!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_001 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 = [49, 41, 15, 24, 14, 6, 5, 19, 58, 23, 13, 17, 33, 10, 4, 2, 50, 11, 62, 7, 34, 54, 29, 9, 3, 57, 45, 48, 35, 22, 36, 32, 31, 12, 20, 28, 30, 53, 39, 38, 55, 1, 59, 46, 47, 26, 43, 44, 27, 0, 16, 63, 61, 37, 21, 40, 60, 25, 8, 42, 56, 52, 18, 51] 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)) = -73.74280345105653 V(r_1,...,r_N) = -73.74280345105656 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 = [46, 54, 14, 58, 23, 38, 25, 19, 35, 61, 32, 39, 33, 28, 2, 17, 47, 15, 26, 7, 56, 29, 37, 4, 59, 6, 18, 43, 13, 21, 48, 52, 10, 12, 63, 8, 40, 22, 5, 11, 36, 44, 62, 27, 41, 57, 0, 16, 30, 53, 60, 55, 31, 49, 1, 51, 20, 45, 3, 24, 50, 9, 42, 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)) = 48.44981307256896 V(r_1,...,r_N) = 48.44981307256914 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 2.84250046e-01 3.90909288e-01 2.04087999e-01 | 2.84250046e-01 3.90909288e-01 2.04087999e-01 1 1.02692137e+01 -1.84563186e+00 -2.60233644e+01 | 1.02692137e+01 -1.84563186e+00 -2.60233644e+01 2 3.71793840e-01 5.23741241e-01 2.48103149e-01 | 3.71793840e-01 5.23741241e-01 2.48103149e-01 3 -1.58702439e+01 1.04735706e+01 -1.84126941e+01 | -1.58702439e+01 1.04735706e+01 -1.84126941e+01 4 -1.80162521e+01 -4.49704711e+01 -1.94537194e+01 | -1.80162521e+01 -4.49704711e+01 -1.94537194e+01 5 1.51298552e+01 4.62437518e+01 1.78301121e+01 | 1.51298552e+01 4.62437518e+01 1.78301121e+01 6 -9.25743297e+00 9.42288857e-01 2.72152691e+01 | -9.25743297e+00 9.42288857e-01 2.72152691e+01 7 -3.37625517e+01 2.55791929e+01 -2.55738617e+01 | -3.37625517e+01 2.55791929e+01 -2.55738617e+01 8 7.16138114e-02 6.48268608e-01 8.10865319e-01 | 7.16138114e-02 6.48268608e-01 8.10865319e-01 9 1.13941869e+00 -4.87209438e+00 -2.18180055e+00 | 1.13941869e+00 -4.87209438e+00 -2.18180055e+00 10 1.42939453e+00 1.86380840e+00 -2.89164618e-02 | 1.42939453e+00 1.86380840e+00 -2.89164618e-02 11 1.28206650e+01 -8.81726102e+00 -1.86012889e+01 | 1.28206650e+01 -8.81726102e+00 -1.86012889e+01 12 -5.31772232e+00 -1.09599623e+01 -1.19483698e+00 | -5.31772232e+00 -1.09599623e+01 -1.19483698e+00 13 4.38044058e+00 1.17275715e+01 1.63743263e-01 | 4.38044058e+00 1.17275715e+01 1.63743263e-01 14 1.10934665e+01 -1.12131358e+01 1.98537235e+01 | 1.10934665e+01 -1.12131358e+01 1.98537235e+01 15 -1.18909612e+01 -6.67251111e+00 -6.02552410e+01 | -1.18909612e+01 -6.67251111e+00 -6.02552410e+01 16 -4.08082121e+00 -2.33939031e+00 -2.14193117e+00 | -4.08082121e+00 -2.33939031e+00 -2.14193117e+00 17 1.21745068e+00 -1.57626062e+00 4.59996872e+00 | 1.21745068e+00 -1.57626062e+00 4.59996872e+00 18 1.50234855e+00 6.07627928e+00 -5.02325493e+00 | 1.50234855e+00 6.07627928e+00 -5.02325493e+00 19 -7.42198739e+00 3.11994887e+00 -1.44332906e+00 | -7.42198739e+00 3.11994887e+00 -1.44332906e+00 20 4.66125590e-01 -2.77443505e+00 1.35724451e+00 | 4.66125590e-01 -2.77443505e+00 1.35724451e+00 21 1.19475937e+00 -4.26161996e+00 -1.08069231e+00 | 1.19475937e+00 -4.26161996e+00 -1.08069231e+00 22 -1.04967710e+00 -1.07920311e+00 -2.20368421e+00 | -1.04967710e+00 -1.07920311e+00 -2.20368421e+00 23 -1.04425309e+01 4.46388669e+00 -7.36075171e+00 | -1.04425309e+01 4.46388669e+00 -7.36075171e+00 24 -1.93714117e+01 -1.87379013e+01 -9.25785262e+00 | -1.93714117e+01 -1.87379013e+01 -9.25785262e+00 25 -5.61596494e+00 -1.97139281e+01 3.14123813e+01 | -5.61596494e+00 -1.97139281e+01 3.14123813e+01 26 2.54008086e+01 3.78115558e+01 -2.10076832e+01 | 2.54008086e+01 3.78115558e+01 -2.10076832e+01 27 -3.43969551e-01 -2.84479729e-01 5.76041210e-02 | -3.43969551e-01 -2.84479729e-01 5.76041210e-02 28 -1.35503979e+01 8.87061295e+00 1.83344877e+01 | -1.35503979e+01 8.87061295e+00 1.83344877e+01 29 3.86911708e+00 -1.64869703e+00 -4.64622928e+00 | 3.86911708e+00 -1.64869703e+00 -4.64622928e+00 30 8.79982928e+00 -3.08947355e+00 1.95490300e+00 | 8.79982928e+00 -3.08947355e+00 1.95490300e+00 31 -1.46341976e+00 1.53009854e+00 -9.88254103e-01 | -1.46341976e+00 1.53009854e+00 -9.88254103e-01 32 -3.84419951e-01 -1.06707848e+00 -6.99024243e-01 | -3.84419951e-01 -1.06707848e+00 -6.99024243e-01 33 2.71919882e+01 -4.33180817e+01 -2.36847537e+01 | 2.71919882e+01 -4.33180817e+01 -2.36847537e+01 34 3.80133259e+01 -2.70873661e+01 2.39144898e+01 | 3.80133259e+01 -2.70873661e+01 2.39144898e+01 35 -1.79136297e+01 2.49306925e+01 -1.76689440e+01 | -1.79136297e+01 2.49306925e+01 -1.76689440e+01 36 -1.17863936e+00 -1.04782079e+00 -6.17353592e-01 | -1.17863936e+00 -1.04782079e+00 -6.17353592e-01 37 -2.44544749e+02 -1.44284338e+02 1.14567842e+02 | -2.44544749e+02 -1.44284338e+02 1.14567842e+02 38 -2.55350574e+01 4.61596964e+01 2.37310605e+01 | -2.55350574e+01 4.61596964e+01 2.37310605e+01 39 5.77990160e-01 2.27993519e-01 -1.52949581e+00 | 5.77990160e-01 2.27993519e-01 -1.52949581e+00 40 2.16850661e+00 -9.84062249e-02 7.99718373e-01 | 2.16850661e+00 -9.84062249e-02 7.99718373e-01 41 -1.58369469e+01 3.22444214e+01 -2.51531895e+01 | -1.58369469e+01 3.22444214e+01 -2.51531895e+01 42 4.65644034e+01 -2.52776661e+01 1.67551512e+01 | 4.65644034e+01 -2.52776661e+01 1.67551512e+01 43 2.07127551e+00 3.59725354e-01 -2.77723280e-01 | 2.07127551e+00 3.59725354e-01 -2.77723280e-01 44 1.96600651e+01 -3.48124004e+01 2.28854257e+01 | 1.96600651e+01 -3.48124004e+01 2.28854257e+01 45 -6.80480385e-01 1.40312740e-01 -4.41317694e-01 | -6.80480385e-01 1.40312740e-01 -4.41317694e-01 46 2.59639447e+02 1.23571605e+02 -9.54522604e+01 | 2.59639447e+02 1.23571605e+02 -9.54522604e+01 47 -2.39160997e+00 5.71225191e-01 8.35282102e-01 | -2.39160997e+00 5.71225191e-01 8.35282102e-01 48 -1.10213706e+01 -6.58414366e+00 -9.61476601e+00 | -1.10213706e+01 -6.58414366e+00 -9.61476601e+00 49 5.12268279e-01 1.03170777e+01 8.88966365e+00 | 5.12268279e-01 1.03170777e+01 8.88966365e+00 50 9.42960299e+00 -5.17101618e-01 1.05182768e+01 | 9.42960299e+00 -5.17101618e-01 1.05182768e+01 51 -1.67136016e+01 4.40090735e+01 -8.40755637e+01 | -1.67136016e+01 4.40090735e+01 -8.40755637e+01 52 7.13673731e+00 -2.65686909e+00 4.18454193e+00 | 7.13673731e+00 -2.65686909e+00 4.18454193e+00 53 -4.06468136e-01 -8.89401952e-01 -3.13590719e-01 | -4.06468136e-01 -8.89401952e-01 -3.13590719e-01 54 -1.65295321e+00 -9.09584115e-01 -1.46445323e+00 | -1.65295321e+00 -9.09584115e-01 -1.46445323e+00 55 3.19516130e+00 3.36246149e-01 1.23110928e+00 | 3.19516130e+00 3.36246149e-01 1.23110928e+00 56 -3.50023329e+01 3.44122477e+01 4.56605831e+01 | -3.50023329e+01 3.44122477e+01 4.56605831e+01 57 -2.37604306e+01 -1.42849671e+01 1.43482117e+01 | -2.37604306e+01 -1.42849671e+01 1.43482117e+01 58 2.04146308e+01 1.25365110e+01 -7.67151928e+00 | 2.04146308e+01 1.25365110e+01 -7.67151928e+00 59 1.66653684e-02 5.59823434e-01 4.91745333e-01 | 1.66653684e-02 5.59823434e-01 4.91745333e-01 60 1.45058430e+00 1.18695526e+00 -3.52070539e-01 | 1.45058430e+00 1.18695526e+00 -3.52070539e-01 61 -1.31074188e+00 6.05074137e-02 -8.23087730e-01 | -1.31074188e+00 6.05074137e-02 -8.23087730e-01 62 1.78806522e+01 -4.31840594e+01 8.47957510e+01 | 1.78806522e+01 -4.31840594e+01 8.47957510e+01 63 4.24921146e-01 -1.01385906e+00 -9.32846497e-01 | 4.24921146e-01 -1.01385906e+00 -9.32846497e-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 = [44, 38, 62, 17, 57, 59, 7, 6, 32, 45, 23, 20, 28, 53, 24, 26, 41, 3, 37, 54, 11, 25, 50, 10, 14, 21, 15, 49, 12, 40, 61, 47, 8, 39, 48, 52, 63, 18, 1, 33, 29, 16, 58, 51, 0, 9, 55, 31, 34, 27, 22, 43, 35, 13, 19, 46, 60, 4, 42, 5, 56, 30, 2, 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)) = 1207.9052744516605 V(r_1,...,r_N) = 1207.905274451661 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 1.95284737e+00 2.70806401e+00 1.76989419e+00 | 1.95284737e+00 2.70806401e+00 1.76989419e+00 1 -8.05472585e+01 2.89945829e+01 3.94854679e+02 | -8.05472585e+01 2.89945829e+01 3.94854679e+02 2 7.93795884e+01 -2.26370605e+01 -3.95845331e+02 | 7.93795884e+01 -2.26370605e+01 -3.95845331e+02 3 2.27218717e+02 -3.28335525e+02 -3.14799652e+02 | 2.27218717e+02 -3.28335525e+02 -3.14799652e+02 4 -3.51536811e+00 -1.40071187e+01 -3.80656893e+00 | -3.51536811e+00 -1.40071187e+01 -3.80656893e+00 5 5.33810610e+01 -1.82619858e+01 -6.25447604e+01 | 5.33810610e+01 -1.82619858e+01 -6.25447604e+01 6 -2.58731696e+00 -5.03043309e+00 -3.58969633e+00 | -2.58731696e+00 -5.03043309e+00 -3.58969633e+00 7 -7.16344385e+01 1.34152567e+02 -1.14733708e+02 | -7.16344385e+01 1.34152567e+02 -1.14733708e+02 8 -5.47593928e+01 -1.62333115e+01 -8.31237247e+01 | -5.47593928e+01 -1.62333115e+01 -8.31237247e+01 9 8.88813678e+01 -1.20606003e+02 2.39164250e+01 | 8.88813678e+01 -1.20606003e+02 2.39164250e+01 10 6.04136921e+00 1.50926381e+00 -3.98476361e+00 | 6.04136921e+00 1.50926381e+00 -3.98476361e+00 11 3.92703248e+00 1.09198224e+01 -1.86034295e+01 | 3.92703248e+00 1.09198224e+01 -1.86034295e+01 12 2.40537556e+00 -6.59851332e+00 -1.21039651e+00 | 2.40537556e+00 -6.59851332e+00 -1.21039651e+00 13 6.12088818e+01 -4.82540556e+01 -1.08830075e+02 | 6.12088818e+01 -4.82540556e+01 -1.08830075e+02 14 -5.35984539e+01 1.20978780e+02 3.34402044e+01 | -5.35984539e+01 1.20978780e+02 3.34402044e+01 15 -3.66858479e+01 4.80786325e+01 -1.66930261e+01 | -3.66858479e+01 4.80786325e+01 -1.66930261e+01 16 -1.24920415e+01 -2.08057596e+01 -7.19618376e+00 | -1.24920415e+01 -2.08057596e+01 -7.19618376e+00 17 -1.58326045e+02 -6.38033916e+01 1.61738746e+02 | -1.58326045e+02 -6.38033916e+01 1.61738746e+02 18 1.64398919e+02 9.61049618e+01 -1.59976283e+02 | 1.64398919e+02 9.61049618e+01 -1.59976283e+02 19 -6.65519513e+00 6.56342523e+01 -2.42548463e+01 | -6.65519513e+00 6.56342523e+01 -2.42548463e+01 20 -2.27116555e+02 3.11376722e+02 3.28529314e+02 | -2.27116555e+02 3.11376722e+02 3.28529314e+02 21 -5.25713913e+02 4.67236358e+02 -2.91873850e+02 | -5.25713913e+02 4.67236358e+02 -2.91873850e+02 22 -1.53231253e+01 -1.17082860e+01 -1.72287023e+01 | -1.53231253e+01 -1.17082860e+01 -1.72287023e+01 23 1.04913055e+01 1.17923928e+01 1.41562263e+01 | 1.04913055e+01 1.17923928e+01 1.41562263e+01 24 -2.77596020e+01 -1.47579931e+02 -7.66327333e+01 | -2.77596020e+01 -1.47579931e+02 -7.66327333e+01 25 1.09904464e+02 9.65156063e+01 -1.78804390e+01 | 1.09904464e+02 9.65156063e+01 -1.78804390e+01 26 3.03244783e+00 3.94604688e-02 -1.57473524e+00 | 3.03244783e+00 3.94604688e-02 -1.57473524e+00 27 -2.80331999e+00 -1.12828939e+00 4.74690301e-01 | -2.80331999e+00 -1.12828939e+00 4.74690301e-01 28 5.40677470e+00 -1.25028307e+01 1.25715175e+01 | 5.40677470e+00 -1.25028307e+01 1.25715175e+01 29 3.34960554e+00 1.14236312e+00 2.53098577e+00 | 3.34960554e+00 1.14236312e+00 2.53098577e+00 30 -8.16789617e+01 4.78641630e-01 9.94617509e+01 | -8.16789617e+01 4.78641630e-01 9.94617509e+01 31 -5.16904765e-01 2.50917307e+00 -2.83405398e+00 | -5.16904765e-01 2.50917307e+00 -2.83405398e+00 32 1.74232951e+00 8.88614388e-01 -1.21461700e+00 | 1.74232951e+00 8.88614388e-01 -1.21461700e+00 33 -3.34797011e+02 -4.33639468e+02 2.58072265e+02 | -3.34797011e+02 -4.33639468e+02 2.58072265e+02 34 3.44121394e+02 3.72804819e+02 -1.26637234e+02 | 3.44121394e+02 3.72804819e+02 -1.26637234e+02 35 -1.74510571e+01 1.61325434e+01 -5.49398975e+00 | -1.74510571e+01 1.61325434e+01 -5.49398975e+00 36 -2.93634297e+00 -5.24631054e+01 4.13245384e+01 | -2.93634297e+00 -5.24631054e+01 4.13245384e+01 37 -5.52510132e+01 -5.94587767e+01 7.84315199e+01 | -5.52510132e+01 -5.94587767e+01 7.84315199e+01 38 -4.75210594e+01 -3.69893939e+01 -2.96965881e+01 | -4.75210594e+01 -3.69893939e+01 -2.96965881e+01 39 4.44705470e+01 3.55450533e+01 3.32576074e+01 | 4.44705470e+01 3.55450533e+01 3.32576074e+01 40 -4.12686400e+01 -4.79793882e+01 -2.83963834e+00 | -4.12686400e+01 -4.79793882e+01 -2.83963834e+00 41 6.08945216e+01 1.31271140e+01 -1.91775322e+01 | 6.08945216e+01 1.31271140e+01 -1.91775322e+01 42 -1.23283307e+01 -1.25936605e+00 1.43277260e+02 | -1.23283307e+01 -1.25936605e+00 1.43277260e+02 43 1.35308443e+01 1.99518572e+01 1.85219329e+01 | 1.35308443e+01 1.99518572e+01 1.85219329e+01 44 -7.67224679e+01 -1.40278981e+02 -6.15833210e+01 | -7.67224679e+01 -1.40278981e+02 -6.15833210e+01 45 7.53039405e+01 1.42408036e+02 5.95385943e+01 | 7.53039405e+01 1.42408036e+02 5.95385943e+01 46 4.17601106e+01 5.99201671e+01 -1.90234124e+01 | 4.17601106e+01 5.99201671e+01 -1.90234124e+01 47 -9.00832849e+00 -1.89827348e+01 1.82926887e+01 | -9.00832849e+00 -1.89827348e+01 1.82926887e+01 48 -5.08654071e+01 -2.43972914e+01 -1.35307591e+01 | -5.08654071e+01 -2.43972914e+01 -1.35307591e+01 49 -9.52732408e+01 2.01293435e+02 -2.52131798e+02 | -9.52732408e+01 2.01293435e+02 -2.52131798e+02 50 -1.42742334e+02 -1.05226423e+02 -4.27113682e+01 | -1.42742334e+02 -1.05226423e+02 -4.27113682e+01 51 1.48236134e+02 1.03677962e+02 4.79396984e+01 | 1.48236134e+02 1.03677962e+02 4.79396984e+01 52 1.44770402e+02 -1.78248137e+02 2.51653179e+02 | 1.44770402e+02 -1.78248137e+02 2.51653179e+02 53 3.68848813e+00 -5.66992077e-01 8.49319590e+00 | 3.68848813e+00 -5.66992077e-01 8.49319590e+00 54 -9.38312667e-01 -6.04018457e+00 -3.49381043e+00 | -9.38312667e-01 -6.04018457e+00 -3.49381043e+00 55 4.23449485e+00 2.36623801e+00 1.33461494e+00 | 4.23449485e+00 2.36623801e+00 1.33461494e+00 56 5.20547411e+02 -4.55641881e+02 2.78706348e+02 | 5.20547411e+02 -4.55641881e+02 2.78706348e+02 57 -1.65700328e+02 -4.68714743e+01 -3.56750881e+01 | -1.65700328e+02 -4.68714743e+01 -3.56750881e+01 58 1.42561611e+02 6.19437539e+01 -9.23991231e+01 | 1.42561611e+02 6.19437539e+01 -9.23991231e+01 59 8.28947361e-01 3.45450020e+00 3.58438537e+00 | 8.28947361e-01 3.45450020e+00 3.58438537e+00 60 6.58447712e+01 -3.74884295e+01 5.92656021e+01 | 6.58447712e+01 -3.74884295e+01 5.92656021e+01 61 4.66274574e+00 2.66194341e+00 2.17923617e+00 | 4.66274574e+00 2.66194341e+00 2.17923617e+00 62 -8.95517035e+01 9.01270571e+00 4.45423089e+00 | -8.95517035e+01 9.01270571e+00 4.45423089e+00 63 6.58908676e+01 3.76641363e+01 5.10539073e+01 | 6.58908676e+01 3.76641363e+01 5.10539073e+01 ------------------------------------------------------------------------------------------------------------------------- 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 = [27, 7, 22, 47, 25, 42, 18, 1, 48, 36, 16, 33, 60, 38, 57, 58, 10, 51, 6, 35, 24, 31, 2, 37, 20, 4, 34, 0, 53, 39, 40, 21, 44, 11, 26, 19, 9, 23, 13, 29, 30, 59, 5, 55, 32, 62, 49, 3, 8, 46, 50, 17, 63, 28, 61, 43, 56, 14, 15, 41, 12, 54, 45, 52] 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)) = 332.5144176531358 V(r_1,...,r_N) = 332.51441765313604 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 2.14854152e+00 1.26897929e+00 2.00122789e+00 | 2.14854152e+00 1.26897929e+00 2.00122789e+00 1 -4.08623614e+00 1.10472684e-01 2.74513914e+00 | -4.08623614e+00 1.10472684e-01 2.74513914e+00 2 3.43044707e+00 4.23220542e+00 -4.92998014e+00 | 3.43044707e+00 4.23220542e+00 -4.92998014e+00 3 -2.24230730e+01 -1.16649319e+00 2.95837500e+01 | -2.24230730e+01 -1.16649319e+00 2.95837500e+01 4 -1.18237005e+01 -1.80480881e+01 -1.48476069e+01 | -1.18237005e+01 -1.80480881e+01 -1.48476069e+01 5 5.40608593e+01 -1.08054165e+02 -1.15373123e+02 | 5.40608593e+01 -1.08054165e+02 -1.15373123e+02 6 1.87339970e+00 -2.03484281e-01 3.67468517e-01 | 1.87339970e+00 -2.03484281e-01 3.67468517e-01 7 -6.99124999e+00 -3.23842121e+00 -1.82475100e+00 | -6.99124999e+00 -3.23842121e+00 -1.82475100e+00 8 -2.02548525e+00 1.00765180e+00 5.11305323e-01 | -2.02548525e+00 1.00765180e+00 5.11305323e-01 9 -5.60265448e+00 9.43060261e+00 -2.89661808e+00 | -5.60265448e+00 9.43060261e+00 -2.89661808e+00 10 -6.49814977e-01 4.08117963e-01 7.58583660e-01 | -6.49814977e-01 4.08117963e-01 7.58583660e-01 11 4.94922702e+01 -3.93405353e+01 -7.87972911e+01 | 4.94922702e+01 -3.93405353e+01 -7.87972911e+01 12 3.77608456e+00 -1.04452044e+01 3.11266614e+00 | 3.77608456e+00 -1.04452044e+01 3.11266614e+00 13 2.11475317e+00 1.88063023e+00 -3.26021504e-01 | 2.11475317e+00 1.88063023e+00 -3.26021504e-01 14 -1.08819089e-01 -4.43320700e-01 -6.78647695e-01 | -1.08819089e-01 -4.43320700e-01 -6.78647695e-01 15 2.39239533e+00 -9.68396710e+00 -1.64991832e+01 | 2.39239533e+00 -9.68396710e+00 -1.64991832e+01 16 -4.86859468e+01 -2.62820087e+01 -1.37807951e+01 | -4.86859468e+01 -2.62820087e+01 -1.37807951e+01 17 -4.42707820e+01 -8.16563554e+01 5.31387333e+01 | -4.42707820e+01 -8.16563554e+01 5.31387333e+01 18 9.09183902e+01 9.98852751e+01 -4.02607797e+01 | 9.09183902e+01 9.98852751e+01 -4.02607797e+01 19 4.22190735e+00 5.62156328e+00 3.44491139e+00 | 4.22190735e+00 5.62156328e+00 3.44491139e+00 20 3.15807786e+00 -6.12164264e-01 -3.37226309e-01 | 3.15807786e+00 -6.12164264e-01 -3.37226309e-01 21 -2.98367778e+01 4.15326351e+01 -2.87662305e+01 | -2.98367778e+01 4.15326351e+01 -2.87662305e+01 22 -1.43645005e+00 1.51886226e+00 -1.67940593e-01 | -1.43645005e+00 1.51886226e+00 -1.67940593e-01 23 6.33426035e-01 -7.89752616e-01 1.02152086e+00 | 6.33426035e-01 -7.89752616e-01 1.02152086e+00 24 2.19672264e+01 2.40808227e+00 -2.87833092e+01 | 2.19672264e+01 2.40808227e+00 -2.87833092e+01 25 4.51808120e+01 -4.29331465e+01 -1.47431281e+01 | 4.51808120e+01 -4.29331465e+01 -1.47431281e+01 26 -9.26436949e+01 -8.86808791e+01 -2.05189316e+02 | -9.26436949e+01 -8.86808791e+01 -2.05189316e+02 27 1.15271553e+02 1.07515627e+02 1.77536224e+02 | 1.15271553e+02 1.07515627e+02 1.77536224e+02 28 -4.98989004e+01 3.67126055e+01 8.02611393e+01 | -4.98989004e+01 3.67126055e+01 8.02611393e+01 29 2.77170549e+01 -3.05705365e+01 -1.53411313e+01 | 2.77170549e+01 -3.05705365e+01 -1.53411313e+01 30 -5.86146498e+01 3.29696760e+01 2.75052722e+01 | -5.86146498e+01 3.29696760e+01 2.75052722e+01 31 -6.24232949e+00 3.91943258e+00 -4.48079875e+00 | -6.24232949e+00 3.91943258e+00 -4.48079875e+00 32 -3.15394711e+00 -2.96771939e+00 -6.44488435e+00 | -3.15394711e+00 -2.96771939e+00 -6.44488435e+00 33 4.73687265e+00 3.99060218e+00 5.83362789e+00 | 4.73687265e+00 3.99060218e+00 5.83362789e+00 34 -6.28891657e+01 1.45275791e+02 9.30294838e+01 | -6.28891657e+01 1.45275791e+02 9.30294838e+01 35 7.04172853e+00 -2.45974772e+01 -2.23530849e+01 | 7.04172853e+00 -2.45974772e+01 -2.23530849e+01 36 -1.01545648e+02 -1.88312580e+02 -1.32737604e+02 | -1.01545648e+02 -1.88312580e+02 -1.32737604e+02 37 1.01743979e+02 1.89557883e+02 1.31346478e+02 | 1.01743979e+02 1.89557883e+02 1.31346478e+02 38 -4.97396714e+01 -6.45567406e+01 8.47165846e+00 | -4.97396714e+01 -6.45567406e+01 8.47165846e+00 39 5.05728423e+01 6.45532024e+01 -9.80715476e+00 | 5.05728423e+01 6.45532024e+01 -9.80715476e+00 40 3.79323517e+01 -2.94259962e+01 3.96609420e+01 | 3.79323517e+01 -2.94259962e+01 3.96609420e+01 41 3.77312007e+01 -1.40179708e+02 -4.63998804e+01 | 3.77312007e+01 -1.40179708e+02 -4.63998804e+01 42 4.75345952e+01 2.90293027e+01 -3.01635747e+01 | 4.75345952e+01 2.90293027e+01 -3.01635747e+01 43 -2.64321705e-01 -2.49742919e+00 -2.91963892e-01 | -2.64321705e-01 -2.49742919e+00 -2.91963892e-01 44 -4.82021540e+01 -4.55623903e+01 -2.25445903e+01 | -4.82021540e+01 -4.55623903e+01 -2.25445903e+01 45 4.71074380e+01 4.67474513e+01 2.17554754e+01 | 4.71074380e+01 4.67474513e+01 2.17554754e+01 46 -9.91669154e+01 8.48211741e+01 6.67238644e+01 | -9.91669154e+01 8.48211741e+01 6.67238644e+01 47 2.93821844e+01 1.59096408e+01 2.04059269e+01 | 2.93821844e+01 1.59096408e+01 2.04059269e+01 48 -6.63652322e+00 1.14288493e+01 3.30144580e+00 | -6.63652322e+00 1.14288493e+01 3.30144580e+00 49 -3.91786493e+01 1.15502464e+00 -1.45919122e+01 | -3.91786493e+01 1.15502464e+00 -1.45919122e+01 50 1.80625738e+01 2.60617462e+01 -4.15163938e+01 | 1.80625738e+01 2.60617462e+01 -4.15163938e+01 51 1.30368140e+00 4.63193940e-01 2.27890573e+00 | 1.30368140e+00 4.63193940e-01 2.27890573e+00 52 -8.43016951e+01 -1.12374131e+02 -8.83566412e+00 | -8.43016951e+01 -1.12374131e+02 -8.83566412e+00 53 1.07148295e+02 9.58392020e+01 7.90809849e+01 | 1.07148295e+02 9.58392020e+01 7.90809849e+01 54 -1.12355347e+01 1.20748871e+01 4.69520721e+00 | -1.12355347e+01 1.20748871e+01 4.69520721e+00 55 9.57851472e-01 -1.33923629e+00 -8.62404247e-01 | 9.57851472e-01 -1.33923629e+00 -8.62404247e-01 56 -2.33283441e+00 -2.82803054e+01 4.91671923e+01 | -2.33283441e+00 -2.82803054e+01 4.91671923e+01 57 -1.00309083e+02 -1.42234674e+01 -8.30949868e+01 | -1.00309083e+02 -1.42234674e+01 -8.30949868e+01 58 -2.21919410e+01 2.51539503e+01 1.79459964e+01 | -2.21919410e+01 2.51539503e+01 1.79459964e+01 59 -1.55590120e+00 -7.34233982e-01 1.32229200e+00 | -1.55590120e+00 -7.34233982e-01 1.32229200e+00 60 9.46948415e+01 1.00251022e+01 7.39453845e+01 | 9.46948415e+01 1.00251022e+01 7.39453845e+01 61 5.52663170e+00 4.63406385e+00 9.11539348e+00 | 5.52663170e+00 4.63406385e+00 9.11539348e+00 62 -3.62292287e+00 -6.92928250e-01 -2.85801080e+00 | -3.62292287e+00 -6.92928250e-01 -2.85801080e+00 63 1.83320724e+00 7.49379709e-01 4.57787087e-01 | 1.83320724e+00 7.49379709e-01 4.57787087e-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.