!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-permutation-symmetry !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check whether a model is invariant with respect to atom permutations that preserve species, i.e. swapping any two atoms with the same species must not change the energy or forces. This must be true for all models. The check is performed for a randomly distorted non-periodic diamond cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. The energy and forces of each configuration are compared with one where each atom is randomly swapped with another atom of the same species. The energy and forces must remain unchanged. The verification check will pass if these conditions are satisfied for all configurations that the model is able to compute. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_MEAM_KimJungLee_2009_FeTiC__SM_531038274471_000 Supported species : C Fe Ti random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = C (Configuration in file "config-C.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [48, 31, 17, 30, 58, 36, 16, 27, 35, 19, 43, 12, 11, 55, 23, 21, 6, 2, 47, 9, 34, 15, 60, 14, 44, 46, 59, 7, 37, 54, 3, 1, 52, 45, 20, 8, 5, 28, 63, 61, 41, 40, 57, 10, 24, 33, 25, 18, 0, 53, 62, 56, 32, 49, 29, 13, 51, 42, 4, 26, 22, 39, 50, 38] 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)) = -209.150667138 V(r_1,...,r_N) = -209.150667138 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 4.88293684e+00 1.69693418e+00 2.29873723e+00 | 4.88293684e+00 1.69693418e+00 2.29873723e+00 1 -5.05188595e+00 -1.99316518e+00 -9.85070311e-01 | -5.05188595e+00 -1.99316518e+00 -9.85070311e-01 2 2.18586229e+00 2.22524958e+00 1.45108729e+00 | 2.18586229e+00 2.22524958e+00 1.45108729e+00 3 -9.08647545e-01 -2.80131240e+00 -5.85035564e-02 | -9.08647545e-01 -2.80131240e+00 -5.85035564e-02 4 1.75314132e+00 2.22367078e+00 -6.03378014e-01 | 1.75314132e+00 2.22367078e+00 -6.03378014e-01 5 -8.46585646e-01 -1.54042289e+00 1.71144995e+00 | -8.46585646e-01 -1.54042289e+00 1.71144995e+00 6 4.93250954e-01 7.80294184e-01 8.05038574e-01 | 4.93250954e-01 7.80294184e-01 8.05038574e-01 7 -9.59211785e-01 6.44943427e-01 -2.99894970e+00 | -9.59211785e-01 6.44943427e-01 -2.99894970e+00 8 2.08555907e+00 1.68097320e+00 2.54735366e+00 | 2.08555907e+00 1.68097320e+00 2.54735366e+00 9 -8.15022022e-01 -1.57343699e+00 -1.65767175e+00 | -8.15022022e-01 -1.57343699e+00 -1.65767175e+00 10 -6.51892688e-01 -5.89297192e-01 1.09655824e+00 | -6.51892688e-01 -5.89297192e-01 1.09655824e+00 11 3.18981316e-01 2.97324140e-01 -2.97537372e-01 | 3.18981316e-01 2.97324140e-01 -2.97537372e-01 12 -3.23411286e+00 -1.59055676e+00 -3.77226046e+00 | -3.23411286e+00 -1.59055676e+00 -3.77226046e+00 13 9.37488687e-01 1.10851155e+00 1.63210638e+00 | 9.37488687e-01 1.10851155e+00 1.63210638e+00 14 2.11404171e+00 1.14473871e+00 2.71817056e+00 | 2.11404171e+00 1.14473871e+00 2.71817056e+00 15 -1.41865007e+00 -2.40892015e+00 -2.35029533e+00 | -1.41865007e+00 -2.40892015e+00 -2.35029533e+00 16 4.04474828e+00 2.56899103e+00 3.32382093e+00 | 4.04474828e+00 2.56899103e+00 3.32382093e+00 17 -2.47327940e+00 3.74905826e-01 -5.16792214e+00 | -2.47327940e+00 3.74905826e-01 -5.16792214e+00 18 -7.30056900e-01 -2.44630095e+00 2.98606603e+00 | -7.30056900e-01 -2.44630095e+00 2.98606603e+00 19 -2.86964759e+00 1.42835223e+00 -2.17033292e+00 | -2.86964759e+00 1.42835223e+00 -2.17033292e+00 20 3.26848313e+00 -6.27539436e+00 -3.73843166e+00 | 3.26848313e+00 -6.27539436e+00 -3.73843166e+00 21 -7.62729429e+00 1.14932216e+00 3.78915576e+00 | -7.62729429e+00 1.14932216e+00 3.78915576e+00 22 -1.28443159e+00 -4.53316034e-01 -3.35047983e+00 | -1.28443159e+00 -4.53316034e-01 -3.35047983e+00 23 2.84077755e+00 -2.13533090e+00 4.45468051e+00 | 2.84077755e+00 -2.13533090e+00 4.45468051e+00 24 2.03526235e+00 1.22889347e+00 3.36751017e+00 | 2.03526235e+00 1.22889347e+00 3.36751017e+00 25 -2.27642370e+00 -2.20642059e-01 -3.58783880e+00 | -2.27642370e+00 -2.20642059e-01 -3.58783880e+00 26 4.15076765e+00 -3.39869524e-01 4.63563356e+00 | 4.15076765e+00 -3.39869524e-01 4.63563356e+00 27 -4.62248328e+00 -1.34266222e+00 -3.09573928e+00 | -4.62248328e+00 -1.34266222e+00 -3.09573928e+00 28 1.31392922e+00 3.86956740e+00 1.46107691e+00 | 1.31392922e+00 3.86956740e+00 1.46107691e+00 29 -3.06747201e+00 -1.93307317e+00 -1.89743337e+00 | -3.06747201e+00 -1.93307317e+00 -1.89743337e+00 30 4.97096772e+00 -3.19463531e+00 4.50232740e+00 | 4.97096772e+00 -3.19463531e+00 4.50232740e+00 31 -2.20153708e+00 3.47043262e-01 -2.91231893e+00 | -2.20153708e+00 3.47043262e-01 -2.91231893e+00 32 3.04739212e+00 2.85100778e+00 3.24158828e+00 | 3.04739212e+00 2.85100778e+00 3.24158828e+00 33 -9.26005299e-01 -4.18497660e+00 -9.87882255e-01 | -9.26005299e-01 -4.18497660e+00 -9.87882255e-01 34 -2.98507219e-02 5.67754924e-01 2.62578105e+00 | -2.98507219e-02 5.67754924e-01 2.62578105e+00 35 1.46018832e+00 1.70302413e+00 -1.83302934e+00 | 1.46018832e+00 1.70302413e+00 -1.83302934e+00 36 -8.89250796e-01 2.47781818e+00 -2.27182657e+00 | -8.89250796e-01 2.47781818e+00 -2.27182657e+00 37 -2.32708899e+00 -2.13411359e+00 8.64170663e-02 | -2.32708899e+00 -2.13411359e+00 8.64170663e-02 38 1.07516884e+00 8.58937140e-01 1.27329969e+00 | 1.07516884e+00 8.58937140e-01 1.27329969e+00 39 -1.94181067e-01 4.31021418e-01 -1.52619858e+00 | -1.94181067e-01 4.31021418e-01 -1.52619858e+00 40 -1.40682158e-02 2.05620842e+00 -3.05849185e+00 | -1.40682158e-02 2.05620842e+00 -3.05849185e+00 41 -4.44538539e+00 2.45291443e+00 1.44249669e-01 | -4.44538539e+00 2.45291443e+00 1.44249669e-01 42 -1.14297892e-01 -3.12472688e-01 2.54246224e-01 | -1.14297892e-01 -3.12472688e-01 2.54246224e-01 43 -1.69511571e+00 6.25861622e-01 1.01411994e+00 | -1.69511571e+00 6.25861622e-01 1.01411994e+00 44 4.33306457e+00 -9.50563783e-01 2.37787226e+00 | 4.33306457e+00 -9.50563783e-01 2.37787226e+00 45 -1.31222182e+00 -1.13924419e+00 -1.83727060e+00 | -1.31222182e+00 -1.13924419e+00 -1.83727060e+00 46 3.69680950e+00 4.50033567e+00 -2.51182963e+00 | 3.69680950e+00 4.50033567e+00 -2.51182963e+00 47 -1.42700606e+00 2.89811172e-01 -1.16733805e+00 | -1.42700606e+00 2.89811172e-01 -1.16733805e+00 48 2.39204717e+00 -6.32800164e-01 -7.62144561e-01 | 2.39204717e+00 -6.32800164e-01 -7.62144561e-01 49 -7.54892208e-01 1.49141094e+00 -1.33566594e+00 | -7.54892208e-01 1.49141094e+00 -1.33566594e+00 50 2.30370641e-01 4.92837245e+00 4.18492964e+00 | 2.30370641e-01 4.92837245e+00 4.18492964e+00 51 -1.74656125e-01 -5.51848914e-01 -5.05285163e-01 | -1.74656125e-01 -5.51848914e-01 -5.05285163e-01 52 1.88619143e+00 -1.52867155e+00 2.19781675e+00 | 1.88619143e+00 -1.52867155e+00 2.19781675e+00 53 -8.69912314e-01 -5.69961384e-01 -1.81597688e+00 | -8.69912314e-01 -5.69961384e-01 -1.81597688e+00 54 5.60124216e+00 5.17213369e-01 1.51015468e+00 | 5.60124216e+00 5.17213369e-01 1.51015468e+00 55 -4.67991025e+00 -1.55682523e+00 -2.55723101e+00 | -4.67991025e+00 -1.55682523e+00 -2.55723101e+00 56 2.78268560e+00 8.81149950e-01 -8.63778153e-01 | 2.78268560e+00 8.81149950e-01 -8.63778153e-01 57 -1.41331411e+00 -1.50861285e+00 3.43150895e+00 | -1.41331411e+00 -1.50861285e+00 3.43150895e+00 58 1.88958831e+00 -1.21531449e+00 1.45242481e+00 | 1.88958831e+00 -1.21531449e+00 1.45242481e+00 59 -1.96924747e+00 -6.78417744e-01 -9.27655883e-02 | -1.96924747e+00 -6.78417744e-01 -9.27655883e-02 60 1.51365270e+00 1.57993186e+00 1.84395240e+00 | 1.51365270e+00 1.57993186e+00 1.84395240e+00 61 -2.86229009e+00 -1.64769508e+00 -3.50212550e+00 | -2.86229009e+00 -1.64769508e+00 -3.50212550e+00 62 -6.69530145e-01 -1.94621641e-01 -1.37582457e+00 | -6.69530145e-01 -1.94621641e-01 -1.37582457e+00 63 5.02259617e-01 -1.33801261e+00 -1.77030690e+00 | 5.02259617e-01 -1.33801261e+00 -1.77030690e+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 = [43, 60, 3, 2, 13, 24, 52, 48, 49, 31, 58, 17, 62, 4, 16, 22, 14, 11, 51, 53, 45, 30, 15, 57, 5, 40, 32, 29, 63, 27, 21, 9, 26, 34, 33, 38, 42, 59, 35, 56, 25, 55, 36, 0, 50, 20, 54, 61, 7, 8, 44, 18, 6, 19, 46, 41, 39, 23, 10, 37, 1, 47, 12, 28] 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)) = -15.9080259137 V(r_1,...,r_N) = -15.9080259137 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 -2.08640935e-01 -3.09103084e-01 -4.54989930e-01 | -2.08640935e-01 -3.09103084e-01 -4.54989930e-01 1 -2.38379382e+01 -1.38491916e+01 2.09693303e+01 | -2.38379382e+01 -1.38491916e+01 2.09693303e+01 2 2.55150988e+01 1.33835056e+01 -2.15394635e+01 | 2.55150988e+01 1.33835056e+01 -2.15394635e+01 3 1.56932891e+00 -4.30975773e+00 -1.38797365e+00 | 1.56932891e+00 -4.30975773e+00 -1.38797365e+00 4 2.67919929e-01 7.92625341e-01 3.49569251e-01 | 2.67919929e-01 7.92625341e-01 3.49569251e-01 5 -2.94192888e-01 1.63132525e-01 2.62286705e+00 | -2.94192888e-01 1.63132525e-01 2.62286705e+00 6 -2.83392362e+00 -5.58133366e+00 -7.74880806e+00 | -2.83392362e+00 -5.58133366e+00 -7.74880806e+00 7 2.91602892e+00 -4.65259168e-02 6.41728244e+00 | 2.91602892e+00 -4.65259168e-02 6.41728244e+00 8 -2.81208828e+00 -2.16605711e+00 -1.55855727e+00 | -2.81208828e+00 -2.16605711e+00 -1.55855727e+00 9 1.02472344e+01 -5.23843671e+00 -3.24199251e+00 | 1.02472344e+01 -5.23843671e+00 -3.24199251e+00 10 -3.19570653e-01 -5.79594533e-01 -3.40872407e-01 | -3.19570653e-01 -5.79594533e-01 -3.40872407e-01 11 1.05168731e+00 -1.40002478e+00 1.83130507e-01 | 1.05168731e+00 -1.40002478e+00 1.83130507e-01 12 1.16509834e-01 -2.79904565e+00 -2.07651368e+00 | 1.16509834e-01 -2.79904565e+00 -2.07651368e+00 13 3.79380458e+01 -1.95493662e+01 -6.42790477e+00 | 3.79380458e+01 -1.95493662e+01 -6.42790477e+00 14 -9.24696295e+00 1.00359986e+01 2.39406274e+00 | -9.24696295e+00 1.00359986e+01 2.39406274e+00 15 7.18105354e+00 -5.33482957e+00 -6.54978964e+00 | 7.18105354e+00 -5.33482957e+00 -6.54978964e+00 16 -5.98342570e+00 -6.70799762e+00 -1.25402839e+01 | -5.98342570e+00 -6.70799762e+00 -1.25402839e+01 17 -6.84711984e+00 1.09776971e+01 5.16342616e+00 | -6.84711984e+00 1.09776971e+01 5.16342616e+00 18 3.75988288e+00 4.98423370e+00 -4.13764560e+00 | 3.75988288e+00 4.98423370e+00 -4.13764560e+00 19 -4.51788235e+00 3.49513267e+00 -2.19729004e+00 | -4.51788235e+00 3.49513267e+00 -2.19729004e+00 20 2.89328934e+00 -1.97382314e+01 1.37494687e+01 | 2.89328934e+00 -1.97382314e+01 1.37494687e+01 21 5.84412640e+00 8.14438358e+00 6.13048411e+00 | 5.84412640e+00 8.14438358e+00 6.13048411e+00 22 -6.07526426e+00 4.03650479e+00 3.50307512e-01 | -6.07526426e+00 4.03650479e+00 3.50307512e-01 23 -8.04988848e+00 1.11010135e+00 -1.41980422e+01 | -8.04988848e+00 1.11010135e+00 -1.41980422e+01 24 4.14102654e+00 2.91895916e-01 -3.90271257e+00 | 4.14102654e+00 2.91895916e-01 -3.90271257e+00 25 3.59167080e+00 -8.71902711e+00 -1.75172560e+01 | 3.59167080e+00 -8.71902711e+00 -1.75172560e+01 26 -1.02504523e+02 -8.59926969e+01 -2.11825383e+01 | -1.02504523e+02 -8.59926969e+01 -2.11825383e+01 27 1.02182772e+02 8.55976830e+01 2.16084436e+01 | 1.02182772e+02 8.55976830e+01 2.16084436e+01 28 6.80209357e+00 -7.67157684e+00 5.96733501e+00 | 6.80209357e+00 -7.67157684e+00 5.96733501e+00 29 2.48895650e+00 -4.17656869e-01 -2.59151571e+00 | 2.48895650e+00 -4.17656869e-01 -2.59151571e+00 30 -8.66500741e+00 1.33795831e+01 9.92613744e+00 | -8.66500741e+00 1.33795831e+01 9.92613744e+00 31 -5.71763959e+00 6.69462677e+00 -8.30874313e-01 | -5.71763959e+00 6.69462677e+00 -8.30874313e-01 32 -3.13622086e+00 -1.72312049e+00 -4.04363710e+00 | -3.13622086e+00 -1.72312049e+00 -4.04363710e+00 33 2.16565366e+00 3.02170442e+00 2.69937309e+00 | 2.16565366e+00 3.02170442e+00 2.69937309e+00 34 -1.89756429e+01 -2.15866780e+01 5.72450857e-01 | -1.89756429e+01 -2.15866780e+01 5.72450857e-01 35 1.81513701e+01 2.25392052e+01 -3.57939726e-01 | 1.81513701e+01 2.25392052e+01 -3.57939726e-01 36 1.50419967e+00 -9.27972798e-01 1.41972335e+00 | 1.50419967e+00 -9.27972798e-01 1.41972335e+00 37 -1.23719309e+00 -3.97925494e-01 -4.50584169e-01 | -1.23719309e+00 -3.97925494e-01 -4.50584169e-01 38 -5.73930290e+00 -4.62937665e+00 -5.82657954e+00 | -5.73930290e+00 -4.62937665e+00 -5.82657954e+00 39 6.78366193e+00 4.44419721e+00 4.71255469e+00 | 6.78366193e+00 4.44419721e+00 4.71255469e+00 40 5.36117427e-01 6.63806387e-01 -2.27965172e-01 | 5.36117427e-01 6.63806387e-01 -2.27965172e-01 41 1.55137379e+00 -7.40679135e-01 1.03468694e-01 | 1.55137379e+00 -7.40679135e-01 1.03468694e-01 42 -3.42079889e+01 1.76939561e+01 1.00013983e+01 | -3.42079889e+01 1.76939561e+01 1.00013983e+01 43 -6.16890405e-01 -3.88354115e-01 4.87517621e-01 | -6.16890405e-01 -3.88354115e-01 4.87517621e-01 44 -2.25328007e-01 1.12568916e+00 -4.34790859e-01 | -2.25328007e-01 1.12568916e+00 -4.34790859e-01 45 -8.37861429e-01 6.88963630e-02 -7.44031957e-01 | -8.37861429e-01 6.88963630e-02 -7.44031957e-01 46 -3.57687867e-01 2.06421898e+00 -5.46100698e-01 | -3.57687867e-01 2.06421898e+00 -5.46100698e-01 47 -1.19349310e+00 -1.75050430e+00 1.42088254e+00 | -1.19349310e+00 -1.75050430e+00 1.42088254e+00 48 -2.99298981e-01 6.00583190e+00 2.12134015e+00 | -2.99298981e-01 6.00583190e+00 2.12134015e+00 49 -3.24846497e+00 -1.81622026e+00 2.46039815e+00 | -3.24846497e+00 -1.81622026e+00 2.46039815e+00 50 1.06181338e+01 4.84800171e+00 7.24216541e+00 | 1.06181338e+01 4.84800171e+00 7.24216541e+00 51 -5.74378629e+00 4.98206571e+00 -3.43459129e+00 | -5.74378629e+00 4.98206571e+00 -3.43459129e+00 52 2.38243366e+00 -3.49478476e+00 5.09433984e+00 | 2.38243366e+00 -3.49478476e+00 5.09433984e+00 53 -3.71042313e+00 -4.86319156e+00 8.08417823e+00 | -3.71042313e+00 -4.86319156e+00 8.08417823e+00 54 -2.82620653e+01 -3.42491938e+01 -2.80942767e+01 | -2.82620653e+01 -3.42491938e+01 -2.80942767e+01 55 2.90768898e+01 3.35884435e+01 2.76956563e+01 | 2.90768898e+01 3.35884435e+01 2.76956563e+01 56 -9.21664356e+00 9.28736344e+00 5.32955611e+00 | -9.21664356e+00 9.28736344e+00 5.32955611e+00 57 -6.16872247e+00 1.01486512e+00 -2.69369391e+00 | -6.16872247e+00 1.01486512e+00 -2.69369391e+00 58 4.80884813e+00 -5.72979192e+00 4.97696906e+00 | 4.80884813e+00 -5.72979192e+00 4.97696906e+00 59 1.13618857e+00 1.63527120e+00 7.16792267e-02 | 1.13618857e+00 1.63527120e+00 7.16792267e-02 60 3.28205163e+00 -6.07999569e+00 -4.07954280e+00 | 3.28205163e+00 -6.07999569e+00 -4.07954280e+00 61 2.36663252e+00 3.74691087e+00 6.21360102e+00 | 2.36663252e+00 3.74691087e+00 6.21360102e+00 62 3.53084952e+00 -7.76712445e+00 -1.29352978e+01 | 3.53084952e+00 -7.76712445e+00 -1.29352978e+01 63 4.68995273e+00 6.73783548e+00 7.75495840e+00 | 4.68995273e+00 6.73783548e+00 7.75495840e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ti (Configuration in file "config-Ti.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [26, 41, 55, 33, 44, 43, 42, 30, 23, 14, 59, 52, 47, 51, 9, 28, 22, 40, 38, 50, 60, 36, 16, 8, 37, 56, 0, 61, 15, 49, 7, 53, 62, 3, 63, 58, 21, 24, 18, 48, 17, 1, 6, 5, 4, 46, 45, 12, 39, 29, 19, 13, 11, 31, 57, 2, 25, 54, 35, 10, 20, 27, 32, 34] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -25.3604536953 V(r_1,...,r_N) = -25.3604536953 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 -2.76912055e-01 -8.48399814e-01 -6.94591633e-01 | -2.76912055e-01 -8.48399814e-01 -6.94591633e-01 1 5.89483475e+00 -4.01156477e+00 -2.94735975e+00 | 5.89483475e+00 -4.01156477e+00 -2.94735975e+00 2 -3.44353713e+00 4.42789054e-01 -5.61460618e+00 | -3.44353713e+00 4.42789054e-01 -5.61460618e+00 3 7.14046725e+00 -1.02236225e+01 -4.33163763e+00 | 7.14046725e+00 -1.02236225e+01 -4.33163763e+00 4 -6.46344414e+00 -1.80249011e+01 -9.40236278e+00 | -6.46344414e+00 -1.80249011e+01 -9.40236278e+00 5 5.47970460e+00 1.85712139e+01 7.64363201e+00 | 5.47970460e+00 1.85712139e+01 7.64363201e+00 6 -1.01394836e+01 2.70367038e-01 1.02501179e+00 | -1.01394836e+01 2.70367038e-01 1.02501179e+00 7 8.70054501e-01 2.93631395e+00 3.34405171e+00 | 8.70054501e-01 2.93631395e+00 3.34405171e+00 8 -1.10273858e+01 -4.59389626e+00 -3.42830894e-01 | -1.10273858e+01 -4.59389626e+00 -3.42830894e-01 9 -7.53184944e+00 -1.76564369e+01 1.25157402e+01 | -7.53184944e+00 -1.76564369e+01 1.25157402e+01 10 1.84642999e+01 2.13755941e+01 -1.43579495e+01 | 1.84642999e+01 2.13755941e+01 -1.43579495e+01 11 3.53083091e+00 -2.79694433e+00 -1.48833458e+00 | 3.53083091e+00 -2.79694433e+00 -1.48833458e+00 12 -6.16731964e-01 -1.05912175e-01 1.63985193e+00 | -6.16731964e-01 -1.05912175e-01 1.63985193e+00 13 1.60362817e+00 -2.23694424e+00 -3.12038850e+00 | 1.60362817e+00 -2.23694424e+00 -3.12038850e+00 14 -1.86677711e+00 2.75072440e+00 3.83775470e-01 | -1.86677711e+00 2.75072440e+00 3.83775470e-01 15 7.58509086e+00 1.25581089e+00 -3.61707928e+00 | 7.58509086e+00 1.25581089e+00 -3.61707928e+00 16 9.90049527e-01 -6.46716962e-01 6.50899028e-01 | 9.90049527e-01 -6.46716962e-01 6.50899028e-01 17 -2.83383438e+00 -1.32714543e+01 1.26832516e+01 | -2.83383438e+00 -1.32714543e+01 1.26832516e+01 18 5.86437920e+00 1.10202260e+01 -1.56795359e+01 | 5.86437920e+00 1.10202260e+01 -1.56795359e+01 19 -1.02427118e+01 2.31664980e+01 -6.46578191e+00 | -1.02427118e+01 2.31664980e+01 -6.46578191e+00 20 -5.43414450e+00 7.14617040e+00 9.48745649e+00 | -5.43414450e+00 7.14617040e+00 9.48745649e+00 21 -2.36621732e+00 -2.45582943e+00 5.57361605e+00 | -2.36621732e+00 -2.45582943e+00 5.57361605e+00 22 -4.42347293e+00 -9.71602648e-02 2.22118263e+00 | -4.42347293e+00 -9.71602648e-02 2.22118263e+00 23 5.35356258e-01 -2.88649125e-01 -7.57547587e-01 | 5.35356258e-01 -2.88649125e-01 -7.57547587e-01 24 -7.36142566e+00 -7.41681194e+00 -5.69226007e+00 | -7.36142566e+00 -7.41681194e+00 -5.69226007e+00 25 2.01384795e+00 8.79596164e+00 -4.11525134e+00 | 2.01384795e+00 8.79596164e+00 -4.11525134e+00 26 3.69834940e+00 4.14205208e+00 -3.79422331e+00 | 3.69834940e+00 4.14205208e+00 -3.79422331e+00 27 -8.37537827e-01 -7.99072117e-01 4.56782241e-01 | -8.37537827e-01 -7.99072117e-01 4.56782241e-01 28 4.58775483e+00 -5.32985373e+00 1.10842022e+01 | 4.58775483e+00 -5.32985373e+00 1.10842022e+01 29 1.52274365e-01 -1.91101223e+00 -6.62966894e-02 | 1.52274365e-01 -1.91101223e+00 -6.62966894e-02 30 1.00007635e+01 -1.40449428e+01 2.79972763e+00 | 1.00007635e+01 -1.40449428e+01 2.79972763e+00 31 -5.88777687e-01 9.75832020e-01 -1.80860935e+00 | -5.88777687e-01 9.75832020e-01 -1.80860935e+00 32 -1.42218528e+01 -1.00634739e+01 -1.61425859e+01 | -1.42218528e+01 -1.00634739e+01 -1.61425859e+01 33 1.43239995e+01 9.84619285e+00 1.62768093e+01 | 1.43239995e+01 9.84619285e+00 1.62768093e+01 34 -1.89674950e+01 -2.14136540e+01 -1.79103301e+01 | -1.89674950e+01 -2.14136540e+01 -1.79103301e+01 35 8.24093626e+00 -2.15821435e+00 1.70169955e+01 | 8.24093626e+00 -2.15821435e+00 1.70169955e+01 36 -2.07526672e-01 -3.56196859e-01 -3.01115624e-01 | -2.07526672e-01 -3.56196859e-01 -3.01115624e-01 37 -1.11208030e+01 -8.67391510e+00 1.02104817e+01 | -1.11208030e+01 -8.67391510e+00 1.02104817e+01 38 1.91062559e-01 -1.52930216e+00 -2.05416275e+00 | 1.91062559e-01 -1.52930216e+00 -2.05416275e+00 39 4.78362735e-01 2.09418917e+00 1.13407993e+00 | 4.78362735e-01 2.09418917e+00 1.13407993e+00 40 -8.50164610e+00 -7.51611842e+00 -2.49796894e+00 | -8.50164610e+00 -7.51611842e+00 -2.49796894e+00 41 5.22137338e+00 8.75402107e+00 1.33205796e+00 | 5.22137338e+00 8.75402107e+00 1.33205796e+00 42 -7.62491540e+00 -1.16424984e+00 -1.61498680e+00 | -7.62491540e+00 -1.16424984e+00 -1.61498680e+00 43 8.15722522e+00 6.54542635e+00 5.03747610e+00 | 8.15722522e+00 6.54542635e+00 5.03747610e+00 44 1.53830505e+00 -2.85432308e+00 2.34995679e+00 | 1.53830505e+00 -2.85432308e+00 2.34995679e+00 45 -5.78506428e-01 9.91207099e-01 -7.17207198e-01 | -5.78506428e-01 9.91207099e-01 -7.17207198e-01 46 1.08773103e+01 9.38754598e+00 -7.05544408e+00 | 1.08773103e+01 9.38754598e+00 -7.05544408e+00 47 -6.95065449e+00 -1.24060460e+01 4.92033333e+00 | -6.95065449e+00 -1.24060460e+01 4.92033333e+00 48 -1.99193600e+00 1.01466524e-01 -4.30565510e+00 | -1.99193600e+00 1.01466524e-01 -4.30565510e+00 49 -2.39082898e-01 -3.18710498e+00 4.21771561e-02 | -2.39082898e-01 -3.18710498e+00 4.21771561e-02 50 -1.28214689e+01 -9.67798235e+00 -8.64700705e+00 | -1.28214689e+01 -9.67798235e+00 -8.64700705e+00 51 1.30591999e+01 1.26881453e+01 7.76986576e+00 | 1.30591999e+01 1.26881453e+01 7.76986576e+00 52 -2.90682414e+00 3.52885352e+00 1.49763990e+01 | -2.90682414e+00 3.52885352e+00 1.49763990e+01 53 -4.85221387e+00 -6.66738499e+00 1.15238025e+01 | -4.85221387e+00 -6.66738499e+00 1.15238025e+01 54 -5.19169904e+00 -1.01295520e+01 -1.34669161e+01 | -5.19169904e+00 -1.01295520e+01 -1.34669161e+01 55 4.54873829e+00 1.16081546e+01 1.57538288e+01 | 4.54873829e+00 1.16081546e+01 1.57538288e+01 56 7.08645468e+00 1.90430828e+01 -7.49614817e+00 | 7.08645468e+00 1.90430828e+01 -7.49614817e+00 57 3.34218278e+00 -9.84371738e+00 -7.39015919e+00 | 3.34218278e+00 -9.84371738e+00 -7.39015919e+00 58 1.18595240e-01 2.91317837e+00 -2.07087155e+00 | 1.18595240e-01 2.91317837e+00 -2.07087155e+00 59 5.27613363e+00 4.58603725e+00 2.81175119e+00 | 5.27613363e+00 4.58603725e+00 2.81175119e+00 60 2.39887985e+00 8.44115775e+00 -5.28589936e+00 | 2.39887985e+00 8.44115775e+00 -5.28589936e+00 61 3.77293363e+00 4.80223591e+00 3.90081630e+00 | 3.77293363e+00 4.80223591e+00 3.90081630e+00 62 2.06281559e+00 4.84780850e+00 -6.12443539e+00 | 2.06281559e+00 4.84780850e+00 -6.12443539e+00 63 2.52467340e+00 1.37310410e+00 8.11527901e-01 | 2.52467340e+00 1.37310410e+00 8.11527901e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = C Fe Ti (Configuration in file "config-CFeTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [31, 40, 60, 51, 6, 25, 4, 28, 50, 10, 9, 45, 27, 43, 29, 20, 57, 58, 35, 33, 15, 23, 36, 21, 37, 5, 32, 12, 7, 14, 59, 0, 26, 19, 44, 18, 22, 24, 39, 38, 1, 47, 46, 13, 34, 11, 42, 41, 55, 49, 8, 3, 61, 63, 54, 48, 62, 16, 17, 30, 2, 52, 56, 53] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -149.790429354 V(r_1,...,r_N) = -149.790429354 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 -3.41115343e-01 -6.93230880e-02 -3.50783275e-01 | -3.41115343e-01 -6.93230880e-02 -3.50783275e-01 1 -1.63851839e+00 -2.71521520e+00 5.73139468e+00 | -1.63851839e+00 -2.71521520e+00 5.73139468e+00 2 2.55956482e+00 1.74608617e+00 -3.19736575e+00 | 2.55956482e+00 1.74608617e+00 -3.19736575e+00 3 2.24952465e+00 -1.12267172e+00 3.61368617e+00 | 2.24952465e+00 -1.12267172e+00 3.61368617e+00 4 3.22738127e-01 2.27021085e+00 -1.28615916e-01 | 3.22738127e-01 2.27021085e+00 -1.28615916e-01 5 -2.62333283e+01 1.40604899e+00 -3.02079514e+01 | -2.62333283e+01 1.40604899e+00 -3.02079514e+01 6 7.93199402e-01 -7.35844164e-01 3.54423827e-01 | 7.93199402e-01 -7.35844164e-01 3.54423827e-01 7 -2.31207118e+01 -2.39948391e+01 2.99148148e+01 | -2.31207118e+01 -2.39948391e+01 2.99148148e+01 8 7.29119861e-01 1.09803120e+00 8.77090038e-01 | 7.29119861e-01 1.09803120e+00 8.77090038e-01 9 -5.88436015e+00 -2.95140904e+00 2.90835535e+00 | -5.88436015e+00 -2.95140904e+00 2.90835535e+00 10 2.45849508e+00 2.66160939e+00 -3.56146095e+00 | 2.45849508e+00 2.66160939e+00 -3.56146095e+00 11 1.01129588e+00 -1.10323044e+00 1.31807468e+00 | 1.01129588e+00 -1.10323044e+00 1.31807468e+00 12 -2.68277832e+00 -2.34044801e+00 -1.73318534e+00 | -2.68277832e+00 -2.34044801e+00 -1.73318534e+00 13 2.33559615e+00 4.49986181e+00 2.91130135e+00 | 2.33559615e+00 4.49986181e+00 2.91130135e+00 14 -2.49950039e+00 -4.53603146e-01 -2.54908900e+00 | -2.49950039e+00 -4.53603146e-01 -2.54908900e+00 15 -6.30613344e-01 5.78039615e+00 -2.20994505e+00 | -6.30613344e-01 5.78039615e+00 -2.20994505e+00 16 -6.55281074e+00 -1.35093117e+01 -9.77140976e+00 | -6.55281074e+00 -1.35093117e+01 -9.77140976e+00 17 7.41888704e+00 1.13436039e+01 1.12698621e+01 | 7.41888704e+00 1.13436039e+01 1.12698621e+01 18 -3.97329261e-02 1.27083557e+00 1.90523644e+00 | -3.97329261e-02 1.27083557e+00 1.90523644e+00 19 6.01020857e-01 -1.43502560e+00 -7.84664732e-01 | 6.01020857e-01 -1.43502560e+00 -7.84664732e-01 20 2.32806973e+01 2.34747193e+01 -3.09860598e+01 | 2.32806973e+01 2.34747193e+01 -3.09860598e+01 21 3.35152358e+01 -2.42015991e+01 -2.27655309e+01 | 3.35152358e+01 -2.42015991e+01 -2.27655309e+01 22 1.44285422e+00 4.36257950e-01 -6.01445930e-01 | 1.44285422e+00 4.36257950e-01 -6.01445930e-01 23 -1.16020778e+00 -4.20211006e-01 -9.49130993e-02 | -1.16020778e+00 -4.20211006e-01 -9.49130993e-02 24 -3.12605997e+00 -1.09511314e+00 -1.22841547e+00 | -3.12605997e+00 -1.09511314e+00 -1.22841547e+00 25 3.65372798e+00 -1.20708257e+00 3.66102369e+00 | 3.65372798e+00 -1.20708257e+00 3.66102369e+00 26 -7.24594411e+00 3.27619993e+00 -9.29492214e+00 | -7.24594411e+00 3.27619993e+00 -9.29492214e+00 27 5.89727300e+00 -2.94336709e+00 1.00539375e+01 | 5.89727300e+00 -2.94336709e+00 1.00539375e+01 28 -3.00488710e+00 -4.35670700e-01 6.42252092e-01 | -3.00488710e+00 -4.35670700e-01 6.42252092e-01 29 5.69893062e-01 6.77786354e-01 -5.38278430e-01 | 5.69893062e-01 6.77786354e-01 -5.38278430e-01 30 -2.45482265e+00 -5.26800995e+00 -4.78564649e+00 | -2.45482265e+00 -5.26800995e+00 -4.78564649e+00 31 2.91803719e+00 3.95743782e+00 5.84284950e+00 | 2.91803719e+00 3.95743782e+00 5.84284950e+00 32 -1.85249972e+00 -2.46305915e+00 -4.65442046e+00 | -1.85249972e+00 -2.46305915e+00 -4.65442046e+00 33 3.09767570e+00 1.72116846e-01 2.25042014e+00 | 3.09767570e+00 1.72116846e-01 2.25042014e+00 34 1.58862203e+00 2.69363470e+00 6.34343642e-01 | 1.58862203e+00 2.69363470e+00 6.34343642e-01 35 4.32637986e+00 -2.80550228e+00 -2.28390375e-01 | 4.32637986e+00 -2.80550228e+00 -2.28390375e-01 36 -1.62474523e+00 1.15007954e+00 6.62673364e-01 | -1.62474523e+00 1.15007954e+00 6.62673364e-01 37 -1.43084728e+00 -3.24134437e-01 -1.20300507e-01 | -1.43084728e+00 -3.24134437e-01 -1.20300507e-01 38 -1.23766109e+01 -3.89295390e+00 -8.78777014e+00 | -1.23766109e+01 -3.89295390e+00 -8.78777014e+00 39 5.89247737e+00 1.80057650e+00 1.72615304e+01 | 5.89247737e+00 1.80057650e+00 1.72615304e+01 40 2.53613967e+00 -1.81889896e+01 1.46856584e+01 | 2.53613967e+00 -1.81889896e+01 1.46856584e+01 41 2.68067174e+01 1.86256548e+01 1.22833217e+01 | 2.68067174e+01 1.86256548e+01 1.22833217e+01 42 7.67281012e-01 -4.13415833e+00 6.20478025e-01 | 7.67281012e-01 -4.13415833e+00 6.20478025e-01 43 -2.58014383e+00 -1.11775631e+00 -5.62810901e-01 | -2.58014383e+00 -1.11775631e+00 -5.62810901e-01 44 1.21238140e-01 6.80619494e-01 -8.91628555e-02 | 1.21238140e-01 6.80619494e-01 -8.91628555e-02 45 -2.26221027e+00 5.84734142e-01 -4.87021094e-01 | -2.26221027e+00 5.84734142e-01 -4.87021094e-01 46 8.90137463e-01 2.02853062e+00 -1.33539166e+00 | 8.90137463e-01 2.02853062e+00 -1.33539166e+00 47 4.86019555e-02 2.12831163e+00 -3.07157346e+00 | 4.86019555e-02 2.12831163e+00 -3.07157346e+00 48 1.00554784e+00 9.07721952e-01 1.70332349e+00 | 1.00554784e+00 9.07721952e-01 1.70332349e+00 49 1.43199266e+00 -1.64367888e-01 2.20473928e-01 | 1.43199266e+00 -1.64367888e-01 2.20473928e-01 50 -3.49822443e+01 2.29712085e+01 2.19209276e+01 | -3.49822443e+01 2.29712085e+01 2.19209276e+01 51 1.58075498e+00 -1.26014942e+00 1.52338226e+00 | 1.58075498e+00 -1.26014942e+00 1.52338226e+00 52 2.29218415e+00 6.33851398e+00 -7.93170302e+00 | 2.29218415e+00 6.33851398e+00 -7.93170302e+00 53 -2.80510399e+00 -2.53728224e+00 9.36601205e-01 | -2.80510399e+00 -2.53728224e+00 9.36601205e-01 54 -5.40155406e+00 -1.82890058e+01 -1.02824590e+01 | -5.40155406e+00 -1.82890058e+01 -1.02824590e+01 55 6.61841315e+00 1.72383381e+01 9.75302841e+00 | 6.61841315e+00 1.72383381e+01 9.75302841e+00 56 3.01183188e+00 1.79272008e+00 2.57403909e+00 | 3.01183188e+00 1.79272008e+00 2.57403909e+00 57 -7.95519134e-01 1.88433888e+00 -1.54565733e+00 | -7.95519134e-01 1.88433888e+00 -1.54565733e+00 58 -3.48331042e+01 -4.35345731e+01 -2.57255711e+01 | -3.48331042e+01 -4.35345731e+01 -2.57255711e+01 59 3.25824139e+01 4.22062267e+01 2.65020250e+01 | 3.25824139e+01 4.22062267e+01 2.65020250e+01 60 1.27801286e+00 -3.49607004e+00 1.67225936e+00 | 1.27801286e+00 -3.49607004e+00 1.67225936e+00 61 -1.55750307e+00 6.79394607e-02 -1.82020809e+00 | -1.55750307e+00 6.79394607e-02 -1.82020809e+00 62 -7.92545663e-01 -5.03054969e+00 -9.65035525e+00 | -7.92545663e-01 -5.03054969e+00 -9.65035525e+00 63 2.27644045e+00 6.07017557e+00 4.87369032e+00 | 2.27644045e+00 6.07017557e+00 4.87369032e+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.