!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_EAM_BonnyCastinBullens_2013_FeCrW__SM_699257350704_000 Supported species : Cr Fe W random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [24, 14, 11, 46, 6, 20, 4, 40, 58, 45, 49, 2, 48, 54, 1, 57, 22, 18, 17, 44, 5, 39, 16, 41, 0, 55, 30, 52, 38, 42, 26, 35, 37, 56, 53, 31, 63, 32, 28, 21, 7, 23, 29, 50, 19, 9, 3, 61, 12, 10, 43, 60, 27, 34, 13, 25, 33, 15, 8, 62, 51, 47, 59, 36] 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)) = -73.7428034511 V(r_1,...,r_N) = -73.7428034511 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 -1.96691069e+00 -1.96290726e+00 -2.65317578e+00 | -1.96691069e+00 -1.96290726e+00 -2.65317578e+00 1 -3.14329119e-01 -3.25934680e+00 6.50496022e+00 | -3.14329119e-01 -3.25934680e+00 6.50496022e+00 2 1.53793402e+00 6.20605847e+00 -3.35318328e+00 | 1.53793402e+00 6.20605847e+00 -3.35318328e+00 3 -4.40761886e-01 -1.77412738e-01 -4.57963254e+00 | -4.40761886e-01 -1.77412738e-01 -4.57963254e+00 4 -2.04938152e+00 3.57192182e-02 1.08380894e+00 | -2.04938152e+00 3.57192182e-02 1.08380894e+00 5 2.48895769e+00 1.75337610e+00 -1.61540802e+00 | 2.48895769e+00 1.75337610e+00 -1.61540802e+00 6 -3.73463171e-01 -1.19090044e+00 -7.02901881e-01 | -3.73463171e-01 -1.19090044e+00 -7.02901881e-01 7 -8.69495369e+00 1.77969463e+01 -4.85845334e+00 | -8.69495369e+00 1.77969463e+01 -4.85845334e+00 8 -1.11385527e+00 1.87085465e-01 -5.68033030e-01 | -1.11385527e+00 1.87085465e-01 -5.68033030e-01 9 -1.16204205e+00 2.17262637e+00 1.99905182e+00 | -1.16204205e+00 2.17262637e+00 1.99905182e+00 10 -1.21265061e+00 -2.59416060e+00 -1.80451015e+00 | -1.21265061e+00 -2.59416060e+00 -1.80451015e+00 11 1.98579438e-01 2.83607472e+00 1.81033566e+00 | 1.98579438e-01 2.83607472e+00 1.81033566e+00 12 7.45363480e-01 -1.60727051e+00 -1.13641449e+00 | 7.45363480e-01 -1.60727051e+00 -1.13641449e+00 13 3.25075492e+01 -1.00524870e+01 -9.79144507e+00 | 3.25075492e+01 -1.00524870e+01 -9.79144507e+00 14 -1.16994098e+00 -9.83329816e-01 2.06852978e-01 | -1.16994098e+00 -9.83329816e-01 2.06852978e-01 15 4.35544974e+00 -1.20951966e+00 1.43484726e+00 | 4.35544974e+00 -1.20951966e+00 1.43484726e+00 16 -2.08486842e+00 -3.04551382e+00 -3.33909974e+00 | -2.08486842e+00 -3.04551382e+00 -3.33909974e+00 17 1.16211710e-01 1.11872077e+00 5.92973408e+00 | 1.16211710e-01 1.11872077e+00 5.92973408e+00 18 2.46819609e+00 1.35031887e+00 -1.62287118e+00 | 2.46819609e+00 1.35031887e+00 -1.62287118e+00 19 -8.59294241e+00 5.39172852e+00 -5.38331989e+00 | -8.59294241e+00 5.39172852e+00 -5.38331989e+00 20 1.79140058e+00 2.90389803e+00 -5.26630530e+00 | 1.79140058e+00 2.90389803e+00 -5.26630530e+00 21 2.71224617e+00 1.02153029e-01 -5.69598837e-01 | 2.71224617e+00 1.02153029e-01 -5.69598837e-01 22 -1.25298251e+00 -1.64380628e+00 -2.95471803e+00 | -1.25298251e+00 -1.64380628e+00 -2.95471803e+00 23 1.76391732e+00 1.53952184e+00 2.46142746e+00 | 1.76391732e+00 1.53952184e+00 2.46142746e+00 24 -3.81889339e-01 -1.63207643e+00 -3.97303759e-01 | -3.81889339e-01 -1.63207643e+00 -3.97303759e-01 25 -4.78495722e+00 1.24197457e+01 -6.02452151e+00 | -4.78495722e+00 1.24197457e+01 -6.02452151e+00 26 -4.15063083e+00 -9.06274461e-01 -9.63498728e-01 | -4.15063083e+00 -9.06274461e-01 -9.63498728e-01 27 3.38036938e+00 5.62754864e-01 1.36645849e+00 | 3.38036938e+00 5.62754864e-01 1.36645849e+00 28 4.05486558e+00 -1.18530530e+01 8.19511805e+00 | 4.05486558e+00 -1.18530530e+01 8.19511805e+00 29 8.53736923e-01 -8.44877629e-02 -2.68979569e-02 | 8.53736923e-01 -8.44877629e-02 -2.68979569e-02 30 7.83066434e+00 -5.01080104e+00 4.47915897e+00 | 7.83066434e+00 -5.01080104e+00 4.47915897e+00 31 -3.89602936e+00 4.98979898e-01 -1.07512239e+00 | -3.89602936e+00 4.98979898e-01 -1.07512239e+00 32 -9.16987475e-01 5.58565308e-01 -2.29313916e+00 | -9.16987475e-01 5.58565308e-01 -2.29313916e+00 33 -7.39628885e-01 1.93076481e+00 2.82261546e-01 | -7.39628885e-01 1.93076481e+00 2.82261546e-01 34 7.34303346e+00 -2.06575585e+01 1.05345691e+01 | 7.34303346e+00 -2.06575585e+01 1.05345691e+01 35 -1.36669915e+00 -7.58971750e-01 2.41513940e+00 | -1.36669915e+00 -7.58971750e-01 2.41513940e+00 36 2.84862133e+00 -2.41384137e-01 1.35910047e+00 | 2.84862133e+00 -2.41384137e-01 1.35910047e+00 37 6.84974649e-02 -3.51047218e-01 -7.09997603e-01 | 6.84974649e-02 -3.51047218e-01 -7.09997603e-01 38 -3.07701855e+00 -3.50730856e+00 -4.45055856e+00 | -3.07701855e+00 -3.50730856e+00 -4.45055856e+00 39 -5.18611264e+00 -5.15585443e+00 9.76718945e+00 | -5.18611264e+00 -5.15585443e+00 9.76718945e+00 40 -7.84423155e-01 -4.28993962e-01 1.14524785e+00 | -7.84423155e-01 -4.28993962e-01 1.14524785e+00 41 -3.00825280e+00 6.55637803e+00 -3.26570477e+00 | -3.00825280e+00 6.55637803e+00 -3.26570477e+00 42 -3.23279057e+01 9.21724183e+00 9.42193256e+00 | -3.23279057e+01 9.21724183e+00 9.42193256e+00 43 2.28252224e-01 2.20077078e+00 1.71496900e+00 | 2.28252224e-01 2.20077078e+00 1.71496900e+00 44 3.87295047e+00 -6.37494505e+00 3.72668394e+00 | 3.87295047e+00 -6.37494505e+00 3.72668394e+00 45 -3.99284604e-01 -2.89951115e-02 -4.88621882e-01 | -3.99284604e-01 -2.89951115e-02 -4.88621882e-01 46 -1.44194227e+00 4.96803182e-02 -1.34189557e+00 | -1.44194227e+00 4.96803182e-02 -1.34189557e+00 47 5.99744589e-01 1.46065697e+00 7.23036194e-01 | 5.99744589e-01 1.46065697e+00 7.23036194e-01 48 -6.76922775e-01 1.81114171e-02 6.94221245e-01 | -6.76922775e-01 1.81114171e-02 6.94221245e-01 49 -8.41948248e-02 -5.63959845e-01 9.96300397e-01 | -8.41948248e-02 -5.63959845e-01 9.96300397e-01 50 -4.15496380e-02 -1.66643067e+00 -1.99249814e+00 | -4.15496380e-02 -1.66643067e+00 -1.99249814e+00 51 9.36224058e-01 2.53034228e+00 9.78941147e-01 | 9.36224058e-01 2.53034228e+00 9.78941147e-01 52 7.76922233e+00 8.45307615e+00 -6.82161844e+00 | 7.76922233e+00 8.45307615e+00 -6.82161844e+00 53 8.35299286e-01 -1.62698875e+00 6.37075449e-01 | 8.35299286e-01 -1.62698875e+00 6.37075449e-01 54 -2.06059850e+00 -7.21272803e-01 -7.08477058e-01 | -2.06059850e+00 -7.21272803e-01 -7.08477058e-01 55 1.97565925e+00 4.28784604e-01 1.67450092e-01 | 1.97565925e+00 4.28784604e-01 1.67450092e-01 56 -8.87390295e-01 7.21863344e-01 2.57969806e-01 | -8.87390295e-01 7.21863344e-01 2.57969806e-01 57 -1.21236570e-01 -7.92591433e+00 -1.44086771e+01 | -1.21236570e-01 -7.92591433e+00 -1.44086771e+01 58 3.66044852e+00 -9.45366032e-01 3.05247933e+00 | 3.66044852e+00 -9.45366032e-01 3.05247933e+00 59 -1.35922990e+00 -7.92743078e-01 -3.32914008e-01 | -1.35922990e+00 -7.92743078e-01 -3.32914008e-01 60 4.91538456e+00 -2.49487266e+00 2.82293524e+00 | 4.91538456e+00 -2.49487266e+00 2.82293524e+00 61 -3.62245540e-02 8.74782923e-01 7.21411433e-01 | -3.62245540e-02 8.74782923e-01 7.21411433e-01 62 -5.18226661e+00 9.31417843e+00 8.37308476e+00 | -5.18226661e+00 9.31417843e+00 8.37308476e+00 63 1.48167878e+00 2.65049145e-01 2.36764833e-01 | 1.48167878e+00 2.65049145e-01 2.36764833e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [5, 28, 40, 27, 51, 0, 32, 22, 58, 41, 21, 59, 37, 45, 36, 56, 50, 38, 33, 54, 57, 10, 7, 47, 61, 44, 42, 3, 1, 39, 35, 34, 6, 18, 31, 30, 14, 12, 17, 29, 2, 9, 26, 63, 25, 13, 53, 23, 49, 48, 16, 4, 55, 46, 19, 52, 15, 20, 8, 11, 62, 24, 60, 43] 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)) = 181.298379346 V(r_1,...,r_N) = 181.298379346 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 -4.64432021e+00 -5.33567603e+00 -1.45882837e+00 | -4.64432021e+00 -5.33567603e+00 -1.45882837e+00 1 -8.67078421e+00 -3.88974081e+00 4.14742771e+00 | -8.67078421e+00 -3.88974081e+00 4.14742771e+00 2 1.36396468e+01 1.02357709e+01 -3.21381973e+00 | 1.36396468e+01 1.02357709e+01 -3.21381973e+00 3 -2.93366228e+01 1.07076769e+02 -7.77031097e+01 | -2.93366228e+01 1.07076769e+02 -7.77031097e+01 4 8.18507475e-02 9.56791175e-02 2.17787373e+00 | 8.18507475e-02 9.56791175e-02 2.17787373e+00 5 -2.19318312e+01 -3.44570328e+01 1.66646464e+01 | -2.19318312e+01 -3.44570328e+01 1.66646464e+01 6 -9.94477782e+00 -2.04747307e+01 -9.69566362e+00 | -9.94477782e+00 -2.04747307e+01 -9.69566362e+00 7 1.23131990e+01 1.82100241e+01 9.07084856e+00 | 1.23131990e+01 1.82100241e+01 9.07084856e+00 8 -4.42881565e+00 -2.18365251e+00 -1.60323420e+00 | -4.42881565e+00 -2.18365251e+00 -1.60323420e+00 9 3.77902830e+00 2.56814975e+00 2.71339007e+00 | 3.77902830e+00 2.56814975e+00 2.71339007e+00 10 -3.12934510e+01 -5.81294953e+01 -6.87918431e+01 | -3.12934510e+01 -5.81294953e+01 -6.87918431e+01 11 3.30192857e+01 5.57055954e+01 6.20252105e+01 | 3.30192857e+01 5.57055954e+01 6.20252105e+01 12 -1.04355839e+00 6.90239770e-01 5.62349732e-01 | -1.04355839e+00 6.90239770e-01 5.62349732e-01 13 3.87808102e-01 -4.38700228e-01 -2.68119340e-01 | 3.87808102e-01 -4.38700228e-01 -2.68119340e-01 14 7.30349832e+01 -8.48959942e+01 3.32305508e+01 | 7.30349832e+01 -8.48959942e+01 3.32305508e+01 15 7.99557858e+00 -7.21991925e+00 -5.59201703e-01 | 7.99557858e+00 -7.21991925e+00 -5.59201703e-01 16 -1.15101337e+00 -5.21419793e-01 -1.72809151e+00 | -1.15101337e+00 -5.21419793e-01 -1.72809151e+00 17 -2.82834077e+01 1.65302839e+00 -1.08706080e+01 | -2.82834077e+01 1.65302839e+00 -1.08706080e+01 18 -1.64981316e+00 -2.01075221e+00 -3.78887441e-01 | -1.64981316e+00 -2.01075221e+00 -3.78887441e-01 19 -1.27790167e+00 8.55385548e+00 -4.59022211e+00 | -1.27790167e+00 8.55385548e+00 -4.59022211e+00 20 2.63894918e+01 -2.66304851e+00 7.42713523e+00 | 2.63894918e+01 -2.66304851e+00 7.42713523e+00 21 4.45921082e+01 -1.05659720e+02 -3.35629129e+01 | 4.45921082e+01 -1.05659720e+02 -3.35629129e+01 22 -4.19823893e+01 -2.87095035e+01 -2.51782235e+01 | -4.19823893e+01 -2.87095035e+01 -2.51782235e+01 23 4.21406097e+01 2.83458963e+01 2.51484085e+01 | 4.21406097e+01 2.83458963e+01 2.51484085e+01 24 -5.10434222e+01 -9.36388573e+01 -9.73004872e+01 | -5.10434222e+01 -9.36388573e+01 -9.73004872e+01 25 4.89799638e+01 9.27692825e+01 9.89410183e+01 | 4.89799638e+01 9.27692825e+01 9.89410183e+01 26 1.92678789e+00 1.15030584e+00 -2.29646495e-01 | 1.92678789e+00 1.15030584e+00 -2.29646495e-01 27 -5.45281778e-01 -8.99451406e-01 -3.90827179e-02 | -5.45281778e-01 -8.99451406e-01 -3.90827179e-02 28 5.56731910e-01 2.55070047e+00 4.10448474e+00 | 5.56731910e-01 2.55070047e+00 4.10448474e+00 29 -9.75111287e-02 1.54048826e+00 7.82573794e-01 | -9.75111287e-02 1.54048826e+00 7.82573794e-01 30 3.54297881e+00 -7.10445919e+00 5.23423819e+00 | 3.54297881e+00 -7.10445919e+00 5.23423819e+00 31 -1.00601964e+02 1.89982524e+02 -2.95822913e+02 | -1.00601964e+02 1.89982524e+02 -2.95822913e+02 32 9.24326023e-01 6.53175874e-01 -5.13695026e-01 | 9.24326023e-01 6.53175874e-01 -5.13695026e-01 33 -2.81670122e+00 -2.14253740e+00 2.12076780e+00 | -2.81670122e+00 -2.14253740e+00 2.12076780e+00 34 -1.84861320e+01 1.43796632e+01 2.41874683e+01 | -1.84861320e+01 1.43796632e+01 2.41874683e+01 35 9.47798215e+00 -1.02914916e+01 -9.33060433e+00 | 9.47798215e+00 -1.02914916e+01 -9.33060433e+00 36 -3.64663452e-01 2.91869237e-01 -1.21908833e+00 | -3.64663452e-01 2.91869237e-01 -1.21908833e+00 37 1.04744455e+00 8.69624513e-01 -2.54212919e-01 | 1.04744455e+00 8.69624513e-01 -2.54212919e-01 38 -2.59572518e+00 -1.79011585e+00 -1.49111004e+00 | -2.59572518e+00 -1.79011585e+00 -1.49111004e+00 39 -1.50458232e+02 -1.40742531e+02 1.48412550e+02 | -1.50458232e+02 -1.40742531e+02 1.48412550e+02 40 4.36689159e-01 1.01990618e+00 1.14824987e-01 | 4.36689159e-01 1.01990618e+00 1.14824987e-01 41 -1.83472890e+00 3.01282126e+00 -7.59532772e+00 | -1.83472890e+00 3.01282126e+00 -7.59532772e+00 42 -4.70071154e+01 -6.02598557e+01 -5.19161329e+01 | -4.70071154e+01 -6.02598557e+01 -5.19161329e+01 43 5.20929083e+01 6.06296126e+01 5.11214751e+01 | 5.20929083e+01 6.06296126e+01 5.11214751e+01 44 -7.74096885e+00 -1.00061425e+01 1.12821399e+00 | -7.74096885e+00 -1.00061425e+01 1.12821399e+00 45 6.52277537e+00 5.18371664e+00 6.41914947e+00 | 6.52277537e+00 5.18371664e+00 6.41914947e+00 46 -1.48376616e+01 -4.97431601e-01 -1.01813648e+01 | -1.48376616e+01 -4.97431601e-01 -1.01813648e+01 47 1.57903094e+01 -7.19751411e-01 1.05770998e+01 | 1.57903094e+01 -7.19751411e-01 1.05770998e+01 48 -3.18162127e+00 -2.16818218e+00 -1.98147461e+00 | -3.18162127e+00 -2.16818218e+00 -1.98147461e+00 49 5.16616537e+01 -3.74827737e+01 -4.92844874e+01 | 5.16616537e+01 -3.74827737e+01 -4.92844874e+01 50 -4.52095226e+01 1.00843423e+02 3.26378048e+01 | -4.52095226e+01 1.00843423e+02 3.26378048e+01 51 4.68140856e+00 5.03752730e+00 7.17883254e+00 | 4.68140856e+00 5.03752730e+00 7.17883254e+00 52 1.42861510e+02 1.54108090e+02 -1.37822443e+02 | 1.42861510e+02 1.54108090e+02 -1.37822443e+02 53 -2.00496155e+00 -2.31867036e+00 5.50169244e-01 | -2.00496155e+00 -2.31867036e+00 5.50169244e-01 54 -4.81898184e+01 4.13276792e+01 5.26877545e+01 | -4.81898184e+01 4.13276792e+01 5.26877545e+01 55 -6.93832584e-02 -1.08663052e+00 -8.69792306e-01 | -6.93832584e-02 -1.08663052e+00 -8.69792306e-01 56 -1.31729588e+01 6.52531135e+00 2.79982378e+00 | -1.31729588e+01 6.52531135e+00 2.79982378e+00 57 -2.08620910e+00 1.33241718e-01 -3.72923555e+00 | -2.08620910e+00 1.33241718e-01 -3.72923555e+00 58 9.85043052e+01 -1.89001937e+02 2.92385169e+02 | 9.85043052e+01 -1.89001937e+02 2.92385169e+02 59 1.10003711e+00 -4.81074568e-01 2.51850132e+00 | 1.10003711e+00 -4.81074568e-01 2.51850132e+00 60 1.51227214e+00 -3.34858467e+00 2.50498952e+00 | 1.51227214e+00 -3.34858467e+00 2.50498952e+00 61 -1.01234778e+00 1.68601622e-02 -1.48940873e+00 | -1.01234778e+00 1.68601622e-02 -1.48940873e+00 62 -1.21178245e-01 5.81279908e+00 1.46623775e+00 | -1.21178245e-01 5.81279908e+00 1.46623775e+00 63 1.23121296e-01 -4.03765890e-01 -3.67715918e-01 | 1.23121296e-01 -4.03765890e-01 -3.67715918e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = W (Configuration in file "config-W.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [1, 0, 17, 32, 33, 47, 19, 23, 50, 25, 16, 45, 31, 44, 62, 61, 10, 2, 54, 6, 63, 53, 37, 7, 59, 9, 29, 35, 46, 26, 36, 12, 3, 4, 51, 27, 30, 22, 49, 41, 57, 39, 52, 48, 13, 11, 28, 5, 43, 38, 8, 34, 42, 21, 18, 60, 58, 40, 56, 24, 55, 15, 14, 20] 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)) = 1092.28796161 V(r_1,...,r_N) = 1092.28796161 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 -1.33522013e+00 -2.98297548e+00 -1.69074839e+00 | -1.33522013e+00 -2.98297548e+00 -1.69074839e+00 1 4.96670145e+01 -6.34131434e+01 -5.63692475e+01 | 4.96670145e+01 -6.34131434e+01 -5.63692475e+01 2 7.78109853e+01 2.75674050e+00 -5.97982166e+01 | 7.78109853e+01 2.75674050e+00 -5.97982166e+01 3 8.29995539e+01 -6.79908898e+01 2.77512938e+00 | 8.29995539e+01 -6.79908898e+01 2.77512938e+00 4 -6.60791714e+01 -4.38871621e+01 -3.77720084e+01 | -6.60791714e+01 -4.38871621e+01 -3.77720084e+01 5 3.51078834e+01 5.12032596e+01 4.41343602e+00 | 3.51078834e+01 5.12032596e+01 4.41343602e+00 6 -1.25878770e+02 6.45239545e+01 1.18831104e+02 | -1.25878770e+02 6.45239545e+01 1.18831104e+02 7 -1.74170264e+01 2.87119428e+01 -2.07093869e+01 | -1.74170264e+01 2.87119428e+01 -2.07093869e+01 8 -1.00880749e+01 -7.32429470e+00 -1.14147565e+01 | -1.00880749e+01 -7.32429470e+00 -1.14147565e+01 9 -8.11034775e+01 3.61005665e+01 -1.64004727e+01 | -8.11034775e+01 3.61005665e+01 -1.64004727e+01 10 -2.79531923e+01 -5.01314438e+01 -6.50482086e+01 | -2.79531923e+01 -5.01314438e+01 -6.50482086e+01 11 1.67333548e+02 -4.50080359e+01 -7.79561782e+01 | 1.67333548e+02 -4.50080359e+01 -7.79561782e+01 12 1.05473398e+02 -4.02235002e+01 1.42439330e+01 | 1.05473398e+02 -4.02235002e+01 1.42439330e+01 13 1.96821593e+02 -1.27951447e+02 -9.60347518e+01 | 1.96821593e+02 -1.27951447e+02 -9.60347518e+01 14 -2.72357629e+02 -1.05575072e+02 -9.37548909e+01 | -2.72357629e+02 -1.05575072e+02 -9.37548909e+01 15 2.15619796e+02 1.20613460e+02 9.17237376e+01 | 2.15619796e+02 1.20613460e+02 9.17237376e+01 16 -2.21132629e+01 -8.51171181e+01 -3.01473567e+01 | -2.21132629e+01 -8.51171181e+01 -3.01473567e+01 17 2.45421844e+01 6.66817505e+01 -1.65145366e+00 | 2.45421844e+01 6.66817505e+01 -1.65145366e+00 18 -3.39600642e+01 -5.76554252e+01 -5.99855461e+01 | -3.39600642e+01 -5.76554252e+01 -5.99855461e+01 19 3.78280526e+01 5.88308028e+01 5.87155970e+01 | 3.78280526e+01 5.88308028e+01 5.87155970e+01 20 -1.26654231e+02 4.08917430e+01 2.37006098e+01 | -1.26654231e+02 4.08917430e+01 2.37006098e+01 21 -7.86819352e+01 5.07694316e+01 -9.45269480e+01 | -7.86819352e+01 5.07694316e+01 -9.45269480e+01 22 -5.99181126e+01 -3.36096326e+01 -4.95944172e+01 | -5.99181126e+01 -3.36096326e+01 -4.95944172e+01 23 5.04425480e+01 4.84055775e+01 8.12156630e+01 | 5.04425480e+01 4.84055775e+01 8.12156630e+01 24 2.03406761e+01 -1.49501437e+01 -7.94479202e+01 | 2.03406761e+01 -1.49501437e+01 -7.94479202e+01 25 2.39611931e+02 -9.99423702e+01 -7.84968207e+01 | 2.39611931e+02 -9.99423702e+01 -7.84968207e+01 26 -3.02294961e+01 -1.43370585e+02 -5.62016336e+01 | -3.02294961e+01 -1.43370585e+02 -5.62016336e+01 27 2.88544313e+01 1.40185174e+02 5.95546112e+01 | 2.88544313e+01 1.40185174e+02 5.95546112e+01 28 -1.24101243e+02 9.47624797e+01 1.07603380e+02 | -1.24101243e+02 9.47624797e+01 1.07603380e+02 29 1.68578403e+01 2.28945274e+01 9.12190813e+00 | 1.68578403e+01 2.28945274e+01 9.12190813e+00 30 -2.09570461e+02 1.59787737e+02 1.13716446e+02 | -2.09570461e+02 1.59787737e+02 1.13716446e+02 31 -1.37188512e+02 1.93635462e+02 -3.34851042e+02 | -1.37188512e+02 1.93635462e+02 -3.34851042e+02 32 -7.54884702e+01 -4.89150087e+01 -7.80524009e+00 | -7.54884702e+01 -4.89150087e+01 -7.80524009e+00 33 -1.79673112e+02 -2.75628281e+02 1.13805862e+02 | -1.79673112e+02 -2.75628281e+02 1.13805862e+02 34 2.74117856e+02 3.02615787e+02 -8.25922886e+01 | 2.74117856e+02 3.02615787e+02 -8.25922886e+01 35 -8.56534370e+01 -9.77591236e+01 3.88141324e+01 | -8.56534370e+01 -9.77591236e+01 3.88141324e+01 36 -7.05456808e+01 -7.06131847e+01 -6.23255880e+01 | -7.05456808e+01 -7.06131847e+01 -6.23255880e+01 37 4.93254634e+01 5.10736854e+01 7.72975648e+01 | 4.93254634e+01 5.10736854e+01 7.72975648e+01 38 -2.31364273e+02 -1.23388767e+02 -1.74549858e+02 | -2.31364273e+02 -1.23388767e+02 -1.74549858e+02 39 2.25304492e+02 1.01075485e+02 1.83779887e+02 | 2.25304492e+02 1.01075485e+02 1.83779887e+02 40 1.20229401e+01 -2.10645090e+01 3.98292124e+01 | 1.20229401e+01 -2.10645090e+01 3.98292124e+01 41 -1.39902241e+02 1.12581700e+02 -3.13762985e+00 | -1.39902241e+02 1.12581700e+02 -3.13762985e+00 42 -1.69974791e+02 1.12128838e+02 1.19399662e+02 | -1.69974791e+02 1.12128838e+02 1.19399662e+02 43 4.66550375e+01 -4.50200895e+01 -5.05911638e+01 | 4.66550375e+01 -4.50200895e+01 -5.05911638e+01 44 1.54020886e+02 -1.15043124e+02 9.58848003e+00 | 1.54020886e+02 -1.15043124e+02 9.58848003e+00 45 -1.73593253e+00 1.14945297e+00 -3.18047439e+00 | -1.73593253e+00 1.14945297e+00 -3.18047439e+00 46 1.31129606e+01 -3.89565078e+00 1.66807388e+01 | 1.31129606e+01 -3.89565078e+00 1.66807388e+01 47 -3.20944754e+01 -2.91982351e+01 3.78104631e+01 | -3.20944754e+01 -2.91982351e+01 3.78104631e+01 48 1.21982314e+00 -2.71891775e-01 -9.75852147e-02 | 1.21982314e+00 -2.71891775e-01 -9.75852147e-02 49 7.84276594e+01 -6.41971860e+01 -1.02312752e+02 | 7.84276594e+01 -6.41971860e+01 -1.02312752e+02 50 -7.92034952e+00 1.20739767e-01 -2.45556921e+00 | -7.92034952e+00 1.20739767e-01 -2.45556921e+00 51 -1.67271039e+01 3.01368391e+01 8.11881507e+00 | -1.67271039e+01 3.01368391e+01 8.11881507e+00 52 6.91197833e-01 -6.36317078e+01 -7.33699324e+01 | 6.91197833e-01 -6.36317078e+01 -7.33699324e+01 53 3.64841490e+01 4.99024127e+01 6.55757354e+01 | 3.64841490e+01 4.99024127e+01 6.55757354e+01 54 -1.79650032e+02 -2.55896031e+01 3.75294016e+00 | -1.79650032e+02 -2.55896031e+01 3.75294016e+00 55 7.67371818e+01 1.23432026e+02 9.05990109e+01 | 7.67371818e+01 1.23432026e+02 9.05990109e+01 56 1.43490987e+02 3.64240039e+01 2.78420828e+01 | 1.43490987e+02 3.64240039e+01 2.78420828e+01 57 -5.80401675e+01 8.55480413e+01 -1.08059393e+02 | -5.80401675e+01 8.55480413e+01 -1.08059393e+02 58 1.18976273e+02 -1.94958308e+02 3.29258358e+02 | 1.18976273e+02 -1.94958308e+02 3.29258358e+02 59 1.08960312e+01 4.01666692e+00 1.20004091e+01 | 1.08960312e+01 4.01666692e+00 1.20004091e+01 60 -3.04787214e+01 -2.46274952e+02 -3.68780299e+01 | -3.04787214e+01 -2.46274952e+02 -3.68780299e+01 61 1.39396750e+02 2.08664594e+02 1.59045880e+02 | 1.39396750e+02 2.08664594e+02 1.59045880e+02 62 -2.63779278e+01 1.73943829e+01 1.33817143e+01 | -2.63779278e+01 1.73943829e+01 1.33817143e+01 63 6.54735760e-02 -2.43640317e+00 -2.98899485e+00 | 6.54735760e-02 -2.43640317e+00 -2.98899485e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cr Fe W (Configuration in file "config-CrFeW.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [1, 0, 56, 53, 45, 18, 63, 15, 61, 20, 47, 35, 49, 22, 54, 7, 42, 32, 5, 28, 9, 33, 13, 58, 29, 57, 43, 31, 19, 24, 37, 27, 17, 21, 44, 11, 51, 30, 48, 62, 59, 41, 16, 26, 34, 4, 50, 10, 38, 12, 46, 36, 55, 3, 14, 52, 2, 25, 23, 40, 60, 8, 39, 6] 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)) = 747.149992793 V(r_1,...,r_N) = 747.149992793 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 -1.95544932e-01 7.57469436e-01 -3.92254975e-01 | -1.95544932e-01 7.57469436e-01 -3.92254975e-01 1 1.79939463e+02 3.68662174e+01 -1.05894791e+02 | 1.79939463e+02 3.68662174e+01 -1.05894791e+02 2 8.37822701e+00 9.01940397e+00 -1.20627279e+01 | 8.37822701e+00 9.01940397e+00 -1.20627279e+01 3 -8.50380541e-01 5.31910078e+00 -2.95925696e+00 | -8.50380541e-01 5.31910078e+00 -2.95925696e+00 4 1.91632627e+01 -1.62462342e+02 2.65911838e+01 | 1.91632627e+01 -1.62462342e+02 2.65911838e+01 5 -2.09357251e+02 8.00778410e+00 6.63350070e+00 | -2.09357251e+02 8.00778410e+00 6.63350070e+00 6 -2.07891316e+02 1.16906718e+02 9.19835588e+01 | -2.07891316e+02 1.16906718e+02 9.19835588e+01 7 -2.09193191e+01 3.46568365e+01 -4.94209170e+01 | -2.09193191e+01 3.46568365e+01 -4.94209170e+01 8 -1.44162489e-01 6.04322129e-01 5.89876279e-01 | -1.44162489e-01 6.04322129e-01 5.89876279e-01 9 3.04000663e+00 1.84280436e-01 -2.30731184e+00 | 3.04000663e+00 1.84280436e-01 -2.30731184e+00 10 -1.84279879e+02 -6.47772720e+01 -2.87632830e+02 | -1.84279879e+02 -6.47772720e+01 -2.87632830e+02 11 1.82261817e+02 6.52597460e+01 2.88852536e+02 | 1.82261817e+02 6.52597460e+01 2.88852536e+02 12 -6.52721583e+00 -2.90503784e+00 -2.85377060e+00 | -6.52721583e+00 -2.90503784e+00 -2.85377060e+00 13 5.44560736e+00 3.46035284e+00 4.51838345e+00 | 5.44560736e+00 3.46035284e+00 4.51838345e+00 14 2.08856785e+02 -1.15039476e+01 -9.02684641e-01 | 2.08856785e+02 -1.15039476e+01 -9.02684641e-01 15 2.93294905e+01 -4.85291484e+01 -8.25145388e+01 | 2.93294905e+01 -4.85291484e+01 -8.25145388e+01 16 7.31890348e-01 -4.84235173e-01 8.94520411e-01 | 7.31890348e-01 -4.84235173e-01 8.94520411e-01 17 1.13945277e+01 -2.54105123e+01 -1.57976378e+02 | 1.13945277e+01 -2.54105123e+01 -1.57976378e+02 18 5.30136740e-02 -2.08001533e-01 4.52112539e-01 | 5.30136740e-02 -2.08001533e-01 4.52112539e-01 19 -1.89741443e+01 1.41294379e+01 -2.24509213e+01 | -1.89741443e+01 1.41294379e+01 -2.24509213e+01 20 9.86101895e+01 -6.80520222e+01 6.49350024e+01 | 9.86101895e+01 -6.80520222e+01 6.49350024e+01 21 2.16448118e+00 -5.04578947e+00 -3.16463202e+00 | 2.16448118e+00 -5.04578947e+00 -3.16463202e+00 22 -1.08074769e+02 9.45055809e+01 9.33368048e+01 | -1.08074769e+02 9.45055809e+01 9.33368048e+01 23 -1.58789861e+01 1.85088133e+01 -2.50970320e+01 | -1.58789861e+01 1.85088133e+01 -2.50970320e+01 24 -2.52554295e-01 -8.42864389e-01 3.70354705e-01 | -2.52554295e-01 -8.42864389e-01 3.70354705e-01 25 -3.37966419e+00 -2.78986716e+00 1.07919364e+00 | -3.37966419e+00 -2.78986716e+00 1.07919364e+00 26 -8.95111358e-01 5.53397509e-01 -5.00070839e+00 | -8.95111358e-01 5.53397509e-01 -5.00070839e+00 27 1.80294032e+00 2.92019517e+00 3.38611786e+00 | 1.80294032e+00 2.92019517e+00 3.38611786e+00 28 1.40765138e+01 6.62212208e+00 -3.00649741e+00 | 1.40765138e+01 6.62212208e+00 -3.00649741e+00 29 1.01133162e+01 -1.05888009e+01 -1.28545734e+01 | 1.01133162e+01 -1.05888009e+01 -1.28545734e+01 30 4.64173258e+00 -3.72451388e+01 1.70278873e+00 | 4.64173258e+00 -3.72451388e+01 1.70278873e+00 31 1.46999629e+01 2.16799686e+01 2.20575501e+01 | 1.46999629e+01 2.16799686e+01 2.20575501e+01 32 -7.28588090e+01 -1.80300381e+02 -6.17214461e+01 | -7.28588090e+01 -1.80300381e+02 -6.17214461e+01 33 7.37319381e+01 1.80732563e+02 6.12222557e+01 | 7.37319381e+01 1.80732563e+02 6.12222557e+01 34 3.87532163e+01 -6.16624702e+01 3.79833832e+01 | 3.87532163e+01 -6.16624702e+01 3.79833832e+01 35 8.92070867e+01 -8.74319930e+01 -8.30945390e+01 | 8.92070867e+01 -8.74319930e+01 -8.30945390e+01 36 -1.17072451e+01 -3.70196173e+00 -1.11942295e+01 | -1.17072451e+01 -3.70196173e+00 -1.11942295e+01 37 1.07008754e+01 5.40620701e+00 1.13770062e+01 | 1.07008754e+01 5.40620701e+00 1.13770062e+01 38 -1.44087394e+01 -1.29048607e+01 -9.45577944e+00 | -1.44087394e+01 -1.29048607e+01 -9.45577944e+00 39 1.63061666e+01 1.17770365e+01 9.05587439e+00 | 1.63061666e+01 1.17770365e+01 9.05587439e+00 40 -1.65897873e+02 -8.59950141e+01 -1.19900311e+02 | -1.65897873e+02 -8.59950141e+01 -1.19900311e+02 41 1.27717901e+02 2.81614366e+01 1.31095782e+02 | 1.27717901e+02 2.81614366e+01 1.31095782e+02 42 3.52044403e+01 5.99735715e+01 -1.29230029e+01 | 3.52044403e+01 5.99735715e+01 -1.29230029e+01 43 6.40658455e+01 -2.45107841e+01 -6.82206910e+01 | 6.40658455e+01 -2.45107841e+01 -6.82206910e+01 44 1.40858320e+00 -2.77517213e-01 4.93174208e-01 | 1.40858320e+00 -2.77517213e-01 4.93174208e-01 45 -7.92071433e-01 8.08108786e-01 -9.39534190e-01 | -7.92071433e-01 8.08108786e-01 -9.39534190e-01 46 -1.47579120e+02 -1.38574059e+02 -1.10027521e+02 | -1.47579120e+02 -1.38574059e+02 -1.10027521e+02 47 8.87812099e+01 1.05051322e+02 1.62587261e+02 | 8.87812099e+01 1.05051322e+02 1.62587261e+02 48 -1.64426945e+01 2.76273885e+01 1.36178644e+01 | -1.64426945e+01 2.76273885e+01 1.36178644e+01 49 -5.18224870e+01 6.58047212e+01 -1.73721295e+01 | -5.18224870e+01 6.58047212e+01 -1.73721295e+01 50 1.00569718e+01 -1.35830898e+01 2.58389765e+01 | 1.00569718e+01 -1.35830898e+01 2.58389765e+01 51 -2.59538280e+02 3.72225760e+02 -5.21240740e+02 | -2.59538280e+02 3.72225760e+02 -5.21240740e+02 52 -4.17513951e+01 2.36324650e+01 8.91282993e+01 | -4.17513951e+01 2.36324650e+01 8.91282993e+01 53 3.27528369e+00 3.33190259e+00 2.60456627e+00 | 3.27528369e+00 3.33190259e+00 2.60456627e+00 54 -1.03501747e+00 6.67537618e-01 4.49496616e-02 | -1.03501747e+00 6.67537618e-01 4.49496616e-02 55 2.20478361e+00 -2.07220027e+00 -1.55602888e+00 | 2.20478361e+00 -2.07220027e+00 -1.55602888e+00 56 -4.09952489e+01 2.75068019e+01 7.19056748e+01 | -4.09952489e+01 2.75068019e+01 7.19056748e+01 57 9.55542240e-01 1.04260887e+01 1.80006746e+01 | 9.55542240e-01 1.04260887e+01 1.80006746e+01 58 -2.35273883e+01 -1.11837773e+01 -2.00172956e+00 | -2.35273883e+01 -1.11837773e+01 -2.00172956e+00 59 1.19574860e+01 2.00909605e+01 1.46114431e+01 | 1.19574860e+01 2.00909605e+01 1.46114431e+01 60 -1.08413391e+00 5.38771232e+01 1.67165648e+01 | -1.08413391e+00 5.38771232e+01 1.67165648e+01 61 5.89018291e-01 1.71109987e+00 1.30128035e+00 | 5.89018291e-01 1.71109987e+00 1.30128035e+00 62 2.54807117e+02 -3.74763035e+02 5.19601428e+02 | 2.54807117e+02 -3.74763035e+02 5.19601428e+02 63 2.63410748e+00 -9.67718326e-01 1.56956707e+00 | 2.63410748e+00 -9.67718326e-01 1.56956707e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.