!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_AlmyrasSangiovanniSarakinos_2019_NAlTi__MO_958395190627_001 Supported species : Al N Ti 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 = [38, 55, 35, 16, 32, 44, 25, 21, 56, 14, 19, 63, 24, 20, 9, 62, 3, 50, 39, 10, 13, 7, 36, 30, 12, 6, 33, 60, 40, 31, 23, 29, 4, 26, 37, 2, 22, 34, 0, 18, 28, 49, 51, 58, 5, 47, 59, 45, 61, 41, 17, 42, 57, 54, 53, 1, 8, 52, 43, 46, 27, 48, 15, 11] 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)) = 31.842118556600287 V(r_1,...,r_N) = 31.84211855660022 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 -3.46030851e+00 -2.82697512e+00 -2.59473149e+00 | -3.46030851e+00 -2.82697512e+00 -2.59473149e+00 1 -8.29242252e+00 -2.48959273e+01 1.74416672e+01 | -8.29242252e+00 -2.48959273e+01 1.74416672e+01 2 7.32071889e-03 1.11584735e+01 -2.79529585e+01 | 7.32071889e-03 1.11584735e+01 -2.79529585e+01 3 1.96554402e+00 1.72794709e+01 3.52307447e+00 | 1.96554402e+00 1.72794709e+01 3.52307447e+00 4 -1.65358828e+00 -3.22778895e+00 -4.42755426e+00 | -1.65358828e+00 -3.22778895e+00 -4.42755426e+00 5 3.07024613e+00 5.85779553e+00 -1.79142576e+00 | 3.07024613e+00 5.85779553e+00 -1.79142576e+00 6 -2.54318048e+00 -2.36304186e+00 -3.55775833e+00 | -2.54318048e+00 -2.36304186e+00 -3.55775833e+00 7 -2.29490756e+01 6.03853348e+01 -3.63316820e+01 | -2.29490756e+01 6.03853348e+01 -3.63316820e+01 8 -4.90861609e+00 -1.96683367e+00 -3.66600628e+00 | -4.90861609e+00 -1.96683367e+00 -3.66600628e+00 9 -4.05514310e+00 4.86850744e+00 1.58578286e-02 | -4.05514310e+00 4.86850744e+00 1.58578286e-02 10 1.73494444e-01 -2.29964129e-01 -2.95079928e+00 | 1.73494444e-01 -2.29964129e-01 -2.95079928e+00 11 1.57525614e+00 1.66075889e+00 1.23469864e+00 | 1.57525614e+00 1.66075889e+00 1.23469864e+00 12 -3.49871092e+01 -2.34694374e+01 -2.15338624e+01 | -3.49871092e+01 -2.34694374e+01 -2.15338624e+01 13 4.02917547e+01 2.02316089e+01 2.85518594e+01 | 4.02917547e+01 2.02316089e+01 2.85518594e+01 14 1.19224982e+01 -4.73717830e+00 6.59500968e+00 | 1.19224982e+01 -4.73717830e+00 6.59500968e+00 15 -6.22186011e-02 -5.12723883e-01 1.35115376e+00 | -6.22186011e-02 -5.12723883e-01 1.35115376e+00 16 -6.63006518e+00 -7.23858777e+00 -1.42894316e+01 | -6.63006518e+00 -7.23858777e+00 -1.42894316e+01 17 5.80879006e+00 5.25248729e+00 1.52178390e+01 | 5.80879006e+00 5.25248729e+00 1.52178390e+01 18 2.11446694e+00 7.26540213e-01 -8.37247230e-01 | 2.11446694e+00 7.26540213e-01 -8.37247230e-01 19 -4.51465544e+01 2.70428363e+01 -3.01190789e+01 | -4.51465544e+01 2.70428363e+01 -3.01190789e+01 20 -1.72776450e+01 -7.93046892e+00 -8.59968879e+00 | -1.72776450e+01 -7.93046892e+00 -8.59968879e+00 21 1.61941535e+01 1.22419971e+01 9.31073107e+00 | 1.61941535e+01 1.22419971e+01 9.31073107e+00 22 -1.54760561e+00 -1.39965847e+00 -1.99420585e+00 | -1.54760561e+00 -1.39965847e+00 -1.99420585e+00 23 -3.84037334e-01 5.07394027e+00 -1.74569902e+00 | -3.84037334e-01 5.07394027e+00 -1.74569902e+00 24 -2.83607751e-01 -1.16312146e-01 3.61320025e-02 | -2.83607751e-01 -1.16312146e-01 3.61320025e-02 25 -1.55552780e+01 1.42046280e+01 -1.27366221e+01 | -1.55552780e+01 1.42046280e+01 -1.27366221e+01 26 -1.89519548e+00 -7.97826153e-01 -1.15886573e+00 | -1.89519548e+00 -7.97826153e-01 -1.15886573e+00 27 1.83271075e+00 5.72991768e-01 1.58435736e+00 | 1.83271075e+00 5.72991768e-01 1.58435736e+00 28 1.20156131e+01 -1.58978839e+01 1.01478154e+01 | 1.20156131e+01 -1.58978839e+01 1.01478154e+01 29 2.67601185e+00 2.40561473e+00 2.41090541e+00 | 2.67601185e+00 2.40561473e+00 2.41090541e+00 30 4.42606445e+01 -2.67036365e+01 2.97939773e+01 | 4.42606445e+01 -2.67036365e+01 2.97939773e+01 31 -2.09208091e+01 7.48834824e+00 -1.11745618e+01 | -2.09208091e+01 7.48834824e+00 -1.11745618e+01 32 -4.02036644e+00 6.95614719e-01 -5.70668616e-01 | -4.02036644e+00 6.95614719e-01 -5.70668616e-01 33 -6.55861243e+00 5.74400462e+00 -1.50177751e+00 | -6.55861243e+00 5.74400462e+00 -1.50177751e+00 34 2.70556609e+01 -6.33823140e+01 3.66114188e+01 | 2.70556609e+01 -6.33823140e+01 3.66114188e+01 35 -3.87799367e+00 -7.54740111e+00 4.32293607e+00 | -3.87799367e+00 -7.54740111e+00 4.32293607e+00 36 8.42666529e+00 -5.89947098e+00 3.72006896e+00 | 8.42666529e+00 -5.89947098e+00 3.72006896e+00 37 -9.62341060e+00 -1.05224653e+01 7.14035805e+00 | -9.62341060e+00 -1.05224653e+01 7.14035805e+00 38 -7.16420913e+00 -4.30979820e+00 -6.12093618e+00 | -7.16420913e+00 -4.30979820e+00 -6.12093618e+00 39 -1.02265925e+01 -1.00471333e+01 1.62970402e+01 | -1.02265925e+01 -1.00471333e+01 1.62970402e+01 40 1.02875335e-01 -2.63701761e+00 1.73884349e+00 | 1.02875335e-01 -2.63701761e+00 1.73884349e+00 41 -2.16277248e+01 3.74475235e+01 -2.05028252e+01 | -2.16277248e+01 3.74475235e+01 -2.05028252e+01 42 -4.83987564e+01 -5.22049172e+01 -4.52936938e+01 | -4.83987564e+01 -5.22049172e+01 -4.52936938e+01 43 4.69552027e+01 5.19979138e+01 4.53761909e+01 | 4.69552027e+01 5.19979138e+01 4.53761909e+01 44 2.44866409e+01 -3.70249711e+01 1.89943650e+01 | 2.44866409e+01 -3.70249711e+01 1.89943650e+01 45 3.09029868e-01 5.99475891e-01 6.39058249e-01 | 3.09029868e-01 5.99475891e-01 6.39058249e-01 46 7.27666948e+00 1.13591663e+01 -6.44502749e+00 | 7.27666948e+00 1.13591663e+01 -6.44502749e+00 47 3.69959854e+00 -3.71990304e+00 1.00643044e+00 | 3.69959854e+00 -3.71990304e+00 1.00643044e+00 48 -3.98632098e+00 3.82901836e+00 4.55165326e+00 | -3.98632098e+00 3.82901836e+00 4.55165326e+00 49 -9.05702765e+00 -4.86033585e+00 6.79221457e+00 | -9.05702765e+00 -4.86033585e+00 6.79221457e+00 50 7.71471355e-01 -1.25047025e+01 -1.56192631e+01 | 7.71471355e-01 -1.25047025e+01 -1.56192631e+01 51 1.19735191e+01 1.21692655e+01 1.27845915e+01 | 1.19735191e+01 1.21692655e+01 1.27845915e+01 52 1.62064812e+01 1.61391386e+01 -9.96820470e+00 | 1.62064812e+01 1.61391386e+01 -9.96820470e+00 53 -3.69844090e+00 4.01408645e+00 5.90082855e-01 | -3.69844090e+00 4.01408645e+00 5.90082855e-01 54 -2.74901429e+00 -2.66966795e+00 -2.07304544e+00 | -2.74901429e+00 -2.66966795e+00 -2.07304544e+00 55 3.36578746e+00 2.67255120e+00 2.05970819e+00 | 3.36578746e+00 2.67255120e+00 2.05970819e+00 56 5.50898845e+00 4.47745688e+00 -5.28328841e+00 | 5.50898845e+00 4.47745688e+00 -5.28328841e+00 57 2.18558947e+01 -3.09165928e+01 -3.88913936e+01 | 2.18558947e+01 -3.09165928e+01 -3.88913936e+01 58 2.14557297e+01 -8.18791791e+00 1.20797416e+01 | 2.14557297e+01 -8.18791791e+00 1.20797416e+01 59 -3.92936854e-01 1.53204934e-01 1.33613391e-01 | -3.92936854e-01 1.53204934e-01 1.33613391e-01 60 -1.25375119e+01 -1.17812190e+01 -1.12136587e+01 | -1.25375119e+01 -1.17812190e+01 -1.12136587e+01 61 1.61320597e+01 7.40924239e+00 1.13682761e+01 | 1.61320597e+01 7.40924239e+00 1.13682761e+01 62 -2.34627044e+01 3.62841031e+01 3.69300441e+01 | -2.34627044e+01 3.62841031e+01 3.69300441e+01 63 4.43303400e-01 1.08697203e+00 5.94247677e-01 | 4.43303400e-01 1.08697203e+00 5.94247677e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = N (Configuration in file "config-N.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [17, 45, 30, 6, 29, 15, 3, 19, 62, 37, 60, 41, 32, 39, 56, 5, 55, 0, 35, 7, 21, 20, 25, 40, 33, 22, 27, 26, 44, 4, 2, 47, 12, 24, 51, 18, 57, 9, 61, 13, 23, 11, 58, 53, 28, 1, 52, 31, 63, 50, 49, 34, 46, 43, 59, 16, 14, 36, 42, 54, 10, 38, 8, 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)) = 59.03390098597506 V(r_1,...,r_N) = 59.03390098597508 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 3.87314603e+00 1.96216350e+00 3.44668513e+00 | 3.87314603e+00 1.96216350e+00 3.44668513e+00 1 -5.07393660e+00 -3.75480027e+00 -4.83316598e+00 | -5.07393660e+00 -3.75480027e+00 -4.83316598e+00 2 9.79944885e-01 2.43005128e+00 -4.22816771e-01 | 9.79944885e-01 2.43005128e+00 -4.22816771e-01 3 -1.72189281e+00 -2.11630585e-01 -4.04568841e+00 | -1.72189281e+00 -2.11630585e-01 -4.04568841e+00 4 3.38778988e+00 6.74257981e+00 7.64810078e+00 | 3.38778988e+00 6.74257981e+00 7.64810078e+00 5 -1.79183897e-01 -8.03257785e+00 -8.92901940e+00 | -1.79183897e-01 -8.03257785e+00 -8.92901940e+00 6 -1.85444272e+00 1.15885953e-01 -9.99211312e-01 | -1.85444272e+00 1.15885953e-01 -9.99211312e-01 7 2.24994227e+00 1.71128023e+00 8.57586132e+00 | 2.24994227e+00 1.71128023e+00 8.57586132e+00 8 4.95908954e-02 -4.72269571e-01 -1.45386022e+00 | 4.95908954e-02 -4.72269571e-01 -1.45386022e+00 9 2.74707101e+00 1.16249923e+00 -2.25332334e+00 | 2.74707101e+00 1.16249923e+00 -2.25332334e+00 10 7.23725453e-01 9.26020924e-01 3.45458212e+00 | 7.23725453e-01 9.26020924e-01 3.45458212e+00 11 -8.27460413e-01 -1.76562657e+00 -4.77449089e+00 | -8.27460413e-01 -1.76562657e+00 -4.77449089e+00 12 3.34996804e-01 -1.47949871e+00 1.08867593e-01 | 3.34996804e-01 -1.47949871e+00 1.08867593e-01 13 1.69499584e+00 -1.57940366e+00 8.97600427e-01 | 1.69499584e+00 -1.57940366e+00 8.97600427e-01 14 -3.14932795e+00 -3.34741409e+00 2.02445974e+00 | -3.14932795e+00 -3.34741409e+00 2.02445974e+00 15 -2.54909534e+00 1.44393879e+00 2.08787353e+00 | -2.54909534e+00 1.44393879e+00 2.08787353e+00 16 -9.55362680e-01 5.37847560e-01 -1.14369070e+00 | -9.55362680e-01 5.37847560e-01 -1.14369070e+00 17 2.95688134e-01 -7.04898229e-01 -1.95720797e+00 | 2.95688134e-01 -7.04898229e-01 -1.95720797e+00 18 -1.19948753e+00 5.85816101e-01 6.60620396e-01 | -1.19948753e+00 5.85816101e-01 6.60620396e-01 19 5.73880010e+00 -3.33140102e+00 2.51636777e+00 | 5.73880010e+00 -3.33140102e+00 2.51636777e+00 20 -2.94059886e-01 -3.66294776e+00 1.38860152e+00 | -2.94059886e-01 -3.66294776e+00 1.38860152e+00 21 -1.03174257e+00 -8.94676009e-02 -1.19541311e+00 | -1.03174257e+00 -8.94676009e-02 -1.19541311e+00 22 3.69766444e-01 2.41826587e+00 1.13434686e-01 | 3.69766444e-01 2.41826587e+00 1.13434686e-01 23 2.33039649e-01 -4.45656283e+00 2.07896709e+00 | 2.33039649e-01 -4.45656283e+00 2.07896709e+00 24 5.79224914e+00 6.66694593e+00 3.55069887e+00 | 5.79224914e+00 6.66694593e+00 3.55069887e+00 25 -4.95509517e+00 -6.93197915e+00 -5.73198477e+00 | -4.95509517e+00 -6.93197915e+00 -5.73198477e+00 26 1.82922214e+00 1.53490824e+00 -4.14461067e-01 | 1.82922214e+00 1.53490824e+00 -4.14461067e-01 27 -5.16520128e-01 6.85557242e-01 -1.54995917e+00 | -5.16520128e-01 6.85557242e-01 -1.54995917e+00 28 1.98766986e+00 4.71456253e-01 8.63701279e-01 | 1.98766986e+00 4.71456253e-01 8.63701279e-01 29 1.32468894e+00 -1.69689507e+00 -1.20996804e+00 | 1.32468894e+00 -1.69689507e+00 -1.20996804e+00 30 -5.16153593e+00 6.15105103e+00 -6.88376167e+00 | -5.16153593e+00 6.15105103e+00 -6.88376167e+00 31 8.87948834e+00 -6.43857610e+00 7.40353040e+00 | 8.87948834e+00 -6.43857610e+00 7.40353040e+00 32 -6.20117626e-01 -1.37827381e+00 3.09691728e-02 | -6.20117626e-01 -1.37827381e+00 3.09691728e-02 33 -6.39967261e+00 6.86126234e+00 6.88470470e+00 | -6.39967261e+00 6.86126234e+00 6.88470470e+00 34 -3.80056954e+00 5.03945429e+00 -7.39969395e+00 | -3.80056954e+00 5.03945429e+00 -7.39969395e+00 35 4.77918338e+00 -9.57043181e+00 7.36466636e+00 | 4.77918338e+00 -9.57043181e+00 7.36466636e+00 36 1.88158206e+00 5.32220770e-01 2.78886858e+00 | 1.88158206e+00 5.32220770e-01 2.78886858e+00 37 1.37581140e+00 -2.78438840e+00 -1.76666449e+00 | 1.37581140e+00 -2.78438840e+00 -1.76666449e+00 38 3.93632609e+00 -6.60498592e+00 -5.76153255e+00 | 3.93632609e+00 -6.60498592e+00 -5.76153255e+00 39 -1.89930995e+00 -5.47294348e-02 1.94819436e+00 | -1.89930995e+00 -5.47294348e-02 1.94819436e+00 40 2.55465367e+00 -3.80849541e-01 2.31509512e+00 | 2.55465367e+00 -3.80849541e-01 2.31509512e+00 41 -1.96113723e+00 -3.00652805e+00 -2.93995495e+00 | -1.96113723e+00 -3.00652805e+00 -2.93995495e+00 42 4.00851649e+00 6.81080508e+00 5.52342135e+00 | 4.00851649e+00 6.81080508e+00 5.52342135e+00 43 -2.84044541e+00 -4.70038157e+00 -3.80224210e+00 | -2.84044541e+00 -4.70038157e+00 -3.80224210e+00 44 2.44142089e+00 1.69970215e+00 2.83856239e+00 | 2.44142089e+00 1.69970215e+00 2.83856239e+00 45 -8.55276096e-01 -3.02817852e+00 -1.18007860e+00 | -8.55276096e-01 -3.02817852e+00 -1.18007860e+00 46 -7.19780042e+00 6.92262020e+00 -3.82543821e+00 | -7.19780042e+00 6.92262020e+00 -3.82543821e+00 47 8.61476404e-01 1.53584802e+00 3.18676942e-01 | 8.61476404e-01 1.53584802e+00 3.18676942e-01 48 -9.12290545e-01 9.36088621e-02 1.35388732e+00 | -9.12290545e-01 9.36088621e-02 1.35388732e+00 49 -2.95254462e+00 -1.73019441e+00 2.48013895e-01 | -2.95254462e+00 -1.73019441e+00 2.48013895e-01 50 -2.70214795e+00 5.47513078e+00 -2.57823414e+00 | -2.70214795e+00 5.47513078e+00 -2.57823414e+00 51 -3.70213969e+00 1.58254186e-01 3.09688099e-01 | -3.70213969e+00 1.58254186e-01 3.09688099e-01 52 9.75252302e+00 1.36548433e+01 3.50269590e+00 | 9.75252302e+00 1.36548433e+01 3.50269590e+00 53 -9.32416009e+00 -1.18234135e+01 -5.76176667e-01 | -9.32416009e+00 -1.18234135e+01 -5.76176667e-01 54 6.69237443e-01 8.18560218e-01 1.29128090e+00 | 6.69237443e-01 8.18560218e-01 1.29128090e+00 55 -1.71545810e+00 -4.85888594e-02 -1.01666258e+00 | -1.71545810e+00 -4.85888594e-02 -1.01666258e+00 56 3.41782590e+00 9.21625830e-01 4.50254090e-01 | 3.41782590e+00 9.21625830e-01 4.50254090e-01 57 -7.95227714e+00 5.57285653e+00 6.13398863e+00 | -7.95227714e+00 5.57285653e+00 6.13398863e+00 58 -4.98920943e+00 9.46086431e+00 -8.53261899e+00 | -4.98920943e+00 9.46086431e+00 -8.53261899e+00 59 1.12298662e+00 8.81064949e-01 5.55595043e-01 | 1.12298662e+00 8.81064949e-01 5.55595043e-01 60 1.97647368e+00 -4.11937194e+00 8.32252634e-02 | 1.97647368e+00 -4.11937194e+00 8.32252634e-02 61 1.49582793e+00 -5.89629637e-02 8.45650601e-01 | 1.49582793e+00 -5.89629637e-02 8.45650601e-01 62 6.76797205e+00 -6.01907075e+00 -5.76236279e+00 | 6.76797205e+00 -6.01907075e+00 -5.76236279e+00 63 -2.39932738e-01 1.27930878e+00 1.33229145e+00 | -2.39932738e-01 1.27930878e+00 1.33229145e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ti (Configuration in file "config-Ti.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [33, 50, 14, 24, 30, 17, 31, 47, 35, 45, 61, 13, 52, 11, 2, 48, 46, 5, 54, 27, 49, 42, 23, 22, 3, 29, 34, 19, 59, 25, 4, 6, 63, 0, 26, 8, 62, 60, 39, 38, 44, 43, 21, 41, 40, 9, 16, 7, 15, 20, 1, 58, 12, 57, 18, 56, 55, 53, 51, 28, 37, 10, 36, 32] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 234.87403795865606 V(r_1,...,r_N) = 234.8740379586562 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 -9.81945918e-02 -1.31148103e+00 -1.24679016e+00 | -9.81945918e-02 -1.31148103e+00 -1.24679016e+00 1 1.57085844e+01 -7.62825466e+00 -8.25017662e+00 | 1.57085844e+01 -7.62825466e+00 -8.25017662e+00 2 -2.49250895e+00 -2.67469489e+00 -9.96988203e+00 | -2.49250895e+00 -2.67469489e+00 -9.96988203e+00 3 1.34218324e+01 -2.56119440e+01 -1.85301906e+01 | 1.34218324e+01 -2.56119440e+01 -1.85301906e+01 4 -5.67496969e+00 -6.16140799e+01 -3.34155157e+01 | -5.67496969e+00 -6.16140799e+01 -3.34155157e+01 5 9.31134675e+00 6.39580673e+01 2.88279382e+01 | 9.31134675e+00 6.39580673e+01 2.88279382e+01 6 -2.81114485e+01 5.29977612e-01 5.65692726e+00 | -2.81114485e+01 5.29977612e-01 5.65692726e+00 7 4.36069725e+00 3.42246839e+00 7.28385258e+00 | 4.36069725e+00 3.42246839e+00 7.28385258e+00 8 -3.41330921e+01 -1.25808022e+01 -1.91286222e+00 | -3.41330921e+01 -1.25808022e+01 -1.91286222e+00 9 -1.15230214e+01 -4.23467188e+01 4.51495555e+01 | -1.15230214e+01 -4.23467188e+01 4.51495555e+01 10 5.06826247e+01 5.83479742e+01 -3.95682380e+01 | 5.06826247e+01 5.83479742e+01 -3.95682380e+01 11 3.92242505e+01 -5.44889689e+01 -4.34094099e+01 | 3.92242505e+01 -5.44889689e+01 -4.34094099e+01 12 -2.09542532e+01 -1.00913836e+01 -8.39114016e+00 | -2.09542532e+01 -1.00913836e+01 -8.39114016e+00 13 4.64246144e+00 3.60302826e-01 -4.50999601e+00 | 4.64246144e+00 3.60302826e-01 -4.50999601e+00 14 5.97932206e+00 -1.92044694e+00 1.41012819e+00 | 5.97932206e+00 -1.92044694e+00 1.41012819e+00 15 -4.07639067e+00 7.40092261e+00 -4.71301856e+00 | -4.07639067e+00 7.40092261e+00 -4.71301856e+00 16 1.59319852e+00 -1.25722143e+00 6.55063729e-01 | 1.59319852e+00 -1.25722143e+00 6.55063729e-01 17 -1.00673306e+01 -4.05805314e+01 4.14544170e+01 | -1.00673306e+01 -4.05805314e+01 4.14544170e+01 18 2.04101398e+01 3.69213878e+01 -4.88914182e+01 | 2.04101398e+01 3.69213878e+01 -4.88914182e+01 19 -2.03996345e+01 4.59325932e+01 -2.66053798e+01 | -2.03996345e+01 4.59325932e+01 -2.66053798e+01 20 -1.20727722e+01 2.78114823e+01 2.67587246e+01 | -1.20727722e+01 2.78114823e+01 2.67587246e+01 21 -2.32798739e+01 -2.17151825e+01 2.87559185e+01 | -2.32798739e+01 -2.17151825e+01 2.87559185e+01 22 -1.25841334e+01 1.63251666e+00 6.26509819e+00 | -1.25841334e+01 1.63251666e+00 6.26509819e+00 23 -7.38919784e-02 -1.74770428e+00 -3.65410790e+00 | -7.38919784e-02 -1.74770428e+00 -3.65410790e+00 24 -2.74001215e+01 -2.94903098e+01 -2.30696237e+01 | -2.74001215e+01 -2.94903098e+01 -2.30696237e+01 25 3.29046179e+01 1.99653360e+01 1.79674300e+01 | 3.29046179e+01 1.99653360e+01 1.79674300e+01 26 3.88727251e+00 5.34908087e+00 -4.27357938e+00 | 3.88727251e+00 5.34908087e+00 -4.27357938e+00 27 -6.20114367e-01 -5.92854609e-01 6.61353412e-01 | -6.20114367e-01 -5.92854609e-01 6.61353412e-01 28 -3.68863530e+01 5.15253580e+01 4.00257589e+01 | -3.68863530e+01 5.15253580e+01 4.00257589e+01 29 9.01267806e+00 -3.98751659e+00 -1.42639056e+01 | 9.01267806e+00 -3.98751659e+00 -1.42639056e+01 30 4.05990411e+01 -1.77212534e+01 3.80757741e+00 | 4.05990411e+01 -1.77212534e+01 3.80757741e+00 31 -2.40014161e+00 4.97970927e+00 1.91187136e+00 | -2.40014161e+00 4.97970927e+00 1.91187136e+00 32 -2.80004143e+00 -3.01425452e+00 -1.14604524e+00 | -2.80004143e+00 -3.01425452e+00 -1.14604524e+00 33 -1.58391313e+01 -5.96162739e+00 -6.05575681e+00 | -1.58391313e+01 -5.96162739e+00 -6.05575681e+00 34 -4.28557811e+01 -5.93932066e+01 -4.03944638e+01 | -4.28557811e+01 -5.93932066e+01 -4.03944638e+01 35 2.26720730e+01 -1.71822150e+01 4.10653362e+01 | 2.26720730e+01 -1.71822150e+01 4.10653362e+01 36 6.66323930e+00 9.86290866e+00 2.91495563e+00 | 6.66323930e+00 9.86290866e+00 2.91495563e+00 37 -2.25984027e+01 -3.09565974e+01 2.62831762e+01 | -2.25984027e+01 -3.09565974e+01 2.62831762e+01 38 -9.81247673e+00 -1.64309286e+01 -1.80656129e+01 | -9.81247673e+00 -1.64309286e+01 -1.80656129e+01 39 9.16827674e+00 1.96604984e+01 1.54316205e+01 | 9.16827674e+00 1.96604984e+01 1.54316205e+01 40 -6.17182931e+00 -1.28349364e+01 -4.18421510e+00 | -6.17182931e+00 -1.28349364e+01 -4.18421510e+00 41 6.20722430e+00 1.82603711e+01 1.04286056e+01 | 6.20722430e+00 1.82603711e+01 1.04286056e+01 42 -1.70004246e+01 -1.31126027e+01 -4.57203702e+00 | -1.70004246e+01 -1.31126027e+01 -4.57203702e+00 43 1.74948578e+01 1.33193577e+01 1.32298827e+01 | 1.74948578e+01 1.33193577e+01 1.32298827e+01 44 -2.81691809e+00 -5.69022842e+00 -3.81102491e+00 | -2.81691809e+00 -5.69022842e+00 -3.81102491e+00 45 3.56991978e+00 4.30321546e+00 1.10764202e+00 | 3.56991978e+00 4.30321546e+00 1.10764202e+00 46 2.94654127e+01 3.17015840e+01 -2.04888146e+01 | 2.94654127e+01 3.17015840e+01 -2.04888146e+01 47 -2.17322149e+01 -3.92037879e+01 1.51563091e+01 | -2.17322149e+01 -3.92037879e+01 1.51563091e+01 48 -1.14407868e+01 -5.01794698e-01 -1.02500915e+01 | -1.14407868e+01 -5.01794698e-01 -1.02500915e+01 49 1.32486691e+01 -1.01111316e+01 2.26061708e+00 | 1.32486691e+01 -1.01111316e+01 2.26061708e+00 50 5.05772744e+00 1.62055980e+00 2.65198061e+00 | 5.05772744e+00 1.62055980e+00 2.65198061e+00 51 -2.69424124e+01 5.55850258e+01 5.40315393e+00 | -2.69424124e+01 5.55850258e+01 5.40315393e+00 52 -3.39073849e+01 -1.55729856e+01 1.53362604e+01 | -3.39073849e+01 -1.55729856e+01 1.53362604e+01 53 1.25686946e+01 4.16140654e+01 3.48714105e+01 | 1.25686946e+01 4.16140654e+01 3.48714105e+01 54 -6.01588171e+00 4.71427634e+00 1.25469930e+00 | -6.01588171e+00 4.71427634e+00 1.25469930e+00 55 1.53424618e+00 2.64422090e+00 3.32686648e+00 | 1.53424618e+00 2.64422090e+00 3.32686648e+00 56 5.03795796e+01 4.64799072e+01 -4.10665791e+01 | 5.03795796e+01 4.64799072e+01 -4.10665791e+01 57 -1.84752168e+01 -6.70015527e+01 2.14534117e+01 | -1.84752168e+01 -6.70015527e+01 2.14534117e+01 58 7.20765486e+00 6.59183693e+01 -8.20103123e+00 | 7.20765486e+00 6.59183693e+01 -8.20103123e+00 59 5.65697022e+00 4.18288725e+00 4.84393889e+00 | 5.65697022e+00 4.18288725e+00 4.84393889e+00 60 1.73426071e+01 3.76390469e+01 -1.91633650e+01 | 1.73426071e+01 3.76390469e+01 -1.91633650e+01 61 4.34305413e+00 3.84615107e+00 2.78294934e+00 | 4.34305413e+00 3.84615107e+00 2.78294934e+00 62 2.58262457e+01 -5.29103488e+01 -3.32794792e+00 | 2.58262457e+01 -5.29103488e+01 -3.32794792e+00 63 1.11262893e+00 -2.25007467e+00 -9.92211491e-01 | 1.11262893e+00 -2.25007467e+00 -9.92211491e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al N Ti (Configuration in file "config-AlNTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [18, 41, 56, 27, 14, 53, 29, 23, 26, 30, 16, 61, 37, 44, 4, 24, 10, 55, 0, 40, 54, 42, 34, 7, 15, 49, 8, 3, 63, 6, 9, 46, 35, 48, 22, 32, 51, 12, 58, 43, 19, 1, 21, 39, 13, 62, 31, 57, 33, 25, 50, 36, 59, 5, 20, 17, 2, 47, 38, 52, 60, 11, 45, 28] 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)) = -27.064104332481268 V(r_1,...,r_N) = -27.06410433248121 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 8.45493283e-01 1.30542748e+00 8.97076719e-01 | 8.45493283e-01 1.30542748e+00 8.97076719e-01 1 -3.78507829e+00 2.84694290e-01 -1.01854860e+00 | -3.78507829e+00 2.84694290e-01 -1.01854860e+00 2 -9.57913313e+00 -2.86966930e+01 -9.92862562e+00 | -9.57913313e+00 -2.86966930e+01 -9.92862562e+00 3 1.21847007e+01 3.32329762e+01 7.67923480e+00 | 1.21847007e+01 3.32329762e+01 7.67923480e+00 4 -1.43499522e-01 -2.72572023e+00 2.54928504e+00 | -1.43499522e-01 -2.72572023e+00 2.54928504e+00 5 3.14412445e-01 -2.53036483e-01 -6.38861964e-01 | 3.14412445e-01 -2.53036483e-01 -6.38861964e-01 6 -5.52608430e+00 -3.58538325e+00 -6.85631626e+00 | -5.52608430e+00 -3.58538325e+00 -6.85631626e+00 7 3.39013212e+00 4.56546579e+00 2.91721379e+00 | 3.39013212e+00 4.56546579e+00 2.91721379e+00 8 -9.49382322e+00 -5.51269923e+00 -8.39189897e+00 | -9.49382322e+00 -5.51269923e+00 -8.39189897e+00 9 7.96105734e+00 9.10779259e+00 7.41079159e+00 | 7.96105734e+00 9.10779259e+00 7.41079159e+00 10 -1.19854311e+00 -1.06698214e+00 5.50424621e-01 | -1.19854311e+00 -1.06698214e+00 5.50424621e-01 11 -6.24914188e-01 1.61316104e+00 2.28470149e+00 | -6.24914188e-01 1.61316104e+00 2.28470149e+00 12 -5.32753763e+00 -1.85990529e+01 -2.34426181e+01 | -5.32753763e+00 -1.85990529e+01 -2.34426181e+01 13 4.86695345e+00 1.96830968e+01 2.59146279e+01 | 4.86695345e+00 1.96830968e+01 2.59146279e+01 14 6.83673450e-01 -4.54970451e+00 -1.06321972e+00 | 6.83673450e-01 -4.54970451e+00 -1.06321972e+00 15 1.66689549e+01 -1.64034915e+01 -2.25213976e+01 | 1.66689549e+01 -1.64034915e+01 -2.25213976e+01 16 2.49785034e+00 -3.56453067e-01 3.41404524e+00 | 2.49785034e+00 -3.56453067e-01 3.41404524e+00 17 -2.04056368e+01 -1.21720460e+01 1.48269274e+00 | -2.04056368e+01 -1.21720460e+01 1.48269274e+00 18 1.40128106e+01 1.53366338e+01 -9.94346574e+00 | 1.40128106e+01 1.53366338e+01 -9.94346574e+00 19 5.50410362e-01 2.20598692e+00 -2.21486160e+00 | 5.50410362e-01 2.20598692e+00 -2.21486160e+00 20 -7.70562033e+00 -1.05244496e+01 -3.76569800e+00 | -7.70562033e+00 -1.05244496e+01 -3.76569800e+00 21 5.11185687e+00 -1.47252256e+01 1.65855332e+01 | 5.11185687e+00 -1.47252256e+01 1.65855332e+01 22 7.31448461e-01 2.16359840e+00 1.08504469e+00 | 7.31448461e-01 2.16359840e+00 1.08504469e+00 23 7.53956756e-01 -2.28616407e+00 3.24383922e-01 | 7.53956756e-01 -2.28616407e+00 3.24383922e-01 24 -2.03252508e+00 1.08780733e+00 2.20674226e+00 | -2.03252508e+00 1.08780733e+00 2.20674226e+00 25 -2.54958118e+01 7.42753342e+00 -3.47784249e+01 | -2.54958118e+01 7.42753342e+00 -3.47784249e+01 26 -1.64110967e+01 -2.53158006e+01 -1.70139398e+01 | -1.64110967e+01 -2.53158006e+01 -1.70139398e+01 27 1.85144417e+01 3.09873850e+01 1.52636729e+01 | 1.85144417e+01 3.09873850e+01 1.52636729e+01 28 1.49955062e+01 -2.47978311e+01 2.90571440e+01 | 1.49955062e+01 -2.47978311e+01 2.90571440e+01 29 8.05963101e+00 4.70817332e+00 4.02072891e+00 | 8.05963101e+00 4.70817332e+00 4.02072891e+00 30 5.35329593e+00 1.61484518e+01 -4.98540349e+00 | 5.35329593e+00 1.61484518e+01 -4.98540349e+00 31 -2.98618084e+00 6.04992525e+00 -8.77905354e+00 | -2.98618084e+00 6.04992525e+00 -8.77905354e+00 32 -2.94888163e+00 1.58736779e-01 -7.90183325e+00 | -2.94888163e+00 1.58736779e-01 -7.90183325e+00 33 1.00086180e+00 1.70065680e+00 7.92254819e+00 | 1.00086180e+00 1.70065680e+00 7.92254819e+00 34 3.08115747e+00 6.06909378e-01 3.40403441e+00 | 3.08115747e+00 6.06909378e-01 3.40403441e+00 35 -1.48802123e+01 1.49248377e+01 -4.36320111e+01 | -1.48802123e+01 1.49248377e+01 -4.36320111e+01 36 -1.71482122e+01 -1.68079879e+01 -8.56632985e+00 | -1.71482122e+01 -1.68079879e+01 -8.56632985e+00 37 1.47962671e+01 8.56263009e+00 1.63054481e+01 | 1.47962671e+01 8.56263009e+00 1.63054481e+01 38 4.09538828e-01 -1.18893048e+00 -2.56876278e+00 | 4.09538828e-01 -1.18893048e+00 -2.56876278e+00 39 -1.59065035e+00 -3.54490768e+00 5.77208782e+00 | -1.59065035e+00 -3.54490768e+00 5.77208782e+00 40 -1.51444202e+00 1.21857934e+00 -1.45249037e+00 | -1.51444202e+00 1.21857934e+00 -1.45249037e+00 41 5.64513843e+00 -7.78026521e+00 -1.71280780e+00 | 5.64513843e+00 -7.78026521e+00 -1.71280780e+00 42 2.48375783e-01 -3.03792126e+00 -3.35685273e-01 | 2.48375783e-01 -3.03792126e+00 -3.35685273e-01 43 3.02122238e+00 2.72976270e+00 5.75642447e-01 | 3.02122238e+00 2.72976270e+00 5.75642447e-01 44 -1.66438077e+01 -1.08888381e+01 -8.49052557e+00 | -1.66438077e+01 -1.08888381e+01 -8.49052557e+00 45 1.55245400e+01 1.20200063e+01 7.75640621e+00 | 1.55245400e+01 1.20200063e+01 7.75640621e+00 46 2.00357073e+01 -2.18176543e+01 2.44955762e+01 | 2.00357073e+01 -2.18176543e+01 2.44955762e+01 47 -8.50254757e-01 1.42473673e+00 1.04549772e+01 | -8.50254757e-01 1.42473673e+00 1.04549772e+01 48 1.40815865e+00 -1.33038397e+00 1.15822265e+00 | 1.40815865e+00 -1.33038397e+00 1.15822265e+00 49 2.74749022e+00 2.24542071e+00 -5.85138102e+00 | 2.74749022e+00 2.24542071e+00 -5.85138102e+00 50 2.88105772e-01 9.97904862e-01 -7.54308970e-01 | 2.88105772e-01 9.97904862e-01 -7.54308970e-01 51 -1.40204430e+00 1.30460758e-01 6.99783837e-01 | -1.40204430e+00 1.30460758e-01 6.99783837e-01 52 -7.77622943e+00 1.34513390e+01 8.72619985e+00 | -7.77622943e+00 1.34513390e+01 8.72619985e+00 53 1.50923127e+00 -2.30377443e-01 -6.47300587e-01 | 1.50923127e+00 -2.30377443e-01 -6.47300587e-01 54 -5.17480745e+00 2.23148718e+00 3.11693712e+00 | -5.17480745e+00 2.23148718e+00 3.11693712e+00 55 1.49833191e-01 -6.87870626e-01 -9.19262305e-01 | 1.49833191e-01 -6.87870626e-01 -9.19262305e-01 56 -1.43726152e+01 2.10229793e+01 1.78306360e+01 | -1.43726152e+01 2.10229793e+01 1.78306360e+01 57 -6.79924177e+00 6.88915476e+00 -5.67736146e+00 | -6.79924177e+00 6.88915476e+00 -5.67736146e+00 58 -1.89047451e+01 -2.71005666e+01 -1.35577011e+01 | -1.89047451e+01 -2.71005666e+01 -1.35577011e+01 59 2.42642878e+01 2.49797246e+01 2.38763761e+01 | 2.42642878e+01 2.49797246e+01 2.38763761e+01 60 4.77661859e+00 -5.60118287e+00 5.76589727e-01 | 4.77661859e+00 -5.60118287e+00 5.76589727e-01 61 5.41083906e+00 4.13950379e+00 3.16634384e+00 | 5.41083906e+00 4.13950379e+00 3.16634384e+00 62 -2.49163595e+00 -2.14732050e+00 -1.10614189e+00 | -2.49163595e+00 -2.14732050e+00 -1.10614189e+00 63 1.39930549e+00 -1.60800023e+00 -9.64916411e-01 | 1.39930549e+00 -1.60800023e+00 -9.64916411e-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.