!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KimKimJung_2017_NiAlTi__MO_478967255435_000 Supported species : Al Ni 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 = [35, 22, 27, 49, 11, 19, 55, 31, 38, 54, 15, 4, 50, 46, 40, 10, 17, 16, 58, 5, 53, 39, 1, 44, 52, 63, 28, 2, 26, 32, 45, 7, 29, 43, 37, 0, 59, 34, 8, 21, 14, 56, 57, 33, 23, 30, 13, 61, 51, 3, 12, 48, 24, 20, 9, 6, 41, 42, 18, 36, 62, 47, 60, 25] 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)) = 16.989058405364606 V(r_1,...,r_N) = 16.98905840536462 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -2.55538749e+00 -1.67213281e+00 -2.39461343e+00 | -2.55538749e+00 -1.67213281e+00 -2.39461343e+00 1 -1.02096000e+01 -1.42014129e+01 8.03739134e+00 | -1.02096000e+01 -1.42014129e+01 8.03739134e+00 2 -1.16426783e+00 5.99898565e+00 -2.66844327e+01 | -1.16426783e+00 5.99898565e+00 -2.66844327e+01 3 6.28540447e+00 1.47587113e+01 9.75782069e+00 | 6.28540447e+00 1.47587113e+01 9.75782069e+00 4 2.46831550e+00 -5.82492632e+00 6.80883879e+00 | 2.46831550e+00 -5.82492632e+00 6.80883879e+00 5 4.82019443e-01 1.61558146e+00 -9.78971535e-01 | 4.82019443e-01 1.61558146e+00 -9.78971535e-01 6 -1.99358858e+00 -3.83251091e+00 -5.10178056e+00 | -1.99358858e+00 -3.83251091e+00 -5.10178056e+00 7 -9.63127893e+00 4.71887903e+01 -2.56010458e+01 | -9.63127893e+00 4.71887903e+01 -2.56010458e+01 8 -9.36676664e+00 -1.05410630e+01 -1.35533797e+01 | -9.36676664e+00 -1.05410630e+01 -1.35533797e+01 9 6.85005709e+00 5.25559161e+00 1.79800904e+01 | 6.85005709e+00 5.25559161e+00 1.79800904e+01 10 5.64665197e+00 2.91446538e+00 -7.92064343e+00 | 5.64665197e+00 2.91446538e+00 -7.92064343e+00 11 3.01992240e+00 -1.75322630e+00 -7.58069219e-01 | 3.01992240e+00 -1.75322630e+00 -7.58069219e-01 12 -5.00471556e+00 -3.35558208e+00 -5.91524947e+00 | -5.00471556e+00 -3.35558208e+00 -5.91524947e+00 13 2.00632352e+01 -8.77093356e+00 -4.17970751e+00 | 2.00632352e+01 -8.77093356e+00 -4.17970751e+00 14 -9.07392635e-01 -9.09895002e-02 1.30608127e+00 | -9.07392635e-01 -9.09895002e-02 1.30608127e+00 15 1.59816705e+00 -2.33630969e+00 -1.82315229e+00 | 1.59816705e+00 -2.33630969e+00 -1.82315229e+00 16 -2.52898125e+00 -1.53339656e+00 -1.81776774e+00 | -2.52898125e+00 -1.53339656e+00 -1.81776774e+00 17 -4.46300121e+00 -1.57381149e+01 1.93390472e+01 | -4.46300121e+00 -1.57381149e+01 1.93390472e+01 18 4.59744579e+00 1.65854455e+01 -1.96042456e+01 | 4.59744579e+00 1.65854455e+01 -1.96042456e+01 19 -2.95175610e+01 2.03024708e+01 -2.00972094e+01 | -2.95175610e+01 2.03024708e+01 -2.00972094e+01 20 -1.07267417e+01 -9.39023938e+00 -8.49050106e+00 | -1.07267417e+01 -9.39023938e+00 -8.49050106e+00 21 1.76137994e+01 1.18424284e+01 7.60825502e+00 | 1.76137994e+01 1.18424284e+01 7.60825502e+00 22 -2.87057703e+00 -7.74770097e+00 -1.37306428e+01 | -2.87057703e+00 -7.74770097e+00 -1.37306428e+01 23 2.05286248e+00 7.87117922e+00 1.43342384e+01 | 2.05286248e+00 7.87117922e+00 1.43342384e+01 24 -9.99175947e-01 -7.59452658e-01 -9.31440716e-01 | -9.99175947e-01 -7.59452658e-01 -9.31440716e-01 25 -1.03642659e+01 1.37297592e+01 -9.91517128e+00 | -1.03642659e+01 1.37297592e+01 -9.91517128e+00 26 -1.02451900e+00 -3.76788572e-01 -4.98327657e-01 | -1.02451900e+00 -3.76788572e-01 -4.98327657e-01 27 6.03953474e-01 -2.22076977e-01 9.55928261e-01 | 6.03953474e-01 -2.22076977e-01 9.55928261e-01 28 8.83431408e+00 -1.14233014e+01 1.22138646e+01 | 8.83431408e+00 -1.14233014e+01 1.22138646e+01 29 1.70736696e+00 3.20675334e-01 9.71852596e-01 | 1.70736696e+00 3.20675334e-01 9.71852596e-01 30 2.93141416e+01 -1.75928455e+01 1.72824051e+01 | 2.93141416e+01 -1.75928455e+01 1.72824051e+01 31 -1.56203474e+01 6.67361884e+00 -8.37784145e+00 | -1.56203474e+01 6.67361884e+00 -8.37784145e+00 32 -4.71285814e+00 -4.57329030e+00 -2.35598343e+00 | -4.71285814e+00 -4.57329030e+00 -2.35598343e+00 33 -1.91813300e+00 -4.40176900e+00 6.25772914e+00 | -1.91813300e+00 -4.40176900e+00 6.25772914e+00 34 2.49022950e+01 -3.86445888e+01 2.22199227e+01 | 2.49022950e+01 -3.86445888e+01 2.22199227e+01 35 -4.81590789e+00 -6.68816834e+00 4.86512798e+00 | -4.81590789e+00 -6.68816834e+00 4.86512798e+00 36 -5.38012156e+00 4.73518283e-01 2.18348514e+00 | -5.38012156e+00 4.73518283e-01 2.18348514e+00 37 -7.58661507e+00 -2.14776032e+01 1.59142341e+01 | -7.58661507e+00 -2.14776032e+01 1.59142341e+01 38 -6.58556167e+00 -5.36619921e+00 -5.66289623e+00 | -6.58556167e+00 -5.36619921e+00 -5.66289623e+00 39 -7.41372766e+00 -6.84677160e+00 1.37196790e+01 | -7.41372766e+00 -6.84677160e+00 1.37196790e+01 40 4.24169517e+00 -2.43826672e+00 -3.81343965e-01 | 4.24169517e+00 -2.43826672e+00 -3.81343965e-01 41 -1.74376972e+01 2.38611716e+01 -1.17490078e+01 | -1.74376972e+01 2.38611716e+01 -1.17490078e+01 42 -1.55465071e+01 6.74907053e+00 3.82688415e+00 | -1.55465071e+01 6.74907053e+00 3.82688415e+00 43 3.34063548e+00 6.68557546e+00 4.35948685e+00 | 3.34063548e+00 6.68557546e+00 4.35948685e+00 44 1.62355659e+01 -2.55355556e+01 1.34103491e+01 | 1.62355659e+01 -2.55355556e+01 1.34103491e+01 45 -1.07717449e-01 1.82388517e-01 -1.53255583e-01 | -1.07717449e-01 1.82388517e-01 -1.53255583e-01 46 8.88373888e+00 1.99189010e+01 -1.23394547e+01 | 8.88373888e+00 1.99189010e+01 -1.23394547e+01 47 4.25522161e+00 -4.37329491e+00 -1.25740171e+00 | 4.25522161e+00 -4.37329491e+00 -1.25740171e+00 48 -1.10865193e+01 3.85010971e+00 6.04935085e+00 | -1.10865193e+01 3.85010971e+00 6.04935085e+00 49 4.32658583e-01 -1.75763726e+00 -9.90176437e-01 | 4.32658583e-01 -1.75763726e+00 -9.90176437e-01 50 -7.90281192e+00 -1.12037438e+01 -1.15760673e+01 | -7.90281192e+00 -1.12037438e+01 -1.15760673e+01 51 7.68599126e+00 1.18411989e+01 1.08196647e+01 | 7.68599126e+00 1.18411989e+01 1.08196647e+01 52 1.23676422e+01 1.27928201e+01 -7.68811624e+00 | 1.23676422e+01 1.27928201e+01 -7.68811624e+00 53 -3.41497507e+00 4.25315927e+00 1.54437938e+00 | -3.41497507e+00 4.25315927e+00 1.54437938e+00 54 -6.09275647e+00 6.77165505e-01 -1.60348099e+00 | -6.09275647e+00 6.77165505e-01 -1.60348099e+00 55 3.96514153e+00 1.01052551e+00 3.01917395e+00 | 3.96514153e+00 1.01052551e+00 3.01917395e+00 56 7.86124836e-02 5.53895913e+00 -2.63691392e+00 | 7.86124836e-02 5.53895913e+00 -2.63691392e+00 57 1.75211178e+01 -2.38607843e+01 -2.97134921e+01 | 1.75211178e+01 -2.38607843e+01 -2.97134921e+01 58 1.66714243e+01 -5.47293320e+00 1.01948449e+01 | 1.66714243e+01 -5.47293320e+00 1.01948449e+01 59 -3.45466144e-01 -4.44050908e-01 5.15023690e-01 | -3.45466144e-01 -4.44050908e-01 5.15023690e-01 60 -2.17778803e+00 -2.65928007e+00 -3.48044210e+00 | -2.17778803e+00 -2.65928007e+00 -3.48044210e+00 61 3.72061081e+00 3.38341263e+00 4.05958900e+00 | 3.72061081e+00 3.38341263e+00 4.05958900e+00 62 -1.49704995e+01 2.66817894e+01 3.05286801e+01 | -1.49704995e+01 2.66817894e+01 3.05286801e+01 63 1.00382338e+00 -5.05275880e-02 -1.21192548e-01 | 1.00382338e+00 -5.05275880e-02 -1.21192548e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [52, 33, 13, 20, 24, 60, 55, 35, 43, 49, 15, 54, 25, 2, 19, 10, 45, 46, 50, 14, 3, 38, 48, 41, 4, 12, 63, 56, 47, 36, 34, 58, 40, 1, 30, 7, 29, 57, 21, 42, 32, 23, 39, 8, 61, 16, 17, 28, 22, 9, 18, 53, 0, 51, 11, 6, 27, 37, 31, 62, 5, 44, 59, 26] 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)) = -50.96784248521104 V(r_1,...,r_N) = -50.96784248521102 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 -9.19395533e+00 -7.81324813e+00 -1.00345832e+01 | -9.19395533e+00 -7.81324813e+00 -1.00345832e+01 1 4.12295292e+00 -9.09753942e+00 2.35227402e+01 | 4.12295292e+00 -9.09753942e+00 2.35227402e+01 2 -3.80802428e-01 2.27357035e+01 -1.88667539e+01 | -3.80802428e-01 2.27357035e+01 -1.88667539e+01 3 -1.07653161e+01 -1.70735368e+01 1.05154644e+00 | -1.07653161e+01 -1.70735368e+01 1.05154644e+00 4 5.34657309e+00 -5.15241027e+00 5.04032941e+00 | 5.34657309e+00 -5.15241027e+00 5.04032941e+00 5 1.51649089e+01 -2.22442022e+01 -1.85338672e+01 | 1.51649089e+01 -2.22442022e+01 -1.85338672e+01 6 -7.50817267e+00 -3.70666068e+00 -2.89817754e+00 | -7.50817267e+00 -3.70666068e+00 -2.89817754e+00 7 -6.99417685e+00 -5.27517880e+01 2.60056732e+01 | -6.99417685e+00 -5.27517880e+01 2.60056732e+01 8 -7.78023687e-02 5.49412297e-01 1.05578671e+00 | -7.78023687e-02 5.49412297e-01 1.05578671e+00 9 -1.23053190e+00 -2.81954974e+00 2.00917394e+00 | -1.23053190e+00 -2.81954974e+00 2.00917394e+00 10 9.13283345e-01 9.41365282e-01 -2.43151074e+00 | 9.13283345e-01 9.41365282e-01 -2.43151074e+00 11 -3.43452629e-01 1.24372620e+00 9.80293300e-01 | -3.43452629e-01 1.24372620e+00 9.80293300e-01 12 -2.52161058e+00 -1.66155238e+01 -6.66548225e+00 | -2.52161058e+00 -1.66155238e+01 -6.66548225e+00 13 4.44248582e+00 9.82683549e+00 5.40759225e-01 | 4.44248582e+00 9.82683549e+00 5.40759225e-01 14 -6.10575878e+00 -3.48691349e+00 -5.89446391e+00 | -6.10575878e+00 -3.48691349e+00 -5.89446391e+00 15 -6.68413743e+00 4.14889215e+00 1.75689956e+00 | -6.68413743e+00 4.14889215e+00 1.75689956e+00 16 8.20826002e-01 -5.41086630e-02 8.15540821e-01 | 8.20826002e-01 -5.41086630e-02 8.15540821e-01 17 -4.41560158e+00 4.83658374e+00 -4.59784635e+00 | -4.41560158e+00 4.83658374e+00 -4.59784635e+00 18 1.16758913e+00 7.40297668e-01 -3.67150568e-01 | 1.16758913e+00 7.40297668e-01 -3.67150568e-01 19 1.64488674e-01 -6.11606795e-01 1.57361416e-01 | 1.64488674e-01 -6.11606795e-01 1.57361416e-01 20 1.53715384e+01 5.26801865e+01 -2.10866577e+01 | 1.53715384e+01 5.26801865e+01 -2.10866577e+01 21 -7.66258238e+00 9.62407846e+00 -8.96988909e+00 | -7.66258238e+00 9.62407846e+00 -8.96988909e+00 22 6.16038590e-01 -3.67862253e-01 3.15146512e-01 | 6.16038590e-01 -3.67862253e-01 3.15146512e-01 23 -2.20966284e+01 7.75090817e+00 -8.48778746e+00 | -2.20966284e+01 7.75090817e+00 -8.48778746e+00 24 9.53657600e+00 1.77940905e+01 -1.22692128e+00 | 9.53657600e+00 1.77940905e+01 -1.22692128e+00 25 2.12889186e+00 -6.16680804e+00 -6.73835313e+00 | 2.12889186e+00 -6.16680804e+00 -6.73835313e+00 26 -7.32259166e+00 -1.17164204e+01 -2.01881855e+00 | -7.32259166e+00 -1.17164204e+01 -2.01881855e+00 27 7.58229085e+00 1.21619025e+01 2.27145460e+00 | 7.58229085e+00 1.21619025e+01 2.27145460e+00 28 -9.56836417e+00 -8.91804238e+00 1.54775383e+00 | -9.56836417e+00 -8.91804238e+00 1.54775383e+00 29 1.60451519e+01 1.32640030e+01 -1.61638056e-01 | 1.60451519e+01 1.32640030e+01 -1.61638056e-01 30 -3.51358638e+00 5.50805830e+00 1.98368638e+00 | -3.51358638e+00 5.50805830e+00 1.98368638e+00 31 -1.67529090e+00 1.61116842e+00 1.06570036e+00 | -1.67529090e+00 1.61116842e+00 1.06570036e+00 32 7.24382074e-01 2.49871092e-01 3.49301507e-01 | 7.24382074e-01 2.49871092e-01 3.49301507e-01 33 -8.19577528e+00 3.20516706e+01 -1.69082919e+01 | -8.19577528e+00 3.20516706e+01 -1.69082919e+01 34 -1.68775840e+01 1.75646589e+01 1.74297089e+01 | -1.68775840e+01 1.75646589e+01 1.74297089e+01 35 2.86366399e+00 1.78558423e+00 4.33298916e+00 | 2.86366399e+00 1.78558423e+00 4.33298916e+00 36 7.06172389e+00 -3.21765607e+01 1.68748295e+01 | 7.06172389e+00 -3.21765607e+01 1.68748295e+01 37 -3.12585958e+00 -3.05196946e+00 1.21628548e+00 | -3.12585958e+00 -3.05196946e+00 1.21628548e+00 38 5.73649364e-01 4.30789789e-01 -4.08065524e-01 | 5.73649364e-01 4.30789789e-01 -4.08065524e-01 39 1.95667615e-01 -4.20602567e-02 -6.80382578e-01 | 1.95667615e-01 -4.20602567e-02 -6.80382578e-01 40 1.56352697e-01 7.48757223e-01 -3.89619724e-01 | 1.56352697e-01 7.48757223e-01 -3.89619724e-01 41 9.93858485e+00 -1.70900233e+01 -2.46603310e+01 | 9.93858485e+00 -1.70900233e+01 -2.46603310e+01 42 5.77187368e+00 1.65940715e+00 1.39548152e+01 | 5.77187368e+00 1.65940715e+00 1.39548152e+01 43 -6.55657548e-01 -2.86766244e-01 3.30377185e-01 | -6.55657548e-01 -2.86766244e-01 3.30377185e-01 44 1.89286588e+00 -8.29215425e+00 -4.29252200e-01 | 1.89286588e+00 -8.29215425e+00 -4.29252200e-01 45 2.24409831e+00 4.34065523e+00 4.01284266e+00 | 2.24409831e+00 4.34065523e+00 4.01284266e+00 46 -1.01308294e+01 2.41425320e+01 2.03648461e+01 | -1.01308294e+01 2.41425320e+01 2.03648461e+01 47 -1.03407034e-01 -5.81647002e+00 3.13071309e+00 | -1.03407034e-01 -5.81647002e+00 3.13071309e+00 48 -5.37381624e-01 -1.44851178e+00 -7.79629528e-01 | -5.37381624e-01 -1.44851178e+00 -7.79629528e-01 49 3.97939183e+00 -1.56167233e+00 -1.11606267e+00 | 3.97939183e+00 -1.56167233e+00 -1.11606267e+00 50 1.47007363e+01 -2.20247618e+01 -1.60420684e+00 | 1.47007363e+01 -2.20247618e+01 -1.60420684e+00 51 6.79499525e+00 1.32442012e+01 1.01473343e+01 | 6.79499525e+00 1.32442012e+01 1.01473343e+01 52 -6.25179853e+00 -1.42785495e+01 -1.50412970e+01 | -6.25179853e+00 -1.42785495e+01 -1.50412970e+01 53 5.56904402e+00 1.41376601e+01 1.44566040e+01 | 5.56904402e+00 1.41376601e+01 1.44566040e+01 54 -1.69844468e+00 3.32347131e+00 2.32557159e+00 | -1.69844468e+00 3.32347131e+00 2.32557159e+00 55 -4.09903947e-02 -7.83074638e-01 -9.02532874e-01 | -4.09903947e-02 -7.83074638e-01 -9.02532874e-01 56 8.70063569e+00 -7.93926269e+00 6.29483187e+00 | 8.70063569e+00 -7.93926269e+00 6.29483187e+00 57 -3.08041974e-01 2.50481309e+00 -2.57036601e+00 | -3.08041974e-01 2.50481309e+00 -2.57036601e+00 58 -1.18944060e+01 -8.41662213e+00 -1.31884568e+01 | -1.18944060e+01 -8.41662213e+00 -1.31884568e+01 59 1.19422049e+01 6.59145219e+00 1.37565020e+01 | 1.19422049e+01 6.59145219e+00 1.37565020e+01 60 -1.43957712e+00 1.04499304e+00 -1.72212618e+00 | -1.43957712e+00 1.04499304e+00 -1.72212618e+00 61 3.19057577e+00 3.41303114e+00 1.35188234e-01 | 3.19057577e+00 3.41303114e+00 1.35188234e-01 62 -8.41094635e+00 -5.00156832e+00 -2.28304950e+01 | -8.41094635e+00 -5.00156832e+00 -2.28304950e+01 63 8.00702050e+00 4.15548798e+00 2.29784299e+01 | 8.00702050e+00 4.15548798e+00 2.29784299e+01 ------------------------------------------------------------------------------------------------------------------------- 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 = [49, 22, 39, 16, 62, 43, 29, 36, 19, 51, 13, 35, 42, 10, 32, 58, 3, 21, 30, 8, 61, 17, 1, 45, 27, 57, 31, 24, 34, 6, 18, 26, 14, 48, 28, 11, 7, 47, 50, 2, 60, 56, 12, 5, 63, 23, 53, 37, 33, 0, 38, 9, 54, 46, 52, 59, 41, 25, 15, 55, 40, 20, 4, 44] 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)) = 68.9583574196004 V(r_1,...,r_N) = 68.95835741960038 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 -1.82169435e+01 -9.56236845e+00 -9.69517495e+00 | -1.82169435e+01 -9.56236845e+00 -9.69517495e+00 1 9.39863963e+00 1.43017208e+01 -8.23762582e-01 | 9.39863963e+00 1.43017208e+01 -8.23762582e-01 2 1.81977277e+00 -4.32290550e-01 -3.09022028e+00 | 1.81977277e+00 -4.32290550e-01 -3.09022028e+00 3 -2.80494649e-01 1.23444199e+00 1.15851753e+00 | -2.80494649e-01 1.23444199e+00 1.15851753e+00 4 6.61377487e+00 -6.55830157e+00 1.34702734e+01 | 6.61377487e+00 -6.55830157e+00 1.34702734e+01 5 -7.44014056e+00 7.49180451e+00 -5.76152978e+00 | -7.44014056e+00 7.49180451e+00 -5.76152978e+00 6 1.05020994e-01 -1.17468149e-01 -2.65929918e-01 | 1.05020994e-01 -1.17468149e-01 -2.65929918e-01 7 2.71204830e+01 -3.95354597e+00 -1.95217837e+01 | 2.71204830e+01 -3.95354597e+00 -1.95217837e+01 8 -2.97085230e+01 -3.32786070e+01 -2.21153933e+01 | -2.97085230e+01 -3.32786070e+01 -2.21153933e+01 9 1.14059366e+01 1.76545964e+01 2.15163948e+01 | 1.14059366e+01 1.76545964e+01 2.15163948e+01 10 1.72862426e+01 1.17408721e+01 -5.13406183e+00 | 1.72862426e+01 1.17408721e+01 -5.13406183e+00 11 2.11057344e+01 -2.82613151e+01 -3.72782492e+01 | 2.11057344e+01 -2.82613151e+01 -3.72782492e+01 12 -3.26286364e+01 -6.24351106e+01 -7.42999444e+01 | -3.26286364e+01 -6.24351106e+01 -7.42999444e+01 13 3.17672289e+01 6.35429925e+01 7.40144076e+01 | 3.17672289e+01 6.35429925e+01 7.40144076e+01 14 7.30534121e-01 -3.34101088e+00 -3.06529583e+00 | 7.30534121e-01 -3.34101088e+00 -3.06529583e+00 15 -2.82467689e+00 9.09855917e+00 7.11462919e+00 | -2.82467689e+00 9.09855917e+00 7.11462919e+00 16 1.23960851e+00 -2.27282524e-01 1.07112056e+00 | 1.23960851e+00 -2.27282524e-01 1.07112056e+00 17 -6.09014597e+00 2.50130474e+01 -1.77535188e+01 | -6.09014597e+00 2.50130474e+01 -1.77535188e+01 18 -1.33970415e+00 -7.56588544e-01 -2.83570322e+00 | -1.33970415e+00 -7.56588544e-01 -2.83570322e+00 19 1.48615295e+00 1.35082423e+00 1.99977078e+00 | 1.48615295e+00 1.35082423e+00 1.99977078e+00 20 7.75356718e-01 -2.67022661e+01 2.38175076e+00 | 7.75356718e-01 -2.67022661e+01 2.38175076e+00 21 2.72983641e+00 -6.42328564e-01 5.27633271e+00 | 2.72983641e+00 -6.42328564e-01 5.27633271e+00 22 -5.01496264e+00 -4.05549314e+00 -1.65404249e+00 | -5.01496264e+00 -4.05549314e+00 -1.65404249e+00 23 2.16449128e+00 4.35985469e+00 2.98475054e+00 | 2.16449128e+00 4.35985469e+00 2.98475054e+00 24 -1.00231649e+01 -1.31599165e+01 -1.71718600e+01 | -1.00231649e+01 -1.31599165e+01 -1.71718600e+01 25 1.26125736e+01 4.77668506e+00 1.49467501e+01 | 1.26125736e+01 4.77668506e+00 1.49467501e+01 26 -2.25287407e+00 4.33588462e+00 1.19644624e-01 | -2.25287407e+00 4.33588462e+00 1.19644624e-01 27 5.50579318e-01 -2.76128625e-01 1.57487089e+00 | 5.50579318e-01 -2.76128625e-01 1.57487089e+00 28 -1.60155328e+01 2.67059406e+01 3.19017147e+01 | -1.60155328e+01 2.67059406e+01 3.19017147e+01 29 1.50217306e+01 -1.74537894e+01 -1.57519679e+01 | 1.50217306e+01 -1.74537894e+01 -1.57519679e+01 30 -9.67359995e+00 -3.85451570e+00 -1.18853148e+01 | -9.67359995e+00 -3.85451570e+00 -1.18853148e+01 31 7.69124663e+00 1.16646952e+01 1.19050697e+01 | 7.69124663e+00 1.16646952e+01 1.19050697e+01 32 -5.33093792e-01 -1.22205942e-01 -1.36745050e+00 | -5.33093792e-01 -1.22205942e-01 -1.36745050e+00 33 -6.76674477e+00 1.59256060e+00 -4.66781506e+00 | -6.76674477e+00 1.59256060e+00 -4.66781506e+00 34 -9.54106801e+00 -2.83421347e+01 -1.97756415e+01 | -9.54106801e+00 -2.83421347e+01 -1.97756415e+01 35 1.40534825e+01 2.38423570e+01 1.18904707e+01 | 1.40534825e+01 2.38423570e+01 1.18904707e+01 36 1.70638997e+00 -7.60371398e+00 6.15172353e+00 | 1.70638997e+00 -7.60371398e+00 6.15172353e+00 37 -1.25610471e+00 -3.73727709e+00 6.27555323e+00 | -1.25610471e+00 -3.73727709e+00 6.27555323e+00 38 -8.38441618e-01 3.19339703e-01 -1.76121649e-01 | -8.38441618e-01 3.19339703e-01 -1.76121649e-01 39 2.45183537e-02 -5.14320000e+00 6.14036751e+00 | 2.45183537e-02 -5.14320000e+00 6.14036751e+00 40 3.49924725e+00 -1.41798461e+01 2.40696315e+00 | 3.49924725e+00 -1.41798461e+01 2.40696315e+00 41 7.22642295e-01 -1.27580769e+01 -1.22834192e+01 | 7.22642295e-01 -1.27580769e+01 -1.22834192e+01 42 -1.45814931e+01 -4.33342036e+00 -1.13935606e+01 | -1.45814931e+01 -4.33342036e+00 -1.13935606e+01 43 1.63750335e+01 5.44456962e+00 1.29247433e+01 | 1.63750335e+01 5.44456962e+00 1.29247433e+01 44 -4.57993527e+00 -2.24479588e+00 -3.90825141e+00 | -4.57993527e+00 -2.24479588e+00 -3.90825141e+00 45 3.28248408e+00 3.52451986e+00 3.48599125e+00 | 3.28248408e+00 3.52451986e+00 3.48599125e+00 46 4.44620553e+00 1.90099121e+01 1.03093210e+01 | 4.44620553e+00 1.90099121e+01 1.03093210e+01 47 -8.30406324e+00 -6.12490904e+00 1.25133051e+01 | -8.30406324e+00 -6.12490904e+00 1.25133051e+01 48 -2.70053459e+01 4.49672646e+00 2.51449776e+01 | -2.70053459e+01 4.49672646e+00 2.51449776e+01 49 4.07124880e+00 2.70184902e+00 -3.55807417e+00 | 4.07124880e+00 2.70184902e+00 -3.55807417e+00 50 2.56456532e+00 -8.91050646e+00 -1.47189906e+01 | 2.56456532e+00 -8.91050646e+00 -1.47189906e+01 51 -1.74296509e+00 1.11733904e+01 1.72791242e+01 | -1.74296509e+00 1.11733904e+01 1.72791242e+01 52 -1.04711162e+00 3.00934342e+00 1.06860356e+00 | -1.04711162e+00 3.00934342e+00 1.06860356e+00 53 -2.53269647e+00 -3.67264164e+00 1.72576312e+00 | -2.53269647e+00 -3.67264164e+00 1.72576312e+00 54 -6.18885730e+00 1.09952304e+00 -1.72379768e-01 | -6.18885730e+00 1.09952304e+00 -1.72379768e-01 55 2.28453206e+00 2.24029447e+00 1.08396882e+00 | 2.28453206e+00 2.24029447e+00 1.08396882e+00 56 3.80058726e-01 -1.31233925e+00 5.41501646e+00 | 3.80058726e-01 -1.31233925e+00 5.41501646e+00 57 -7.59892169e+00 -1.13789689e+01 3.51910414e+00 | -7.59892169e+00 -1.13789689e+01 3.51910414e+00 58 1.75841788e+00 2.88042252e+01 1.06796235e+01 | 1.75841788e+00 2.88042252e+01 1.06796235e+01 59 1.03592233e+00 1.12128893e+00 1.72943500e+00 | 1.03592233e+00 1.12128893e+00 1.72943500e+00 60 5.00954877e+00 9.22227618e+00 -6.89477731e+00 | 5.00954877e+00 9.22227618e+00 -6.89477731e+00 61 -3.95192288e-01 7.69790430e-01 -5.08596023e-01 | -3.95192288e-01 7.69790430e-01 -5.08596023e-01 62 -1.45669344e+01 -4.92152903e+00 -1.71423270e+01 | -1.45669344e+01 -4.92152903e+00 -1.71423270e+01 63 1.61491274e+01 8.21000685e+00 1.34911048e+01 | 1.61491274e+01 8.21000685e+00 1.34911048e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Ni Ti (Configuration in file "config-AlNiTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [5, 3, 11, 1, 25, 0, 18, 9, 44, 7, 32, 2, 37, 28, 46, 54, 22, 20, 6, 57, 17, 58, 16, 27, 55, 4, 52, 23, 13, 34, 43, 38, 10, 50, 29, 62, 61, 12, 31, 53, 60, 47, 56, 30, 8, 49, 14, 41, 59, 45, 33, 51, 26, 39, 15, 24, 42, 19, 21, 48, 40, 36, 35, 63] 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)) = 84.6925928535954 V(r_1,...,r_N) = 84.69259285359524 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 -4.44910584e+00 -1.44228945e+00 -4.76856575e+00 | -4.44910584e+00 -1.44228945e+00 -4.76856575e+00 1 -5.23086164e+00 -1.30211065e+01 1.23856389e+01 | -5.23086164e+00 -1.30211065e+01 1.23856389e+01 2 3.85716147e+00 9.99431129e+00 -6.85236657e+00 | 3.85716147e+00 9.99431129e+00 -6.85236657e+00 3 -2.27666118e+01 3.11570952e+01 -3.24199052e+01 | -2.27666118e+01 3.11570952e+01 -3.24199052e+01 4 -1.43187790e+00 -2.08143097e+00 -3.61090959e+00 | -1.43187790e+00 -2.08143097e+00 -3.61090959e+00 5 1.25675711e+00 4.21403383e+00 4.09430054e-01 | 1.25675711e+00 4.21403383e+00 4.09430054e-01 6 -6.33724801e+00 -3.81657250e+00 -5.08875908e+00 | -6.33724801e+00 -3.81657250e+00 -5.08875908e+00 7 -2.46189734e+01 -1.44979889e+01 1.05926780e+00 | -2.46189734e+01 -1.44979889e+01 1.05926780e+00 8 -2.13534288e+00 -9.43079975e-01 -2.54873734e+00 | -2.13534288e+00 -9.43079975e-01 -2.54873734e+00 9 1.42253000e+01 -1.26022687e+01 -3.58006011e+00 | 1.42253000e+01 -1.26022687e+01 -3.58006011e+00 10 -1.00918473e+01 -8.46614456e+00 -6.51538145e+00 | -1.00918473e+01 -8.46614456e+00 -6.51538145e+00 11 1.15229868e+01 6.37054971e+00 5.54306656e+00 | 1.15229868e+01 6.37054971e+00 5.54306656e+00 12 -6.38691848e+01 -8.68000490e+01 -4.96491558e+01 | -6.38691848e+01 -8.68000490e+01 -4.96491558e+01 13 6.32285728e+01 8.74300477e+01 5.04386582e+01 | 6.32285728e+01 8.74300477e+01 5.04386582e+01 14 1.37926087e+01 -1.18618245e+01 4.01388639e+01 | 1.37926087e+01 -1.18618245e+01 4.01388639e+01 15 1.48692770e+01 -1.66960050e+01 -1.70497346e+01 | 1.48692770e+01 -1.66960050e+01 -1.70497346e+01 16 -1.63029879e-01 -2.50119976e+00 1.35438733e-01 | -1.63029879e-01 -2.50119976e+00 1.35438733e-01 17 -1.97624977e+00 -4.74791405e-01 -7.53803833e-01 | -1.97624977e+00 -4.74791405e-01 -7.53803833e-01 18 2.35206992e+00 3.12365910e+00 -1.49355630e+00 | 2.35206992e+00 3.12365910e+00 -1.49355630e+00 19 3.20509494e-01 -1.23469863e+00 1.54481584e-01 | 3.20509494e-01 -1.23469863e+00 1.54481584e-01 20 2.17595900e+01 2.71274238e+01 -1.45907523e+01 | 2.17595900e+01 2.71274238e+01 -1.45907523e+01 21 -2.28832089e+01 -2.52506711e+01 1.70815891e+01 | -2.28832089e+01 -2.52506711e+01 1.70815891e+01 22 -1.92986018e+00 -2.84543844e+00 -5.40996360e+00 | -1.92986018e+00 -2.84543844e+00 -5.40996360e+00 23 1.18511361e+00 5.51289687e+00 4.58555647e+00 | 1.18511361e+00 5.51289687e+00 4.58555647e+00 24 1.03967986e+00 6.53559688e-01 1.09207711e+00 | 1.03967986e+00 6.53559688e-01 1.09207711e+00 25 -1.45104307e+01 2.22564156e+01 -9.32793350e+00 | -1.45104307e+01 2.22564156e+01 -9.32793350e+00 26 -3.63504553e-01 1.45580625e+00 -4.00301813e+00 | -3.63504553e-01 1.45580625e+00 -4.00301813e+00 27 2.74596871e-01 5.98309239e-03 8.39306596e-01 | 2.74596871e-01 5.98309239e-03 8.39306596e-01 28 8.08801809e+00 -2.33794919e+01 1.31139778e+01 | 8.08801809e+00 -2.33794919e+01 1.31139778e+01 29 3.34209799e+01 -3.52752006e+01 -5.71025262e+01 | 3.34209799e+01 -3.52752006e+01 -5.71025262e+01 30 1.69238091e+01 2.92898499e+01 -2.21637336e+01 | 1.69238091e+01 2.92898499e+01 -2.21637336e+01 31 -4.66746411e+00 7.88148311e+00 -3.27721671e+00 | -4.66746411e+00 7.88148311e+00 -3.27721671e+00 32 -6.70528259e-01 2.61533749e-02 -1.79397124e+00 | -6.70528259e-01 2.61533749e-02 -1.79397124e+00 33 -6.70491469e+01 3.96384910e+01 -5.78136846e+01 | -6.70491469e+01 3.96384910e+01 -5.78136846e+01 34 6.69026396e+00 -1.53187731e+01 1.60249646e+01 | 6.69026396e+00 -1.53187731e+01 1.60249646e+01 35 2.14054245e+00 5.21708978e+00 5.24094679e+00 | 2.14054245e+00 5.21708978e+00 5.24094679e+00 36 -1.10887555e+01 -6.31120397e+01 1.73063090e+01 | -1.10887555e+01 -6.31120397e+01 1.73063090e+01 37 8.01661856e+01 2.00178112e+01 4.15343103e+01 | 8.01661856e+01 2.00178112e+01 4.15343103e+01 38 -8.59437920e-01 -9.75766163e-01 3.93593197e-01 | -8.59437920e-01 -9.75766163e-01 3.93593197e-01 39 -1.15898288e+01 -1.87019266e+01 6.48124216e+00 | -1.15898288e+01 -1.87019266e+01 6.48124216e+00 40 2.31364097e+00 -6.27402287e-01 2.61956983e+00 | 2.31364097e+00 -6.27402287e-01 2.61956983e+00 41 -1.43661858e+01 -3.73657132e+01 1.23097358e+01 | -1.43661858e+01 -3.73657132e+01 1.23097358e+01 42 1.27911156e+01 3.76002447e+01 -1.36705748e+01 | 1.27911156e+01 3.76002447e+01 -1.36705748e+01 43 3.10210288e-01 -3.94741227e-01 4.00949496e-01 | 3.10210288e-01 -3.94741227e-01 4.00949496e-01 44 -2.74780281e-01 3.10942117e-01 1.00418119e+00 | -2.74780281e-01 3.10942117e-01 1.00418119e+00 45 -4.89776627e-01 -4.93873542e-01 -8.29665522e-01 | -4.89776627e-01 -4.93873542e-01 -8.29665522e-01 46 -1.52495936e+01 -3.00632251e+01 -2.27366516e+01 | -1.52495936e+01 -3.00632251e+01 -2.27366516e+01 47 1.40751972e+01 3.10884055e+01 2.27426504e+01 | 1.40751972e+01 3.10884055e+01 2.27426504e+01 48 -5.46401041e+00 -5.58886570e+00 -2.54668852e+00 | -5.46401041e+00 -5.58886570e+00 -2.54668852e+00 49 6.54723335e+00 6.52345144e+00 1.67544703e+00 | 6.54723335e+00 6.52345144e+00 1.67544703e+00 50 1.75024402e+00 -2.11156308e+00 8.41630411e-01 | 1.75024402e+00 -2.11156308e+00 8.41630411e-01 51 -1.69161342e+01 1.62757407e+01 -1.57832270e+01 | -1.69161342e+01 1.62757407e+01 -1.57832270e+01 52 2.21853341e+00 1.01934951e+01 -1.44574338e+01 | 2.21853341e+00 1.01934951e+01 -1.44574338e+01 53 9.91014331e+00 9.95182818e+00 7.43341535e+00 | 9.91014331e+00 9.95182818e+00 7.43341535e+00 54 -4.78853449e-01 -1.02935435e+00 -1.29662201e+00 | -4.78853449e-01 -1.02935435e+00 -1.29662201e+00 55 1.78905648e+00 -1.35350087e-01 4.79906903e-01 | 1.78905648e+00 -1.35350087e-01 4.79906903e-01 56 -7.38340933e+00 1.28956501e+01 2.04502971e+01 | -7.38340933e+00 1.28956501e+01 2.04502971e+01 57 -4.41417386e+00 2.37162247e+00 -9.11714449e+00 | -4.41417386e+00 2.37162247e+00 -9.11714449e+00 58 -2.47211299e+01 3.15582778e+01 5.94516258e+01 | -2.47211299e+01 3.15582778e+01 5.94516258e+01 59 -6.15379737e-01 -2.07168860e-01 9.34698926e-01 | -6.15379737e-01 -2.07168860e-01 9.34698926e-01 60 -2.21451543e+01 -1.65085137e+01 -8.35040811e+00 | -2.21451543e+01 -1.65085137e+01 -8.35040811e+00 61 2.51452163e+01 1.26971151e+01 1.89307058e+01 | 2.51452163e+01 1.26971151e+01 1.89307058e+01 62 1.74473948e+01 -1.87165273e+01 1.51217366e+01 | 1.74473948e+01 -1.87165273e+01 1.51217366e+01 63 -2.10927998e-01 1.70162208e+00 2.46881758e-01 | -2.10927998e-01 1.70162208e+00 2.46881758e-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.