!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = [19, 62, 14, 59, 22, 17, 61, 11, 15, 18, 13, 7, 35, 10, 2, 8, 28, 5, 9, 0, 27, 50, 4, 24, 23, 34, 46, 20, 16, 57, 51, 53, 52, 55, 25, 12, 58, 39, 48, 37, 47, 49, 60, 44, 43, 56, 26, 40, 38, 41, 21, 30, 32, 31, 63, 33, 45, 29, 36, 3, 42, 6, 1, 54] 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)) = 31.8428614122 V(r_1,...,r_N) = 31.8428614122 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 = [25, 23, 28, 13, 21, 47, 35, 10, 16, 56, 7, 32, 55, 3, 45, 46, 8, 34, 44, 39, 43, 4, 62, 1, 27, 0, 36, 24, 2, 60, 61, 57, 11, 58, 17, 6, 26, 38, 37, 19, 53, 42, 41, 20, 18, 14, 15, 5, 59, 51, 52, 49, 50, 40, 63, 12, 9, 31, 33, 48, 29, 30, 22, 54] 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)) = 61.5348621463 V(r_1,...,r_N) = 61.5348621463 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 1.34003027e-01 8.39965378e-02 1.11282947e-01 | 1.34003027e-01 8.39965378e-02 1.11282947e-01 1 3.11642465e+00 -6.52848276e+00 3.62126054e+00 | 3.11642465e+00 -6.52848276e+00 3.62126054e+00 2 1.50516112e+00 1.41031703e+00 -1.03055742e+00 | 1.50516112e+00 1.41031703e+00 -1.03055742e+00 3 2.24908196e+00 -4.13779507e-01 -4.27174445e+00 | 2.24908196e+00 -4.13779507e-01 -4.27174445e+00 4 -2.44421759e+00 2.14972347e+00 -4.91945789e+00 | -2.44421759e+00 2.14972347e+00 -4.91945789e+00 5 -2.26244226e-01 7.63591480e-01 3.03503916e-01 | -2.26244226e-01 7.63591480e-01 3.03503916e-01 6 -1.15899969e-01 1.31037124e+00 2.15628658e+00 | -1.15899969e-01 1.31037124e+00 2.15628658e+00 7 -2.84554241e+00 -2.80120319e+00 -1.74773526e+00 | -2.84554241e+00 -2.80120319e+00 -1.74773526e+00 8 -2.71419341e-01 -7.27444072e-01 -7.55875690e-01 | -2.71419341e-01 -7.27444072e-01 -7.55875690e-01 9 3.79287840e+00 6.10260021e+00 -7.19900646e+00 | 3.79287840e+00 6.10260021e+00 -7.19900646e+00 10 -2.33525437e+00 -3.90091679e+00 4.26072228e+00 | -2.33525437e+00 -3.90091679e+00 4.26072228e+00 11 5.01899831e-01 1.08928488e+00 -2.47617893e+00 | 5.01899831e-01 1.08928488e+00 -2.47617893e+00 12 2.57564055e+00 -2.02528711e+00 2.38231676e+00 | 2.57564055e+00 -2.02528711e+00 2.38231676e+00 13 -1.43453818e+00 -3.38752562e+00 1.57217098e+00 | -1.43453818e+00 -3.38752562e+00 1.57217098e+00 14 8.56336587e-02 -5.94616444e-01 6.72211265e-02 | 8.56336587e-02 -5.94616444e-01 6.72211265e-02 15 1.68226007e+00 1.91328585e+00 -4.13458179e-01 | 1.68226007e+00 1.91328585e+00 -4.13458179e-01 16 -1.56902797e+00 1.03860248e+00 -1.34576393e+00 | -1.56902797e+00 1.03860248e+00 -1.34576393e+00 17 6.46988497e+00 -6.37329018e+00 7.10481071e+00 | 6.46988497e+00 -6.37329018e+00 7.10481071e+00 18 -8.49946036e-01 4.45803863e-01 -1.84440140e+00 | -8.49946036e-01 4.45803863e-01 -1.84440140e+00 19 6.91025314e+00 -2.23404764e+00 3.64887435e+00 | 6.91025314e+00 -2.23404764e+00 3.64887435e+00 20 -6.48534968e+00 7.67444137e+00 -7.13692331e+00 | -6.48534968e+00 7.67444137e+00 -7.13692331e+00 21 -2.78278054e-01 -1.04451920e+00 -9.53760308e-02 | -2.78278054e-01 -1.04451920e+00 -9.53760308e-02 22 -1.53150963e+00 1.71935750e+00 1.79443512e-01 | -1.53150963e+00 1.71935750e+00 1.79443512e-01 23 -6.42201352e-01 1.92356332e-01 1.54637666e+00 | -6.42201352e-01 1.92356332e-01 1.54637666e+00 24 -3.83045102e+00 -1.08123658e+00 1.55595246e-01 | -3.83045102e+00 -1.08123658e+00 1.55595246e-01 25 -5.15402162e-01 1.39041840e-01 -2.13091051e-01 | -5.15402162e-01 1.39041840e-01 -2.13091051e-01 26 3.98781510e+00 5.10690558e+00 -5.08228350e-01 | 3.98781510e+00 5.10690558e+00 -5.08228350e-01 27 -3.81610924e+00 -4.94591601e+00 3.17338475e-01 | -3.81610924e+00 -4.94591601e+00 3.17338475e-01 28 3.45394311e+00 2.03683281e+00 5.84474464e+00 | 3.45394311e+00 2.03683281e+00 5.84474464e+00 29 2.58401069e-01 -3.10444950e+00 -5.72973555e+00 | 2.58401069e-01 -3.10444950e+00 -5.72973555e+00 30 -2.91065528e+00 1.10560559e+01 3.47280540e+00 | -2.91065528e+00 1.10560559e+01 3.47280540e+00 31 -2.10353360e+00 -3.02994296e+00 -9.58735810e+00 | -2.10353360e+00 -3.02994296e+00 -9.58735810e+00 32 -1.46942406e+00 -7.65543478e-01 -4.36951457e-02 | -1.46942406e+00 -7.65543478e-01 -4.36951457e-02 33 6.08191168e+00 -8.07044231e+00 6.01690403e+00 | 6.08191168e+00 -8.07044231e+00 6.01690403e+00 34 -1.05829297e+00 6.43906895e-01 7.12944336e-01 | -1.05829297e+00 6.43906895e-01 7.12944336e-01 35 2.59219320e+00 -5.83128594e-01 -2.91567351e+00 | 2.59219320e+00 -5.83128594e-01 -2.91567351e+00 36 -6.77834379e+00 4.59047108e+00 -4.97549892e+00 | -6.77834379e+00 4.59047108e+00 -4.97549892e+00 37 3.16954322e+00 1.31432905e+00 2.11281978e-01 | 3.16954322e+00 1.31432905e+00 2.11281978e-01 38 3.13762329e+00 1.82910123e+00 4.89644890e+00 | 3.13762329e+00 1.82910123e+00 4.89644890e+00 39 -5.99433239e+00 -2.29898701e+00 -2.58290212e+00 | -5.99433239e+00 -2.29898701e+00 -2.58290212e+00 40 -3.85335437e-01 -1.29261775e+00 -7.67382012e-01 | -3.85335437e-01 -1.29261775e+00 -7.67382012e-01 41 1.89526424e+00 -2.79734552e+00 3.59942679e+00 | 1.89526424e+00 -2.79734552e+00 3.59942679e+00 42 1.69095710e+00 -2.30716217e+00 -2.61310529e+00 | 1.69095710e+00 -2.30716217e+00 -2.61310529e+00 43 -6.37659722e+00 1.31354853e+01 3.39627421e+00 | -6.37659722e+00 1.31354853e+01 3.39627421e+00 44 2.23001751e+00 4.24949094e+00 -1.05256551e+00 | 2.23001751e+00 4.24949094e+00 -1.05256551e+00 45 -2.96266519e+00 -4.03934481e+00 -2.54611433e-01 | -2.96266519e+00 -4.03934481e+00 -2.54611433e-01 46 -2.31347216e+00 9.13825246e-01 1.95735339e+00 | -2.31347216e+00 9.13825246e-01 1.95735339e+00 47 7.51847195e-01 -3.93863474e+00 1.05070689e+00 | 7.51847195e-01 -3.93863474e+00 1.05070689e+00 48 -1.15601706e+00 -5.98427620e-02 -2.16120750e-01 | -1.15601706e+00 -5.98427620e-02 -2.16120750e-01 49 -5.76275213e+00 1.71596771e+00 5.50476225e+00 | -5.76275213e+00 1.71596771e+00 5.50476225e+00 50 3.25541064e+00 4.83707631e+00 7.72207947e-01 | 3.25541064e+00 4.83707631e+00 7.72207947e-01 51 -5.88190429e+00 -9.35666160e-01 -3.17770124e+00 | -5.88190429e+00 -9.35666160e-01 -3.17770124e+00 52 -7.46604711e-01 2.80919367e+00 6.24847538e-01 | -7.46604711e-01 2.80919367e+00 6.24847538e-01 53 4.06876697e+00 7.40358380e+00 -5.90593977e+00 | 4.06876697e+00 7.40358380e+00 -5.90593977e+00 54 6.64298025e+00 1.59617341e-01 1.07881059e+00 | 6.64298025e+00 1.59617341e-01 1.07881059e+00 55 -1.02076694e+00 -3.41697500e+00 -3.23352714e+00 | -1.02076694e+00 -3.41697500e+00 -3.23352714e+00 56 -2.29948111e+00 -8.14320960e-01 4.41123848e+00 | -2.29948111e+00 -8.14320960e-01 4.41123848e+00 57 -8.34580402e-01 2.85397707e+00 1.09237291e+00 | -8.34580402e-01 2.85397707e+00 1.09237291e+00 58 1.37714741e+00 1.66859596e+00 -3.97210301e-01 | 1.37714741e+00 1.66859596e+00 -3.97210301e-01 59 8.29694800e-01 4.05169423e-01 -9.61212105e-01 | 8.29694800e-01 4.05169423e-01 -9.61212105e-01 60 9.78061362e+00 -1.25078108e+01 -2.85265049e+00 | 9.78061362e+00 -1.25078108e+01 -2.85265049e+00 61 1.07103597e+00 4.64521840e-02 1.39357297e+00 | 1.07103597e+00 4.64521840e-02 1.39357297e+00 62 -5.91099211e+00 -7.96965127e+00 6.13965043e+00 | -5.91099211e+00 -7.96965127e+00 6.13965043e+00 63 -1.41145659e-01 1.18131920e+00 1.62112996e+00 | -1.41145659e-01 1.18131920e+00 1.62112996e+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 = [58, 35, 56, 15, 13, 39, 45, 17, 36, 40, 34, 27, 33, 4, 20, 3, 21, 7, 22, 57, 14, 16, 18, 31, 51, 28, 61, 11, 25, 55, 48, 23, 62, 12, 10, 1, 8, 60, 43, 5, 9, 59, 44, 38, 42, 6, 53, 63, 30, 52, 54, 24, 49, 46, 50, 29, 2, 19, 0, 41, 37, 26, 32, 47] 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)) = 297.612593477 V(r_1,...,r_N) = 297.612593477 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 -9.01240060e+00 -6.00157842e+00 -3.63783049e+00 | -9.01240060e+00 -6.00157842e+00 -3.63783049e+00 1 -4.27011669e+01 -1.55457436e+01 4.00806056e+00 | -4.27011669e+01 -1.55457436e+01 4.00806056e+00 2 3.01458138e+01 3.43078308e+01 -2.06897228e+01 | 3.01458138e+01 3.43078308e+01 -2.06897228e+01 3 -5.42030846e+01 -6.32722301e+01 2.72104704e+01 | -5.42030846e+01 -6.32722301e+01 2.72104704e+01 4 -1.32187136e+01 -3.29839685e+01 -1.13234727e+01 | -1.32187136e+01 -3.29839685e+01 -1.13234727e+01 5 3.59537221e+01 1.56461700e+01 2.71916769e+01 | 3.59537221e+01 1.56461700e+01 2.71916769e+01 6 -1.29568054e+01 -4.51672834e+00 -4.55445497e+00 | -1.29568054e+01 -4.51672834e+00 -4.55445497e+00 7 -1.78220378e+01 4.38135167e+01 -4.68322148e+01 | -1.78220378e+01 4.38135167e+01 -4.68322148e+01 8 -3.60821859e+00 -5.40338865e+00 -2.86712170e+00 | -3.60821859e+00 -5.40338865e+00 -2.86712170e+00 9 -5.52344399e+00 -1.39220870e+00 8.42205943e+00 | -5.52344399e+00 -1.39220870e+00 8.42205943e+00 10 -5.40845172e+00 -7.36945047e+00 -1.71590845e+01 | -5.40845172e+00 -7.36945047e+00 -1.71590845e+01 11 9.64244307e+00 1.15999163e+01 9.45678901e+00 | 9.64244307e+00 1.15999163e+01 9.45678901e+00 12 -1.51206390e+00 -5.46876931e+00 -3.50894652e+00 | -1.51206390e+00 -5.46876931e+00 -3.50894652e+00 13 1.82912186e+01 -1.00611032e+01 -4.40476697e+00 | 1.82912186e+01 -1.00611032e+01 -4.40476697e+00 14 -2.63565034e+01 -3.74466769e+01 -3.34545214e+01 | -2.63565034e+01 -3.74466769e+01 -3.34545214e+01 15 3.86860630e+01 3.43443754e+01 4.77114602e+01 | 3.86860630e+01 3.43443754e+01 4.77114602e+01 16 5.76792796e-01 -1.41504869e+00 -3.50842351e-01 | 5.76792796e-01 -1.41504869e+00 -3.50842351e-01 17 -9.84096759e+00 -1.10671725e+01 7.29198224e+00 | -9.84096759e+00 -1.10671725e+01 7.29198224e+00 18 6.86984960e+00 5.99313469e+00 -1.51902963e+01 | 6.86984960e+00 5.99313469e+00 -1.51902963e+01 19 5.76657003e+00 4.15374260e+00 3.03301497e+00 | 5.76657003e+00 4.15374260e+00 3.03301497e+00 20 -5.25241951e+00 6.99708610e+00 1.63003828e+00 | -5.25241951e+00 6.99708610e+00 1.63003828e+00 21 -1.89275356e+01 4.22380684e+01 -1.19186168e+01 | -1.89275356e+01 4.22380684e+01 -1.19186168e+01 22 -3.65913535e+01 -4.46684276e+01 -2.63805762e+01 | -3.65913535e+01 -4.46684276e+01 -2.63805762e+01 23 3.45060749e+01 4.94930330e+01 2.06349841e+01 | 3.45060749e+01 4.94930330e+01 2.06349841e+01 24 3.04733866e+01 6.54719067e+01 -4.58517802e+01 | 3.04733866e+01 6.54719067e+01 -4.58517802e+01 25 -2.46036936e+00 -1.26505231e+00 4.04859642e+00 | -2.46036936e+00 -1.26505231e+00 4.04859642e+00 26 -2.19570308e+01 -5.27136047e+00 -1.09259902e+01 | -2.19570308e+01 -5.27136047e+00 -1.09259902e+01 27 2.21722981e+01 8.07671926e+00 1.18458498e+01 | 2.21722981e+01 8.07671926e+00 1.18458498e+01 28 2.61016969e+00 -3.36898955e+01 -3.40748950e+01 | 2.61016969e+00 -3.36898955e+01 -3.40748950e+01 29 2.04309539e+01 1.97834979e+01 1.16294938e+01 | 2.04309539e+01 1.97834979e+01 1.16294938e+01 30 -1.30680806e+01 -1.22567334e+01 -1.74034150e+01 | -1.30680806e+01 -1.22567334e+01 -1.74034150e+01 31 2.62952914e+01 1.87900665e+01 9.13121957e+00 | 2.62952914e+01 1.87900665e+01 9.13121957e+00 32 -1.68077537e+01 -9.75558110e+00 -1.95921440e+01 | -1.68077537e+01 -9.75558110e+00 -1.95921440e+01 33 -8.87405716e+00 -8.46456660e+00 -5.61885308e+01 | -8.87405716e+00 -8.46456660e+00 -5.61885308e+01 34 1.91053961e+01 -4.12105035e+01 6.05469870e+01 | 1.91053961e+01 -4.12105035e+01 6.05469870e+01 35 -4.18318274e+01 -1.61135196e+01 2.48018953e+01 | -4.18318274e+01 -1.61135196e+01 2.48018953e+01 36 1.23705940e+01 3.15267361e+00 6.32901148e+01 | 1.23705940e+01 3.15267361e+00 6.32901148e+01 37 5.86995473e+00 4.01192630e-01 6.19986901e+00 | 5.86995473e+00 4.01192630e-01 6.19986901e+00 38 8.99183366e+00 -7.63588597e-01 -1.75930610e+01 | 8.99183366e+00 -7.63588597e-01 -1.75930610e+01 39 9.04003523e+00 2.89116286e+00 1.77905972e+01 | 9.04003523e+00 2.89116286e+00 1.77905972e+01 40 -2.81715799e+01 -2.49287001e+01 -2.73899125e+01 | -2.81715799e+01 -2.49287001e+01 -2.73899125e+01 41 8.49708229e+00 -2.86023170e+01 7.30774403e+01 | 8.49708229e+00 -2.86023170e+01 7.30774403e+01 42 3.92551431e+01 4.64556481e+01 -5.46268013e+01 | 3.92551431e+01 4.64556481e+01 -5.46268013e+01 43 2.15650400e+01 -3.37065563e+00 -3.16471764e+01 | 2.15650400e+01 -3.37065563e+00 -3.16471764e+01 44 -1.64226281e+01 -2.70206032e+01 -1.51981884e+01 | -1.64226281e+01 -2.70206032e+01 -1.51981884e+01 45 1.49448599e+01 2.71528400e+01 1.33299033e+01 | 1.49448599e+01 2.71528400e+01 1.33299033e+01 46 -3.89691860e+01 1.74152580e+01 9.80861051e+00 | -3.89691860e+01 1.74152580e+01 9.80861051e+00 47 -7.19165622e+00 -3.85160248e+00 1.55182408e+01 | -7.19165622e+00 -3.85160248e+00 1.55182408e+01 48 -4.56977868e+00 -5.08785285e+00 -1.75945428e+00 | -4.56977868e+00 -5.08785285e+00 -1.75945428e+00 49 -9.30712023e-01 -4.24384548e+01 2.51253674e+01 | -9.30712023e-01 -4.24384548e+01 2.51253674e+01 50 1.56957022e+01 3.92706559e+01 -1.82702155e+01 | 1.56957022e+01 3.92706559e+01 -1.82702155e+01 51 -7.93012699e+00 2.76260683e+00 6.33022885e+00 | -7.93012699e+00 2.76260683e+00 6.33022885e+00 52 -1.85064094e+01 -3.69939504e+01 8.01367104e+00 | -1.85064094e+01 -3.69939504e+01 8.01367104e+00 53 1.15731578e+01 3.90187647e+01 2.92475119e+00 | 1.15731578e+01 3.90187647e+01 2.92475119e+00 54 -1.17351915e+01 -1.76905182e+01 -1.31569398e+01 | -1.17351915e+01 -1.76905182e+01 -1.31569398e+01 55 1.14073637e+01 1.78250396e+01 1.46839980e+01 | 1.14073637e+01 1.78250396e+01 1.46839980e+01 56 5.56807600e+01 -2.26371970e+01 -7.17108399e+00 | 5.56807600e+01 -2.26371970e+01 -7.17108399e+00 57 4.10162682e+01 -5.53999352e+01 -4.00676816e+00 | 4.10162682e+01 -5.53999352e+01 -4.00676816e+00 58 -1.93163420e+01 -1.60566978e+01 -4.18867150e+00 | -1.93163420e+01 -1.60566978e+01 -4.18867150e+00 59 8.62356977e+00 3.28469682e+01 2.96757599e+01 | 8.62356977e+00 3.28469682e+01 2.96757599e+01 60 -1.20959449e+01 1.05730547e+01 1.62242432e+01 | -1.20959449e+01 1.05730547e+01 1.62242432e+01 61 -8.26322946e-01 3.33210278e+00 -5.61814988e-01 | -8.26322946e-01 3.33210278e+00 -5.61814988e-01 62 -3.44210156e+01 5.33352421e+01 -2.27381792e+00 | -3.44210156e+01 5.33352421e+01 -2.27381792e+00 63 2.96377171e+00 2.33950633e+00 3.56575568e+00 | 2.96377171e+00 2.33950633e+00 3.56575568e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [7, 43, 45, 27, 49, 60, 42, 0, 18, 33, 46, 29, 48, 21, 62, 41, 38, 44, 8, 20, 19, 13, 35, 37, 57, 47, 61, 3, 59, 11, 51, 50, 34, 9, 32, 22, 36, 23, 16, 63, 56, 15, 6, 1, 17, 2, 10, 25, 12, 4, 31, 30, 58, 55, 54, 53, 40, 24, 52, 28, 5, 26, 14, 39] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 87.55286643 V(r_1,...,r_N) = 87.55286643 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 1.79014043e+00 1.47893481e+00 1.32122709e+00 | 1.79014043e+00 1.47893481e+00 1.32122709e+00 1 -5.03454181e+00 -2.46604924e+00 3.58331829e-01 | -5.03454181e+00 -2.46604924e+00 3.58331829e-01 2 1.20441458e+00 2.96719095e+00 -3.45570066e+00 | 1.20441458e+00 2.96719095e+00 -3.45570066e+00 3 -1.24861101e+02 -5.33963567e+01 1.21950109e+02 | -1.24861101e+02 -5.33963567e+01 1.21950109e+02 4 1.20141670e+00 -1.24990496e+00 3.59512293e+00 | 1.20141670e+00 -1.24990496e+00 3.59512293e+00 5 2.50662785e+00 -3.18678267e+00 -5.89104444e+00 | 2.50662785e+00 -3.18678267e+00 -5.89104444e+00 6 -1.03118945e+01 2.62361332e+00 -1.63427183e+01 | -1.03118945e+01 2.62361332e+00 -1.63427183e+01 7 3.00866787e+00 -4.71215774e+00 1.13061400e+01 | 3.00866787e+00 -4.71215774e+00 1.13061400e+01 8 -7.21748337e-01 -8.22687982e-01 -1.03212862e+00 | -7.21748337e-01 -8.22687982e-01 -1.03212862e+00 9 3.53009881e+01 -1.22406526e+02 -6.09562764e+01 | 3.53009881e+01 -1.22406526e+02 -6.09562764e+01 10 5.64951711e+00 1.99953210e+00 -6.43480135e-02 | 5.64951711e+00 1.99953210e+00 -6.43480135e-02 11 1.13664057e+01 -1.65216386e+01 -3.44876101e+01 | 1.13664057e+01 -1.65216386e+01 -3.44876101e+01 12 -1.60831188e+00 -4.07747727e-01 -3.47752626e-01 | -1.60831188e+00 -4.07747727e-01 -3.47752626e-01 13 -1.20310553e-01 1.65749735e+00 3.61527272e-01 | -1.20310553e-01 1.65749735e+00 3.61527272e-01 14 -3.73189435e+01 1.20023665e+02 6.10766846e+01 | -3.73189435e+01 1.20023665e+02 6.10766846e+01 15 4.78234806e+01 -2.38011233e+01 -1.99884662e+01 | 4.78234806e+01 -2.38011233e+01 -1.99884662e+01 16 1.24512640e+00 6.04908037e-01 1.61262447e-02 | 1.24512640e+00 6.04908037e-01 1.61262447e-02 17 1.12192831e+00 -1.88504593e+00 -3.15857599e-01 | 1.12192831e+00 -1.88504593e+00 -3.15857599e-01 18 -8.10732914e-01 -7.11629956e-01 -2.73389595e+00 | -8.10732914e-01 -7.11629956e-01 -2.73389595e+00 19 -1.20281814e+01 1.58116931e+01 -1.65708541e+01 | -1.20281814e+01 1.58116931e+01 -1.65708541e+01 20 2.97532932e+00 5.09096505e-01 -6.86605783e-01 | 2.97532932e+00 5.09096505e-01 -6.86605783e-01 21 3.30862786e+01 -2.50788867e+01 -5.00401444e+01 | 3.30862786e+01 -2.50788867e+01 -5.00401444e+01 22 -1.97132889e+01 -1.14647804e+01 -2.33727153e+01 | -1.97132889e+01 -1.14647804e+01 -2.33727153e+01 23 5.73554613e+00 1.85343227e+01 1.76811527e+01 | 5.73554613e+00 1.85343227e+01 1.76811527e+01 24 1.21658872e+02 5.48579818e+01 -1.19644106e+02 | 1.21658872e+02 5.48579818e+01 -1.19644106e+02 25 -3.73980348e+01 -2.96647544e+01 3.46635214e+01 | -3.73980348e+01 -2.96647544e+01 3.46635214e+01 26 3.01537235e+01 1.89978421e+01 -3.67302326e+01 | 3.01537235e+01 1.89978421e+01 -3.67302326e+01 27 6.82257966e+00 1.01029007e+01 2.85809941e+00 | 6.82257966e+00 1.01029007e+01 2.85809941e+00 28 -1.34893039e+01 1.46163531e+01 3.20781402e+01 | -1.34893039e+01 1.46163531e+01 3.20781402e+01 29 1.46983335e+00 -3.54467901e-01 -1.80843220e+00 | 1.46983335e+00 -3.54467901e-01 -1.80843220e+00 30 1.18820524e+01 -1.42538073e+01 1.55414942e+01 | 1.18820524e+01 -1.42538073e+01 1.55414942e+01 31 -2.97195744e+01 4.11696366e+01 -4.35763013e+01 | -2.97195744e+01 4.11696366e+01 -4.35763013e+01 32 2.62367441e-01 -2.67307563e-01 5.80803859e-01 | 2.62367441e-01 -2.67307563e-01 5.80803859e-01 33 -1.34108971e+02 -1.32418351e+02 1.74367652e+01 | -1.34108971e+02 -1.32418351e+02 1.74367652e+01 34 1.37656222e+02 1.36810560e+02 -7.24994534e+00 | 1.37656222e+02 1.36810560e+02 -7.24994534e+00 35 3.19162327e+00 -7.26148693e+00 -1.40750342e+01 | 3.19162327e+00 -7.26148693e+00 -1.40750342e+01 36 7.19064254e-01 -1.17577371e+00 1.96975776e+00 | 7.19064254e-01 -1.17577371e+00 1.96975776e+00 37 1.24190349e+00 7.17315843e-01 -3.06288335e+00 | 1.24190349e+00 7.17315843e-01 -3.06288335e+00 38 1.15659404e+00 -4.17634464e-01 -1.54084078e+00 | 1.15659404e+00 -4.17634464e-01 -1.54084078e+00 39 -1.07203362e+00 -5.10794234e-01 2.39775579e+00 | -1.07203362e+00 -5.10794234e-01 2.39775579e+00 40 -3.54658825e+01 -2.04742546e+01 -4.94002706e+01 | -3.54658825e+01 -2.04742546e+01 -4.94002706e+01 41 -5.60932243e+00 2.54091818e+01 1.87373508e+01 | -5.60932243e+00 2.54091818e+01 1.87373508e+01 42 5.34894817e+00 -8.02489565e+00 4.50950957e+00 | 5.34894817e+00 -8.02489565e+00 4.50950957e+00 43 -1.88170710e+00 -1.42328333e+00 -2.03796837e+00 | -1.88170710e+00 -1.42328333e+00 -2.03796837e+00 44 4.40554732e+01 -6.17641093e+00 2.97024829e+01 | 4.40554732e+01 -6.17641093e+00 2.97024829e+01 45 1.84534573e+00 1.24452569e+00 1.97840201e+00 | 1.84534573e+00 1.24452569e+00 1.97840201e+00 46 -2.64518402e+00 1.41428800e+00 1.05580520e+00 | -2.64518402e+00 1.41428800e+00 1.05580520e+00 47 -2.03476593e+00 -1.17218163e-02 -7.21232849e-01 | -2.03476593e+00 -1.17218163e-02 -7.21232849e-01 48 -1.81702303e+01 -1.35249492e+01 -1.49614501e+01 | -1.81702303e+01 -1.35249492e+01 -1.49614501e+01 49 1.95132443e+01 3.34961276e+00 1.58737638e+01 | 1.95132443e+01 3.34961276e+00 1.58737638e+01 50 -3.16689679e+01 2.71028820e+01 5.49512498e+01 | -3.16689679e+01 2.71028820e+01 5.49512498e+01 51 9.24375365e-01 5.45868760e-01 -7.12747444e-01 | 9.24375365e-01 5.45868760e-01 -7.12747444e-01 52 -1.12488164e+01 1.34053325e+01 3.77638482e+00 | -1.12488164e+01 1.34053325e+01 3.77638482e+00 53 -2.12123839e+01 -3.66571312e+01 1.62377761e+01 | -2.12123839e+01 -3.66571312e+01 1.62377761e+01 54 2.97849477e-01 -1.87534165e+00 -2.51545474e+00 | 2.97849477e-01 -1.87534165e+00 -2.51545474e+00 55 2.28673912e+00 1.09905866e+00 5.99611835e-01 | 2.28673912e+00 1.09905866e+00 5.99611835e-01 56 -4.40368618e+01 2.19526450e+01 2.70471326e+01 | -4.40368618e+01 2.19526450e+01 2.70471326e+01 57 -1.45097144e-02 1.40395911e+00 -1.31411771e+00 | -1.45097144e-02 1.40395911e+00 -1.31411771e+00 58 2.80122655e+01 -4.05379610e+01 4.68657210e+01 | 2.80122655e+01 -4.05379610e+01 4.68657210e+01 59 -2.39065173e-01 -2.85586530e-01 9.01711659e-01 | -2.39065173e-01 -2.85586530e-01 9.01711659e-01 60 -1.86467304e+01 -1.08914849e+01 -1.37461268e+01 | -1.86467304e+01 -1.08914849e+01 -1.37461268e+01 61 1.85115379e+01 1.44567508e+01 1.49180477e+01 | 1.85115379e+01 1.44567508e+01 1.49180477e+01 62 1.46032709e+01 2.98340218e+01 -2.53432725e+01 | 1.46032709e+01 2.98340218e+01 -2.53432725e+01 63 1.55616469e+01 9.61754565e+00 1.23788259e+01 | 1.55616469e+01 9.61754565e+00 1.23788259e+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.