!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_MEAM_AlmyrasSangiovanniSarakinos_2019_NAlTi__SM_871795249052_000 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)) = 31.84286141221766 V(r_1,...,r_N) = 31.842861412217673 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 -3.46030943e+00 -2.82697575e+00 -2.59473229e+00 | -3.46030943e+00 -2.82697575e+00 -2.59473229e+00 1 -8.29249452e+00 -2.48960983e+01 1.74417673e+01 | -8.29249452e+00 -2.48960983e+01 1.74417673e+01 2 7.32755663e-03 1.11585537e+01 -2.79531384e+01 | 7.32755663e-03 1.11585537e+01 -2.79531384e+01 3 1.96558800e+00 1.72795652e+01 3.52314058e+00 | 1.96558800e+00 1.72795652e+01 3.52314058e+00 4 -1.65359029e+00 -3.22779061e+00 -4.42755532e+00 | -1.65359029e+00 -3.22779061e+00 -4.42755532e+00 5 3.07024774e+00 5.85779790e+00 -1.79142591e+00 | 3.07024774e+00 5.85779790e+00 -1.79142591e+00 6 -2.54318048e+00 -2.36304186e+00 -3.55775833e+00 | -2.54318048e+00 -2.36304186e+00 -3.55775833e+00 7 -2.29493990e+01 6.03861166e+01 -3.63321379e+01 | -2.29493990e+01 6.03861166e+01 -3.63321379e+01 8 -4.90861674e+00 -1.96683389e+00 -3.66600703e+00 | -4.90861674e+00 -1.96683389e+00 -3.66600703e+00 9 -4.05515617e+00 4.86851542e+00 1.58454315e-02 | -4.05515617e+00 4.86851542e+00 1.58454315e-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 -3.49874521e+01 -2.34696154e+01 -2.15340947e+01 | -3.49874521e+01 -2.34696154e+01 -2.15340947e+01 13 4.02921113e+01 2.02317792e+01 2.85521049e+01 | 4.02921113e+01 2.02317792e+01 2.85521049e+01 14 1.19225203e+01 -4.73718115e+00 6.59502407e+00 | 1.19225203e+01 -4.73718115e+00 6.59502407e+00 15 -6.22186011e-02 -5.12723883e-01 1.35115376e+00 | -6.22186011e-02 -5.12723883e-01 1.35115376e+00 16 -6.63007993e+00 -7.23860163e+00 -1.42894663e+01 | -6.63007993e+00 -7.23860163e+00 -1.42894663e+01 17 5.80880481e+00 5.25250115e+00 1.52178737e+01 | 5.80880481e+00 5.25250115e+00 1.52178737e+01 18 2.11446694e+00 7.26540213e-01 -8.37247230e-01 | 2.11446694e+00 7.26540213e-01 -8.37247230e-01 19 -4.51469954e+01 2.70431052e+01 -3.01193780e+01 | -4.51469954e+01 2.70431052e+01 -3.01193780e+01 20 -1.72777317e+01 -7.93053278e+00 -8.59973777e+00 | -1.72777317e+01 -7.93053278e+00 -8.59973777e+00 21 1.61942412e+01 1.22420616e+01 9.31077909e+00 | 1.61942412e+01 1.22420616e+01 9.31077909e+00 22 -1.54760563e+00 -1.39965848e+00 -1.99420588e+00 | -1.54760563e+00 -1.39965848e+00 -1.99420588e+00 23 -3.84037312e-01 5.07394028e+00 -1.74569900e+00 | -3.84037312e-01 5.07394028e+00 -1.74569900e+00 24 -2.83607751e-01 -1.16312146e-01 3.61320025e-02 | -2.83607751e-01 -1.16312146e-01 3.61320025e-02 25 -1.55553413e+01 1.42046949e+01 -1.27366798e+01 | -1.55553413e+01 1.42046949e+01 -1.27366798e+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 1.20156759e+01 -1.58979513e+01 1.01478729e+01 | 1.20156759e+01 -1.58979513e+01 1.01478729e+01 29 2.67601235e+00 2.40561527e+00 2.41090568e+00 | 2.67601235e+00 2.40561527e+00 2.41090568e+00 30 4.42610854e+01 -2.67039054e+01 2.97942764e+01 | 4.42610854e+01 -2.67039054e+01 2.97942764e+01 31 -2.09208988e+01 7.48838210e+00 -1.11746155e+01 | -2.09208988e+01 7.48838210e+00 -1.11746155e+01 32 -4.02036671e+00 6.95614750e-01 -5.70668482e-01 | -4.02036671e+00 6.95614750e-01 -5.70668482e-01 33 -6.55862229e+00 5.74401210e+00 -1.50178166e+00 | -6.55862229e+00 5.74401210e+00 -1.50178166e+00 34 2.70559857e+01 -6.33830977e+01 3.66118742e+01 | 2.70559857e+01 -6.33830977e+01 3.66118742e+01 35 -3.87800450e+00 -7.54741225e+00 4.32294317e+00 | -3.87800450e+00 -7.54741225e+00 4.32294317e+00 36 8.42667515e+00 -5.89947846e+00 3.72007312e+00 | 8.42667515e+00 -5.89947846e+00 3.72007312e+00 37 -9.62343253e+00 -1.05224922e+01 7.14037556e+00 | -9.62343253e+00 -1.05224922e+01 7.14037556e+00 38 -7.16421975e+00 -4.30980686e+00 -6.12094509e+00 | -7.16421975e+00 -4.30980686e+00 -6.12094509e+00 39 -1.02266618e+01 -1.00471965e+01 1.62970962e+01 | -1.02266618e+01 -1.00471965e+01 1.62970962e+01 40 1.02875941e-01 -2.63701839e+00 1.73884452e+00 | 1.02875941e-01 -2.63701839e+00 1.73884452e+00 41 -2.16279160e+01 3.74478331e+01 -2.05029868e+01 | -2.16279160e+01 3.74478331e+01 -2.05029868e+01 42 -4.83993128e+01 -5.22055215e+01 -4.52942152e+01 | -4.83993128e+01 -5.22055215e+01 -4.52942152e+01 43 4.69557591e+01 5.19985181e+01 4.53767122e+01 | 4.69557591e+01 5.19985181e+01 4.53767122e+01 44 2.44868323e+01 -3.70252807e+01 1.89945266e+01 | 2.44868323e+01 -3.70252807e+01 1.89945266e+01 45 3.09029868e-01 5.99475891e-01 6.39058249e-01 | 3.09029868e-01 5.99475891e-01 6.39058249e-01 46 7.27669135e+00 1.13591933e+01 -6.44504495e+00 | 7.27669135e+00 1.13591933e+01 -6.44504495e+00 47 3.69959888e+00 -3.71990364e+00 1.00643045e+00 | 3.69959888e+00 -3.71990364e+00 1.00643045e+00 48 -3.98632332e+00 3.82901958e+00 4.55165467e+00 | -3.98632332e+00 3.82901958e+00 4.55165467e+00 49 -9.05703735e+00 -4.86033719e+00 6.79222006e+00 | -9.05703735e+00 -4.86033719e+00 6.79222006e+00 50 7.71443260e-01 -1.25047506e+01 -1.56193184e+01 | 7.71443260e-01 -1.25047506e+01 -1.56193184e+01 51 1.19735568e+01 1.21693149e+01 1.27846414e+01 | 1.19735568e+01 1.21693149e+01 1.27846414e+01 52 1.62065611e+01 1.61392105e+01 -9.96825180e+00 | 1.62065611e+01 1.61392105e+01 -9.96825180e+00 53 -3.69844124e+00 4.01408705e+00 5.90082841e-01 | -3.69844124e+00 4.01408705e+00 5.90082841e-01 54 -2.74901453e+00 -2.66966815e+00 -2.07304561e+00 | -2.74901453e+00 -2.66966815e+00 -2.07304561e+00 55 3.36578770e+00 2.67255140e+00 2.05970835e+00 | 3.36578770e+00 2.67255140e+00 2.05970835e+00 56 5.50899895e+00 4.47746765e+00 -5.28329564e+00 | 5.50899895e+00 4.47746765e+00 -5.28329564e+00 57 2.18560816e+01 -3.09169218e+01 -3.88917707e+01 | 2.18560816e+01 -3.09169218e+01 -3.88917707e+01 58 2.14558193e+01 -8.18795177e+00 1.20797953e+01 | 2.14558193e+01 -8.18795177e+00 1.20797953e+01 59 -3.92936854e-01 1.53204934e-01 1.33613391e-01 | -3.92936854e-01 1.53204934e-01 1.33613391e-01 60 -1.25375702e+01 -1.17812428e+01 -1.12136999e+01 | -1.25375702e+01 -1.17812428e+01 -1.12136999e+01 61 1.61321180e+01 7.40926623e+00 1.13683173e+01 | 1.61321180e+01 7.40926623e+00 1.13683173e+01 62 -2.34628910e+01 3.62844324e+01 3.69304214e+01 | -2.34628910e+01 3.62844324e+01 3.69304214e+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)) = 59.03390098597502 V(r_1,...,r_N) = 59.03390098597506 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)) = 234.87527526039395 V(r_1,...,r_N) = 234.87527526039386 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 1.57085996e+01 -7.62826377e+00 -8.25018993e+00 | 1.57085996e+01 -7.62826377e+00 -8.25018993e+00 2 -2.49250922e+00 -2.67469519e+00 -9.96988236e+00 | -2.49250922e+00 -2.67469519e+00 -9.96988236e+00 3 1.34218934e+01 -2.56120231e+01 -1.85302796e+01 | 1.34218934e+01 -2.56120231e+01 -1.85302796e+01 4 -5.67512562e+00 -6.16145035e+01 -3.34157348e+01 | -5.67512562e+00 -6.16145035e+01 -3.34157348e+01 5 9.31150268e+00 6.39584909e+01 2.88281574e+01 | 9.31150268e+00 6.39584909e+01 2.88281574e+01 6 -2.81114674e+01 5.29982981e-01 5.65693864e+00 | -2.81114674e+01 5.29982981e-01 5.65693864e+00 7 4.36070087e+00 3.42247206e+00 7.28385456e+00 | 4.36070087e+00 3.42247206e+00 7.28385456e+00 8 -3.41331653e+01 -1.25808398e+01 -1.91287138e+00 | -3.41331653e+01 -1.25808398e+01 -1.91287138e+00 9 -1.15237537e+01 -4.23476125e+01 4.51501980e+01 | -1.15237537e+01 -4.23476125e+01 4.51501980e+01 10 5.06834303e+01 5.83489054e+01 -3.95688713e+01 | 5.06834303e+01 5.83489054e+01 -3.95688713e+01 11 3.92247518e+01 -5.44896210e+01 -4.34099394e+01 | 3.92247518e+01 -5.44896210e+01 -4.34099394e+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 -4.07639099e+00 7.40092277e+00 -4.71301879e+00 | -4.07639099e+00 7.40092277e+00 -4.71301879e+00 16 1.59319852e+00 -1.25722143e+00 6.55063729e-01 | 1.59319852e+00 -1.25722143e+00 6.55063729e-01 17 -1.00674927e+01 -4.05808063e+01 4.14547457e+01 | -1.00674927e+01 -4.05808063e+01 4.14547457e+01 18 2.04103051e+01 3.69216621e+01 -4.88917485e+01 | 2.04103051e+01 3.69216621e+01 -4.88917485e+01 19 -2.03997829e+01 4.59328357e+01 -2.66055336e+01 | -2.03997829e+01 4.59328357e+01 -2.66055336e+01 20 -1.20728331e+01 2.78115615e+01 2.67588141e+01 | -1.20728331e+01 2.78115615e+01 2.67588141e+01 21 -2.32799575e+01 -2.17152489e+01 2.87560194e+01 | -2.32799575e+01 -2.17152489e+01 2.87560194e+01 22 -1.25841366e+01 1.63251721e+00 6.26509981e+00 | -1.25841366e+01 1.63251721e+00 6.26509981e+00 23 -7.38919784e-02 -1.74770428e+00 -3.65410790e+00 | -7.38919784e-02 -1.74770428e+00 -3.65410790e+00 24 -2.74002842e+01 -2.94904758e+01 -2.30697247e+01 | -2.74002842e+01 -2.94904758e+01 -2.30697247e+01 25 3.29047822e+01 1.99654993e+01 1.79675296e+01 | 3.29047822e+01 1.99654993e+01 1.79675296e+01 26 3.88727284e+00 5.34908122e+00 -4.27357976e+00 | 3.88727284e+00 5.34908122e+00 -4.27357976e+00 27 -6.20114367e-01 -5.92854609e-01 6.61353412e-01 | -6.20114367e-01 -5.92854609e-01 6.61353412e-01 28 -3.68868542e+01 5.15260101e+01 4.00262884e+01 | -3.68868542e+01 5.15260101e+01 4.00262884e+01 29 9.01267898e+00 -3.98751757e+00 -1.42639073e+01 | 9.01267898e+00 -3.98751757e+00 -1.42639073e+01 30 4.05992714e+01 -1.77214270e+01 3.80763188e+00 | 4.05992714e+01 -1.77214270e+01 3.80763188e+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 -1.58391320e+01 -5.96162712e+00 -6.05575735e+00 | -1.58391320e+01 -5.96162712e+00 -6.05575735e+00 34 -4.28568607e+01 -5.93942980e+01 -4.03954050e+01 | -4.28568607e+01 -5.93942980e+01 -4.03954050e+01 35 2.26726186e+01 -1.71819320e+01 4.10665632e+01 | 2.26726186e+01 -1.71819320e+01 4.10665632e+01 36 6.66323982e+00 9.86290825e+00 2.91495607e+00 | 6.66323982e+00 9.86290825e+00 2.91495607e+00 37 -2.25986036e+01 -3.09567659e+01 2.62833452e+01 | -2.25986036e+01 -3.09567659e+01 2.62833452e+01 38 -9.81248954e+00 -1.64309481e+01 -1.80656309e+01 | -9.81248954e+00 -1.64309481e+01 -1.80656309e+01 39 9.16828954e+00 1.96605179e+01 1.54316385e+01 | 9.16828954e+00 1.96605179e+01 1.54316385e+01 40 -6.17184527e+00 -1.28349573e+01 -4.18423386e+00 | -6.17184527e+00 -1.28349573e+01 -4.18423386e+00 41 6.20724026e+00 1.82603920e+01 1.04286244e+01 | 6.20724026e+00 1.82603920e+01 1.04286244e+01 42 -1.70004439e+01 -1.31126148e+01 -4.57205222e+00 | -1.70004439e+01 -1.31126148e+01 -4.57205222e+00 43 1.74948774e+01 1.33193696e+01 1.32298982e+01 | 1.74948774e+01 1.33193696e+01 1.32298982e+01 44 -2.81691810e+00 -5.69022843e+00 -3.81102492e+00 | -2.81691810e+00 -5.69022843e+00 -3.81102492e+00 45 3.56991979e+00 4.30321548e+00 1.10764203e+00 | 3.56991979e+00 4.30321548e+00 1.10764203e+00 46 2.94656138e+01 3.17017526e+01 -2.04889834e+01 | 2.94656138e+01 3.17017526e+01 -2.04889834e+01 47 -2.17323096e+01 -3.92039535e+01 1.51563854e+01 | -2.17323096e+01 -3.92039535e+01 1.51563854e+01 48 -1.14407910e+01 -5.01795306e-01 -1.02500954e+01 | -1.14407910e+01 -5.01795306e-01 -1.02500954e+01 49 1.32486739e+01 -1.01111316e+01 2.26062054e+00 | 1.32486739e+01 -1.01111316e+01 2.26062054e+00 50 5.05772744e+00 1.62055980e+00 2.65198061e+00 | 5.05772744e+00 1.62055980e+00 2.65198061e+00 51 -2.69425815e+01 5.55853546e+01 5.40317991e+00 | -2.69425815e+01 5.55853546e+01 5.40317991e+00 52 -3.39076196e+01 -1.55729931e+01 1.53363871e+01 | -3.39076196e+01 -1.55729931e+01 1.53363871e+01 53 1.25687664e+01 4.16142648e+01 3.48715879e+01 | 1.25687664e+01 4.16142648e+01 3.48715879e+01 54 -6.01588221e+00 4.71427697e+00 1.25469975e+00 | -6.01588221e+00 4.71427697e+00 1.25469975e+00 55 1.53424618e+00 2.64422090e+00 3.32686648e+00 | 1.53424618e+00 2.64422090e+00 3.32686648e+00 56 5.03802765e+01 4.64805235e+01 -4.10671691e+01 | 5.03802765e+01 4.64805235e+01 -4.10671691e+01 57 -1.84753432e+01 -6.70020473e+01 2.14535416e+01 | -1.84753432e+01 -6.70020473e+01 2.14535416e+01 58 7.20778023e+00 6.59188647e+01 -8.20115953e+00 | 7.20778023e+00 6.59188647e+01 -8.20115953e+00 59 5.65697037e+00 4.18288738e+00 4.84393899e+00 | 5.65697037e+00 4.18288738e+00 4.84393899e+00 60 1.73427018e+01 3.76392125e+01 -1.91634413e+01 | 1.73427018e+01 3.76392125e+01 -1.91634413e+01 61 4.34305413e+00 3.84615107e+00 2.78294934e+00 | 4.34305413e+00 3.84615107e+00 2.78294934e+00 62 2.58264148e+01 -5.29106776e+01 -3.32797390e+00 | 2.58264148e+01 -5.29106776e+01 -3.32797390e+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)) = -27.06367582732589 V(r_1,...,r_N) = -27.063675827325874 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 -9.57915585e+00 -2.86967482e+01 -9.92864849e+00 | -9.57915585e+00 -2.86967482e+01 -9.92864849e+00 3 1.21847234e+01 3.32330314e+01 7.67925768e+00 | 1.21847234e+01 3.32330314e+01 7.67925768e+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 -5.52609289e+00 -3.58538695e+00 -6.85632386e+00 | -5.52609289e+00 -3.58538695e+00 -6.85632386e+00 7 3.39014072e+00 4.56546949e+00 2.91722139e+00 | 3.39014072e+00 4.56546949e+00 2.91722139e+00 8 -9.49382576e+00 -5.51270067e+00 -8.39190118e+00 | -9.49382576e+00 -5.51270067e+00 -8.39190118e+00 9 7.96105988e+00 9.10779403e+00 7.41079379e+00 | 7.96105988e+00 9.10779403e+00 7.41079379e+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 -5.32754553e+00 -1.85990757e+01 -2.34426490e+01 | -5.32754553e+00 -1.85990757e+01 -2.34426490e+01 13 4.86696135e+00 1.96831195e+01 2.59146589e+01 | 4.86696135e+00 1.96831195e+01 2.59146589e+01 14 6.83673450e-01 -4.54970451e+00 -1.06321972e+00 | 6.83673450e-01 -4.54970451e+00 -1.06321972e+00 15 1.66689979e+01 -1.64035453e+01 -2.25214624e+01 | 1.66689979e+01 -1.64035453e+01 -2.25214624e+01 16 2.49785034e+00 -3.56453067e-01 3.41404524e+00 | 2.49785034e+00 -3.56453067e-01 3.41404524e+00 17 -2.04056484e+01 -1.21720591e+01 1.48270065e+00 | -2.04056484e+01 -1.21720591e+01 1.48270065e+00 18 1.40128220e+01 1.53366470e+01 -9.94347386e+00 | 1.40128220e+01 1.53366470e+01 -9.94347386e+00 19 5.50410362e-01 2.20598692e+00 -2.21486160e+00 | 5.50410362e-01 2.20598692e+00 -2.21486160e+00 20 -7.70562011e+00 -1.05244497e+01 -3.76569779e+00 | -7.70562011e+00 -1.05244497e+01 -3.76569779e+00 21 5.11185512e+00 -1.47252325e+01 1.65855364e+01 | 5.11185512e+00 -1.47252325e+01 1.65855364e+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 -2.54958645e+01 7.42756935e+00 -3.47785100e+01 | -2.54958645e+01 7.42756935e+00 -3.47785100e+01 26 -1.64120769e+01 -2.53173432e+01 -1.70145965e+01 | -1.64120769e+01 -2.53173432e+01 -1.70145965e+01 27 1.85154220e+01 3.09889277e+01 1.52643295e+01 | 1.85154220e+01 3.09889277e+01 1.52643295e+01 28 1.49955436e+01 -2.47978835e+01 2.90572160e+01 | 1.49955436e+01 -2.47978835e+01 2.90572160e+01 29 8.05964625e+00 4.70818977e+00 4.02074199e+00 | 8.05964625e+00 4.70818977e+00 4.02074199e+00 30 5.35329768e+00 1.61484587e+01 -4.98540664e+00 | 5.35329768e+00 1.61484587e+01 -4.98540664e+00 31 -2.98618145e+00 6.04992558e+00 -8.77905421e+00 | -2.98618145e+00 6.04992558e+00 -8.77905421e+00 32 -2.94888186e+00 1.58736733e-01 -7.90183375e+00 | -2.94888186e+00 1.58736733e-01 -7.90183375e+00 33 1.00086203e+00 1.70065684e+00 7.92254869e+00 | 1.00086203e+00 1.70065684e+00 7.92254869e+00 34 3.08115747e+00 6.06909378e-01 3.40403441e+00 | 3.08115747e+00 6.06909378e-01 3.40403441e+00 35 -1.48803150e+01 1.49249659e+01 -4.36321728e+01 | -1.48803150e+01 1.49249659e+01 -4.36321728e+01 36 -1.71482145e+01 -1.68079900e+01 -8.56633103e+00 | -1.71482145e+01 -1.68079900e+01 -8.56633103e+00 37 1.47962691e+01 8.56263160e+00 1.63054498e+01 | 1.47962691e+01 8.56263160e+00 1.63054498e+01 38 4.09538828e-01 -1.18893048e+00 -2.56876278e+00 | 4.09538828e-01 -1.18893048e+00 -2.56876278e+00 39 -1.59065036e+00 -3.54490769e+00 5.77208785e+00 | -1.59065036e+00 -3.54490769e+00 5.77208785e+00 40 -1.51444202e+00 1.21857934e+00 -1.45249037e+00 | -1.51444202e+00 1.21857934e+00 -1.45249037e+00 41 5.64513844e+00 -7.78026522e+00 -1.71280780e+00 | 5.64513844e+00 -7.78026522e+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 -1.66438175e+01 -1.08888455e+01 -8.49053039e+00 | -1.66438175e+01 -1.08888455e+01 -8.49053039e+00 45 1.55245498e+01 1.20200137e+01 7.75641103e+00 | 1.55245498e+01 1.20200137e+01 7.75641103e+00 46 2.00358218e+01 -2.18177940e+01 2.44957278e+01 | 2.00358218e+01 -2.18177940e+01 2.44957278e+01 47 -8.50254433e-01 1.42473709e+00 1.04549777e+01 | -8.50254433e-01 1.42473709e+00 1.04549777e+01 48 1.40815865e+00 -1.33038397e+00 1.15822265e+00 | 1.40815865e+00 -1.33038397e+00 1.15822265e+00 49 2.74749031e+00 2.24542069e+00 -5.85138106e+00 | 2.74749031e+00 2.24542069e+00 -5.85138106e+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 -7.77624134e+00 1.34513509e+01 8.72620902e+00 | -7.77624134e+00 1.34513509e+01 8.72620902e+00 53 1.50923127e+00 -2.30377443e-01 -6.47300587e-01 | 1.50923127e+00 -2.30377443e-01 -6.47300587e-01 54 -5.17480753e+00 2.23148720e+00 3.11693716e+00 | -5.17480753e+00 2.23148720e+00 3.11693716e+00 55 1.49833191e-01 -6.87870626e-01 -9.19262305e-01 | 1.49833191e-01 -6.87870626e-01 -9.19262305e-01 56 -1.43726582e+01 2.10230331e+01 1.78307009e+01 | -1.43726582e+01 2.10230331e+01 1.78307009e+01 57 -6.79924233e+00 6.88915555e+00 -5.67736233e+00 | -6.79924233e+00 6.88915555e+00 -5.67736233e+00 58 -1.89047924e+01 -2.71006151e+01 -1.35577449e+01 | -1.89047924e+01 -2.71006151e+01 -1.35577449e+01 59 2.42643357e+01 2.49797727e+01 2.38764205e+01 | 2.42643357e+01 2.49797727e+01 2.38764205e+01 60 4.77661916e+00 -5.60118364e+00 5.76590591e-01 | 4.77661916e+00 -5.60118364e+00 5.76590591e-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.