!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005 Supported species : Cu Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [23, 4, 6, 19, 1, 35, 2, 46, 20, 56, 61, 41, 17, 51, 54, 28, 27, 12, 24, 3, 8, 50, 48, 0, 18, 26, 25, 16, 15, 49, 53, 37, 34, 58, 32, 5, 52, 31, 45, 44, 47, 11, 59, 57, 39, 38, 7, 40, 22, 29, 21, 13, 36, 30, 14, 63, 9, 43, 33, 42, 62, 10, 60, 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)) = 29.136572327115168 V(r_1,...,r_N) = 29.13657232711514 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 -1.58520166e+00 -9.20837810e-01 -1.46840346e+00 | -1.58520166e+00 -9.20837810e-01 -1.46840346e+00 1 -8.68180077e+00 -2.35473284e+01 1.64039427e+01 | -8.68180077e+00 -2.35473284e+01 1.64039427e+01 2 -1.08604310e+00 9.21912327e+00 -2.85382476e+01 | -1.08604310e+00 9.21912327e+00 -2.85382476e+01 3 9.04001141e+00 1.50448570e+01 1.14598111e+01 | 9.04001141e+00 1.50448570e+01 1.14598111e+01 4 6.28723268e-01 5.18886834e-01 1.46036610e-01 | 6.28723268e-01 5.18886834e-01 1.46036610e-01 5 -1.66780512e-01 -4.28937160e-01 -8.43433612e-01 | -1.66780512e-01 -4.28937160e-01 -8.43433612e-01 6 -4.38175801e-01 -5.35147364e-01 -1.04833633e+00 | -4.38175801e-01 -5.35147364e-01 -1.04833633e+00 7 -2.48881360e+01 7.67875498e+01 -5.32713264e+01 | -2.48881360e+01 7.67875498e+01 -5.32713264e+01 8 -1.76684145e+00 1.92768421e-01 -1.72207465e+00 | -1.76684145e+00 1.92768421e-01 -1.72207465e+00 9 -3.75037990e+00 2.33336888e+00 -4.32472475e+00 | -3.75037990e+00 2.33336888e+00 -4.32472475e+00 10 -6.43906971e-01 3.06924011e-01 9.55552195e-01 | -6.43906971e-01 3.06924011e-01 9.55552195e-01 11 3.71331744e+00 -6.65519389e+00 -6.21379161e+00 | 3.71331744e+00 -6.65519389e+00 -6.21379161e+00 12 -5.56620267e+01 -2.63804929e+01 -2.02791300e+01 | -5.56620267e+01 -2.63804929e+01 -2.02791300e+01 13 6.47075871e+01 2.31140755e+01 1.96920966e+01 | 6.47075871e+01 2.31140755e+01 1.96920966e+01 14 -1.22061421e+01 -2.92408911e+00 -1.76021407e+01 | -1.22061421e+01 -2.92408911e+00 -1.76021407e+01 15 1.60604444e+01 3.05438521e+00 1.77984902e+01 | 1.60604444e+01 3.05438521e+00 1.77984902e+01 16 -1.22404756e+01 -1.30556467e+01 -1.10350311e+01 | -1.22404756e+01 -1.30556467e+01 -1.10350311e+01 17 1.33126456e+01 1.28428505e+01 1.20523371e+01 | 1.33126456e+01 1.28428505e+01 1.20523371e+01 18 -4.32748219e-02 -4.92367180e-01 9.84582207e-01 | -4.32748219e-02 -4.92367180e-01 9.84582207e-01 19 -4.78066580e+01 2.87100819e+01 -3.22585674e+01 | -4.78066580e+01 2.87100819e+01 -3.22585674e+01 20 -5.04723527e+00 -2.13145680e+00 -7.09469993e+00 | -5.04723527e+00 -2.13145680e+00 -7.09469993e+00 21 7.86490771e+00 8.55138419e+00 2.94119933e+00 | 7.86490771e+00 8.55138419e+00 2.94119933e+00 22 -3.86619099e+00 -2.86940386e+00 -6.53515511e+00 | -3.86619099e+00 -2.86940386e+00 -6.53515511e+00 23 2.03042710e+00 5.05999081e+00 5.11751414e+00 | 2.03042710e+00 5.05999081e+00 5.11751414e+00 24 -9.75631123e-01 -2.57347943e+00 -1.50541346e+00 | -9.75631123e-01 -2.57347943e+00 -1.50541346e+00 25 -1.07924764e+01 1.60316154e+01 -8.58487419e+00 | -1.07924764e+01 1.60316154e+01 -8.58487419e+00 26 5.37810410e-02 -7.89749248e-01 1.62828337e+00 | 5.37810410e-02 -7.89749248e-01 1.62828337e+00 27 -1.43224640e+00 -1.20656062e+00 1.19410663e-01 | -1.43224640e+00 -1.20656062e+00 1.19410663e-01 28 4.26644727e+00 -9.12197502e+00 1.43879828e+01 | 4.26644727e+00 -9.12197502e+00 1.43879828e+01 29 2.71580412e+00 2.27793185e+00 2.70033447e+00 | 2.71580412e+00 2.27793185e+00 2.70033447e+00 30 4.71285503e+01 -2.95962722e+01 3.10777499e+01 | 4.71285503e+01 -2.95962722e+01 3.10777499e+01 31 -1.79963652e+01 5.89268850e+00 -1.01014451e+01 | -1.79963652e+01 5.89268850e+00 -1.01014451e+01 32 -5.12718010e+01 -4.43959517e+01 -3.22905132e+01 | -5.12718010e+01 -4.43959517e+01 -3.22905132e+01 33 5.17475445e+01 4.50180279e+01 3.29798058e+01 | 5.17475445e+01 4.50180279e+01 3.29798058e+01 34 3.46949599e+01 -8.22832160e+01 4.72736072e+01 | 3.46949599e+01 -8.22832160e+01 4.72736072e+01 35 -1.85310760e+00 -4.67777420e+00 6.58361790e+00 | -1.85310760e+00 -4.67777420e+00 6.58361790e+00 36 1.78707438e-01 7.17567418e-01 -9.93249323e-01 | 1.78707438e-01 7.17567418e-01 -9.93249323e-01 37 -1.46116566e+01 -1.31255654e+01 1.28419064e+01 | -1.46116566e+01 -1.31255654e+01 1.28419064e+01 38 -1.93489823e+01 -1.55185420e+01 -1.93710196e+01 | -1.93489823e+01 -1.55185420e+01 -1.93710196e+01 39 5.41227509e+00 2.00409613e+00 2.71604127e+01 | 5.41227509e+00 2.00409613e+00 2.71604127e+01 40 -4.06801077e-01 2.23688819e-01 1.75964383e+00 | -4.06801077e-01 2.23688819e-01 1.75964383e+00 41 -2.42191294e+01 3.29985409e+01 -1.89963548e+01 | -2.42191294e+01 3.29985409e+01 -1.89963548e+01 42 -2.72292263e+00 2.13065471e+00 2.83368508e+00 | -2.72292263e+00 2.13065471e+00 2.83368508e+00 43 3.26146427e+00 -1.54250965e+00 -1.54658040e+00 | 3.26146427e+00 -1.54250965e+00 -1.54658040e+00 44 2.29048610e+01 -3.61498022e+01 1.96067534e+01 | 2.29048610e+01 -3.61498022e+01 1.96067534e+01 45 -1.09576398e+00 2.73641327e-02 -1.23506600e+00 | -1.09576398e+00 2.73641327e-02 -1.23506600e+00 46 1.28119884e+01 1.49080129e+01 -1.08515341e+01 | 1.28119884e+01 1.49080129e+01 -1.08515341e+01 47 8.78887543e-01 1.05305818e-01 -8.38319256e-01 | 8.78887543e-01 1.05305818e-01 -8.38319256e-01 48 -1.00120572e+01 4.45224358e+00 9.06672137e+00 | -1.00120572e+01 4.45224358e+00 9.06672137e+00 49 -3.09712101e+01 -1.38748281e+01 2.66270136e+01 | -3.09712101e+01 -1.38748281e+01 2.66270136e+01 50 3.15847496e+01 5.98700725e+00 -2.99343261e+01 | 3.15847496e+01 5.98700725e+00 -2.99343261e+01 51 3.67076435e+00 3.03959933e+00 3.41043280e+00 | 3.67076435e+00 3.03959933e+00 3.41043280e+00 52 1.40622006e+01 1.39500710e+01 -9.48410077e+00 | 1.40622006e+01 1.39500710e+01 -9.48410077e+00 53 5.59851568e-02 7.54971225e-01 -4.27751224e-01 | 5.59851568e-02 7.54971225e-01 -4.27751224e-01 54 -1.80411053e+00 1.11843745e-01 8.34844842e-01 | -1.80411053e+00 1.11843745e-01 8.34844842e-01 55 1.34114445e+00 1.31376201e-01 -4.00492973e-01 | 1.34114445e+00 1.31376201e-01 -4.00492973e-01 56 1.11013858e+00 1.69719006e+00 -2.85380875e+00 | 1.11013858e+00 1.69719006e+00 -2.85380875e+00 57 2.04143327e+01 -3.68353418e+01 -4.18449021e+01 | 2.04143327e+01 -3.68353418e+01 -4.18449021e+01 58 1.84876391e+01 -5.86084909e+00 1.13693224e+01 | 1.84876391e+01 -5.86084909e+00 1.13693224e+01 59 -9.36397699e-01 -7.36492684e-01 3.37025365e-03 | -9.36397699e-01 -7.36492684e-01 3.37025365e-03 60 -3.02883675e+00 4.04693833e+00 1.75670670e+00 | -3.02883675e+00 4.04693833e+00 1.75670670e+00 61 -4.83083788e-01 5.02789499e-01 5.71722964e-01 | -4.83083788e-01 5.02789499e-01 5.71722964e-01 62 -2.13752527e+01 3.37401282e+01 4.02926009e+01 | -2.13752527e+01 3.37401282e+01 4.02926009e+01 63 1.07681269e+00 1.74391121e+00 1.05732254e+00 | 1.07681269e+00 1.74391121e+00 1.05732254e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [56, 24, 55, 15, 60, 25, 40, 27, 20, 37, 63, 34, 41, 35, 30, 3, 18, 48, 16, 62, 8, 23, 59, 21, 1, 5, 32, 7, 42, 45, 14, 49, 26, 53, 11, 13, 50, 9, 39, 38, 6, 12, 28, 46, 58, 29, 43, 54, 17, 31, 36, 61, 57, 33, 47, 2, 0, 52, 44, 22, 4, 51, 19, 10] 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)) = 67.32425833633481 V(r_1,...,r_N) = 67.32425833633489 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 5.88207285e-01 6.06739992e-01 6.79052044e-01 | 5.88207285e-01 6.06739992e-01 6.79052044e-01 1 -3.30769198e+00 -1.15183041e+00 4.09089407e-02 | -3.30769198e+00 -1.15183041e+00 4.09089407e-02 2 -1.58683000e+01 -4.23943461e+01 -2.08831644e+01 | -1.58683000e+01 -4.23943461e+01 -2.08831644e+01 3 1.72201553e+01 4.57851753e+01 1.92641447e+01 | 1.72201553e+01 4.57851753e+01 1.92641447e+01 4 -4.69384041e-02 -1.51502310e+00 5.93466985e-01 | -4.69384041e-02 -1.51502310e+00 5.93466985e-01 5 -3.22436245e+01 2.18455307e+01 -1.86191414e+01 | -3.22436245e+01 2.18455307e+01 -1.86191414e+01 6 -8.17600080e-02 -4.22387848e-01 3.98910924e-01 | -8.17600080e-02 -4.22387848e-01 3.98910924e-01 7 8.04907817e-01 -2.02284341e+00 -6.75236604e-01 | 8.04907817e-01 -2.02284341e+00 -6.75236604e-01 8 7.10787365e-02 -9.01448387e-01 1.05510591e+00 | 7.10787365e-02 -9.01448387e-01 1.05510591e+00 9 -1.65609378e+01 -1.02808198e+01 1.98191554e+01 | -1.65609378e+01 -1.02808198e+01 1.98191554e+01 10 1.66425766e+01 1.16952870e+01 -2.19304828e+01 | 1.66425766e+01 1.16952870e+01 -2.19304828e+01 11 7.34388667e+01 -8.70575249e+01 -1.92250980e+01 | 7.34388667e+01 -8.70575249e+01 -1.92250980e+01 12 -2.26617357e+01 -1.25133727e+01 -1.30004301e+01 | -2.26617357e+01 -1.25133727e+01 -1.30004301e+01 13 2.32703487e+01 1.10600559e+01 1.40627396e+01 | 2.32703487e+01 1.10600559e+01 1.40627396e+01 14 -3.41347627e-01 -5.14366982e-01 2.63131920e-01 | -3.41347627e-01 -5.14366982e-01 2.63131920e-01 15 -4.30204871e-01 5.80787036e-01 2.13760773e+00 | -4.30204871e-01 5.80787036e-01 2.13760773e+00 16 -4.67370150e+00 -1.03529869e+00 -7.21235222e+00 | -4.67370150e+00 -1.03529869e+00 -7.21235222e+00 17 5.27956777e+00 1.24525168e+00 8.02186155e+00 | 5.27956777e+00 1.24525168e+00 8.02186155e+00 18 -1.36186432e+01 -1.20801456e+01 -1.85203315e+01 | -1.36186432e+01 -1.20801456e+01 -1.85203315e+01 19 1.34954173e+01 1.08480100e+01 1.92485098e+01 | 1.34954173e+01 1.08480100e+01 1.92485098e+01 20 -1.37386566e+01 -1.87765513e+01 -1.93573355e+01 | -1.37386566e+01 -1.87765513e+01 -1.93573355e+01 21 4.79546554e+01 -8.89068676e+00 4.65867230e-01 | 4.79546554e+01 -8.89068676e+00 4.65867230e-01 22 -1.79633610e+01 -1.90983715e+01 -9.41414916e+00 | -1.79633610e+01 -1.90983715e+01 -9.41414916e+00 23 1.88297179e+01 1.82870194e+01 9.08271319e+00 | 1.88297179e+01 1.82870194e+01 9.08271319e+00 24 -3.52219348e-02 2.53129471e-01 7.91874130e-01 | -3.52219348e-02 2.53129471e-01 7.91874130e-01 25 -5.67800201e+01 1.03873738e+02 -1.83504659e+02 | -5.67800201e+01 1.03873738e+02 -1.83504659e+02 26 -1.22864911e+01 -9.53560279e+01 -2.63258591e+01 | -1.22864911e+01 -9.53560279e+01 -2.63258591e+01 27 1.20518755e+01 9.48800854e+01 2.67381197e+01 | 1.20518755e+01 9.48800854e+01 2.67381197e+01 28 -1.67002425e+01 -1.58770467e+01 2.01787355e+02 | -1.67002425e+01 -1.58770467e+01 2.01787355e+02 29 8.00180562e-01 -1.46281384e+00 -6.40625200e-01 | 8.00180562e-01 -1.46281384e+00 -6.40625200e-01 30 3.66972211e-01 -2.34885137e+00 -1.94594371e+00 | 3.66972211e-01 -2.34885137e+00 -1.94594371e+00 31 -3.12257886e-01 1.21185531e+00 2.18470746e+00 | -3.12257886e-01 1.21185531e+00 2.18470746e+00 32 1.15454168e+00 9.87228571e-01 -5.04415388e-01 | 1.15454168e+00 9.87228571e-01 -5.04415388e-01 33 -7.87189319e+01 2.52559715e+01 -1.94487444e+01 | -7.87189319e+01 2.52559715e+01 -1.94487444e+01 34 8.27462745e+00 1.83366448e+01 -1.44891705e+01 | 8.27462745e+00 1.83366448e+01 -1.44891705e+01 35 -2.98886047e+01 -2.66063943e+01 2.39023130e+00 | -2.98886047e+01 -2.66063943e+01 2.39023130e+00 36 6.67151075e+01 -4.94520766e+01 2.45416929e+01 | 6.67151075e+01 -4.94520766e+01 2.45416929e+01 37 3.24735720e+00 5.38087934e+00 8.15835099e+00 | 3.24735720e+00 5.38087934e+00 8.15835099e+00 38 -1.73371868e+00 -1.71980091e+00 -2.36671987e+00 | -1.73371868e+00 -1.71980091e+00 -2.36671987e+00 39 1.82593538e+00 2.44010045e+00 1.74042106e+00 | 1.82593538e+00 2.44010045e+00 1.74042106e+00 40 3.17949178e+01 -2.07354463e+01 1.80179410e+01 | 3.17949178e+01 -2.07354463e+01 1.80179410e+01 41 -5.07716745e+01 -4.07076776e+01 2.93879306e+01 | -5.07716745e+01 -4.07076776e+01 2.93879306e+01 42 4.93290198e+01 4.16851218e+01 -2.83071205e+01 | 4.93290198e+01 4.16851218e+01 -2.83071205e+01 43 1.43985102e-01 1.91114444e+00 1.05840756e+00 | 1.43985102e-01 1.91114444e+00 1.05840756e+00 44 -2.29194500e+00 -4.07689776e+00 -1.40043692e+00 | -2.29194500e+00 -4.07689776e+00 -1.40043692e+00 45 1.58558780e+00 5.22023870e+00 8.39865902e-01 | 1.58558780e+00 5.22023870e+00 8.39865902e-01 46 -2.76229383e+01 -2.88675354e+01 -6.55832253e+01 | -2.76229383e+01 -2.88675354e+01 -6.55832253e+01 47 2.82365751e+01 2.84786834e+01 6.52790814e+01 | 2.82365751e+01 2.84786834e+01 6.52790814e+01 48 -7.91379338e-01 1.35559726e+00 1.21779101e+00 | -7.91379338e-01 1.35559726e+00 1.21779101e+00 49 -4.40943072e+01 3.73318328e+01 -3.27074294e+01 | -4.40943072e+01 3.73318328e+01 -3.27074294e+01 50 -3.25179521e+01 2.75601972e+01 1.95217905e+01 | -3.25179521e+01 2.75601972e+01 1.95217905e+01 51 -5.51375763e-01 -2.22841365e-03 -1.42603315e-01 | -5.51375763e-01 -2.22841365e-03 -1.42603315e-01 52 4.31217756e+01 -3.81380691e+01 3.27377852e+01 | 4.31217756e+01 -3.81380691e+01 3.27377852e+01 53 -2.17090909e-01 1.60074860e+00 1.23736907e+00 | -2.17090909e-01 1.60074860e+00 1.23736907e+00 54 -1.33213600e+00 -2.70819047e+00 -1.44666615e+00 | -1.33213600e+00 -2.70819047e+00 -1.44666615e+00 55 1.50210299e+00 2.81717996e+00 1.65124900e+00 | 1.50210299e+00 2.81717996e+00 1.65124900e+00 56 3.07047987e+01 2.61240376e+01 -4.93272148e+00 | 3.07047987e+01 2.61240376e+01 -4.93272148e+00 57 -2.82918649e+01 2.98514407e+01 -5.21058892e+01 | -2.82918649e+01 2.98514407e+01 -5.21058892e+01 58 5.03909501e+00 1.25770431e+01 -1.61455225e+01 | 5.03909501e+00 1.25770431e+01 -1.61455225e+01 59 -1.88085030e+00 -1.41974621e+00 3.76082571e-01 | -1.88085030e+00 -1.41974621e+00 3.76082571e-01 60 2.41960213e+01 -4.76707315e+01 6.58598634e+01 | 2.41960213e+01 -4.76707315e+01 6.58598634e+01 61 2.03440309e+00 3.13022181e+00 1.00779754e+00 | 2.03440309e+00 3.13022181e+00 1.00779754e+00 62 -2.16795334e+00 3.08833329e+00 3.00043476e-01 | -2.16795334e+00 3.08833329e+00 3.00043476e-01 63 8.03480541e-01 -1.50075877e+00 -1.12345320e+00 | 8.03480541e-01 -1.50075877e+00 -1.12345320e+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, 32, 27, 28, 39, 23, 22, 48, 26, 12, 34, 54, 9, 30, 0, 17, 40, 15, 35, 56, 50, 57, 6, 5, 43, 52, 8, 2, 3, 53, 13, 60, 1, 62, 10, 18, 46, 49, 45, 4, 16, 61, 47, 24, 51, 38, 36, 42, 7, 37, 20, 44, 25, 29, 11, 59, 19, 21, 63, 55, 31, 41, 33, 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)) = 75.8527102823689 V(r_1,...,r_N) = 75.85271028236869 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 1.19994740e+00 1.17932127e+00 1.12601031e+00 | 1.19994740e+00 1.17932127e+00 1.12601031e+00 1 -1.67330661e+01 4.89751235e+00 8.36746304e+01 | -1.67330661e+01 4.89751235e+00 8.36746304e+01 2 1.69976167e+01 -4.94621793e+00 -8.21363171e+01 | 1.69976167e+01 -4.94621793e+00 -8.21363171e+01 3 5.75467973e+01 -7.90080695e+01 -7.85577904e+01 | 5.75467973e+01 -7.90080695e+01 -7.85577904e+01 4 -1.84431612e+00 -1.58858297e+00 -2.15971665e+00 | -1.84431612e+00 -1.58858297e+00 -2.15971665e+00 5 4.90865098e+00 -3.27667050e-01 -2.52188074e+00 | 4.90865098e+00 -3.27667050e-01 -2.52188074e+00 6 1.20197881e+00 -1.27737121e+00 1.60439768e-01 | 1.20197881e+00 -1.27737121e+00 1.60439768e-01 7 -1.60465213e+01 2.58598553e+01 -2.35510826e+01 | -1.60465213e+01 2.58598553e+01 -2.35510826e+01 8 -2.71144414e+01 -7.53328044e+00 -3.17060054e+01 | -2.71144414e+01 -7.53328044e+00 -3.17060054e+01 9 2.69813573e+01 8.87921212e+00 3.23438342e+01 | 2.69813573e+01 8.87921212e+00 3.23438342e+01 10 -1.06934871e+00 -5.54523137e-01 1.07908218e+00 | -1.06934871e+00 -5.54523137e-01 1.07908218e+00 11 -8.64889225e-01 6.49376491e-01 1.06202065e+00 | -8.64889225e-01 6.49376491e-01 1.06202065e+00 12 -1.80522922e-01 1.28931923e+00 3.14860550e-01 | -1.80522922e-01 1.28931923e+00 3.14860550e-01 13 -1.18687304e+00 3.55296003e-01 -3.24330898e-01 | -1.18687304e+00 3.55296003e-01 -3.24330898e-01 14 -4.44782682e-01 -7.06297893e-01 -3.79307822e-01 | -4.44782682e-01 -7.06297893e-01 -3.79307822e-01 15 1.48932924e+00 -1.29844160e+00 4.57931060e-01 | 1.48932924e+00 -1.29844160e+00 4.57931060e-01 16 -1.35351146e-01 -5.44717236e-01 1.93881687e-02 | -1.35351146e-01 -5.44717236e-01 1.93881687e-02 17 -1.18197202e+01 -1.20288817e+01 1.35253458e+01 | -1.18197202e+01 -1.20288817e+01 1.35253458e+01 18 1.49501100e+01 1.16394870e+01 -1.37009122e+01 | 1.49501100e+01 1.16394870e+01 -1.37009122e+01 19 -1.43435813e+00 4.87575480e+00 -2.32069390e+00 | -1.43435813e+00 4.87575480e+00 -2.32069390e+00 20 -5.74861975e+01 7.90576371e+01 7.85694734e+01 | -5.74861975e+01 7.90576371e+01 7.85694734e+01 21 -1.64249396e+02 1.46586638e+02 -9.19331513e+01 | -1.64249396e+02 1.46586638e+02 -9.19331513e+01 22 -1.51779910e+00 9.38280528e-02 4.52457422e-01 | -1.51779910e+00 9.38280528e-02 4.52457422e-01 23 6.67494311e-01 -5.90134774e-01 1.66266061e+00 | 6.67494311e-01 -5.90134774e-01 1.66266061e+00 24 -8.02792639e+00 -1.90013607e+01 -1.32756540e+01 | -8.02792639e+00 -1.90013607e+01 -1.32756540e+01 25 2.42908404e+01 4.23207995e+00 -5.94895047e+00 | 2.42908404e+01 4.23207995e+00 -5.94895047e+00 26 -3.99037895e-01 1.23418229e+00 1.59627281e-02 | -3.99037895e-01 1.23418229e+00 1.59627281e-02 27 -1.14882933e+00 -1.25596876e+00 8.97583850e-01 | -1.14882933e+00 -1.25596876e+00 8.97583850e-01 28 -2.83430583e+01 -5.88749155e+00 -2.67390691e+00 | -2.83430583e+01 -5.88749155e+00 -2.67390691e+00 29 2.66438619e+01 6.06405641e+00 2.01297141e+00 | 2.66438619e+01 6.06405641e+00 2.01297141e+00 30 -1.45967559e+01 7.12051943e+00 2.37383982e+01 | -1.45967559e+01 7.12051943e+00 2.37383982e+01 31 3.94190093e-01 -1.35591812e+00 8.92909799e-02 | 3.94190093e-01 -1.35591812e+00 8.92909799e-02 32 1.40696443e+00 1.49544254e+00 -6.15354523e-01 | 1.40696443e+00 1.49544254e+00 -6.15354523e-01 33 -6.50552696e+01 -1.02094758e+02 6.53689253e+01 | -6.50552696e+01 -1.02094758e+02 6.53689253e+01 34 6.59844207e+01 7.19952004e+01 -4.07376541e+01 | 6.59844207e+01 7.19952004e+01 -4.07376541e+01 35 8.65144606e+00 9.32890727e+00 4.51719498e-01 | 8.65144606e+00 9.32890727e+00 4.51719498e-01 36 -1.42842569e-01 -3.95619998e-01 3.32252318e-01 | -1.42842569e-01 -3.95619998e-01 3.32252318e-01 37 -2.49762861e+00 7.22747083e-01 3.59042000e-01 | -2.49762861e+00 7.22747083e-01 3.59042000e-01 38 -1.93123077e+00 -3.18469502e+00 -3.82300805e+00 | -1.93123077e+00 -3.18469502e+00 -3.82300805e+00 39 4.39589212e+00 3.27157848e+00 1.40582976e+00 | 4.39589212e+00 3.27157848e+00 1.40582976e+00 40 -3.73547638e+00 -1.20217672e+00 -1.79440443e+00 | -3.73547638e+00 -1.20217672e+00 -1.79440443e+00 41 6.52777760e+00 -1.01592154e+01 -2.58407987e-01 | 6.52777760e+00 -1.01592154e+01 -2.58407987e-01 42 -3.71883267e+01 -6.60992157e+01 -2.12217892e+01 | -3.71883267e+01 -6.60992157e+01 -2.12217892e+01 43 4.01647331e+01 6.78974314e+01 1.95227553e+01 | 4.01647331e+01 6.78974314e+01 1.95227553e+01 44 -7.12525953e+00 -7.53901797e+00 -1.56190065e+00 | -7.12525953e+00 -7.53901797e+00 -1.56190065e+00 45 6.34479041e+00 8.22942445e+00 4.84306560e-01 | 6.34479041e+00 8.22942445e+00 4.84306560e-01 46 -1.09310878e+00 9.02608084e+00 3.30824987e+00 | -1.09310878e+00 9.02608084e+00 3.30824987e+00 47 -2.73965323e+00 -3.96340643e-01 2.75938429e+00 | -2.73965323e+00 -3.96340643e-01 2.75938429e+00 48 -1.55984941e+01 -1.33392767e+01 3.04199653e+00 | -1.55984941e+01 -1.33392767e+01 3.04199653e+00 49 8.86057015e+00 1.33296003e+01 -1.35651606e+01 | 8.86057015e+00 1.33296003e+01 -1.35651606e+01 50 9.83526801e-01 1.29291061e+00 4.90784382e-01 | 9.83526801e-01 1.29291061e+00 4.90784382e-01 51 -6.66057324e+00 3.50383585e+01 -4.03836007e+01 | -6.66057324e+00 3.50383585e+01 -4.03836007e+01 52 4.91083377e+00 -2.28063093e+00 8.42335680e+00 | 4.91083377e+00 -2.28063093e+00 8.42335680e+00 53 1.38563497e+00 2.54894737e-01 1.49786573e+00 | 1.38563497e+00 2.54894737e-01 1.49786573e+00 54 9.63838137e-01 -1.60037767e+00 -2.03743657e+00 | 9.63838137e-01 -1.60037767e+00 -2.03743657e+00 55 6.26334882e-01 4.25615745e-01 4.67993624e-01 | 6.26334882e-01 4.25615745e-01 4.67993624e-01 56 1.63100822e+02 -1.44235587e+02 9.23994886e+01 | 1.63100822e+02 -1.44235587e+02 9.23994886e+01 57 -1.90036189e+01 -5.15229111e+00 1.19965896e+01 | -1.90036189e+01 -5.15229111e+00 1.19965896e+01 58 2.28783794e+01 1.68422628e+00 -1.79714919e+01 | 2.28783794e+01 1.68422628e+00 -1.79714919e+01 59 -1.65042596e+00 -1.49889977e+00 4.59533471e-01 | -1.65042596e+00 -1.49889977e+00 4.59533471e-01 60 3.14999472e+00 9.66680814e-01 -1.55219299e+00 | 3.14999472e+00 9.66680814e-01 -1.55219299e+00 61 -1.41015229e+00 5.42227486e-01 -1.37323904e+00 | -1.41015229e+00 5.42227486e-01 -1.37323904e+00 62 -7.90663886e+00 -3.58245768e+01 4.07900712e+01 | -7.90663886e+00 -3.58245768e+01 4.07900712e+01 63 1.07737577e+01 3.39220190e+00 3.32285461e+00 | 1.07737577e+01 3.39220190e+00 3.32285461e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cu Fe Ni (Configuration in file "config-CuFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [37, 39, 18, 43, 38, 51, 34, 8, 7, 20, 26, 16, 49, 48, 42, 59, 11, 28, 2, 22, 9, 29, 19, 30, 53, 55, 10, 62, 17, 21, 23, 46, 33, 32, 6, 41, 40, 0, 4, 1, 36, 35, 14, 3, 45, 44, 31, 60, 13, 12, 54, 5, 56, 24, 50, 25, 52, 63, 58, 15, 47, 61, 27, 57] 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)) = 158.94662524478176 V(r_1,...,r_N) = 158.94662524478196 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 1.01548860e+00 1.02980139e+00 1.22868802e+00 | 1.01548860e+00 1.02980139e+00 1.22868802e+00 1 -2.49178149e+00 -1.65755281e+00 -2.29120013e+00 | -2.49178149e+00 -1.65755281e+00 -2.29120013e+00 2 6.76005880e-01 2.36970728e+00 -5.84341231e-01 | 6.76005880e-01 2.36970728e+00 -5.84341231e-01 3 -2.34477887e+01 3.96832794e+01 -1.17265114e+01 | -2.34477887e+01 3.96832794e+01 -1.17265114e+01 4 -3.63349079e+00 -1.42075751e+01 -3.45644209e+00 | -3.63349079e+00 -1.42075751e+01 -3.45644209e+00 5 1.01405470e+01 4.64197128e+00 1.68671065e+00 | 1.01405470e+01 4.64197128e+00 1.68671065e+00 6 -2.89590829e+01 -1.77646389e+01 -4.13749329e+01 | -2.89590829e+01 -1.77646389e+01 -4.13749329e+01 7 2.57750356e+01 1.78139490e+01 4.18671329e+01 | 2.57750356e+01 1.78139490e+01 4.18671329e+01 8 -5.33229786e+01 -7.14893047e+01 -4.13982766e+01 | -5.33229786e+01 -7.14893047e+01 -4.13982766e+01 9 9.60979800e+00 3.81229677e+01 6.59792165e+01 | 9.60979800e+00 3.81229677e+01 6.59792165e+01 10 4.43152310e+01 3.30342776e+01 -2.44336145e+01 | 4.43152310e+01 3.30342776e+01 -2.44336145e+01 11 -7.74336533e-01 3.21251279e-01 8.74123350e-01 | -7.74336533e-01 3.21251279e-01 8.74123350e-01 12 -1.49987089e+01 -1.17018638e+01 -1.62736502e+01 | -1.49987089e+01 -1.17018638e+01 -1.62736502e+01 13 1.43565707e+01 1.26237876e+01 1.62779282e+01 | 1.43565707e+01 1.26237876e+01 1.62779282e+01 14 2.22021971e+01 -4.03113827e+01 1.42053235e+01 | 2.22021971e+01 -4.03113827e+01 1.42053235e+01 15 -6.35401195e+01 -7.66034842e+01 3.32066089e+01 | -6.35401195e+01 -7.66034842e+01 3.32066089e+01 16 3.36366499e-02 -2.13142796e+00 6.33668491e-01 | 3.36366499e-02 -2.13142796e+00 6.33668491e-01 17 -5.00098654e+01 -5.97764785e+01 3.99650259e+01 | -5.00098654e+01 -5.97764785e+01 3.99650259e+01 18 5.14180439e+01 6.12389588e+01 -3.82363562e+01 | 5.14180439e+01 6.12389588e+01 -3.82363562e+01 19 -1.53802876e+01 1.28072352e+01 -3.42375609e+00 | -1.53802876e+01 1.28072352e+01 -3.42375609e+00 20 -8.32534078e-01 2.80262933e+00 -4.96043565e-01 | -8.32534078e-01 2.80262933e+00 -4.96043565e-01 21 2.26965281e+01 -7.23248038e+00 -1.66974592e+01 | 2.26965281e+01 -7.23248038e+00 -1.66974592e+01 22 1.43651124e+00 -2.40803284e-01 -1.07885565e-02 | 1.43651124e+00 -2.40803284e-01 -1.07885565e-02 23 -5.59998681e+00 1.19670990e+01 -3.43684809e+00 | -5.59998681e+00 1.19670990e+01 -3.43684809e+00 24 -5.57291015e+00 -1.04723938e+01 -8.88885334e+00 | -5.57291015e+00 -1.04723938e+01 -8.88885334e+00 25 7.32184880e+00 1.02681747e+01 6.23456271e+00 | 7.32184880e+00 1.02681747e+01 6.23456271e+00 26 1.41819793e+00 7.08857539e-01 -2.78968996e-01 | 1.41819793e+00 7.08857539e-01 -2.78968996e-01 27 3.46790657e-01 -5.45929272e-01 -2.34797403e-01 | 3.46790657e-01 -5.45929272e-01 -2.34797403e-01 28 4.72851873e+01 6.98357118e+01 -4.56524783e+01 | 4.72851873e+01 6.98357118e+01 -4.56524783e+01 29 1.55112243e+01 6.98928053e+00 7.81221068e+00 | 1.55112243e+01 6.98928053e+00 7.81221068e+00 30 1.77927020e+01 -1.15044677e+01 2.26292780e+00 | 1.77927020e+01 -1.15044677e+01 2.26292780e+00 31 -2.37210193e+00 1.22414343e+00 -5.83634067e-01 | -2.37210193e+00 1.22414343e+00 -5.83634067e-01 32 1.32895364e+00 1.53770582e+00 -7.04248263e-01 | 1.32895364e+00 1.53770582e+00 -7.04248263e-01 33 2.70488239e-01 4.83373318e-01 -1.15791352e+00 | 2.70488239e-01 4.83373318e-01 -1.15791352e+00 34 -1.30341197e+01 -8.89477389e+00 -1.31012195e+01 | -1.30341197e+01 -8.89477389e+00 -1.31012195e+01 35 8.26663741e+00 1.45983394e+01 2.19633052e+01 | 8.26663741e+00 1.45983394e+01 2.19633052e+01 36 7.24279258e-01 -2.39645113e+00 -1.11257712e+00 | 7.24279258e-01 -2.39645113e+00 -1.11257712e+00 37 -1.68333490e+01 -4.22778607e+00 9.49367270e+00 | -1.68333490e+01 -4.22778607e+00 9.49367270e+00 38 3.41929387e-02 4.58128118e-01 -3.84507021e-01 | 3.41929387e-02 4.58128118e-01 -3.84507021e-01 39 -2.97807484e+00 -8.43585099e+00 8.93021364e+00 | -2.97807484e+00 -8.43585099e+00 8.93021364e+00 40 -3.26528675e+00 -1.95679523e+00 -2.91320968e+00 | -3.26528675e+00 -1.95679523e+00 -2.91320968e+00 41 -8.05237433e+01 6.60250383e+01 -3.96794136e+01 | -8.05237433e+01 6.60250383e+01 -3.96794136e+01 42 6.28611656e-01 -2.73433890e+00 3.91182082e+00 | 6.28611656e-01 -2.73433890e+00 3.91182082e+00 43 -1.41540841e+00 -2.63928106e-02 6.48368373e-01 | -1.41540841e+00 -2.63928106e-02 6.48368373e-01 44 9.30204146e+01 -7.33314669e+01 2.91888632e+01 | 9.30204146e+01 -7.33314669e+01 2.91888632e+01 45 -7.27909882e-01 1.05897379e+00 -8.10342055e-01 | -7.27909882e-01 1.05897379e+00 -8.10342055e-01 46 5.68275608e+00 1.51553060e+01 2.55356343e+00 | 5.68275608e+00 1.51553060e+01 2.55356343e+00 47 2.30240810e+00 2.56054346e+00 5.21244681e-01 | 2.30240810e+00 2.56054346e+00 5.21244681e-01 48 -4.07801904e+01 -2.85808080e+01 -3.53541142e+01 | -4.07801904e+01 -2.85808080e+01 -3.53541142e+01 49 1.06568709e+01 -1.44117376e+01 8.99305348e+01 | 1.06568709e+01 -1.44117376e+01 8.99305348e+01 50 1.12572113e+01 3.58328905e+01 -3.30816401e+01 | 1.12572113e+01 3.58328905e+01 -3.30816401e+01 51 -5.26401503e-01 -7.22442417e-01 -8.75310656e-01 | -5.26401503e-01 -7.22442417e-01 -8.75310656e-01 52 -6.59384670e+01 -6.01685274e+01 -2.46697325e+01 | -6.59384670e+01 -6.01685274e+01 -2.46697325e+01 53 6.80788538e+01 6.82447602e+01 1.52807788e+01 | 6.80788538e+01 6.82447602e+01 1.52807788e+01 54 -1.34887259e+01 1.91445622e+00 -1.30133282e+01 | -1.34887259e+01 1.91445622e+00 -1.30133282e+01 55 1.47327724e+01 -3.25699037e+00 1.19736643e+01 | 1.47327724e+01 -3.25699037e+00 1.19736643e+01 56 -3.22254303e+01 -1.53062960e+01 -6.77509400e+00 | -3.22254303e+01 -1.53062960e+01 -6.77509400e+00 57 2.66688833e+01 1.59699103e+01 -1.11041312e+00 | 2.66688833e+01 1.59699103e+01 -1.11041312e+00 58 -8.36224944e-02 1.25628937e+00 2.26896890e+00 | -8.36224944e-02 1.25628937e+00 2.26896890e+00 59 -9.11445544e-01 -9.20052786e-01 -6.32671666e-01 | -9.11445544e-01 -9.20052786e-01 -6.32671666e-01 60 5.65282487e+00 -5.38041150e-01 6.99095994e+00 | 5.65282487e+00 -5.38041150e-01 6.99095994e+00 61 -2.92550036e-01 -8.94057984e-01 -4.97430315e-01 | -2.92550036e-01 -8.94057984e-01 -4.97430315e-01 62 -7.31769851e+01 -9.20666941e+01 -5.45173502e+00 | -7.31769851e+01 -9.20666941e+01 -5.45173502e+00 63 7.44799804e+01 9.19304894e+01 4.91376713e+00 | 7.44799804e+01 9.19304894e+01 4.91376713e+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.