!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Buckingham_GhoshSomayajuluArya_2015_ThCeO__SM_681317476351_000 Supported species : Ce O Th random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ce (Configuration in file "config-Ce.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [57, 20, 36, 4, 3, 41, 23, 26, 32, 25, 29, 42, 47, 27, 55, 52, 40, 33, 44, 51, 1, 53, 49, 6, 37, 9, 7, 13, 54, 10, 61, 45, 8, 17, 58, 56, 2, 24, 62, 46, 16, 5, 11, 48, 18, 31, 39, 12, 43, 22, 59, 19, 15, 21, 28, 14, 35, 0, 34, 50, 63, 30, 38, 60] 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)) = 37249.92650573806 V(r_1,...,r_N) = 37249.92650573809 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -8.05812135e+01 -6.63600138e+01 -6.54877293e+01 | -8.05812135e+01 -6.63600138e+01 -6.54877293e+01 1 -5.46380551e+01 -9.19181849e+01 -6.16118197e+01 | -5.46380551e+01 -9.19181849e+01 -6.16118197e+01 2 -3.71823789e+01 -2.46655587e+01 -1.25898801e+02 | -3.71823789e+01 -2.46655587e+01 -1.25898801e+02 3 -9.18938949e+00 -3.10508503e+00 -1.16186334e+02 | -9.18938949e+00 -3.10508503e+00 -1.16186334e+02 4 -3.88101390e+01 -1.20171054e+02 -2.49410039e+01 | -3.88101390e+01 -1.20171054e+02 -2.49410039e+01 5 6.54264609e+00 -1.04338046e+02 -2.40465452e+01 | 6.54264609e+00 -1.04338046e+02 -2.40465452e+01 6 -1.24255131e+02 -3.27363334e+01 -3.75412437e+01 | -1.24255131e+02 -3.27363334e+01 -3.75412437e+01 7 -9.17469747e+01 2.87813326e+01 -3.16141019e+01 | -9.17469747e+01 2.87813326e+01 -3.16141019e+01 8 9.73957352e+00 -8.10494643e+01 -9.48492043e+01 | 9.73957352e+00 -8.10494643e+01 -9.48492043e+01 9 3.90367812e+01 -7.20622378e+01 -6.48648158e+01 | 3.90367812e+01 -7.20622378e+01 -6.48648158e+01 10 4.57314294e+01 -3.67327013e+01 -1.20437052e+02 | 4.57314294e+01 -3.67327013e+01 -1.20437052e+02 11 1.14694610e+02 -4.81132004e+00 -5.66844081e+01 | 1.14694610e+02 -4.81132004e+00 -5.66844081e+01 12 5.69828549e+01 -1.19330955e+02 -3.32871814e+01 | 5.69828549e+01 -1.19330955e+02 -3.32871814e+01 13 1.32070172e+02 -4.48648033e+01 -1.26215546e+01 | 1.32070172e+02 -4.48648033e+01 -1.26215546e+01 14 1.14456907e+01 -5.10325352e+01 -5.18003788e+01 | 1.14456907e+01 -5.10325352e+01 -5.18003788e+01 15 5.84827536e+01 -2.52626193e+01 -1.67140457e+01 | 5.84827536e+01 -2.52626193e+01 -1.67140457e+01 16 -9.57718274e+01 3.02780064e+00 -8.78925553e+01 | -9.57718274e+01 3.02780064e+00 -8.78925553e+01 17 -8.10607289e+01 3.82912410e+01 -7.34662739e+01 | -8.10607289e+01 3.82912410e+01 -7.34662739e+01 18 -4.05577051e+01 6.08475124e+01 -1.13682859e+02 | -4.05577051e+01 6.08475124e+01 -1.13682859e+02 19 -4.67016519e+01 1.28623828e+02 -8.68222247e+01 | -4.67016519e+01 1.28623828e+02 -8.68222247e+01 20 -5.41181682e+01 1.72027658e+01 -6.54305990e+01 | -5.41181682e+01 1.72027658e+01 -6.54305990e+01 21 2.53250739e+01 4.73933195e+01 -1.98317181e+01 | 2.53250739e+01 4.73933195e+01 -1.98317181e+01 22 -9.81265976e+01 7.68967378e+01 -4.56753396e+01 | -9.81265976e+01 7.68967378e+01 -4.56753396e+01 23 -7.30363578e+01 1.16157864e+02 5.82615341e+00 | -7.30363578e+01 1.16157864e+02 5.82615341e+00 24 1.26375042e+01 1.67707343e+01 -1.31407695e+02 | 1.26375042e+01 1.67707343e+01 -1.31407695e+02 25 4.08790575e+01 4.18841621e+01 -8.71530127e+01 | 4.08790575e+01 4.18841621e+01 -8.71530127e+01 26 4.56811411e+01 7.67711823e+01 -9.78769435e+01 | 4.56811411e+01 7.67711823e+01 -9.78769435e+01 27 8.89212572e+01 7.36374552e+01 -4.17266573e+01 | 8.89212572e+01 7.36374552e+01 -4.17266573e+01 28 9.79706729e+01 -6.98541433e+00 -3.45200862e+01 | 9.79706729e+01 -6.98541433e+00 -3.45200862e+01 29 1.32534089e+02 3.19432445e+01 -2.21393147e+00 | 1.32534089e+02 3.19432445e+01 -2.21393147e+00 30 2.98828898e+01 8.46123956e+01 -4.51966185e+01 | 2.98828898e+01 8.46123956e+01 -4.51966185e+01 31 2.51787753e+01 1.26653455e+02 -1.98963085e+01 | 2.51787753e+01 1.26653455e+02 -1.98963085e+01 32 -9.88336897e+01 -9.68867208e+01 -8.40740296e-01 | -9.88336897e+01 -9.68867208e+01 -8.40740296e-01 33 -7.05343556e+01 -7.19553101e+01 4.15415299e+01 | -7.05343556e+01 -7.19553101e+01 4.15415299e+01 34 -4.56899511e+01 -8.07117466e+01 2.76354156e+01 | -4.56899511e+01 -8.07117466e+01 2.76354156e+01 35 -2.74935269e+01 -3.99521583e+01 7.35247641e+01 | -2.74935269e+01 -3.99521583e+01 7.35247641e+01 36 -4.50607226e+01 -1.03392342e+02 7.22218553e+01 | -4.50607226e+01 -1.03392342e+02 7.22218553e+01 37 -1.95782642e+01 -8.71439935e+01 1.13598816e+02 | -1.95782642e+01 -8.71439935e+01 1.13598816e+02 38 -1.15658654e+02 -3.78504715e+01 6.56891499e+01 | -1.15658654e+02 -3.78504715e+01 6.56891499e+01 39 -7.48660664e+01 -1.53036405e+01 1.26576116e+02 | -7.48660664e+01 -1.53036405e+01 1.26576116e+02 40 -4.86319886e-02 -1.26643728e+02 1.96101680e+01 | -4.86319886e-02 -1.26643728e+02 1.96101680e+01 41 3.76833280e+01 -5.79329695e+01 3.43338814e+01 | 3.76833280e+01 -5.79329695e+01 3.43338814e+01 42 7.89074018e+01 -5.56582285e+01 3.57392931e+00 | 7.89074018e+01 -5.56582285e+01 3.57392931e+00 43 1.33220894e+02 1.26882168e+01 5.48842807e+01 | 1.33220894e+02 1.26882168e+01 5.48842807e+01 44 7.42574905e+01 -1.31328708e+02 6.35889234e+01 | 7.42574905e+01 -1.31328708e+02 6.35889234e+01 45 7.03909947e+01 -4.47785424e+01 7.88261306e+01 | 7.03909947e+01 -4.47785424e+01 7.88261306e+01 46 1.78210563e+01 -3.83496342e+01 9.05306287e+01 | 1.78210563e+01 -3.83496342e+01 9.05306287e+01 47 3.88844337e+01 -1.15334272e+01 1.23333724e+02 | 3.88844337e+01 -1.15334272e+01 1.23333724e+02 48 -1.43176862e+02 1.16900525e+01 2.30707531e+01 | -1.43176862e+02 1.16900525e+01 2.30707531e+01 49 -8.83394340e+01 4.74307987e+01 4.08331584e+01 | -8.83394340e+01 4.74307987e+01 4.08331584e+01 50 -4.38396386e+01 8.50305173e+01 7.95128920e+00 | -4.38396386e+01 8.50305173e+01 7.95128920e+00 51 -1.35375997e+01 1.26339472e+02 4.45152616e+01 | -1.35375997e+01 1.26339472e+02 4.45152616e+01 52 -4.06846766e+01 3.50720082e+01 9.02537512e+01 | -4.06846766e+01 3.50720082e+01 9.02537512e+01 53 -8.04954703e+00 4.01210528e+01 1.27460945e+02 | -8.04954703e+00 4.01210528e+01 1.27460945e+02 54 -9.77771426e+01 5.84570859e+01 5.69469298e+01 | -9.77771426e+01 5.84570859e+01 5.69469298e+01 55 -3.37677094e+01 8.10966726e+01 7.61663578e+01 | -3.37677094e+01 8.10966726e+01 7.61663578e+01 56 1.87735326e+01 1.11752248e+01 2.62735389e+01 | 1.87735326e+01 1.11752248e+01 2.62735389e+01 57 5.06535383e+01 1.87352382e+01 1.20274002e+01 | 5.06535383e+01 1.87352382e+01 1.20274002e+01 58 9.79539238e+01 8.24361318e+01 1.59467496e+01 | 9.79539238e+01 8.24361318e+01 1.59467496e+01 59 8.08985297e+01 7.65750281e+01 3.26530802e+01 | 8.08985297e+01 7.65750281e+01 3.26530802e+01 60 9.13816948e+01 1.21942293e+01 6.96810669e+01 | 9.13816948e+01 1.21942293e+01 6.96810669e+01 61 8.18743018e+01 2.91268702e+01 8.61834734e+01 | 8.18743018e+01 2.91268702e+01 8.61834734e+01 62 2.21543902e+01 1.00251790e+02 1.07010937e+02 | 2.21543902e+01 1.00251790e+02 1.07010937e+02 63 2.41203078e+01 8.69325280e+01 7.99496213e+01 | 2.41203078e+01 8.69325280e+01 7.99496213e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = O (Configuration in file "config-O.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [3, 28, 48, 0, 40, 63, 19, 38, 42, 11, 41, 9, 14, 27, 12, 35, 56, 60, 30, 6, 32, 25, 59, 58, 34, 21, 55, 13, 1, 33, 18, 49, 20, 29, 24, 15, 45, 57, 7, 52, 4, 10, 8, 47, 62, 36, 54, 43, 2, 31, 51, 50, 39, 61, 46, 26, 16, 37, 23, 22, 17, 53, 44, 5] 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)) = 9579.479482007424 V(r_1,...,r_N) = 9579.479482007422 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 -2.06851342e+01 -1.57342729e+01 -1.96421896e+01 | -2.06851342e+01 -1.57342729e+01 -1.96421896e+01 1 -2.42399300e+01 -4.11415409e+00 -4.41772631e+01 | -2.42399300e+01 -4.11415409e+00 -4.41772631e+01 2 -8.69621396e+00 -9.70937045e+00 -3.45515030e+01 | -8.69621396e+00 -9.70937045e+00 -3.45515030e+01 3 -3.01487143e-01 -4.71446726e+00 -2.52097776e+01 | -3.01487143e-01 -4.71446726e+00 -2.52097776e+01 4 3.83949192e+00 -4.70770292e+01 1.82124775e+01 | 3.83949192e+00 -4.70770292e+01 1.82124775e+01 5 -2.93324177e+01 9.37466937e+00 -2.81164038e+01 | -2.93324177e+01 9.37466937e+00 -2.81164038e+01 6 -3.16543018e+01 -5.96897414e+00 -1.01901628e+01 | -3.16543018e+01 -5.96897414e+00 -1.01901628e+01 7 -1.13440843e+01 -2.80615911e+01 -2.08625825e+01 | -1.13440843e+01 -2.80615911e+01 -2.08625825e+01 8 -4.93786766e-01 -2.58054965e+01 -2.85309271e+01 | -4.93786766e-01 -2.58054965e+01 -2.85309271e+01 9 3.16937606e+01 -2.84815264e+01 -2.27930604e+01 | 3.16937606e+01 -2.84815264e+01 -2.27930604e+01 10 1.52824443e+01 -7.64606763e+00 -2.96031571e+01 | 1.52824443e+01 -7.64606763e+00 -2.96031571e+01 11 2.92521887e+01 -3.03237297e+00 -1.57733877e+01 | 2.92521887e+01 -3.03237297e+00 -1.57733877e+01 12 1.60912852e+01 -4.04030745e+01 -9.28097782e+00 | 1.60912852e+01 -4.04030745e+01 -9.28097782e+00 13 3.33111678e+01 -1.06490175e+01 1.97495373e+00 | 3.33111678e+01 -1.06490175e+01 1.97495373e+00 14 -1.21307324e+01 -8.13246710e+00 -1.14714275e+01 | -1.21307324e+01 -8.13246710e+00 -1.14714275e+01 15 1.75362292e+01 4.98017421e+00 1.85895094e-01 | 1.75362292e+01 4.98017421e+00 1.85895094e-01 16 -2.36765374e+01 -6.94229916e-01 -2.64478033e+01 | -2.36765374e+01 -6.94229916e-01 -2.64478033e+01 17 -1.78912018e+01 1.38675274e+01 -2.40745328e+01 | -1.78912018e+01 1.38675274e+01 -2.40745328e+01 18 -1.03379854e+01 1.52511218e+01 -2.91388347e+01 | -1.03379854e+01 1.52511218e+01 -2.91388347e+01 19 -1.76284410e+00 2.97332578e+01 -1.52911997e+01 | -1.76284410e+00 2.97332578e+01 -1.52911997e+01 20 -1.60653866e+01 6.89274827e+00 -1.33868979e+01 | -1.60653866e+01 6.89274827e+00 -1.33868979e+01 21 -1.10430686e+01 1.18795033e+01 -6.95142625e+00 | -1.10430686e+01 1.18795033e+01 -6.95142625e+00 22 -3.19829007e+01 8.31833741e+00 -7.59233385e+00 | -3.19829007e+01 8.31833741e+00 -7.59233385e+00 23 -1.56930142e+01 4.19607551e+01 -7.00290749e-01 | -1.56930142e+01 4.19607551e+01 -7.00290749e-01 24 2.92598615e-01 5.12508609e+00 -3.62997072e+01 | 2.92598615e-01 5.12508609e+00 -3.62997072e+01 25 1.23727698e+01 6.15426038e+00 -2.59751092e+01 | 1.23727698e+01 6.15426038e+00 -2.59751092e+01 26 -2.79148251e+00 -2.31986726e+00 -3.45882604e+01 | -2.79148251e+00 -2.31986726e+00 -3.45882604e+01 27 3.52032995e+01 3.50377448e+01 6.48978400e-02 | 3.52032995e+01 3.50377448e+01 6.48978400e-02 28 1.80470313e+01 -3.77304645e+00 -1.47657438e+01 | 1.80470313e+01 -3.77304645e+00 -1.47657438e+01 29 4.95347422e+01 1.83005454e+01 -1.40018528e+00 | 4.95347422e+01 1.83005454e+01 -1.40018528e+00 30 2.43105496e+00 1.01023135e+01 -9.72480331e+00 | 2.43105496e+00 1.01023135e+01 -9.72480331e+00 31 1.58206747e+01 4.50759275e+01 -7.87168270e+00 | 1.58206747e+01 4.50759275e+01 -7.87168270e+00 32 -3.20023939e+01 -2.37445014e+01 -7.59027622e-02 | -3.20023939e+01 -2.37445014e+01 -7.59027622e-02 33 -2.48431292e+01 -2.20590455e+01 1.49972086e+01 | -2.48431292e+01 -2.20590455e+01 1.49972086e+01 34 -1.00692218e+01 -6.37482815e+00 -1.50224427e+00 | -1.00692218e+01 -6.37482815e+00 -1.50224427e+00 35 1.08012892e+00 -1.15995748e+01 1.75109780e+01 | 1.08012892e+00 -1.15995748e+01 1.75109780e+01 36 -1.01304245e+01 -3.50403117e+01 1.85361766e+01 | -1.01304245e+01 -3.50403117e+01 1.85361766e+01 37 -9.22846163e+00 -2.29889054e+01 3.99703206e+01 | -9.22846163e+00 -2.29889054e+01 3.99703206e+01 38 -2.95012856e+01 -1.01820918e+01 1.44322239e+01 | -2.95012856e+01 -1.01820918e+01 1.44322239e+01 39 -1.57978730e+01 -9.52943015e-01 3.37779893e+01 | -1.57978730e+01 -9.52943015e-01 3.37779893e+01 40 3.48532179e+01 -6.93346504e+01 2.32374122e+01 | 3.48532179e+01 -6.93346504e+01 2.32374122e+01 41 2.71774953e+00 -2.95461162e+01 -8.89397356e+00 | 2.71774953e+00 -2.95461162e+01 -8.89397356e+00 42 6.82496064e+00 -1.98694279e+01 -9.81936201e+00 | 6.82496064e+00 -1.98694279e+01 -9.81936201e+00 43 5.41750739e+01 -9.76220628e-01 1.70188620e+01 | 5.41750739e+01 -9.76220628e-01 1.70188620e+01 44 2.66549613e+01 -3.60347156e+01 2.12792963e+01 | 2.66549613e+01 -3.60347156e+01 2.12792963e+01 45 2.73039905e+01 -8.88840130e+00 2.55118870e+01 | 2.73039905e+01 -8.88840130e+00 2.55118870e+01 46 8.31554082e+00 4.02618380e+00 2.84444679e+01 | 8.31554082e+00 4.02618380e+00 2.84444679e+01 47 9.19535205e+00 -5.46760622e-01 3.64788955e+01 | 9.19535205e+00 -5.46760622e-01 3.64788955e+01 48 -5.19217805e+01 2.99866342e+01 2.14834480e+01 | -5.19217805e+01 2.99866342e+01 2.14834480e+01 49 -2.76170756e+01 7.95860385e+00 2.84034917e+01 | -2.76170756e+01 7.95860385e+00 2.84034917e+01 50 -1.75096647e+01 3.20540273e+01 -9.70850437e+00 | -1.75096647e+01 3.20540273e+01 -9.70850437e+00 51 -2.63231524e+00 4.29069756e+01 7.49143816e-01 | -2.63231524e+00 4.29069756e+01 7.49143816e-01 52 -1.80807231e+01 2.24807613e+00 2.28704760e+01 | -1.80807231e+01 2.24807613e+00 2.28704760e+01 53 -1.86873695e+00 1.07825512e+01 3.46871786e+01 | -1.86873695e+00 1.07825512e+01 3.46871786e+01 54 -2.85989739e+01 1.42843713e+01 8.18371428e+00 | -2.85989739e+01 1.42843713e+01 8.18371428e+00 55 -8.98025359e+00 2.05624174e+01 2.26262669e+01 | -8.98025359e+00 2.05624174e+01 2.26262669e+01 56 5.99747357e+00 2.25360455e-01 8.61172510e+00 | 5.99747357e+00 2.25360455e-01 8.61172510e+00 57 -1.79018511e+00 4.27715089e+01 6.99949084e+00 | -1.79018511e+00 4.27715089e+01 6.99949084e+00 58 1.59729029e+01 2.26139852e+01 1.00727568e+01 | 1.59729029e+01 2.26139852e+01 1.00727568e+01 59 1.73063971e+01 2.23876167e+01 8.03874792e+00 | 1.73063971e+01 2.23876167e+01 8.03874792e+00 60 3.15206807e+01 -1.78914914e+01 3.14819516e+01 | 3.15206807e+01 -1.78914914e+01 3.14819516e+01 61 2.28093186e+01 7.51639717e+00 1.87757240e+01 | 2.28093186e+01 7.51639717e+00 1.87757240e+01 62 7.29823452e+00 2.20656146e+01 2.66414747e+01 | 7.29823452e+00 2.20656146e+01 2.66414747e+01 63 7.96028638e+00 1.79027149e+01 2.31520858e+01 | 7.96028638e+00 1.79027149e+01 2.31520858e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Th (Configuration in file "config-Th.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [22, 38, 27, 34, 33, 29, 37, 13, 9, 8, 30, 24, 35, 7, 18, 16, 15, 26, 14, 56, 46, 32, 0, 40, 11, 51, 17, 2, 63, 5, 10, 43, 21, 4, 3, 12, 52, 6, 1, 44, 23, 60, 55, 31, 39, 47, 20, 45, 49, 48, 61, 25, 36, 59, 62, 42, 19, 58, 57, 53, 41, 50, 54, 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)) = 37377.24557261542 V(r_1,...,r_N) = 37377.24557261543 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 -5.81221793e+01 -7.45407209e+01 -6.10812745e+01 | -5.81221793e+01 -7.45407209e+01 -6.10812745e+01 1 -6.38107384e+01 -5.34063002e+01 -6.88211968e+01 | -6.38107384e+01 -5.34063002e+01 -6.88211968e+01 2 -2.24415205e+01 -4.16323250e+01 -1.17707148e+02 | -2.24415205e+01 -4.16323250e+01 -1.17707148e+02 3 -1.39914603e+01 -1.29557496e+01 -8.61202519e+01 | -1.39914603e+01 -1.29557496e+01 -8.61202519e+01 4 -2.78417110e+01 -1.10497184e+02 -3.31960804e+01 | -2.78417110e+01 -1.10497184e+02 -3.31960804e+01 5 -8.40062953e+00 -1.03236256e+02 -1.78737793e+01 | -8.40062953e+00 -1.03236256e+02 -1.78737793e+01 6 -1.12800924e+02 -5.02750128e+01 -3.05323991e+01 | -1.12800924e+02 -5.02750128e+01 -3.05323991e+01 7 -9.10936270e+01 -1.85272866e+01 -2.98695479e+00 | -9.10936270e+01 -1.85272866e+01 -2.98695479e+00 8 2.63303285e+00 -9.23105527e+01 -8.70554098e+01 | 2.63303285e+00 -9.23105527e+01 -8.70554098e+01 9 3.92536945e+01 -7.13820700e+01 -6.78523415e+01 | 3.92536945e+01 -7.13820700e+01 -6.78523415e+01 10 5.40623329e+01 -2.78241791e+01 -1.06206785e+02 | 5.40623329e+01 -2.78241791e+01 -1.06206785e+02 11 1.12917347e+02 -1.33902587e+01 -6.55746432e+01 | 1.12917347e+02 -1.33902587e+01 -6.55746432e+01 12 7.11093217e+01 -9.85297198e+01 -4.11085090e+01 | 7.11093217e+01 -9.85297198e+01 -4.11085090e+01 13 1.24875679e+02 -5.90136525e+01 -2.08703733e+01 | 1.24875679e+02 -5.90136525e+01 -2.08703733e+01 14 8.44197198e+00 -4.89364508e+01 -6.13215436e+01 | 8.44197198e+00 -4.89364508e+01 -6.13215436e+01 15 6.94505459e+01 -1.70237250e+01 -8.94441017e+00 | 6.94505459e+01 -1.70237250e+01 -8.94441017e+00 16 -1.11777565e+02 -1.85438258e+01 -8.02601345e+01 | -1.11777565e+02 -1.85438258e+01 -8.02601345e+01 17 -6.91182097e+01 3.47822496e+01 -8.20995238e+01 | -6.91182097e+01 3.47822496e+01 -8.20995238e+01 18 -3.40311020e+01 6.67609274e+01 -1.11427634e+02 | -3.40311020e+01 6.67609274e+01 -1.11427634e+02 19 -5.04819574e+01 1.63901686e+02 -1.14007218e+02 | -5.04819574e+01 1.63901686e+02 -1.14007218e+02 20 -5.75799604e+01 2.14420458e+01 -5.06062642e+01 | -5.75799604e+01 2.14420458e+01 -5.06062642e+01 21 -1.95534219e+01 5.42435751e+01 -1.69393707e+01 | -1.95534219e+01 5.42435751e+01 -1.69393707e+01 22 -1.05332687e+02 8.33999639e+01 -4.02718547e+01 | -1.05332687e+02 8.33999639e+01 -4.02718547e+01 23 -7.69422857e+01 1.18975035e+02 -2.23863361e+01 | -7.69422857e+01 1.18975035e+02 -2.23863361e+01 24 7.43371788e+00 2.06895351e+01 -1.31822348e+02 | 7.43371788e+00 2.06895351e+01 -1.31822348e+02 25 4.39807052e+01 3.20236848e+01 -8.69715366e+01 | 4.39807052e+01 3.20236848e+01 -8.69715366e+01 26 5.48580223e+01 4.96447577e+01 -1.14517189e+02 | 5.48580223e+01 4.96447577e+01 -1.14517189e+02 27 8.56826381e+01 8.28537514e+01 -5.10458304e+01 | 8.56826381e+01 8.28537514e+01 -5.10458304e+01 28 9.79433769e+01 1.72452202e+01 -4.29487731e+01 | 9.79433769e+01 1.72452202e+01 -4.29487731e+01 29 1.31192339e+02 4.41033570e+01 -1.33765897e+01 | 1.31192339e+02 4.41033570e+01 -1.33765897e+01 30 2.32562097e+01 4.12406062e+01 -3.07213256e+01 | 2.32562097e+01 4.12406062e+01 -3.07213256e+01 31 5.25248162e+01 1.38669542e+02 -1.00645858e+01 | 5.25248162e+01 1.38669542e+02 -1.00645858e+01 32 -7.92181556e+01 -7.85935225e+01 2.57989106e+00 | -7.92181556e+01 -7.85935225e+01 2.57989106e+00 33 -7.61107363e+01 -8.13193499e+01 3.88662903e+01 | -7.61107363e+01 -8.13193499e+01 3.88662903e+01 34 -5.69370932e+01 -4.97154310e+01 1.92989786e+01 | -5.69370932e+01 -4.97154310e+01 1.92989786e+01 35 -2.68617123e+01 -8.24090982e+00 5.49525006e+01 | -2.68617123e+01 -8.24090982e+00 5.49525006e+01 36 -2.66205565e+01 -1.13465503e+02 5.95418820e+01 | -2.66205565e+01 -1.13465503e+02 5.95418820e+01 37 -1.99776989e+01 -9.17590547e+01 1.14652647e+02 | -1.99776989e+01 -9.17590547e+01 1.14652647e+02 38 -1.18396842e+02 -3.83178579e+01 5.23692989e+01 | -1.18396842e+02 -3.83178579e+01 5.23692989e+01 39 -6.00781622e+01 -2.03367359e+01 1.17684042e+02 | -6.00781622e+01 -2.03367359e+01 1.17684042e+02 40 8.81589181e+00 -1.45936368e+02 -2.87699392e+00 | 8.81589181e+00 -1.45936368e+02 -2.87699392e+00 41 3.01079623e+01 -8.83527347e+01 5.24347948e+01 | 3.01079623e+01 -8.83527347e+01 5.24347948e+01 42 9.58297047e+01 -3.77731852e+01 -8.93449149e-01 | 9.58297047e+01 -3.77731852e+01 -8.93449149e-01 43 1.28746577e+02 -1.08217671e+01 4.20540925e+01 | 1.28746577e+02 -1.08217671e+01 4.20540925e+01 44 6.25657713e+01 -1.07535272e+02 6.48792234e+01 | 6.25657713e+01 -1.07535272e+02 6.48792234e+01 45 7.66385996e+01 -4.77677480e+01 9.16348988e+01 | 7.66385996e+01 -4.77677480e+01 9.16348988e+01 46 1.37457108e+01 -3.27030268e+01 8.43129161e+01 | 1.37457108e+01 -3.27030268e+01 8.43129161e+01 47 4.64111009e+01 -2.32847879e+01 1.29637208e+02 | 4.64111009e+01 -2.32847879e+01 1.29637208e+02 48 -1.50176130e+02 6.46283744e+00 -6.38507126e+00 | -1.50176130e+02 6.46283744e+00 -6.38507126e+00 49 -8.14252716e+01 3.61325566e+01 5.17214859e+01 | -8.14252716e+01 3.61325566e+01 5.17214859e+01 50 -4.50224565e+01 9.26625041e+01 2.35502100e+01 | -4.50224565e+01 9.26625041e+01 2.35502100e+01 51 2.19788660e+00 1.35801709e+02 3.78555859e+01 | 2.19788660e+00 1.35801709e+02 3.78555859e+01 52 -5.88164851e+01 1.92339273e+01 1.02938309e+02 | -5.88164851e+01 1.92339273e+01 1.02938309e+02 53 -8.47541637e-01 2.18060067e+01 1.36180574e+02 | -8.47541637e-01 2.18060067e+01 1.36180574e+02 54 -1.18349107e+02 5.62597058e+01 7.68227453e+01 | -1.18349107e+02 5.62597058e+01 7.68227453e+01 55 -4.59771256e+01 8.29059955e+01 7.47901015e+01 | -4.59771256e+01 8.29059955e+01 7.47901015e+01 56 2.00469752e+01 1.85863881e+00 1.75368648e+01 | 2.00469752e+01 1.85863881e+00 1.75368648e+01 57 4.99957589e+01 6.04107525e+01 5.79138868e+01 | 4.99957589e+01 6.04107525e+01 5.79138868e+01 58 8.47632551e+01 7.80841481e+01 1.08509707e+01 | 8.47632551e+01 7.80841481e+01 1.08509707e+01 59 8.26932431e+01 1.01345813e+02 3.99187219e+01 | 8.26932431e+01 1.01345813e+02 3.99187219e+01 60 7.29061010e+01 2.26470852e+01 7.89133142e+01 | 7.29061010e+01 2.26470852e+01 7.89133142e+01 61 8.76978241e+01 2.95579297e+01 7.37124877e+01 | 8.76978241e+01 2.95579297e+01 7.37124877e+01 62 5.32207725e+00 9.02187177e+01 8.97478994e+01 | 5.32207725e+00 9.02187177e+01 8.97478994e+01 63 4.00348627e+01 8.25842596e+01 8.95233090e+01 | 4.00348627e+01 8.25842596e+01 8.95233090e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ce O Th (Configuration in file "config-CeOTh.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [19, 29, 4, 44, 2, 48, 49, 26, 12, 63, 37, 45, 8, 15, 39, 13, 56, 31, 43, 0, 34, 27, 51, 30, 47, 59, 7, 21, 38, 1, 23, 17, 33, 32, 20, 42, 41, 10, 28, 14, 40, 36, 35, 18, 3, 11, 52, 24, 5, 6, 53, 22, 46, 50, 60, 57, 16, 55, 58, 25, 54, 62, 61, 9] 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)) = 9739.300429121191 V(r_1,...,r_N) = 9739.300429121191 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 -2.32613480e+01 -2.76045390e+01 -2.43121254e+01 | -2.32613480e+01 -2.76045390e+01 -2.43121254e+01 1 1.10404020e+01 2.05776232e+01 1.71794573e+01 | 1.10404020e+01 2.05776232e+01 1.71794573e+01 2 1.03512329e+01 1.34713755e+01 2.67451638e+01 | 1.03512329e+01 1.34713755e+01 2.67451638e+01 3 4.17649250e+00 -2.95408283e+01 -7.34836207e+01 | 4.17649250e+00 -2.95408283e+01 -7.34836207e+01 4 -1.49829915e+02 -1.38823456e+02 -9.20165972e+01 | -1.49829915e+02 -1.38823456e+02 -9.20165972e+01 5 1.35562662e+02 1.10218008e+02 7.06559227e+01 | 1.35562662e+02 1.10218008e+02 7.06559227e+01 6 -5.24477899e+01 -4.20375227e+01 -1.44139266e+01 | -5.24477899e+01 -4.20375227e+01 -1.44139266e+01 7 -6.25488597e+01 -3.18396589e+01 -3.08252298e+01 | -6.25488597e+01 -3.18396589e+01 -3.08252298e+01 8 -2.88124279e+01 -4.52020767e+01 -4.24776652e+01 | -2.88124279e+01 -4.52020767e+01 -4.24776652e+01 9 5.17915287e+00 -3.21134154e+01 -4.93175004e+01 | 5.17915287e+00 -3.21134154e+01 -4.93175004e+01 10 1.50962763e+01 4.82326040e+00 -6.57742391e+01 | 1.50962763e+01 4.82326040e+00 -6.57742391e+01 11 2.43917772e+02 -1.34069902e+01 -1.75943396e+02 | 2.43917772e+02 -1.34069902e+01 -1.75943396e+02 12 2.08316672e+01 -6.93034348e+01 -1.43475020e+01 | 2.08316672e+01 -6.93034348e+01 -1.43475020e+01 13 7.68802946e+01 -2.81474819e+01 -1.06324248e+01 | 7.68802946e+01 -2.81474819e+01 -1.06324248e+01 14 7.61387537e+00 1.12222983e+01 2.01608338e+01 | 7.61387537e+00 1.12222983e+01 2.01608338e+01 15 3.18489853e+01 2.59064886e+01 -2.83106862e+01 | 3.18489853e+01 2.59064886e+01 -2.83106862e+01 16 -5.05853987e+01 1.84688889e+00 -4.67643025e+01 | -5.05853987e+01 1.84688889e+00 -4.67643025e+01 17 -6.55840506e+01 4.91508330e+01 -4.20616776e+01 | -6.55840506e+01 4.91508330e+01 -4.20616776e+01 18 -9.45069363e+00 3.65048421e+01 -5.83844815e+01 | -9.45069363e+00 3.65048421e+01 -5.83844815e+01 19 -1.83231295e+01 9.50818514e+01 -2.65130497e+01 | -1.83231295e+01 9.50818514e+01 -2.65130497e+01 20 -2.39437428e+01 1.94508638e+01 -3.46436462e+01 | -2.39437428e+01 1.94508638e+01 -3.46436462e+01 21 2.87452671e+00 5.41985749e+01 -1.32739361e+00 | 2.87452671e+00 5.41985749e+01 -1.32739361e+00 22 2.85939925e+01 -2.37392376e+01 3.72226290e+00 | 2.85939925e+01 -2.37392376e+01 3.72226290e+00 23 -7.65881267e+00 -1.88422244e+01 -6.63526274e+01 | -7.65881267e+00 -1.88422244e+01 -6.63526274e+01 24 -2.96302656e+01 -1.93160014e+01 -6.12911250e+00 | -2.96302656e+01 -1.93160014e+01 -6.12911250e+00 25 4.41494256e+01 3.61676279e+01 -4.68082553e+00 | 4.41494256e+01 3.61676279e+01 -4.68082553e+00 26 6.03373846e+00 -7.23950464e+00 -3.95122731e+01 | 6.03373846e+00 -7.23950464e+00 -3.95122731e+01 27 5.48624741e+01 6.52697018e+01 -5.86119953e+00 | 5.48624741e+01 6.52697018e+01 -5.86119953e+00 28 -2.06500177e+02 2.21149029e+01 1.57483427e+02 | -2.06500177e+02 2.21149029e+01 1.57483427e+02 29 -1.82757134e+01 -2.07911123e+01 -1.06267153e+01 | -1.82757134e+01 -2.07911123e+01 -1.06267153e+01 30 9.39618853e+00 -5.62162114e+01 2.63341336e+01 | 9.39618853e+00 -5.62162114e+01 2.63341336e+01 31 2.11293236e+01 5.34163359e+01 4.33593384e+00 | 2.11293236e+01 5.34163359e+01 4.33593384e+00 32 1.72225072e+01 2.18316579e+01 -2.86869361e+00 | 1.72225072e+01 2.18316579e+01 -2.86869361e+00 33 3.71263167e+01 2.18851629e+01 -9.62132180e+00 | 3.71263167e+01 2.18851629e+01 -9.62132180e+00 34 -4.81624968e+01 -6.26946315e+01 2.84951263e+01 | -4.81624968e+01 -6.26946315e+01 2.84951263e+01 35 -2.99847660e+01 -3.09311110e+00 1.68952575e+01 | -2.99847660e+01 -3.09311110e+00 1.68952575e+01 36 -5.33037808e+01 -5.85595852e+01 1.79832663e+01 | -5.33037808e+01 -5.85595852e+01 1.79832663e+01 37 -2.84022754e+01 -1.18864539e+01 7.43470204e+01 | -2.84022754e+01 -1.18864539e+01 7.43470204e+01 38 5.55047396e+00 -1.67936476e+01 -2.77937721e+01 | 5.55047396e+00 -1.67936476e+01 -2.77937721e+01 39 5.55344436e+01 2.96689952e+01 -1.65224969e+01 | 5.55344436e+01 2.96689952e+01 -1.65224969e+01 40 -4.14992037e+01 -8.01776633e+01 6.60435054e+00 | -4.14992037e+01 -8.01776633e+01 6.60435054e+00 41 3.21614001e+01 -3.69437985e+01 2.89929043e+01 | 3.21614001e+01 -3.69437985e+01 2.89929043e+01 42 5.08065977e+01 -8.52433890e-01 -4.75026356e+00 | 5.08065977e+01 -8.52433890e-01 -4.75026356e+00 43 5.89528328e+01 3.35452853e+01 3.07306176e+01 | 5.89528328e+01 3.35452853e+01 3.07306176e+01 44 3.24422569e+01 -6.84826138e+01 3.24957909e+01 | 3.24422569e+01 -6.84826138e+01 3.24957909e+01 45 4.50673722e+01 -4.27424121e+00 6.49532788e+01 | 4.50673722e+01 -4.27424121e+00 6.49532788e+01 46 2.30241811e+01 -1.31075190e+01 7.92248186e+01 | 2.30241811e+01 -1.31075190e+01 7.92248186e+01 47 -1.39016698e+01 -6.28603123e+00 -2.89527063e+01 | -1.39016698e+01 -6.28603123e+00 -2.89527063e+01 48 -9.67306964e+01 2.00502496e+01 3.44281557e+01 | -9.67306964e+01 2.00502496e+01 3.44281557e+01 49 -6.66547861e+01 4.46573026e+01 5.42700077e+01 | -6.66547861e+01 4.46573026e+01 5.42700077e+01 50 8.91094938e-01 7.24465069e+01 7.37847252e+01 | 8.91094938e-01 7.24465069e+01 7.37847252e+01 51 5.37311672e+00 -3.66965756e+01 -7.74694634e+00 | 5.37311672e+00 -3.66965756e+01 -7.74694634e+00 52 -5.07719226e+01 4.53797891e+00 7.45646594e+01 | -5.07719226e+01 4.53797891e+00 7.45646594e+01 53 -3.31235743e+01 3.31085295e+01 6.97681932e+01 | -3.31235743e+01 3.31085295e+01 6.97681932e+01 54 -2.79394042e+01 -5.05301123e+01 -3.16913252e+01 | -2.79394042e+01 -5.05301123e+01 -3.16913252e+01 55 7.39123047e+01 1.12708976e+01 -5.40112745e+00 | 7.39123047e+01 1.12708976e+01 -5.40112745e+00 56 3.43307405e+01 4.43992636e+01 1.07315193e+01 | 3.43307405e+01 4.43992636e+01 1.07315193e+01 57 -2.68660553e+01 -1.74944953e+01 -1.12478729e+01 | -2.68660553e+01 -1.74944953e+01 -1.12478729e+01 58 -3.94492381e+01 -2.10790551e+01 -1.96646336e+01 | -3.94492381e+01 -2.10790551e+01 -1.96646336e+01 59 5.07745627e+01 4.74226361e+01 2.61195031e+01 | 5.07745627e+01 4.74226361e+01 2.61195031e+01 60 -6.87294249e+01 -8.05031100e+01 -7.95187356e+01 | -6.87294249e+01 -8.05031100e+01 -7.95187356e+01 61 9.11543347e+01 8.05176761e+01 9.85259289e+01 | 9.11543347e+01 8.05176761e+01 9.85259289e+01 62 1.80032257e+00 3.65721626e+01 1.01505859e+01 | 1.80032257e+00 3.65721626e+01 1.01505859e+01 63 2.67082775e+01 5.22829916e+01 5.08092689e+01 | 2.67082775e+01 5.22829916e+01 5.08092689e+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.