!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_IMD_BrommerGaehler_2006A_AlNiCo__MO_122703700223_003 Supported species : Al Co Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Al (Configuration in file "config-Al.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [26, 59, 29, 61, 22, 44, 57, 45, 28, 12, 36, 33, 9, 53, 51, 63, 37, 35, 42, 50, 23, 31, 4, 20, 30, 40, 0, 41, 8, 2, 24, 21, 62, 11, 39, 17, 10, 16, 60, 34, 25, 27, 18, 47, 5, 7, 48, 43, 46, 58, 19, 14, 54, 13, 52, 56, 55, 6, 49, 1, 38, 3, 32, 15] 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)) = 158.315608498 V(r_1,...,r_N) = 158.315608498 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 -4.35260458e+00 -2.76748414e+00 -3.48131166e+00 | -4.35260458e+00 -2.76748414e+00 -3.48131166e+00 1 -1.42994576e+01 -2.21911042e+01 1.22987091e+01 | -1.42994576e+01 -2.21911042e+01 1.22987091e+01 2 -1.83175870e+00 1.06668556e+01 -3.82043846e+01 | -1.83175870e+00 1.06668556e+01 -3.82043846e+01 3 1.60167931e+01 2.11959448e+01 1.76039698e+01 | 1.60167931e+01 2.11959448e+01 1.76039698e+01 4 3.28629510e+00 -8.25428817e+00 9.34612909e+00 | 3.28629510e+00 -8.25428817e+00 9.34612909e+00 5 1.81815419e+00 2.21477472e+00 1.08832023e+00 | 1.81815419e+00 2.21477472e+00 1.08832023e+00 6 -1.25052941e+01 -1.10202926e+01 -1.47121186e+01 | -1.25052941e+01 -1.10202926e+01 -1.47121186e+01 7 8.73839023e+00 5.17498950e+01 -3.42687537e+01 | 8.73839023e+00 5.17498950e+01 -3.42687537e+01 8 -1.90449177e+00 -3.51405075e-01 -1.40047761e+00 | -1.90449177e+00 -3.51405075e-01 -1.40047761e+00 9 -1.30653313e+01 9.36004251e+00 -1.50638338e+01 | -1.30653313e+01 9.36004251e+00 -1.50638338e+01 10 -9.30973075e+00 -7.99294055e+00 -9.42298285e+00 | -9.30973075e+00 -7.99294055e+00 -9.42298285e+00 11 9.79824549e+00 8.74570735e+00 7.55851527e+00 | 9.79824549e+00 8.74570735e+00 7.55851527e+00 12 -2.05560266e+01 -3.00600216e+01 -7.69580549e+00 | -2.05560266e+01 -3.00600216e+01 -7.69580549e+00 13 3.93095557e+01 1.39355354e+01 2.16097499e+01 | 3.93095557e+01 1.39355354e+01 2.16097499e+01 14 -1.81030979e+01 -1.00197032e+01 -1.58341320e+01 | -1.81030979e+01 -1.00197032e+01 -1.58341320e+01 15 1.46236952e+01 1.21842499e+01 1.80808349e+01 | 1.46236952e+01 1.21842499e+01 1.80808349e+01 16 -2.56065144e+00 -2.52888833e+00 -2.57296852e+00 | -2.56065144e+00 -2.52888833e+00 -2.57296852e+00 17 -4.13363711e+00 4.58128110e+00 -1.05758360e+00 | -4.13363711e+00 4.58128110e+00 -1.05758360e+00 18 -3.14405625e+00 -3.41237713e+00 -5.74841321e+00 | -3.14405625e+00 -3.41237713e+00 -5.74841321e+00 19 -3.97197779e+01 3.02539546e+01 -2.44357211e+01 | -3.97197779e+01 3.02539546e+01 -2.44357211e+01 20 -8.87184168e+00 -1.61188476e+01 -8.38473851e+00 | -8.87184168e+00 -1.61188476e+01 -8.38473851e+00 21 2.26074542e+01 1.33560948e+01 1.05423034e+01 | 2.26074542e+01 1.33560948e+01 1.05423034e+01 22 -7.55233111e+00 -8.80664989e+00 -1.66648732e+01 | -7.55233111e+00 -8.80664989e+00 -1.66648732e+01 23 6.64260720e+00 1.13236156e+01 1.63738110e+01 | 6.64260720e+00 1.13236156e+01 1.63738110e+01 24 -1.42114207e+00 -1.39488976e+00 -9.05516450e-01 | -1.42114207e+00 -1.39488976e+00 -9.05516450e-01 25 -1.64072252e+01 1.80872077e+01 -1.39840697e+01 | -1.64072252e+01 1.80872077e+01 -1.39840697e+01 26 -2.01789273e+00 -2.96322429e-01 -1.34360040e+00 | -2.01789273e+00 -2.96322429e-01 -1.34360040e+00 27 1.40004542e+00 -1.80110225e-01 1.68276751e+00 | 1.40004542e+00 -1.80110225e-01 1.68276751e+00 28 1.59375440e+01 -1.75254766e+01 1.60463199e+01 | 1.59375440e+01 -1.75254766e+01 1.60463199e+01 29 1.76691243e+00 -5.59692303e-01 1.30653541e+00 | 1.76691243e+00 -5.59692303e-01 1.30653541e+00 30 4.19884191e+01 -2.56710713e+01 2.75580409e+01 | 4.19884191e+01 -2.56710713e+01 2.75580409e+01 31 -2.46952866e+01 9.53247506e+00 -1.29785232e+01 | -2.46952866e+01 9.53247506e+00 -1.29785232e+01 32 -1.29207896e+00 -5.62778346e-01 -2.25012242e+00 | -1.29207896e+00 -5.62778346e-01 -2.25012242e+00 33 -3.92429457e+01 6.60525914e+01 -6.07102393e+01 | -3.92429457e+01 6.60525914e+01 -6.07102393e+01 34 2.67740516e+01 -5.94230508e+01 3.29912324e+01 | 2.67740516e+01 -5.94230508e+01 3.29912324e+01 35 -4.67939354e+00 -7.14388111e+00 4.73173563e+00 | -4.67939354e+00 -7.14388111e+00 4.73173563e+00 36 4.24376980e+01 -6.61123904e+01 6.14709217e+01 | 4.24376980e+01 -6.61123904e+01 6.14709217e+01 37 -1.18032688e+01 -1.40846541e+01 9.10062347e+00 | -1.18032688e+01 -1.40846541e+01 9.10062347e+00 38 -1.11597019e+01 -6.96000073e+00 -8.89008690e+00 | -1.11597019e+01 -6.96000073e+00 -8.89008690e+00 39 -1.01483481e+01 -1.06525534e+01 2.16358467e+01 | -1.01483481e+01 -1.06525534e+01 2.16358467e+01 40 -8.42170385e+00 -4.85899739e+00 -2.77627922e+00 | -8.42170385e+00 -4.85899739e+00 -2.77627922e+00 41 -1.61455034e+01 4.25748158e+01 -1.96169994e+01 | -1.61455034e+01 4.25748158e+01 -1.96169994e+01 42 -9.87696540e+00 -2.84209930e+00 -5.57326379e+00 | -9.87696540e+00 -2.84209930e+00 -5.57326379e+00 43 6.63752322e+00 9.41457520e+00 8.06246140e+00 | 6.63752322e+00 9.41457520e+00 8.06246140e+00 44 2.40765601e+01 -4.01702086e+01 1.96353119e+01 | 2.40765601e+01 -4.01702086e+01 1.96353119e+01 45 9.44656832e-01 9.83331353e-01 9.94284973e-01 | 9.44656832e-01 9.83331353e-01 9.94284973e-01 46 -2.85145777e-01 2.24870361e+00 -1.84321022e+01 | -2.85145777e-01 2.24870361e+00 -1.84321022e+01 47 9.09638990e+00 1.42938768e+01 1.10838763e+01 | 9.09638990e+00 1.42938768e+01 1.10838763e+01 48 -2.55638356e+01 1.54567066e+01 1.83185866e+01 | -2.55638356e+01 1.54567066e+01 1.83185866e+01 49 -2.23551792e-01 -1.29516195e+00 1.66189685e-01 | -2.23551792e-01 -1.29516195e+00 1.66189685e-01 50 -1.10009177e+01 -1.71542080e+01 -1.60699739e+01 | -1.10009177e+01 -1.71542080e+01 -1.60699739e+01 51 1.18531497e+01 1.69771910e+01 1.56168531e+01 | 1.18531497e+01 1.69771910e+01 1.56168531e+01 52 2.02567842e+01 2.01663597e+01 -1.26348930e+01 | 2.02567842e+01 2.01663597e+01 -1.26348930e+01 53 -8.09900330e+00 -1.23338169e+01 1.43677667e+01 | -8.09900330e+00 -1.23338169e+01 1.43677667e+01 54 -2.13763919e+00 -1.13019930e-01 2.69880819e-01 | -2.13763919e+00 -1.13019930e-01 2.69880819e-01 55 2.57287617e+00 3.19127560e-01 6.76944929e-01 | 2.57287617e+00 3.19127560e-01 6.76944929e-01 56 3.12074953e+00 1.12597769e+00 -6.54642697e+00 | 3.12074953e+00 1.12597769e+00 -6.54642697e+00 57 2.19748178e+01 -3.14207674e+01 -3.96291889e+01 | 2.19748178e+01 -3.14207674e+01 -3.96291889e+01 58 2.42811230e+01 -8.47538369e+00 1.41702051e+01 | 2.42811230e+01 -8.47538369e+00 1.41702051e+01 59 1.55468469e-01 -1.17365850e-01 -7.26492309e-02 | 1.55468469e-01 -1.17365850e-01 -7.26492309e-02 60 -1.25490922e+00 -2.61464795e-01 -2.60907066e-01 | -1.25490922e+00 -2.61464795e-01 -2.60907066e-01 61 9.84049727e-01 8.03347648e-01 9.21334679e-01 | 9.84049727e-01 8.03347648e-01 9.21334679e-01 62 -1.09922481e+01 4.55546203e+01 2.62210976e+01 | -1.09922481e+01 4.55546203e+01 2.62210976e+01 63 -3.21213893e-01 -2.54909764e-02 9.17805249e-02 | -3.21213893e-01 -2.54909764e-02 9.17805249e-02 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [26, 34, 60, 9, 16, 57, 59, 51, 54, 3, 14, 46, 19, 53, 10, 33, 4, 38, 40, 12, 27, 43, 58, 39, 41, 37, 0, 20, 31, 42, 61, 28, 63, 15, 1, 47, 45, 25, 17, 23, 18, 24, 29, 21, 49, 36, 11, 35, 62, 44, 52, 7, 50, 13, 8, 56, 55, 5, 22, 6, 2, 30, 48, 32] 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)) = -30.5487274349 V(r_1,...,r_N) = -30.5487274349 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 1.35424002e-01 7.13443769e-01 7.47810254e-01 | 1.35424002e-01 7.13443769e-01 7.47810254e-01 1 -3.05667997e+00 -7.01988222e+00 2.25278768e+00 | -3.05667997e+00 -7.01988222e+00 2.25278768e+00 2 -1.82509391e+01 -9.93015743e+00 -3.53567933e+01 | -1.82509391e+01 -9.93015743e+00 -3.53567933e+01 3 1.64851363e+01 1.92598551e+01 2.58405652e+01 | 1.64851363e+01 1.92598551e+01 2.58405652e+01 4 -5.10067974e+00 -3.10772036e+00 -2.08304677e+00 | -5.10067974e+00 -3.10772036e+00 -2.08304677e+00 5 -1.10135322e+02 4.63036992e+01 -4.52142312e+01 | -1.10135322e+02 4.63036992e+01 -4.52142312e+01 6 1.89487755e-01 8.60951288e-01 1.45849994e-02 | 1.89487755e-01 8.60951288e-01 1.45849994e-02 7 1.04958178e+01 -1.78094290e+01 -3.16104967e+00 | 1.04958178e+01 -1.78094290e+01 -3.16104967e+00 8 -7.34673157e-01 9.98682532e-01 3.69708058e-01 | -7.34673157e-01 9.98682532e-01 3.69708058e-01 9 1.99239157e-01 -3.50854521e-01 -1.03008780e-01 | 1.99239157e-01 -3.50854521e-01 -1.03008780e-01 10 -5.05650710e+00 -1.40137479e+01 -5.38652410e+00 | -5.05650710e+00 -1.40137479e+01 -5.38652410e+00 11 5.42313187e+00 1.36722312e+01 5.53472414e+00 | 5.42313187e+00 1.36722312e+01 5.53472414e+00 12 9.72221999e-01 6.14151955e-01 5.80378109e-01 | 9.72221999e-01 6.14151955e-01 5.80378109e-01 13 -8.19219250e-01 1.18089352e-02 3.21077555e-01 | -8.19219250e-01 1.18089352e-02 3.21077555e-01 14 6.16377240e+00 -3.72624327e+00 4.50897509e+00 | 6.16377240e+00 -3.72624327e+00 4.50897509e+00 15 -1.59139992e+00 -7.22173845e+00 5.80152072e+00 | -1.59139992e+00 -7.22173845e+00 5.80152072e+00 16 7.30465647e-01 9.95809145e-02 1.08935152e+00 | 7.30465647e-01 9.95809145e-02 1.08935152e+00 17 -1.23730580e-01 2.09037562e+00 -4.75908517e-01 | -1.23730580e-01 2.09037562e+00 -4.75908517e-01 18 -3.16845820e-02 8.99229639e-02 -1.62377578e-02 | -3.16845820e-02 8.99229639e-02 -1.62377578e-02 19 -7.60081513e-01 -1.07102028e+00 7.82331096e-01 | -7.60081513e-01 -1.07102028e+00 7.82331096e-01 20 6.47866402e-01 6.47156056e-01 -2.44592159e+00 | 6.47866402e-01 6.47156056e-01 -2.44592159e+00 21 5.06812520e+00 -4.54471796e+00 -9.06688267e+00 | 5.06812520e+00 -4.54471796e+00 -9.06688267e+00 22 1.69736454e+00 -5.08470135e-01 2.36033837e-01 | 1.69736454e+00 -5.08470135e-01 2.36033837e-01 23 -5.06008163e-01 -2.41124927e-01 -9.48765924e-01 | -5.06008163e-01 -2.41124927e-01 -9.48765924e-01 24 -3.76996546e+00 -2.36148447e+00 -6.08736724e+00 | -3.76996546e+00 -2.36148447e+00 -6.08736724e+00 25 2.61982253e+00 6.84036012e+00 -3.26962685e+00 | 2.61982253e+00 6.84036012e+00 -3.26962685e+00 26 -1.04924826e+00 -6.40963352e-01 -1.04770585e-01 | -1.04924826e+00 -6.40963352e-01 -1.04770585e-01 27 -4.46771126e-01 -1.02157486e-02 9.14644093e-01 | -4.46771126e-01 -1.02157486e-02 9.14644093e-01 28 -1.42686046e+00 -5.80529722e+00 -7.94481496e+00 | -1.42686046e+00 -5.80529722e+00 -7.94481496e+00 29 1.67331373e+01 -1.34072017e+00 8.93078988e-01 | 1.67331373e+01 -1.34072017e+00 8.93078988e-01 30 -6.35800549e+00 -6.18818328e+00 -3.58586060e+00 | -6.35800549e+00 -6.18818328e+00 -3.58586060e+00 31 7.56870934e+00 7.62886083e+00 2.55411465e+00 | 7.56870934e+00 7.62886083e+00 2.55411465e+00 32 -3.04519622e+00 -2.54986031e+00 -2.44101023e+00 | -3.04519622e+00 -2.54986031e+00 -2.44101023e+00 33 1.72415216e+00 3.85612742e+00 2.75071942e+00 | 1.72415216e+00 3.85612742e+00 2.75071942e+00 34 -4.33729621e+00 -1.15600810e+01 -4.92962074e+00 | -4.33729621e+00 -1.15600810e+01 -4.92962074e+00 35 5.96688561e+00 9.08340854e+00 4.12530222e-01 | 5.96688561e+00 9.08340854e+00 4.12530222e-01 36 1.61959597e+00 3.04116738e-01 6.67121570e-01 | 1.61959597e+00 3.04116738e-01 6.67121570e-01 37 -2.78654285e-01 6.13252113e-01 -1.50497421e+00 | -2.78654285e-01 6.13252113e-01 -1.50497421e+00 38 -1.56128385e-01 1.61190561e-01 -6.55283613e-01 | -1.56128385e-01 1.61190561e-01 -6.55283613e-01 39 -1.14686270e+00 -1.40788717e+00 2.12001749e+00 | -1.14686270e+00 -1.40788717e+00 2.12001749e+00 40 1.15668897e+02 -4.49210113e+01 4.72632341e+01 | 1.15668897e+02 -4.49210113e+01 4.72632341e+01 41 -2.18222671e+01 1.32631504e+01 -1.01356526e+01 | -2.18222671e+01 1.32631504e+01 -1.01356526e+01 42 -6.56527985e+01 -2.41804338e+01 -8.01176703e+00 | -6.56527985e+01 -2.41804338e+01 -8.01176703e+00 43 6.70488020e+01 2.29157822e+01 6.68266673e+00 | 6.70488020e+01 2.29157822e+01 6.68266673e+00 44 2.26149766e+01 -1.56391050e+01 8.68224122e+00 | 2.26149766e+01 -1.56391050e+01 8.68224122e+00 45 -2.80820468e-03 8.71156374e-01 2.02846843e+00 | -2.80820468e-03 8.71156374e-01 2.02846843e+00 46 7.94552427e-01 -7.98433928e-02 8.16966177e-01 | 7.94552427e-01 -7.98433928e-02 8.16966177e-01 47 8.57108714e-01 -1.35795916e-01 -1.35733412e+00 | 8.57108714e-01 -1.35795916e-01 -1.35733412e+00 48 -1.38469577e+01 1.49879716e+01 4.98630048e+00 | -1.38469577e+01 1.49879716e+01 4.98630048e+00 49 -1.11154476e+01 -7.77977352e+00 9.33581937e+00 | -1.11154476e+01 -7.77977352e+00 9.33581937e+00 50 5.21703946e+00 1.35285570e+01 1.04496386e+00 | 5.21703946e+00 1.35285570e+01 1.04496386e+00 51 -3.96491184e+00 4.24503211e+00 -3.44461448e+00 | -3.96491184e+00 4.24503211e+00 -3.44461448e+00 52 -4.44100771e+00 -1.10412898e+00 3.60256869e-01 | -4.44100771e+00 -1.10412898e+00 3.60256869e-01 53 1.17028009e+00 5.61446261e+00 3.44619804e+00 | 1.17028009e+00 5.61446261e+00 3.44619804e+00 54 -1.07171322e+00 -9.37087059e-01 -7.72083731e-01 | -1.07171322e+00 -9.37087059e-01 -7.72083731e-01 55 8.32950086e-01 8.80442190e-01 4.70621415e-01 | 8.32950086e-01 8.80442190e-01 4.70621415e-01 56 -2.02880941e+00 8.92291575e-01 2.77290337e+00 | -2.02880941e+00 8.92291575e-01 2.77290337e+00 57 -1.29702878e+01 1.13432799e+01 -7.90653279e+00 | -1.29702878e+01 1.13432799e+01 -7.90653279e+00 58 -9.76680119e+00 9.85052049e+00 6.03169022e+00 | -9.76680119e+00 9.85052049e+00 6.03169022e+00 59 -8.84639799e-01 -7.45696348e-01 1.47886619e-02 | -8.84639799e-01 -7.45696348e-01 1.47886619e-02 60 1.26090993e+01 -1.17138365e+01 9.68980268e+00 | 1.26090993e+01 -1.17138365e+01 9.68980268e+00 61 -3.47935055e-01 -8.29626838e-02 1.16321868e+00 | -3.47935055e-01 -8.29626838e-02 1.16321868e+00 62 3.76621941e+00 -4.06384896e+00 3.84816373e+00 | 3.76621941e+00 -4.06384896e+00 3.84816373e+00 63 1.07801762e+00 5.51500551e-01 -6.20694612e-01 | 1.07801762e+00 5.51500551e-01 -6.20694612e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [53, 51, 8, 63, 61, 20, 35, 10, 2, 36, 7, 18, 46, 21, 41, 30, 39, 60, 11, 42, 5, 13, 62, 50, 29, 33, 55, 54, 32, 24, 15, 56, 28, 25, 43, 6, 9, 48, 58, 16, 59, 14, 19, 34, 45, 44, 12, 49, 37, 47, 23, 1, 57, 0, 27, 26, 31, 52, 38, 40, 17, 4, 22, 3] 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)) = 94.0980023022 V(r_1,...,r_N) = 94.0980023022 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 -4.84279777e+00 -1.98609323e+01 -2.01130381e+01 | -4.84279777e+00 -1.98609323e+01 -2.01130381e+01 1 1.76175235e+00 2.03449804e+01 1.73073206e+01 | 1.76175235e+00 2.03449804e+01 1.73073206e+01 2 -3.21825137e-01 -1.10156505e-02 -1.60380081e+00 | -3.21825137e-01 -1.10156505e-02 -1.60380081e+00 3 -1.00412320e+01 -2.16078996e+01 2.68816736e+00 | -1.00412320e+01 -2.16078996e+01 2.68816736e+00 4 -5.22739902e-03 -2.09157604e+00 1.33834178e+00 | -5.22739902e-03 -2.09157604e+00 1.33834178e+00 5 -8.65923491e+00 -2.31866264e+01 1.61719037e+00 | -8.65923491e+00 -2.31866264e+01 1.61719037e+00 6 -2.51862659e+00 8.45376625e-02 2.03661694e+00 | -2.51862659e+00 8.45376625e-02 2.03661694e+00 7 1.93725502e-01 1.50092680e+00 1.38084303e+00 | 1.93725502e-01 1.50092680e+00 1.38084303e+00 8 3.01839372e+00 -8.12369964e-01 -1.72027019e+00 | 3.01839372e+00 -8.12369964e-01 -1.72027019e+00 9 -8.40585354e-01 -1.23710205e+00 -1.12830707e+00 | -8.40585354e-01 -1.23710205e+00 -1.12830707e+00 10 2.57774953e+00 2.81294033e-01 -1.12629119e+00 | 2.57774953e+00 2.81294033e-01 -1.12629119e+00 11 -1.34111345e+00 -3.67642211e-01 -1.19184417e+00 | -1.34111345e+00 -3.67642211e-01 -1.19184417e+00 12 8.13233885e-01 -2.46628624e+00 -1.52094269e+00 | 8.13233885e-01 -2.46628624e+00 -1.52094269e+00 13 2.27105218e+01 -2.26713935e+01 -2.01986731e+01 | 2.27105218e+01 -2.26713935e+01 -2.01986731e+01 14 1.02318825e+01 2.08715808e+01 -4.89843383e-01 | 1.02318825e+01 2.08715808e+01 -4.89843383e-01 15 6.43032325e-01 1.77195690e+00 5.06900903e+00 | 6.43032325e-01 1.77195690e+00 5.06900903e+00 16 -2.18131665e+00 -4.48255529e-01 -2.63353361e+00 | -2.18131665e+00 -4.48255529e-01 -2.63353361e+00 17 -3.57502897e+00 1.04951430e+00 -7.05498331e-01 | -3.57502897e+00 1.04951430e+00 -7.05498331e-01 18 1.26138468e+00 3.31985332e+00 -9.21788061e-01 | 1.26138468e+00 3.31985332e+00 -9.21788061e-01 19 1.95528350e+00 -8.51527352e-01 -1.25781870e+00 | 1.95528350e+00 -8.51527352e-01 -1.25781870e+00 20 -2.42813116e-01 -4.68143718e-01 -6.09729759e-02 | -2.42813116e-01 -4.68143718e-01 -6.09729759e-02 21 -6.87932200e+01 3.52806479e+01 -3.43562042e+01 | -6.87932200e+01 3.52806479e+01 -3.43562042e+01 22 -1.76231825e+00 4.25086758e-01 -5.30677017e-01 | -1.76231825e+00 4.25086758e-01 -5.30677017e-01 23 1.74797430e-02 1.48114436e+00 -1.00828270e+00 | 1.74797430e-02 1.48114436e+00 -1.00828270e+00 24 6.86417447e+00 1.86506485e+01 -6.63961968e+00 | 6.86417447e+00 1.86506485e+01 -6.63961968e+00 25 2.42873633e+00 4.02280464e+00 1.63167664e+00 | 2.42873633e+00 4.02280464e+00 1.63167664e+00 26 -1.45120867e+00 -1.54601589e+00 6.17840986e-01 | -1.45120867e+00 -1.54601589e+00 6.17840986e-01 27 -1.89778279e-01 1.03740651e+00 -4.74722844e-01 | -1.89778279e-01 1.03740651e+00 -4.74722844e-01 28 1.56205998e+00 -8.04806382e-01 -2.36423634e+00 | 1.56205998e+00 -8.04806382e-01 -2.36423634e+00 29 5.94444751e+00 -3.80022319e+00 -5.33787548e+00 | 5.94444751e+00 -3.80022319e+00 -5.33787548e+00 30 -1.03478390e+00 4.02535087e+00 -3.65770240e+00 | -1.03478390e+00 4.02535087e+00 -3.65770240e+00 31 7.41837757e-01 7.46822247e-01 1.40282632e+00 | 7.41837757e-01 7.46822247e-01 1.40282632e+00 32 -8.51917458e-01 -1.05238242e+00 1.28369722e+00 | -8.51917458e-01 -1.05238242e+00 1.28369722e+00 33 1.90576403e-02 -2.34484288e+00 3.08414844e+00 | 1.90576403e-02 -2.34484288e+00 3.08414844e+00 34 4.21123071e+00 6.61237648e-01 -5.74156318e+00 | 4.21123071e+00 6.61237648e-01 -5.74156318e+00 35 -1.52624022e+01 1.02167071e+00 -1.81954712e+00 | -1.52624022e+01 1.02167071e+00 -1.81954712e+00 36 8.86537950e-02 -1.35224643e+00 1.48977553e+00 | 8.86537950e-02 -1.35224643e+00 1.48977553e+00 37 -5.11318031e-01 -3.97784926e+00 3.82251535e-01 | -5.11318031e-01 -3.97784926e+00 3.82251535e-01 38 -9.52450015e-01 -3.80816061e-02 2.63387927e+00 | -9.52450015e-01 -3.80816061e-02 2.63387927e+00 39 -5.44549447e-01 -1.78507785e+00 -9.46754509e-01 | -5.44549447e-01 -1.78507785e+00 -9.46754509e-01 40 -4.67912865e-01 1.86393198e-01 2.52537880e+00 | -4.67912865e-01 1.86393198e-01 2.52537880e+00 41 2.15712765e+01 -1.37671454e+01 -1.52996200e+01 | 2.15712765e+01 -1.37671454e+01 -1.52996200e+01 42 -1.80910076e+01 2.25733457e+01 2.14489210e+01 | -1.80910076e+01 2.25733457e+01 2.14489210e+01 43 7.72758480e+01 -9.90704795e+01 -9.30937241e+01 | 7.72758480e+01 -9.90704795e+01 -9.30937241e+01 44 -8.70972510e-02 -1.42048819e+00 1.75987733e-01 | -8.70972510e-02 -1.42048819e+00 1.75987733e-01 45 4.38050679e-02 -1.00602997e+00 -7.47263087e-02 | 4.38050679e-02 -1.00602997e+00 -7.47263087e-02 46 -4.79408380e+00 3.93020295e+00 1.82184707e+01 | -4.79408380e+00 3.93020295e+00 1.82184707e+01 47 3.04311505e-01 -1.04534897e+00 2.89486482e-01 | 3.04311505e-01 -1.04534897e+00 2.89486482e-01 48 -3.31293068e-03 4.44074227e-02 -4.91532838e+00 | -3.31293068e-03 4.44074227e-02 -4.91532838e+00 49 -1.63514242e+00 1.65670187e+00 1.96353812e+00 | -1.63514242e+00 1.65670187e+00 1.96353812e+00 50 8.67481198e-01 1.89570431e+00 1.74476549e+00 | 8.67481198e-01 1.89570431e+00 1.74476549e+00 51 1.62037370e+00 -1.64688197e+00 1.14420482e+00 | 1.62037370e+00 -1.64688197e+00 1.14420482e+00 52 -1.44748951e+01 -5.35276815e+00 -5.96338962e+00 | -1.44748951e+01 -5.35276815e+00 -5.96338962e+00 53 8.75561568e+00 1.32244023e+01 1.16713889e+01 | 8.75561568e+00 1.32244023e+01 1.16713889e+01 54 8.16737057e-01 7.74077985e-01 -3.23247176e-01 | 8.16737057e-01 7.74077985e-01 -3.23247176e-01 55 -1.56923181e+00 3.65418537e-02 -2.30805134e-01 | -1.56923181e+00 3.65418537e-02 -2.30805134e-01 56 6.56481216e+01 -3.65531200e+01 3.79748901e+01 | 6.56481216e+01 -3.65531200e+01 3.79748901e+01 57 4.20417400e-01 3.34118954e+00 -9.31057516e-02 | 4.20417400e-01 3.34118954e+00 -9.31057516e-02 58 -6.99834264e+01 -8.89534697e+01 -6.45701729e+01 | -6.99834264e+01 -8.89534697e+01 -6.45701729e+01 59 6.86507077e+01 9.66112255e+01 6.74688234e+01 | 6.86507077e+01 9.66112255e+01 6.74688234e+01 60 -7.66251857e+01 9.99615688e+01 9.44418109e+01 | -7.66251857e+01 9.99615688e+01 9.44418109e+01 61 -5.57039721e-01 -5.11079106e-01 -2.20151090e-01 | -5.57039721e-01 -5.11079106e-01 -2.20151090e-01 62 2.11127324e+00 2.36879052e+00 4.27665247e-02 | 2.11127324e+00 2.36879052e+00 4.27665247e-02 63 -9.18523242e-01 -1.07290911e+00 -7.39939701e-01 | -9.18523242e-01 -1.07290911e+00 -7.39939701e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Co Ni (Configuration in file "config-AlCoNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [63, 15, 58, 24, 42, 31, 55, 19, 47, 59, 40, 29, 14, 62, 12, 1, 30, 60, 38, 7, 22, 23, 20, 21, 3, 44, 37, 46, 51, 11, 16, 5, 53, 36, 41, 61, 33, 26, 18, 54, 10, 34, 4, 45, 25, 43, 27, 8, 56, 49, 52, 28, 50, 32, 39, 6, 48, 57, 2, 9, 17, 35, 13, 0] 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)) = -67.435669651 V(r_1,...,r_N) = -67.435669651 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 1.01079451e+00 8.40104338e-01 7.93849515e-01 | 1.01079451e+00 8.40104338e-01 7.93849515e-01 1 -2.61456245e-01 -1.38285539e+01 -2.21431063e+00 | -2.61456245e-01 -1.38285539e+01 -2.21431063e+00 2 -4.69561092e-01 -1.91561170e-01 1.23846832e+00 | -4.69561092e-01 -1.91561170e-01 1.23846832e+00 3 5.87406242e+00 -6.63277357e+00 -6.71231830e+00 | 5.87406242e+00 -6.63277357e+00 -6.71231830e+00 4 -4.43999189e+00 -6.95548223e+00 -1.99612926e+00 | -4.43999189e+00 -6.95548223e+00 -1.99612926e+00 5 4.57663322e+00 8.15781359e+00 2.94927155e+00 | 4.57663322e+00 8.15781359e+00 2.94927155e+00 6 1.46604645e+00 1.31215027e+01 1.40074296e+00 | 1.46604645e+00 1.31215027e+01 1.40074296e+00 7 2.22535667e+01 -1.86275547e+01 -3.20757027e+01 | 2.22535667e+01 -1.86275547e+01 -3.20757027e+01 8 -2.29852753e+00 -7.57633874e+00 -4.62005186e+00 | -2.29852753e+00 -7.57633874e+00 -4.62005186e+00 9 2.18542759e+00 8.67958254e+00 5.77719156e+00 | 2.18542759e+00 8.67958254e+00 5.77719156e+00 10 -4.99312888e+00 -4.83594705e+00 -5.18045116e+00 | -4.99312888e+00 -4.83594705e+00 -5.18045116e+00 11 5.25440083e+00 3.42381908e+00 4.32929567e+00 | 5.25440083e+00 3.42381908e+00 4.32929567e+00 12 -6.48331555e-01 1.48109420e+00 8.80282236e-01 | -6.48331555e-01 1.48109420e+00 8.80282236e-01 13 1.58117107e+00 -3.31652436e+00 -1.78906281e+00 | 1.58117107e+00 -3.31652436e+00 -1.78906281e+00 14 -4.15131791e+00 -2.20121233e+00 -1.15708101e+00 | -4.15131791e+00 -2.20121233e+00 -1.15708101e+00 15 2.45585670e+00 3.68997839e+00 1.57045628e+00 | 2.45585670e+00 3.68997839e+00 1.57045628e+00 16 3.75052346e-01 8.89088351e-01 -2.60180110e-01 | 3.75052346e-01 8.89088351e-01 -2.60180110e-01 17 6.19856006e-01 -9.70637103e+00 7.19002584e+00 | 6.19856006e-01 -9.70637103e+00 7.19002584e+00 18 -3.06221842e+00 1.17723486e+01 -7.43004613e+00 | -3.06221842e+00 1.17723486e+01 -7.43004613e+00 19 4.45676894e-01 -1.51972909e+00 1.47837138e+00 | 4.45676894e-01 -1.51972909e+00 1.47837138e+00 20 -5.21905815e+00 7.88111675e-01 1.06517982e+01 | -5.21905815e+00 7.88111675e-01 1.06517982e+01 21 -9.60968591e+00 1.05036008e+01 -7.43379358e+00 | -9.60968591e+00 1.05036008e+01 -7.43379358e+00 22 1.77933881e+00 1.12909578e+00 -4.54281334e-01 | 1.77933881e+00 1.12909578e+00 -4.54281334e-01 23 -9.53530375e-01 2.79264681e+00 -4.99055823e+00 | -9.53530375e-01 2.79264681e+00 -4.99055823e+00 24 -3.98553904e+00 -4.71170215e+00 -1.43146702e+00 | -3.98553904e+00 -4.71170215e+00 -1.43146702e+00 25 -8.11846651e+00 -5.58793673e+00 1.42357935e+01 | -8.11846651e+00 -5.58793673e+00 1.42357935e+01 26 1.28436630e+01 1.30070726e+01 -1.25331179e+01 | 1.28436630e+01 1.30070726e+01 -1.25331179e+01 27 -4.38264075e-01 -5.42020661e-01 -2.64800759e-01 | -4.38264075e-01 -5.42020661e-01 -2.64800759e-01 28 -3.76997700e+00 -4.54331469e+00 -6.34293744e+00 | -3.76997700e+00 -4.54331469e+00 -6.34293744e+00 29 9.85876021e+00 -6.71247076e+00 -2.52072939e+00 | 9.85876021e+00 -6.71247076e+00 -2.52072939e+00 30 1.56870095e+00 2.15609298e+00 -5.20216680e-01 | 1.56870095e+00 2.15609298e+00 -5.20216680e-01 31 -4.20068757e+00 1.55921850e+00 8.77440158e-02 | -4.20068757e+00 1.55921850e+00 8.77440158e-02 32 -1.80640504e+01 -1.87754986e+01 -1.17295066e+01 | -1.80640504e+01 -1.87754986e+01 -1.17295066e+01 33 1.69957204e+01 2.09774936e+01 1.08044667e+01 | 1.69957204e+01 2.09774936e+01 1.08044667e+01 34 -3.78408981e+00 -1.21229093e+01 -5.73946587e-01 | -3.78408981e+00 -1.21229093e+01 -5.73946587e-01 35 -3.17861078e-01 8.09946161e+00 -8.21909626e-01 | -3.17861078e-01 8.09946161e+00 -8.21909626e-01 36 2.74803861e+00 9.24700329e-02 2.35599947e-03 | 2.74803861e+00 9.24700329e-02 2.35599947e-03 37 -7.39134848e+00 -1.58047843e+00 6.98529900e+00 | -7.39134848e+00 -1.58047843e+00 6.98529900e+00 38 1.74587253e-01 1.04739315e+00 1.23128943e+00 | 1.74587253e-01 1.04739315e+00 1.23128943e+00 39 -7.39433371e+00 -5.65111779e+00 9.97249510e+00 | -7.39433371e+00 -5.65111779e+00 9.97249510e+00 40 -2.30955632e+00 -4.00296454e+00 -7.04905030e+00 | -2.30955632e+00 -4.00296454e+00 -7.04905030e+00 41 1.32796953e+00 4.76528024e+00 5.37714865e+00 | 1.32796953e+00 4.76528024e+00 5.37714865e+00 42 -1.35071834e+00 1.86738731e-01 3.47862579e+00 | -1.35071834e+00 1.86738731e-01 3.47862579e+00 43 6.26182157e+00 -1.05605961e+01 -4.27595962e+00 | 6.26182157e+00 -1.05605961e+01 -4.27595962e+00 44 -2.64407216e-01 8.13838240e-01 -1.50699915e-01 | -2.64407216e-01 8.13838240e-01 -1.50699915e-01 45 -8.66892979e-01 7.18367601e-01 -3.97696294e-01 | -8.66892979e-01 7.18367601e-01 -3.97696294e-01 46 7.46702006e+00 1.94008221e+00 -7.72585898e+00 | 7.46702006e+00 1.94008221e+00 -7.72585898e+00 47 8.06480240e-01 -3.87007602e-01 6.62047978e-01 | 8.06480240e-01 -3.87007602e-01 6.62047978e-01 48 -2.18293423e+01 1.79249696e+01 3.24279991e+01 | -2.18293423e+01 1.79249696e+01 3.24279991e+01 49 1.61254061e-02 -7.32747261e+00 5.26109906e+00 | 1.61254061e-02 -7.32747261e+00 5.26109906e+00 50 1.55721554e+00 3.70899624e+00 -2.14008005e+00 | 1.55721554e+00 3.70899624e+00 -2.14008005e+00 51 1.21841373e+00 -1.69694556e+00 -8.19835766e-01 | 1.21841373e+00 -1.69694556e+00 -8.19835766e-01 52 5.61723358e+00 3.16466543e+00 -1.11841522e+01 | 5.61723358e+00 3.16466543e+00 -1.11841522e+01 53 1.25513962e+00 1.22516095e+00 4.89265667e-01 | 1.25513962e+00 1.22516095e+00 4.89265667e-01 54 5.31202955e-01 -8.80610483e-01 1.32195678e-01 | 5.31202955e-01 -8.80610483e-01 1.32195678e-01 55 -1.41863923e-01 -4.60040722e-01 -4.96727064e-01 | -1.41863923e-01 -4.60040722e-01 -4.96727064e-01 56 1.33345605e+01 -6.98391120e+00 7.65895048e+00 | 1.33345605e+01 -6.98391120e+00 7.65895048e+00 57 -5.12915012e+00 7.40072648e+00 -2.19747283e+00 | -5.12915012e+00 7.40072648e+00 -2.19747283e+00 58 -2.54211012e+00 1.03876117e+01 9.40523908e+00 | -2.54211012e+00 1.03876117e+01 9.40523908e+00 59 -1.06235592e+00 -4.37344523e-01 -9.16352669e-01 | -1.06235592e+00 -4.37344523e-01 -9.16352669e-01 60 -6.31108619e+00 2.16200841e+00 1.69642593e+00 | -6.31108619e+00 2.16200841e+00 1.69642593e+00 61 2.77458576e+00 7.49978489e-01 4.07656162e+00 | 2.77458576e+00 7.49978489e-01 4.07656162e+00 62 -6.24107428e-01 -8.98938614e+00 -6.72392352e+00 | -6.24107428e-01 -8.98938614e+00 -6.72392352e+00 63 -2.32106107e-01 7.98936316e+00 4.88565209e+00 | -2.32106107e-01 7.98936316e+00 4.88565209e+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.