!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KangSaLee_2009_ZrAgCu__MO_813575892799_001 Supported species : Ag Cu Zr random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ag (Configuration in file "config-Ag.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [7, 6, 20, 18, 15, 44, 1, 0, 31, 32, 49, 27, 46, 57, 38, 4, 34, 24, 3, 29, 2, 35, 25, 52, 17, 22, 47, 11, 60, 19, 41, 8, 9, 51, 16, 21, 43, 48, 14, 61, 45, 30, 54, 36, 5, 40, 12, 26, 37, 10, 62, 33, 23, 59, 42, 56, 55, 13, 63, 53, 28, 39, 50, 58] 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)) = 285.7491878450289 V(r_1,...,r_N) = 285.749187845029 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 -6.73200485e+00 -4.29190966e+00 -6.41240985e+00 | -6.73200485e+00 -4.29190966e+00 -6.41240985e+00 1 -1.98706278e+01 -5.76664874e+01 4.39032231e+01 | -1.98706278e+01 -5.76664874e+01 4.39032231e+01 2 -3.16350465e+00 2.24467436e+01 -7.64252685e+01 | -3.16350465e+00 2.24467436e+01 -7.64252685e+01 3 2.56872985e+01 3.38333368e+01 2.86806884e+01 | 2.56872985e+01 3.38333368e+01 2.86806884e+01 4 -2.95718968e+00 -1.04734756e+01 -7.82930720e+00 | -2.95718968e+00 -1.04734756e+01 -7.82930720e+00 5 1.11774581e+01 9.01629501e+00 3.30960384e+00 | 1.11774581e+01 9.01629501e+00 3.30960384e+00 6 -2.26789726e+00 -2.64850306e+00 -2.36569127e+00 | -2.26789726e+00 -2.64850306e+00 -2.36569127e+00 7 -5.86550283e+01 1.47193074e+02 -8.73034727e+01 | -5.86550283e+01 1.47193074e+02 -8.73034727e+01 8 -8.50105176e+00 -4.33940797e+00 -8.28673571e+00 | -8.50105176e+00 -4.33940797e+00 -8.28673571e+00 9 -2.45344346e+01 2.14936031e+01 -1.48646254e+01 | -2.45344346e+01 2.14936031e+01 -1.48646254e+01 10 -1.86503889e+01 -1.95258939e+01 -1.56632956e+01 | -1.86503889e+01 -1.95258939e+01 -1.56632956e+01 11 2.09759994e+01 2.11910660e+01 1.39145644e+01 | 2.09759994e+01 2.11910660e+01 1.39145644e+01 12 2.40834515e+01 -2.75796625e+01 1.93253520e+01 | 2.40834515e+01 -2.75796625e+01 1.93253520e+01 13 6.78804600e+01 -1.06093079e+01 -5.30757471e+01 | 6.78804600e+01 -1.06093079e+01 -5.30757471e+01 14 -2.61656487e+00 -3.31364232e+00 -4.66089293e+00 | -2.61656487e+00 -3.31364232e+00 -4.66089293e+00 15 3.11342958e+00 3.18089119e+00 8.19413513e+00 | 3.11342958e+00 3.18089119e+00 8.19413513e+00 16 -4.94830521e+01 -1.66788029e+01 -4.71800130e+01 | -4.94830521e+01 -1.66788029e+01 -4.71800130e+01 17 4.73816209e+01 1.40170236e+01 4.90817587e+01 | 4.73816209e+01 1.40170236e+01 4.90817587e+01 18 -7.82560984e-01 1.16558924e+00 -4.64656156e+00 | -7.82560984e-01 1.16558924e+00 -4.64656156e+00 19 -9.39923737e+01 6.04667570e+01 -6.29719383e+01 | -9.39923737e+01 6.04667570e+01 -6.29719383e+01 20 -3.95463061e+01 -2.50818215e+01 -2.64315734e+01 | -3.95463061e+01 -2.50818215e+01 -2.64315734e+01 21 4.67748379e+01 3.12240369e+01 2.40844099e+01 | 4.67748379e+01 3.12240369e+01 2.40844099e+01 22 -1.13238773e+01 -1.64424195e+01 -3.01995693e+01 | -1.13238773e+01 -1.64424195e+01 -3.01995693e+01 23 1.07996085e+01 1.70460532e+01 3.04317310e+01 | 1.07996085e+01 1.70460532e+01 3.04317310e+01 24 -5.24387320e+00 -6.33946671e+00 -6.89178605e+00 | -5.24387320e+00 -6.33946671e+00 -6.89178605e+00 25 -3.17168381e+01 3.69871818e+01 -2.19776749e+01 | -3.17168381e+01 3.69871818e+01 -2.19776749e+01 26 -8.06024424e+00 2.99344948e-01 -1.08103042e+01 | -8.06024424e+00 2.99344948e-01 -1.08103042e+01 27 1.10803246e+01 4.67817734e+00 7.57851412e+00 | 1.10803246e+01 4.67817734e+00 7.57851412e+00 28 3.26052666e+01 -4.19365069e+01 2.58159027e+01 | 3.26052666e+01 -4.19365069e+01 2.58159027e+01 29 5.62530437e+00 6.34802373e+00 3.06254398e+00 | 5.62530437e+00 6.34802373e+00 3.06254398e+00 30 9.20053788e+01 -5.66419079e+01 5.85303773e+01 | 9.20053788e+01 -5.66419079e+01 5.85303773e+01 31 -4.21310034e+01 1.98545354e+01 -2.16699774e+01 | -4.21310034e+01 1.98545354e+01 -2.16699774e+01 32 -9.53645397e+00 -1.44228566e+00 -1.63925519e+00 | -9.53645397e+00 -1.44228566e+00 -1.63925519e+00 33 -5.18443010e+00 6.53150219e+00 -8.96175819e+00 | -5.18443010e+00 6.53150219e+00 -8.96175819e+00 34 6.09225469e+01 -1.51808702e+02 8.75622831e+01 | 6.09225469e+01 -1.51808702e+02 8.75622831e+01 35 -1.45915531e+01 -2.28389623e+01 2.09453178e+01 | -1.45915531e+01 -2.28389623e+01 2.09453178e+01 36 8.86651265e+00 -1.01002392e+01 9.53386866e+00 | 8.86651265e+00 -1.01002392e+01 9.53386866e+00 37 -6.64719096e+00 -6.60865004e+00 4.87213291e+00 | -6.64719096e+00 -6.60865004e+00 4.87213291e+00 38 -1.35018091e+01 -3.98703540e+00 -4.94584800e+00 | -1.35018091e+01 -3.98703540e+00 -4.94584800e+00 39 -2.90641751e+01 -2.68107873e+01 3.38857247e+01 | -2.90641751e+01 -2.68107873e+01 3.38857247e+01 40 -6.38551971e-01 -2.14784003e+00 1.72182652e+00 | -6.38551971e-01 -2.14784003e+00 1.72182652e+00 41 -4.20923256e+01 7.37763618e+01 -5.85052561e+01 | -4.20923256e+01 7.37763618e+01 -5.85052561e+01 42 -6.53032407e+01 1.18566431e+01 5.03975124e+01 | -6.53032407e+01 1.18566431e+01 5.03975124e+01 43 5.75882309e+00 8.66180047e+00 7.09405359e+00 | 5.75882309e+00 8.66180047e+00 7.09405359e+00 44 5.03792744e+01 -8.49791506e+01 4.33057394e+01 | 5.03792744e+01 -8.49791506e+01 4.33057394e+01 45 1.80780353e-01 1.85264162e+00 2.01649531e+00 | 1.80780353e-01 1.85264162e+00 2.01649531e+00 46 -1.15719939e+01 3.22691177e-02 -5.54213214e+00 | -1.15719939e+01 3.22691177e-02 -5.54213214e+00 47 9.26679803e+00 1.61880708e+01 1.53792707e+01 | 9.26679803e+00 1.61880708e+01 1.53792707e+01 48 -2.45173227e+01 -2.55597165e+01 -1.67198536e+01 | -2.45173227e+01 -2.55597165e+01 -1.67198536e+01 49 1.77520761e+01 2.81117942e+01 2.29750165e+01 | 1.77520761e+01 2.81117942e+01 2.29750165e+01 50 -2.46527036e+01 -3.06806517e+01 -3.05154170e+01 | -2.46527036e+01 -3.06806517e+01 -3.05154170e+01 51 2.15464834e+01 3.20707169e+01 2.97412225e+01 | 2.15464834e+01 3.20707169e+01 2.97412225e+01 52 3.54755949e+01 3.69551272e+01 -2.78848804e+01 | 3.54755949e+01 3.69551272e+01 -2.78848804e+01 53 3.52948517e+00 7.47638999e-02 2.92530986e+00 | 3.52948517e+00 7.47638999e-02 2.92530986e+00 54 -1.34636604e+00 2.19847270e+00 2.24349838e+00 | -1.34636604e+00 2.19847270e+00 2.24349838e+00 55 -1.13299147e-01 -3.15674437e-01 -3.59598873e-01 | -1.13299147e-01 -3.15674437e-01 -3.59598873e-01 56 1.34408732e+01 1.59568910e+01 -1.66885847e+01 | 1.34408732e+01 1.59568910e+01 -1.66885847e+01 57 4.96125608e+01 -7.32885070e+01 -9.02098975e+01 | 4.96125608e+01 -7.32885070e+01 -9.02098975e+01 58 4.59047653e+01 -1.69135580e+01 2.72543856e+01 | 4.59047653e+01 -1.69135580e+01 2.72543856e+01 59 -9.39761140e-01 -1.76150609e-01 5.25981025e-02 | -9.39761140e-01 -1.76150609e-01 5.25981025e-02 60 -1.91383134e+01 -7.40448819e+00 -1.69218974e+01 | -1.91383134e+01 -7.40448819e+00 -1.69218974e+01 61 2.13960229e+01 5.80305128e+00 1.94162058e+01 | 2.13960229e+01 5.80305128e+00 1.94162058e+01 62 -4.52072821e+01 7.71435227e+01 9.08693125e+01 | -4.52072821e+01 7.71435227e+01 9.08693125e+01 63 1.05255839e+00 9.76253245e-01 4.56644362e-01 | 1.05255839e+00 9.76253245e-01 4.56644362e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [31, 7, 6, 18, 13, 30, 2, 1, 23, 21, 59, 17, 61, 4, 42, 47, 37, 11, 3, 35, 62, 9, 49, 8, 27, 28, 56, 24, 25, 44, 5, 0, 51, 54, 55, 19, 57, 16, 46, 40, 39, 52, 14, 60, 29, 58, 38, 15, 50, 22, 48, 32, 41, 63, 33, 34, 26, 36, 45, 10, 43, 12, 20, 53] 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)) = 10.491861718116256 V(r_1,...,r_N) = 10.49186171811626 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 -3.01429146e+01 -2.18407661e+01 -4.36609565e+01 | -3.01429146e+01 -2.18407661e+01 -4.36609565e+01 1 2.78755605e+01 2.14853702e+01 4.10726458e+01 | 2.78755605e+01 2.14853702e+01 4.10726458e+01 2 4.13019647e-01 7.87256272e-01 1.88245055e-01 | 4.13019647e-01 7.87256272e-01 1.88245055e-01 3 -7.21871150e-01 7.71765823e-02 -3.01590426e-01 | -7.21871150e-01 7.71765823e-02 -3.01590426e-01 4 3.81753639e+00 -1.35120768e+00 2.57044652e+00 | 3.81753639e+00 -1.35120768e+00 2.57044652e+00 5 1.86988853e+01 -1.42832646e+01 -1.17101007e+01 | 1.86988853e+01 -1.42832646e+01 -1.17101007e+01 6 -1.22951738e+00 2.17082437e+00 7.64072636e-01 | -1.22951738e+00 2.17082437e+00 7.64072636e-01 7 -1.06523161e+01 1.32620258e+01 -1.07804955e+01 | -1.06523161e+01 1.32620258e+01 -1.07804955e+01 8 -1.05506042e+01 -3.00901994e+01 -1.28786871e+01 | -1.05506042e+01 -3.00901994e+01 -1.28786871e+01 9 -8.50919617e+00 2.25554383e+01 1.61954752e+01 | -8.50919617e+00 2.25554383e+01 1.61954752e+01 10 1.85196691e+01 7.64509430e+00 -4.45608083e+00 | 1.85196691e+01 7.64509430e+00 -4.45608083e+00 11 -1.10198246e-01 7.22787052e-01 2.09464336e-01 | -1.10198246e-01 7.22787052e-01 2.09464336e-01 12 2.84070013e-01 -7.61298413e-02 6.94455275e-01 | 2.84070013e-01 -7.61298413e-02 6.94455275e-01 13 4.31560189e+00 -9.11086294e+00 -1.10350077e+01 | 4.31560189e+00 -9.11086294e+00 -1.10350077e+01 14 -2.30901560e+01 -5.25159917e+00 -5.45910016e+00 | -2.30901560e+01 -5.25159917e+00 -5.45910016e+00 15 2.73538254e+01 -1.37106383e+00 -2.73816989e+00 | 2.73538254e+01 -1.37106383e+00 -2.73816989e+00 16 -8.33132721e-01 -1.86046914e+00 -5.53697711e-01 | -8.33132721e-01 -1.86046914e+00 -5.53697711e-01 17 5.31439744e-01 1.15623896e+00 1.50410279e+00 | 5.31439744e-01 1.15623896e+00 1.50410279e+00 18 -4.99612715e+00 -5.23688897e+00 -1.34771143e+01 | -4.99612715e+00 -5.23688897e+00 -1.34771143e+01 19 4.71776634e+00 6.64797485e+00 1.27309131e+01 | 4.71776634e+00 6.64797485e+00 1.27309131e+01 20 -6.12311806e+00 -4.15700375e+00 -3.69859881e+00 | -6.12311806e+00 -4.15700375e+00 -3.69859881e+00 21 -1.82124019e+00 -1.21832803e+01 2.41073176e+01 | -1.82124019e+00 -1.21832803e+01 2.41073176e+01 22 -2.67243576e+00 -2.00664813e-01 -2.67210699e+00 | -2.67243576e+00 -2.00664813e-01 -2.67210699e+00 23 -3.05527545e+01 3.80305036e+01 -4.76659885e+01 | -3.05527545e+01 3.80305036e+01 -4.76659885e+01 24 2.68909551e-01 1.81950496e-01 2.29651981e-01 | 2.68909551e-01 1.81950496e-01 2.29651981e-01 25 -1.21479277e+01 7.46093460e+00 -1.05704654e+01 | -1.21479277e+01 7.46093460e+00 -1.05704654e+01 26 -2.75777563e-01 -4.29757306e-01 2.37334898e-01 | -2.75777563e-01 -4.29757306e-01 2.37334898e-01 27 1.23528494e-01 1.08970973e-01 2.28732015e-01 | 1.23528494e-01 1.08970973e-01 2.28732015e-01 28 -4.73742880e+00 -2.52483999e+01 1.48831650e+00 | -4.73742880e+00 -2.52483999e+01 1.48831650e+00 29 1.88802719e+01 1.59291083e+01 5.72404535e+00 | 1.88802719e+01 1.59291083e+01 5.72404535e+00 30 9.78935562e+00 1.42856258e+01 -2.16845791e+01 | 9.78935562e+00 1.42856258e+01 -2.16845791e+01 31 -1.58180210e+01 1.25410861e+01 -1.48598930e+01 | -1.58180210e+01 1.25410861e+01 -1.48598930e+01 32 -3.90786621e+00 -7.52091400e+00 -2.12767864e+00 | -3.90786621e+00 -7.52091400e+00 -2.12767864e+00 33 1.67432747e+01 -2.41052441e+01 -3.27487522e+00 | 1.67432747e+01 -2.41052441e+01 -3.27487522e+00 34 -7.46438225e+00 -4.81747161e-01 2.15070874e+01 | -7.46438225e+00 -4.81747161e-01 2.15070874e+01 35 -1.44372962e+01 1.61038837e+01 -1.34094257e+01 | -1.44372962e+01 1.61038837e+01 -1.34094257e+01 36 4.97758874e-02 2.13563379e-01 1.48723530e-01 | 4.97758874e-02 2.13563379e-01 1.48723530e-01 37 -7.89563617e-01 1.48118736e-01 -7.00648026e-01 | -7.89563617e-01 1.48118736e-01 -7.00648026e-01 38 -1.18599498e+01 2.47095722e+01 1.18711890e+01 | -1.18599498e+01 2.47095722e+01 1.18711890e+01 39 8.24331064e-01 -2.16894142e-01 -5.45264070e-01 | 8.24331064e-01 -2.16894142e-01 -5.45264070e-01 40 -7.56978711e+00 -8.10092193e+00 2.64209418e+00 | -7.56978711e+00 -8.10092193e+00 2.64209418e+00 41 6.14459293e+00 7.13604306e+00 -1.91892921e+00 | 6.14459293e+00 7.13604306e+00 -1.91892921e+00 42 -3.43907569e+00 7.62700394e+00 9.74718681e+00 | -3.43907569e+00 7.62700394e+00 9.74718681e+00 43 2.42467692e+01 -3.42113821e+01 -1.69362725e+01 | 2.42467692e+01 -3.42113821e+01 -1.69362725e+01 44 1.23752406e-01 1.21407711e+00 8.95702249e-01 | 1.23752406e-01 1.21407711e+00 8.95702249e-01 45 -3.73988349e-01 -9.59720320e-01 -1.11665198e+00 | -3.73988349e-01 -9.59720320e-01 -1.11665198e+00 46 1.28262517e+01 -1.75812793e+01 1.20634743e+01 | 1.28262517e+01 -1.75812793e+01 1.20634743e+01 47 -1.00117660e+01 -9.38222920e+00 1.28056365e+01 | -1.00117660e+01 -9.38222920e+00 1.28056365e+01 48 -1.88823626e+00 5.86865758e+00 -4.60431956e+00 | -1.88823626e+00 5.86865758e+00 -4.60431956e+00 49 -8.89130143e+00 -1.27832083e+01 2.07314082e+01 | -8.89130143e+00 -1.27832083e+01 2.07314082e+01 50 3.85602445e+01 -2.44009762e+01 2.83274568e+01 | 3.85602445e+01 -2.44009762e+01 2.83274568e+01 51 1.04470541e+00 1.46069371e+00 1.94286767e+00 | 1.04470541e+00 1.46069371e+00 1.94286767e+00 52 -1.79304747e+01 -1.64647340e+01 -1.78876171e+01 | -1.79304747e+01 -1.64647340e+01 -1.78876171e+01 53 1.78861624e+01 1.52873973e+01 1.97155360e+01 | 1.78861624e+01 1.52873973e+01 1.97155360e+01 54 1.15393962e+00 3.27553911e-02 2.31016658e-01 | 1.15393962e+00 3.27553911e-02 2.31016658e-01 55 -3.92773442e-01 -4.40472635e-01 -9.23221482e-01 | -3.92773442e-01 -4.40472635e-01 -9.23221482e-01 56 -3.32338342e+00 8.87985861e+00 6.71585858e+00 | -3.32338342e+00 8.87985861e+00 6.71585858e+00 57 7.03179505e+00 -6.70653938e+00 -8.94049955e+00 | 7.03179505e+00 -6.70653938e+00 -8.94049955e+00 58 9.65759345e+00 -1.68384913e+01 1.26944628e+01 | 9.65759345e+00 -1.68384913e+01 1.26944628e+01 59 3.91951825e+00 6.27746743e+00 5.18737146e+00 | 3.91951825e+00 6.27746743e+00 5.18737146e+00 60 -1.31883434e+01 4.45397896e+01 6.71273315e+00 | -1.31883434e+01 4.45397896e+01 6.71273315e+00 61 1.67050996e+00 1.19314681e+00 1.38379193e+00 | 1.67050996e+00 1.19314681e+00 1.38379193e+00 62 -6.57626873e+00 8.05099131e+00 7.91473113e+00 | -6.57626873e+00 8.05099131e+00 7.91473113e+00 63 -4.43462486e-01 -9.05074665e-01 -5.95511524e-01 | -4.43462486e-01 -9.05074665e-01 -5.95511524e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Zr (Configuration in file "config-Zr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [16, 23, 60, 49, 56, 20, 51, 26, 22, 34, 40, 27, 41, 59, 44, 57, 0, 19, 61, 17, 5, 42, 8, 1, 39, 43, 7, 11, 47, 62, 33, 63, 35, 30, 9, 32, 37, 36, 55, 24, 10, 12, 21, 25, 14, 58, 48, 28, 46, 3, 54, 6, 53, 52, 50, 38, 4, 15, 45, 13, 2, 18, 29, 31] 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)) = 15.66530523309962 V(r_1,...,r_N) = 15.665305233099591 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 -2.65151441e+00 -1.58774398e+00 -1.58415966e+01 | -2.65151441e+00 -1.58774398e+00 -1.58415966e+01 1 -4.77795405e+00 -3.09079181e-01 1.07193022e+01 | -4.77795405e+00 -3.09079181e-01 1.07193022e+01 2 -1.05705051e+01 -5.36571190e+00 -6.76705331e+00 | -1.05705051e+01 -5.36571190e+00 -6.76705331e+00 3 5.52016485e+00 1.01210764e+01 5.17510866e+00 | 5.52016485e+00 1.01210764e+01 5.17510866e+00 4 3.29223434e+00 -5.81362380e+00 -6.47884975e+00 | 3.29223434e+00 -5.81362380e+00 -6.47884975e+00 5 5.05276783e+00 -1.73039970e+01 4.00222197e+00 | 5.05276783e+00 -1.73039970e+01 4.00222197e+00 6 -1.75161857e+00 -4.70440723e+01 -9.53683558e+00 | -1.75161857e+00 -4.70440723e+01 -9.53683558e+00 7 -2.68393060e+00 3.68060630e+01 1.25507145e+01 | -2.68393060e+00 3.68060630e+01 1.25507145e+01 8 -2.48638343e+00 -1.76127875e+00 -1.64511869e+00 | -2.48638343e+00 -1.76127875e+00 -1.64511869e+00 9 1.01826171e+00 1.38887086e+00 -3.83764606e-01 | 1.01826171e+00 1.38887086e+00 -3.83764606e-01 10 -9.02861513e+00 -1.37479626e+01 -2.34219130e+01 | -9.02861513e+00 -1.37479626e+01 -2.34219130e+01 11 8.79647491e+00 9.23355612e+00 1.95731321e+01 | 8.79647491e+00 9.23355612e+00 1.95731321e+01 12 5.13309039e+00 -2.74734865e+00 -8.93262407e-01 | 5.13309039e+00 -2.74734865e+00 -8.93262407e-01 13 1.69688484e+01 -1.52377038e+01 -3.17593745e+00 | 1.69688484e+01 -1.52377038e+01 -3.17593745e+00 14 -8.10422192e+00 -1.19340436e+01 8.34529771e+00 | -8.10422192e+00 -1.19340436e+01 8.34529771e+00 15 -7.16390145e+00 -1.30958581e+00 -1.16762500e+01 | -7.16390145e+00 -1.30958581e+00 -1.16762500e+01 16 -2.29176790e+01 -1.69754271e+01 -2.37697020e+01 | -2.29176790e+01 -1.69754271e+01 -2.37697020e+01 17 2.27638179e+01 4.23904345e+00 2.13156848e+01 | 2.27638179e+01 4.23904345e+00 2.13156848e+01 18 -4.27661086e+00 6.67113444e-01 -2.53164587e+00 | -4.27661086e+00 6.67113444e-01 -2.53164587e+00 19 8.78797502e+00 8.25073916e+00 1.90295565e+00 | 8.78797502e+00 8.25073916e+00 1.90295565e+00 20 1.25304418e+01 4.47731946e+00 -6.04049410e+00 | 1.25304418e+01 4.47731946e+00 -6.04049410e+00 21 -4.90559459e+00 1.60101680e+00 -3.38392558e+00 | -4.90559459e+00 1.60101680e+00 -3.38392558e+00 22 1.93812345e+00 3.37885813e+00 1.99663224e+00 | 1.93812345e+00 3.37885813e+00 1.99663224e+00 23 -4.12970797e+00 6.58418462e+00 -5.62537129e+00 | -4.12970797e+00 6.58418462e+00 -5.62537129e+00 24 9.39776975e-01 2.06128730e+00 -1.07369460e+01 | 9.39776975e-01 2.06128730e+00 -1.07369460e+01 25 -7.40698839e-01 -1.43655403e+01 -8.29326797e+00 | -7.40698839e-01 -1.43655403e+01 -8.29326797e+00 26 -1.08376062e+01 -6.28626226e+00 -1.48369136e+01 | -1.08376062e+01 -6.28626226e+00 -1.48369136e+01 27 6.95824521e+00 5.45455097e+00 1.51799930e+01 | 6.95824521e+00 5.45455097e+00 1.51799930e+01 28 1.82114948e+01 4.82710726e+00 -5.34194779e-01 | 1.82114948e+01 4.82710726e+00 -5.34194779e-01 29 6.08415687e+00 -1.25773337e+01 -3.48001819e+00 | 6.08415687e+00 -1.25773337e+01 -3.48001819e+00 30 1.05501208e+00 1.79785392e+01 1.78672797e+01 | 1.05501208e+00 1.79785392e+01 1.78672797e+01 31 -5.71826171e+00 8.69565670e+00 -5.63703083e+00 | -5.71826171e+00 8.69565670e+00 -5.63703083e+00 32 -1.17498256e+01 -1.54669973e+01 -1.95341143e+01 | -1.17498256e+01 -1.54669973e+01 -1.95341143e+01 33 1.13487556e+01 1.35321688e+01 1.27123086e+01 | 1.13487556e+01 1.35321688e+01 1.27123086e+01 34 -5.71749031e+00 1.11972333e+01 -5.31361515e+00 | -5.71749031e+00 1.11972333e+01 -5.31361515e+00 35 5.17139548e+00 -8.64885946e+00 -1.05505532e+01 | 5.17139548e+00 -8.64885946e+00 -1.05505532e+01 36 7.35907022e-01 -2.56203881e+00 -1.38471627e+00 | 7.35907022e-01 -2.56203881e+00 -1.38471627e+00 37 -4.70521757e+00 1.43223551e+00 5.94730417e+00 | -4.70521757e+00 1.43223551e+00 5.94730417e+00 38 -2.78314870e+00 5.21553375e+00 6.89845959e+00 | -2.78314870e+00 5.21553375e+00 6.89845959e+00 39 -1.18548271e+01 1.33699491e-01 6.51664702e+00 | -1.18548271e+01 1.33699491e-01 6.51664702e+00 40 -1.14245848e+01 -8.74494495e+00 -8.53944740e+00 | -1.14245848e+01 -8.74494495e+00 -8.53944740e+00 41 1.18702673e+01 4.85262043e+00 -2.47816499e+00 | 1.18702673e+01 4.85262043e+00 -2.47816499e+00 42 -1.51441995e+01 2.01626415e+01 3.00690800e+00 | -1.51441995e+01 2.01626415e+01 3.00690800e+00 43 1.84785739e+00 -1.19765207e+00 1.77343000e+00 | 1.84785739e+00 -1.19765207e+00 1.77343000e+00 44 -6.69289881e+00 -9.92251868e+00 3.30374966e+00 | -6.69289881e+00 -9.92251868e+00 3.30374966e+00 45 8.65612723e+00 8.99887306e+00 9.48360831e+00 | 8.65612723e+00 8.99887306e+00 9.48360831e+00 46 1.34007520e+00 -2.92544900e+00 -8.23781410e+00 | 1.34007520e+00 -2.92544900e+00 -8.23781410e+00 47 4.33077534e+00 4.24113611e+00 5.91415969e+00 | 4.33077534e+00 4.24113611e+00 5.91415969e+00 48 -5.93424923e+00 5.44085056e+00 9.11266184e+00 | -5.93424923e+00 5.44085056e+00 9.11266184e+00 49 1.07479871e+01 -1.90830406e+01 -5.77551980e+00 | 1.07479871e+01 -1.90830406e+01 -5.77551980e+00 50 -1.87853379e+01 -2.37804625e+01 -2.52848276e+01 | -1.87853379e+01 -2.37804625e+01 -2.52848276e+01 51 2.22865146e+01 1.78777689e+01 2.49227913e+01 | 2.22865146e+01 1.78777689e+01 2.49227913e+01 52 7.03648147e+00 9.88020466e+00 6.88505695e+00 | 7.03648147e+00 9.88020466e+00 6.88505695e+00 53 -3.98745651e+00 1.68500145e+00 9.03111988e-01 | -3.98745651e+00 1.68500145e+00 9.03111988e-01 54 -2.43063301e+01 7.73425482e+00 2.78026463e+00 | -2.43063301e+01 7.73425482e+00 2.78026463e+00 55 1.36882430e+01 1.16514801e+01 1.14615876e+01 | 1.36882430e+01 1.16514801e+01 1.14615876e+01 56 -3.64487957e+00 8.29793248e+00 9.35703815e+00 | -3.64487957e+00 8.29793248e+00 9.35703815e+00 57 -7.33649060e+00 4.28576368e+00 -1.48284945e+01 | -7.33649060e+00 4.28576368e+00 -1.48284945e+01 58 -9.52157111e+00 1.99517469e+00 -7.40846790e+00 | -9.52157111e+00 1.99517469e+00 -7.40846790e+00 59 1.04104387e+01 4.25413558e+00 1.81925354e+01 | 1.04104387e+01 4.25413558e+00 1.81925354e+01 60 6.11042989e+00 -1.74191303e+01 3.48403674e+00 | 6.11042989e+00 -1.74191303e+01 3.48403674e+00 61 5.02697428e+00 1.47844325e+01 1.05707766e+01 | 5.02697428e+00 1.47844325e+01 1.05707766e+01 62 -1.18700589e+01 -1.38152248e+01 -7.40089686e+00 | -1.18700589e+01 -1.38152248e+01 -7.40089686e+00 63 1.25442540e+01 1.45149090e+01 9.57196485e+00 | 1.25442540e+01 1.45149090e+01 9.57196485e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ag Cu Zr (Configuration in file "config-AgCuZr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [63, 5, 57, 25, 16, 1, 40, 38, 43, 30, 21, 50, 20, 32, 34, 36, 4, 44, 62, 28, 12, 10, 61, 29, 41, 3, 54, 35, 19, 23, 9, 60, 13, 42, 14, 27, 15, 45, 7, 58, 6, 24, 33, 8, 17, 37, 59, 52, 51, 56, 11, 48, 47, 53, 26, 55, 49, 2, 39, 46, 31, 22, 18, 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)) = 150.72645319809754 V(r_1,...,r_N) = 150.72645319809757 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 1.02348865e+00 5.74795389e-01 4.64136944e-01 | 1.02348865e+00 5.74795389e-01 4.64136944e-01 1 -1.79591858e+01 -7.19175869e+00 1.60217273e+01 | -1.79591858e+01 -7.19175869e+00 1.60217273e+01 2 5.14402447e+00 1.40660933e+01 -1.37860931e+01 | 5.14402447e+00 1.40660933e+01 -1.37860931e+01 3 -1.07513211e+01 6.95765708e+00 -2.43062435e+01 | -1.07513211e+01 6.95765708e+00 -2.43062435e+01 4 -1.00335644e+01 -2.19039569e+01 -1.03186691e+01 | -1.00335644e+01 -2.19039569e+01 -1.03186691e+01 5 2.72023199e+01 1.20530781e+01 -2.24995194e+00 | 2.72023199e+01 1.20530781e+01 -2.24995194e+00 6 -1.45266989e+01 -7.23679316e+00 -2.29611708e+01 | -1.45266989e+01 -7.23679316e+00 -2.29611708e+01 7 -5.82500790e+00 1.60046799e+01 5.24821068e+00 | -5.82500790e+00 1.60046799e+01 5.24821068e+00 8 4.76125764e+00 -9.64400737e+00 -4.74637534e+00 | 4.76125764e+00 -9.64400737e+00 -4.74637534e+00 9 6.95645375e+00 1.68506850e+00 3.05108934e+00 | 6.95645375e+00 1.68506850e+00 3.05108934e+00 10 -2.97969854e-01 7.94296845e-02 -7.26165870e-01 | -2.97969854e-01 7.94296845e-02 -7.26165870e-01 11 1.36010039e+01 -1.54715198e+01 -3.52089389e+00 | 1.36010039e+01 -1.54715198e+01 -3.52089389e+00 12 -1.48088437e+01 -1.78901657e+01 -1.87096014e+01 | -1.48088437e+01 -1.78901657e+01 -1.87096014e+01 13 1.50734540e+01 1.79859709e+01 1.84326861e+01 | 1.50734540e+01 1.79859709e+01 1.84326861e+01 14 1.73938002e+01 -2.31374719e+01 1.14867982e+01 | 1.73938002e+01 -2.31374719e+01 1.14867982e+01 15 2.39447905e+01 -2.79688067e+01 -3.34903444e+01 | 2.39447905e+01 -2.79688067e+01 -3.34903444e+01 16 -3.89740836e+01 -7.27117533e+01 -3.73250549e+01 | -3.89740836e+01 -7.27117533e+01 -3.73250549e+01 17 2.19315681e+01 5.79069622e+01 3.59655668e+01 | 2.19315681e+01 5.79069622e+01 3.59655668e+01 18 1.73583201e+01 1.39092862e+01 7.53113245e-01 | 1.73583201e+01 1.39092862e+01 7.53113245e-01 19 6.05750989e-01 1.48820093e+00 3.58043686e-01 | 6.05750989e-01 1.48820093e+00 3.58043686e-01 20 -6.47502381e+01 3.48729715e+00 -3.59633287e+01 | -6.47502381e+01 3.48729715e+00 -3.59633287e+01 21 4.59533058e+01 6.23326943e+00 4.67227986e+01 | 4.59533058e+01 6.23326943e+00 4.67227986e+01 22 -2.49300297e-01 -9.58804576e-01 3.74822612e-01 | -2.49300297e-01 -9.58804576e-01 3.74822612e-01 23 -6.73981081e+00 1.02444935e+01 -9.28565869e+00 | -6.73981081e+00 1.02444935e+01 -9.28565869e+00 24 9.88233053e-01 1.35863400e+00 -1.08480983e+00 | 9.88233053e-01 1.35863400e+00 -1.08480983e+00 25 -3.43147656e+01 2.52751885e+01 -1.62231622e+01 | -3.43147656e+01 2.52751885e+01 -1.62231622e+01 26 -2.91512715e+01 -4.70203099e+01 -2.44779914e+01 | -2.91512715e+01 -4.70203099e+01 -2.44779914e+01 27 3.13004515e+01 4.99826231e+01 2.25745272e+01 | 3.13004515e+01 4.99826231e+01 2.25745272e+01 28 1.80454036e+01 -1.53620544e+01 2.32411156e+01 | 1.80454036e+01 -1.53620544e+01 2.32411156e+01 29 3.43889514e+01 -6.13833617e+00 -5.61957974e+01 | 3.43889514e+01 -6.13833617e+00 -5.61957974e+01 30 -1.39191612e-01 6.18856391e+00 -1.22490328e+00 | -1.39191612e-01 6.18856391e+00 -1.22490328e+00 31 3.25085855e+00 4.53442470e+00 1.40675755e+00 | 3.25085855e+00 4.53442470e+00 1.40675755e+00 32 -1.23672661e+01 9.34118878e-01 -2.42908504e+01 | -1.23672661e+01 9.34118878e-01 -2.42908504e+01 33 1.14324139e+01 2.60849083e+00 2.08486385e+01 | 1.14324139e+01 2.60849083e+00 2.08486385e+01 34 4.20852470e+00 -1.91667172e+00 3.21489446e+01 | 4.20852470e+00 -1.91667172e+00 3.21489446e+01 35 -1.33844296e+01 1.40193716e+01 -3.74446408e+01 | -1.33844296e+01 1.40193716e+01 -3.74446408e+01 36 -8.34924177e+01 -7.91043876e+01 -4.28972205e+01 | -8.34924177e+01 -7.91043876e+01 -4.28972205e+01 37 8.12002220e+01 7.30628400e+01 4.86085606e+01 | 8.12002220e+01 7.30628400e+01 4.86085606e+01 38 5.69580760e-01 -2.95183716e-02 7.46167451e-02 | 5.69580760e-01 -2.95183716e-02 7.46167451e-02 39 -2.00107996e-01 -1.07335744e+00 4.82257085e-01 | -2.00107996e-01 -1.07335744e+00 4.82257085e-01 40 -8.66357088e+00 -7.85609294e+00 -2.29024915e+01 | -8.66357088e+00 -7.85609294e+00 -2.29024915e+01 41 1.09882467e+01 7.24987177e+00 2.14631820e+01 | 1.09882467e+01 7.24987177e+00 2.14631820e+01 42 -2.88507482e+01 -2.69928432e+01 -2.07111103e+01 | -2.88507482e+01 -2.69928432e+01 -2.07111103e+01 43 2.82802715e+01 2.64443437e+01 2.11144042e+01 | 2.82802715e+01 2.64443437e+01 2.11144042e+01 44 -1.95180800e+01 -7.15581891e+00 -1.01527806e+01 | -1.95180800e+01 -7.15581891e+00 -1.01527806e+01 45 1.94317037e+01 8.22075091e+00 9.78763039e+00 | 1.94317037e+01 8.22075091e+00 9.78763039e+00 46 1.64480262e+01 -1.37440865e+01 3.33882099e+01 | 1.64480262e+01 -1.37440865e+01 3.33882099e+01 47 -4.45549492e+00 -4.84516486e+00 6.90907607e+00 | -4.45549492e+00 -4.84516486e+00 6.90907607e+00 48 -1.13344203e+00 1.64772410e+00 -4.81228797e-01 | -1.13344203e+00 1.64772410e+00 -4.81228797e-01 49 3.12974971e+00 1.08915569e-01 1.87556300e+00 | 3.12974971e+00 1.08915569e-01 1.87556300e+00 50 5.04441870e+00 -1.34587988e+01 4.99453892e+00 | 5.04441870e+00 -1.34587988e+01 4.99453892e+00 51 -2.84221534e+00 1.31428088e+01 -1.27561363e+01 | -2.84221534e+00 1.31428088e+01 -1.27561363e+01 52 -2.79184758e-01 2.11762590e+00 2.68202457e-01 | -2.79184758e-01 2.11762590e+00 2.68202457e-01 53 -2.99608753e+00 -6.04032888e+00 6.06614590e+00 | -2.99608753e+00 -6.04032888e+00 6.06614590e+00 54 -5.91815453e+00 3.32980434e+00 2.19258736e+00 | -5.91815453e+00 3.32980434e+00 2.19258736e+00 55 9.91721360e-01 -1.23295316e+00 -1.37841716e+00 | 9.91721360e-01 -1.23295316e+00 -1.37841716e+00 56 -1.98019386e+01 2.15995080e+01 3.31192358e+01 | -1.98019386e+01 2.15995080e+01 3.31192358e+01 57 -4.88537531e+00 6.56758296e+00 -1.23955724e+00 | -4.88537531e+00 6.56758296e+00 -1.23955724e+00 58 -3.61605729e+01 2.08073928e+00 5.03527725e+01 | -3.61605729e+01 2.08073928e+00 5.03527725e+01 59 3.96569526e+00 5.04056433e+00 6.25342697e+00 | 3.96569526e+00 5.04056433e+00 6.25342697e+00 60 -5.14774351e+00 -1.24415504e+01 -1.95957164e+01 | -5.14774351e+00 -1.24415504e+01 -1.95957164e+01 61 1.46109095e+01 1.50576410e+01 1.89209793e+01 | 1.46109095e+01 1.50576410e+01 1.89209793e+01 62 8.72245624e+00 -3.50453992e+00 7.36926157e+00 | 8.72245624e+00 -3.50453992e+00 7.36926157e+00 63 6.70707008e-01 -1.21656715e+00 -1.89326202e+00 | 6.70707008e-01 -1.21656715e+00 -1.89326202e+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.