!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ZhouJohnsonWadley_2004NISTretabulation_CuAgAu__MO_318213562153_000 Supported species : Ag Au Cu random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ag (Configuration in file "config-Ag.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [7, 6, 20, 18, 15, 44, 1, 0, 31, 32, 49, 27, 46, 57, 38, 4, 34, 24, 3, 29, 2, 35, 25, 52, 17, 22, 47, 11, 60, 19, 41, 8, 9, 51, 16, 21, 43, 48, 14, 61, 45, 30, 54, 36, 5, 40, 12, 26, 37, 10, 62, 33, 23, 59, 42, 56, 55, 13, 63, 53, 28, 39, 50, 58] 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)) = 160.37650610249113 V(r_1,...,r_N) = 160.37650610249108 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 -5.22402105e+00 -3.55411105e+00 -4.50354779e+00 | -5.22402105e+00 -3.55411105e+00 -4.50354779e+00 1 -1.20066534e+01 -3.52038754e+01 2.60134967e+01 | -1.20066534e+01 -3.52038754e+01 2.60134967e+01 2 -2.16945611e+00 1.31783979e+01 -4.54201172e+01 | -2.16945611e+00 1.31783979e+01 -4.54201172e+01 3 1.67935450e+01 2.29032250e+01 1.78422313e+01 | 1.67935450e+01 2.29032250e+01 1.78422313e+01 4 -1.66052244e+00 -6.83805086e+00 -4.67011894e+00 | -1.66052244e+00 -6.83805086e+00 -4.67011894e+00 5 7.98149573e+00 7.14250745e+00 4.49296419e-01 | 7.98149573e+00 7.14250745e+00 4.49296419e-01 6 -4.05254948e+00 -2.55416324e+00 -3.21803369e+00 | -4.05254948e+00 -2.55416324e+00 -3.21803369e+00 7 -3.34139463e+01 8.78141994e+01 -5.22789576e+01 | -3.34139463e+01 8.78141994e+01 -5.22789576e+01 8 -5.80121714e+00 -1.48487553e+00 -5.39899918e+00 | -5.80121714e+00 -1.48487553e+00 -5.39899918e+00 9 -1.43947882e+01 1.05948944e+01 -6.73894413e+00 | -1.43947882e+01 1.05948944e+01 -6.73894413e+00 10 -1.22813553e+01 -1.19987248e+01 -1.13531135e+01 | -1.22813553e+01 -1.19987248e+01 -1.13531135e+01 11 1.33664461e+01 1.35768005e+01 9.38350791e+00 | 1.33664461e+01 1.35768005e+01 9.38350791e+00 12 1.30252995e+01 -1.76077510e+01 1.03118669e+01 | 1.30252995e+01 -1.76077510e+01 1.03118669e+01 13 4.14933614e+01 -4.91947197e+00 -3.12549967e+01 | 4.14933614e+01 -4.91947197e+00 -3.12549967e+01 14 -2.21546951e+00 -1.64192315e+00 -4.29623435e+00 | -2.21546951e+00 -1.64192315e+00 -4.29623435e+00 15 1.92415850e+00 1.38139075e+00 6.03771722e+00 | 1.92415850e+00 1.38139075e+00 6.03771722e+00 16 -3.09923204e+01 -1.10752879e+01 -2.95147523e+01 | -3.09923204e+01 -1.10752879e+01 -2.95147523e+01 17 2.92072858e+01 7.45884308e+00 3.18909580e+01 | 2.92072858e+01 7.45884308e+00 3.18909580e+01 18 7.17224794e-01 1.82810146e+00 -3.01588493e+00 | 7.17224794e-01 1.82810146e+00 -3.01588493e+00 19 -6.09487679e+01 3.86673174e+01 -4.08949892e+01 | -6.09487679e+01 3.86673174e+01 -4.08949892e+01 20 -2.06186621e+01 -1.15708466e+01 -1.71262321e+01 | -2.06186621e+01 -1.15708466e+01 -1.71262321e+01 21 2.70402394e+01 1.91243915e+01 9.45011030e+00 | 2.70402394e+01 1.91243915e+01 9.45011030e+00 22 -6.96646588e+00 -1.11905342e+01 -1.98564342e+01 | -6.96646588e+00 -1.11905342e+01 -1.98564342e+01 23 7.28128643e+00 1.10085079e+01 2.03761115e+01 | 7.28128643e+00 1.10085079e+01 2.03761115e+01 24 -5.24063063e+00 -4.65259403e+00 -5.56403862e+00 | -5.24063063e+00 -4.65259403e+00 -5.56403862e+00 25 -1.61526304e+01 2.09420154e+01 -1.03509032e+01 | -1.61526304e+01 2.09420154e+01 -1.03509032e+01 26 -6.20421526e+00 9.63733585e-01 -7.37028057e+00 | -6.20421526e+00 9.63733585e-01 -7.37028057e+00 27 6.93550714e+00 3.37977536e+00 5.18891517e+00 | 6.93550714e+00 3.37977536e+00 5.18891517e+00 28 1.74703638e+01 -2.48250103e+01 1.39213423e+01 | 1.74703638e+01 -2.48250103e+01 1.39213423e+01 29 5.41794181e+00 4.69900789e+00 2.55204492e+00 | 5.41794181e+00 4.69900789e+00 2.55204492e+00 30 5.98872679e+01 -3.58036795e+01 3.78594106e+01 | 5.98872679e+01 -3.58036795e+01 3.78594106e+01 31 -2.64215176e+01 1.16612058e+01 -1.43902035e+01 | -2.64215176e+01 1.16612058e+01 -1.43902035e+01 32 -6.31232671e+00 -4.00524961e-01 -1.55813223e+00 | -6.31232671e+00 -4.00524961e-01 -1.55813223e+00 33 -1.11622590e+01 9.55559515e+00 -4.79136023e+00 | -1.11622590e+01 9.55559515e+00 -4.79136023e+00 34 3.63136664e+01 -9.56449798e+01 5.14125513e+01 | 3.63136664e+01 -9.56449798e+01 5.14125513e+01 35 -4.88249984e-01 -7.38797126e+00 6.27953572e+00 | -4.88249984e-01 -7.38797126e+00 6.27953572e+00 36 1.07997898e+01 -9.56208743e+00 8.44141323e+00 | 1.07997898e+01 -9.56208743e+00 8.44141323e+00 37 -7.73952541e+00 -6.88744289e+00 3.44772112e+00 | -7.73952541e+00 -6.88744289e+00 3.44772112e+00 38 -1.33852794e+01 -7.65795154e+00 -1.00297173e+01 | -1.33852794e+01 -7.65795154e+00 -1.00297173e+01 39 -1.17618549e+01 -1.26458155e+01 2.52675917e+01 | -1.17618549e+01 -1.26458155e+01 2.52675917e+01 40 1.43745552e+00 -2.13240092e+00 2.26642677e+00 | 1.43745552e+00 -2.13240092e+00 2.26642677e+00 41 -2.98468767e+01 4.73717999e+01 -3.11624899e+01 | -2.98468767e+01 4.73717999e+01 -3.11624899e+01 42 -3.75922400e+01 4.38358760e+00 2.83825172e+01 | -3.75922400e+01 4.38358760e+00 2.83825172e+01 43 3.91175552e+00 6.84387946e+00 6.38829881e+00 | 3.91175552e+00 6.84387946e+00 6.38829881e+00 44 3.14794037e+01 -5.26752015e+01 2.57758236e+01 | 3.14794037e+01 -5.26752015e+01 2.57758236e+01 45 1.09143404e-01 1.06160500e+00 6.60587695e-01 | 1.09143404e-01 1.06160500e+00 6.60587695e-01 46 4.68852392e+00 8.78519256e+00 1.08787710e+00 | 4.68852392e+00 8.78519256e+00 1.08787710e+00 47 2.27944227e+01 -1.98048367e+01 1.88171455e+00 | 2.27944227e+01 -1.98048367e+01 1.88171455e+00 48 -1.66677939e+01 -1.29559435e+01 -9.14634515e+00 | -1.66677939e+01 -1.29559435e+01 -9.14634515e+00 49 9.07378102e+00 1.69622403e+01 1.38611327e+01 | 9.07378102e+00 1.69622403e+01 1.38611327e+01 50 -1.53292193e+01 -1.76375529e+01 -1.80349044e+01 | -1.53292193e+01 -1.76375529e+01 -1.80349044e+01 51 1.28068845e+01 1.97387038e+01 1.83183798e+01 | 1.28068845e+01 1.97387038e+01 1.83183798e+01 52 1.99348093e+01 2.41795375e+01 -1.41318872e+01 | 1.99348093e+01 2.41795375e+01 -1.41318872e+01 53 -1.91449476e+01 2.30998560e+01 8.69246713e-01 | -1.91449476e+01 2.30998560e+01 8.69246713e-01 54 -3.90633349e-01 1.34493005e+00 1.20177811e+00 | -3.90633349e-01 1.34493005e+00 1.20177811e+00 55 2.09821998e-01 -6.34984402e-01 -7.12750206e-01 | 2.09821998e-01 -6.34984402e-01 -7.12750206e-01 56 1.71392259e+00 -1.66045943e+00 -7.77320037e-01 | 1.71392259e+00 -1.66045943e+00 -7.77320037e-01 57 2.97207584e+01 -4.50349773e+01 -5.37246959e+01 | 2.97207584e+01 -4.50349773e+01 -5.37246959e+01 58 2.88588871e+01 -9.83841023e+00 1.70494347e+01 | 2.88588871e+01 -9.83841023e+00 1.70494347e+01 59 -9.12731566e-01 -7.31171096e-01 3.78055690e-01 | -9.12731566e-01 -7.31171096e-01 3.78055690e-01 60 -2.35978860e+00 -5.46133605e+00 -1.20395956e+01 | -2.35978860e+00 -5.46133605e+00 -1.20395956e+01 61 3.18419695e+00 6.37335635e+00 1.29444025e+01 | 3.18419695e+00 6.37335635e+00 1.29444025e+01 62 -2.62194947e+01 4.83390781e+01 5.67220841e+01 | -2.62194947e+01 4.83390781e+01 5.67220841e+01 63 4.99764096e-01 -6.88729401e-01 -5.87602766e-01 | 4.99764096e-01 -6.88729401e-01 -5.87602766e-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 = [11, 43, 25, 30, 20, 18, 49, 45, 33, 17, 16, 0, 39, 50, 55, 53, 10, 9, 5, 52, 4, 57, 24, 38, 22, 2, 54, 46, 58, 36, 3, 44, 51, 8, 62, 63, 29, 56, 23, 12, 61, 59, 47, 1, 31, 7, 27, 42, 60, 6, 13, 32, 19, 15, 26, 14, 37, 21, 28, 41, 48, 40, 34, 35] 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)) = 112.46138814929529 V(r_1,...,r_N) = 112.4613881492955 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 -6.38182633e+01 -4.60186469e+01 -9.25795850e+01 | -6.38182633e+01 -4.60186469e+01 -9.25795850e+01 1 5.96242674e+01 4.45286036e+01 8.60470804e+01 | 5.96242674e+01 4.45286036e+01 8.60470804e+01 2 -1.06118308e+00 -2.21508285e+00 -2.35709013e+00 | -1.06118308e+00 -2.21508285e+00 -2.35709013e+00 3 -5.62065177e-01 1.31872918e+00 1.86654775e+00 | -5.62065177e-01 1.31872918e+00 1.86654775e+00 4 7.13310885e+00 -3.77139039e+00 3.80015486e+00 | 7.13310885e+00 -3.77139039e+00 3.80015486e+00 5 2.58394510e+01 -3.05812148e+01 -8.43337221e+00 | 2.58394510e+01 -3.05812148e+01 -8.43337221e+00 6 -3.32364371e+00 5.39643010e+00 1.63510343e+00 | -3.32364371e+00 5.39643010e+00 1.63510343e+00 7 -1.00606604e+01 1.18133190e+01 -1.19923902e+01 | -1.00606604e+01 1.18133190e+01 -1.19923902e+01 8 -2.33164860e+01 -5.94222894e+01 -2.49424560e+01 | -2.33164860e+01 -5.94222894e+01 -2.49424560e+01 9 1.76359633e+01 5.72695348e+01 2.42760963e+01 | 1.76359633e+01 5.72695348e+01 2.42760963e+01 10 1.09531866e-01 -2.05530360e+00 -4.89785394e+00 | 1.09531866e-01 -2.05530360e+00 -4.89785394e+00 11 4.94582804e+00 3.45188233e+00 -8.43493480e-02 | 4.94582804e+00 3.45188233e+00 -8.43493480e-02 12 5.37637987e-01 -1.95180983e+00 2.29590884e+00 | 5.37637987e-01 -1.95180983e+00 2.29590884e+00 13 6.31409625e+00 -1.36199010e+01 -2.04074957e+01 | 6.31409625e+00 -1.36199010e+01 -2.04074957e+01 14 5.68761777e+00 7.26331083e+00 -1.30275471e+01 | 5.68761777e+00 7.26331083e+00 -1.30275471e+01 15 1.74880190e+00 -1.25625678e+01 -4.95699297e+00 | 1.74880190e+00 -1.25625678e+01 -4.95699297e+00 16 2.22718747e-01 -1.10174805e+00 1.76405266e-01 | 2.22718747e-01 -1.10174805e+00 1.76405266e-01 17 -5.74461546e-01 -9.01026468e+00 -2.34249600e+00 | -5.74461546e-01 -9.01026468e+00 -2.34249600e+00 18 -1.22748624e-01 -3.77520690e-01 -9.47743831e+00 | -1.22748624e-01 -3.77520690e-01 -9.47743831e+00 19 9.92645059e-01 8.24752840e+00 4.33389323e+00 | 9.92645059e-01 8.24752840e+00 4.33389323e+00 20 -1.72797840e+01 -2.19469736e+01 -1.38622252e+01 | -1.72797840e+01 -2.19469736e+01 -1.38622252e+01 21 -2.44518052e-01 -6.47557496e+00 5.46423096e+01 | -2.44518052e-01 -6.47557496e+00 5.46423096e+01 22 -8.47819013e+00 3.76596241e+00 5.72161455e-01 | -8.47819013e+00 3.76596241e+00 5.72161455e-01 23 -1.30917560e+01 4.03458733e+01 -1.75875999e+01 | -1.30917560e+01 4.03458733e+01 -1.75875999e+01 24 1.34866662e+00 9.71747296e-01 -9.28187741e-01 | 1.34866662e+00 9.71747296e-01 -9.28187741e-01 25 -2.31910974e+01 1.40850788e+01 -2.18254518e+01 | -2.31910974e+01 1.40850788e+01 -2.18254518e+01 26 -1.53689460e+00 -1.88582734e+00 -1.58909595e+00 | -1.53689460e+00 -1.88582734e+00 -1.58909595e+00 27 1.27852733e+00 1.35201394e+00 2.06176741e+00 | 1.27852733e+00 1.35201394e+00 2.06176741e+00 28 6.77158971e-01 -3.52663844e+01 2.55409008e+00 | 6.77158971e-01 -3.52663844e+01 2.55409008e+00 29 3.96024009e+01 2.49728748e+01 1.02874632e+01 | 3.96024009e+01 2.49728748e+01 1.02874632e+01 30 3.19549420e+01 2.12176995e+01 -5.36326574e+01 | 3.19549420e+01 2.12176995e+01 -5.36326574e+01 31 -2.90489448e+01 2.21599931e+01 -2.73215489e+01 | -2.90489448e+01 2.21599931e+01 -2.73215489e+01 32 -1.17876651e+01 -4.63982994e+01 -1.31833131e+01 | -1.17876651e+01 -4.63982994e+01 -1.31833131e+01 33 -8.29843370e+00 3.54608758e+01 2.54456935e+01 | -8.29843370e+00 3.54608758e+01 2.54456935e+01 34 -3.53714581e+00 1.72372709e+01 1.95036735e+01 | -3.53714581e+00 1.72372709e+01 1.95036735e+01 35 -3.18410995e+01 2.36134694e+01 -1.53080790e+01 | -3.18410995e+01 2.36134694e+01 -1.53080790e+01 36 -1.68207805e-01 -2.24055664e-01 -1.10681771e+00 | -1.68207805e-01 -2.24055664e-01 -1.10681771e+00 37 1.89738267e+00 -6.08667228e+00 -4.85810097e-01 | 1.89738267e+00 -6.08667228e+00 -4.85810097e-01 38 -1.86585672e+00 -5.96011427e+00 7.12638290e+00 | -1.86585672e+00 -5.96011427e+00 7.12638290e+00 39 -2.98695919e+01 -3.60148856e+01 5.95325522e+01 | -2.98695919e+01 -3.60148856e+01 5.95325522e+01 40 -1.39066237e+01 -1.73544286e+01 6.61632562e+00 | -1.39066237e+01 -1.73544286e+01 6.61632562e+00 41 1.47941176e+01 1.50213607e+01 -4.81299447e+00 | 1.47941176e+01 1.50213607e+01 -4.81299447e+00 42 -4.69078519e+00 1.23827803e+01 1.51808697e+01 | -4.69078519e+00 1.23827803e+01 1.51808697e+01 43 4.64273298e+01 -6.11910406e+01 -3.30683611e+01 | 4.64273298e+01 -6.11910406e+01 -3.30683611e+01 44 1.07880263e-01 1.28195105e+00 2.50454881e-01 | 1.07880263e-01 1.28195105e+00 2.50454881e-01 45 -1.02095820e+00 -1.46201318e-01 -1.29870504e+00 | -1.02095820e+00 -1.46201318e-01 -1.29870504e+00 46 2.40395208e+01 -3.26109023e+01 2.00413504e+01 | 2.40395208e+01 -3.26109023e+01 2.00413504e+01 47 -2.62745933e+01 -1.90004396e+01 3.36020565e+01 | -2.62745933e+01 -1.90004396e+01 3.36020565e+01 48 1.28955313e+00 7.16146727e+00 -6.16441831e+00 | 1.28955313e+00 7.16146727e+00 -6.16441831e+00 49 -1.54499758e+01 -1.82563248e+01 4.82397417e+01 | -1.54499758e+01 -1.82563248e+01 4.82397417e+01 50 1.68377143e+01 -1.45258637e+01 -1.13746551e+01 | 1.68377143e+01 -1.45258637e+01 -1.13746551e+01 51 -6.46828469e-02 2.37505891e+00 -2.82025809e-01 | -6.46828469e-02 2.37505891e+00 -2.82025809e-01 52 1.68887444e+01 3.56635387e+01 -5.78761137e+01 | 1.68887444e+01 3.56635387e+01 -5.78761137e+01 53 3.28491721e+00 3.62058487e+00 6.35034566e+00 | 3.28491721e+00 3.62058487e+00 6.35034566e+00 54 -9.06169003e-01 -8.62818755e-01 -1.57767087e+00 | -9.06169003e-01 -8.62818755e-01 -1.57767087e+00 55 1.83321868e+00 9.17839415e-02 6.83979161e-01 | 1.83321868e+00 9.17839415e-02 6.83979161e-01 56 -3.54803940e+00 8.01312940e+00 -3.14118423e+00 | -3.54803940e+00 8.01312940e+00 -3.14118423e+00 57 -9.24358105e-01 2.32770096e+00 -7.05366506e+00 | -9.24358105e-01 2.32770096e+00 -7.05366506e+00 58 2.42041190e+01 -1.36650596e+01 3.45288249e+01 | 2.42041190e+01 -1.36650596e+01 3.45288249e+01 59 -2.17579859e-01 -2.30461269e-01 9.05223136e-01 | -2.17579859e-01 -2.30461269e-01 9.05223136e-01 60 -7.11698286e+00 7.75733367e+01 1.26704052e+01 | -7.11698286e+00 7.75733367e+01 1.26704052e+01 61 7.57359953e-01 2.91417256e+00 2.41591760e-01 | 7.57359953e-01 2.91417256e+00 2.41591760e-01 62 -8.08215179e+00 1.93190593e+00 -1.35394650e+00 | -8.08215179e+00 1.93190593e+00 -1.35394650e+00 63 7.26637537e+00 5.95909908e+00 4.86514149e+00 | 7.26637537e+00 5.95909908e+00 4.86514149e+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 = [2, 17, 0, 20, 7, 38, 56, 4, 41, 42, 61, 32, 28, 34, 54, 18, 43, 1, 15, 58, 3, 31, 36, 51, 44, 55, 39, 49, 12, 62, 46, 21, 11, 37, 13, 60, 22, 33, 5, 26, 48, 8, 9, 16, 24, 47, 30, 45, 40, 27, 53, 23, 57, 50, 14, 25, 6, 52, 19, 63, 35, 10, 29, 59] 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)) = 138.26958345674944 V(r_1,...,r_N) = 138.2695834567493 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 9.03300740e-01 6.17528148e-01 8.03002899e-01 | 9.03300740e-01 6.17528148e-01 8.03002899e-01 1 4.57255612e+00 -3.27582181e+00 -3.94418647e+00 | 4.57255612e+00 -3.27582181e+00 -3.94418647e+00 2 6.73283949e-02 -2.71324358e-01 7.27123446e-01 | 6.73283949e-02 -2.71324358e-01 7.27123446e-01 3 -2.19264409e+00 -3.90757708e-01 4.06737388e+00 | -2.19264409e+00 -3.90757708e-01 4.06737388e+00 4 -9.05371700e-01 -5.75514038e-01 -1.83678199e+00 | -9.05371700e-01 -5.75514038e-01 -1.83678199e+00 5 -1.07922212e+01 9.57607089e-01 -1.31817530e+01 | -1.07922212e+01 9.57607089e-01 -1.31817530e+01 6 -6.96937734e+00 2.75831525e+00 2.53710871e+00 | -6.96937734e+00 2.75831525e+00 2.53710871e+00 7 2.58785704e+00 9.15179486e-01 9.53872887e-01 | 2.58785704e+00 9.15179486e-01 9.53872887e-01 8 -3.44407036e-01 8.97653961e-01 8.42419452e-01 | -3.44407036e-01 8.97653961e-01 8.42419452e-01 9 -2.01753185e+01 -1.73531900e+01 3.04811719e+01 | -2.01753185e+01 -1.73531900e+01 3.04811719e+01 10 1.95584368e+01 1.74553217e+01 -2.99417403e+01 | 1.95584368e+01 1.74553217e+01 -2.99417403e+01 11 8.23197842e+01 -6.92136005e+01 -1.04095709e+02 | 8.23197842e+01 -6.92136005e+01 -1.04095709e+02 12 -3.22067994e-01 1.28150833e+00 4.25919465e-01 | -3.22067994e-01 1.28150833e+00 4.25919465e-01 13 -1.57909921e-01 8.55454146e-02 -9.42270578e-01 | -1.57909921e-01 8.55454146e-02 -9.42270578e-01 14 -7.05374196e+01 -9.71619229e+01 -7.90495211e+01 | -7.05374196e+01 -9.71619229e+01 -7.90495211e+01 15 6.42121931e+01 1.01971528e+02 7.52659645e+01 | 6.42121931e+01 1.01971528e+02 7.52659645e+01 16 5.36973786e-01 -2.37854538e-01 7.35712792e-01 | 5.36973786e-01 -2.37854538e-01 7.35712792e-01 17 -9.23885445e+01 6.43922365e+01 -1.37583522e+02 | -9.23885445e+01 6.43922365e+01 -1.37583522e+02 18 -3.79046037e+01 -1.86553993e+01 -1.83125727e+01 | -3.79046037e+01 -1.86553993e+01 -1.83125727e+01 19 3.59941571e+01 1.84911664e+01 1.66822566e+01 | 3.59941571e+01 1.84911664e+01 1.66822566e+01 20 9.00418205e+01 -6.40083538e+01 1.36690577e+02 | 9.00418205e+01 -6.40083538e+01 1.36690577e+02 21 5.53996941e+00 -7.20491946e+00 -1.72628924e+01 | 5.53996941e+00 -7.20491946e+00 -1.72628924e+01 22 -1.54233926e+01 -4.86875826e+00 -2.80706896e+01 | -1.54233926e+01 -4.86875826e+00 -2.80706896e+01 23 1.62268557e+01 3.55603153e+00 2.84470296e+01 | 1.62268557e+01 3.55603153e+00 2.84470296e+01 24 2.26436107e+00 -7.91575129e-01 -4.49931506e+00 | 2.26436107e+00 -7.91575129e-01 -4.49931506e+00 25 -1.48385230e+01 -1.47249493e+01 2.26763305e+01 | -1.48385230e+01 -1.47249493e+01 2.26763305e+01 26 1.22855403e+01 1.00535402e+01 -2.40649843e+01 | 1.22855403e+01 1.00535402e+01 -2.40649843e+01 27 2.92542952e+00 3.13179117e+00 2.76105477e+00 | 2.92542952e+00 3.13179117e+00 2.76105477e+00 28 -8.27307471e+01 6.88766669e+01 1.03289448e+02 | -8.27307471e+01 6.88766669e+01 1.03289448e+02 29 -7.56616686e-01 4.23471113e-01 9.72196069e-01 | -7.56616686e-01 4.23471113e-01 9.72196069e-01 30 9.04210657e-01 -2.01901879e-01 3.50869368e+00 | 9.04210657e-01 -2.01901879e-01 3.50869368e+00 31 2.82634435e+00 8.65405178e+00 -8.67269926e+00 | 2.82634435e+00 8.65405178e+00 -8.67269926e+00 32 1.12108082e+00 1.14911316e+00 -2.33996390e-01 | 1.12108082e+00 1.14911316e+00 -2.33996390e-01 33 -2.30979990e+01 2.65798627e+01 -2.68635296e+01 | -2.30979990e+01 2.65798627e+01 -2.68635296e+01 34 -1.20391635e+00 -3.55208070e-01 -1.92109575e+00 | -1.20391635e+00 -3.55208070e-01 -1.92109575e+00 35 -4.16498762e+00 3.77568311e+00 -2.71575944e+00 | -4.16498762e+00 3.77568311e+00 -2.71575944e+00 36 2.35102885e+01 -2.69114396e+01 2.59297231e+01 | 2.35102885e+01 -2.69114396e+01 2.59297231e+01 37 -1.34810008e+01 -1.05279730e+01 7.23838142e+00 | -1.34810008e+01 -1.05279730e+01 7.23838142e+00 38 -1.51330354e+01 -1.58081848e+01 1.98976501e-01 | -1.51330354e+01 -1.58081848e+01 1.98976501e-01 39 4.34878563e+00 4.14935355e+00 3.09678235e+00 | 4.34878563e+00 4.14935355e+00 3.09678235e+00 40 1.06602954e+01 7.41119508e-01 1.45115201e+01 | 1.06602954e+01 7.41119508e-01 1.45115201e+01 41 1.37002654e+00 7.75729117e+00 -1.24749956e+01 | 1.37002654e+00 7.75729117e+00 -1.24749956e+01 42 3.33591406e+00 -6.18329243e+00 4.69073142e+00 | 3.33591406e+00 -6.18329243e+00 4.69073142e+00 43 7.34711244e-01 4.65419993e-02 -7.82648216e-01 | 7.34711244e-01 4.65419993e-02 -7.82648216e-01 44 3.36322189e-01 -7.18981850e+00 1.32377527e+01 | 3.36322189e-01 -7.18981850e+00 1.32377527e+01 45 -9.79360420e-01 3.43539637e-01 -1.10961986e+00 | -9.79360420e-01 3.43539637e-01 -1.10961986e+00 46 1.11245545e+01 -3.54241262e+01 -5.16017459e+01 | 1.11245545e+01 -3.54241262e+01 -5.16017459e+01 47 8.34316784e+00 4.29755341e+01 4.78599988e+01 | 8.34316784e+00 4.29755341e+01 4.78599988e+01 48 -1.65102332e+00 -5.55211534e+00 -5.17389546e+00 | -1.65102332e+00 -5.55211534e+00 -5.17389546e+00 49 3.12156925e+00 6.13563646e+00 5.12686003e+00 | 3.12156925e+00 6.13563646e+00 5.12686003e+00 50 -1.12170887e+01 1.23429750e+01 6.49239917e+00 | -1.12170887e+01 1.23429750e+01 6.49239917e+00 51 -2.83076264e-01 -8.75701024e-01 3.99300884e-01 | -2.83076264e-01 -8.75701024e-01 3.99300884e-01 52 -3.97805631e+01 -2.64567382e+01 -3.57620092e+01 | -3.97805631e+01 -2.64567382e+01 -3.57620092e+01 53 4.86490143e+01 3.62118017e+01 3.21659538e+01 | 4.86490143e+01 3.62118017e+01 3.21659538e+01 54 -1.03049294e+00 -9.73684207e-01 -2.73393568e+00 | -1.03049294e+00 -9.73684207e-01 -2.73393568e+00 55 2.09620142e+00 1.38321669e-01 1.52216742e+00 | 2.09620142e+00 1.38321669e-01 1.52216742e+00 56 -6.79698366e+00 -4.78349862e+00 -1.93990455e+00 | -6.79698366e+00 -4.78349862e+00 -1.93990455e+00 57 1.54687133e+01 -2.71975257e+00 1.05992870e+01 | 1.54687133e+01 -2.71975257e+00 1.05992870e+01 58 -2.50741779e+00 -9.64665466e+00 9.07996163e+00 | -2.50741779e+00 -9.64665466e+00 9.07996163e+00 59 -1.15568297e+00 -8.53052840e-01 9.49622677e-03 | -1.15568297e+00 -8.53052840e-01 9.49622677e-03 60 -8.47558145e+00 2.74696443e-02 -4.00948504e+00 | -8.47558145e+00 2.74696443e-02 -4.00948504e+00 61 8.31963581e+00 1.35674347e+00 5.80345830e+00 | 8.31963581e+00 1.35674347e+00 5.80345830e+00 62 8.54541922e-01 5.68579297e+00 8.95008981e-02 | 8.54541922e-01 5.68579297e+00 8.95008981e-02 63 2.35433152e-01 -7.38839944e-01 -1.13825016e+00 | 2.35433152e-01 -7.38839944e-01 -1.13825016e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ag Au Cu (Configuration in file "config-AgAuCu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [59, 37, 39, 16, 56, 38, 57, 25, 10, 32, 8, 43, 62, 47, 18, 19, 3, 31, 14, 15, 58, 60, 49, 33, 26, 7, 24, 54, 46, 36, 53, 17, 9, 23, 52, 48, 29, 1, 5, 2, 41, 40, 51, 11, 50, 45, 28, 13, 35, 22, 44, 42, 34, 30, 27, 63, 4, 6, 20, 0, 21, 61, 12, 55] 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)) = 94.61130491937534 V(r_1,...,r_N) = 94.61130491937516 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 -8.19296863e-01 -7.13813552e-01 7.47263536e-02 | -8.19296863e-01 -7.13813552e-01 7.47263536e-02 1 -8.09529663e+00 2.01855368e+00 6.67889518e+00 | -8.09529663e+00 2.01855368e+00 6.67889518e+00 2 4.70323228e+00 3.45731703e+00 -1.83745590e+01 | 4.70323228e+00 3.45731703e+00 -1.83745590e+01 3 1.11602275e+00 -3.05556364e-01 -7.42685933e+00 | 1.11602275e+00 -3.05556364e-01 -7.42685933e+00 4 1.39622162e+01 -1.69445256e+01 5.29541384e+00 | 1.39622162e+01 -1.69445256e+01 5.29541384e+00 5 3.88885275e+01 -1.21002683e+01 -4.51612378e+01 | 3.88885275e+01 -1.21002683e+01 -4.51612378e+01 6 -3.34385957e+01 -3.92114345e-01 -3.80244610e+01 | -3.34385957e+01 -3.92114345e-01 -3.80244610e+01 7 2.28403954e+01 1.13204472e+01 3.94700879e+01 | 2.28403954e+01 1.13204472e+01 3.94700879e+01 8 5.21063863e-01 -4.69344829e-02 -6.39173555e-01 | 5.21063863e-01 -4.69344829e-02 -6.39173555e-01 9 -8.90980230e+00 -1.33937904e+01 6.75741724e+00 | -8.90980230e+00 -1.33937904e+01 6.75741724e+00 10 1.63274536e+00 -2.16082954e+00 -1.56295107e+01 | 1.63274536e+00 -2.16082954e+00 -1.56295107e+01 11 1.09787509e+01 1.20109818e+01 8.07843749e+00 | 1.09787509e+01 1.20109818e+01 8.07843749e+00 12 -5.12484067e+00 -8.70207601e+00 -6.52906145e+00 | -5.12484067e+00 -8.70207601e+00 -6.52906145e+00 13 7.26348035e+00 5.46573629e+00 4.06333456e+00 | 7.26348035e+00 5.46573629e+00 4.06333456e+00 14 5.71204576e-01 -4.20103563e+00 1.37043467e+00 | 5.71204576e-01 -4.20103563e+00 1.37043467e+00 15 -1.82138602e+01 2.83414932e+01 -3.02142577e+01 | -1.82138602e+01 2.83414932e+01 -3.02142577e+01 16 -1.12165208e+00 -3.49066130e+00 -1.43543738e+00 | -1.12165208e+00 -3.49066130e+00 -1.43543738e+00 17 8.28316779e+00 -1.52938542e+01 -5.43668271e+00 | 8.28316779e+00 -1.52938542e+01 -5.43668271e+00 18 4.09586552e+00 5.74848130e-01 -1.14145579e+01 | 4.09586552e+00 5.74848130e-01 -1.14145579e+01 19 5.06041314e+00 4.82592374e+00 3.45213511e+00 | 5.06041314e+00 4.82592374e+00 3.45213511e+00 20 -1.26121334e+01 4.46930267e-01 -1.92430440e+00 | -1.26121334e+01 4.46930267e-01 -1.92430440e+00 21 4.78884498e+01 -6.80374944e+01 -3.98237453e+01 | 4.78884498e+01 -6.80374944e+01 -3.98237453e+01 22 -2.14540053e+01 5.80931498e+00 7.47233785e+00 | -2.14540053e+01 5.80931498e+00 7.47233785e+00 23 5.00744553e+00 7.18517033e+00 7.89185305e+00 | 5.00744553e+00 7.18517033e+00 7.89185305e+00 24 -2.38619164e+01 -1.38901678e+01 -3.21310811e+01 | -2.38619164e+01 -1.38901678e+01 -3.21310811e+01 25 1.95126801e+01 4.76759173e+00 3.44735039e+01 | 1.95126801e+01 4.76759173e+00 3.44735039e+01 26 2.57843531e+00 7.12910414e+00 -5.06516613e+00 | 2.57843531e+00 7.12910414e+00 -5.06516613e+00 27 1.46687099e+00 8.08825974e-01 2.51495540e+00 | 1.46687099e+00 8.08825974e-01 2.51495540e+00 28 -3.06584836e+01 -3.03111637e+01 -6.87222694e+01 | -3.06584836e+01 -3.03111637e+01 -6.87222694e+01 29 3.09748961e+01 3.03699559e+01 6.88913046e+01 | 3.09748961e+01 3.03699559e+01 6.88913046e+01 30 1.35283453e+01 7.26790440e+00 -1.33199022e+01 | 1.35283453e+01 7.26790440e+00 -1.33199022e+01 31 -1.87664894e+00 5.47050650e+00 -5.14371371e+00 | -1.87664894e+00 5.47050650e+00 -5.14371371e+00 32 -1.29269607e+01 -2.20451432e+01 -1.30189361e+01 | -1.29269607e+01 -2.20451432e+01 -1.30189361e+01 33 1.06526298e+01 1.97447410e+01 1.32257007e+01 | 1.06526298e+01 1.97447410e+01 1.32257007e+01 34 -3.40735174e+01 1.26706322e+01 4.45285377e+01 | -3.40735174e+01 1.26706322e+01 4.45285377e+01 35 -8.19830286e+00 -5.41341331e+00 8.95762470e+00 | -8.19830286e+00 -5.41341331e+00 8.95762470e+00 36 4.68568745e-01 -4.92607976e-01 -3.77051039e-01 | 4.68568745e-01 -4.92607976e-01 -3.77051039e-01 37 -9.81609632e+00 -1.43798380e+01 7.04537119e+00 | -9.81609632e+00 -1.43798380e+01 7.04537119e+00 38 -4.36300039e-01 1.08065523e+00 6.87827973e-01 | -4.36300039e-01 1.08065523e+00 6.87827973e-01 39 -1.33283184e+01 -1.27041545e+01 9.31384318e+00 | -1.33283184e+01 -1.27041545e+01 9.31384318e+00 40 7.65442561e-01 -3.12508628e-02 -2.01064681e-01 | 7.65442561e-01 -3.12508628e-02 -2.01064681e-01 41 -3.68957774e+01 1.40046844e+01 -1.69830989e+01 | -3.68957774e+01 1.40046844e+01 -1.69830989e+01 42 1.74231752e+01 -2.55278326e+01 3.25903312e+01 | 1.74231752e+01 -2.55278326e+01 3.25903312e+01 43 1.01577450e+01 -1.36747791e+01 -3.29975055e+01 | 1.01577450e+01 -1.36747791e+01 -3.29975055e+01 44 3.76478638e+01 -1.58063408e+01 1.42324977e+01 | 3.76478638e+01 -1.58063408e+01 1.42324977e+01 45 1.04789986e-01 8.86464427e-01 1.81396825e-01 | 1.04789986e-01 8.86464427e-01 1.81396825e-01 46 4.11679359e+00 1.58310226e+01 -7.26407390e+00 | 4.11679359e+00 1.58310226e+01 -7.26407390e+00 47 2.47334416e+00 -8.69084897e-01 3.00054984e+00 | 2.47334416e+00 -8.69084897e-01 3.00054984e+00 48 -3.51763684e+00 1.26238784e+00 4.31949604e+00 | -3.51763684e+00 1.26238784e+00 4.31949604e+00 49 -6.77844727e+00 -8.59514488e-01 1.03415569e+01 | -6.77844727e+00 -8.59514488e-01 1.03415569e+01 50 -5.67559627e+01 7.31080289e+01 4.30743382e+01 | -5.67559627e+01 7.31080289e+01 4.30743382e+01 51 -5.25933499e-01 3.42332545e+00 8.22649035e-02 | -5.25933499e-01 3.42332545e+00 8.22649035e-02 52 4.11713040e+00 3.06740615e+00 -1.13677918e+01 | 4.11713040e+00 3.06740615e+00 -1.13677918e+01 53 6.47048713e+00 4.54205210e+00 9.31263749e+00 | 6.47048713e+00 4.54205210e+00 9.31263749e+00 54 1.06405454e-01 -1.29546906e+00 -8.29157071e-01 | 1.06405454e-01 -1.29546906e+00 -8.29157071e-01 55 1.36681486e+00 8.94586926e-02 -1.95931759e-01 | 1.36681486e+00 8.94586926e-02 -1.95931759e-01 56 1.35450208e+01 -1.46090149e-01 -5.54749554e+00 | 1.35450208e+01 -1.46090149e-01 -5.54749554e+00 57 -5.95052710e+01 -3.73449765e+01 3.61265455e+01 | -5.95052710e+01 -3.73449765e+01 3.61265455e+01 58 5.86388634e+01 2.64942502e+01 -3.13342291e+01 | 5.86388634e+01 2.64942502e+01 -3.13342291e+01 59 5.07845603e+00 7.70108124e+00 2.61755739e+00 | 5.07845603e+00 7.70108124e+00 2.61755739e+00 60 -8.77011077e+00 1.59023972e+01 3.17520314e+01 | -8.77011077e+00 1.59023972e+01 3.17520314e+01 61 -3.12583181e-01 4.02426572e-01 -2.49887377e-01 | -3.12583181e-01 4.02426572e-01 -2.49887377e-01 62 2.30076476e+00 1.41763906e+00 -2.09292691e+00 | 2.30076476e+00 1.41763906e+00 -2.09292691e+00 63 1.71924618e+00 1.67552245e+00 1.00018418e+00 | 1.71924618e+00 1.67552245e+00 1.00018418e+00 ------------------------------------------------------------------------------------------------------------------------- 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.