!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ShimKoKim_2013_AlVH__MO_344724145339_001 Supported species : Al H V 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)) = 16.98905804754252 V(r_1,...,r_N) = 16.989058047542507 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 -2.55538748e+00 -1.67213281e+00 -2.39461343e+00 | -2.55538748e+00 -1.67213281e+00 -2.39461343e+00 1 -1.02096000e+01 -1.42014128e+01 8.03739132e+00 | -1.02096000e+01 -1.42014128e+01 8.03739132e+00 2 -1.16426783e+00 5.99898564e+00 -2.66844327e+01 | -1.16426783e+00 5.99898564e+00 -2.66844327e+01 3 6.28540446e+00 1.47587113e+01 9.75782067e+00 | 6.28540446e+00 1.47587113e+01 9.75782067e+00 4 2.46831549e+00 -5.82492631e+00 6.80883878e+00 | 2.46831549e+00 -5.82492631e+00 6.80883878e+00 5 4.82019443e-01 1.61558146e+00 -9.78971533e-01 | 4.82019443e-01 1.61558146e+00 -9.78971533e-01 6 -1.99358857e+00 -3.83251091e+00 -5.10178055e+00 | -1.99358857e+00 -3.83251091e+00 -5.10178055e+00 7 -9.63127891e+00 4.71887902e+01 -2.56010458e+01 | -9.63127891e+00 4.71887902e+01 -2.56010458e+01 8 -9.36676662e+00 -1.05410630e+01 -1.35533797e+01 | -9.36676662e+00 -1.05410630e+01 -1.35533797e+01 9 6.85005707e+00 5.25559160e+00 1.79800903e+01 | 6.85005707e+00 5.25559160e+00 1.79800903e+01 10 5.64665195e+00 2.91446537e+00 -7.92064341e+00 | 5.64665195e+00 2.91446537e+00 -7.92064341e+00 11 3.01992240e+00 -1.75322630e+00 -7.58069217e-01 | 3.01992240e+00 -1.75322630e+00 -7.58069217e-01 12 -5.00471555e+00 -3.35558207e+00 -5.91524946e+00 | -5.00471555e+00 -3.35558207e+00 -5.91524946e+00 13 2.00632351e+01 -8.77093354e+00 -4.17970750e+00 | 2.00632351e+01 -8.77093354e+00 -4.17970750e+00 14 -9.07392634e-01 -9.09894999e-02 1.30608126e+00 | -9.07392634e-01 -9.09894999e-02 1.30608126e+00 15 1.59816705e+00 -2.33630969e+00 -1.82315228e+00 | 1.59816705e+00 -2.33630969e+00 -1.82315228e+00 16 -2.52898124e+00 -1.53339656e+00 -1.81776774e+00 | -2.52898124e+00 -1.53339656e+00 -1.81776774e+00 17 -4.46300120e+00 -1.57381148e+01 1.93390472e+01 | -4.46300120e+00 -1.57381148e+01 1.93390472e+01 18 4.59744578e+00 1.65854455e+01 -1.96042455e+01 | 4.59744578e+00 1.65854455e+01 -1.96042455e+01 19 -2.95175609e+01 2.03024708e+01 -2.00972094e+01 | -2.95175609e+01 2.03024708e+01 -2.00972094e+01 20 -1.07267417e+01 -9.39023936e+00 -8.49050105e+00 | -1.07267417e+01 -9.39023936e+00 -8.49050105e+00 21 1.76137994e+01 1.18424284e+01 7.60825501e+00 | 1.76137994e+01 1.18424284e+01 7.60825501e+00 22 -2.87057702e+00 -7.74770095e+00 -1.37306428e+01 | -2.87057702e+00 -7.74770095e+00 -1.37306428e+01 23 2.05286247e+00 7.87117920e+00 1.43342383e+01 | 2.05286247e+00 7.87117920e+00 1.43342383e+01 24 -9.99175945e-01 -7.59452657e-01 -9.31440713e-01 | -9.99175945e-01 -7.59452657e-01 -9.31440713e-01 25 -1.03642659e+01 1.37297592e+01 -9.91517126e+00 | -1.03642659e+01 1.37297592e+01 -9.91517126e+00 26 -1.02451900e+00 -3.76788572e-01 -4.98327655e-01 | -1.02451900e+00 -3.76788572e-01 -4.98327655e-01 27 6.03953472e-01 -2.22076978e-01 9.55928260e-01 | 6.03953472e-01 -2.22076978e-01 9.55928260e-01 28 8.83431406e+00 -1.14233013e+01 1.22138646e+01 | 8.83431406e+00 -1.14233013e+01 1.22138646e+01 29 1.70736696e+00 3.20675333e-01 9.71852594e-01 | 1.70736696e+00 3.20675333e-01 9.71852594e-01 30 2.93141415e+01 -1.75928454e+01 1.72824051e+01 | 2.93141415e+01 -1.75928454e+01 1.72824051e+01 31 -1.56203474e+01 6.67361883e+00 -8.37784143e+00 | -1.56203474e+01 6.67361883e+00 -8.37784143e+00 32 -4.71285813e+00 -4.57329029e+00 -2.35598343e+00 | -4.71285813e+00 -4.57329029e+00 -2.35598343e+00 33 -1.91813299e+00 -4.40176900e+00 6.25772913e+00 | -1.91813299e+00 -4.40176900e+00 6.25772913e+00 34 2.49022949e+01 -3.86445887e+01 2.22199226e+01 | 2.49022949e+01 -3.86445887e+01 2.22199226e+01 35 -4.81590788e+00 -6.68816833e+00 4.86512797e+00 | -4.81590788e+00 -6.68816833e+00 4.86512797e+00 36 -5.38012155e+00 4.73518283e-01 2.18348513e+00 | -5.38012155e+00 4.73518283e-01 2.18348513e+00 37 -7.58661505e+00 -2.14776031e+01 1.59142341e+01 | -7.58661505e+00 -2.14776031e+01 1.59142341e+01 38 -6.58556165e+00 -5.36619920e+00 -5.66289622e+00 | -6.58556165e+00 -5.36619920e+00 -5.66289622e+00 39 -7.41372765e+00 -6.84677159e+00 1.37196790e+01 | -7.41372765e+00 -6.84677159e+00 1.37196790e+01 40 4.24169516e+00 -2.43826671e+00 -3.81343965e-01 | 4.24169516e+00 -2.43826671e+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 6.74907051e+00 3.82688414e+00 | -1.55465071e+01 6.74907051e+00 3.82688414e+00 43 3.34063547e+00 6.68557545e+00 4.35948684e+00 | 3.34063547e+00 6.68557545e+00 4.35948684e+00 44 1.62355658e+01 -2.55355555e+01 1.34103491e+01 | 1.62355658e+01 -2.55355555e+01 1.34103491e+01 45 -1.07717449e-01 1.82388517e-01 -1.53255584e-01 | -1.07717449e-01 1.82388517e-01 -1.53255584e-01 46 8.88373886e+00 1.99189010e+01 -1.23394547e+01 | 8.88373886e+00 1.99189010e+01 -1.23394547e+01 47 4.25522160e+00 -4.37329490e+00 -1.25740171e+00 | 4.25522160e+00 -4.37329490e+00 -1.25740171e+00 48 -1.10865193e+01 3.85010970e+00 6.04935084e+00 | -1.10865193e+01 3.85010970e+00 6.04935084e+00 49 4.32658582e-01 -1.75763725e+00 -9.90176435e-01 | 4.32658582e-01 -1.75763725e+00 -9.90176435e-01 50 -7.90281191e+00 -1.12037438e+01 -1.15760673e+01 | -7.90281191e+00 -1.12037438e+01 -1.15760673e+01 51 7.68599124e+00 1.18411989e+01 1.08196647e+01 | 7.68599124e+00 1.18411989e+01 1.08196647e+01 52 1.23676422e+01 1.27928201e+01 -7.68811622e+00 | 1.23676422e+01 1.27928201e+01 -7.68811622e+00 53 -3.41497506e+00 4.25315926e+00 1.54437938e+00 | -3.41497506e+00 4.25315926e+00 1.54437938e+00 54 -6.09275645e+00 6.77165504e-01 -1.60348099e+00 | -6.09275645e+00 6.77165504e-01 -1.60348099e+00 55 3.96514152e+00 1.01052551e+00 3.01917394e+00 | 3.96514152e+00 1.01052551e+00 3.01917394e+00 56 7.86124810e-02 5.53895912e+00 -2.63691392e+00 | 7.86124810e-02 5.53895912e+00 -2.63691392e+00 57 1.75211178e+01 -2.38607843e+01 -2.97134920e+01 | 1.75211178e+01 -2.38607843e+01 -2.97134920e+01 58 1.66714243e+01 -5.47293319e+00 1.01948449e+01 | 1.66714243e+01 -5.47293319e+00 1.01948449e+01 59 -3.45466144e-01 -4.44050908e-01 5.15023690e-01 | -3.45466144e-01 -4.44050908e-01 5.15023690e-01 60 -2.17778802e+00 -2.65928007e+00 -3.48044209e+00 | -2.17778802e+00 -2.65928007e+00 -3.48044209e+00 61 3.72061080e+00 3.38341262e+00 4.05958899e+00 | 3.72061080e+00 3.38341262e+00 4.05958899e+00 62 -1.49704994e+01 2.66817893e+01 3.05286801e+01 | -1.49704994e+01 2.66817893e+01 3.05286801e+01 63 1.00382338e+00 -5.05275884e-02 -1.21192548e-01 | 1.00382338e+00 -5.05275884e-02 -1.21192548e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = H (Configuration in file "config-H.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [37, 21, 39, 19, 8, 54, 36, 28, 4, 57, 26, 45, 20, 52, 34, 24, 23, 41, 27, 3, 12, 1, 42, 16, 15, 35, 10, 18, 7, 38, 63, 33, 55, 31, 14, 25, 6, 0, 29, 2, 59, 17, 22, 47, 49, 11, 62, 43, 58, 44, 61, 56, 13, 60, 5, 32, 51, 9, 48, 40, 53, 50, 46, 30] 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)) = -11.681768479365036 V(r_1,...,r_N) = -11.68176847936503 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 6.36237567e-01 5.32763047e-01 6.76152702e-01 | 6.36237567e-01 5.32763047e-01 6.76152702e-01 1 -1.62417256e-01 3.75442970e-01 -1.37805260e+00 | -1.62417256e-01 3.75442970e-01 -1.37805260e+00 2 -2.57938830e-01 -9.38588642e-01 8.20632675e-01 | -2.57938830e-01 -9.38588642e-01 8.20632675e-01 3 4.78531091e-01 6.80313048e-01 -9.69493938e-02 | 4.78531091e-01 6.80313048e-01 -9.69493938e-02 4 -1.24946732e-01 1.18530137e-01 -1.06956006e-01 | -1.24946732e-01 1.18530137e-01 -1.06956006e-01 5 7.04995675e-01 -1.48192840e+00 8.36803610e-01 | 7.04995675e-01 -1.48192840e+00 8.36803610e-01 6 7.72304146e-01 4.15704655e-01 2.77976846e-01 | 7.72304146e-01 4.15704655e-01 2.77976846e-01 7 2.38824480e-01 2.22805540e+00 -1.47140536e+00 | 2.38824480e-01 2.22805540e+00 -1.47140536e+00 8 8.07362420e-01 6.04538577e-01 6.09989811e-01 | 8.07362420e-01 6.04538577e-01 6.09989811e-01 9 -9.02340969e-01 -4.43625042e-01 -4.94459983e-01 | -9.02340969e-01 -4.43625042e-01 -4.94459983e-01 10 1.01501087e+00 9.20883160e-01 1.23031915e+00 | 1.01501087e+00 9.20883160e-01 1.23031915e+00 11 -9.97708680e-01 -9.00262999e-01 -1.26691382e+00 | -9.97708680e-01 -9.00262999e-01 -1.26691382e+00 12 9.84534289e-02 3.93426674e-01 1.08676774e-01 | 9.84534289e-02 3.93426674e-01 1.08676774e-01 13 -1.69413327e+00 7.45616131e-01 2.90069974e+00 | -1.69413327e+00 7.45616131e-01 2.90069974e+00 14 1.12371363e-01 -1.50122510e-01 -9.54393380e-02 | 1.12371363e-01 -1.50122510e-01 -9.54393380e-02 15 2.61384040e-01 7.07533284e-01 -2.55409998e-01 | 2.61384040e-01 7.07533284e-01 -2.55409998e-01 16 1.25425190e-02 1.07590560e-02 1.26871265e-02 | 1.25425190e-02 1.07590560e-02 1.26871265e-02 17 1.36364166e-02 -4.80662024e-03 3.97426297e-02 | 1.36364166e-02 -4.80662024e-03 3.97426297e-02 18 -1.03536416e-02 -3.16638189e-03 8.98061090e-02 | -1.03536416e-02 -3.16638189e-03 8.98061090e-02 19 2.52127682e-01 -4.04258283e-02 1.42230158e-01 | 2.52127682e-01 -4.04258283e-02 1.42230158e-01 20 -1.13825456e+00 -2.56824321e+00 1.04045140e+00 | -1.13825456e+00 -2.56824321e+00 1.04045140e+00 21 5.72187787e-01 -6.85016255e-01 6.46771409e-01 | 5.72187787e-01 -6.85016255e-01 6.46771409e-01 22 1.26207282e-01 6.26370540e-02 8.41381707e-02 | 1.26207282e-01 6.26370540e-02 8.41381707e-02 23 -5.07819986e-02 -1.19796599e-01 -1.19851722e-01 | -5.07819986e-02 -1.19796599e-01 -1.19851722e-01 24 -5.86115573e-01 -7.90906396e-01 5.31208864e-02 | -5.86115573e-01 -7.90906396e-01 5.31208864e-02 25 7.07005120e-02 1.71476356e-01 2.58817772e-02 | 7.07005120e-02 1.71476356e-01 2.58817772e-02 26 4.87884511e-01 3.94238692e-01 2.26613049e-01 | 4.87884511e-01 3.94238692e-01 2.26613049e-01 27 -5.61138125e-01 -5.15513487e-01 -1.87660818e-01 | -5.61138125e-01 -5.15513487e-01 -1.87660818e-01 28 3.82087036e-01 -1.25955280e-01 3.45082723e-01 | 3.82087036e-01 -1.25955280e-01 3.45082723e-01 29 -6.95273001e-01 -5.55671792e-01 -1.68074980e-01 | -6.95273001e-01 -5.55671792e-01 -1.68074980e-01 30 7.73553542e-01 1.27582007e+00 7.03496193e-01 | 7.73553542e-01 1.27582007e+00 7.03496193e-01 31 -9.92136515e-01 -1.31997100e+00 -8.96856646e-01 | -9.92136515e-01 -1.31997100e+00 -8.96856646e-01 32 1.28212919e-01 1.46541484e-01 9.20951315e-02 | 1.28212919e-01 1.46541484e-01 9.20951315e-02 33 -4.11302767e-02 -4.89711825e-01 2.29830038e-01 | -4.11302767e-02 -4.89711825e-01 2.29830038e-01 34 9.05875699e-01 3.75843392e-01 1.09397460e+00 | 9.05875699e-01 3.75843392e-01 1.09397460e+00 35 -9.06320642e-01 -3.69295787e-01 -9.93289503e-01 | -9.06320642e-01 -3.69295787e-01 -9.93289503e-01 36 -5.14787532e-02 3.83989436e-01 -2.87880648e-01 | -5.14787532e-02 3.83989436e-01 -2.87880648e-01 37 -3.49365720e-02 -4.59160675e-02 -3.23600395e-02 | -3.49365720e-02 -4.59160675e-02 -3.23600395e-02 38 3.38663690e-01 1.56917992e-01 3.39628063e-01 | 3.38663690e-01 1.56917992e-01 3.39628063e-01 39 -1.40551038e-01 1.11673007e-01 -4.61896159e-01 | -1.40551038e-01 1.11673007e-01 -4.61896159e-01 40 -6.98376825e-01 1.44457761e+00 -8.58776326e-01 | -6.98376825e-01 1.44457761e+00 -8.58776326e-01 41 -9.68555265e-01 1.41557204e+00 1.36692729e+00 | -9.68555265e-01 1.41557204e+00 1.36692729e+00 42 1.66891655e+00 -1.18816257e+00 -3.01039931e+00 | 1.66891655e+00 -1.18816257e+00 -3.01039931e+00 43 -1.18841795e-02 3.45860966e-03 3.47885074e-02 | -1.18841795e-02 3.45860966e-03 3.47885074e-02 44 2.62187716e-01 6.43723721e-01 5.84844973e-02 | 2.62187716e-01 6.43723721e-01 5.84844973e-02 45 -2.49447522e-01 -6.45768573e-01 -6.53672615e-02 | -2.49447522e-01 -6.45768573e-01 -6.53672615e-02 46 9.63560260e-01 -1.43325879e+00 -1.28869370e+00 | 9.63560260e-01 -1.43325879e+00 -1.28869370e+00 47 7.42506484e-02 4.41082021e-01 -2.14284989e-02 | 7.42506484e-02 4.41082021e-01 -2.14284989e-02 48 3.35222468e-01 2.48293137e-01 2.46446801e-01 | 3.35222468e-01 2.48293137e-01 2.46446801e-01 49 -3.90412599e-01 -1.99893292e-01 -2.05536421e-01 | -3.90412599e-01 -1.99893292e-01 -2.05536421e-01 50 4.21867980e-01 1.58982628e+00 1.26801914e+00 | 4.21867980e-01 1.58982628e+00 1.26801914e+00 51 -4.50795360e-01 -1.53831717e+00 -1.26644340e+00 | -4.50795360e-01 -1.53831717e+00 -1.26644340e+00 52 -2.21410004e-02 1.15693351e-01 3.77956630e-01 | -2.21410004e-02 1.15693351e-01 3.77956630e-01 53 -1.86154664e-01 -3.78066616e-01 -2.37502372e-01 | -1.86154664e-01 -3.78066616e-01 -2.37502372e-01 54 3.42752877e-01 1.92948907e-01 1.90739276e-01 | 3.42752877e-01 1.92948907e-01 1.90739276e-01 55 -3.15150449e-01 -2.36067245e-01 -2.28256371e-01 | -3.15150449e-01 -2.36067245e-01 -2.28256371e-01 56 -5.12071118e-01 6.84293079e-01 -6.12190573e-01 | -5.12071118e-01 6.84293079e-01 -6.12190573e-01 57 -3.03152179e-02 6.36237740e-02 -1.60567776e-03 | -3.03152179e-02 6.36237740e-02 -1.60567776e-03 58 1.45657607e-01 -3.11873978e-03 6.15139556e-02 | 1.45657607e-01 -3.11873978e-03 6.15139556e-02 59 -1.70803939e-01 -3.85598821e-02 -1.93979733e-02 | -1.70803939e-01 -3.85598821e-02 -1.93979733e-02 60 5.73566517e-01 2.93072023e-01 -1.71725753e-01 | 5.73566517e-01 2.93072023e-01 -1.71725753e-01 61 -6.40809361e-01 -7.13901289e-01 7.34818216e-02 | -6.40809361e-01 -7.13901289e-01 7.34818216e-02 62 1.18730530e-01 8.32679689e-02 1.39657874e-01 | 1.18730530e-01 8.32679689e-02 1.39657874e-01 63 -1.00993884e-01 -1.08097861e-01 -1.44035906e-01 | -1.00993884e-01 -1.08097861e-01 -1.44035906e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = V (Configuration in file "config-V.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [22, 58, 39, 51, 50, 16, 24, 43, 52, 49, 48, 47, 27, 37, 34, 57, 5, 26, 33, 23, 40, 25, 0, 19, 6, 21, 17, 12, 38, 46, 44, 36, 53, 18, 14, 45, 31, 13, 28, 2, 20, 62, 59, 7, 30, 35, 29, 11, 10, 9, 4, 3, 8, 32, 55, 54, 60, 15, 1, 42, 56, 63, 41, 61] 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)) = -193.03169735616746 V(r_1,...,r_N) = -193.03169735616743 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 7.45793238e-02 -2.46877757e+00 -1.03619492e-01 | 7.45793238e-02 -2.46877757e+00 -1.03619492e-01 1 5.32186707e-01 2.80009063e+00 3.40584572e-01 | 5.32186707e-01 2.80009063e+00 3.40584572e-01 2 5.41664521e-01 2.37308277e-01 -1.14345945e-02 | 5.41664521e-01 2.37308277e-01 -1.14345945e-02 3 2.28881821e-02 -1.30708771e+00 -4.20591529e-01 | 2.28881821e-02 -1.30708771e+00 -4.20591529e-01 4 -5.64771317e-01 5.70679376e-01 1.61832326e-01 | -5.64771317e-01 5.70679376e-01 1.61832326e-01 5 1.44752453e+00 -2.37826866e+00 -1.75088970e+00 | 1.44752453e+00 -2.37826866e+00 -1.75088970e+00 6 -4.23766304e+00 -6.30670450e+00 -5.22877494e+00 | -4.23766304e+00 -6.30670450e+00 -5.22877494e+00 7 3.83665682e+00 4.86391343e+00 5.00942978e+00 | 3.83665682e+00 4.86391343e+00 5.00942978e+00 8 -3.91947148e+00 -9.54794568e+00 -3.74484935e+00 | -3.91947148e+00 -9.54794568e+00 -3.74484935e+00 9 4.11965153e+00 8.44336829e+00 2.66647658e+00 | 4.11965153e+00 8.44336829e+00 2.66647658e+00 10 7.58795262e-02 3.97764653e-01 8.60006993e-01 | 7.58795262e-02 3.97764653e-01 8.60006993e-01 11 -6.90287936e-01 -4.49631838e-01 9.75667144e-02 | -6.90287936e-01 -4.49631838e-01 9.75667144e-02 12 -2.70010214e-01 5.93807688e-01 1.84459592e-02 | -2.70010214e-01 5.93807688e-01 1.84459592e-02 13 -3.71581362e-01 -5.49999758e-03 -3.44061090e-02 | -3.71581362e-01 -5.49999758e-03 -3.44061090e-02 14 -9.56011634e-01 1.42685828e+00 -3.55027025e-01 | -9.56011634e-01 1.42685828e+00 -3.55027025e-01 15 2.65255792e+00 -4.68402335e+00 -3.91267467e-01 | 2.65255792e+00 -4.68402335e+00 -3.91267467e-01 16 2.86349454e-01 -4.58469534e-01 2.06964684e-01 | 2.86349454e-01 -4.58469534e-01 2.06964684e-01 17 -8.29647875e-01 7.70450289e-01 -3.56442057e-01 | -8.29647875e-01 7.70450289e-01 -3.56442057e-01 18 -1.28893255e+00 -1.96045082e+00 -1.00102911e+00 | -1.28893255e+00 -1.96045082e+00 -1.00102911e+00 19 8.88431653e-01 1.96762587e+00 1.24417841e+00 | 8.88431653e-01 1.96762587e+00 1.24417841e+00 20 -2.00557323e+01 -1.51657716e+01 -3.16231307e+00 | -2.00557323e+01 -1.51657716e+01 -3.16231307e+00 21 2.10677456e+01 1.61166198e+01 3.95395704e+00 | 2.10677456e+01 1.61166198e+01 3.95395704e+00 22 5.43393938e-01 -4.08707485e-01 1.05793097e-01 | 5.43393938e-01 -4.08707485e-01 1.05793097e-01 23 -1.48698895e+00 1.09935342e+00 -1.72249941e+00 | -1.48698895e+00 1.09935342e+00 -1.72249941e+00 24 -3.63668351e-02 -3.72072614e-01 1.07448907e+00 | -3.63668351e-02 -3.72072614e-01 1.07448907e+00 25 -9.09040967e-01 1.57598438e+00 -5.05474500e-01 | -9.09040967e-01 1.57598438e+00 -5.05474500e-01 26 3.73225973e-01 4.61464560e-01 1.82761741e-01 | 3.73225973e-01 4.61464560e-01 1.82761741e-01 27 -4.43492466e-01 -7.47799797e-01 1.59821506e-01 | -4.43492466e-01 -7.47799797e-01 1.59821506e-01 28 5.53174743e-01 -1.93126368e+00 7.38687475e-01 | 5.53174743e-01 -1.93126368e+00 7.38687475e-01 29 1.75850339e+00 -5.25274378e-01 -9.53432001e-01 | 1.75850339e+00 -5.25274378e-01 -9.53432001e-01 30 2.33290744e-01 -3.80555286e-01 4.02857675e-01 | 2.33290744e-01 -3.80555286e-01 4.02857675e-01 31 -7.59824979e+00 1.09185570e+01 -3.07896426e+00 | -7.59824979e+00 1.09185570e+01 -3.07896426e+00 32 1.23516524e+00 9.00156945e-01 -4.40751691e-01 | 1.23516524e+00 9.00156945e-01 -4.40751691e-01 33 -1.98862438e+00 -1.32676312e+00 1.72424243e-01 | -1.98862438e+00 -1.32676312e+00 1.72424243e-01 34 -3.01685224e+00 -7.44371873e-01 -4.83042836e+00 | -3.01685224e+00 -7.44371873e-01 -4.83042836e+00 35 2.71471031e+00 4.06942708e+00 5.01483107e+00 | 2.71471031e+00 4.06942708e+00 5.01483107e+00 36 6.83056885e-01 -2.45936104e+00 -2.95686710e+00 | 6.83056885e-01 -2.45936104e+00 -2.95686710e+00 37 -2.23500728e+00 4.25094019e-01 3.40585583e+00 | -2.23500728e+00 4.25094019e-01 3.40585583e+00 38 -9.53837086e-01 -2.16827183e-01 -5.10447242e-01 | -9.53837086e-01 -2.16827183e-01 -5.10447242e-01 39 -1.36514383e+00 -4.48982531e-01 2.29994644e+00 | -1.36514383e+00 -4.48982531e-01 2.29994644e+00 40 8.76166141e-01 1.36427310e-01 7.94483066e-01 | 8.76166141e-01 1.36427310e-01 7.94483066e-01 41 5.05192273e-01 -4.88922098e-01 -1.81379697e+00 | 5.05192273e-01 -4.88922098e-01 -1.81379697e+00 42 -1.78777043e-02 -2.65197469e-01 -6.31524626e-02 | -1.78777043e-02 -2.65197469e-01 -6.31524626e-02 43 -1.71932011e-01 -1.89042924e-01 3.27104662e-01 | -1.71932011e-01 -1.89042924e-01 3.27104662e-01 44 3.17476033e-01 1.21446159e+00 -7.02971696e-02 | 3.17476033e-01 1.21446159e+00 -7.02971696e-02 45 -1.20684400e+00 -6.12780306e-03 -1.18949071e+00 | -1.20684400e+00 -6.12780306e-03 -1.18949071e+00 46 1.13931212e+00 -1.51466125e+00 -1.49826450e+00 | 1.13931212e+00 -1.51466125e+00 -1.49826450e+00 47 1.05759921e+00 3.65371959e+00 1.66705063e+00 | 1.05759921e+00 3.65371959e+00 1.66705063e+00 48 -1.99486361e+00 -1.35231655e+00 -9.61804759e-01 | -1.99486361e+00 -1.35231655e+00 -9.61804759e-01 49 2.80188405e+00 1.45546238e+00 -7.21496775e-01 | 2.80188405e+00 1.45546238e+00 -7.21496775e-01 50 2.05813179e+00 -1.56391341e+00 1.53223245e+00 | 2.05813179e+00 -1.56391341e+00 1.53223245e+00 51 -3.29564973e-01 -1.47555883e-01 -6.69478657e-01 | -3.29564973e-01 -1.47555883e-01 -6.69478657e-01 52 -3.67097181e+00 -1.83533058e+00 -3.46263397e+00 | -3.67097181e+00 -1.83533058e+00 -3.46263397e+00 53 6.41834735e+00 2.12741705e+00 2.78201730e+00 | 6.41834735e+00 2.12741705e+00 2.78201730e+00 54 -2.00839477e+00 4.41041338e-01 1.24235094e+00 | -2.00839477e+00 4.41041338e-01 1.24235094e+00 55 8.18743896e-01 6.44341549e-01 2.65017012e-01 | 8.18743896e-01 6.44341549e-01 2.65017012e-01 56 -1.91876874e+00 5.28192199e+00 1.99791922e+00 | -1.91876874e+00 5.28192199e+00 1.99791922e+00 57 -5.20421479e-01 -3.07228012e-01 1.28629000e+00 | -5.20421479e-01 -3.07228012e-01 1.28629000e+00 58 6.23354084e+00 -9.48450341e+00 2.88527362e+00 | 6.23354084e+00 -9.48450341e+00 2.88527362e+00 59 -1.10991418e+00 -1.18926763e+00 -4.97794357e-01 | -1.10991418e+00 -1.18926763e+00 -4.97794357e-01 60 -4.20884902e+00 -3.43239040e+00 -7.54194535e+00 | -4.20884902e+00 -3.43239040e+00 -7.54194535e+00 61 4.23034328e+00 3.36902994e+00 7.28180996e+00 | 4.23034328e+00 3.36902994e+00 7.28180996e+00 62 -3.29914373e+00 -1.98917522e+00 -2.24487177e+00 | -3.29914373e+00 -1.98917522e+00 -2.24487177e+00 63 3.57788553e+00 2.09789612e+00 2.11607643e+00 | 3.57788553e+00 2.09789612e+00 2.11607643e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al H V (Configuration in file "config-AlHV.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [19, 22, 28, 15, 60, 43, 33, 29, 40, 32, 48, 51, 24, 27, 61, 3, 54, 55, 42, 0, 26, 53, 1, 41, 12, 47, 20, 13, 2, 7, 34, 35, 9, 6, 30, 31, 46, 63, 56, 50, 8, 23, 18, 5, 58, 49, 36, 25, 10, 45, 39, 11, 59, 21, 16, 17, 38, 57, 44, 52, 4, 14, 62, 37] 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)) = -64.31073219367454 V(r_1,...,r_N) = -64.31073219367457 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 8.41009601e-01 1.22649760e+00 3.48338904e-01 | 8.41009601e-01 1.22649760e+00 3.48338904e-01 1 -1.30358747e+00 -1.08008667e+00 3.40879193e-01 | -1.30358747e+00 -1.08008667e+00 3.40879193e-01 2 2.44165790e-01 3.37063112e-01 1.98172643e-01 | 2.44165790e-01 3.37063112e-01 1.98172643e-01 3 9.43761515e-01 2.58429444e-01 -1.15443456e+00 | 9.43761515e-01 2.58429444e-01 -1.15443456e+00 4 -2.38815281e+00 -4.91731384e-01 -3.00435050e+00 | -2.38815281e+00 -4.91731384e-01 -3.00435050e+00 5 1.07468766e+00 2.73188700e+00 3.77407190e+00 | 1.07468766e+00 2.73188700e+00 3.77407190e+00 6 5.74383528e-01 -1.60843219e+00 -3.61960259e-01 | 5.74383528e-01 -1.60843219e+00 -3.61960259e-01 7 2.21326658e+01 -2.01948374e+01 -1.34128982e+01 | 2.21326658e+01 -2.01948374e+01 -1.34128982e+01 8 3.23213957e-01 3.11737302e-01 2.33908336e-01 | 3.23213957e-01 3.11737302e-01 2.33908336e-01 9 6.77028877e-02 -3.08273910e-01 -1.07026943e-01 | 6.77028877e-02 -3.08273910e-01 -1.07026943e-01 10 -2.53885539e-01 4.65950206e-01 1.19467233e+00 | -2.53885539e-01 4.65950206e-01 1.19467233e+00 11 -1.48769982e+00 2.15352214e-01 1.74317491e-01 | -1.48769982e+00 2.15352214e-01 1.74317491e-01 12 -4.22917340e-01 1.32598316e+00 -3.13233578e-01 | -4.22917340e-01 1.32598316e+00 -3.13233578e-01 13 3.04223071e-01 -2.93004153e-01 -7.90139743e-02 | 3.04223071e-01 -2.93004153e-01 -7.90139743e-02 14 -7.92073595e-01 -4.67791915e-01 1.98348519e-01 | -7.92073595e-01 -4.67791915e-01 1.98348519e-01 15 2.05685376e+00 -1.04360074e-01 -3.62000250e-01 | 2.05685376e+00 -1.04360074e-01 -3.62000250e-01 16 6.24682120e-01 1.02172130e-01 5.14725926e-01 | 6.24682120e-01 1.02172130e-01 5.14725926e-01 17 2.86032774e-01 -1.22879563e+00 7.38121413e-01 | 2.86032774e-01 -1.22879563e+00 7.38121413e-01 18 -9.91189585e-01 -8.45638223e-01 -1.27328055e+00 | -9.91189585e-01 -8.45638223e-01 -1.27328055e+00 19 1.17921198e+00 2.51714100e-01 1.28638727e+00 | 1.17921198e+00 2.51714100e-01 1.28638727e+00 20 -1.63038097e+00 -3.67884975e-01 8.58456041e-02 | -1.63038097e+00 -3.67884975e-01 8.58456041e-02 21 3.66191283e+00 -3.89548295e+00 3.16807112e-01 | 3.66191283e+00 -3.89548295e+00 3.16807112e-01 22 1.47173881e+00 3.62986213e-02 9.88020238e-01 | 1.47173881e+00 3.62986213e-02 9.88020238e-01 23 -7.88108610e+01 6.19019929e+01 -4.39251924e+01 | -7.88108610e+01 6.19019929e+01 -4.39251924e+01 24 2.87801255e-01 7.88659879e-01 1.52183016e+00 | 2.87801255e-01 7.88659879e-01 1.52183016e+00 25 -1.07255440e+00 -5.33281904e+00 2.74685762e+00 | -1.07255440e+00 -5.33281904e+00 2.74685762e+00 26 8.55404434e-01 4.31413398e+00 -1.26126335e+00 | 8.55404434e-01 4.31413398e+00 -1.26126335e+00 27 -1.25074224e+00 -4.26566033e-01 8.83961923e-01 | -1.25074224e+00 -4.26566033e-01 8.83961923e-01 28 1.17588967e-01 7.37464633e-01 -1.10452884e+00 | 1.17588967e-01 7.37464633e-01 -1.10452884e+00 29 -1.24714652e+00 -7.23302450e-01 -4.27677497e-01 | -1.24714652e+00 -7.23302450e-01 -4.27677497e-01 30 5.85867450e-01 -2.17070940e-01 -8.77942678e-01 | 5.85867450e-01 -2.17070940e-01 -8.77942678e-01 31 6.51080568e-01 -6.49360179e-01 -1.21402140e+00 | 6.51080568e-01 -6.49360179e-01 -1.21402140e+00 32 4.56838097e-01 1.07819651e+00 -3.42280503e-02 | 4.56838097e-01 1.07819651e+00 -3.42280503e-02 33 9.91536785e+00 -1.18906967e+01 -5.97733204e+00 | 9.91536785e+00 -1.18906967e+01 -5.97733204e+00 34 1.60107565e-01 1.96160077e-01 -4.86112241e-02 | 1.60107565e-01 1.96160077e-01 -4.86112241e-02 35 -1.37026613e+01 -4.21395720e+00 6.52758793e+00 | -1.37026613e+01 -4.21395720e+00 6.52758793e+00 36 5.78541132e-01 2.13889991e+00 -1.40968156e+00 | 5.78541132e-01 2.13889991e+00 -1.40968156e+00 37 4.69914888e-01 1.97459871e-01 2.50269098e-01 | 4.69914888e-01 1.97459871e-01 2.50269098e-01 38 -1.05188486e+01 1.13593875e+01 3.91673458e+00 | -1.05188486e+01 1.13593875e+01 3.91673458e+00 39 -3.71996980e+00 -6.02722326e+00 3.68350363e+00 | -3.71996980e+00 -6.02722326e+00 3.68350363e+00 40 1.36756932e+00 -1.33807231e+00 1.11526940e+00 | 1.36756932e+00 -1.33807231e+00 1.11526940e+00 41 -1.47688963e+00 -2.12091181e+00 -1.34609739e-01 | -1.47688963e+00 -2.12091181e+00 -1.34609739e-01 42 -3.07247071e+01 -2.76325248e+01 -4.82271335e+01 | -3.07247071e+01 -2.76325248e+01 -4.82271335e+01 43 3.27784654e+01 2.83613707e+01 4.66427916e+01 | 3.27784654e+01 2.83613707e+01 4.66427916e+01 44 6.90550781e-01 1.31234201e+00 1.36264979e-01 | 6.90550781e-01 1.31234201e+00 1.36264979e-01 45 -1.30341215e+00 -5.22253924e-01 -8.22947920e-01 | -1.30341215e+00 -5.22253924e-01 -8.22947920e-01 46 -1.84137236e+00 -5.56782318e-01 -7.10037264e-01 | -1.84137236e+00 -5.56782318e-01 -7.10037264e-01 47 -3.33358196e+01 -4.17820753e+01 3.49918753e+01 | -3.33358196e+01 -4.17820753e+01 3.49918753e+01 48 -2.27311600e+01 2.05162909e+01 8.96825683e+00 | -2.27311600e+01 2.05162909e+01 8.96825683e+00 49 3.45618984e+00 2.59193110e+00 4.44135389e+00 | 3.45618984e+00 2.59193110e+00 4.44135389e+00 50 7.42256488e+01 -5.97757631e+01 4.43564416e+01 | 7.42256488e+01 -5.97757631e+01 4.43564416e+01 51 6.23087301e-01 -1.40449693e+00 7.31446812e-01 | 6.23087301e-01 -1.40449693e+00 7.31446812e-01 52 3.72366471e+00 2.46581199e+00 -2.45553038e+00 | 3.72366471e+00 2.46581199e+00 -2.45553038e+00 53 6.11710150e-01 3.73096055e+00 -5.19885403e-01 | 6.11710150e-01 3.73096055e+00 -5.19885403e-01 54 3.24537719e-01 -6.91969902e-01 2.48215237e-01 | 3.24537719e-01 -6.91969902e-01 2.48215237e-01 55 2.83914266e-01 -4.61176872e-01 -1.40988946e+00 | 2.83914266e-01 -4.61176872e-01 -1.40988946e+00 56 1.02876144e+01 9.47037251e-01 -7.89785219e+00 | 1.02876144e+01 9.47037251e-01 -7.89785219e+00 57 -8.65668078e+00 1.09801715e+01 -1.01988523e+01 | -8.65668078e+00 1.09801715e+01 -1.01988523e+01 58 -7.06065359e+00 -4.59056004e-01 -5.12258289e+00 | -7.06065359e+00 -4.59056004e-01 -5.12258289e+00 59 7.33108038e+00 2.31966942e+00 5.48933260e+00 | 7.33108038e+00 2.31966942e+00 5.48933260e+00 60 3.98516458e+01 3.39649600e+01 -2.18403147e+01 | 3.98516458e+01 3.39649600e+01 -2.18403147e+01 61 4.70768551e-01 7.23111975e-01 6.95972234e-01 | 4.70768551e-01 7.23111975e-01 6.95972234e-01 62 7.96239359e-02 -4.09404257e-01 -1.80776471e+00 | 7.96239359e-02 -4.09404257e-01 -1.80776471e+00 63 7.52536674e-01 -3.67294798e-01 -2.44503990e-01 | 7.52536674e-01 -3.67294798e-01 -2.44503990e-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.