!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_DickelBaskesAslam_2018_MgAlZn__MO_093637366498_001 Supported species : Al Mg Zn 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 = [52, 5, 63, 59, 33, 1, 40, 24, 30, 36, 60, 18, 27, 39, 46, 20, 57, 54, 11, 32, 15, 61, 62, 56, 7, 47, 45, 12, 50, 58, 8, 48, 19, 4, 55, 37, 9, 35, 44, 13, 6, 42, 41, 49, 38, 26, 14, 25, 31, 43, 28, 53, 0, 51, 17, 34, 23, 16, 29, 3, 10, 21, 22, 2] 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)) = 148.1364185844445 V(r_1,...,r_N) = 148.13641858444458 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 -4.28202571e+00 -2.93176692e+00 -3.95951846e+00 | -4.28202571e+00 -2.93176692e+00 -3.95951846e+00 1 -1.79975130e+01 -2.67841328e+01 1.45905148e+01 | -1.79975130e+01 -2.67841328e+01 1.45905148e+01 2 -2.42628050e+00 1.13090468e+01 -4.68693365e+01 | -2.42628050e+00 1.13090468e+01 -4.68693365e+01 3 1.72606473e+01 2.33459481e+01 2.01845349e+01 | 1.72606473e+01 2.33459481e+01 2.01845349e+01 4 2.46051670e+00 -1.00364202e+01 9.25825522e+00 | 2.46051670e+00 -1.00364202e+01 9.25825522e+00 5 -3.85634580e+00 5.96595142e+00 -8.54680173e+00 | -3.85634580e+00 5.96595142e+00 -8.54680173e+00 6 -1.15931150e+01 -5.83279739e+00 -7.03457772e+00 | -1.15931150e+01 -5.83279739e+00 -7.03457772e+00 7 -1.77876445e+01 6.59742524e+01 -2.62479458e+01 | -1.77876445e+01 6.59742524e+01 -2.62479458e+01 8 -1.93696262e+00 3.31524155e-02 -2.01896792e+00 | -1.93696262e+00 3.31524155e-02 -2.01896792e+00 9 -1.40448625e+01 1.13538195e+01 -1.77938606e+01 | -1.40448625e+01 1.13538195e+01 -1.77938606e+01 10 -9.88214137e+00 -9.39472670e+00 -9.34401400e+00 | -9.88214137e+00 -9.39472670e+00 -9.34401400e+00 11 1.05405198e+01 9.07200346e+00 7.42646228e+00 | 1.05405198e+01 9.07200346e+00 7.42646228e+00 12 -2.12375592e+01 -3.39362751e+01 -7.80280064e+00 | -2.12375592e+01 -3.39362751e+01 -7.80280064e+00 13 3.93105805e+01 2.04443346e+01 2.73641815e+01 | 3.93105805e+01 2.04443346e+01 2.73641815e+01 14 -3.70068120e+00 -3.14134220e+00 -6.49402989e+00 | -3.70068120e+00 -3.14134220e+00 -6.49402989e+00 15 4.15208017e+00 3.13094973e+00 5.63401327e+00 | 4.15208017e+00 3.13094973e+00 5.63401327e+00 16 -2.22338092e+00 -3.04294532e+00 -1.99439708e+00 | -2.22338092e+00 -3.04294532e+00 -1.99439708e+00 17 -4.83490338e-03 -1.37402230e+00 2.57902925e+00 | -4.83490338e-03 -1.37402230e+00 2.57902925e+00 18 -1.29719786e+01 -8.63751140e+00 -2.00618194e+01 | -1.29719786e+01 -8.63751140e+00 -2.00618194e+01 19 -3.31518262e+01 4.18816262e+01 -1.55301123e+01 | -3.31518262e+01 4.18816262e+01 -1.55301123e+01 20 -2.25557857e+01 -1.53173018e+01 -1.73987910e+01 | -2.25557857e+01 -1.53173018e+01 -1.73987910e+01 21 2.98512815e+01 2.06837201e+01 1.36712844e+01 | 2.98512815e+01 2.06837201e+01 1.36712844e+01 22 -7.98587824e+00 -9.03163942e+00 -1.74734338e+01 | -7.98587824e+00 -9.03163942e+00 -1.74734338e+01 23 6.49457543e+00 1.11844882e+01 1.90022677e+01 | 6.49457543e+00 1.11844882e+01 1.90022677e+01 24 -9.25266256e+00 -8.75031735e+00 -1.29201335e+01 | -9.25266256e+00 -8.75031735e+00 -1.29201335e+01 25 -1.24601021e+01 2.84434233e+01 -3.30897143e+00 | -1.24601021e+01 2.84434233e+01 -3.30897143e+00 26 -3.61796998e-01 2.15683271e+00 -3.90131285e+00 | -3.61796998e-01 2.15683271e+00 -3.90131285e+00 27 1.31616342e+00 6.06630855e-01 7.77802668e-01 | 1.31616342e+00 6.06630855e-01 7.77802668e-01 28 1.04799318e+01 -3.65313754e+01 1.00530339e+01 | 1.04799318e+01 -3.65313754e+01 1.00530339e+01 29 1.12584790e+01 1.32157462e+01 8.66555976e+00 | 1.12584790e+01 1.32157462e+01 8.66555976e+00 30 4.70706173e+01 -2.87926173e+01 2.94281885e+01 | 4.70706173e+01 -2.87926173e+01 2.94281885e+01 31 -2.80272634e+01 1.15690088e+01 -1.55082189e+01 | -2.80272634e+01 1.15690088e+01 -1.55082189e+01 32 3.33176251e-01 2.11946564e-01 -3.23104709e-01 | 3.33176251e-01 2.11946564e-01 -3.23104709e-01 33 -1.73978307e+01 2.32907968e+01 -3.78054969e+01 | -1.73978307e+01 2.32907968e+01 -3.78054969e+01 34 2.52123008e+01 -6.05707627e+01 3.27332451e+01 | 2.52123008e+01 -6.05707627e+01 3.27332451e+01 35 -9.22947475e+00 -1.51025378e+01 1.17548605e+01 | -9.22947475e+00 -1.51025378e+01 1.17548605e+01 36 1.61655773e+01 -2.61879674e+01 3.92800154e+01 | 1.61655773e+01 -2.61879674e+01 3.92800154e+01 37 -1.20640665e+01 -1.59952788e+01 1.09430714e+01 | -1.20640665e+01 -1.59952788e+01 1.09430714e+01 38 -1.15588263e+01 -9.21156270e+00 -9.87898915e+00 | -1.15588263e+01 -9.21156270e+00 -9.87898915e+00 39 -1.39225461e+01 -1.35270369e+01 2.49675047e+01 | -1.39225461e+01 -1.35270369e+01 2.49675047e+01 40 3.44252451e+00 -5.51201300e+00 9.67511551e+00 | 3.44252451e+00 -5.51201300e+00 9.67511551e+00 41 -2.77805659e+01 4.00981177e+01 -2.10108901e+01 | -2.77805659e+01 4.00981177e+01 -2.10108901e+01 42 -2.15451999e+01 -3.79628128e+01 -1.95608766e+01 | -2.15451999e+01 -3.79628128e+01 -1.95608766e+01 43 2.69727151e+01 4.35829875e+01 1.70707476e+01 | 2.69727151e+01 4.35829875e+01 1.70707476e+01 44 2.70269385e+01 -4.72655728e+01 2.21528443e+01 | 2.70269385e+01 -4.72655728e+01 2.21528443e+01 45 6.57060943e-01 1.74632592e+00 1.76971826e+00 | 6.57060943e-01 1.74632592e+00 1.76971826e+00 46 9.07916051e-01 5.91817018e+00 -1.15959356e+01 | 9.07916051e-01 5.91817018e+00 -1.15959356e+01 47 9.35476123e+00 1.14516218e+01 4.41257564e+00 | 9.35476123e+00 1.14516218e+01 4.41257564e+00 48 -4.85910756e+00 -6.25733141e+00 -5.56469554e-01 | -4.85910756e+00 -6.25733141e+00 -5.56469554e-01 49 1.89017440e+01 -1.51939835e+01 -1.99370328e+01 | 1.89017440e+01 -1.51939835e+01 -1.99370328e+01 50 -1.45238039e+01 -2.04754980e+01 -1.95931600e+01 | -1.45238039e+01 -2.04754980e+01 -1.95931600e+01 51 1.40534661e+01 2.07617960e+01 1.94896470e+01 | 1.40534661e+01 2.07617960e+01 1.94896470e+01 52 9.66165062e+00 1.57578838e+01 -1.77396866e+01 | 9.66165062e+00 1.57578838e+01 -1.77396866e+01 53 1.26288142e+01 5.43476174e+00 4.86083629e+00 | 1.26288142e+01 5.43476174e+00 4.86083629e+00 54 -1.78389094e+01 2.03948904e+01 2.14527058e+01 | -1.78389094e+01 2.03948904e+01 2.14527058e+01 55 1.68956181e+00 1.56881957e+00 1.31243058e+00 | 1.68956181e+00 1.56881957e+00 1.31243058e+00 56 5.55368031e+00 1.02259918e+01 -7.92889924e+00 | 5.55368031e+00 1.02259918e+01 -7.92889924e+00 57 2.02553180e+01 -3.62467912e+01 -5.40730096e+01 | 2.02553180e+01 -3.62467912e+01 -5.40730096e+01 58 2.85032056e+01 -9.79481387e+00 1.85607783e+01 | 2.85032056e+01 -9.79481387e+00 1.85607783e+01 59 1.25199421e-01 1.73980122e-01 1.42044831e+00 | 1.25199421e-01 1.73980122e-01 1.42044831e+00 60 4.79392140e+00 -6.72515337e+00 2.73881733e+00 | 4.79392140e+00 -6.72515337e+00 2.73881733e+00 61 4.12258217e+00 3.27879578e+00 4.94414539e+00 | 4.12258217e+00 3.27879578e+00 4.94414539e+00 62 -2.25346663e+01 4.58644812e+01 4.65333221e+01 | -2.25346663e+01 4.58644812e+01 4.65333221e+01 63 4.38130971e-01 -5.67993791e-01 -4.95363159e-01 | 4.38130971e-01 -5.67993791e-01 -4.95363159e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Mg (Configuration in file "config-Mg.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [21, 4, 18, 19, 1, 26, 32, 62, 51, 39, 49, 59, 35, 29, 37, 22, 41, 31, 2, 3, 25, 0, 15, 45, 46, 20, 5, 52, 44, 13, 50, 17, 6, 63, 53, 12, 38, 14, 36, 9, 61, 16, 56, 55, 28, 23, 24, 60, 54, 10, 30, 8, 27, 34, 48, 43, 42, 58, 57, 11, 47, 40, 7, 33] 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)) = 153.15297867677413 V(r_1,...,r_N) = 153.1529786767741 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 -1.66096305e+01 -2.33197174e+01 -1.75662952e+01 | -1.66096305e+01 -2.33197174e+01 -1.75662952e+01 1 1.64396566e+01 2.24697439e+01 1.74736807e+01 | 1.64396566e+01 2.24697439e+01 1.74736807e+01 2 -7.66353840e+00 -8.28885215e+00 -3.53567642e+00 | -7.66353840e+00 -8.28885215e+00 -3.53567642e+00 3 1.09861043e+01 6.54696666e-01 -1.37509719e+01 | 1.09861043e+01 6.54696666e-01 -1.37509719e+01 4 -1.84427356e+01 -2.66266027e+01 -7.30134142e+00 | -1.84427356e+01 -2.66266027e+01 -7.30134142e+00 5 1.53792862e+01 2.62230605e+01 1.89524830e+00 | 1.53792862e+01 2.62230605e+01 1.89524830e+00 6 -6.86032033e+00 -2.25619816e+00 -3.35041080e+00 | -6.86032033e+00 -2.25619816e+00 -3.35041080e+00 7 -2.20884894e+00 4.54998695e+00 5.29425339e-01 | -2.20884894e+00 4.54998695e+00 5.29425339e-01 8 -3.67793900e+00 -5.00627862e-01 -4.64436257e+00 | -3.67793900e+00 -5.00627862e-01 -4.64436257e+00 9 -5.34544507e+00 2.37325579e+00 -4.41360242e+00 | -5.34544507e+00 2.37325579e+00 -4.41360242e+00 10 -5.74441249e+00 -1.69074014e-04 -5.94929509e+00 | -5.74441249e+00 -1.69074014e-04 -5.94929509e+00 11 4.92103282e+00 8.91534942e-02 6.49466363e+00 | 4.92103282e+00 8.91534942e-02 6.49466363e+00 12 5.72489575e+00 -4.75199148e+00 5.97545769e+00 | 5.72489575e+00 -4.75199148e+00 5.97545769e+00 13 1.03725930e+01 -1.76934122e+00 -2.29113734e+00 | 1.03725930e+01 -1.76934122e+00 -2.29113734e+00 14 3.83110277e+00 -6.46583944e+00 -3.90010805e+00 | 3.83110277e+00 -6.46583944e+00 -3.90010805e+00 15 -6.80536308e-01 1.54546451e+00 4.04389092e+00 | -6.80536308e-01 1.54546451e+00 4.04389092e+00 16 -5.55527944e+00 -3.69198515e+00 -5.76503499e+00 | -5.55527944e+00 -3.69198515e+00 -5.76503499e+00 17 2.20397344e+01 -3.16562632e+01 -1.63028373e+01 | 2.20397344e+01 -3.16562632e+01 -1.63028373e+01 18 -4.97266872e+00 -9.02762356e-01 -5.91293843e+00 | -4.97266872e+00 -9.02762356e-01 -5.91293843e+00 19 5.15385400e+00 1.70143786e+00 4.53967986e+00 | 5.15385400e+00 1.70143786e+00 4.53967986e+00 20 -9.87874578e+00 1.07373188e+01 1.67642808e+01 | -9.87874578e+00 1.07373188e+01 1.67642808e+01 21 -5.91743283e-01 4.03860988e+00 3.46984951e+00 | -5.91743283e-01 4.03860988e+00 3.46984951e+00 22 -1.69846868e+01 3.38428308e+01 2.26287080e+01 | -1.69846868e+01 3.38428308e+01 2.26287080e+01 23 -8.36355032e+00 2.17883102e+01 -1.06281253e+01 | -8.36355032e+00 2.17883102e+01 -1.06281253e+01 24 5.95242141e+00 7.78984026e+00 -9.60665886e+00 | 5.95242141e+00 7.78984026e+00 -9.60665886e+00 25 -8.78015569e+00 -3.68067476e+00 4.68387253e+00 | -8.78015569e+00 -3.68067476e+00 4.68387253e+00 26 1.37027582e+00 7.37761343e-01 -1.53158342e+01 | 1.37027582e+00 7.37761343e-01 -1.53158342e+01 27 6.91453215e+00 5.29673951e+00 4.75445486e+00 | 6.91453215e+00 5.29673951e+00 4.75445486e+00 28 -5.06411423e+00 -5.61168654e+00 1.83304563e+00 | -5.06411423e+00 -5.61168654e+00 1.83304563e+00 29 7.84659321e+00 1.95698448e-01 2.41933213e+00 | 7.84659321e+00 1.95698448e-01 2.41933213e+00 30 -2.22858601e+00 5.67080525e-01 -8.73635144e+00 | -2.22858601e+00 5.67080525e-01 -8.73635144e+00 31 -2.47487306e+01 3.31155348e+01 -8.93037307e+00 | -2.47487306e+01 3.31155348e+01 -8.93037307e+00 32 -2.05664637e+00 -1.74266475e+00 -2.64610193e+00 | -2.05664637e+00 -1.74266475e+00 -2.64610193e+00 33 3.50937913e+00 3.62047173e+00 -3.10065736e+00 | 3.50937913e+00 3.62047173e+00 -3.10065736e+00 34 1.62745324e+00 -3.21804824e+00 2.51643992e+00 | 1.62745324e+00 -3.21804824e+00 2.51643992e+00 35 8.27289067e+00 -1.59428684e+01 -8.97015551e+00 | 8.27289067e+00 -1.59428684e+01 -8.97015551e+00 36 6.19332820e+00 -5.88797459e+00 1.20804055e+00 | 6.19332820e+00 -5.88797459e+00 1.20804055e+00 37 -2.05130350e-01 -1.36444902e+00 1.17845445e+00 | -2.05130350e-01 -1.36444902e+00 1.17845445e+00 38 -1.02141303e+01 2.82192073e+00 5.39804281e+00 | -1.02141303e+01 2.82192073e+00 5.39804281e+00 39 9.23800631e-01 4.03503634e-01 1.92179708e+00 | 9.23800631e-01 4.03503634e-01 1.92179708e+00 40 1.74596690e-01 -6.44192080e+00 -1.11255686e+00 | 1.74596690e-01 -6.44192080e+00 -1.11255686e+00 41 1.49328451e+00 7.44224879e-01 5.08850283e+00 | 1.49328451e+00 7.44224879e-01 5.08850283e+00 42 -1.04970251e+00 2.79203475e+00 5.11469787e+00 | -1.04970251e+00 2.79203475e+00 5.11469787e+00 43 3.77241004e+00 -2.48877509e+00 -1.23221964e+00 | 3.77241004e+00 -2.48877509e+00 -1.23221964e+00 44 -4.07797251e-01 -2.03570109e+00 -5.87038373e-01 | -4.07797251e-01 -2.03570109e+00 -5.87038373e-01 45 1.33808660e+00 1.56192584e+00 1.33597252e+00 | 1.33808660e+00 1.56192584e+00 1.33597252e+00 46 1.25273936e+00 -2.12663087e+00 4.18588971e+00 | 1.25273936e+00 -2.12663087e+00 4.18588971e+00 47 2.22196359e+00 -5.27223497e-01 3.41043837e+00 | 2.22196359e+00 -5.27223497e-01 3.41043837e+00 48 -3.30896722e+00 -3.55171129e+00 -3.20351158e+00 | -3.30896722e+00 -3.55171129e+00 -3.20351158e+00 49 6.89280066e+00 2.40366270e+00 -3.14817783e+00 | 6.89280066e+00 2.40366270e+00 -3.14817783e+00 50 4.73091091e+00 -1.99658989e+01 9.89011641e+00 | 4.73091091e+00 -1.99658989e+01 9.89011641e+00 51 -1.66434673e+00 3.92190278e+00 -1.47579597e+00 | -1.66434673e+00 3.92190278e+00 -1.47579597e+00 52 -1.42803319e+01 1.49981991e+01 1.02325344e+01 | -1.42803319e+01 1.49981991e+01 1.02325344e+01 53 -3.29703606e+00 -2.55350375e+00 3.46391866e+00 | -3.29703606e+00 -2.55350375e+00 3.46391866e+00 54 -5.46664268e+00 1.43135047e+00 6.76764687e+00 | -5.46664268e+00 1.43135047e+00 6.76764687e+00 55 1.33756038e-01 5.68538414e-01 -2.01179989e-01 | 1.33756038e-01 5.68538414e-01 -2.01179989e-01 56 4.25658341e+00 -2.55279723e+00 -2.80207218e-01 | 4.25658341e+00 -2.55279723e+00 -2.80207218e-01 57 -1.30853985e+01 9.36450542e+00 -3.23175766e+01 | -1.30853985e+01 9.36450542e+00 -3.23175766e+01 58 2.84250602e+01 -2.74705853e+01 1.21125051e+01 | 2.84250602e+01 -2.74705853e+01 1.21125051e+01 59 1.40796460e+00 4.15484004e-01 1.76641667e+00 | 1.40796460e+00 4.15484004e-01 1.76641667e+00 60 7.47560804e+00 -7.70698971e+00 3.00169152e+01 | 7.47560804e+00 -7.70698971e+00 3.00169152e+01 61 3.28647143e+00 2.32492556e+00 3.29807638e+00 | 3.28647143e+00 2.32492556e+00 3.29807638e+00 62 -2.40942417e-03 -2.97390339e+00 -5.29326372e+00 | -2.40942417e-03 -2.97390339e+00 -5.29326372e+00 63 5.11903639e+00 2.98518308e+00 5.05780146e+00 | 5.11903639e+00 2.98518308e+00 5.05780146e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Zn (Configuration in file "config-Zn.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [50, 37, 9, 43, 36, 7, 15, 5, 16, 2, 48, 53, 49, 21, 31, 6, 8, 19, 25, 17, 59, 13, 28, 42, 44, 18, 54, 39, 22, 33, 61, 14, 45, 29, 56, 52, 4, 1, 62, 27, 60, 55, 23, 3, 24, 32, 63, 57, 10, 12, 0, 58, 35, 11, 26, 41, 34, 47, 51, 20, 40, 30, 38, 46] 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)) = 368.9644865864267 V(r_1,...,r_N) = 368.9644865864267 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 -8.47968792e-01 -8.94260635e-01 -9.10524272e-01 | -8.47968792e-01 -8.94260635e-01 -9.10524272e-01 1 1.11070046e+01 -1.43144310e+01 -1.93872935e+01 | 1.11070046e+01 -1.43144310e+01 -1.93872935e+01 2 -2.35417368e+01 -2.47090821e+01 -3.12346528e+01 | -2.35417368e+01 -2.47090821e+01 -3.12346528e+01 3 2.65016255e+01 2.70668763e+01 2.92630852e+01 | 2.65016255e+01 2.70668763e+01 2.92630852e+01 4 -2.10392363e+01 -1.57427406e+01 -2.45531635e+01 | -2.10392363e+01 -1.57427406e+01 -2.45531635e+01 5 1.17436660e+01 -1.56371947e+01 2.24098716e+01 | 1.17436660e+01 -1.56371947e+01 2.24098716e+01 6 -1.71555922e+01 1.17055095e+01 2.01116184e+01 | -1.71555922e+01 1.17055095e+01 2.01116184e+01 7 -1.57762699e+01 6.31049194e+00 -1.38713557e+01 | -1.57762699e+01 6.31049194e+00 -1.38713557e+01 8 8.12222253e-02 1.47577000e-01 1.16647695e-01 | 8.12222253e-02 1.47577000e-01 1.16647695e-01 9 2.77055848e+00 4.37042037e+00 -3.09117848e+01 | 2.77055848e+00 4.37042037e+00 -3.09117848e+01 10 6.93891639e-01 5.00270749e+00 -6.40726509e+00 | 6.93891639e-01 5.00270749e+00 -6.40726509e+00 11 1.40716309e+01 -8.09146873e+00 -2.11112983e+01 | 1.40716309e+01 -8.09146873e+00 -2.11112983e+01 12 -2.87428299e+00 -1.40391574e+01 3.58746967e+01 | -2.87428299e+00 -1.40391574e+01 3.58746967e+01 13 2.06232599e+00 1.26755810e+00 4.17948864e-01 | 2.06232599e+00 1.26755810e+00 4.17948864e-01 14 1.52171187e+01 1.17139549e+01 -1.40447640e+01 | 1.52171187e+01 1.17139549e+01 -1.40447640e+01 15 8.07708624e+01 -1.69363366e+02 -9.28662314e+01 | 8.07708624e+01 -1.69363366e+02 -9.28662314e+01 16 -8.57341210e+00 -7.30574419e+00 -4.19497628e+00 | -8.57341210e+00 -7.30574419e+00 -4.19497628e+00 17 -5.51699690e+01 -5.34608883e+01 2.98966555e+01 | -5.51699690e+01 -5.34608883e+01 2.98966555e+01 18 6.25460566e+01 6.09392481e+01 -2.71376773e+01 | 6.25460566e+01 6.09392481e+01 -2.71376773e+01 19 -1.88102162e+01 1.05929908e+01 -1.98215238e+01 | -1.88102162e+01 1.05929908e+01 -1.98215238e+01 20 -4.72385334e+01 -2.11978005e+01 -2.36573694e+01 | -4.72385334e+01 -2.11978005e+01 -2.36573694e+01 21 5.16817069e+01 2.45062528e+01 2.00281433e+01 | 5.16817069e+01 2.45062528e+01 2.00281433e+01 22 -1.07974759e+00 -4.79355204e-01 -1.22298129e-01 | -1.07974759e+00 -4.79355204e-01 -1.22298129e-01 23 -2.99774686e+01 5.62339168e+01 -5.67051306e+01 | -2.99774686e+01 5.62339168e+01 -5.67051306e+01 24 -4.09717714e-01 -1.97201938e+00 -1.74352868e+00 | -4.09717714e-01 -1.97201938e+00 -1.74352868e+00 25 -8.48468894e+00 -8.76835309e+00 1.06418703e+01 | -8.48468894e+00 -8.76835309e+00 1.06418703e+01 26 -1.36438221e+01 -1.61254193e+01 -3.01696944e+01 | -1.36438221e+01 -1.61254193e+01 -3.01696944e+01 27 2.30896927e+01 2.53527743e+01 1.83837870e+01 | 2.30896927e+01 2.53527743e+01 1.83837870e+01 28 -1.21425109e+01 7.64623691e+00 2.08460867e+01 | -1.21425109e+01 7.64623691e+00 2.08460867e+01 29 3.73054648e+00 -7.72309972e-01 -6.43383663e-01 | 3.73054648e+00 -7.72309972e-01 -6.43383663e-01 30 -2.69531146e+01 -4.63721578e+01 -3.22873124e+01 | -2.69531146e+01 -4.63721578e+01 -3.22873124e+01 31 4.46160851e+01 3.90310638e+01 5.35395368e+01 | 4.46160851e+01 3.90310638e+01 5.35395368e+01 32 2.11657764e-01 2.55475799e-01 -7.49232331e-02 | 2.11657764e-01 2.55475799e-01 -7.49232331e-02 33 -1.14137408e+01 1.27755801e+01 -1.51906977e+01 | -1.14137408e+01 1.27755801e+01 -1.51906977e+01 34 9.87440215e+00 1.09758718e+01 3.11875349e+01 | 9.87440215e+00 1.09758718e+01 3.11875349e+01 35 -2.38888442e+01 1.62760450e+01 -2.53907995e+01 | -2.38888442e+01 1.62760450e+01 -2.53907995e+01 36 3.89874550e+00 -2.00950043e+01 7.67101101e+00 | 3.89874550e+00 -2.00950043e+01 7.67101101e+00 37 6.58145033e+00 4.25177978e+00 8.17695846e+00 | 6.58145033e+00 4.25177978e+00 8.17695846e+00 38 -3.54877378e+01 -3.68695035e+01 -2.31905151e+01 | -3.54877378e+01 -3.68695035e+01 -2.31905151e+01 39 3.29219188e+01 3.43070573e+01 2.62789552e+01 | 3.29219188e+01 3.43070573e+01 2.62789552e+01 40 -1.03076248e+01 -9.02218935e+00 -1.38537803e+00 | -1.03076248e+01 -9.02218935e+00 -1.38537803e+00 41 4.76861379e+00 1.32620784e+00 1.69917081e+00 | 4.76861379e+00 1.32620784e+00 1.69917081e+00 42 -1.36709467e+01 -7.33610277e+00 -2.68257043e+00 | -1.36709467e+01 -7.33610277e+00 -2.68257043e+00 43 2.07743254e+01 1.29515530e+01 -6.59031859e-01 | 2.07743254e+01 1.29515530e+01 -6.59031859e-01 44 -1.12831701e+01 -2.76116496e+01 -2.14180342e+01 | -1.12831701e+01 -2.76116496e+01 -2.14180342e+01 45 1.18883920e+01 2.69004595e+01 2.22944370e+01 | 1.18883920e+01 2.69004595e+01 2.22944370e+01 46 2.22003984e+01 -2.28243812e+01 1.81565223e+01 | 2.22003984e+01 -2.28243812e+01 1.81565223e+01 47 2.07031936e+00 7.38959932e+00 1.07349658e+01 | 2.07031936e+00 7.38959932e+00 1.07349658e+01 48 -1.05293615e+01 -6.78270059e+00 -1.05957170e+01 | -1.05293615e+01 -6.78270059e+00 -1.05957170e+01 49 -1.69298873e+01 -2.62182481e+00 -4.44737037e+01 | -1.69298873e+01 -2.62182481e+00 -4.44737037e+01 50 2.75023087e+01 -5.43715450e+01 5.83713807e+01 | 2.75023087e+01 -5.43715450e+01 5.83713807e+01 51 1.17204426e+00 1.26546745e+00 8.34875135e-01 | 1.17204426e+00 1.26546745e+00 8.34875135e-01 52 2.23556292e+01 1.03649137e+01 5.13443769e+01 | 2.23556292e+01 1.03649137e+01 5.13443769e+01 53 3.02152810e+00 -1.45765844e+00 5.56223049e+00 | 3.02152810e+00 -1.45765844e+00 5.56223049e+00 54 -2.73365458e+01 -1.21341665e+01 -2.57702456e+01 | -2.73365458e+01 -1.21341665e+01 -2.57702456e+01 55 2.64924531e+01 1.37552624e+01 2.61185940e+01 | 2.64924531e+01 1.37552624e+01 2.61185940e+01 56 -8.38667335e+01 1.67298847e+02 9.10131019e+01 | -8.38667335e+01 1.67298847e+02 9.10131019e+01 57 -2.93399957e+01 -6.13871019e+01 9.44316820e+01 | -2.93399957e+01 -6.13871019e+01 9.44316820e+01 58 5.85216976e+01 4.88689028e+01 -1.09301775e+02 | 5.85216976e+01 4.88689028e+01 -1.09301775e+02 59 1.59360081e+00 1.69700697e+00 1.01157776e+00 | 1.59360081e+00 1.69700697e+00 1.01157776e+00 60 -2.02949040e+01 -2.72163205e+01 -1.55907173e+01 | -2.02949040e+01 -2.72163205e+01 -1.55907173e+01 61 1.96938579e+01 2.87062582e+01 1.76419227e+01 | 1.96938579e+01 2.87062582e+01 1.76419227e+01 62 -2.89076237e+01 1.73530808e+01 1.26308901e+01 | -2.89076237e+01 1.73530808e+01 1.26308901e+01 63 7.48066314e-01 3.68949433e-01 8.15201198e-01 | 7.48066314e-01 3.68949433e-01 8.15201198e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Mg Zn (Configuration in file "config-AlMgZn.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [63, 48, 43, 59, 36, 28, 61, 49, 13, 62, 57, 29, 39, 8, 34, 42, 38, 44, 47, 26, 33, 53, 50, 60, 31, 27, 19, 25, 5, 11, 56, 24, 45, 20, 14, 41, 4, 55, 16, 12, 51, 35, 15, 2, 17, 32, 52, 18, 1, 7, 22, 40, 46, 21, 54, 37, 30, 10, 58, 3, 23, 6, 9, 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)) = 111.5500662147624 V(r_1,...,r_N) = 111.55006621476241 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 -2.54115196e-01 3.68945957e-01 -2.03171287e-01 | -2.54115196e-01 3.68945957e-01 -2.03171287e-01 1 -5.85492345e+00 -2.05983845e+01 1.70470529e+01 | -5.85492345e+00 -2.05983845e+01 1.70470529e+01 2 -1.11312969e+01 -3.76813271e+00 -3.22790840e+01 | -1.11312969e+01 -3.76813271e+00 -3.22790840e+01 3 1.62154790e+01 2.35428998e+01 1.00733528e+01 | 1.62154790e+01 2.35428998e+01 1.00733528e+01 4 -1.23491806e+00 -7.20570969e+00 2.90017904e+00 | -1.23491806e+00 -7.20570969e+00 2.90017904e+00 5 -5.72275371e+00 -5.43682571e+00 6.95959832e+00 | -5.72275371e+00 -5.43682571e+00 6.95959832e+00 6 -3.91021937e+00 4.04090367e-01 1.39546037e+00 | -3.91021937e+00 4.04090367e-01 1.39546037e+00 7 -6.27988892e+01 -4.09969660e+01 6.89881951e+01 | -6.27988892e+01 -4.09969660e+01 6.89881951e+01 8 -3.46636968e+00 -3.36406005e+00 -2.06185636e+00 | -3.46636968e+00 -3.36406005e+00 -2.06185636e+00 9 3.41606837e+00 -1.43657488e+01 1.64370450e+01 | 3.41606837e+00 -1.43657488e+01 1.64370450e+01 10 7.79818213e-01 1.63893650e+01 -1.75618798e+01 | 7.79818213e-01 1.63893650e+01 -1.75618798e+01 11 1.59911740e+01 -1.61603922e+01 -2.59708405e+01 | 1.59911740e+01 -1.61603922e+01 -2.59708405e+01 12 -6.81605397e-01 -2.63472644e+00 -8.53650623e-01 | -6.81605397e-01 -2.63472644e+00 -8.53650623e-01 13 1.88502957e+00 5.73090246e-01 1.20925840e+00 | 1.88502957e+00 5.73090246e-01 1.20925840e+00 14 6.20181536e+00 6.49731325e+00 -7.18349962e+00 | 6.20181536e+00 6.49731325e+00 -7.18349962e+00 15 9.18976768e+00 -1.19157473e+01 -2.24096688e+01 | 9.18976768e+00 -1.19157473e+01 -2.24096688e+01 16 -5.34490466e-01 -2.63683478e-01 -1.30673034e-01 | -5.34490466e-01 -2.63683478e-01 -1.30673034e-01 17 -4.61924749e+00 -2.95527832e+00 4.30781192e-01 | -4.61924749e+00 -2.95527832e+00 4.30781192e-01 18 -1.74149202e-01 -7.09598430e+00 -1.17150031e+01 | -1.74149202e-01 -7.09598430e+00 -1.17150031e+01 19 4.20897475e+00 1.31561661e+01 9.21942040e+00 | 4.20897475e+00 1.31561661e+01 9.21942040e+00 20 5.47656768e+01 3.82216664e+01 -6.35959410e+01 | 5.47656768e+01 3.82216664e+01 -6.35959410e+01 21 5.43351947e+00 8.62059227e-01 4.03163121e+00 | 5.43351947e+00 8.62059227e-01 4.03163121e+00 22 -1.14272082e+00 8.06418462e-01 -5.82120947e-01 | -1.14272082e+00 8.06418462e-01 -5.82120947e-01 23 -1.23647985e+00 7.03072490e-01 -4.37585295e-01 | -1.23647985e+00 7.03072490e-01 -4.37585295e-01 24 6.68914923e+00 3.57030460e+00 -6.90617932e+00 | 6.68914923e+00 3.57030460e+00 -6.90617932e+00 25 7.86623526e+00 -5.36597716e+00 -1.45270902e+01 | 7.86623526e+00 -5.36597716e+00 -1.45270902e+01 26 -1.06945069e+01 -6.16807643e+00 -1.17083732e+01 | -1.06945069e+01 -6.16807643e+00 -1.17083732e+01 27 1.04439171e+01 5.92516835e+00 1.20407813e+01 | 1.04439171e+01 5.92516835e+00 1.20407813e+01 28 -1.43973724e+01 1.69022194e+01 2.60188453e+01 | -1.43973724e+01 1.69022194e+01 2.60188453e+01 29 2.09626434e+00 -4.62342070e-01 -1.75200350e+00 | 2.09626434e+00 -4.62342070e-01 -1.75200350e+00 30 -1.16184465e+01 -3.35004332e+01 -3.06431763e+00 | -1.16184465e+01 -3.35004332e+01 -3.06431763e+00 31 8.26423574e+00 4.41158090e+01 1.35167881e+01 | 8.26423574e+00 4.41158090e+01 1.35167881e+01 32 9.65533111e-02 1.11403687e-01 -5.57073517e-01 | 9.65533111e-02 1.11403687e-01 -5.57073517e-01 33 -6.56828404e+00 7.51726001e+00 -6.91357010e+00 | -6.56828404e+00 7.51726001e+00 -6.91357010e+00 34 -1.30221965e+00 -1.55378747e+00 1.09183138e+00 | -1.30221965e+00 -1.55378747e+00 1.09183138e+00 35 -1.17445142e+01 -1.38913853e+00 9.03278863e+00 | -1.17445142e+01 -1.38913853e+00 9.03278863e+00 36 8.52416964e+00 -8.58619583e+00 6.57555571e+00 | 8.52416964e+00 -8.58619583e+00 6.57555571e+00 37 -2.91150166e+01 -3.83354101e+01 1.49701973e+01 | -2.91150166e+01 -3.83354101e+01 1.49701973e+01 38 -1.96794854e+00 8.84682657e-01 6.27012676e-01 | -1.96794854e+00 8.84682657e-01 6.27012676e-01 39 -7.02595693e-02 -1.21400203e+00 7.81383769e-01 | -7.02595693e-02 -1.21400203e+00 7.81383769e-01 40 -7.36812580e-02 1.27901666e-02 2.40890858e-01 | -7.36812580e-02 1.27901666e-02 2.40890858e-01 41 -3.20079557e+01 3.16107687e+01 -1.92761623e+01 | -3.20079557e+01 3.16107687e+01 -1.92761623e+01 42 -9.19337401e+00 -2.17040540e+01 -8.23327328e+00 | -9.19337401e+00 -2.17040540e+01 -8.23327328e+00 43 1.86721875e+01 1.07591030e+01 8.24806375e+00 | 1.86721875e+01 1.07591030e+01 8.24806375e+00 44 3.17580761e+01 -3.30719393e+01 1.90623336e+01 | 3.17580761e+01 -3.30719393e+01 1.90623336e+01 45 4.89903550e-01 8.27733954e-01 1.01711841e-01 | 4.89903550e-01 8.27733954e-01 1.01711841e-01 46 3.94653874e+00 3.64770292e+01 -3.04286622e+01 | 3.94653874e+00 3.64770292e+01 -3.04286622e+01 47 2.46808754e+01 2.12488653e+00 1.63447081e+01 | 2.46808754e+01 2.12488653e+00 1.63447081e+01 48 -2.63310034e+00 -3.35566562e-01 8.86900699e-02 | -2.63310034e+00 -3.35566562e-01 8.86900699e-02 49 -1.70745993e+01 -2.57355568e+00 -3.41423632e+01 | -1.70745993e+01 -2.57355568e+00 -3.41423632e+01 50 -5.28542474e+00 -1.74092156e+01 -7.87071473e+00 | -5.28542474e+00 -1.74092156e+01 -7.87071473e+00 51 3.75602368e+00 1.76908453e+01 1.08797034e+01 | 3.75602368e+00 1.76908453e+01 1.08797034e+01 52 1.39951259e+01 2.77259535e+00 3.02546615e+01 | 1.39951259e+01 2.77259535e+00 3.02546615e+01 53 2.83466577e+00 -1.81805283e+00 3.08568105e+00 | 2.83466577e+00 -1.81805283e+00 3.08568105e+00 54 -3.42027181e-01 -8.59504843e-02 -3.06884459e-01 | -3.42027181e-01 -8.59504843e-02 -3.06884459e-01 55 5.06893150e-01 2.53636526e-01 5.67019512e-01 | 5.06893150e-01 2.53636526e-01 5.67019512e-01 56 -2.93460591e+00 1.81724967e+01 8.35195562e+00 | -2.93460591e+00 1.81724967e+01 8.35195562e+00 57 -1.53548476e+00 -5.58240940e+00 -1.67221558e+00 | -1.53548476e+00 -5.58240940e+00 -1.67221558e+00 58 -2.30577234e+00 -1.99586622e+00 -2.31998978e+00 | -2.30577234e+00 -1.99586622e+00 -2.31998978e+00 59 1.94567650e+00 3.53393523e+00 3.43626224e+00 | 1.94567650e+00 3.53393523e+00 3.43626224e+00 60 -2.99552320e+00 -7.87619860e-01 -5.34049137e-01 | -2.99552320e+00 -7.87619860e-01 -5.34049137e-01 61 3.26629700e+00 6.48141036e+00 7.33704547e+00 | 3.26629700e+00 6.48141036e+00 7.33704547e+00 62 -1.57883775e+00 -1.10597102e+00 -3.98568030e+00 | -1.57883775e+00 -1.10597102e+00 -3.98568030e+00 63 2.81022717e-01 8.53803727e+00 7.83769144e+00 | 2.81022717e-01 8.53803727e+00 7.83769144e+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.