!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MendelevBorovikov_2020_FeNiCr__MO_922363340570_000 Supported species : Cr Fe Ni 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 = [23, 4, 6, 19, 1, 35, 2, 46, 20, 56, 61, 41, 17, 51, 54, 28, 27, 12, 24, 3, 8, 50, 48, 0, 18, 26, 25, 16, 15, 49, 53, 37, 34, 58, 32, 5, 52, 31, 45, 44, 47, 11, 59, 57, 39, 38, 7, 40, 22, 29, 21, 13, 36, 30, 14, 63, 9, 43, 33, 42, 62, 10, 60, 55] 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)) = 146.89713722282772 V(r_1,...,r_N) = 146.8971372228276 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 -2.00906217e+00 -1.14107012e+00 -1.77519350e+00 | -2.00906217e+00 -1.14107012e+00 -1.77519350e+00 1 -1.09561962e+01 -2.85075316e+01 1.89730310e+01 | -1.09561962e+01 -2.85075316e+01 1.89730310e+01 2 -5.63637362e-01 1.18778385e+01 -3.41960076e+01 | -5.63637362e-01 1.18778385e+01 -3.41960076e+01 3 1.13256124e+01 1.94728422e+01 1.46906948e+01 | 1.13256124e+01 1.94728422e+01 1.46906948e+01 4 6.37661389e+00 1.24298583e+00 -2.26277657e+00 | 6.37661389e+00 1.24298583e+00 -2.26277657e+00 5 -4.60428887e-02 -9.14566723e-01 -7.34275787e-01 | -4.60428887e-02 -9.14566723e-01 -7.34275787e-01 6 -1.42170972e+00 -4.03082457e-01 -1.28105161e+00 | -1.42170972e+00 -4.03082457e-01 -1.28105161e+00 7 -3.55427118e+01 9.17014473e+01 -6.21255988e+01 | -3.55427118e+01 9.17014473e+01 -6.21255988e+01 8 -2.02064245e+00 -3.69618344e-01 -1.93685284e+00 | -2.02064245e+00 -3.69618344e-01 -1.93685284e+00 9 -4.33258640e+00 2.28567976e+00 -3.90342813e+00 | -4.33258640e+00 2.28567976e+00 -3.90342813e+00 10 -1.20380873e-01 4.44127013e-01 -1.80844647e-01 | -1.20380873e-01 4.44127013e-01 -1.80844647e-01 11 4.54948799e+00 -6.70424133e+00 -6.78135326e+00 | 4.54948799e+00 -6.70424133e+00 -6.78135326e+00 12 -7.03536852e+01 -3.27763974e+01 -2.60054372e+01 | -7.03536852e+01 -3.27763974e+01 -2.60054372e+01 13 7.99443411e+01 2.92962482e+01 2.57483032e+01 | 7.99443411e+01 2.92962482e+01 2.57483032e+01 14 -1.45493703e+01 -3.66183768e+00 -2.08441783e+01 | -1.45493703e+01 -3.66183768e+00 -2.08441783e+01 15 1.92279873e+01 3.95291655e+00 2.03481390e+01 | 1.92279873e+01 3.95291655e+00 2.03481390e+01 16 -1.44778955e+01 -1.53066473e+01 -1.31450699e+01 | -1.44778955e+01 -1.53066473e+01 -1.31450699e+01 17 1.55341988e+01 1.46851671e+01 1.41270298e+01 | 1.55341988e+01 1.46851671e+01 1.41270298e+01 18 -4.18277546e-01 -7.21356541e-01 2.38211576e-01 | -4.18277546e-01 -7.21356541e-01 2.38211576e-01 19 -5.95037535e+01 3.62874445e+01 -3.97870664e+01 | -5.95037535e+01 3.62874445e+01 -3.97870664e+01 20 -3.29784977e+01 -2.38726505e+01 -6.42393690e+00 | -3.29784977e+01 -2.38726505e+01 -6.42393690e+00 21 3.99988356e+01 2.87945660e+01 1.75325069e+00 | 3.99988356e+01 2.87945660e+01 1.75325069e+00 22 -9.02341418e+00 -7.29306285e+00 -5.00416008e+01 | -9.02341418e+00 -7.29306285e+00 -5.00416008e+01 23 4.63277390e+00 1.07931048e+01 4.66724851e+01 | 4.63277390e+00 1.07931048e+01 4.66724851e+01 24 -1.67859134e+00 -2.88508561e+00 -2.12524831e+00 | -1.67859134e+00 -2.88508561e+00 -2.12524831e+00 25 -1.30398481e+01 1.30881273e+01 -5.90365402e+00 | -1.30398481e+01 1.30881273e+01 -5.90365402e+00 26 1.27428357e-03 4.11725866e+00 -4.20952273e+00 | 1.27428357e-03 4.11725866e+00 -4.20952273e+00 27 -1.97352930e-01 -3.56870091e-01 2.50432500e-01 | -1.97352930e-01 -3.56870091e-01 2.50432500e-01 28 -7.26673954e+00 -2.30937389e+01 1.06580196e+01 | -7.26673954e+00 -2.30937389e+01 1.06580196e+01 29 1.61082758e+01 1.38080064e+01 1.00630458e+01 | 1.61082758e+01 1.38080064e+01 1.00630458e+01 30 5.89358674e+01 -3.54929881e+01 3.88725737e+01 | 5.89358674e+01 -3.54929881e+01 3.88725737e+01 31 -1.51093138e+01 7.04674716e+00 -7.69961675e+00 | -1.51093138e+01 7.04674716e+00 -7.69961675e+00 32 -6.44613848e+00 -2.58667776e+00 2.13079560e+00 | -6.44613848e+00 -2.58667776e+00 2.13079560e+00 33 8.21015850e-01 7.06841653e-01 1.38300526e+00 | 8.21015850e-01 7.06841653e-01 1.38300526e+00 34 4.16328758e+01 -1.00870094e+02 5.70966008e+01 | 4.16328758e+01 -1.00870094e+02 5.70966008e+01 35 -1.00829285e+02 -2.52852801e+02 3.01821619e+02 | -1.00829285e+02 -2.52852801e+02 3.01821619e+02 36 -6.83708218e-01 9.72436680e-02 -1.14093879e+00 | -6.83708218e-01 9.72436680e-02 -1.14093879e+00 37 -8.83545772e+00 -1.01362125e+01 9.60261008e+00 | -8.83545772e+00 -1.01362125e+01 9.60261008e+00 38 -5.18848356e+00 -3.68383012e+00 -6.45587873e+00 | -5.18848356e+00 -3.68383012e+00 -6.45587873e+00 39 -1.15743132e+01 -1.10069308e+01 1.69491260e+01 | -1.15743132e+01 -1.10069308e+01 1.69491260e+01 40 -3.80591268e-01 -2.04107676e-01 1.27191118e+00 | -3.80591268e-01 -2.04107676e-01 1.27191118e+00 41 -2.96034267e+01 4.21193345e+01 -2.32066611e+01 | -2.96034267e+01 4.21193345e+01 -2.32066611e+01 42 -3.00744182e+00 2.78184363e+00 2.81026389e+00 | -3.00744182e+00 2.78184363e+00 2.81026389e+00 43 3.30116673e+00 -1.84740121e+00 -2.22965065e+00 | 3.30116673e+00 -1.84740121e+00 -2.22965065e+00 44 2.80098637e+01 -4.57261457e+01 2.39186642e+01 | 2.80098637e+01 -4.57261457e+01 2.39186642e+01 45 -5.15004156e-01 3.50959815e-01 -3.37898989e-01 | -5.15004156e-01 3.50959815e-01 -3.37898989e-01 46 7.05317471e+00 1.21101903e+01 -7.71535861e+00 | 7.05317471e+00 1.21101903e+01 -7.71535861e+00 47 8.48999400e-01 8.90201555e-01 -2.60502058e-01 | 8.48999400e-01 8.90201555e-01 -2.60502058e-01 48 -1.17802272e+01 5.14231518e+00 9.57511655e+00 | -1.17802272e+01 5.14231518e+00 9.57511655e+00 49 -3.82122948e+01 -1.76476882e+01 3.45461548e+01 | -3.82122948e+01 -1.76476882e+01 3.45461548e+01 50 4.10184961e+01 7.76790722e+00 -3.61698924e+01 | 4.10184961e+01 7.76790722e+00 -3.61698924e+01 51 4.20032750e+00 3.90240371e+00 3.35542238e+00 | 4.20032750e+00 3.90240371e+00 3.35542238e+00 52 1.69521628e+01 1.53807133e+01 -1.12463184e+01 | 1.69521628e+01 1.53807133e+01 -1.12463184e+01 53 2.19153388e-01 5.86429534e-01 3.16922540e-01 | 2.19153388e-01 5.86429534e-01 3.16922540e-01 54 -2.37327837e+00 -1.08391769e-01 8.11000964e-01 | -2.37327837e+00 -1.08391769e-01 8.11000964e-01 55 1.63437392e+00 3.79352544e-01 1.07589153e-01 | 1.63437392e+00 3.79352544e-01 1.07589153e-01 56 1.01253418e+02 2.53448097e+02 -2.99489521e+02 | 1.01253418e+02 2.53448097e+02 -2.99489521e+02 57 2.45765966e+01 -4.59647023e+01 -5.21947929e+01 | 2.45765966e+01 -4.59647023e+01 -5.21947929e+01 58 1.47636034e+01 -7.50536323e+00 8.78898044e+00 | 1.47636034e+01 -7.50536323e+00 8.78898044e+00 59 1.66538899e-01 2.32422720e-01 5.30283155e-01 | 1.66538899e-01 2.32422720e-01 5.30283155e-01 60 -2.83452995e+00 3.75054090e+00 1.62088949e+00 | -2.83452995e+00 3.75054090e+00 1.62088949e+00 61 -1.06185894e-01 3.25952532e-01 1.37695868e+00 | -1.06185894e-01 3.25952532e-01 1.37695868e+00 62 -2.59456042e+01 4.28301957e+01 5.01033353e+01 | -2.59456042e+01 4.28301957e+01 5.01033353e+01 63 8.38644587e-01 1.94363990e+00 1.29766117e+00 | 8.38644587e-01 1.94363990e+00 1.29766117e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Fe (Configuration in file "config-Fe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [49, 62, 12, 9, 47, 20, 57, 35, 54, 3, 45, 18, 2, 59, 29, 24, 48, 52, 11, 63, 5, 46, 41, 31, 15, 40, 56, 30, 42, 14, 27, 23, 60, 55, 50, 7, 44, 43, 51, 61, 25, 22, 28, 37, 36, 10, 21, 4, 16, 0, 34, 38, 17, 58, 8, 33, 26, 6, 53, 13, 32, 39, 1, 19] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 94.69601849201969 V(r_1,...,r_N) = 94.69601849202026 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 4.22480948e-01 3.64686085e-01 5.15287679e-01 | 4.22480948e-01 3.64686085e-01 5.15287679e-01 1 -7.67754052e+00 -4.14793285e+00 3.64534936e+00 | -7.67754052e+00 -4.14793285e+00 3.64534936e+00 2 -1.46893887e+01 -5.36990780e+01 -2.97000999e+01 | -1.46893887e+01 -5.36990780e+01 -2.97000999e+01 3 1.55875501e+01 4.62532818e+01 3.07008744e+01 | 1.55875501e+01 4.62532818e+01 3.07008744e+01 4 -2.13915238e-01 -2.21413812e+00 3.71710792e-01 | -2.13915238e-01 -2.21413812e+00 3.71710792e-01 5 -4.45475341e+01 2.81753350e+01 -2.51873856e+01 | -4.45475341e+01 2.81753350e+01 -2.51873856e+01 6 -8.11878942e-01 -2.94944180e-01 4.69598390e-01 | -8.11878942e-01 -2.94944180e-01 4.69598390e-01 7 -5.92687462e+00 -9.82304409e+00 8.97493300e+00 | -5.92687462e+00 -9.82304409e+00 8.97493300e+00 8 -9.87983018e-01 1.19174362e-01 6.27585752e-01 | -9.87983018e-01 1.19174362e-01 6.27585752e-01 9 -2.84446281e+01 -3.30158845e+01 2.21109014e+01 | -2.84446281e+01 -3.30158845e+01 2.21109014e+01 10 2.21378308e+01 1.90239832e+01 -2.69241025e+01 | 2.21378308e+01 1.90239832e+01 -2.69241025e+01 11 6.39936926e+00 1.50711370e+01 2.31992341e+00 | 6.39936926e+00 1.50711370e+01 2.31992341e+00 12 -9.60474539e+00 -5.69004539e+00 -5.55978039e+00 | -9.60474539e+00 -5.69004539e+00 -5.55978039e+00 13 1.46385400e+01 -1.13164530e+00 -4.80433074e+00 | 1.46385400e+01 -1.13164530e+00 -4.80433074e+00 14 -4.74981630e+01 -3.22377395e+01 -2.68675128e+01 | -4.74981630e+01 -3.22377395e+01 -2.68675128e+01 15 4.05508882e+01 2.76599237e+01 3.04231122e+01 | 4.05508882e+01 2.76599237e+01 3.04231122e+01 16 -6.18565914e+00 -3.67406785e+00 -7.68589345e+00 | -6.18565914e+00 -3.67406785e+00 -7.68589345e+00 17 -5.03212494e+01 3.04544837e+01 -4.66371734e+01 | -5.03212494e+01 3.04544837e+01 -4.66371734e+01 18 9.81206411e-01 1.42304485e+00 -6.08689539e-01 | 9.81206411e-01 1.42304485e+00 -6.08689539e-01 19 -5.62330912e-01 3.78763260e-01 -4.53110193e-01 | -5.62330912e-01 3.78763260e-01 -4.53110193e-01 20 6.42924609e+01 -1.87658196e+01 4.72292220e+01 | 6.42924609e+01 -1.87658196e+01 4.72292220e+01 21 2.57645036e+01 -5.53156088e+01 -6.05136248e+00 | 2.57645036e+01 -5.53156088e+01 -6.05136248e+00 22 -2.90450945e+01 -2.91963315e+01 -1.46688240e+01 | -2.90450945e+01 -2.91963315e+01 -1.46688240e+01 23 2.97631519e+01 2.85675908e+01 1.44169174e+01 | 2.97631519e+01 2.85675908e+01 1.44169174e+01 24 5.27432925e+00 1.13579539e+01 -5.40228814e+00 | 5.27432925e+00 1.13579539e+01 -5.40228814e+00 25 -1.30730981e+01 -1.32165486e+01 6.07874830e+00 | -1.30730981e+01 -1.32165486e+01 6.07874830e+00 26 1.44656665e+01 1.37159311e+01 -4.91122760e+00 | 1.44656665e+01 1.37159311e+01 -4.91122760e+00 27 -2.39253426e-01 -3.34759200e-01 6.96937127e-01 | -2.39253426e-01 -3.34759200e-01 6.96937127e-01 28 7.17323886e+00 4.17548177e+00 -1.13705464e+00 | 7.17323886e+00 4.17548177e+00 -1.13705464e+00 29 1.96498112e+01 -2.23690219e+00 -1.61279852e+01 | 1.96498112e+01 -2.23690219e+00 -1.61279852e+01 30 1.76405467e+01 1.78182781e+01 -1.94766294e+01 | 1.76405467e+01 1.78182781e+01 -1.94766294e+01 31 -7.49126476e+00 1.25440885e+01 -1.63896223e+00 | -7.49126476e+00 1.25440885e+01 -1.63896223e+00 32 7.01267385e-01 5.82994483e-01 -3.79559147e-01 | 7.01267385e-01 5.82994483e-01 -3.79559147e-01 33 -7.32356799e+01 3.32241586e+01 -4.10002349e+01 | -7.32356799e+01 3.32241586e+01 -4.10002349e+01 34 -5.74791208e+01 -3.76243192e+01 2.14945565e+00 | -5.74791208e+01 -3.76243192e+01 2.14945565e+00 35 5.46549429e+01 3.78588956e+01 -4.32182213e+00 | 5.46549429e+01 3.78588956e+01 -4.32182213e+00 36 7.38621592e+01 -6.40278004e+01 1.34223850e+01 | 7.38621592e+01 -6.40278004e+01 1.34223850e+01 37 4.69921615e+00 1.23683819e+01 2.44751838e+01 | 4.69921615e+00 1.23683819e+01 2.44751838e+01 38 -1.09191163e+01 9.13351443e+00 4.14335729e+00 | -1.09191163e+01 9.13351443e+00 4.14335729e+00 39 1.82653226e+00 2.94617146e+00 1.24652614e+00 | 1.82653226e+00 2.94617146e+00 1.24652614e+00 40 4.35009935e+01 -2.77758241e+01 2.61763009e+01 | 4.35009935e+01 -2.77758241e+01 2.61763009e+01 41 -6.10568827e+01 -4.70153481e+01 3.50220629e+01 | -6.10568827e+01 -4.70153481e+01 3.50220629e+01 42 5.54614673e+01 5.70683667e+01 -2.41857061e+01 | 5.54614673e+01 5.70683667e+01 -2.41857061e+01 43 -4.64307213e-01 2.07658141e-01 -1.77500179e-01 | -4.64307213e-01 2.07658141e-01 -1.77500179e-01 44 8.83843063e-02 -4.56749216e-01 3.48074116e-01 | 8.83843063e-02 -4.56749216e-01 3.48074116e-01 45 -4.30599652e-01 3.35992285e-01 -7.35533034e-01 | -4.30599652e-01 3.35992285e-01 -7.35533034e-01 46 1.18445790e+00 -2.42928989e-01 -7.56778306e-01 | 1.18445790e+00 -2.42928989e-01 -7.56778306e-01 47 5.27947261e-01 4.83293144e-01 2.41879335e-01 | 5.27947261e-01 4.83293144e-01 2.41879335e-01 48 -1.08580346e-01 7.90030472e-01 3.83884074e-01 | -1.08580346e-01 7.90030472e-01 3.83884074e-01 49 -5.43934577e+01 4.58907082e+01 -3.88456548e+01 | -5.43934577e+01 4.58907082e+01 -3.88456548e+01 50 -4.31976580e+01 3.58474022e+01 2.55363845e+01 | -4.31976580e+01 3.58474022e+01 2.55363845e+01 51 -8.64612830e-02 -5.64365219e-01 1.19560881e-01 | -8.64612830e-02 -5.64365219e-01 1.19560881e-01 52 4.95163708e+01 -5.00998025e+01 3.30935442e+01 | 4.95163708e+01 -5.00998025e+01 3.30935442e+01 53 5.21778964e+00 3.24472218e+00 5.51406471e+00 | 5.21778964e+00 3.24472218e+00 5.51406471e+00 54 -8.22419296e-01 -1.80603537e+00 -9.54659220e-01 | -8.22419296e-01 -1.80603537e+00 -9.54659220e-01 55 1.44211565e+00 1.17864273e+00 2.70012198e-01 | 1.44211565e+00 1.17864273e+00 2.70012198e-01 56 5.48919074e+00 8.02331122e+00 -1.52628859e+00 | 5.48919074e+00 8.02331122e+00 -1.52628859e+00 57 -2.27873112e+01 4.12789622e+01 -8.26402776e+01 | -2.27873112e+01 4.12789622e+01 -8.26402776e+01 58 -1.25214821e+01 -1.06728106e+01 1.77608001e+01 | -1.25214821e+01 -1.06728106e+01 1.77608001e+01 59 -7.82133038e-01 -8.20021155e-01 -1.93660282e-01 | -7.82133038e-01 -8.20021155e-01 -1.93660282e-01 60 2.24168712e+01 -5.67669400e+01 7.16541783e+01 | 2.24168712e+01 -5.67669400e+01 7.16541783e+01 61 6.97313577e+00 6.02172663e+00 4.96568989e+00 | 6.97313577e+00 6.02172663e+00 4.96568989e+00 62 -1.23256334e+01 2.17376726e+00 -4.96232784e-01 | -1.23256334e+01 2.17376726e+00 -4.96232784e-01 63 5.62702820e+00 7.10559726e+00 4.95187410e+00 | 5.62702820e+00 7.10559726e+00 4.95187410e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [25, 9, 47, 17, 52, 40, 14, 16, 30, 1, 56, 53, 29, 21, 6, 60, 7, 3, 58, 41, 45, 13, 27, 42, 43, 0, 57, 22, 48, 12, 8, 44, 36, 37, 49, 38, 32, 33, 35, 54, 5, 19, 23, 24, 31, 20, 51, 2, 28, 34, 62, 46, 4, 11, 39, 63, 10, 26, 18, 61, 15, 59, 50, 55] 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)) = 280.8658877067009 V(r_1,...,r_N) = 280.8658877067006 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 -1.21547836e+00 -3.08313015e+00 -1.03627053e+00 | -1.21547836e+00 -3.08313015e+00 -1.03627053e+00 1 -8.62257334e+01 -9.18099568e+00 1.04071312e+02 | -8.62257334e+01 -9.18099568e+00 1.04071312e+02 2 9.24313598e+01 1.17658558e+01 -1.08242514e+02 | 9.24313598e+01 1.17658558e+01 -1.08242514e+02 3 1.19284105e+01 -3.07223267e+01 -1.34065348e+01 | 1.19284105e+01 -3.07223267e+01 -1.34065348e+01 4 -2.47805553e+01 -1.09442345e+02 -8.06571365e+01 | -2.47805553e+01 -1.09442345e+02 -8.06571365e+01 5 2.29317444e+01 1.10170102e+02 7.65967825e+01 | 2.29317444e+01 1.10170102e+02 7.65967825e+01 6 -2.01801858e+01 -2.98008708e+01 -3.16256167e+01 | -2.01801858e+01 -2.98008708e+01 -3.16256167e+01 7 1.70521763e+01 2.97251036e+01 3.70948943e+01 | 1.70521763e+01 2.97251036e+01 3.70948943e+01 8 -4.09794233e-01 4.45857817e-01 3.43039793e-01 | -4.09794233e-01 4.45857817e-01 3.43039793e-01 9 -2.60279593e+01 1.90977874e+01 -1.24010530e+01 | -2.60279593e+01 1.90977874e+01 -1.24010530e+01 10 2.44618653e+00 5.49356551e+00 -6.04723112e+00 | 2.44618653e+00 5.49356551e+00 -6.04723112e+00 11 -8.03273208e-01 -7.01057182e-02 3.49615986e-01 | -8.03273208e-01 -7.01057182e-02 3.49615986e-01 12 2.35594771e+01 -2.40923611e+01 1.90484680e+01 | 2.35594771e+01 -2.40923611e+01 1.90484680e+01 13 9.14668520e+00 -1.08902834e+01 -3.33605819e+00 | 9.14668520e+00 -1.08902834e+01 -3.33605819e+00 14 1.29644880e+00 4.32326093e-01 1.28967791e+00 | 1.29644880e+00 4.32326093e-01 1.28967791e+00 15 -3.39318508e+01 4.76825781e+01 -4.35387765e+01 | -3.39318508e+01 4.76825781e+01 -4.35387765e+01 16 1.70161472e-01 -8.56911266e-01 -3.83101720e-01 | 1.70161472e-01 -8.56911266e-01 -3.83101720e-01 17 6.00208985e+01 -2.53762579e+01 -3.60677807e+01 | 6.00208985e+01 -2.53762579e+01 -3.60677807e+01 18 1.58382389e+00 -8.69272031e-01 -1.88994629e+00 | 1.58382389e+00 -8.69272031e-01 -1.88994629e+00 19 8.70084609e-01 9.58915946e-01 8.00233797e-01 | 8.70084609e-01 9.58915946e-01 8.00233797e-01 20 -1.93419184e+01 2.04154950e+01 -4.89320212e+00 | -1.93419184e+01 2.04154950e+01 -4.89320212e+00 21 4.58134522e+00 1.01040854e+01 1.90782018e+01 | 4.58134522e+00 1.01040854e+01 1.90782018e+01 22 -6.15989054e+01 2.49699789e+01 3.87672067e+01 | -6.15989054e+01 2.49699789e+01 3.87672067e+01 23 -1.09179086e+01 1.11583615e+01 -8.14920043e+00 | -1.09179086e+01 1.11583615e+01 -8.14920043e+00 24 4.94265207e-01 5.01258810e-01 -4.03398494e-01 | 4.94265207e-01 5.01258810e-01 -4.03398494e-01 25 -1.63448034e+00 4.03844706e+00 -1.54243586e+01 | -1.63448034e+00 4.03844706e+00 -1.54243586e+01 26 -3.66391121e-02 4.81325513e-01 1.80203091e-01 | -3.66391121e-02 4.81325513e-01 1.80203091e-01 27 -9.77877822e-01 -7.67777884e-01 4.08265184e-01 | -9.77877822e-01 -7.67777884e-01 4.08265184e-01 28 -3.30656885e+01 -1.48723568e+01 -2.51664261e+01 | -3.30656885e+01 -1.48723568e+01 -2.51664261e+01 29 3.79774817e+01 2.68971412e+01 3.30290181e+01 | 3.79774817e+01 2.68971412e+01 3.30290181e+01 30 2.75552438e-01 -7.72004810e-01 -5.28949862e-01 | 2.75552438e-01 -7.72004810e-01 -5.28949862e-01 31 5.46330640e-01 1.05687160e+00 2.97487293e-01 | 5.46330640e-01 1.05687160e+00 2.97487293e-01 32 6.02076878e-01 5.11092264e-01 -7.56922092e-02 | 6.02076878e-01 5.11092264e-01 -7.56922092e-02 33 6.98170717e+01 -4.05236027e+02 -3.13726996e+02 | 6.98170717e+01 -4.05236027e+02 -3.13726996e+02 34 -7.92876611e-01 1.05994559e+00 8.99870679e-01 | -7.92876611e-01 1.05994559e+00 8.99870679e-01 35 -5.06296603e+01 -7.61817377e+01 5.34592880e+01 | -5.06296603e+01 -7.61817377e+01 5.34592880e+01 36 5.25484936e-01 5.32932057e-01 -3.80036029e-01 | 5.25484936e-01 5.32932057e-01 -3.80036029e-01 37 -3.33370380e+00 -7.80803200e-01 2.39831129e+00 | -3.33370380e+00 -7.80803200e-01 2.39831129e+00 38 -6.92344819e+01 4.04273668e+02 3.11343306e+02 | -6.92344819e+01 4.04273668e+02 3.11343306e+02 39 6.85779902e-01 1.57899179e+00 1.34511526e+00 | 6.85779902e-01 1.57899179e+00 1.34511526e+00 40 2.33423184e+00 -9.69411131e-01 3.47727280e+00 | 2.33423184e+00 -9.69411131e-01 3.47727280e+00 41 1.78154160e+02 -9.32063954e+01 -5.40127810e+01 | 1.78154160e+02 -9.32063954e+01 -5.40127810e+01 42 1.81701938e+01 -5.50486519e+01 5.25987609e+01 | 1.81701938e+01 -5.50486519e+01 5.25987609e+01 43 1.20491040e+00 1.09083672e+00 2.07520808e+00 | 1.20491040e+00 1.09083672e+00 2.07520808e+00 44 -5.11113683e-01 -2.60652636e-01 3.10317314e-02 | -5.11113683e-01 -2.60652636e-01 3.10317314e-02 45 4.75743662e-03 7.27636055e-01 -3.87224730e-01 | 4.75743662e-03 7.27636055e-01 -3.87224730e-01 46 -1.75922784e+02 9.46241675e+01 5.03285200e+01 | -1.75922784e+02 9.46241675e+01 5.03285200e+01 47 4.04222418e-01 6.11499642e-01 -3.32948770e-01 | 4.04222418e-01 6.11499642e-01 -3.32948770e-01 48 3.74011225e-01 1.52226298e+00 1.01821355e+00 | 3.74011225e-01 1.52226298e+00 1.01821355e+00 49 -1.42892852e+02 1.15468469e+02 -4.68034744e+01 | -1.42892852e+02 1.15468469e+02 -4.68034744e+01 50 1.07272508e+01 -1.30639976e+01 7.30740885e+00 | 1.07272508e+01 -1.30639976e+01 7.30740885e+00 51 1.17808041e+00 7.11663358e-02 7.82419628e-01 | 1.17808041e+00 7.11663358e-02 7.82419628e-01 52 1.14835952e+02 -1.25972865e+02 2.28945662e+01 | 1.14835952e+02 -1.25972865e+02 2.28945662e+01 53 2.94569245e+01 9.17265972e+00 2.23882419e+01 | 2.94569245e+01 9.17265972e+00 2.23882419e+01 54 -9.37879594e+00 -5.08009466e+00 -4.76517722e+00 | -9.37879594e+00 -5.08009466e+00 -4.76517722e+00 55 8.91464569e+00 5.56713536e+00 4.67455307e+00 | 8.91464569e+00 5.56713536e+00 4.67455307e+00 56 4.73346678e+01 7.23753450e+01 -5.49389891e+01 | 4.73346678e+01 7.23753450e+01 -5.49389891e+01 57 3.32817560e+00 1.90055354e+00 1.10126936e+00 | 3.32817560e+00 1.90055354e+00 1.10126936e+00 58 -3.19248421e+01 -2.92516356e+01 -1.77464570e+01 | -3.19248421e+01 -2.92516356e+01 -1.77464570e+01 59 3.17831803e+01 3.01642193e+01 1.75020804e+01 | 3.17831803e+01 3.01642193e+01 1.75020804e+01 60 -1.13076833e+01 -7.39839897e+00 -8.95813985e+00 | -1.13076833e+01 -7.39839897e+00 -8.95813985e+00 61 1.07398193e+01 6.52321752e+00 8.19845411e+00 | 1.07398193e+01 6.52321752e+00 8.19845411e+00 62 -1.36642158e+02 -1.91580512e+02 -1.38780824e+02 | -1.36642158e+02 -1.91580512e+02 -1.38780824e+02 63 1.35831171e+02 1.91657327e+02 1.38927998e+02 | 1.35831171e+02 1.91657327e+02 1.38927998e+02 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cr Fe Ni (Configuration in file "config-CrFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [2, 39, 0, 47, 31, 24, 30, 27, 61, 58, 19, 60, 16, 34, 59, 56, 12, 21, 49, 10, 26, 17, 38, 43, 5, 32, 20, 7, 35, 42, 6, 4, 25, 53, 13, 28, 44, 63, 22, 1, 62, 48, 29, 23, 36, 51, 54, 3, 41, 18, 50, 45, 55, 33, 46, 52, 15, 57, 9, 14, 11, 8, 40, 37] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 98.22798695911555 V(r_1,...,r_N) = 98.2279869591155 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 1.78128240e+00 -4.51885965e+01 -2.61666707e+01 | 1.78128240e+00 -4.51885965e+01 -2.61666707e+01 1 1.55943246e+01 1.40223444e+01 6.83149591e+00 | 1.55943246e+01 1.40223444e+01 6.83149591e+00 2 -4.23720686e+00 -2.81303704e+00 -1.45100026e+00 | -4.23720686e+00 -2.81303704e+00 -1.45100026e+00 3 3.61531068e+00 1.89197835e+00 3.67141096e+00 | 3.61531068e+00 1.89197835e+00 3.67141096e+00 4 -9.41153440e+00 -5.02754110e+00 -1.19913804e+01 | -9.41153440e+00 -5.02754110e+00 -1.19913804e+01 5 -4.00828532e+01 2.67863829e+01 -3.15028023e+01 | -4.00828532e+01 2.67863829e+01 -3.15028023e+01 6 -1.91422869e+01 2.94078812e+01 1.98805304e+01 | -1.91422869e+01 2.94078812e+01 1.98805304e+01 7 -1.59700186e+01 -1.77056811e+01 1.06370138e+01 | -1.59700186e+01 -1.77056811e+01 1.06370138e+01 8 -1.28124729e+01 -4.28616292e+01 -5.72015194e+00 | -1.28124729e+01 -4.28616292e+01 -5.72015194e+00 9 1.22254233e+01 4.27731774e+01 6.49937102e+00 | 1.22254233e+01 4.27731774e+01 6.49937102e+00 10 -1.00158496e+00 -3.93718156e-01 -1.22277289e+00 | -1.00158496e+00 -3.93718156e-01 -1.22277289e+00 11 8.72834534e-01 9.15211728e-01 1.90954188e+00 | 8.72834534e-01 9.15211728e-01 1.90954188e+00 12 -8.70808235e+00 -7.17814065e-01 -8.78775370e+00 | -8.70808235e+00 -7.17814065e-01 -8.78775370e+00 13 7.45207453e+00 2.09296957e+00 8.87528204e+00 | 7.45207453e+00 2.09296957e+00 8.87528204e+00 14 5.23585443e+00 4.96194568e+00 -7.53185404e+00 | 5.23585443e+00 4.96194568e+00 -7.53185404e+00 15 -3.38700419e+01 -2.40176339e+01 1.05515070e+01 | -3.38700419e+01 -2.40176339e+01 1.05515070e+01 16 8.60891123e-01 2.17471281e-01 5.79317410e-01 | 8.60891123e-01 2.17471281e-01 5.79317410e-01 17 6.12557540e+01 -1.13312761e+02 -1.07649486e+02 | 6.12557540e+01 -1.13312761e+02 -1.07649486e+02 18 -4.53927599e+00 -6.34305158e+00 -4.30418378e+00 | -4.53927599e+00 -6.34305158e+00 -4.30418378e+00 19 5.25513319e+00 5.57189619e+00 4.86684160e+00 | 5.25513319e+00 5.57189619e+00 4.86684160e+00 20 1.81748812e+01 1.72377946e+01 -9.25582416e+00 | 1.81748812e+01 1.72377946e+01 -9.25582416e+00 21 3.73639255e+01 -5.25388139e+01 -3.67014175e+01 | 3.73639255e+01 -5.25388139e+01 -3.67014175e+01 22 -6.41164389e+01 1.11489270e+02 1.05782187e+02 | -6.41164389e+01 1.11489270e+02 1.05782187e+02 23 -3.06303512e+00 9.01361205e+00 -5.55926068e+00 | -3.06303512e+00 9.01361205e+00 -5.55926068e+00 24 5.91720581e-01 -6.25405042e-01 -6.68023178e+00 | 5.91720581e-01 -6.25405042e-01 -6.68023178e+00 25 1.81460719e+00 -3.86514970e+00 -1.99240341e+00 | 1.81460719e+00 -3.86514970e+00 -1.99240341e+00 26 -1.55067672e+00 -4.86600753e-01 -3.82108298e-01 | -1.55067672e+00 -4.86600753e-01 -3.82108298e-01 27 7.23552604e-01 -2.52740372e-01 1.30768536e+00 | 7.23552604e-01 -2.52740372e-01 1.30768536e+00 28 3.21735352e+01 2.39825396e+01 -1.09006678e+01 | 3.21735352e+01 2.39825396e+01 -1.09006678e+01 29 1.37127301e+00 1.12384429e+00 4.68102471e-01 | 1.37127301e+00 1.12384429e+00 4.68102471e-01 30 -6.70068482e+01 -5.89309839e+01 -4.27028422e+01 | -6.70068482e+01 -5.89309839e+01 -4.27028422e+01 31 6.55667076e+01 6.71726683e+01 4.95774008e+01 | 6.55667076e+01 6.71726683e+01 4.95774008e+01 32 -3.68815708e+00 -2.95748619e+00 -8.13340861e-01 | -3.68815708e+00 -2.95748619e+00 -8.13340861e-01 33 -2.94339714e+01 -2.22638866e+01 4.49786320e+01 | -2.94339714e+01 -2.22638866e+01 4.49786320e+01 34 3.34608991e+01 2.64727399e+01 -4.48496172e+01 | 3.34608991e+01 2.64727399e+01 -4.48496172e+01 35 -1.81864859e+01 -2.03837359e+01 1.18029153e+01 | -1.81864859e+01 -2.03837359e+01 1.18029153e+01 36 6.40043337e-01 1.57633280e-01 5.14339691e-02 | 6.40043337e-01 1.57633280e-01 5.14339691e-02 37 -4.36804357e+00 -5.69943613e+00 9.15016500e+00 | -4.36804357e+00 -5.69943613e+00 9.15016500e+00 38 -1.41976875e+00 1.82608948e+00 6.05545493e-01 | -1.41976875e+00 1.82608948e+00 6.05545493e-01 39 4.21732095e-01 7.46825834e-02 2.36835640e-01 | 4.21732095e-01 7.46825834e-02 2.36835640e-01 40 4.49460036e+01 -3.00229969e+01 4.94075337e+01 | 4.49460036e+01 -3.00229969e+01 4.94075337e+01 41 2.51457314e+01 -9.45574498e+00 -4.00773664e+01 | 2.51457314e+01 -9.45574498e+00 -4.00773664e+01 42 -1.01403339e+00 -1.14492523e+00 -9.51384832e-01 | -1.01403339e+00 -1.14492523e+00 -9.51384832e-01 43 1.80744060e+00 5.53614698e-01 1.03832702e+00 | 1.80744060e+00 5.53614698e-01 1.03832702e+00 44 -2.23176401e-01 7.41027888e-01 -3.52433344e-01 | -2.23176401e-01 7.41027888e-01 -3.52433344e-01 45 -7.50147846e-01 2.86344814e-01 -5.94868257e-01 | -7.50147846e-01 2.86344814e-01 -5.94868257e-01 46 -2.15721377e+01 1.65131031e+01 2.95607910e+01 | -2.15721377e+01 1.65131031e+01 2.95607910e+01 47 7.61614842e-01 7.88207152e-01 3.94560178e-01 | 7.61614842e-01 7.88207152e-01 3.94560178e-01 48 -6.92155592e+00 -1.80285928e+00 -3.19647956e+00 | -6.92155592e+00 -1.80285928e+00 -3.19647956e+00 49 -7.37997291e+01 5.49534122e+01 -7.49036362e+01 | -7.37997291e+01 5.49534122e+01 -7.49036362e+01 50 -3.20441980e+01 4.61120582e+01 4.22254710e+01 | -3.20441980e+01 4.61120582e+01 4.22254710e+01 51 -1.40629546e+00 1.44222035e+00 -3.98297836e+00 | -1.40629546e+00 1.44222035e+00 -3.98297836e+00 52 8.03523167e+01 -5.37481994e+01 7.87331678e+01 | 8.03523167e+01 -5.37481994e+01 7.87331678e+01 53 5.64902081e-01 2.00261557e-01 3.72151643e-02 | 5.64902081e-01 2.00261557e-01 3.72151643e-02 54 -2.15986130e+01 -6.04239903e+00 -9.64452138e+00 | -2.15986130e+01 -6.04239903e+00 -9.64452138e+00 55 2.25548556e+01 4.91045599e+00 8.59551604e+00 | 2.25548556e+01 4.91045599e+00 8.59551604e+00 56 1.94454753e+01 1.90130346e+01 -1.14422035e+01 | 1.94454753e+01 1.90130346e+01 -1.14422035e+01 57 -1.76770556e+01 4.34404874e+01 -3.73934218e+01 | -1.76770556e+01 4.34404874e+01 -3.73934218e+01 58 -6.61117194e+01 -5.56734515e+01 -7.67110628e+01 | -6.61117194e+01 -5.56734515e+01 -7.67110628e+01 59 6.66745605e+01 5.48730678e+01 7.71691933e+01 | 6.66745605e+01 5.48730678e+01 7.71691933e+01 60 1.88409890e+01 -4.74769639e+01 3.44593178e+01 | 1.88409890e+01 -4.74769639e+01 3.44593178e+01 61 4.41108168e-01 2.51611454e-01 3.18683809e-01 | 4.41108168e-01 2.51611454e-01 3.18683809e-01 62 -3.76712658e+00 -3.10876148e+00 -3.52351409e+00 | -3.76712658e+00 -3.10876148e+00 -3.52351409e+00 63 1.50781429e+00 3.59096426e+00 8.73664889e+00 | 1.50781429e+00 3.59096426e+00 8.73664889e+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.