94362026e+01 2.52525479e+01 -9.61086247e+00 | -3.94362026e+01 2.52525479e+01 -9.61086247e+00 20 2.92952290e+00 7.93924583e+00 -1.95479751e+01 | 2.92952290e+00 7.93924583e+00 -1.95479751e+01 21 3.56083026e+01 2.42731083e+01 -2.68015583e+00 | 3.56083026e+01 2.42731083e+01 -2.68015583e+00 22 -1.48001263e+01 -1.01560650e+01 -2.24006379e+01 | -1.48001263e+01 -1.01560650e+01 -2.24006379e+01 23 1.54313967e+01 1.00240233e+01 2.21068783e+01 | 1.54313967e+01 1.00240233e+01 2.21068783e+01 24 -6.09788462e+00 -4.38940208e+00 -7.70178948e+00 | -6.09788462e+00 -4.38940208e+00 -7.70178948e+00 25 -8.78328331e-01 3.89128923e+00 5.11333179e+00 | -8.78328331e-01 3.89128923e+00 5.11333179e+00 26 7.90007374e-01 2.55631916e+00 -2.58920052e+00 | 7.90007374e-01 2.55631916e+00 -2.58920052e+00 27 8.86479012e-01 2.35282343e-01 1.10636813e+00 | 8.86479012e-01 2.35282343e-01 1.10636813e+00 28 3.65843598e+00 -1.00821674e+01 1.70754582e+00 | 3.65843598e+00 -1.00821674e+01 1.70754582e+00 29 3.80789960e+00 3.56799495e-01 3.15440051e+00 | 3.80789960e+00 3.56799495e-01 3.15440051e+00 30 2.72646751e+01 -2.72198856e+01 -2.01445955e+00 | 2.72646751e+01 -2.72198856e+01 -2.01445955e+00 31 6.23958723e+00 8.24744697e+00 1.06218112e+01 | 6.23958723e+00 8.24744697e+00 1.06218112e+01 32 -1.99882589e+01 -1.89614169e+01 -8.65922856e+00 | -1.99882589e+01 -1.89614169e+01 -8.65922856e+00 33 2.01565201e+01 1.94261377e+01 7.50066148e+00 | 2.01565201e+01 1.94261377e+01 7.50066148e+00 34 1.31997937e+01 -4.76168532e+01 7.17360417e+01 | 1.31997937e+01 -4.76168532e+01 7.17360417e+01 35 -9.50625201e-01 -1.80537434e+01 2.48376435e+01 | -9.50625201e-01 -1.80537434e+01 2.48376435e+01 36 -1.93651627e+00 -1.13460935e+00 -5.31220122e-01 | -1.93651627e+00 -1.13460935e+00 -5.31220122e-01 37 -2.72342288e+01 -3.93360799e+01 1.34500944e+01 | -2.72342288e+01 -3.93360799e+01 1.34500944e+01 38 -8.06574558e+00 -4.55575592e+00 -4.98990795e+00 | -8.06574558e+00 -4.55575592e+00 -4.98990795e+00 39 1.39946906e+00 -6.19776147e+00 8.31830758e+00 | 1.39946906e+00 -6.19776147e+00 8.31830758e+00 40 1.84046724e+00 -1.59848175e+00 5.15270446e+00 | 1.84046724e+00 -1.59848175e+00 5.15270446e+00 41 -3.33344764e+01 8.29889060e+01 -1.81823266e+01 | -3.33344764e+01 8.29889060e+01 -1.81823266e+01 42 -2.93876125e+01 -1.57232061e+01 -1.63645443e+01 | -2.93876125e+01 -1.57232061e+01 -1.63645443e+01 43 2.43464942e+01 1.90974517e+01 2.00868500e+01 | 2.43464942e+01 1.90974517e+01 2.00868500e+01 44 3.31217375e+01 -8.37682534e+01 1.65707063e+01 | 3.31217375e+01 -8.37682534e+01 1.65707063e+01 45 4.85769856e-01 7.39239819e-01 5.94808538e-01 | 4.85769856e-01 7.39239819e-01 5.94808538e-01 46 2.68326732e+01 3.82353493e+01 -1.36598237e+01 | 2.68326732e+01 3.82353493e+01 -1.36598237e+01 47 6.23322599e+00 -2.25564613e+00 2.90646865e+00 | 6.23322599e+00 -2.25564613e+00 2.90646865e+00 48 -2.23984109e+00 1.15446949e+00 1.59547137e+00 | -2.23984109e+00 1.15446949e+00 1.59547137e+00 49 6.86263668e+00 -6.52767528e+00 -1.50625412e+01 | 6.86263668e+00 -6.52767528e+00 -1.50625412e+01 50 -8.96160303e+00 -1.80128421e+01 -1.99063631e+01 | -8.96160303e+00 -1.80128421e+01 -1.99063631e+01 51 4.54168640e+00 2.43081856e+01 2.08933108e+01 | 4.54168640e+00 2.43081856e+01 2.08933108e+01 52 4.75150512e+00 1.09630332e+01 -5.21021752e+00 | 4.75150512e+00 1.09630332e+01 -5.21021752e+00 53 -3.09010045e+00 4.63299364e+00 8.48464120e-03 | -3.09010045e+00 4.63299364e+00 8.48464120e-03 54 -1.28141917e+01 2.19326693e-01 9.39843234e+00 | -1.28141917e+01 2.19326693e-01 9.39843234e+00 55 6.90165899e+00 4.31017368e+00 4.89040426e+00 | 6.90165899e+00 4.31017368e+00 4.89040426e+00 56 4.50345297e-01 9.61914562e+00 -1.18289715e+01 | 4.50345297e-01 9.61914562e+00 -1.18289715e+01 57 2.58996238e+00 -2.08254951e+00 -2.61882908e+00 | 2.58996238e+00 -2.08254951e+00 -2.61882908e+00 58 -6.28302798e-01 3.97362878e-01 6.09365839e-01 | -6.28302798e-01 3.97362878e-01 6.09365839e-01 59 1.56531747e+00 8.99334954e-01 1.99445967e+00 | 1.56531747e+00 8.99334954e-01 1.99445967e+00 60 -2.65493156e+00 3.60476323e+00 3.22277300e+00 | -2.65493156e+00 3.60476323e+00 3.22277300e+00 61 7.91427316e-02 1.56366865e-01 2.65095338e-01 | 7.91427316e-02 1.56366865e-01 2.65095338e-01 62 7.55207829e-01 1.94926797e+00 3.21176297e+00 | 7.55207829e-01 1.94926797e+00 3.21176297e+00 63 -3.00532126e-01 -2.00818944e-01 -1.34195075e-01 | -3.00532126e-01 -2.00818944e-01 -1.34195075e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [54, 48, 19, 28, 61, 26, 42, 9, 35, 7, 37, 59, 62, 50, 29, 56, 58, 20, 36, 2, 17, 43, 32, 31, 53, 34, 5, 46, 3, 14, 45, 23, 22, 63, 25, 8, 18, 10, 39, 38, 60, 57, 6, 21, 51, 30, 27, 49, 1, 47, 13, 44, 55, 24, 0, 52, 15, 41, 16, 11, 40, 4, 12, 33] 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)) = 23.3456240476 V(r_1,...,r_N) = 23.3456240476 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 -5.97651868e-01 -1.52484636e+00 -1.16053861e+00 | -5.97651868e-01 -1.52484636e+00 -1.16053861e+00 1 5.88189433e+00 -1.42642302e+01 -1.24972387e+01 | 5.88189433e+00 -1.42642302e+01 -1.24972387e+01 2 -3.72928476e-01 1.46500997e-01 1.62215767e+00 | -3.72928476e-01 1.46500997e-01 1.62215767e+00 3 4.55808697e+01 -1.26080089e+02 -6.19850616e+01 | 4.55808697e+01 -1.26080089e+02 -6.19850616e+01 4 2.37866787e+00 2.17786693e-01 6.85725262e-01 | 2.37866787e+00 2.17786693e-01 6.85725262e-01 5 -1.32955756e+00 3.34259273e+00 -1.90914181e+01 | -1.32955756e+00 3.34259273e+00 -1.90914181e+01 6 -6.95317121e+00 1.66175095e+01 1.25382186e+01 | -6.95317121e+00 1.66175095e+01 1.25382186e+01 7 -9.73426405e-01 1.93259216e-02 2.22457574e+00 | -9.73426405e-01 1.93259216e-02 2.22457574e+00 8 -3.37796755e-02 7.72683033e-01 6.11301892e-01 | -3.37796755e-02 7.72683033e-01 6.11301892e-01 9 -8.54512726e+00 -6.27051730e+00 3.20050696e+00 | -8.54512726e+00 -6.27051730e+00 3.20050696e+00 10 4.32159877e+00 -4.88252069e+00 -1.08086415e+01 | 4.32159877e+00 -4.88252069e+00 -1.08086415e+01 11 4.22574947e+00 1.11016723e+01 6.67198111e+00 | 4.22574947e+00 1.11016723e+01 6.67198111e+00 12 -3.66579289e+01 -7.87266224e+01 -1.02393792e+02 | -3.66579289e+01 -7.87266224e+01 -1.02393792e+02 13 3.72303569e+01 7.83324961e+01 1.02775814e+02 | 3.72303569e+01 7.83324961e+01 1.02775814e+02 14 -2.30311326e-01 -4.61697719e-01 -4.66245681e-01 | -2.30311326e-01 -4.61697719e-01 -4.66245681e-01 15 2.56842023e+00 -5.32291582e+00 -1.49030255e+01 | 2.56842023e+00 -5.32291582e+00 -1.49030255e+01 16 1.68815231e-01 -2.96766351e-01 -2.40378449e-02 | 1.68815231e-01 -2.96766351e-01 -2.40378449e-02 17 1.44144434e-01 -2.64798619e+00 -7.00311530e-01 | 1.44144434e-01 -2.64798619e+00 -7.00311530e-01 18 7.07218304e-01 1.50667759e+00 -3.99437760e-01 | 7.07218304e-01 1.50667759e+00 -3.99437760e-01 19 1.10727122e+00 -1.93860679e-01 4.00381309e-01 | 1.10727122e+00 -1.93860679e-01 4.00381309e-01 20 -4.58556962e+01 1.21823124e+02 5.31439916e+01 | -4.58556962e+01 1.21823124e+02 5.31439916e+01 21 4.28621342e+00 -3.91462255e+00 1.73917155e+00 | 4.28621342e+00 -3.91462255e+00 1.73917155e+00 22 -6.26269842e-01 1.91144177e+00 1.80906248e+00 | -6.26269842e-01 1.91144177e+00 1.80906248e+00 23 -1.30495860e+00 1.46425757e+00 -1.50797711e+00 | -1.30495860e+00 1.46425757e+00 -1.50797711e+00 24 7.11194242e-01 -2.99710950e+00 -5.55510534e-01 | 7.11194242e-01 -2.99710950e+00 -5.55510534e-01 25 -3.62174216e+00 -6.25592782e-01 4.19930040e+00 | -3.62174216e+00 -6.25592782e-01 4.19930040e+00 26 4.08338781e+00 2.09868524e+00 -2.99470632e+00 | 4.08338781e+00 2.09868524e+00 -2.99470632e+00 27 -1.27449962e-01 1.19101427e-01 -6.96731197e-01 | -1.27449962e-01 1.19101427e-01 -6.96731197e-01 28 -7.08223573e-01 1.47298245e+00 1.61750309e-01 | -7.08223573e-01 1.47298245e+00 1.61750309e-01 29 -1.49071226e+00 -2.86798501e-01 5.14110001e-01 | -1.49071226e+00 -2.86798501e-01 5.14110001e-01 30 -4.86251755e+00 7.95975476e-01 -7.26173111e-01 | -4.86251755e+00 7.95975476e-01 -7.26173111e-01 31 4.00260499e+00 6.63237897e-01 8.33648415e-01 | 4.00260499e+00 6.63237897e-01 8.33648415e-01 32 -1.35537311e+02 -1.03325852e+01 -6.85824321e+01 | -1.35537311e+02 -1.03325852e+01 -6.85824321e+01 33 1.08316712e+02 -6.25973602e+00 7.75342062e+01 | 1.08316712e+02 -6.25973602e+00 7.75342062e+01 34 1.53844844e+01 2.21456143e+01 4.52340813e+00 | 1.53844844e+01 2.21456143e+01 4.52340813e+00 35 2.89591860e-01 3.84362348e+00 -6.86904384e-02 | 2.89591860e-01 3.84362348e+00 -6.86904384e-02 36 1.43985148e+00 -9.27082120e-01 1.21375123e+00 | 1.43985148e+00 -9.27082120e-01 1.21375123e+00 37 -4.86676749e-01 3.20838587e-01 -3.65500268e-02 | -4.86676749e-01 3.20838587e-01 -3.65500268e-02 38 2.98093714e-01 4.23472964e-01 -1.21956200e+00 | 2.98093714e-01 4.23472964e-01 -1.21956200e+00 39 -2.31532555e-01 -5.64087217e+00 3.08446247e+00 | -2.31532555e-01 -5.64087217e+00 3.08446247e+00 40 1.02182753e+01 -1.07837827e+01 3.29792017e+00 | 1.02182753e+01 -1.07837827e+01 3.29792017e+00 41 -2.81493562e+00 -1.61081133e+01 7.49233438e+00 | -2.81493562e+00 -1.61081133e+01 7.49233438e+00 42 6.49854427e+00 1.40340919e+01 -9.21052968e+00 | 6.49854427e+00 1.40340919e+01 -9.21052968e+00 43 -6.96563016e-01 2.40893265e-01 1.10306443e-01 | -6.96563016e-01 2.40893265e-01 1.10306443e-01 44 -1.72708711e+01 -2.42477594e+01 -5.85062040e+00 | -1.72708711e+01 -2.42477594e+01 -5.85062040e+00 45 1.80483393e+01 2.34335756e+01 6.24934014e+00 | 1.80483393e+01 2.34335756e+01 6.24934014e+00 46 -3.48973399e+00 4.27890073e-01 1.20052229e+00 | -3.48973399e+00 4.27890073e-01 1.20052229e+00 47 -5.64367839e+00 -1.40555145e+00 -9.80536472e-01 | -5.64367839e+00 -1.40555145e+00 -9.80536472e-01 48 8.46614230e-01 -8.40521911e-01 -1.77383805e-01 | 8.46614230e-01 -8.40521911e-01 -1.77383805e-01 49 -6.16295403e+01 3.02760964e+01 -5.22230107e+01 | -6.16295403e+01 3.02760964e+01 -5.22230107e+01 50 -4.02893400e+00 6.48213769e-01 1.86298792e+00 | -4.02893400e+00 6.48213769e-01 1.86298792e+00 51 -1.76962546e+00 8.08552137e+00 2.33060828e+00 | -1.76962546e+00 8.08552137e+00 2.33060828e+00 52 5.95578034e+01 -2.69003120e+01 4.86643838e+01 | 5.95578034e+01 -2.69003120e+01 4.86643838e+01 53 1.64655275e+00 3.50870868e+00 7.76681303e-01 | 1.64655275e+00 3.50870868e+00 7.76681303e-01 54 1.56666564e-01 -2.99040583e-01 1.25591001e-01 | 1.56666564e-01 -2.99040583e-01 1.25591001e-01 55 3.57288598e-01 -1.18736220e+00 -4.29195131e-01 | 3.57288598e-01 -1.18736220e+00 -4.29195131e-01 56 -3.79963773e+00 2.90874541e+00 1.34513574e+01 | -3.79963773e+00 2.90874541e+00 1.34513574e+01 57 1.35510359e+01 -1.06598524e+01 5.05700193e-01 | 1.35510359e+01 -1.06598524e+01 5.05700193e-01 58 9.05096111e-01 3.72647483e-01 -4.87734776e-01 | 9.05096111e-01 3.72647483e-01 -4.87734776e-01 59 -8.41309503e-01 -1.26854497e+00 -4.82992233e-01 | -8.41309503e-01 -1.26854497e+00 -4.82992233e-01 60 5.57415530e+00 -9.76329154e-01 1.80325974e+00 | 5.57415530e+00 -9.76329154e-01 1.80325974e+00 61 8.78470030e-01 4.38646548e+00 -8.32510375e-01 | 8.78470030e-01 4.38646548e+00 -8.32510375e-01 62 -8.87760317e+00 9.84501149e+00 5.12605915e+00 | -8.87760317e+00 9.84501149e+00 5.12605915e+00 63 4.34235731e-02 -9.73839303e-01 -9.91982008e-01 | 4.34235731e-02 -9.73839303e-01 -9.91982008e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [46, 14, 38, 4, 3, 17, 21, 42, 41, 37, 19, 39, 53, 58, 1, 32, 36, 5, 59, 10, 22, 6, 20, 49, 26, 56, 24, 52, 29, 28, 62, 43, 15, 51, 54, 47, 16, 9, 2, 11, 60, 8, 7, 31, 48, 55, 0, 35, 44, 23, 63, 33, 27, 12, 34, 45, 25, 61, 13, 18, 40, 57, 30, 50] 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)) = 121.930909958 V(r_1,...,r_N) = 121.930909958 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 7.21656911e-02 1.17856891e+00 1.20882665e+00 | 7.21656911e-02 1.17856891e+00 1.20882665e+00 1 -2.85179526e+01 4.07189354e+01 -7.58873855e-01 | -2.85179526e+01 4.07189354e+01 -7.58873855e-01 2 -4.86375332e-01 -6.91296784e+00 -2.04123057e+00 | -4.86375332e-01 -6.91296784e+00 -2.04123057e+00 3 -1.10046776e+01 -6.59017779e+00 6.35149350e+00 | -1.10046776e+01 -6.59017779e+00 6.35149350e+00 4 2.69563782e+01 -4.27718291e+01 -4.63318132e-01 | 2.69563782e+01 -4.27718291e+01 -4.63318132e-01 5 6.15838131e+00 1.26763160e+00 -5.38761362e+00 | 6.15838131e+00 1.26763160e+00 -5.38761362e+00 6 -7.83392151e+01 -6.46823703e+01 -2.95339978e+01 | -7.83392151e+01 -6.46823703e+01 -2.95339978e+01 7 7.19775944e+01 6.23623010e+01 3.49847563e+01 | 7.19775944e+01 6.23623010e+01 3.49847563e+01 8 1.81975506e+00 -3.58921420e-02 5.95924295e-01 | 1.81975506e+00 -3.58921420e-02 5.95924295e-01 9 8.98493312e-01 -5.39627308e+00 -5.20125249e+00 | 8.98493312e-01 -5.39627308e+00 -5.20125249e+00 10 -5.34111148e+01 -1.46408426e+02 -1.96018421e+00 | -5.34111148e+01 -1.46408426e+02 -1.96018421e+00 11 5.62424023e+01 1.46651615e+02 -1.08132057e+00 | 5.62424023e+01 1.46651615e+02 -1.08132057e+00 12 2.37145248e-01 -1.74696942e+00 -5.21003091e-01 | 2.37145248e-01 -1.74696942e+00 -5.21003091e-01 13 2.93030378e+00 -3.22076501e+00 -1.40874076e+00 | 2.93030378e+00 -3.22076501e+00 -1.40874076e+00 14 -7.21143604e+00 2.35411029e+00 -8.07010097e+00 | -7.21143604e+00 2.35411029e+00 -8.07010097e+00 15 1.36214049e+01 -9.49806424e+00 2.35389941e+00 | 1.36214049e+01 -9.49806424e+00 2.35389941e+00 16 -3.25285816e+00 -1.79945193e-01 -3.11062394e+00 | -3.25285816e+00 -1.79945193e-01 -3.11062394e+00 17 -1.32735975e+01 1.61170128e+01 -1.22773322e+01 | -1.32735975e+01 1.61170128e+01 -1.22773322e+01 18 -1.81223562e+00 3.22040963e-01 -8.06636698e-01 | -1.81223562e+00 3.22040963e-01 -8.06636698e-01 19 2.14380988e+00 -8.84646383e-01 1.14828130e+00 | 2.14380988e+00 -8.84646383e-01 1.14828130e+00 20 1.74356698e+01 -1.25764147e+01 7.21140094e+00 | 1.74356698e+01 -1.25764147e+01 7.21140094e+00 21 5.23846319e+00 -1.51445978e+00 -1.35798635e+01 | 5.23846319e+00 -1.51445978e+00 -1.35798635e+01 22 -4.43070965e-01 1.73660526e+00 -5.89160825e-01 | -4.43070965e-01 1.73660526e+00 -5.89160825e-01 23 -1.22722088e+00 9.75392608e-01 6.92156533e-01 | -1.22722088e+00 9.75392608e-01 6.92156533e-01 24 1.38170543e+01 1.25455639e+01 -8.76828204e+00 | 1.38170543e+01 1.25455639e+01 -8.76828204e+00 25 -7.03318783e+01 -1.04983428e+02 2.71319959e+01 | -7.03318783e+01 -1.04983428e+02 2.71319959e+01 26 7.23313763e+01 1.05279238e+02 -2.83179066e+01 | 7.23313763e+01 1.05279238e+02 -2.83179066e+01 27 1.04975649e+00 4.86439855e-01 -1.45969018e+00 | 1.04975649e+00 4.86439855e-01 -1.45969018e+00 28 -3.00898673e+00 1.53389223e+00 5.13616199e-01 | -3.00898673e+00 1.53389223e+00 5.13616199e-01 29 9.83632377e+01 -1.56177013e+01 -4.56143618e+01 | 9.83632377e+01 -1.56177013e+01 -4.56143618e+01 30 3.48623313e+00 -8.34609316e-01 -7.67718876e-01 | 3.48623313e+00 -8.34609316e-01 -7.67718876e-01 31 2.14052981e-01 5.93555522e-01 -1.05145598e+00 | 2.14052981e-01 5.93555522e-01 -1.05145598e+00 32 1.77608371e+00 1.29842904e+00 2.58434899e+00 | 1.77608371e+00 1.29842904e+00 2.58434899e+00 33 -2.46348974e+00 -7.80985977e-01 1.85787981e+00 | -2.46348974e+00 -7.80985977e-01 1.85787981e+00 34 -6.91112291e+00 4.00668405e+00 2.76950447e+00 | -6.91112291e+00 4.00668405e+00 2.76950447e+00 35 8.53123322e+00 -5.67179781e+00 -1.50322580e+00 | 8.53123322e+00 -5.67179781e+00 -1.50322580e+00 36 -5.94370728e-01 8.80921847e-01 -5.18422463e-02 | -5.94370728e-01 8.80921847e-01 -5.18422463e-02 37 -7.35180389e-01 -2.44215256e+00 7.62823438e-01 | -7.35180389e-01 -2.44215256e+00 7.62823438e-01 38 1.04191252e+00 -2.41100186e+00 -1.92901335e-03 | 1.04191252e+00 -2.41100186e+00 -1.92901335e-03 39 -6.73760013e-01 -1.54542238e+00 1.14949360e+00 | -6.73760013e-01 -1.54542238e+00 1.14949360e+00 40 -2.63090007e+00 -8.17812770e+00 1.64696002e-01 | -2.63090007e+00 -8.17812770e+00 1.64696002e-01 41 7.99565206e+00 -7.35863067e+00 -5.86622474e+00 | 7.99565206e+00 -7.35863067e+00 -5.86622474e+00 42 -8.80844897e+00 -8.06574124e+00 -6.54381307e+00 | -8.80844897e+00 -8.06574124e+00 -6.54381307e+00 43 1.20780189e+01 8.29598380e+00 8.19960535e+00 | 1.20780189e+01 8.29598380e+00 8.19960535e+00 44 5.61038657e-01 -3.22860987e-01 1.50506734e+00 | 5.61038657e-01 -3.22860987e-01 1.50506734e+00 45 -5.91757349e-01 -4.69907337e-01 3.90871666e-02 | -5.91757349e-01 -4.69907337e-01 3.90871666e-02 46 -4.21353902e+00 7.62163503e+00 1.09831841e+01 | -4.21353902e+00 7.62163503e+00 1.09831841e+01 47 -1.02603288e+01 5.69957755e-01 4.52879807e+00 | -1.02603288e+01 5.69957755e-01 4.52879807e+00 48 -4.17422875e+00 -4.80929530e-01 -1.42432654e+00 | -4.17422875e+00 -4.80929530e-01 -1.42432654e+00 49 -3.24609233e+01 -1.62780749e+01 2.55336879e+01 | -3.24609233e+01 -1.62780749e+01 2.55336879e+01 50 2.50921312e+01 2.17054209e+01 -1.17783522e+01 | 2.50921312e+01 2.17054209e+01 -1.17783522e+01 51 -8.03428132e-01 2.59406094e-02 2.20870546e+00 | -8.03428132e-01 2.59406094e-02 2.20870546e+00 52 -1.04948655e+01 3.39198158e+00 -1.71737239e+00 | -1.04948655e+01 3.39198158e+00 -1.71737239e+00 53 3.26387560e+00 1.59680703e+00 2.98761034e+00 | 3.26387560e+00 1.59680703e+00 2.98761034e+00 54 -1.43356904e+01 -1.86040332e+01 -2.89111099e+01 | -1.43356904e+01 -1.86040332e+01 -2.89111099e+01 55 1.29619301e+01 2.07719096e+01 3.09349152e+01 | 1.29619301e+01 2.07719096e+01 3.09349152e+01 56 -6.79833313e+00 1.24029207e+01 8.91080372e+00 | -6.79833313e+00 1.24029207e+01 8.91080372e+00 57 4.64741304e-02 2.47200290e+00 2.70604145e+00 | 4.64741304e-02 2.47200290e+00 2.70604145e+00 58 -9.72873328e+01 1.80624494e+01 4.48875743e+01 | -9.72873328e+01 1.80624494e+01 4.48875743e+01 59 -1.36063882e+00 -1.26215899e+00 -1.69528183e+00 | -1.36063882e+00 -1.26215899e+00 -1.69528183e+00 60 8.73187693e+00 -4.08111773e+00 -5.25970120e+00 | 8.73187693e+00 -4.08111773e+00 -5.25970120e+00 61 7.48432777e-01 4.06928250e+00 2.13698319e+00 | 7.48432777e-01 4.06928250e+00 2.13698319e+00 62 1.99966504e+00 1.64116935e+00 2.08541914e+00 | 1.99966504e+00 1.64116935e+00 2.08541914e+00 63 -1.90304430e+00 -1.12851598e+00 -1.60473231e+00 | -1.90304430e+00 -1.12851598e+00 -1.60473231e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Co Ni (Configuration in file "config-AlCoNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [40, 41, 53, 28, 39, 60, 32, 38, 12, 31, 33, 16, 8, 23, 34, 44, 11, 35, 46, 22, 56, 45, 19, 13, 29, 57, 59, 63, 3, 24, 51, 9, 6, 10, 14, 17, 54, 48, 7, 4, 0, 1, 58, 43, 15, 21, 18, 55, 37, 50, 49, 30, 61, 2, 36, 47, 20, 25, 42, 26, 5, 52, 62, 27] 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)) = -55.0253163568 V(r_1,...,r_N) = -55.0253163568 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 -5.28507108e+00 -1.23537588e+01 -7.67165627e+00 | -5.28507108e+00 -1.23537588e+01 -7.67165627e+00 1 3.41857161e+00 1.26201450e+01 8.58591445e+00 | 3.41857161e+00 1.26201450e+01 8.58591445e+00 2 1.13436729e+00 9.00089654e-01 -5.31853301e-01 | 1.13436729e+00 9.00089654e-01 -5.31853301e-01 3 -2.30599846e+01 3.96166874e+01 -1.24926276e+01 | -2.30599846e+01 3.96166874e+01 -1.24926276e+01 4 1.39545958e+00 6.89965441e-01 1.28844042e+00 | 1.39545958e+00 6.89965441e-01 1.28844042e+00 5 -4.42742581e+00 -2.15289582e+00 9.89366720e+00 | -4.42742581e+00 -2.15289582e+00 9.89366720e+00 6 1.07492643e+00 -1.17241783e-02 2.55502548e-02 | 1.07492643e+00 -1.17241783e-02 2.55502548e-02 7 -6.14557331e-01 2.03556833e+00 9.45301069e-01 | -6.14557331e-01 2.03556833e+00 9.45301069e-01 8 3.89392689e+00 2.40053221e+00 2.77971668e+00 | 3.89392689e+00 2.40053221e+00 2.77971668e+00 9 -3.80942190e+00 -1.66331107e-03 -2.24948885e+00 | -3.80942190e+00 -1.66331107e-03 -2.24948885e+00 10 -1.18543401e+00 -8.80006055e-01 -3.61935304e-01 | -1.18543401e+00 -8.80006055e-01 -3.61935304e-01 11 1.07865919e+00 -5.76781269e+00 -7.95396138e+00 | 1.07865919e+00 -5.76781269e+00 -7.95396138e+00 12 -7.26755155e+00 -1.32035269e+01 -2.08671989e+01 | -7.26755155e+00 -1.32035269e+01 -2.08671989e+01 13 1.10390569e+01 6.95755159e+00 2.07137354e+01 | 1.10390569e+01 6.95755159e+00 2.07137354e+01 14 2.88818023e+01 -3.68282462e+01 5.79850059e+00 | 2.88818023e+01 -3.68282462e+01 5.79850059e+00 15 1.32735986e+00 -1.18399791e+00 9.26083314e-01 | 1.32735986e+00 -1.18399791e+00 9.26083314e-01 16 8.88534040e-01 1.59785635e+00 -2.90432262e-01 | 8.88534040e-01 1.59785635e+00 -2.90432262e-01 17 -6.54439098e+00 -5.06472243e+00 8.53898861e+00 | -6.54439098e+00 -5.06472243e+00 8.53898861e+00 18 4.89786278e+00 2.69103411e+00 -9.22664312e+00 | 4.89786278e+00 2.69103411e+00 -9.22664312e+00 19 2.52588994e+00 2.14377709e-01 1.19936413e+00 | 2.52588994e+00 2.14377709e-01 1.19936413e+00 20 -1.15283131e+00 -1.44398880e+00 -2.58448218e+00 | -1.15283131e+00 -1.44398880e+00 -2.58448218e+00 21 -8.50697729e-01 2.44314060e+00 -2.11981749e+00 | -8.50697729e-01 2.44314060e+00 -2.11981749e+00 22 1.42215018e+00 -2.06339783e+00 1.61236246e+00 | 1.42215018e+00 -2.06339783e+00 1.61236246e+00 23 -1.29460763e+01 2.16131242e+01 -1.09694747e+01 | -1.29460763e+01 2.16131242e+01 -1.09694747e+01 24 -1.59835637e+00 3.25389159e-01 1.70790889e+00 | -1.59835637e+00 3.25389159e-01 1.70790889e+00 25 -5.89173642e-01 -1.01861757e+01 7.27414969e+00 | -5.89173642e-01 -1.01861757e+01 7.27414969e+00 26 8.85401074e-01 8.47358209e+00 -8.07540210e+00 | 8.85401074e-01 8.47358209e+00 -8.07540210e+00 27 -1.41836029e-01 -5.32493822e-01 6.07020550e-01 | -1.41836029e-01 -5.32493822e-01 6.07020550e-01 28 -1.91334705e+00 7.77824818e+00 7.81744041e+00 | -1.91334705e+00 7.77824818e+00 7.81744041e+00 29 -1.14198119e+00 -1.02389284e+00 2.44731251e+00 | -1.14198119e+00 -1.02389284e+00 2.44731251e+00 30 -2.08682542e+00 -4.31711046e+00 -4.75545817e+00 | -2.08682542e+00 -4.31711046e+00 -4.75545817e+00 31 1.75078202e+00 4.74547372e+00 5.18275184e+00 | 1.75078202e+00 4.74547372e+00 5.18275184e+00 32 -5.74634337e-01 -1.90076279e+00 -3.41372440e-01 | -5.74634337e-01 -1.90076279e+00 -3.41372440e-01 33 -1.93292524e+01 1.83982192e+01 -1.40969241e+00 | -1.93292524e+01 1.83982192e+01 -1.40969241e+00 34 1.75362367e+00 1.47949315e+00 -3.31556694e+00 | 1.75362367e+00 1.47949315e+00 -3.31556694e+00 35 -2.16141309e+00 2.14895037e+00 -1.88844231e+00 | -2.16141309e+00 2.14895037e+00 -1.88844231e+00 36 2.98679638e+01 -2.42194932e+01 4.92944385e+00 | 2.98679638e+01 -2.42194932e+01 4.92944385e+00 37 -9.06292082e+00 -1.61759671e+00 7.84434045e+00 | -9.06292082e+00 -1.61759671e+00 7.84434045e+00 38 -9.48642509e+00 8.05880361e+00 -5.92622533e-01 | -9.48642509e+00 8.05880361e+00 -5.92622533e-01 39 -7.37407004e+00 -8.03567813e+00 3.47461753e+00 | -7.37407004e+00 -8.03567813e+00 3.47461753e+00 40 -2.56280316e+00 -3.42083143e+00 -8.30253936e+00 | -2.56280316e+00 -3.42083143e+00 -8.30253936e+00 41 3.23621348e+00 2.67018630e+00 7.11935745e+00 | 3.23621348e+00 2.67018630e+00 7.11935745e+00 42 -2.02986309e+00 4.90713763e+00 1.53049560e-01 | -2.02986309e+00 4.90713763e+00 1.53049560e-01 43 -1.86967318e+00 6.74699397e-01 -1.03119035e+00 | -1.86967318e+00 6.74699397e-01 -1.03119035e+00 44 -9.44371790e+00 -8.08943814e+00 -6.45292730e+00 | -9.44371790e+00 -8.08943814e+00 -6.45292730e+00 45 8.69242292e+00 8.74039473e+00 5.98454133e+00 | 8.69242292e+00 8.74039473e+00 5.98454133e+00 46 1.02520846e+01 1.49009596e+00 -6.41424606e+00 | 1.02520846e+01 1.49009596e+00 -6.41424606e+00 47 -4.57529447e+00 -3.14193314e+00 3.92396360e+00 | -4.57529447e+00 -3.14193314e+00 3.92396360e+00 48 1.63357081e+00 -1.28906241e+00 -2.47807479e+00 | 1.63357081e+00 -1.28906241e+00 -2.47807479e+00 49 -1.80434155e+01 -8.20190652e+00 2.75589453e+01 | -1.80434155e+01 -8.20190652e+00 2.75589453e+01 50 2.92082976e+01 -1.16776943e+01 -1.58804016e+01 | 2.92082976e+01 -1.16776943e+01 -1.58804016e+01 51 1.33119451e+00 -1.05768715e+00 -3.00881556e-01 | 1.33119451e+00 -1.05768715e+00 -3.00881556e-01 52 6.58852022e+00 4.57382169e+00 -5.83341256e+00 | 6.58852022e+00 4.57382169e+00 -5.83341256e+00 53 1.93966721e+00 1.81374403e+00 7.73198269e-01 | 1.93966721e+00 1.81374403e+00 7.73198269e-01 54 -2.22264378e+00 -2.44085570e+00 -2.40272385e+00 | -2.22264378e+00 -2.44085570e+00 -2.40272385e+00 55 2.21495902e+00 1.72435957e+00 2.24091679e+00 | 2.21495902e+00 1.72435957e+00 2.24091679e+00 56 -1.60204538e+00 -5.01006842e-02 3.77362771e+00 | -1.60204538e+00 -5.01006842e-02 3.77362771e+00 57 -1.61139601e+01 9.33150637e+00 -1.07981535e+01 | -1.61139601e+01 9.33150637e+00 -1.07981535e+01 58 -2.89286145e-01 -7.63411627e-01 -9.44132003e-01 | -2.89286145e-01 -7.63411627e-01 -9.44132003e-01 59 -4.40250577e-01 -4.80517143e-01 -1.11910454e+00 | -4.40250577e-01 -4.80517143e-01 -1.11910454e+00 60 1.99713611e+01 -6.57510664e+00 4.96668642e+00 | 1.99713611e+01 -6.57510664e+00 4.96668642e+00 61 -3.94202878e-01 -4.72926546e-01 4.09375809e-01 | -3.94202878e-01 -4.72926546e-01 4.09375809e-01 62 -8.68827094e-01 -2.34108164e+00 -1.16830618e+00 | -8.68827094e-01 -2.34108164e+00 -1.16830618e+00 63 7.55032274e-01 1.67732003e+00 3.27949375e-01 | 7.55032274e-01 1.67732003e+00 3.27949375e-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.