!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = [6, 51, 53, 29, 28, 13, 0, 37, 21, 17, 59, 31, 50, 5, 49, 20, 52, 9, 43, 46, 15, 8, 62, 56, 44, 55, 40, 45, 4, 3, 58, 11, 47, 39, 60, 41, 48, 7, 42, 33, 26, 35, 38, 18, 24, 27, 19, 32, 36, 14, 12, 1, 16, 2, 61, 25, 23, 63, 30, 10, 34, 54, 22, 57] 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)) = 322.97159489 V(r_1,...,r_N) = 322.97159489 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 = [22, 27, 3, 2, 19, 14, 20, 10, 54, 34, 7, 21, 25, 52, 5, 62, 61, 35, 44, 4, 6, 11, 0, 40, 28, 12, 42, 1, 24, 49, 43, 57, 46, 41, 9, 17, 60, 51, 47, 63, 23, 33, 26, 30, 18, 53, 32, 38, 56, 29, 55, 37, 13, 45, 8, 50, 48, 31, 59, 58, 36, 16, 15, 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)) = -22.7688179361 V(r_1,...,r_N) = -22.7688179361 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 -5.27517072e+00 -9.31343463e+00 -1.33216136e+01 | -5.27517072e+00 -9.31343463e+00 -1.33216136e+01 1 1.81329439e+01 -1.47843930e+01 -5.84594325e+00 | 1.81329439e+01 -1.47843930e+01 -5.84594325e+00 2 -2.23927707e+01 -2.05210108e+01 -9.42853545e+00 | -2.23927707e+01 -2.05210108e+01 -9.42853545e+00 3 7.55896978e+00 1.40637628e+01 2.02927694e+01 | 7.55896978e+00 1.40637628e+01 2.02927694e+01 4 3.67934464e+00 -5.85516860e+00 2.96309830e+00 | 3.67934464e+00 -5.85516860e+00 2.96309830e+00 5 -1.02742730e+01 -9.63418470e-01 -2.57784213e+01 | -1.02742730e+01 -9.63418470e-01 -2.57784213e+01 6 -2.20460306e+01 1.82043590e+01 1.17001588e+01 | -2.20460306e+01 1.82043590e+01 1.17001588e+01 7 5.52325046e+00 4.50853947e+00 1.00923023e+00 | 5.52325046e+00 4.50853947e+00 1.00923023e+00 8 -2.56894119e+00 -4.38741504e+00 -2.27618270e+00 | -2.56894119e+00 -4.38741504e+00 -2.27618270e+00 9 -3.62452163e+01 1.16713563e+01 1.56520101e+01 | -3.62452163e+01 1.16713563e+01 1.56520101e+01 10 2.22758397e+01 1.53468980e+01 -2.94363110e+01 | 2.22758397e+01 1.53468980e+01 -2.94363110e+01 11 3.29921193e-01 -1.19010586e+00 -6.37812030e-01 | 3.29921193e-01 -1.19010586e+00 -6.37812030e-01 12 1.50291258e+01 -2.03587927e+01 1.70446743e+01 | 1.50291258e+01 -2.03587927e+01 1.70446743e+01 13 2.84951292e+00 -3.78635701e+00 1.12133053e+00 | 2.84951292e+00 -3.78635701e+00 1.12133053e+00 14 -4.07812619e+00 -1.88941508e+00 2.18350400e+00 | -4.07812619e+00 -1.88941508e+00 2.18350400e+00 15 6.23051378e+00 1.24386813e+01 -7.77529656e+00 | 6.23051378e+00 1.24386813e+01 -7.77529656e+00 16 2.01236830e-01 -3.78442368e+00 -3.83184153e+00 | 2.01236830e-01 -3.78442368e+00 -3.83184153e+00 17 5.77498412e+00 -1.02493031e+01 -1.31544052e+01 | 5.77498412e+00 -1.02493031e+01 -1.31544052e+01 18 -6.16373752e-01 -2.08738587e+00 5.02894385e-01 | -6.16373752e-01 -2.08738587e+00 5.02894385e-01 19 -1.02947005e+01 1.43980807e+01 -6.52283271e+00 | -1.02947005e+01 1.43980807e+01 -6.52283271e+00 20 2.56457317e+00 -3.48254022e+00 -1.26122759e+00 | 2.56457317e+00 -3.48254022e+00 -1.26122759e+00 21 -9.10689134e+00 -2.98738062e+00 1.53217821e+01 | -9.10689134e+00 -2.98738062e+00 1.53217821e+01 22 -1.83943033e+01 8.96013446e+00 1.01435211e+01 | -1.83943033e+01 8.96013446e+00 1.01435211e+01 23 7.07011720e+00 7.34594635e+00 2.19637289e+00 | 7.07011720e+00 7.34594635e+00 2.19637289e+00 24 1.24032115e+01 4.45968737e+00 -9.24898458e+00 | 1.24032115e+01 4.45968737e+00 -9.24898458e+00 25 -8.78567713e+00 -1.81261856e+01 -7.75418367e+00 | -8.78567713e+00 -1.81261856e+01 -7.75418367e+00 26 1.63668050e+01 6.52879530e+00 -1.71687124e+01 | 1.63668050e+01 6.52879530e+00 -1.71687124e+01 27 2.62674591e+00 2.68610043e+00 6.34804335e+00 | 2.62674591e+00 2.68610043e+00 6.34804335e+00 28 -2.07288768e+00 4.22330889e+00 -3.30615234e-01 | -2.07288768e+00 4.22330889e+00 -3.30615234e-01 29 4.48593655e+00 -1.52759589e+00 1.68993563e+00 | 4.48593655e+00 -1.52759589e+00 1.68993563e+00 30 1.45341706e+01 3.85649412e+00 1.03660314e+01 | 1.45341706e+01 3.85649412e+00 1.03660314e+01 31 -2.18658075e+00 3.41383093e+00 -1.91013005e-01 | -2.18658075e+00 3.41383093e+00 -1.91013005e-01 32 -7.31077347e+00 -4.83771008e+00 -1.04935359e+01 | -7.31077347e+00 -4.83771008e+00 -1.04935359e+01 33 3.06839651e+00 1.66681816e-01 1.02411514e+01 | 3.06839651e+00 1.66681816e-01 1.02411514e+01 34 2.69668347e+00 1.57755381e+00 -6.78858514e+00 | 2.69668347e+00 1.57755381e+00 -6.78858514e+00 35 2.14580793e+00 1.31353493e+00 -1.94541829e+00 | 2.14580793e+00 1.31353493e+00 -1.94541829e+00 36 -1.56641531e+00 -3.78752131e+00 -6.52032430e-01 | -1.56641531e+00 -3.78752131e+00 -6.52032430e-01 37 1.99598802e-01 4.65931026e-01 2.33012252e+00 | 1.99598802e-01 4.65931026e-01 2.33012252e+00 38 -1.42396144e+00 1.55875599e-02 3.22258183e+00 | -1.42396144e+00 1.55875599e-02 3.22258183e+00 39 -1.05261546e+01 -1.71018534e+00 1.13681738e+01 | -1.05261546e+01 -1.71018534e+00 1.13681738e+01 40 -3.03383565e+00 -1.31720744e+01 2.12543909e+01 | -3.03383565e+00 -1.31720744e+01 2.12543909e+01 41 9.34018350e+00 5.78389676e+00 6.04242278e+00 | 9.34018350e+00 5.78389676e+00 6.04242278e+00 42 -1.60135995e+00 1.72602070e+00 -2.69774940e+00 | -1.60135995e+00 1.72602070e+00 -2.69774940e+00 43 5.95202691e+00 -1.37468587e+00 9.87046976e-01 | 5.95202691e+00 -1.37468587e+00 9.87046976e-01 44 -1.02682409e+01 -1.29699025e+01 -1.33165350e+01 | -1.02682409e+01 -1.29699025e+01 -1.33165350e+01 45 1.23863524e+01 1.19261032e+01 1.32283808e+01 | 1.23863524e+01 1.19261032e+01 1.32283808e+01 46 -5.68482490e+00 -4.44566776e+00 -3.64484986e+00 | -5.68482490e+00 -4.44566776e+00 -3.64484986e+00 47 9.76305000e-01 7.93921478e+00 5.92389546e+00 | 9.76305000e-01 7.93921478e+00 5.92389546e+00 48 -1.34386073e+00 6.28454561e+00 4.29831421e+00 | -1.34386073e+00 6.28454561e+00 4.29831421e+00 49 -7.09872275e-01 2.31418331e+00 -1.07414375e+00 | -7.09872275e-01 2.31418331e+00 -1.07414375e+00 50 -1.00587194e+01 -1.31393750e+01 -4.30976999e+00 | -1.00587194e+01 -1.31393750e+01 -4.30976999e+00 51 8.59754828e+00 1.29054295e+01 6.12450652e+00 | 8.59754828e+00 1.29054295e+01 6.12450652e+00 52 9.76604223e+00 -5.93322583e+00 -8.13476606e+00 | 9.76604223e+00 -5.93322583e+00 -8.13476606e+00 53 1.01673616e+00 3.14869337e-01 3.85376459e+00 | 1.01673616e+00 3.14869337e-01 3.85376459e+00 54 -2.62808576e+01 -1.43876062e+01 -7.64113148e+00 | -2.62808576e+01 -1.43876062e+01 -7.64113148e+00 55 2.34142609e+01 1.74100366e+01 8.68301586e+00 | 2.34142609e+01 1.74100366e+01 8.68301586e+00 56 -5.08677122e+00 -5.39000325e+00 -7.43177859e+00 | -5.08677122e+00 -5.39000325e+00 -7.43177859e+00 57 -1.55018900e+00 -8.39613205e+00 2.55797586e+01 | -1.55018900e+00 -8.39613205e+00 2.55797586e+01 58 1.34281477e+01 1.11436809e+01 -1.82666000e+01 | 1.34281477e+01 1.11436809e+01 -1.82666000e+01 59 -1.17349293e+00 -1.88919269e+00 -2.99592611e-01 | -1.17349293e+00 -1.88919269e+00 -2.99592611e-01 60 -9.57647252e-01 1.11006279e+00 -3.75846355e-01 | -9.57647252e-01 1.11006279e+00 -3.75846355e-01 61 -3.66270918e-01 7.51613666e-01 2.16161280e-01 | -3.66270918e-01 7.51613666e-01 2.16161280e-01 62 -1.34958694e+00 -1.09508950e+01 -3.80052905e+00 | -1.34958694e+00 -1.09508950e+01 -3.80052905e+00 63 4.00548489e+00 1.24235820e+01 2.94775203e+00 | 4.00548489e+00 1.24235820e+01 2.94775203e+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 = [3, 17, 5, 0, 56, 2, 14, 45, 61, 47, 63, 42, 31, 60, 6, 24, 40, 1, 34, 41, 30, 59, 62, 50, 15, 39, 57, 55, 53, 32, 20, 12, 29, 35, 18, 33, 43, 46, 49, 25, 16, 19, 11, 36, 58, 7, 37, 9, 52, 38, 23, 54, 48, 28, 51, 27, 4, 26, 44, 21, 13, 8, 22, 10] 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)) = -130.616056772 V(r_1,...,r_N) = -130.616056772 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 2.24321494e+00 1.07269886e+00 1.23416794e+00 | 2.24321494e+00 1.07269886e+00 1.23416794e+00 1 1.05828455e+00 -1.21127780e+00 -4.15051710e+00 | 1.05828455e+00 -1.21127780e+00 -4.15051710e+00 2 -3.50232364e+00 -7.16006156e+00 -6.94356259e+00 | -3.50232364e+00 -7.16006156e+00 -6.94356259e+00 3 -3.61455544e+00 4.15684532e+00 1.35576817e+01 | -3.61455544e+00 4.15684532e+00 1.35576817e+01 4 2.60132406e+00 -4.79975928e+00 -1.04175831e+01 | 2.60132406e+00 -4.79975928e+00 -1.04175831e+01 5 -1.50946655e+01 -5.45387843e+00 4.62691860e-01 | -1.50946655e+01 -5.45387843e+00 4.62691860e-01 6 -4.37215722e-01 3.84139314e-01 -3.63168698e+00 | -4.37215722e-01 3.84139314e-01 -3.63168698e+00 7 4.65166234e+00 5.64104057e+00 -5.15094981e+00 | 4.65166234e+00 5.64104057e+00 -5.15094981e+00 8 3.28357967e+00 3.25456576e+00 -1.26236979e-01 | 3.28357967e+00 3.25456576e+00 -1.26236979e-01 9 -1.00434115e+01 7.83497280e-01 7.14969104e+00 | -1.00434115e+01 7.83497280e-01 7.14969104e+00 10 7.61514961e-02 -6.59749642e+00 -9.20272651e+00 | 7.61514961e-02 -6.59749642e+00 -9.20272651e+00 11 9.95926021e+00 2.46230545e+00 6.69391232e+00 | 9.95926021e+00 2.46230545e+00 6.69391232e+00 12 -2.88388357e+00 -1.32137428e+01 -7.36197971e+00 | -2.88388357e+00 -1.32137428e+01 -7.36197971e+00 13 5.59546130e+00 8.02422403e+00 4.02779458e+00 | 5.59546130e+00 8.02422403e+00 4.02779458e+00 14 -1.12986108e+01 1.01642678e+01 -3.60805992e+00 | -1.12986108e+01 1.01642678e+01 -3.60805992e+00 15 -3.10613279e+00 -7.39842752e-04 -2.97274908e+00 | -3.10613279e+00 -7.39842752e-04 -2.97274908e+00 16 4.30702739e+00 -9.06873857e+00 4.47148289e+00 | 4.30702739e+00 -9.06873857e+00 4.47148289e+00 17 9.40773428e+00 3.06209529e+00 2.67296486e+00 | 9.40773428e+00 3.06209529e+00 2.67296486e+00 18 -6.53999446e+00 4.57289109e-01 -4.08518862e+00 | -6.53999446e+00 4.57289109e-01 -4.08518862e+00 19 -6.66055454e+00 -4.20221481e-01 4.20029016e+00 | -6.66055454e+00 -4.20221481e-01 4.20029016e+00 20 6.04299961e+00 1.55913804e-01 -3.71526822e+00 | 6.04299961e+00 1.55913804e-01 -3.71526822e+00 21 2.17003534e+00 -2.14459870e+00 -9.24206734e+00 | 2.17003534e+00 -2.14459870e+00 -9.24206734e+00 22 -1.50491382e+00 -7.43535479e+00 3.55382256e+00 | -1.50491382e+00 -7.43535479e+00 3.55382256e+00 23 1.30519498e+00 8.32943512e+00 9.42644345e-02 | 1.30519498e+00 8.32943512e+00 9.42644345e-02 24 -2.45706754e+00 -5.84613975e+00 -4.21652704e+00 | -2.45706754e+00 -5.84613975e+00 -4.21652704e+00 25 -3.31387431e+00 4.57934164e+00 8.16972877e+00 | -3.31387431e+00 4.57934164e+00 8.16972877e+00 26 6.53709352e+00 3.90045066e+00 -3.24090195e+00 | 6.53709352e+00 3.90045066e+00 -3.24090195e+00 27 -3.57773126e+00 -6.16752717e+00 1.27596627e+00 | -3.57773126e+00 -6.16752717e+00 1.27596627e+00 28 -9.24880432e+00 -3.96050332e+00 -1.06215538e+01 | -9.24880432e+00 -3.96050332e+00 -1.06215538e+01 29 3.94875152e+00 2.67070791e+00 1.32767338e+01 | 3.94875152e+00 2.67070791e+00 1.32767338e+01 30 1.72950639e+00 -1.00335391e+01 -3.41426084e+00 | 1.72950639e+00 -1.00335391e+01 -3.41426084e+00 31 -1.00557000e+01 1.12365411e+01 6.81767283e+00 | -1.00557000e+01 1.12365411e+01 6.81767283e+00 32 -1.67540891e+00 -1.26441118e+01 -5.97050515e+00 | -1.67540891e+00 -1.26441118e+01 -5.97050515e+00 33 -2.00827163e+00 5.14659892e+00 2.55273645e-02 | -2.00827163e+00 5.14659892e+00 2.55273645e-02 34 -8.81365647e+00 4.74531423e+00 4.07052012e+00 | -8.81365647e+00 4.74531423e+00 4.07052012e+00 35 2.71335727e+00 -2.28096962e+00 -7.63105103e+00 | 2.71335727e+00 -2.28096962e+00 -7.63105103e+00 36 2.00803549e+00 2.59118210e+00 3.43572114e+00 | 2.00803549e+00 2.59118210e+00 3.43572114e+00 37 2.76036613e+00 -1.97044105e+00 2.49707778e+00 | 2.76036613e+00 -1.97044105e+00 2.49707778e+00 38 -5.94443943e+00 3.62094223e+00 4.97615508e+00 | -5.94443943e+00 3.62094223e+00 4.97615508e+00 39 2.84101281e+00 -1.03690758e+01 2.96959847e+00 | 2.84101281e+00 -1.03690758e+01 2.96959847e+00 40 7.08868727e+00 -3.47247973e+00 -2.58628391e+00 | 7.08868727e+00 -3.47247973e+00 -2.58628391e+00 41 -1.07845156e-01 -4.89941614e+00 5.52263585e+00 | -1.07845156e-01 -4.89941614e+00 5.52263585e+00 42 3.01195459e+00 4.52694138e+00 -2.82637982e+00 | 3.01195459e+00 4.52694138e+00 -2.82637982e+00 43 6.56237923e+00 -1.14820492e+01 2.31065467e-01 | 6.56237923e+00 -1.14820492e+01 2.31065467e-01 44 -6.65301169e+00 -3.69036344e+00 3.26908314e-01 | -6.65301169e+00 -3.69036344e+00 3.26908314e-01 45 9.75957413e+00 5.32550713e+00 4.37402000e+00 | 9.75957413e+00 5.32550713e+00 4.37402000e+00 46 -1.07675207e+00 -7.92850075e-01 -4.72472598e+00 | -1.07675207e+00 -7.92850075e-01 -4.72472598e+00 47 1.69409263e+00 2.15781499e+00 1.41511803e+00 | 1.69409263e+00 2.15781499e+00 1.41511803e+00 48 -2.43884981e+00 8.44145205e-01 4.69629193e+00 | -2.43884981e+00 8.44145205e-01 4.69629193e+00 49 7.40677689e-01 7.02521152e-01 -3.14148999e+00 | 7.40677689e-01 7.02521152e-01 -3.14148999e+00 50 -1.32173428e-02 2.55172513e+00 -1.36400253e+01 | -1.32173428e-02 2.55172513e+00 -1.36400253e+01 51 -1.52063453e+00 5.18332859e+00 7.54414016e+00 | -1.52063453e+00 5.18332859e+00 7.54414016e+00 52 -9.41651991e+00 -4.54336122e+00 -5.63632619e-01 | -9.41651991e+00 -4.54336122e+00 -5.63632619e-01 53 3.57455740e+00 2.53420068e+00 4.36690152e+00 | 3.57455740e+00 2.53420068e+00 4.36690152e+00 54 -7.47338130e+00 -2.49416402e+00 -4.93052231e-01 | -7.47338130e+00 -2.49416402e+00 -4.93052231e-01 55 5.33327613e+00 1.72704611e+00 2.75224667e+00 | 5.33327613e+00 1.72704611e+00 2.75224667e+00 56 1.14113727e+01 1.73456715e+01 1.62800999e+00 | 1.14113727e+01 1.73456715e+01 1.62800999e+00 57 6.17487996e+00 2.47338182e+00 -3.29020343e+00 | 6.17487996e+00 2.47338182e+00 -3.29020343e+00 58 4.75154154e+00 -8.14328783e+00 -3.04484566e+00 | 4.75154154e+00 -8.14328783e+00 -3.04484566e+00 59 3.04822658e-01 -3.24545766e+00 9.41841071e+00 | 3.04822658e-01 -3.24545766e+00 9.41841071e+00 60 -4.34030981e+00 9.62698064e+00 -1.10016621e+01 | -4.34030981e+00 9.62698064e+00 -1.10016621e+01 61 -4.48257974e-01 5.29678945e+00 4.71393009e+00 | -4.48257974e-01 5.29678945e+00 4.71393009e+00 62 -1.50617736e-01 3.18128293e+00 7.13342321e+00 | -1.50617736e-01 3.18128293e+00 7.13342321e+00 63 9.77274374e+00 3.62487342e+00 1.25910886e+00 | 9.77274374e+00 3.62487342e+00 1.25910886e+00 ------------------------------------------------------------------------------------------------------------------------- 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, 49, 58, 25, 55, 6, 5, 51, 39, 21, 36, 60, 41, 24, 52, 56, 34, 29, 22, 32, 50, 9, 18, 31, 13, 3, 47, 35, 37, 17, 44, 23, 19, 62, 16, 27, 10, 28, 59, 8, 42, 12, 40, 45, 30, 43, 54, 26, 63, 1, 20, 7, 14, 0, 46, 4, 15, 57, 2, 38, 11, 61, 33, 48] 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)) = 20.6940198434 V(r_1,...,r_N) = 20.6940198434 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 2.37444646e+00 3.78785090e+00 2.49688524e+00 | 2.37444646e+00 3.78785090e+00 2.49688524e+00 1 -3.38499572e+01 -1.27159044e+01 3.93817221e+01 | -3.38499572e+01 -1.27159044e+01 3.93817221e+01 2 3.53838709e+01 9.88384804e+00 -4.94236971e+01 | 3.53838709e+01 9.88384804e+00 -4.94236971e+01 3 2.86857932e+00 4.46091145e+00 2.86881225e+00 | 2.86857932e+00 4.46091145e+00 2.86881225e+00 4 3.05153084e+00 -2.59726551e+00 1.41771998e+00 | 3.05153084e+00 -2.59726551e+00 1.41771998e+00 5 -2.85095484e+00 1.87075610e+01 -1.11286713e+01 | -2.85095484e+00 1.87075610e+01 -1.11286713e+01 6 -7.19066823e+00 -1.40033142e+00 2.43043669e+00 | -7.19066823e+00 -1.40033142e+00 2.43043669e+00 7 6.78423699e+00 6.12180663e+00 1.60363833e+00 | 6.78423699e+00 6.12180663e+00 1.60363833e+00 8 -7.74219442e+00 -7.24549116e+00 -1.74003836e-01 | -7.74219442e+00 -7.24549116e+00 -1.74003836e-01 9 -7.56432494e+01 -1.04445451e+02 1.10024394e+02 | -7.56432494e+01 -1.04445451e+02 1.10024394e+02 10 8.42801696e+01 1.02068060e+02 -1.35532818e+02 | 8.42801696e+01 1.02068060e+02 -1.35532818e+02 11 1.44336453e+01 -4.29026791e+00 -1.29102282e+00 | 1.44336453e+01 -4.29026791e+00 -1.29102282e+00 12 4.61560955e+00 -4.82970666e+00 4.93932147e+00 | 4.61560955e+00 -4.82970666e+00 4.93932147e+00 13 1.18054524e+00 1.02864604e+00 1.42046209e+00 | 1.18054524e+00 1.02864604e+00 1.42046209e+00 14 -1.28454942e+01 1.15110332e+01 1.11775076e+01 | -1.28454942e+01 1.15110332e+01 1.11775076e+01 15 1.50361110e+00 7.71158902e-01 6.88388746e+00 | 1.50361110e+00 7.71158902e-01 6.88388746e+00 16 3.77017859e+00 -8.06815296e-01 2.87279900e+00 | 3.77017859e+00 -8.06815296e-01 2.87279900e+00 17 -8.57473084e+01 6.99991992e+01 -8.31026227e+01 | -8.57473084e+01 6.99991992e+01 -8.31026227e+01 18 2.23853419e+01 3.59773520e+01 -1.85696139e+01 | 2.23853419e+01 3.59773520e+01 -1.85696139e+01 19 -1.38734655e+01 4.40046911e+01 -2.31967399e+01 | -1.38734655e+01 4.40046911e+01 -2.31967399e+01 20 7.44361606e+01 -1.20551226e+02 8.29196563e+01 | 7.44361606e+01 -1.20551226e+02 8.29196563e+01 21 -2.48855232e+00 -1.23841897e+00 -4.21536368e+00 | -2.48855232e+00 -1.23841897e+00 -4.21536368e+00 22 -2.29299129e+01 -1.43586383e+00 1.15523191e+01 | -2.29299129e+01 -1.43586383e+00 1.15523191e+01 23 9.45279443e+00 8.97342733e+00 4.43947078e+00 | 9.45279443e+00 8.97342733e+00 4.43947078e+00 24 -2.21460041e+01 -2.01990322e+00 -1.35860518e+01 | -2.21460041e+01 -2.01990322e+00 -1.35860518e+01 25 -1.05236452e+01 3.75909850e+01 1.62186799e+00 | -1.05236452e+01 3.75909850e+01 1.62186799e+00 26 -1.27148003e+00 -8.01743313e-02 2.28683556e+00 | -1.27148003e+00 -8.01743313e-02 2.28683556e+00 27 -2.77023325e+00 -1.54858843e+00 1.16351140e+00 | -2.77023325e+00 -1.54858843e+00 1.16351140e+00 28 1.62950246e+01 -2.22315654e+01 1.52438227e+01 | 1.62950246e+01 -2.22315654e+01 1.52438227e+01 29 8.28063868e-01 3.59042488e+00 -2.14824256e+00 | 8.28063868e-01 3.59042488e+00 -2.14824256e+00 30 1.60508206e+01 -4.84619941e+01 2.25483520e+01 | 1.60508206e+01 -4.84619941e+01 2.25483520e+01 31 1.48747121e+00 9.06482036e-01 -2.94705537e+00 | 1.48747121e+00 9.06482036e-01 -2.94705537e+00 32 -4.05172752e+00 -3.37100586e+01 -2.48783819e+01 | -4.05172752e+00 -3.37100586e+01 -2.48783819e+01 33 2.91949263e+00 3.52286148e+01 2.51917077e+01 | 2.91949263e+00 3.52286148e+01 2.51917077e+01 34 -4.74864520e+00 -7.31404327e+00 -9.56897185e+00 | -4.74864520e+00 -7.31404327e+00 -9.56897185e+00 35 2.52535972e+00 7.57728358e-01 1.04510701e+01 | 2.52535972e+00 7.57728358e-01 1.04510701e+01 36 2.66148783e+00 1.94794495e+00 -1.15110722e+00 | 2.66148783e+00 1.94794495e+00 -1.15110722e+00 37 3.73489704e-01 1.22083522e+00 -2.96995962e+00 | 3.73489704e-01 1.22083522e+00 -2.96995962e+00 38 -2.04555305e+01 -1.66421210e+01 -2.39922552e+01 | -2.04555305e+01 -1.66421210e+01 -2.39922552e+01 39 2.59429937e+01 1.62229968e+01 1.97056330e+01 | 2.59429937e+01 1.62229968e+01 1.97056330e+01 40 4.50888436e-01 -2.11178416e+01 1.57849790e+01 | 4.50888436e-01 -2.11178416e+01 1.57849790e+01 41 -3.21679172e+00 -1.88936882e-01 2.24516602e+00 | -3.21679172e+00 -1.88936882e-01 2.24516602e+00 42 -2.17030577e+00 -1.25887131e+00 -7.96825276e-01 | -2.17030577e+00 -1.25887131e+00 -7.96825276e-01 43 -1.94030380e-01 3.32589007e+00 3.35937805e+00 | -1.94030380e-01 3.32589007e+00 3.35937805e+00 44 -3.66002491e+01 -3.47749779e+01 -2.52750923e+01 | -3.66002491e+01 -3.47749779e+01 -2.52750923e+01 45 3.39917710e+01 3.62094144e+01 2.52508113e+01 | 3.39917710e+01 3.62094144e+01 2.52508113e+01 46 -5.01773297e+01 -6.29233130e+01 -1.34529239e+01 | -5.01773297e+01 -6.29233130e+01 -1.34529239e+01 47 4.54153415e+01 5.17268946e+01 8.32568519e+00 | 4.54153415e+01 5.17268946e+01 8.32568519e+00 48 -1.84824092e+00 -2.03196380e+00 1.52015828e+00 | -1.84824092e+00 -2.03196380e+00 1.52015828e+00 49 2.48867391e+00 3.53169097e+00 -4.14995054e+00 | 2.48867391e+00 3.53169097e+00 -4.14995054e+00 50 2.04794518e+00 2.53649217e-01 6.55246146e-01 | 2.04794518e+00 2.53649217e-01 6.55246146e-01 51 -7.83324470e-01 -3.33566598e+00 -2.18064503e+00 | -7.83324470e-01 -3.33566598e+00 -2.18064503e+00 52 -1.95114682e+00 1.78448026e+00 -2.30063407e+00 | -1.95114682e+00 1.78448026e+00 -2.30063407e+00 53 3.46521160e-01 -1.10576398e+00 -2.17870105e+00 | 3.46521160e-01 -1.10576398e+00 -2.17870105e+00 54 -2.03714722e+01 -1.56822837e+01 -2.11805331e+01 | -2.03714722e+01 -1.56822837e+01 -2.11805331e+01 55 1.95988278e+01 1.58437746e+01 2.17735455e+01 | 1.95988278e+01 1.58437746e+01 2.17735455e+01 56 2.19823246e+00 7.99396844e-01 1.05224101e+01 | 2.19823246e+00 7.99396844e-01 1.05224101e+01 57 6.89399331e-01 4.45301852e+00 -5.99319358e+00 | 6.89399331e-01 4.45301852e+00 -5.99319358e+00 58 -3.20237257e+00 4.38532378e-01 9.94697184e-01 | -3.20237257e+00 4.38532378e-01 9.94697184e-01 59 -1.16617723e+00 -1.38102037e-01 -5.05323229e-01 | -1.16617723e+00 -1.38102037e-01 -5.05323229e-01 60 -3.05944369e+00 2.78316620e+00 2.62395391e+00 | -3.05944369e+00 2.78316620e+00 2.62395391e+00 61 1.15548718e+01 1.27524987e+00 7.14268451e+00 | 1.15548718e+01 1.27524987e+00 7.14268451e+00 62 2.61449194e-01 -1.13319737e-02 2.04261422e+00 | 2.61449194e-01 -1.13319737e-02 2.04261422e+00 63 1.22106103e+00 -1.05247330e+00 -9.92761393e-01 | 1.22106103e+00 -1.05247330e+00 -9.92761393e-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.