!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_KimJungLee_2009_FeTiC__MO_110119204723_001 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 = [61, 27, 18, 12, 36, 46, 44, 40, 22, 38, 49, 26, 3, 14, 13, 62, 19, 58, 2, 16, 34, 28, 8, 29, 53, 33, 11, 1, 21, 23, 45, 35, 59, 25, 20, 31, 4, 39, 9, 37, 7, 47, 63, 55, 6, 30, 5, 41, 51, 10, 54, 48, 56, 24, 50, 43, 52, 60, 17, 32, 57, 0, 15, 42] 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)) = -209.15066713803753 V(r_1,...,r_N) = -209.15066713803745 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 = [21, 35, 24, 5, 59, 3, 26, 58, 61, 40, 42, 19, 46, 16, 45, 29, 13, 32, 52, 11, 55, 0, 53, 41, 2, 36, 6, 43, 57, 15, 60, 44, 17, 34, 33, 1, 25, 49, 47, 51, 9, 23, 10, 27, 31, 14, 12, 38, 50, 37, 48, 39, 18, 22, 62, 20, 63, 28, 7, 4, 30, 8, 54, 56] 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)) = -50.26657317567803 V(r_1,...,r_N) = -50.266573175678026 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 -2.78913965e-01 6.45007771e-02 -6.13637853e-01 | -2.78913965e-01 6.45007771e-02 -6.13637853e-01 1 1.07229665e+00 7.45772498e-02 2.11350241e+00 | 1.07229665e+00 7.45772498e-02 2.11350241e+00 2 -1.43335187e-01 1.43034419e+00 5.58293561e-02 | -1.43335187e-01 1.43034419e+00 5.58293561e-02 3 2.23172086e-01 -1.86248308e+00 5.46668893e-01 | 2.23172086e-01 -1.86248308e+00 5.46668893e-01 4 -8.79797928e+00 -6.07206729e+00 -5.37198237e+00 | -8.79797928e+00 -6.07206729e+00 -5.37198237e+00 5 -1.14636835e+01 3.50538863e+01 -1.35599344e+01 | -1.14636835e+01 3.50538863e+01 -1.35599344e+01 6 -1.01198906e+01 -1.32442359e+01 -7.28772016e+00 | -1.01198906e+01 -1.32442359e+01 -7.28772016e+00 7 -4.62686985e+00 1.35536159e+01 1.31373256e+01 | -4.62686985e+00 1.35536159e+01 1.31373256e+01 8 -2.11227464e+00 -1.55747641e+00 2.38793398e-02 | -2.11227464e+00 -1.55747641e+00 2.38793398e-02 9 -2.11163668e+01 -1.76809443e+01 2.20088248e+00 | -2.11163668e+01 -1.76809443e+01 2.20088248e+00 10 2.25556495e+01 1.99807478e+01 -1.08970740e+00 | 2.25556495e+01 1.99807478e+01 -1.08970740e+00 11 -7.57070145e-01 1.55672323e-01 1.39660558e-01 | -7.57070145e-01 1.55672323e-01 1.39660558e-01 12 -3.49022586e-01 5.41362566e-01 -2.12589789e-01 | -3.49022586e-01 5.41362566e-01 -2.12589789e-01 13 1.09266842e+00 -5.66356691e-01 -1.29989734e+00 | 1.09266842e+00 -5.66356691e-01 -1.29989734e+00 14 -5.77516037e+00 -9.75581096e+00 -6.63893372e+00 | -5.77516037e+00 -9.75581096e+00 -6.63893372e+00 15 2.19673270e+00 1.12274682e+01 2.29931160e+00 | 2.19673270e+00 1.12274682e+01 2.29931160e+00 16 1.23408901e+00 -2.37759033e-02 6.67490423e-01 | 1.23408901e+00 -2.37759033e-02 6.67490423e-01 17 4.55447693e+00 -5.17191877e+00 3.37488094e+00 | 4.55447693e+00 -5.17191877e+00 3.37488094e+00 18 3.51844943e+00 1.08307833e+00 -7.14501527e+00 | 3.51844943e+00 1.08307833e+00 -7.14501527e+00 19 -5.06142011e+00 5.97479158e+00 -8.91495117e+00 | -5.06142011e+00 5.97479158e+00 -8.91495117e+00 20 1.18389856e+01 5.17976618e+00 -1.06690983e+01 | 1.18389856e+01 5.17976618e+00 -1.06690983e+01 21 -1.39491801e+01 1.20290502e+01 -1.19828741e+01 | -1.39491801e+01 1.20290502e+01 -1.19828741e+01 22 -1.55935877e+01 -5.52385728e+00 -9.04666083e-01 | -1.55935877e+01 -5.52385728e+00 -9.04666083e-01 23 8.19577430e+00 8.15380468e+00 5.16201494e+00 | 8.19577430e+00 8.15380468e+00 5.16201494e+00 24 -5.70502924e-01 8.22635338e-01 -1.04571226e-01 | -5.70502924e-01 8.22635338e-01 -1.04571226e-01 25 -2.03855420e+00 -1.80072241e+00 -3.74739848e-02 | -2.03855420e+00 -1.80072241e+00 -3.74739848e-02 26 1.26898201e-01 1.71640181e+00 -3.05426723e-01 | 1.26898201e-01 1.71640181e+00 -3.05426723e-01 27 -9.61474338e-01 -9.86277452e-01 1.21370629e-01 | -9.61474338e-01 -9.86277452e-01 1.21370629e-01 28 -2.58032760e+01 -1.83809909e+01 -4.29303106e+01 | -2.58032760e+01 -1.83809909e+01 -4.29303106e+01 29 2.98322336e+01 2.07166137e+01 4.29954918e+01 | 2.98322336e+01 2.07166137e+01 4.29954918e+01 30 2.75249869e+00 -8.46900918e+00 4.69101180e+00 | 2.75249869e+00 -8.46900918e+00 4.69101180e+00 31 1.05692679e+00 2.39551525e+00 3.36898031e+00 | 1.05692679e+00 2.39551525e+00 3.36898031e+00 32 7.48667262e-01 5.70806746e-01 -5.26023352e-01 | 7.48667262e-01 5.70806746e-01 -5.26023352e-01 33 1.89210189e+01 -2.56690816e+01 -1.16211133e+01 | 1.89210189e+01 -2.56690816e+01 -1.16211133e+01 34 2.79107409e+00 -5.05449191e+00 3.93671886e+00 | 2.79107409e+00 -5.05449191e+00 3.93671886e+00 35 -1.15298383e+01 7.10402221e+00 -1.39252678e+01 | -1.15298383e+01 7.10402221e+00 -1.39252678e+01 36 -9.96001432e+00 -2.66191961e+01 -1.14938553e+01 | -9.96001432e+00 -2.66191961e+01 -1.14938553e+01 37 9.27191113e+00 2.63598539e+01 1.09861600e+01 | 9.27191113e+00 2.63598539e+01 1.09861600e+01 38 -1.75453848e+01 2.64107199e+01 1.16427244e+01 | -1.75453848e+01 2.64107199e+01 1.16427244e+01 39 -1.48072815e-01 -1.15447434e+00 -2.64786803e-01 | -1.48072815e-01 -1.15447434e+00 -2.64786803e-01 40 1.83221502e+01 -3.03244022e+01 1.76684803e+01 | 1.83221502e+01 -3.03244022e+01 1.76684803e+01 41 -9.03588392e+00 1.14710445e+01 -9.11081105e+00 | -9.03588392e+00 1.14710445e+01 -9.11081105e+00 42 1.88858309e+00 -3.61935782e+00 6.92645271e+00 | 1.88858309e+00 -3.61935782e+00 6.92645271e+00 43 3.44653694e-01 7.21451495e-01 -5.40753165e-01 | 3.44653694e-01 7.21451495e-01 -5.40753165e-01 44 8.00694794e+00 -9.27135671e+00 1.11344554e+01 | 8.00694794e+00 -9.27135671e+00 1.11344554e+01 45 -8.89686386e-01 7.35329620e-01 -8.45451331e-01 | -8.89686386e-01 7.35329620e-01 -8.45451331e-01 46 9.60654302e+00 -8.53469292e+00 1.18054403e+01 | 9.60654302e+00 -8.53469292e+00 1.18054403e+01 47 2.79172412e+00 1.60289005e+00 1.30801450e+00 | 2.79172412e+00 1.60289005e+00 1.30801450e+00 48 -1.13767128e+00 -3.45359405e+00 -2.97034300e+00 | -1.13767128e+00 -3.45359405e+00 -2.97034300e+00 49 1.19900712e+01 1.36855959e+00 -7.75194073e+00 | 1.19900712e+01 1.36855959e+00 -7.75194073e+00 50 -2.75073893e+00 -2.02797124e+00 -5.59896456e+00 | -2.75073893e+00 -2.02797124e+00 -5.59896456e+00 51 7.22195697e-01 4.94051703e+00 4.03286396e+00 | 7.22195697e-01 4.94051703e+00 4.03286396e+00 52 5.90203036e-01 -1.30996156e+00 -1.26567858e+00 | 5.90203036e-01 -1.30996156e+00 -1.26567858e+00 53 -1.53592509e+00 -4.66695166e-01 6.96354693e+00 | -1.53592509e+00 -4.66695166e-01 6.96354693e+00 54 -1.12729047e+01 2.36728678e+00 1.00572364e+01 | -1.12729047e+01 2.36728678e+00 1.00572364e+01 55 1.37113421e+00 3.46711712e-01 -3.40047242e-02 | 1.37113421e+00 3.46711712e-01 -3.40047242e-02 56 -3.40472270e+00 -2.36704906e+01 -8.18329315e-01 | -3.40472270e+00 -2.36704906e+01 -8.18329315e-01 57 1.60982790e+01 7.06162978e+00 1.55162450e+01 | 1.60982790e+01 7.06162978e+00 1.55162450e+01 58 5.29203728e-02 3.48871874e+00 -2.60218916e+00 | 5.29203728e-02 3.48871874e+00 -2.60218916e+00 59 1.93341560e+00 -2.24747908e-01 1.39578738e+00 | 1.93341560e+00 -2.24747908e-01 1.39578738e+00 60 -2.53137708e+00 -8.07376561e+00 -3.46933727e+00 | -2.53137708e+00 -8.07376561e+00 -3.46933727e+00 61 1.53531706e+00 8.31728720e+00 3.54766665e+00 | 1.53531706e+00 8.31728720e+00 3.54766665e+00 62 3.83824860e+00 -1.87574824e+00 -5.61174003e+00 | 3.83824860e+00 -1.87574824e+00 -5.61174003e+00 63 1.84872310e-01 -5.74707127e-01 -3.00713844e-01 | 1.84872310e-01 -5.74707127e-01 -3.00713844e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [39, 46, 23, 10, 59, 47, 25, 19, 52, 18, 3, 53, 56, 43, 31, 27, 33, 35, 9, 7, 32, 48, 54, 2, 55, 6, 57, 15, 58, 40, 50, 14, 20, 16, 41, 17, 51, 63, 42, 0, 29, 34, 38, 13, 49, 61, 1, 5, 21, 44, 30, 36, 8, 11, 22, 24, 12, 26, 28, 4, 62, 45, 60, 37] 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)) = 44.52405070528978 V(r_1,...,r_N) = 44.52405070528974 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 -1.65526299e+01 -1.60480878e+01 -1.10870708e+01 | -1.65526299e+01 -1.60480878e+01 -1.10870708e+01 1 1.65872741e+01 1.48199721e+01 8.30812442e+00 | 1.65872741e+01 1.48199721e+01 8.30812442e+00 2 -1.04443420e+01 -4.73420905e+00 -9.85601970e+00 | -1.04443420e+01 -4.73420905e+00 -9.85601970e+00 3 -1.87097536e+00 1.27437007e+01 -1.51444020e+00 | -1.87097536e+00 1.27437007e+01 -1.51444020e+00 4 -1.08948383e+00 -3.42901304e-01 7.97711823e-01 | -1.08948383e+00 -3.42901304e-01 7.97711823e-01 5 8.49237977e-01 4.26904772e-01 1.70697576e+00 | 8.49237977e-01 4.26904772e-01 1.70697576e+00 6 -5.17418531e-01 3.30871833e-01 1.30927317e+00 | -5.17418531e-01 3.30871833e-01 1.30927317e+00 7 -1.50714052e+00 -9.97463852e-01 -3.62313193e+00 | -1.50714052e+00 -9.97463852e-01 -3.62313193e+00 8 -9.49105584e-02 4.92744850e-01 8.40059592e-01 | -9.49105584e-02 4.92744850e-01 8.40059592e-01 9 3.94130740e+00 -9.53095627e+00 2.16500483e+01 | 3.94130740e+00 -9.53095627e+00 2.16500483e+01 10 -4.72790476e+00 6.59264264e+00 -2.64477611e+01 | -4.72790476e+00 6.59264264e+00 -2.64477611e+01 11 5.43424109e+00 3.63912768e+00 9.70934716e-02 | 5.43424109e+00 3.63912768e+00 9.70934716e-02 12 -3.96668373e+00 -6.96818529e+00 -1.71597378e+00 | -3.96668373e+00 -6.96818529e+00 -1.71597378e+00 13 2.32459205e+00 5.69387694e+00 2.03582398e+00 | 2.32459205e+00 5.69387694e+00 2.03582398e+00 14 7.05977625e+00 -6.49409604e+00 1.58960247e+01 | 7.05977625e+00 -6.49409604e+00 1.58960247e+01 15 -1.90452156e+01 6.82129628e+00 -1.03283214e+00 | -1.90452156e+01 6.82129628e+00 -1.03283214e+00 16 -5.19018293e-01 -4.37480270e-01 -1.37563444e+00 | -5.19018293e-01 -4.37480270e-01 -1.37563444e+00 17 -3.31364550e+00 -3.47586113e+00 -9.59997895e-01 | -3.31364550e+00 -3.47586113e+00 -9.59997895e-01 18 -3.10703807e+00 -1.28981816e+00 -6.70897717e-01 | -3.10703807e+00 -1.28981816e+00 -6.70897717e-01 19 -3.14426181e-01 1.44575027e+00 1.10368733e+00 | -3.14426181e-01 1.44575027e+00 1.10368733e+00 20 4.14947335e+00 1.49717290e+00 -1.09400818e+00 | 4.14947335e+00 1.49717290e+00 -1.09400818e+00 21 2.92984173e+00 1.08468506e+01 -3.60570511e+01 | 2.92984173e+00 1.08468506e+01 -3.60570511e+01 22 -1.17909998e+01 -6.62312227e+00 5.04553293e-02 | -1.17909998e+01 -6.62312227e+00 5.04553293e-02 23 1.13906280e+01 8.75852024e+00 1.87848314e+00 | 1.13906280e+01 8.75852024e+00 1.87848314e+00 24 2.76693921e+00 -1.03646485e+00 -1.79264469e-01 | 2.76693921e+00 -1.03646485e+00 -1.79264469e-01 25 -1.48588799e+01 -1.49182910e+01 2.28003074e+01 | -1.48588799e+01 -1.49182910e+01 2.28003074e+01 26 1.45929033e+01 1.22832696e+01 -2.52123140e+01 | 1.45929033e+01 1.22832696e+01 -2.52123140e+01 27 7.55744287e-01 9.60983329e-01 1.96518555e+00 | 7.55744287e-01 9.60983329e-01 1.96518555e+00 28 1.93596727e+01 -7.15769868e+00 1.61407970e+00 | 1.93596727e+01 -7.15769868e+00 1.61407970e+00 29 1.25197127e+01 -1.34897182e+01 -5.86006767e+00 | 1.25197127e+01 -1.34897182e+01 -5.86006767e+00 30 -1.17183813e+01 -7.45429791e+00 -7.23535306e+00 | -1.17183813e+01 -7.45429791e+00 -7.23535306e+00 31 7.63315688e+00 1.47910343e+01 1.99464936e+00 | 7.63315688e+00 1.47910343e+01 1.99464936e+00 32 -4.91737687e-01 3.88343474e-02 -1.57562668e+00 | -4.91737687e-01 3.88343474e-02 -1.57562668e+00 33 -4.49896820e+01 3.20454453e+01 -6.64208705e+01 | -4.49896820e+01 3.20454453e+01 -6.64208705e+01 34 -3.89416538e+01 -3.40717860e-01 -1.86450727e+01 | -3.89416538e+01 -3.40717860e-01 -1.86450727e+01 35 3.47988813e+01 4.09870537e+00 1.14649934e+01 | 3.47988813e+01 4.09870537e+00 1.14649934e+01 36 4.56606575e+01 -3.08188130e+01 6.70020656e+01 | 4.56606575e+01 -3.08188130e+01 6.70020656e+01 37 -2.54108820e-01 -2.24256677e+00 1.68601345e+00 | -2.54108820e-01 -2.24256677e+00 1.68601345e+00 38 -9.43371566e+00 -3.32711687e+00 -8.58569053e+00 | -9.43371566e+00 -3.32711687e+00 -8.58569053e+00 39 9.04765938e+00 3.54993966e+00 7.69992352e+00 | 9.04765938e+00 3.54993966e+00 7.69992352e+00 40 -4.50158996e+00 -1.16493693e+01 -9.48321978e-01 | -4.50158996e+00 -1.16493693e+01 -9.48321978e-01 41 -2.90931641e+01 2.83095810e+00 1.49762027e+01 | -2.90931641e+01 2.83095810e+00 1.49762027e+01 42 3.38953608e+01 1.76524515e+00 -2.06110672e+01 | 3.38953608e+01 1.76524515e+00 -2.06110672e+01 43 3.83133449e+00 4.40726349e+00 2.09514375e+00 | 3.83133449e+00 4.40726349e+00 2.09514375e+00 44 -7.75978834e-01 -1.49251105e+00 -9.60928950e-02 | -7.75978834e-01 -1.49251105e+00 -9.60928950e-02 45 9.30782726e-01 1.98926135e+00 3.30556061e-01 | 9.30782726e-01 1.98926135e+00 3.30556061e-01 46 -7.45684260e-01 1.99799636e+00 9.17367533e+00 | -7.45684260e-01 1.99799636e+00 9.17367533e+00 47 -1.46436763e+01 -2.92150493e+01 2.37340359e+01 | -1.46436763e+01 -2.92150493e+01 2.37340359e+01 48 -8.82394640e-01 1.21579796e+00 9.15756839e-01 | -8.82394640e-01 1.21579796e+00 9.15756839e-01 49 -4.71145760e+00 1.31952991e+00 -7.49762808e+00 | -4.71145760e+00 1.31952991e+00 -7.49762808e+00 50 -5.23958578e+00 1.76418305e+00 -1.58549917e+01 | -5.23958578e+00 1.76418305e+00 -1.58549917e+01 51 -1.77313124e+01 1.01326884e+01 5.53034685e+00 | -1.77313124e+01 1.01326884e+01 5.53034685e+00 52 -1.87555013e+01 -1.58790930e+01 -2.93357877e+00 | -1.87555013e+01 -1.58790930e+01 -2.93357877e+00 53 2.00614922e+01 4.57992245e+00 1.23126039e+01 | 2.00614922e+01 4.57992245e+00 1.23126039e+01 54 -2.64258335e+00 -9.07268282e+00 -2.05677752e+00 | -2.64258335e+00 -9.07268282e+00 -2.05677752e+00 55 3.24596166e+00 8.75869711e+00 4.06075560e+00 | 3.24596166e+00 8.75869711e+00 4.06075560e+00 56 -7.80741639e+00 -1.29005345e+01 3.63633881e+01 | -7.80741639e+00 -1.29005345e+01 3.63633881e+01 57 7.11090460e+00 -5.92062543e-01 -3.04531911e-03 | 7.11090460e+00 -5.92062543e-01 -3.04531911e-03 58 -6.64032280e+00 6.07552163e+00 9.41063740e+00 | -6.64032280e+00 6.07552163e+00 9.41063740e+00 59 7.80909808e-01 1.88884488e+00 3.40948006e+00 | 7.80909808e-01 1.88884488e+00 3.40948006e+00 60 1.72706913e+01 3.26220120e+01 -2.16901850e+01 | 1.72706913e+01 3.26220120e+01 -2.16901850e+01 61 -7.53566680e-01 5.34353814e-01 -7.17776642e-01 | -7.53566680e-01 5.34353814e-01 -7.17776642e-01 62 1.08083365e+01 -1.22881111e+01 -4.20910159e+00 | 1.08083365e+01 -1.22881111e+01 -4.20910159e+00 63 1.47367528e+01 7.05736057e+00 1.15540838e+01 | 1.47367528e+01 7.05736057e+00 1.15540838e+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 = [34, 8, 11, 55, 38, 50, 15, 26, 1, 24, 58, 2, 52, 57, 61, 6, 43, 56, 60, 63, 54, 25, 36, 45, 9, 21, 7, 53, 35, 48, 37, 40, 44, 39, 0, 28, 22, 30, 4, 33, 31, 59, 42, 16, 32, 23, 62, 51, 29, 49, 5, 47, 12, 27, 20, 3, 17, 13, 10, 41, 18, 14, 46, 19] 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)) = 2.4503791184354062 V(r_1,...,r_N) = 2.4503791184353747 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 6.78212472e-01 7.47406640e-01 1.30136900e-01 | 6.78212472e-01 7.47406640e-01 1.30136900e-01 1 1.79492876e+00 -3.15229132e+00 -3.21922027e+00 | 1.79492876e+00 -3.15229132e+00 -3.21922027e+00 2 -3.60868666e+01 -3.84343141e+01 -2.03475364e+01 | -3.60868666e+01 -3.84343141e+01 -2.03475364e+01 3 3.42969264e+01 3.83659328e+01 1.77940623e+01 | 3.42969264e+01 3.83659328e+01 1.77940623e+01 4 8.80594685e-01 -2.33877017e+00 1.14178980e+00 | 8.80594685e-01 -2.33877017e+00 1.14178980e+00 5 2.90143379e+00 1.98085671e-01 1.69333756e+00 | 2.90143379e+00 1.98085671e-01 1.69333756e+00 6 -3.05592932e+00 6.26353196e+00 2.46312936e+00 | -3.05592932e+00 6.26353196e+00 2.46312936e+00 7 -2.14313561e+01 -3.50741883e+00 4.18365708e+01 | -2.14313561e+01 -3.50741883e+00 4.18365708e+01 8 -8.08861340e+01 -1.57386888e+02 -1.21818030e+02 | -8.08861340e+01 -1.57386888e+02 -1.21818030e+02 9 8.10844903e+01 1.59409900e+02 1.22895892e+02 | 8.10844903e+01 1.59409900e+02 1.22895892e+02 10 6.30898813e-01 9.96501027e-01 1.31600955e+00 | 6.30898813e-01 9.96501027e-01 1.31600955e+00 11 5.75189509e+01 -6.09421279e+01 1.91604722e+01 | 5.75189509e+01 -6.09421279e+01 1.91604722e+01 12 -6.15684019e+00 -4.47719963e+00 -2.01259155e+00 | -6.15684019e+00 -4.47719963e+00 -2.01259155e+00 13 4.52250507e+00 4.69315691e+00 7.89124225e-01 | 4.52250507e+00 4.69315691e+00 7.89124225e-01 14 -2.17709060e+00 -3.90771060e+00 -2.67583549e+00 | -2.17709060e+00 -3.90771060e+00 -2.67583549e+00 15 -4.82729483e+01 5.65014958e+01 -7.81223261e+01 | -4.82729483e+01 5.65014958e+01 -7.81223261e+01 16 2.94280226e+00 1.22375441e+00 1.44633759e+00 | 2.94280226e+00 1.22375441e+00 1.44633759e+00 17 -1.61680962e+01 3.33913213e+00 -6.34336379e+00 | -1.61680962e+01 3.33913213e+00 -6.34336379e+00 18 2.02585522e+00 3.86394246e+00 -1.57086459e+00 | 2.02585522e+00 3.86394246e+00 -1.57086459e+00 19 -1.77177111e+01 6.42114476e+01 -8.80422102e+01 | -1.77177111e+01 6.42114476e+01 -8.80422102e+01 20 2.27640655e+01 -2.20778153e+00 -3.72111726e+01 | 2.27640655e+01 -2.20778153e+00 -3.72111726e+01 21 5.72371637e+00 1.67544759e+00 1.96551773e+00 | 5.72371637e+00 1.67544759e+00 1.96551773e+00 22 1.98384718e+00 -1.85384330e+00 -1.13130292e+00 | 1.98384718e+00 -1.85384330e+00 -1.13130292e+00 23 -1.64627197e+01 -2.69295869e+00 -4.70879366e+00 | -1.64627197e+01 -2.69295869e+00 -4.70879366e+00 24 -3.04171737e+00 -2.96226263e+00 -3.95221076e+00 | -3.04171737e+00 -2.96226263e+00 -3.95221076e+00 25 -1.96017187e+01 -2.91388536e+00 1.93040031e+01 | -1.96017187e+01 -2.91388536e+00 1.93040031e+01 26 1.33487026e+01 8.66656957e+00 -2.06912271e+01 | 1.33487026e+01 8.66656957e+00 -2.06912271e+01 27 2.07998730e+00 3.55053506e+00 3.74802370e+00 | 2.07998730e+00 3.55053506e+00 3.74802370e+00 28 -5.38689308e+01 5.03801272e+01 -1.99868997e+01 | -5.38689308e+01 5.03801272e+01 -1.99868997e+01 29 1.60584931e+00 -5.07639842e+00 -1.01400577e+01 | 1.60584931e+00 -5.07639842e+00 -1.01400577e+01 30 1.91258217e+01 -6.30346977e+01 8.81957505e+01 | 1.91258217e+01 -6.30346977e+01 8.81957505e+01 31 -6.84628099e-01 -4.97633737e-01 1.46581197e-01 | -6.84628099e-01 -4.97633737e-01 1.46581197e-01 32 1.80035576e+00 1.36248352e+00 -2.54372585e-01 | 1.80035576e+00 1.36248352e+00 -2.54372585e-01 33 7.02381506e-01 -2.05333119e+00 -5.71994314e-01 | 7.02381506e-01 -2.05333119e+00 -5.71994314e-01 34 -4.62315414e+00 -3.12770758e-01 9.88785057e-01 | -4.62315414e+00 -3.12770758e-01 9.88785057e-01 35 2.42470420e+00 9.65182580e-01 -6.39443532e+00 | 2.42470420e+00 9.65182580e-01 -6.39443532e+00 36 -7.74476684e-01 8.62845005e-01 8.10624251e-01 | -7.74476684e-01 8.62845005e-01 8.10624251e-01 37 -2.53214334e-01 -4.45023686e-01 -1.59117193e+00 | -2.53214334e-01 -4.45023686e-01 -1.59117193e+00 38 1.94463684e+00 1.13490922e+00 1.98500293e-01 | 1.94463684e+00 1.13490922e+00 1.98500293e-01 39 -5.77147020e-02 -8.31414571e-02 -1.99820770e+00 | -5.77147020e-02 -8.31414571e-02 -1.99820770e+00 40 1.37004507e+00 1.01280358e+00 -3.36443118e-01 | 1.37004507e+00 1.01280358e+00 -3.36443118e-01 41 -4.30487188e+00 -2.13495267e+00 3.98576029e+00 | -4.30487188e+00 -2.13495267e+00 3.98576029e+00 42 5.43520415e+01 -4.89434508e+01 8.14678184e+01 | 5.43520415e+01 -4.89434508e+01 8.14678184e+01 43 -2.83208099e+00 4.00112821e-01 1.07198383e+00 | -2.83208099e+00 4.00112821e-01 1.07198383e+00 44 2.53851746e+00 1.28655839e+00 1.21055347e+00 | 2.53851746e+00 1.28655839e+00 1.21055347e+00 45 -3.37952361e+00 2.08984567e-01 -1.56997852e+00 | -3.37952361e+00 2.08984567e-01 -1.56997852e+00 46 4.89835572e-01 -3.60993227e+00 8.28510607e+00 | 4.89835572e-01 -3.60993227e+00 8.28510607e+00 47 1.23873348e+00 -5.49582402e-03 -7.15904903e-01 | 1.23873348e+00 -5.49582402e-03 -7.15904903e-01 48 1.05648589e+00 1.07123595e-01 4.37253263e-02 | 1.05648589e+00 1.07123595e-01 4.37253263e-02 49 -1.45689873e+00 1.34302839e+00 -1.99949723e+00 | -1.45689873e+00 1.34302839e+00 -1.99949723e+00 50 1.83998777e+01 -5.30083679e-01 5.72548980e+00 | 1.83998777e+01 -5.30083679e-01 5.72548980e+00 51 -3.20836397e-01 -3.30669243e-01 -1.22556566e+00 | -3.20836397e-01 -3.30669243e-01 -1.22556566e+00 52 -1.34530610e+01 -6.25600604e+00 -8.58684725e+00 | -1.34530610e+01 -6.25600604e+00 -8.58684725e+00 53 1.39290136e+01 4.88265178e+00 7.64702827e+00 | 1.39290136e+01 4.88265178e+00 7.64702827e+00 54 -7.83847340e+00 -1.60700812e+00 -5.07065737e+00 | -7.83847340e+00 -1.60700812e+00 -5.07065737e+00 55 7.81636599e+00 1.62573717e+00 5.00247855e+00 | 7.81636599e+00 1.62573717e+00 5.00247855e+00 56 -1.55703565e+01 1.97626319e-01 -2.51679354e+00 | -1.55703565e+01 1.97626319e-01 -2.51679354e+00 57 1.50815299e+01 3.00395210e+00 3.60376548e+00 | 1.50815299e+01 3.00395210e+00 3.60376548e+00 58 -1.28873267e+00 6.14852806e+00 1.18850341e+01 | -1.28873267e+00 6.14852806e+00 1.18850341e+01 59 -9.90812321e-01 -1.52384348e+00 6.75216922e-01 | -9.90812321e-01 -1.52384348e+00 6.75216922e-01 60 -1.92031428e+00 -9.46982523e+00 -5.02542344e+00 | -1.92031428e+00 -9.46982523e+00 -5.02542344e+00 61 4.10191226e+00 7.61026278e+00 5.68003541e+00 | 4.10191226e+00 7.61026278e+00 5.68003541e+00 62 1.40115159e+00 -1.26188770e+00 -1.48387618e+00 | 1.40115159e+00 -1.26188770e+00 -1.48387618e+00 63 1.20031835e-01 -2.28615295e+00 -9.93832613e-01 | 1.20031835e-01 -2.28615295e+00 -9.93832613e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.