!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_2006B_AlNiCo__MO_128037485276_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 = [12, 51, 55, 60, 59, 23, 36, 35, 17, 63, 57, 49, 0, 22, 32, 43, 28, 8, 54, 61, 39, 38, 13, 5, 41, 42, 46, 37, 16, 33, 34, 62, 14, 29, 30, 7, 6, 27, 21, 20, 45, 24, 25, 15, 48, 40, 26, 58, 44, 11, 56, 1, 53, 52, 18, 2, 50, 10, 47, 4, 3, 19, 31, 9] 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)) = 322.9715948903385 V(r_1,...,r_N) = 322.97159489033845 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 -7.81633933e+00 -3.92930710e+00 -1.21404863e+01 | -7.81633933e+00 -3.92930710e+00 -1.21404863e+01 1 1.27518314e+00 -8.57785871e-01 7.92217530e+00 | 1.27518314e+00 -8.57785871e-01 7.92217530e+00 2 -2.41482060e+00 -9.01285998e-02 -1.57374078e+01 | -2.41482060e+00 -9.01285998e-02 -1.57374078e+01 3 1.34946240e+00 -1.49264038e+01 -1.29693235e+01 | 1.34946240e+00 -1.49264038e+01 -1.29693235e+01 4 -7.95100969e+01 -6.28143771e+01 -7.63802589e+00 | -7.95100969e+01 -6.28143771e+01 -7.63802589e+00 5 3.99236319e+01 -2.97091205e+01 1.07097770e+01 | 3.99236319e+01 -2.97091205e+01 1.07097770e+01 6 -2.16071113e+01 -1.09046479e+01 -1.65496650e+01 | -2.16071113e+01 -1.09046479e+01 -1.65496650e+01 7 -1.47085909e+02 2.57821021e+02 -1.43962824e+02 | -1.47085909e+02 2.57821021e+02 -1.43962824e+02 8 1.26324611e+00 -3.25376099e+00 -5.86064065e+00 | 1.26324611e+00 -3.25376099e+00 -5.86064065e+00 9 1.53706044e+01 -1.87727998e+00 -7.24575571e+00 | 1.53706044e+01 -1.87727998e+00 -7.24575571e+00 10 -2.78509754e+01 -8.95977994e+00 -1.90383654e+01 | -2.78509754e+01 -8.95977994e+00 -1.90383654e+01 11 2.91042420e+01 9.77311882e+00 1.72801596e+01 | 2.91042420e+01 9.77311882e+00 1.72801596e+01 12 -7.59656073e+00 -2.07327676e+01 -2.47472765e+01 | -7.59656073e+00 -2.07327676e+01 -2.47472765e+01 13 2.08839883e+01 2.08034046e+01 9.81101347e+00 | 2.08839883e+01 2.08034046e+01 9.81101347e+00 14 3.40622720e+01 3.16549090e+01 -5.28836583e+01 | 3.40622720e+01 3.16549090e+01 -5.28836583e+01 15 4.07393223e+01 2.10193966e+01 5.61130007e+00 | 4.07393223e+01 2.10193966e+01 5.61130007e+00 16 -7.98489996e+00 -2.25706807e+00 -9.40919756e+00 | -7.98489996e+00 -2.25706807e+00 -9.40919756e+00 17 -4.55331686e+01 1.04937064e+01 -4.62886173e+01 | -4.55331686e+01 1.04937064e+01 -4.62886173e+01 18 -1.96503297e+01 -3.85292712e+00 -2.75775327e+01 | -1.96503297e+01 -3.85292712e+00 -2.75775327e+01 19 -4.91704214e+02 8.00395719e+01 3.30797146e+01 | -4.91704214e+02 8.00395719e+01 3.30797146e+01 20 -1.10460036e+01 -1.33030413e+01 -9.43979839e+00 | -1.10460036e+01 -1.33030413e+01 -9.43979839e+00 21 7.00138211e+01 3.29777338e+00 1.87160384e+00 | 7.00138211e+01 3.29777338e+00 1.87160384e+00 22 -2.10927252e+01 -7.16514982e+00 -1.72085402e+01 | -2.10927252e+01 -7.16514982e+00 -1.72085402e+01 23 -6.58736636e+00 1.83424602e+01 1.10553925e+01 | -6.58736636e+00 1.83424602e+01 1.10553925e+01 24 -3.91585277e-01 -1.13811142e+01 -2.62236366e+01 | -3.91585277e-01 -1.13811142e+01 -2.62236366e+01 25 2.20543012e+01 -7.19347001e+00 2.79494301e+00 | 2.20543012e+01 -7.19347001e+00 2.79494301e+00 26 8.52695056e+00 -8.05254229e-01 -9.44346068e+00 | 8.52695056e+00 -8.05254229e-01 -9.44346068e+00 27 6.80280903e+00 3.76967692e+00 4.80030274e+00 | 6.80280903e+00 3.76967692e+00 4.80030274e+00 28 -1.06456966e+01 -8.65661347e+00 -2.03110686e+01 | -1.06456966e+01 -8.65661347e+00 -2.03110686e+01 29 1.80613901e+01 4.38891401e+00 2.18567894e+01 | 1.80613901e+01 4.38891401e+00 2.18567894e+01 30 5.01976785e+02 1.14181544e+01 -5.60836753e+01 | 5.01976785e+02 1.14181544e+01 -5.60836753e+01 31 2.00559868e+01 1.03445660e+01 1.85633423e+00 | 2.00559868e+01 1.03445660e+01 1.85633423e+00 32 -1.40545431e+01 -1.36503395e+01 -3.83935095e+00 | -1.40545431e+01 -1.36503395e+01 -3.83935095e+00 33 -6.42227221e+00 -2.09160186e+01 1.67070039e+01 | -6.42227221e+00 -2.09160186e+01 1.67070039e+01 34 8.54109609e+01 -2.81825493e+02 1.54183731e+02 | 8.54109609e+01 -2.81825493e+02 1.54183731e+02 35 -1.80076506e+02 -9.97641758e+01 1.03626062e+02 | -1.80076506e+02 -9.97641758e+01 1.03626062e+02 36 -1.75143981e+01 -8.52011137e+00 2.36032183e+00 | -1.75143981e+01 -8.52011137e+00 2.36032183e+00 37 -3.26207820e+01 -4.61715877e+01 4.90328391e+01 | -3.26207820e+01 -4.61715877e+01 4.90328391e+01 38 -2.34649438e+01 -1.83977793e+01 -1.25060589e-01 | -2.34649438e+01 -1.83977793e+01 -1.25060589e-01 39 -4.21480415e+02 -2.59034922e+02 1.92926279e+02 | -4.21480415e+02 -2.59034922e+02 1.92926279e+02 40 -6.00776444e+01 -3.53722117e+01 -1.63529957e+01 | -6.00776444e+01 -3.53722117e+01 -1.63529957e+01 41 -3.33778415e+02 1.55813960e+02 -2.63556479e+02 | -3.33778415e+02 1.55813960e+02 -2.63556479e+02 42 2.48791050e+01 2.12268334e+01 -1.56000663e+01 | 2.48791050e+01 2.12268334e+01 -1.56000663e+01 43 1.36137988e+01 1.13322998e+01 -2.14843483e+00 | 1.36137988e+01 1.13322998e+01 -2.14843483e+00 44 4.11166572e+02 -2.25073301e+02 2.62901952e+02 | 4.11166572e+02 -2.25073301e+02 2.62901952e+02 45 1.48885973e+01 1.89044960e-02 1.82705448e+01 | 1.48885973e+01 1.89044960e-02 1.82705448e+01 46 4.80698425e+00 6.00745658e+01 1.33417612e+01 | 4.80698425e+00 6.00745658e+01 1.33417612e+01 47 1.68962874e+01 9.32479991e-01 2.03573431e+01 | 1.68962874e+01 9.32479991e-01 2.03573431e+01 48 -4.17897675e+01 1.12736902e+01 1.00568481e+01 | -4.17897675e+01 1.12736902e+01 1.00568481e+01 49 -4.52035124e+01 7.76291055e+00 6.47200751e+00 | -4.52035124e+01 7.76291055e+00 6.47200751e+00 50 -1.26213122e+02 -1.05523570e+02 -3.94493404e+02 | -1.26213122e+02 -1.05523570e+02 -3.94493404e+02 51 1.22020285e+02 2.00430790e+02 3.88985320e+02 | 1.22020285e+02 2.00430790e+02 3.88985320e+02 52 3.57503862e+02 2.41462843e+02 -1.09338788e+02 | 3.57503862e+02 2.41462843e+02 -1.09338788e+02 53 3.60204912e+01 2.52920312e+01 3.67583043e+01 | 3.60204912e+01 2.52920312e+01 3.67583043e+01 54 -1.42757617e+01 3.37910383e+00 1.40648335e+00 | -1.42757617e+01 3.37910383e+00 1.40648335e+00 55 -4.01507456e+00 1.09318069e+01 1.11361682e+01 | -4.01507456e+00 1.09318069e+01 1.11361682e+01 56 2.29909036e+02 6.18921671e+01 -1.04306542e+02 | 2.29909036e+02 6.18921671e+01 -1.04306542e+02 57 6.50006390e+01 -3.41144675e+01 -5.15104850e+01 | 6.50006390e+01 -3.41144675e+01 -5.15104850e+01 58 8.89426219e-01 -3.60126063e+00 -6.68733465e+00 | 8.89426219e-01 -3.60126063e+00 -6.68733465e+00 59 6.05751834e+00 7.01756306e+00 6.57421929e+00 | 6.05751834e+00 7.01756306e+00 6.57421929e+00 60 8.42465404e+00 -1.70889081e+00 6.72826769e+00 | 8.42465404e+00 -1.70889081e+00 6.72826769e+00 61 2.52243272e+00 1.74004055e+00 1.83016640e+00 | 2.52243272e+00 1.74004055e+00 1.83016640e+00 62 -9.47845553e+00 5.47660363e+01 6.72340716e+01 | -9.47845553e+00 5.47660363e+01 6.72340716e+01 63 7.50876870e+00 7.82942882e+00 9.17869594e+00 | 7.50876870e+00 7.82942882e+00 9.17869594e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [33, 60, 20, 61, 43, 29, 7, 6, 41, 14, 23, 54, 42, 50, 9, 49, 45, 53, 26, 31, 2, 28, 35, 10, 27, 34, 18, 24, 21, 5, 55, 19, 46, 0, 25, 22, 44, 40, 57, 48, 37, 8, 12, 4, 36, 16, 32, 59, 39, 15, 13, 62, 63, 17, 11, 30, 58, 38, 56, 47, 1, 3, 51, 52] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -8.672531641806582 V(r_1,...,r_N) = -8.672531641806582 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 -1.64465356e+00 -6.29200111e-01 -7.27140317e-01 | -1.64465356e+00 -6.29200111e-01 -7.27140317e-01 1 7.01750967e-01 2.38543412e+01 -9.90985529e+00 | 7.01750967e-01 2.38543412e+01 -9.90985529e+00 2 2.15767625e-01 7.83910917e+00 -7.09638212e+00 | 2.15767625e-01 7.83910917e+00 -7.09638212e+00 3 -4.85505665e+01 2.65863233e+01 -1.78263207e+01 | -4.85505665e+01 2.65863233e+01 -1.78263207e+01 4 2.00274547e+00 -2.89489706e+01 1.99125549e+01 | 2.00274547e+00 -2.89489706e+01 1.99125549e+01 5 -2.80345764e+00 -3.56644189e+00 6.19129820e+00 | -2.80345764e+00 -3.56644189e+00 6.19129820e+00 6 -2.29058578e+00 -2.87347389e+00 -1.92761592e+00 | -2.29058578e+00 -2.87347389e+00 -1.92761592e+00 7 -2.15055997e+01 -6.87305515e+00 2.04320045e+01 | -2.15055997e+01 -6.87305515e+00 2.04320045e+01 8 -1.02167132e+00 4.83321980e-01 2.41786711e-01 | -1.02167132e+00 4.83321980e-01 2.41786711e-01 9 8.51939582e+00 -1.19671640e+01 -3.72130704e+00 | 8.51939582e+00 -1.19671640e+01 -3.72130704e+00 10 -1.23778625e+00 -6.78112328e-01 -1.17616203e+00 | -1.23778625e+00 -6.78112328e-01 -1.17616203e+00 11 3.55111676e+00 1.05481745e+00 -1.74119949e+00 | 3.55111676e+00 1.05481745e+00 -1.74119949e+00 12 8.21150023e+00 -1.35710229e+01 3.25477083e+00 | 8.21150023e+00 -1.35710229e+01 3.25477083e+00 13 1.28489455e+01 -1.21304081e+01 -9.29053976e+00 | 1.28489455e+01 -1.21304081e+01 -9.29053976e+00 14 3.60643761e+01 -1.95928782e+00 9.46298408e+00 | 3.60643761e+01 -1.95928782e+00 9.46298408e+00 15 5.03953307e+00 -1.29584106e+01 -2.35239027e+01 | 5.03953307e+00 -1.29584106e+01 -2.35239027e+01 16 -8.03877371e+00 -2.71469236e+00 -1.89278461e+01 | -8.03877371e+00 -2.71469236e+00 -1.89278461e+01 17 5.31993727e+00 8.97513984e+00 1.28499547e+01 | 5.31993727e+00 8.97513984e+00 1.28499547e+01 18 -4.93089658e+00 -6.43577008e-01 -2.93828997e+00 | -4.93089658e+00 -6.43577008e-01 -2.93828997e+00 19 3.18198688e+00 1.60235821e+00 3.78608845e+00 | 3.18198688e+00 1.60235821e+00 3.78608845e+00 20 2.70487800e+01 5.23485467e+00 -1.89988659e+01 | 2.70487800e+01 5.23485467e+00 -1.89988659e+01 21 -7.20446660e+00 -9.61594696e+00 6.34389884e+00 | -7.20446660e+00 -9.61594696e+00 6.34389884e+00 22 -2.23208880e+00 -1.98311242e+00 -2.60801493e+00 | -2.23208880e+00 -1.98311242e+00 -2.60801493e+00 23 -3.59749437e+01 1.15723602e+01 -1.14097013e+00 | -3.59749437e+01 1.15723602e+01 -1.14097013e+00 24 -8.55278685e-01 1.43543087e+00 1.49790366e+00 | -8.55278685e-01 1.43543087e+00 1.49790366e+00 25 -2.57421177e+01 9.01839223e+00 -6.87150120e+00 | -2.57421177e+01 9.01839223e+00 -6.87150120e+00 26 1.18719060e+01 1.23883032e+01 -2.21532259e+01 | 1.18719060e+01 1.23883032e+01 -2.21532259e+01 27 -6.99877184e-01 -9.19563891e-01 2.16794106e-01 | -6.99877184e-01 -9.19563891e-01 2.16794106e-01 28 7.63811372e+00 -2.95330611e+01 2.15588176e+01 | 7.63811372e+00 -2.95330611e+01 2.15588176e+01 29 8.14383006e+00 9.51944602e+00 3.69094758e+00 | 8.14383006e+00 9.51944602e+00 3.69094758e+00 30 7.02778479e+00 8.59105850e+00 -8.18456398e+00 | 7.02778479e+00 8.59105850e+00 -8.18456398e+00 31 2.29081992e-01 5.19361230e+00 -1.69111863e+00 | 2.29081992e-01 5.19361230e+00 -1.69111863e+00 32 3.85917723e-01 1.67591221e-02 6.72546473e-01 | 3.85917723e-01 1.67591221e-02 6.72546473e-01 33 -3.71127179e+00 6.58303597e+00 -8.45915062e+00 | -3.71127179e+00 6.58303597e+00 -8.45915062e+00 34 -1.71477648e+01 -9.95589802e+00 -1.14790777e+01 | -1.71477648e+01 -9.95589802e+00 -1.14790777e+01 35 1.62160304e+01 7.77211145e+00 7.83333628e+00 | 1.62160304e+01 7.77211145e+00 7.83333628e+00 36 -4.97270200e+00 -1.11984829e+01 6.79385293e+00 | -4.97270200e+00 -1.11984829e+01 6.79385293e+00 37 8.65514096e+00 -1.63798884e+00 7.00363819e+00 | 8.65514096e+00 -1.63798884e+00 7.00363819e+00 38 -1.45688111e+01 -1.16429622e+01 -8.86910303e+00 | -1.45688111e+01 -1.16429622e+01 -8.86910303e+00 39 8.55630637e+00 1.06425454e+01 1.00471024e+01 | 8.55630637e+00 1.06425454e+01 1.00471024e+01 40 -2.96019957e-02 -7.52140485e+00 -6.67524858e+00 | -2.96019957e-02 -7.52140485e+00 -6.67524858e+00 41 4.11826694e+00 7.68502059e+00 6.67794677e+00 | 4.11826694e+00 7.68502059e+00 6.67794677e+00 42 -1.32372923e+01 9.73357917e+00 9.75012938e+00 | -1.32372923e+01 9.73357917e+00 9.75012938e+00 43 2.05484416e+01 -1.93397949e+01 -9.79680171e+00 | 2.05484416e+01 -1.93397949e+01 -9.79680171e+00 44 -8.93598833e+00 -2.92614317e+01 -2.51250075e+01 | -8.93598833e+00 -2.92614317e+01 -2.51250075e+01 45 9.02858587e+00 2.87696264e+01 2.39708612e+01 | 9.02858587e+00 2.87696264e+01 2.39708612e+01 46 -9.36031931e+00 -2.79153587e+00 -8.81818847e+00 | -9.36031931e+00 -2.79153587e+00 -8.81818847e+00 47 9.04334202e+00 6.88485768e+00 8.55501399e+00 | 9.04334202e+00 6.88485768e+00 8.55501399e+00 48 -3.25684226e+00 -8.21843510e+00 -1.76544088e+00 | -3.25684226e+00 -8.21843510e+00 -1.76544088e+00 49 3.51285390e+00 1.34215036e+00 7.16592743e-01 | 3.51285390e+00 1.34215036e+00 7.16592743e-01 50 3.65827312e+01 -1.13777219e+01 2.79897089e+00 | 3.65827312e+01 -1.13777219e+01 2.79897089e+00 51 1.41309878e+00 1.74363802e+00 8.87396814e-01 | 1.41309878e+00 1.74363802e+00 8.87396814e-01 52 2.23678313e+00 4.45365948e+00 1.57761093e-01 | 2.23678313e+00 4.45365948e+00 1.57761093e-01 53 -3.45314867e+00 -1.38175162e+01 1.78223518e+01 | -3.45314867e+00 -1.38175162e+01 1.78223518e+01 54 -9.41628465e+00 -1.98808219e+00 -3.68861981e+00 | -9.41628465e+00 -1.98808219e+00 -3.68861981e+00 55 7.56587615e+00 8.57822414e+00 6.66468993e+00 | 7.56587615e+00 8.57822414e+00 6.66468993e+00 56 -6.35163571e+00 1.06989353e+01 2.57794268e+01 | -6.35163571e+00 1.06989353e+01 2.57794268e+01 57 1.38519013e+01 -8.55308554e+00 -1.63682648e+01 | 1.38519013e+01 -8.55308554e+00 -1.63682648e+01 58 -7.50456406e+00 -5.19734751e+00 -7.77111013e+00 | -7.50456406e+00 -5.19734751e+00 -7.77111013e+00 59 7.09121895e+00 2.03112931e+00 1.01710449e+01 | 7.09121895e+00 2.03112931e+00 1.01710449e+01 60 -2.26707910e+01 1.72953505e+01 1.15654111e+01 | -2.26707910e+01 1.72953505e+01 1.15654111e+01 61 8.43709500e-01 1.56983779e+00 9.22241657e-01 | 8.43709500e-01 1.56983779e+00 9.22241657e-01 62 -1.08644100e+01 2.22982736e+01 -1.03919902e+00 | -1.08644100e+01 2.22982736e+01 -1.03919902e+00 63 2.94743476e+00 2.61958540e+00 2.07991495e+00 | 2.94743476e+00 2.61958540e+00 2.07991495e+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 = [51, 14, 10, 16, 43, 56, 55, 21, 28, 47, 2, 57, 54, 53, 1, 52, 3, 31, 41, 38, 37, 7, 48, 26, 40, 30, 23, 46, 8, 32, 25, 17, 29, 45, 63, 49, 44, 20, 19, 42, 24, 18, 39, 4, 36, 33, 27, 9, 22, 35, 59, 0, 15, 13, 12, 6, 5, 11, 60, 50, 58, 62, 61, 34] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -122.20708891650021 V(r_1,...,r_N) = -122.20708891650037 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 -3.39109881e+00 -1.15202033e+01 -3.28909573e+00 | -3.39109881e+00 -1.15202033e+01 -3.28909573e+00 1 2.52855867e+00 7.93144317e+00 -6.78588002e+00 | 2.52855867e+00 7.93144317e+00 -6.78588002e+00 2 4.24855141e+00 -2.14963895e+00 -7.78309164e+00 | 4.24855141e+00 -2.14963895e+00 -7.78309164e+00 3 -6.11483261e+00 3.89019783e+00 1.69845789e+00 | -6.11483261e+00 3.89019783e+00 1.69845789e+00 4 -6.83582597e+00 -1.38187191e+00 -2.25266117e+00 | -6.83582597e+00 -1.38187191e+00 -2.25266117e+00 5 4.31610112e+00 -7.48895722e-01 1.39680715e+01 | 4.31610112e+00 -7.48895722e-01 1.39680715e+01 6 -5.08222997e+00 8.75503690e-01 1.81692168e+01 | -5.08222997e+00 8.75503690e-01 1.81692168e+01 7 -2.62972638e+00 1.53485512e+00 3.67764907e+00 | -2.62972638e+00 1.53485512e+00 3.67764907e+00 8 -3.05987994e-01 -2.02499321e+00 -4.71338730e+00 | -3.05987994e-01 -2.02499321e+00 -4.71338730e+00 9 7.36081441e+00 6.62095349e-01 -5.49185092e-01 | 7.36081441e+00 6.62095349e-01 -5.49185092e-01 10 -9.09825984e+00 -6.84512853e+00 -3.90463937e+00 | -9.09825984e+00 -6.84512853e+00 -3.90463937e+00 11 5.29586382e+00 6.58474778e+00 9.50777254e+00 | 5.29586382e+00 6.58474778e+00 9.50777254e+00 12 -1.01469275e+00 -3.28268941e+00 3.00299387e-02 | -1.01469275e+00 -3.28268941e+00 3.00299387e-02 13 7.28415916e+00 -3.43643160e+00 2.66065919e-01 | 7.28415916e+00 -3.43643160e+00 2.66065919e-01 14 -4.38174681e+00 6.08073595e+00 -4.98476486e+00 | -4.38174681e+00 6.08073595e+00 -4.98476486e+00 15 -6.57224094e+00 -1.77604882e+00 -6.58805548e+00 | -6.57224094e+00 -1.77604882e+00 -6.58805548e+00 16 5.38219437e+00 -1.48222854e-01 -1.12038286e+00 | 5.38219437e+00 -1.48222854e-01 -1.12038286e+00 17 9.24104185e-01 7.29117038e+00 5.82385532e+00 | 9.24104185e-01 7.29117038e+00 5.82385532e+00 18 -6.15208949e+00 -5.50731928e+00 -8.08690384e+00 | -6.15208949e+00 -5.50731928e+00 -8.08690384e+00 19 3.70187938e+00 3.70406854e+00 1.14530589e+00 | 3.70187938e+00 3.70406854e+00 1.14530589e+00 20 1.44843267e+01 -9.42900099e+00 8.29412911e+00 | 1.44843267e+01 -9.42900099e+00 8.29412911e+00 21 -2.68307664e+00 -4.87290934e+00 4.44540308e+00 | -2.68307664e+00 -4.87290934e+00 4.44540308e+00 22 -6.47905725e+00 -6.58229467e+00 2.11509674e-01 | -6.47905725e+00 -6.58229467e+00 2.11509674e-01 23 9.31335036e+00 7.00281561e+00 2.28864412e+00 | 9.31335036e+00 7.00281561e+00 2.28864412e+00 24 1.23209664e+01 5.27258975e+00 -5.12910964e+00 | 1.23209664e+01 5.27258975e+00 -5.12910964e+00 25 -3.06959755e+00 -5.68241529e-01 1.05909493e+00 | -3.06959755e+00 -5.68241529e-01 1.05909493e+00 26 -5.92886577e+00 1.84272009e+00 6.71127378e-03 | -5.92886577e+00 1.84272009e+00 6.71127378e-03 27 6.48878967e+00 5.25597584e+00 5.16623236e+00 | 6.48878967e+00 5.25597584e+00 5.16623236e+00 28 -5.08772923e+00 -3.23677874e+00 -8.78425777e+00 | -5.08772923e+00 -3.23677874e+00 -8.78425777e+00 29 -6.38358589e+00 3.49516429e+00 9.79972432e-01 | -6.38358589e+00 3.49516429e+00 9.79972432e-01 30 6.15779680e+00 -7.33120064e+00 -2.53853578e-01 | 6.15779680e+00 -7.33120064e+00 -2.53853578e-01 31 -9.92121509e-01 -4.12283487e+00 -9.94742244e+00 | -9.92121509e-01 -4.12283487e+00 -9.94742244e+00 32 -7.36693850e+00 -2.70337700e+00 -5.84054615e+00 | -7.36693850e+00 -2.70337700e+00 -5.84054615e+00 33 9.38638231e-01 1.21717037e+01 8.46024277e+00 | 9.38638231e-01 1.21717037e+01 8.46024277e+00 34 -1.21237350e+01 -5.12255789e-01 -2.00664176e-02 | -1.21237350e+01 -5.12255789e-01 -2.00664176e-02 35 -1.63229904e+00 6.35299999e+00 2.47022479e+00 | -1.63229904e+00 6.35299999e+00 2.47022479e+00 36 5.76326148e+00 -5.57128477e+00 -4.28914240e+00 | 5.76326148e+00 -5.57128477e+00 -4.28914240e+00 37 2.59291485e+00 6.79220878e+00 6.07501680e+00 | 2.59291485e+00 6.79220878e+00 6.07501680e+00 38 -3.61519415e+00 2.03463325e+00 -1.71484129e+01 | -3.61519415e+00 2.03463325e+00 -1.71484129e+01 39 1.00042359e+01 -5.11330618e+00 8.33798659e+00 | 1.00042359e+01 -5.11330618e+00 8.33798659e+00 40 2.15380373e+00 4.39793429e-01 -7.40530322e-01 | 2.15380373e+00 4.39793429e-01 -7.40530322e-01 41 4.25895125e+00 -3.69613283e+00 -4.09806940e+00 | 4.25895125e+00 -3.69613283e+00 -4.09806940e+00 42 -9.68437660e+00 5.01056938e-01 -6.79616539e+00 | -9.68437660e+00 5.01056938e-01 -6.79616539e+00 43 4.11347104e+00 -6.88675838e+00 5.39540074e+00 | 4.11347104e+00 -6.88675838e+00 5.39540074e+00 44 -2.37833285e+00 -4.20669454e+00 -5.50894010e+00 | -2.37833285e+00 -4.20669454e+00 -5.50894010e+00 45 4.97814913e+00 7.43260980e+00 7.25582928e+00 | 4.97814913e+00 7.43260980e+00 7.25582928e+00 46 2.76284561e+00 -7.04413115e+00 -3.97682538e+00 | 2.76284561e+00 -7.04413115e+00 -3.97682538e+00 47 -1.32572743e+00 -2.16364019e-01 -3.31631417e+00 | -1.32572743e+00 -2.16364019e-01 -3.31631417e+00 48 -5.22665348e+00 2.05231792e+00 -1.73178417e+00 | -5.22665348e+00 2.05231792e+00 -1.73178417e+00 49 -6.25854311e+00 3.08868482e+00 -8.97253378e+00 | -6.25854311e+00 3.08868482e+00 -8.97253378e+00 50 2.02794508e+00 -1.06746850e+01 5.51333547e+00 | 2.02794508e+00 -1.06746850e+01 5.51333547e+00 51 7.50920201e+00 1.74904345e+00 -5.44777174e+00 | 7.50920201e+00 1.74904345e+00 -5.44777174e+00 52 -1.01588643e+01 -5.67697201e+00 9.94037369e-01 | -1.01588643e+01 -5.67697201e+00 9.94037369e-01 53 -6.87478897e+00 9.66007880e-02 2.53778934e+00 | -6.87478897e+00 9.66007880e-02 2.53778934e+00 54 -5.46152467e+00 -4.33305064e+00 -1.54369511e+00 | -5.46152467e+00 -4.33305064e+00 -1.54369511e+00 55 2.90367606e+00 6.59998642e+00 9.03263923e+00 | 2.90367606e+00 6.59998642e+00 9.03263923e+00 56 -6.37534241e-01 6.48444324e+00 5.23147628e+00 | -6.37534241e-01 6.48444324e+00 5.23147628e+00 57 4.17790893e+00 -6.46670223e+00 -8.89107780e+00 | 4.17790893e+00 -6.46670223e+00 -8.89107780e+00 58 7.98810104e-01 -1.52221745e+00 1.16577909e+01 | 7.98810104e-01 -1.52221745e+00 1.16577909e+01 59 7.43210372e+00 2.67312550e+00 1.62313455e+00 | 7.43210372e+00 2.67312550e+00 1.62313455e+00 60 -1.69773467e+00 1.35627022e+01 -1.18651572e-01 | -1.69773467e+00 1.35627022e+01 -1.18651572e-01 61 -6.04233335e+00 4.18262745e+00 -2.96452248e+00 | -6.04233335e+00 4.18262745e+00 -2.96452248e+00 62 8.80294325e+00 -4.62927425e-01 4.16185708e+00 | 8.80294325e+00 -4.62927425e-01 4.16185708e+00 63 1.66102894e+00 2.41294275e+00 9.28570512e-02 | 1.66102894e+00 2.41294275e+00 9.28570512e-02 ------------------------------------------------------------------------------------------------------------------------- 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 = [53, 7, 58, 22, 12, 10, 18, 1, 32, 23, 5, 27, 4, 50, 35, 30, 34, 42, 6, 25, 26, 44, 3, 9, 61, 19, 20, 11, 46, 59, 15, 40, 8, 55, 16, 14, 37, 36, 52, 63, 31, 51, 17, 60, 21, 57, 28, 62, 48, 54, 13, 41, 38, 0, 49, 33, 56, 45, 2, 29, 43, 24, 47, 39] 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)) = 28.54439368495798 V(r_1,...,r_N) = 28.544393684958077 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 -2.77430555e+01 -3.00846886e+01 -1.59220424e+01 | -2.77430555e+01 -3.00846886e+01 -1.59220424e+01 1 1.43384919e+01 1.73545918e+01 2.18586754e+01 | 1.43384919e+01 1.73545918e+01 2.18586754e+01 2 1.06327747e+01 1.41656548e+01 -2.44092215e+00 | 1.06327747e+01 1.41656548e+01 -2.44092215e+00 3 -1.61022529e+01 -2.89850213e+01 -1.76670379e-01 | -1.61022529e+01 -2.89850213e+01 -1.76670379e-01 4 -7.88687805e+00 1.27420725e+00 -8.48310867e-01 | -7.88687805e+00 1.27420725e+00 -8.48310867e-01 5 -2.18196087e+01 -2.51329434e+01 2.04466558e+01 | -2.18196087e+01 -2.51329434e+01 2.04466558e+01 6 -1.77065236e+01 -4.47520693e+01 -3.84832782e+01 | -1.77065236e+01 -4.47520693e+01 -3.84832782e+01 7 1.92091286e+01 4.33423253e+01 2.82046534e+01 | 1.92091286e+01 4.33423253e+01 2.82046534e+01 8 1.10101476e+00 1.45920979e+00 -2.51673823e-01 | 1.10101476e+00 1.45920979e+00 -2.51673823e-01 9 -8.32567727e+00 7.76628662e+00 9.06326526e-01 | -8.32567727e+00 7.76628662e+00 9.06326526e-01 10 -1.35745947e+00 7.41025204e-01 -8.68095297e+00 | -1.35745947e+00 7.41025204e-01 -8.68095297e+00 11 7.75286767e+00 -8.81328090e-01 1.98747682e+00 | 7.75286767e+00 -8.81328090e-01 1.98747682e+00 12 2.54034297e+00 -2.60346229e+00 1.27587012e+01 | 2.54034297e+00 -2.60346229e+00 1.27587012e+01 13 -4.30712715e+00 2.01552774e+00 -2.12596350e+00 | -4.30712715e+00 2.01552774e+00 -2.12596350e+00 14 3.05674321e+01 2.79405085e+01 -2.83254094e+01 | 3.05674321e+01 2.79405085e+01 -2.83254094e+01 15 -6.50118325e+00 -2.08231163e+01 7.82339155e+00 | -6.50118325e+00 -2.08231163e+01 7.82339155e+00 16 1.13675577e+00 -2.04118904e+00 9.71960266e-01 | 1.13675577e+00 -2.04118904e+00 9.71960266e-01 17 -5.72448883e+01 5.02479175e+01 -1.78158893e+01 | -5.72448883e+01 5.02479175e+01 -1.78158893e+01 18 -8.00043374e+00 -7.27615498e+00 -3.59172447e+00 | -8.00043374e+00 -7.27615498e+00 -3.59172447e+00 19 -2.80207068e+00 9.03226989e+00 5.71178797e+00 | -2.80207068e+00 9.03226989e+00 5.71178797e+00 20 5.93997380e+01 -4.70127541e+01 2.46009003e+01 | 5.93997380e+01 -4.70127541e+01 2.46009003e+01 21 -6.23937032e+00 1.76807676e+00 -7.27115657e+00 | -6.23937032e+00 1.76807676e+00 -7.27115657e+00 22 -1.56464455e+01 -3.82240068e+01 -1.50917537e+01 | -1.56464455e+01 -3.82240068e+01 -1.50917537e+01 23 2.02177285e+01 3.46735500e+01 1.26736634e+01 | 2.02177285e+01 3.46735500e+01 1.26736634e+01 24 5.83298147e+00 1.88166834e+01 1.20874408e+00 | 5.83298147e+00 1.88166834e+01 1.20874408e+00 25 1.02221309e+02 -5.42094207e+01 -4.71908416e+01 | 1.02221309e+02 -5.42094207e+01 -4.71908416e+01 26 -4.62100500e-01 1.54129493e+00 2.22372385e+00 | -4.62100500e-01 1.54129493e+00 2.22372385e+00 27 -1.49071803e+00 -4.34565175e-01 8.72765169e-01 | -1.49071803e+00 -4.34565175e-01 8.72765169e-01 28 2.81897891e-01 1.30921876e+01 -6.28879172e+00 | 2.81897891e-01 1.30921876e+01 -6.28879172e+00 29 2.01846342e+00 4.70969511e+00 5.17022352e+00 | 2.01846342e+00 4.70969511e+00 5.17022352e+00 30 -8.93464640e+01 5.87344623e+01 5.46167852e+01 | -8.93464640e+01 5.87344623e+01 5.46167852e+01 31 1.50266170e+00 -2.50636648e-01 -1.33442046e+00 | 1.50266170e+00 -2.50636648e-01 -1.33442046e+00 32 -1.25428918e+00 1.51910666e+00 -2.53739579e+00 | -1.25428918e+00 1.51910666e+00 -2.53739579e+00 33 3.95005287e+00 -5.50804253e-01 3.30771480e-01 | 3.95005287e+00 -5.50804253e-01 3.30771480e-01 34 -1.46145539e+00 3.85796929e+00 4.02879891e+00 | -1.46145539e+00 3.85796929e+00 4.02879891e+00 35 -1.42699916e+00 3.83793557e+00 1.32886806e+00 | -1.42699916e+00 3.83793557e+00 1.32886806e+00 36 9.21477215e-01 1.60858332e+00 -8.40784921e-02 | 9.21477215e-01 1.60858332e+00 -8.40784921e-02 37 -2.53650399e+00 -3.73170237e+00 7.22241720e+00 | -2.53650399e+00 -3.73170237e+00 7.22241720e+00 38 2.82220062e+00 3.29009032e+00 -2.00668857e+00 | 2.82220062e+00 3.29009032e+00 -2.00668857e+00 39 -4.50802142e+01 -4.53092875e+01 2.30581037e+01 | -4.50802142e+01 -4.53092875e+01 2.30581037e+01 40 2.04289816e+00 -5.81918740e+00 3.70429202e+00 | 2.04289816e+00 -5.81918740e+00 3.70429202e+00 41 -3.24613371e+00 1.57311906e+00 2.41394609e+00 | -3.24613371e+00 1.57311906e+00 2.41394609e+00 42 5.76824592e+00 1.41887344e+00 5.85243724e-01 | 5.76824592e+00 1.41887344e+00 5.85243724e-01 43 3.03676573e+00 -3.82313497e+00 -4.44719409e+00 | 3.03676573e+00 -3.82313497e+00 -4.44719409e+00 44 -7.45575982e-01 -1.75924539e+00 -9.82516411e-01 | -7.45575982e-01 -1.75924539e+00 -9.82516411e-01 45 9.65754757e-01 5.51226991e+00 -1.90788023e+00 | 9.65754757e-01 5.51226991e+00 -1.90788023e+00 46 -1.11824648e+01 -5.00376372e+00 -1.21503578e+01 | -1.11824648e+01 -5.00376372e+00 -1.21503578e+01 47 6.42490635e+00 2.86055931e+00 3.86519564e+00 | 6.42490635e+00 2.86055931e+00 3.86519564e+00 48 1.80056584e+00 1.65738453e+00 -1.53313669e+00 | 1.80056584e+00 1.65738453e+00 -1.53313669e+00 49 2.89797580e+00 2.88640706e+00 -1.97480944e+00 | 2.89797580e+00 2.88640706e+00 -1.97480944e+00 50 -1.45282194e+00 -3.70836982e+00 -2.50905278e+00 | -1.45282194e+00 -3.70836982e+00 -2.50905278e+00 51 2.93744058e+00 -1.51202893e+00 -1.65824904e+00 | 2.93744058e+00 -1.51202893e+00 -1.65824904e+00 52 4.16901114e+01 4.34825700e+01 -1.90781948e+01 | 4.16901114e+01 4.34825700e+01 -1.90781948e+01 53 -6.63477207e+00 -5.75392458e+01 1.26381035e+01 | -6.63477207e+00 -5.75392458e+01 1.26381035e+01 54 -3.24256606e+00 -5.16463780e+00 -4.38008038e+00 | -3.24256606e+00 -5.16463780e+00 -4.38008038e+00 55 3.85787597e+00 3.45590200e+00 4.71724027e+00 | 3.85787597e+00 3.45590200e+00 4.71724027e+00 56 8.28403354e+00 -4.80563363e+00 -1.08138224e+00 | 8.28403354e+00 -4.80563363e+00 -1.08138224e+00 57 -2.49177690e-01 -3.13905465e+00 6.26320163e+00 | -2.49177690e-01 -3.13905465e+00 6.26320163e+00 58 -1.81414956e+01 -3.70068019e+01 -3.24278182e+01 | -1.81414956e+01 -3.70068019e+01 -3.24278182e+01 59 1.82057157e+01 3.73880074e+01 2.75588583e+01 | 1.82057157e+01 3.73880074e+01 2.75588583e+01 60 -2.86325089e+00 3.39958622e+00 2.01956504e+00 | -2.86325089e+00 3.39958622e+00 2.01956504e+00 61 -1.76136320e+00 1.33486655e+00 -2.17719284e+00 | -1.76136320e+00 1.33486655e+00 -2.17719284e+00 62 6.46335184e+00 5.40158273e+01 -1.40301969e+01 | 6.46335184e+00 5.40158273e+01 -1.40301969e+01 63 3.43837979e+00 -1.90277669e-01 -9.65013575e-01 | 3.43837979e+00 -1.90277669e-01 -9.65013575e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.