!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-permutation-symmetry !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check whether a model is invariant with respect to atom permutations that preserve species, i.e. swapping any two atoms with the same species must not change the energy or forces. This must be true for all models. The check is performed for a randomly distorted non-periodic diamond cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. The energy and forces of each configuration are compared with one where each atom is randomly swapped with another atom of the same species. The energy and forces must remain unchanged. The verification check will pass if these conditions are satisfied for all configurations that the model is able to compute. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------- Results for KIM Model : EAM_Dynamo_SmirnovaKuskinStarikov_2013_UMoXe__MO_679329885632_005 Supported species : Mo U Xe random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Mo (Configuration in file "config-Mo.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [6, 35, 48, 31, 20, 41, 0, 59, 14, 36, 21, 47, 40, 24, 8, 45, 34, 44, 26, 32, 4, 10, 57, 29, 13, 33, 18, 39, 63, 23, 42, 3, 19, 25, 16, 1, 9, 38, 37, 27, 12, 5, 30, 55, 17, 15, 61, 11, 2, 51, 62, 49, 54, 60, 52, 43, 58, 22, 56, 7, 53, 46, 50, 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)) = -202.56765723644253 V(r_1,...,r_N) = -202.56765723644187 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 -1.36663142e+00 -1.29167919e+00 -8.45150008e-01 | -1.36663142e+00 -1.29167919e+00 -8.45150008e-01 1 -1.51881230e+00 -7.63387305e+00 2.66382390e+00 | -1.51881230e+00 -7.63387305e+00 2.66382390e+00 2 -1.18691639e+00 9.73190493e+00 -7.72271335e+00 | -1.18691639e+00 9.73190493e+00 -7.72271335e+00 3 1.51336996e+00 4.88564210e-01 -6.03011229e+00 | 1.51336996e+00 4.88564210e-01 -6.03011229e+00 4 -2.33778032e+00 -4.09324099e+00 1.11835375e+00 | -2.33778032e+00 -4.09324099e+00 1.11835375e+00 5 3.21596810e+00 1.33148444e+00 -1.47250784e+00 | 3.21596810e+00 1.33148444e+00 -1.47250784e+00 6 -1.00475759e+01 -7.03850396e+00 -9.83658644e+00 | -1.00475759e+01 -7.03850396e+00 -9.83658644e+00 7 2.21159931e+00 1.45090576e+01 -2.91854350e+00 | 2.21159931e+00 1.45090576e+01 -2.91854350e+00 8 1.17478409e+00 2.30909987e+00 2.64568694e+00 | 1.17478409e+00 2.30909987e+00 2.64568694e+00 9 -2.19580719e+00 -1.85083719e+00 -1.99286346e+00 | -2.19580719e+00 -1.85083719e+00 -1.99286346e+00 10 -4.26520693e+00 -9.92659788e+00 -7.38636029e+00 | -4.26520693e+00 -9.92659788e+00 -7.38636029e+00 11 6.28761586e+00 8.28672264e+00 2.48023565e+00 | 6.28761586e+00 8.28672264e+00 2.48023565e+00 12 -3.20533728e+00 -4.30613614e+00 -5.47020261e-01 | -3.20533728e+00 -4.30613614e+00 -5.47020261e-01 13 7.62909156e+00 -8.28774636e-01 -4.84392044e+00 | 7.62909156e+00 -8.28774636e-01 -4.84392044e+00 14 -1.06159894e-01 -2.02328360e+00 1.72403675e-01 | -1.06159894e-01 -2.02328360e+00 1.72403675e-01 15 2.10684797e+00 -1.58443533e+00 -4.28576795e-02 | 2.10684797e+00 -1.58443533e+00 -4.28576795e-02 16 8.25063295e-01 6.68178865e-02 5.55882858e-01 | 8.25063295e-01 6.68178865e-02 5.55882858e-01 17 -3.38755995e+00 -4.41077465e+00 2.33885679e+00 | -3.38755995e+00 -4.41077465e+00 2.33885679e+00 18 4.42250775e-01 2.62670796e+00 -5.15930738e+00 | 4.42250775e-01 2.62670796e+00 -5.15930738e+00 19 -8.67147091e+00 7.55420737e+00 -7.24543188e+00 | -8.67147091e+00 7.55420737e+00 -7.24543188e+00 20 2.54452818e+00 1.14457151e+00 -6.04297956e+00 | 2.54452818e+00 1.14457151e+00 -6.04297956e+00 21 7.42484331e+00 1.04965636e+00 -6.55952058e+00 | 7.42484331e+00 1.04965636e+00 -6.55952058e+00 22 -2.37323718e+00 -5.08621874e+00 -7.86279106e+00 | -2.37323718e+00 -5.08621874e+00 -7.86279106e+00 23 2.08593421e-01 8.32282109e+00 7.06406726e+00 | 2.08593421e-01 8.32282109e+00 7.06406726e+00 24 -9.11761503e-01 -9.10227715e-01 -2.04224871e+00 | -9.11761503e-01 -9.10227715e-01 -2.04224871e+00 25 -2.62797273e+00 7.50501768e+00 -4.37334930e+00 | -2.62797273e+00 7.50501768e+00 -4.37334930e+00 26 2.58570078e+00 3.14180103e-01 3.39487612e+00 | 2.58570078e+00 3.14180103e-01 3.39487612e+00 27 -4.59443006e+00 -2.27928143e+00 -1.73573851e+00 | -4.59443006e+00 -2.27928143e+00 -1.73573851e+00 28 2.60975414e+00 -5.86604980e+00 5.76466208e+00 | 2.60975414e+00 -5.86604980e+00 5.76466208e+00 29 4.74577931e+00 2.21408823e+00 1.62493639e+00 | 4.74577931e+00 2.21408823e+00 1.62493639e+00 30 4.08025389e+00 -5.16795988e+00 -4.64485717e-02 | 4.08025389e+00 -5.16795988e+00 -4.64485717e-02 31 3.86957365e+00 5.01307934e+00 3.10944881e+00 | 3.86957365e+00 5.01307934e+00 3.10944881e+00 32 -1.78165119e+00 5.26167185e-02 -4.06856410e-01 | -1.78165119e+00 5.26167185e-02 -4.06856410e-01 33 -1.51069439e+00 -1.71315213e+00 -3.82264804e-01 | -1.51069439e+00 -1.71315213e+00 -3.82264804e-01 34 8.15141047e+00 -1.44006347e+01 5.00797665e+00 | 8.15141047e+00 -1.44006347e+01 5.00797665e+00 35 -4.98026571e-01 -5.89445302e+00 4.54071039e+00 | -4.98026571e-01 -5.89445302e+00 4.54071039e+00 36 -2.44268349e+00 -3.05416924e+00 1.00510244e+00 | -2.44268349e+00 -3.05416924e+00 1.00510244e+00 37 4.58777218e-01 -2.94187970e+00 5.34646674e+00 | 4.58777218e-01 -2.94187970e+00 5.34646674e+00 38 -3.21695619e+00 -2.69023447e+00 -2.05357878e+00 | -3.21695619e+00 -2.69023447e+00 -2.05357878e+00 39 -3.51772807e+00 -3.35256102e+00 6.59728294e+00 | -3.51772807e+00 -3.35256102e+00 6.59728294e+00 40 -1.03803821e+00 -2.25182043e+00 3.52412494e+00 | -1.03803821e+00 -2.25182043e+00 3.52412494e+00 41 -5.98319149e+00 3.65327059e+00 -4.03938288e+00 | -5.98319149e+00 3.65327059e+00 -4.03938288e+00 42 -3.15617771e+00 1.07062671e+00 -2.34492977e+00 | -3.15617771e+00 1.07062671e+00 -2.34492977e+00 43 6.37669913e+00 1.01319996e+01 4.08506512e+00 | 6.37669913e+00 1.01319996e+01 4.08506512e+00 44 7.04928414e+00 -1.24148012e+01 6.44910976e+00 | 7.04928414e+00 -1.24148012e+01 6.44910976e+00 45 -6.69692725e-01 5.24709069e-01 -7.27946496e-01 | -6.69692725e-01 5.24709069e-01 -7.27946496e-01 46 -1.44485908e+00 4.50353203e+00 1.87151111e+00 | -1.44485908e+00 4.50353203e+00 1.87151111e+00 47 1.22936881e+00 1.60383916e+00 4.90306492e-01 | 1.22936881e+00 1.60383916e+00 4.90306492e-01 48 -1.10408267e+01 5.25035234e+00 9.00227825e+00 | -1.10408267e+01 5.25035234e+00 9.00227825e+00 49 -1.45889030e+00 -1.31233530e-01 3.44833613e+00 | -1.45889030e+00 -1.31233530e-01 3.44833613e+00 50 -4.21235059e+00 -2.05816608e+00 -4.60949505e+00 | -4.21235059e+00 -2.05816608e+00 -4.60949505e+00 51 1.86769251e-01 1.04033115e+01 9.58882277e+00 | 1.86769251e-01 1.04033115e+01 9.58882277e+00 52 2.70342206e+00 7.68515684e+00 -2.64071910e+00 | 2.70342206e+00 7.68515684e+00 -2.64071910e+00 53 1.53053166e+00 1.93108546e-01 1.94392676e+00 | 1.53053166e+00 1.93108546e-01 1.94392676e+00 54 2.78226899e+00 1.37456705e-01 5.76542473e-01 | 2.78226899e+00 1.37456705e-01 5.76542473e-01 55 -1.70513966e+00 -2.14874780e+00 -2.50250881e+00 | -1.70513966e+00 -2.14874780e+00 -2.50250881e+00 56 -7.46443326e-01 -4.67865333e+00 2.82509395e+00 | -7.46443326e-01 -4.67865333e+00 2.82509395e+00 57 3.47391538e+00 -4.53525642e+00 -8.37255879e+00 | 3.47391538e+00 -4.53525642e+00 -8.37255879e+00 58 5.11861713e+00 8.83084889e-01 7.50437974e-01 | 5.11861713e+00 8.83084889e-01 7.50437974e-01 59 -1.75763656e+00 -1.55230512e+00 7.90725490e-01 | -1.75763656e+00 -1.55230512e+00 7.90725490e-01 60 7.63629605e+00 -3.58085618e-03 5.47014133e+00 | 7.63629605e+00 -3.58085618e-03 5.47014133e+00 61 -2.13987016e+00 -1.08590836e-02 -2.55326713e+00 | -2.13987016e+00 -1.08590836e-02 -2.55326713e+00 62 -3.79298513e+00 1.17423114e+01 1.07836968e+01 | -3.79298513e+00 1.17423114e+01 1.07836968e+01 63 7.37523620e-01 -2.17297505e+00 -1.69093363e+00 | 7.37523620e-01 -2.17297505e+00 -1.69093363e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = U (Configuration in file "config-U.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [59, 37, 48, 32, 38, 54, 7, 6, 51, 30, 50, 35, 17, 45, 47, 21, 33, 12, 49, 24, 25, 15, 55, 29, 19, 20, 28, 53, 26, 23, 9, 46, 3, 16, 63, 11, 42, 1, 4, 62, 57, 52, 36, 58, 56, 13, 31, 14, 2, 18, 10, 8, 41, 27, 5, 22, 44, 40, 43, 0, 61, 60, 39, 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)) = 335.12394229724106 V(r_1,...,r_N) = 335.123942297241 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 -3.81879653e+00 -2.96268427e+00 -1.94677453e+00 | -3.81879653e+00 -2.96268427e+00 -1.94677453e+00 1 -1.90515328e+01 -2.24058064e+01 3.92340934e+01 | -1.90515328e+01 -2.24058064e+01 3.92340934e+01 2 2.31650800e+01 2.46180047e+01 -3.96516706e+01 | 2.31650800e+01 2.46180047e+01 -3.96516706e+01 3 -3.51951635e+01 1.86545079e+01 -1.83650586e+01 | -3.51951635e+01 1.86545079e+01 -1.83650586e+01 4 -1.07471084e+01 -4.26765247e+01 -7.30633270e+00 | -1.07471084e+01 -4.26765247e+01 -7.30633270e+00 5 3.15302111e+01 2.19254148e+01 -3.11023949e+01 | 3.15302111e+01 2.19254148e+01 -3.11023949e+01 6 -1.83039122e+01 -3.51562622e+00 -1.91278616e+01 | -1.83039122e+01 -3.51562622e+00 -1.91278616e+01 7 7.24822797e+00 6.19892051e+00 1.40455026e+01 | 7.24822797e+00 6.19892051e+00 1.40455026e+01 8 -1.55989923e+01 -2.05934371e+01 -1.42361329e+01 | -1.55989923e+01 -2.05934371e+01 -1.42361329e+01 9 1.01216743e+00 1.04770700e+01 1.77298054e+01 | 1.01216743e+00 1.04770700e+01 1.77298054e+01 10 1.16197617e+01 4.88436368e+00 -5.56951756e+00 | 1.16197617e+01 4.88436368e+00 -5.56951756e+00 11 1.44030968e+01 -1.88694884e+00 -2.36111926e+01 | 1.44030968e+01 -1.88694884e+00 -2.36111926e+01 12 -1.68583800e+01 -2.37440616e+01 -4.20761765e+00 | -1.68583800e+01 -2.37440616e+01 -4.20761765e+00 13 1.79915733e+01 2.25651461e+01 2.04767333e+00 | 1.79915733e+01 2.25651461e+01 2.04767333e+00 14 2.19981989e+01 -2.73689153e+01 7.87285430e+00 | 2.19981989e+01 -2.73689153e+01 7.87285430e+00 15 -2.24614606e+01 3.40621770e+01 -2.16337965e+01 | -2.24614606e+01 3.40621770e+01 -2.16337965e+01 16 -6.95463546e+00 -8.73396455e+00 -1.44572722e+01 | -6.95463546e+00 -8.73396455e+00 -1.44572722e+01 17 -1.78587474e+01 1.81098603e+01 -1.73259357e+01 | -1.78587474e+01 1.81098603e+01 -1.73259357e+01 18 -9.49178466e+00 -5.50735000e+00 -7.42751830e+00 | -9.49178466e+00 -5.50735000e+00 -7.42751830e+00 19 -5.58002553e+00 2.17526246e+01 -3.65229793e+00 | -5.58002553e+00 2.17526246e+01 -3.65229793e+00 20 -7.19494183e+00 -2.87893090e+01 -8.98687882e+00 | -7.19494183e+00 -2.87893090e+01 -8.98687882e+00 21 3.44215238e+01 1.31124822e+01 -9.36208783e+00 | 3.44215238e+01 1.31124822e+01 -9.36208783e+00 22 -1.49923348e+01 -1.19899715e+01 -5.16834711e+01 | -1.49923348e+01 -1.19899715e+01 -5.16834711e+01 23 8.66199656e+00 2.00660815e+01 5.11504190e+01 | 8.66199656e+00 2.00660815e+01 5.11504190e+01 24 -1.84162403e+01 -1.56690875e+01 -2.34868365e+01 | -1.84162403e+01 -1.56690875e+01 -2.34868365e+01 25 2.68647873e+01 -1.04415160e+01 9.58699149e+00 | 2.68647873e+01 -1.04415160e+01 9.58699149e+00 26 -1.82454096e+01 -9.06442170e+00 -2.82300734e+01 | -1.82454096e+01 -9.06442170e+00 -2.82300734e+01 27 2.40091956e+01 1.45020143e+01 2.25107327e+01 | 2.40091956e+01 1.45020143e+01 2.25107327e+01 28 6.64458552e+00 1.68824906e+01 1.70287737e+01 | 6.64458552e+00 1.68824906e+01 1.70287737e+01 29 3.48262165e+00 -1.01943289e+00 1.12306879e+00 | 3.48262165e+00 -1.01943289e+00 1.12306879e+00 30 1.49861486e+00 2.25093271e+00 3.10280528e+01 | 1.49861486e+00 2.25093271e+00 3.10280528e+01 31 -1.01113697e+00 2.61842831e+01 -1.32242312e+01 | -1.01113697e+00 2.61842831e+01 -1.32242312e+01 32 -3.27858093e+01 -3.09754975e+01 -2.64663897e+01 | -3.27858093e+01 -3.09754975e+01 -2.64663897e+01 33 1.54544166e+00 4.29194649e+01 -8.98543242e+00 | 1.54544166e+00 4.29194649e+01 -8.98543242e+00 34 -1.08625212e+01 1.57924838e+01 3.12361486e+01 | -1.08625212e+01 1.57924838e+01 3.12361486e+01 35 8.86818294e+00 -1.68972939e+01 -2.62519304e+01 | 8.86818294e+00 -1.68972939e+01 -2.62519304e+01 36 -9.27761459e+00 -3.59925141e+01 2.28733739e+01 | -9.27761459e+00 -3.59925141e+01 2.28733739e+01 37 1.75733983e+01 5.10958861e+00 3.37114121e+01 | 1.75733983e+01 5.10958861e+00 3.37114121e+01 38 -1.14272012e+00 -7.55874791e-01 -2.72047884e+00 | -1.14272012e+00 -7.55874791e-01 -2.72047884e+00 39 -5.17992898e+00 -5.59852987e+00 1.30407113e+01 | -5.17992898e+00 -5.59852987e+00 1.30407113e+01 40 2.82638390e+00 4.16828215e-01 2.47001960e+00 | 2.82638390e+00 4.16828215e-01 2.47001960e+00 41 -6.96025713e+00 1.69498000e+01 -2.37369724e+01 | -6.96025713e+00 1.69498000e+01 -2.37369724e+01 42 1.69464769e+01 -3.48213310e+01 3.90154389e+01 | 1.69464769e+01 -3.48213310e+01 3.90154389e+01 43 1.93835865e+01 -8.86744311e+00 -1.27387499e+01 | 1.93835865e+01 -8.86744311e+00 -1.27387499e+01 44 2.51017321e+01 -2.87264896e+01 1.02499901e+01 | 2.51017321e+01 -2.87264896e+01 1.02499901e+01 45 -4.56920543e-01 5.66214841e-01 -6.43147495e-01 | -4.56920543e-01 5.66214841e-01 -6.43147495e-01 46 2.41296147e+00 1.58990128e+01 1.01234020e+01 | 2.41296147e+00 1.58990128e+01 1.01234020e+01 47 -1.43613920e+01 -3.09978919e+01 3.09953146e+01 | -1.43613920e+01 -3.09978919e+01 3.09953146e+01 48 -7.21941753e+00 -1.01394933e+01 -8.37760636e+00 | -7.21941753e+00 -1.01394933e+01 -8.37760636e+00 49 -3.25414900e+00 -3.86144497e+01 1.61531504e-01 | -3.25414900e+00 -3.86144497e+01 1.61531504e-01 50 1.40459406e+01 3.40213283e+01 -2.79623065e+00 | 1.40459406e+01 3.40213283e+01 -2.79623065e+00 51 9.18096420e+00 1.09746515e+01 4.04957929e+00 | 9.18096420e+00 1.09746515e+01 4.04957929e+00 52 -1.19459783e+01 2.81276006e+01 1.48905441e+01 | -1.19459783e+01 2.81276006e+01 1.48905441e+01 53 -2.19691631e+01 -3.15094818e+01 4.34990309e+01 | -2.19691631e+01 -3.15094818e+01 4.34990309e+01 54 -3.06811180e+01 2.52862282e+01 3.58446636e+01 | -3.06811180e+01 2.52862282e+01 3.58446636e+01 55 2.45629740e+00 8.83375840e-01 6.08729134e-01 | 2.45629740e+00 8.83375840e-01 6.08729134e-01 56 -7.01506768e+00 -4.19383092e+01 -1.36918924e+01 | -7.01506768e+00 -4.19383092e+01 -1.36918924e+01 57 3.80143870e+01 2.35057143e+01 2.37860759e+01 | 3.80143870e+01 2.35057143e+01 2.37860759e+01 58 -1.96250282e+00 -2.23173780e+01 1.27509171e+01 | -1.96250282e+00 -2.23173780e+01 1.27509171e+01 59 5.47305370e-01 -1.22216290e-01 6.21651343e-01 | 5.47305370e-01 -1.22216290e-01 6.21651343e-01 60 -3.25000194e+00 4.09914017e+01 -1.62091843e+01 | -3.25000194e+00 4.09914017e+01 -1.62091843e+01 61 3.36277252e+00 -8.10387704e+00 2.86937744e+00 | 3.36277252e+00 -8.10387704e+00 2.86937744e+00 62 1.75476300e+01 3.70311863e+01 -3.52381021e+01 | 1.75476300e+01 3.70311863e+01 -3.52381021e+01 63 -4.25993790e+00 8.02587488e+00 -3.70480877e+00 | -4.25993790e+00 8.02587488e+00 -3.70480877e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Xe (Configuration in file "config-Xe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [37, 12, 21, 29, 22, 31, 38, 43, 50, 41, 23, 28, 1, 17, 30, 57, 42, 13, 59, 26, 62, 2, 4, 10, 55, 56, 19, 35, 11, 3, 14, 5, 33, 32, 51, 27, 45, 0, 6, 58, 49, 9, 16, 7, 46, 36, 44, 63, 53, 40, 8, 34, 60, 48, 61, 24, 25, 15, 39, 18, 52, 54, 20, 47] 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)) = 27020.560507906277 V(r_1,...,r_N) = 27020.56050790629 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 -1.89659487e+03 -1.95431747e+03 -1.40089214e+03 | -1.89659487e+03 -1.95431747e+03 -1.40089214e+03 1 1.81522919e+03 1.84279001e+03 1.43493477e+03 | 1.81522919e+03 1.84279001e+03 1.43493477e+03 2 6.55261399e+01 9.28935203e+01 -5.46823885e+01 | 6.55261399e+01 9.28935203e+01 -5.46823885e+01 3 1.85302917e+03 -2.70679833e+03 1.04897123e+03 | 1.85302917e+03 -2.70679833e+03 1.04897123e+03 4 -5.37904197e+02 -6.48085687e+02 -1.75371773e+02 | -5.37904197e+02 -6.48085687e+02 -1.75371773e+02 5 -1.70458229e+03 -1.21888091e+03 1.11133061e+03 | -1.70458229e+03 -1.21888091e+03 1.11133061e+03 6 -1.96493198e+03 -1.96088777e+03 -1.30516234e+03 | -1.96493198e+03 -1.96088777e+03 -1.30516234e+03 7 2.95356034e+03 1.15919776e+03 2.21153150e+02 | 2.95356034e+03 1.15919776e+03 2.21153150e+02 8 -1.05583341e+01 -1.94835145e+01 -1.20904419e+01 | -1.05583341e+01 -1.94835145e+01 -1.20904419e+01 9 -1.09419522e+03 -1.04962173e+03 9.82867457e+02 | -1.09419522e+03 -1.04962173e+03 9.82867457e+02 10 -6.85220125e+02 -5.35411499e+02 -2.96180520e+03 | -6.85220125e+02 -5.35411499e+02 -2.96180520e+03 11 2.10562681e+03 9.83620856e+02 7.03396291e+02 | 2.10562681e+03 9.83620856e+02 7.03396291e+02 12 2.41659115e+01 -5.50117187e+01 2.95945048e+01 | 2.41659115e+01 -5.50117187e+01 2.95945048e+01 13 3.09457463e+02 -9.57773283e+02 -9.95660734e+02 | 3.09457463e+02 -9.57773283e+02 -9.95660734e+02 14 2.13265186e+03 1.88311801e+03 -7.91829434e+02 | 2.13265186e+03 1.88311801e+03 -7.91829434e+02 15 -1.00476687e+03 4.67989427e+02 -7.43190433e+02 | -1.00476687e+03 4.67989427e+02 -7.43190433e+02 16 -2.86773345e+02 -6.12208421e+02 -6.74050320e+02 | -2.86773345e+02 -6.12208421e+02 -6.74050320e+02 17 1.22814250e+03 -1.65942746e+03 -1.10690978e+03 | 1.22814250e+03 -1.65942746e+03 -1.10690978e+03 18 -1.02842448e+03 -1.04737436e+03 -9.62609800e+02 | -1.02842448e+03 -1.04737436e+03 -9.62609800e+02 19 8.12482478e+02 1.22694267e+03 5.64668729e+02 | 8.12482478e+02 1.22694267e+03 5.64668729e+02 20 -2.58745322e+03 8.50207018e+02 1.12371881e+03 | -2.58745322e+03 8.50207018e+02 1.12371881e+03 21 -4.81422423e+02 4.03668703e+02 -7.72817475e+02 | -4.81422423e+02 4.03668703e+02 -7.72817475e+02 22 -1.09102017e+03 2.14544883e+03 1.78207809e+03 | -1.09102017e+03 2.14544883e+03 1.78207809e+03 23 -8.64787085e+02 1.72429442e+03 -2.35632202e+03 | -8.64787085e+02 1.72429442e+03 -2.35632202e+03 24 7.68307382e+02 1.85770226e+03 -2.30400845e+03 | 7.68307382e+02 1.85770226e+03 -2.30400845e+03 25 5.77502119e+01 2.38173877e+01 5.66114618e+01 | 5.77502119e+01 2.38173877e+01 5.66114618e+01 26 -1.43198093e+03 -2.58774557e+03 -6.64908080e+02 | -1.43198093e+03 -2.58774557e+03 -6.64908080e+02 27 1.45794232e+03 2.61276150e+03 6.54486606e+02 | 1.45794232e+03 2.61276150e+03 6.54486606e+02 28 -1.92936558e+03 -1.32079990e+03 -4.82410626e+02 | -1.92936558e+03 -1.32079990e+03 -4.82410626e+02 29 1.75577258e+03 1.98483786e+03 1.53506378e+03 | 1.75577258e+03 1.98483786e+03 1.53506378e+03 30 -2.04527872e+03 -1.12251937e+03 -1.38437750e+03 | -2.04527872e+03 -1.12251937e+03 -1.38437750e+03 31 1.75152146e+03 1.64596868e+03 9.47866669e+02 | 1.75152146e+03 1.64596868e+03 9.47866669e+02 32 -1.66549510e+03 -1.85550963e+03 -1.78363197e+03 | -1.66549510e+03 -1.85550963e+03 -1.78363197e+03 33 4.08949169e+02 -7.33502438e+02 2.52149075e+03 | 4.08949169e+02 -7.33502438e+02 2.52149075e+03 34 6.98823031e+02 2.01877383e+03 -1.89342841e+03 | 6.98823031e+02 2.01877383e+03 -1.89342841e+03 35 -7.88381812e+02 6.54486404e+01 -2.68174412e+02 | -7.88381812e+02 6.54486404e+01 -2.68174412e+02 36 -1.46457773e+03 -1.06185981e+03 -2.26750537e+03 | -1.46457773e+03 -1.06185981e+03 -2.26750537e+03 37 1.60524860e+03 9.01860547e+02 2.44626589e+03 | 1.60524860e+03 9.01860547e+02 2.44626589e+03 38 -3.20974851e+02 2.35617340e+02 2.76132041e+02 | -3.20974851e+02 2.35617340e+02 2.76132041e+02 39 -2.38256748e+02 -1.51001613e+02 3.02707293e+02 | -2.38256748e+02 -1.51001613e+02 3.02707293e+02 40 -5.77266308e+02 -1.89814785e+03 -1.59394373e+03 | -5.77266308e+02 -1.89814785e+03 -1.59394373e+03 41 6.19203635e+02 1.84920422e+03 1.48110516e+03 | 6.19203635e+02 1.84920422e+03 1.48110516e+03 42 -9.04468846e+02 -1.04898543e+03 4.12980689e+02 | -9.04468846e+02 -1.04898543e+03 4.12980689e+02 43 1.61891671e+03 1.48858102e+03 1.34919066e+03 | 1.61891671e+03 1.48858102e+03 1.34919066e+03 44 3.99066287e+01 -4.88159606e+01 2.25570474e+01 | 3.99066287e+01 -4.88159606e+01 2.25570474e+01 45 1.42989173e+00 5.38751372e-01 1.64355397e+00 | 1.42989173e+00 5.38751372e-01 1.64355397e+00 46 8.88244410e+02 -4.19449264e+02 1.72977143e+03 | 8.88244410e+02 -4.19449264e+02 1.72977143e+03 47 -1.11172237e+03 -1.34061630e+03 2.52278834e+03 | -1.11172237e+03 -1.34061630e+03 2.52278834e+03 48 -1.10799798e+03 7.75616213e+02 1.15600941e+03 | -1.10799798e+03 7.75616213e+02 1.15600941e+03 49 -3.76099642e+02 1.24441291e+03 -2.75975411e+03 | -3.76099642e+02 1.24441291e+03 -2.75975411e+03 50 7.53909308e+02 -1.37157515e+03 2.49859726e+03 | 7.53909308e+02 -1.37157515e+03 2.49859726e+03 51 -8.81001503e+00 1.03816673e+01 1.40452890e+01 | -8.81001503e+00 1.03816673e+01 1.40452890e+01 52 -9.64395178e+02 -3.46347156e+03 1.53094197e+03 | -9.64395178e+02 -3.46347156e+03 1.53094197e+03 53 1.80320534e+03 2.11130119e+03 8.85714896e+02 | 1.80320534e+03 2.11130119e+03 8.85714896e+02 54 -7.79041700e+02 -1.83233748e+03 -9.24811407e+02 | -7.79041700e+02 -1.83233748e+03 -9.24811407e+02 55 3.81527419e+02 2.10522398e+03 1.14148799e+03 | 3.81527419e+02 2.10522398e+03 1.14148799e+03 56 1.16631328e+03 1.53975295e+02 -7.83900897e+01 | 1.16631328e+03 1.53975295e+02 -7.83900897e+01 57 8.58033481e+02 -2.06023085e+03 -1.97861078e+03 | 8.58033481e+02 -2.06023085e+03 -1.97861078e+03 58 6.48360916e+02 -5.99372844e+02 6.80474323e+02 | 6.48360916e+02 -5.99372844e+02 6.80474323e+02 59 1.75362347e+00 1.57812091e+00 5.24120189e-01 | 1.75362347e+00 1.57812091e+00 5.24120189e-01 60 6.33936593e+02 4.02616110e+02 -3.06172676e+03 | 6.33936593e+02 4.02616110e+02 -3.06172676e+03 61 5.22815429e+02 8.85679006e+02 6.28160909e+02 | 5.22815429e+02 8.85679006e+02 6.28160909e+02 62 -2.29222468e+03 9.21218078e+02 7.15416035e+02 | -2.29222468e+03 9.21218078e+02 7.15416035e+02 63 1.50322952e+03 1.26393736e+03 1.24432877e+03 | 1.50322952e+03 1.26393736e+03 1.24432877e+03 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Mo U Xe (Configuration in file "config-MoUXe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [23, 9, 26, 41, 33, 32, 24, 30, 12, 1, 28, 48, 8, 63, 38, 45, 50, 47, 20, 31, 18, 34, 25, 0, 6, 22, 2, 52, 10, 44, 7, 19, 5, 4, 21, 60, 39, 53, 14, 36, 42, 3, 40, 46, 29, 15, 43, 17, 11, 58, 16, 57, 27, 37, 54, 56, 55, 51, 49, 59, 35, 62, 61, 13] 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)) = 4164.217732055468 V(r_1,...,r_N) = 4164.2177320554665 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 -7.52180048e+01 -1.25070579e+02 -1.62414520e+02 | -7.52180048e+01 -1.25070579e+02 -1.62414520e+02 1 7.38228349e+01 1.20056844e+02 1.47540184e+02 | 7.38228349e+01 1.20056844e+02 1.47540184e+02 2 -5.25938282e-01 -1.45429477e+00 -2.32695317e+00 | -5.25938282e-01 -1.45429477e+00 -2.32695317e+00 3 1.73667491e+03 -6.40691319e+02 -2.42798984e+03 | 1.73667491e+03 -6.40691319e+02 -2.42798984e+03 4 -1.08874085e+02 -2.88551090e+02 -1.45444667e+02 | -1.08874085e+02 -2.88551090e+02 -1.45444667e+02 5 2.45478035e+02 6.14207934e+01 -1.34357398e+02 | 2.45478035e+02 6.14207934e+01 -1.34357398e+02 6 6.71822932e+00 4.53142840e+01 -5.03189057e+01 | 6.71822932e+00 4.53142840e+01 -5.03189057e+01 7 -1.13169233e+02 1.96324951e+01 -4.89278004e+01 | -1.13169233e+02 1.96324951e+01 -4.89278004e+01 8 -2.02995472e+00 -3.54273177e+00 -7.89604325e+00 | -2.02995472e+00 -3.54273177e+00 -7.89604325e+00 9 1.14029247e+02 -5.50070072e+02 -3.10158359e+01 | 1.14029247e+02 -5.50070072e+02 -3.10158359e+01 10 7.30484916e+00 9.38568661e+00 -2.24986317e+01 | 7.30484916e+00 9.38568661e+00 -2.24986317e+01 11 1.21591644e+01 5.74107198e+00 5.19754215e+00 | 1.21591644e+01 5.74107198e+00 5.19754215e+00 12 1.12741886e+01 -1.14963187e+01 2.96215675e+00 | 1.12741886e+01 -1.14963187e+01 2.96215675e+00 13 1.95519433e+00 -1.46752240e+00 -2.20192424e+00 | 1.95519433e+00 -1.46752240e+00 -2.20192424e+00 14 -1.27692773e+02 5.38290623e+02 4.64713144e+01 | -1.27692773e+02 5.38290623e+02 4.64713144e+01 15 3.99559377e+01 -1.16131589e+02 -1.27835157e+02 | 3.99559377e+01 -1.16131589e+02 -1.27835157e+02 16 2.31453640e-01 -4.85365000e-01 3.73283091e-01 | 2.31453640e-01 -4.85365000e-01 3.73283091e-01 17 -4.02023265e+02 -3.44735223e+02 1.85742942e+02 | -4.02023265e+02 -3.44735223e+02 1.85742942e+02 18 4.03266886e+02 3.36138789e+02 -1.94015368e+02 | 4.03266886e+02 3.36138789e+02 -1.94015368e+02 19 3.30008733e+00 5.55555058e+00 -5.39307812e+00 | 3.30008733e+00 5.55555058e+00 -5.39307812e+00 20 -1.74581221e+03 6.49101586e+02 2.42236582e+03 | -1.74581221e+03 6.49101586e+02 2.42236582e+03 21 -3.67283734e+02 -1.00922078e+03 5.86844598e+02 | -3.67283734e+02 -1.00922078e+03 5.86844598e+02 22 -1.01123963e+01 3.57809132e+00 4.51904571e+00 | -1.01123963e+01 3.57809132e+00 4.51904571e+00 23 1.25440764e+00 2.09963478e+00 1.69173737e+00 | 1.25440764e+00 2.09963478e+00 1.69173737e+00 24 -2.16903630e+00 2.54617947e+00 -1.12286327e+01 | -2.16903630e+00 2.54617947e+00 -1.12286327e+01 25 -2.55500339e+02 1.80839070e+02 -1.90108370e+02 | -2.55500339e+02 1.80839070e+02 -1.90108370e+02 26 -6.19577509e-01 -6.99347869e+00 -8.35902073e+00 | -6.19577509e-01 -6.99347869e+00 -8.35902073e+00 27 6.95720182e+00 1.13243387e+01 2.66942391e+00 | 6.95720182e+00 1.13243387e+01 2.66942391e+00 28 -1.89629312e+02 -1.30973092e+03 -1.20201336e+03 | -1.89629312e+02 -1.30973092e+03 -1.20201336e+03 29 4.62348910e+02 1.12454211e+03 1.39744679e+03 | 4.62348910e+02 1.12454211e+03 1.39744679e+03 30 6.32214854e+02 6.04480991e+02 -1.12930392e+03 | 6.32214854e+02 6.04480991e+02 -1.12930392e+03 31 -2.54811915e+02 1.06839619e+02 -1.47446833e+02 | -2.54811915e+02 1.06839619e+02 -1.47446833e+02 32 -2.11486099e+01 -4.59636235e+01 4.87694882e+01 | -2.11486099e+01 -4.59636235e+01 4.87694882e+01 33 -9.77140852e+00 -2.77762590e+00 -3.56630880e+00 | -9.77140852e+00 -2.77762590e+00 -3.56630880e+00 34 -2.97131159e+01 2.02969714e+02 3.44003018e+02 | -2.97131159e+01 2.02969714e+02 3.44003018e+02 35 -4.09632843e+00 6.62809277e+00 6.94883311e+00 | -4.09632843e+00 6.62809277e+00 6.94883311e+00 36 6.32984017e+00 -9.73714146e+00 -4.40187861e+00 | 6.32984017e+00 -9.73714146e+00 -4.40187861e+00 37 -3.09369277e+00 2.41381138e+00 1.56212315e+01 | -3.09369277e+00 2.41381138e+00 1.56212315e+01 38 -1.67162714e+02 -1.64293193e+02 -2.35246629e+02 | -1.67162714e+02 -1.64293193e+02 -2.35246629e+02 39 -2.07970195e+00 -1.04366522e+02 3.32147329e+02 | -2.07970195e+00 -1.04366522e+02 3.32147329e+02 40 -5.16974866e+00 -8.74680683e+00 -4.75210784e+00 | -5.16974866e+00 -8.74680683e+00 -4.75210784e+00 41 1.70592059e+00 -4.58621702e+00 2.69540545e+00 | 1.70592059e+00 -4.58621702e+00 2.69540545e+00 42 4.26193931e+00 8.55427500e+00 1.90758432e+00 | 4.26193931e+00 8.55427500e+00 1.90758432e+00 43 1.66206841e+01 -1.51857219e+01 -1.92169967e+01 | 1.66206841e+01 -1.51857219e+01 -1.92169967e+01 44 -3.22653161e+02 -2.61557645e+02 -3.76769709e+02 | -3.22653161e+02 -2.61557645e+02 -3.76769709e+02 45 3.23681728e+02 2.60811374e+02 3.78283653e+02 | 3.23681728e+02 2.60811374e+02 3.78283653e+02 46 6.17410323e+00 -6.87743010e+00 7.53385607e+00 | 6.17410323e+00 -6.87743010e+00 7.53385607e+00 47 5.49167411e-01 6.53047604e-02 -5.91323423e-01 | 5.49167411e-01 6.53047604e-02 -5.91323423e-01 48 -2.72357501e+02 -5.17199059e+01 -1.80356361e+02 | -2.72357501e+02 -5.17199059e+01 -1.80356361e+02 49 1.73652828e+02 1.69244048e+02 -1.12865427e+02 | 1.73652828e+02 1.69244048e+02 -1.12865427e+02 50 -6.07464135e+02 -3.92032828e+01 7.55993723e+01 | -6.07464135e+02 -3.92032828e+01 7.55993723e+01 51 3.13301593e+02 4.53331470e+02 4.51842093e+02 | 3.13301593e+02 4.53331470e+02 4.51842093e+02 52 2.61582676e+02 1.49802164e+02 2.00882003e+02 | 2.61582676e+02 1.49802164e+02 2.00882003e+02 53 -8.13872033e-01 4.98238445e-01 1.16804428e-01 | -8.13872033e-01 4.98238445e-01 1.16804428e-01 54 -2.16518456e+00 -5.14861149e+00 -9.46012679e-01 | -2.16518456e+00 -5.14861149e+00 -9.46012679e-01 55 3.32862563e+00 4.02666409e+00 1.83474813e+00 | 3.32862563e+00 4.02666409e+00 1.83474813e+00 56 -1.44299147e+03 -4.75241651e+02 -2.52448185e+03 | -1.44299147e+03 -4.75241651e+02 -2.52448185e+03 57 1.41835797e+03 5.77472780e+02 2.64988298e+03 | 1.41835797e+03 5.77472780e+02 2.64988298e+03 58 2.67934333e+02 -8.48661569e+01 1.58803083e+02 | 2.67934333e+02 -8.48661569e+01 1.58803083e+02 59 7.08423554e+00 4.15107755e+00 -4.62277040e+00 | 7.08423554e+00 4.15107755e+00 -4.62277040e+00 60 -1.56177599e+02 -2.53939453e+02 -1.11960878e+02 | -1.56177599e+02 -2.53939453e+02 -1.11960878e+02 61 1.44692111e+02 2.69156808e+02 1.36376495e+02 | 1.44692111e+02 2.69156808e+02 1.36376495e+02 62 -1.27861702e+01 1.20598860e+00 -4.57835606e+00 | -1.27861702e+01 1.20598860e+00 -4.57835606e+00 63 6.91203823e+00 6.63270091e+00 1.83800454e+01 | 6.91203823e+00 6.63270091e+00 1.83800454e+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.