!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_PlummerRathodSrivastava_2021_TiAlC__MO_992900971352_000 Supported species : Al C 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 = [52, 5, 63, 59, 33, 1, 40, 24, 30, 36, 60, 18, 27, 39, 46, 20, 57, 54, 11, 32, 15, 61, 62, 56, 7, 47, 45, 12, 50, 58, 8, 48, 19, 4, 55, 37, 9, 35, 44, 13, 6, 42, 41, 49, 38, 26, 14, 25, 31, 43, 28, 53, 0, 51, 17, 34, 23, 16, 29, 3, 10, 21, 22, 2] 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)) = -47.07526136486399 V(r_1,...,r_N) = -47.07526136486397 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 -1.66311763e+00 -1.01062441e+00 -1.64617691e+00 | -1.66311763e+00 -1.01062441e+00 -1.64617691e+00 1 -4.43491365e+00 -1.05474161e+01 8.47094733e+00 | -4.43491365e+00 -1.05474161e+01 8.47094733e+00 2 -4.82565669e+00 -1.26669771e+00 -1.77913342e+01 | -4.82565669e+00 -1.26669771e+00 -1.77913342e+01 3 9.41607309e+00 1.20996686e+01 5.96507942e+00 | 9.41607309e+00 1.20996686e+01 5.96507942e+00 4 -7.91117771e+00 -4.04987453e+00 5.57223768e-01 | -7.91117771e+00 -4.04987453e+00 5.57223768e-01 5 5.47741053e+00 -1.98618279e+00 2.71404390e+00 | 5.47741053e+00 -1.98618279e+00 2.71404390e+00 6 -5.13357282e+00 -5.94098779e+00 -6.12628739e+00 | -5.13357282e+00 -5.94098779e+00 -6.12628739e+00 7 -4.97914670e+00 2.44299839e+01 -1.20958245e+01 | -4.97914670e+00 2.44299839e+01 -1.20958245e+01 8 -4.94072182e-01 -5.27971599e-01 -3.07459364e-01 | -4.94072182e-01 -5.27971599e-01 -3.07459364e-01 9 -1.70041941e+00 -5.17530343e-01 3.67109162e-01 | -1.70041941e+00 -5.17530343e-01 3.67109162e-01 10 -4.66444560e+00 -1.64221902e+00 -8.48020145e+00 | -4.66444560e+00 -1.64221902e+00 -8.48020145e+00 11 6.13488588e+00 4.11195002e+00 4.67650429e+00 | 6.13488588e+00 4.11195002e+00 4.67650429e+00 12 -3.10172573e-01 -2.25156146e+00 1.03147784e+00 | -3.10172573e-01 -2.25156146e+00 1.03147784e+00 13 9.42447623e+00 -8.88440394e+00 -1.60333737e+00 | 9.42447623e+00 -8.88440394e+00 -1.60333737e+00 14 -4.50121418e+00 -4.72522860e-01 -5.57925575e+00 | -4.50121418e+00 -4.72522860e-01 -5.57925575e+00 15 8.25781304e+00 6.02861084e+00 4.12388644e+00 | 8.25781304e+00 6.02861084e+00 4.12388644e+00 16 -1.08243265e+00 -2.01814127e+00 -1.77983363e+00 | -1.08243265e+00 -2.01814127e+00 -1.77983363e+00 17 -3.29957560e+00 2.87714831e+00 -1.27590553e+00 | -3.29957560e+00 2.87714831e+00 -1.27590553e+00 18 -1.34164755e+00 -1.92374538e+00 -2.51901955e+00 | -1.34164755e+00 -1.92374538e+00 -2.51901955e+00 19 -1.64213022e+01 1.45147208e+01 -9.65119549e+00 | -1.64213022e+01 1.45147208e+01 -9.65119549e+00 20 -2.30465769e+00 -7.25747634e+00 -4.44676369e+00 | -2.30465769e+00 -7.25747634e+00 -4.44676369e+00 21 9.82968406e+00 7.56383719e+00 3.78636910e+00 | 9.82968406e+00 7.56383719e+00 3.78636910e+00 22 -1.36935396e+00 -4.28458618e+00 -8.06150906e+00 | -1.36935396e+00 -4.28458618e+00 -8.06150906e+00 23 1.79082302e+00 4.99076508e+00 8.94681514e+00 | 1.79082302e+00 4.99076508e+00 8.94681514e+00 24 -4.48013505e-01 -8.13346822e-01 -1.12572287e+00 | -4.48013505e-01 -8.13346822e-01 -1.12572287e+00 25 -5.09852805e+00 7.50555827e+00 -5.61744071e+00 | -5.09852805e+00 7.50555827e+00 -5.61744071e+00 26 -7.75767359e-01 -5.64008149e-01 3.66993541e-01 | -7.75767359e-01 -5.64008149e-01 3.66993541e-01 27 -1.87229472e-01 -6.59916561e-01 8.78512428e-01 | -1.87229472e-01 -6.59916561e-01 8.78512428e-01 28 6.63791879e+00 -7.85261138e+00 4.77122176e+00 | 6.63791879e+00 -7.85261138e+00 4.77122176e+00 29 3.70408018e-01 5.30340013e-01 1.17783286e-01 | 3.70408018e-01 5.30340013e-01 1.17783286e-01 30 1.67382945e+01 -1.00104772e+01 8.81085761e+00 | 1.67382945e+01 -1.00104772e+01 8.81085761e+00 31 -8.95270384e+00 5.21241209e+00 -4.73333893e+00 | -8.95270384e+00 5.21241209e+00 -4.73333893e+00 32 -2.35289253e+00 -2.50268112e+00 -2.00712734e+00 | -2.35289253e+00 -2.50268112e+00 -2.00712734e+00 33 -8.17861498e-01 -3.03471173e+00 4.52278188e+00 | -8.17861498e-01 -3.03471173e+00 4.52278188e+00 34 1.43700345e+01 -2.04601275e+01 1.20256322e+01 | 1.43700345e+01 -2.04601275e+01 1.20256322e+01 35 -2.31615303e+00 -3.20580797e+00 4.48599377e+00 | -2.31615303e+00 -3.20580797e+00 4.48599377e+00 36 -3.34101871e+00 3.41849768e-01 2.02871129e+00 | -3.34101871e+00 3.41849768e-01 2.02871129e+00 37 -3.24009489e+00 -4.49912501e+00 3.99763582e+00 | -3.24009489e+00 -4.49912501e+00 3.99763582e+00 38 -3.49022716e+00 -2.85210154e+00 -3.93042821e+00 | -3.49022716e+00 -2.85210154e+00 -3.93042821e+00 39 -3.44159323e+00 -4.02555918e+00 8.51545194e+00 | -3.44159323e+00 -4.02555918e+00 8.51545194e+00 40 2.82421421e+00 -1.08753030e+00 -2.31362616e+00 | 2.82421421e+00 -1.08753030e+00 -2.31362616e+00 41 -7.02560557e+00 1.31140987e+01 -8.72708864e+00 | -7.02560557e+00 1.31140987e+01 -8.72708864e+00 42 -1.09022211e+01 4.90318778e+00 1.09274437e-01 | -1.09022211e+01 4.90318778e+00 1.09274437e-01 43 3.45277868e+00 3.36182513e+00 3.52968040e+00 | 3.45277868e+00 3.36182513e+00 3.52968040e+00 44 9.16042903e+00 -1.41878152e+01 7.64881185e+00 | 9.16042903e+00 -1.41878152e+01 7.64881185e+00 45 -3.17701654e-01 3.97374374e-01 -8.03541857e-01 | -3.17701654e-01 3.97374374e-01 -8.03541857e-01 46 1.97730706e+00 3.45085804e+00 -3.19582466e+00 | 1.97730706e+00 3.45085804e+00 -3.19582466e+00 47 4.75674936e-01 1.36876906e+00 1.86226504e+00 | 4.75674936e-01 1.36876906e+00 1.86226504e+00 48 -6.43864979e+00 5.40722589e+00 6.60309517e+00 | -6.43864979e+00 5.40722589e+00 6.60309517e+00 49 6.20469115e-01 -7.52629760e-01 -1.88256877e-01 | 6.20469115e-01 -7.52629760e-01 -1.88256877e-01 50 -5.19931565e+00 -5.45156232e+00 -5.90322279e+00 | -5.19931565e+00 -5.45156232e+00 -5.90322279e+00 51 4.06665871e+00 7.33040238e+00 7.04239386e+00 | 4.06665871e+00 7.33040238e+00 7.04239386e+00 52 6.21304277e+00 6.91759919e+00 -4.63339698e+00 | 6.21304277e+00 6.91759919e+00 -4.63339698e+00 53 -3.37020237e+00 -4.28216007e+00 5.90976620e+00 | -3.37020237e+00 -4.28216007e+00 5.90976620e+00 54 -8.20802309e-01 2.28855054e-01 -1.76711932e-02 | -8.20802309e-01 2.28855054e-01 -1.76711932e-02 55 8.27642198e-01 -7.92202769e-02 -4.33010813e-01 | 8.27642198e-01 -7.92202769e-02 -4.33010813e-01 56 -5.86192747e-02 -1.52192885e+00 -2.66406665e+00 | -5.86192747e-02 -1.52192885e+00 -2.66406665e+00 57 1.10890421e+01 -1.04275158e+01 -1.48093566e+01 | 1.10890421e+01 -1.04275158e+01 -1.48093566e+01 58 1.07399428e+01 -3.34249529e+00 7.27377061e+00 | 1.07399428e+01 -3.34249529e+00 7.27377061e+00 59 -4.57703606e-01 -1.58178758e-01 7.86859247e-01 | -4.57703606e-01 -1.58178758e-01 7.86859247e-01 60 -8.07242494e-01 5.55747825e-01 1.32793819e+00 | -8.07242494e-01 5.55747825e-01 1.32793819e+00 61 -5.33282919e-01 1.37182530e+00 -6.23112579e-01 | -5.33282919e-01 1.37182530e+00 -6.23112579e-01 62 -3.88934248e+00 1.91980439e+01 1.05645953e+01 | -3.88934248e+00 1.91980439e+01 1.05645953e+01 63 8.24627954e-01 -1.45920499e+00 -7.29144529e-01 | 8.24627954e-01 -1.45920499e+00 -7.29144529e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = C (Configuration in file "config-C.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [18, 60, 56, 7, 28, 49, 55, 3, 50, 53, 33, 36, 42, 61, 45, 59, 46, 29, 0, 22, 48, 30, 19, 63, 41, 54, 32, 39, 4, 17, 21, 34, 26, 10, 31, 58, 11, 51, 57, 27, 47, 24, 12, 44, 43, 14, 16, 40, 20, 5, 8, 37, 62, 9, 25, 6, 2, 38, 35, 15, 1, 13, 52, 23] 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)) = 3100.266910239518 V(r_1,...,r_N) = 3100.266910239521 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 -3.32457686e+02 -1.64758968e+03 -5.09047943e+02 | -3.32457686e+02 -1.64758968e+03 -5.09047943e+02 1 3.16319109e+02 1.60763473e+03 4.63907275e+02 | 3.16319109e+02 1.60763473e+03 4.63907275e+02 2 -2.48066136e+02 -1.73302672e+02 -1.16810046e+02 | -2.48066136e+02 -1.73302672e+02 -1.16810046e+02 3 8.32249332e+01 1.87988695e+02 2.54642796e+00 | 8.32249332e+01 1.87988695e+02 2.54642796e+00 4 -1.11364838e+02 -6.31602622e+02 2.73202120e+02 | -1.11364838e+02 -6.31602622e+02 2.73202120e+02 5 4.37762384e+01 5.53120689e+02 -3.88379604e+02 | 4.37762384e+01 5.53120689e+02 -3.88379604e+02 6 -2.09333230e+02 -1.09750636e+01 -8.44270511e+01 | -2.09333230e+02 -1.09750636e+01 -8.44270511e+01 7 3.91957145e+01 -1.54656473e+02 -2.28290871e+01 | 3.91957145e+01 -1.54656473e+02 -2.28290871e+01 8 -1.32460733e+01 -6.61687587e-01 -7.71982833e+01 | -1.32460733e+01 -6.61687587e-01 -7.71982833e+01 9 1.85982451e+01 -4.76588304e+01 3.52671206e+01 | 1.85982451e+01 -4.76588304e+01 3.52671206e+01 10 -1.44024877e-01 4.05390599e+01 -1.56201401e+02 | -1.44024877e-01 4.05390599e+01 -1.56201401e+02 11 4.78726349e+01 -2.89322508e+01 9.63512171e+01 | 4.78726349e+01 -2.89322508e+01 9.63512171e+01 12 -9.45815880e+01 -1.25002373e+02 -1.13569368e+02 | -9.45815880e+01 -1.25002373e+02 -1.13569368e+02 13 3.73751673e+02 -3.24903168e+02 1.44838323e+02 | 3.73751673e+02 -3.24903168e+02 1.44838323e+02 14 -8.45952348e+01 -3.45120189e+02 -7.16514980e+01 | -8.45952348e+01 -3.45120189e+02 -7.16514980e+01 15 1.82837765e+02 -5.66282860e+01 2.00910009e+02 | 1.82837765e+02 -5.66282860e+01 2.00910009e+02 16 -6.23524200e+01 -4.91902306e+01 -6.37862162e+01 | -6.23524200e+01 -4.91902306e+01 -6.37862162e+01 17 -2.00065500e+02 -3.54318600e+02 4.78183092e+02 | -2.00065500e+02 -3.54318600e+02 4.78183092e+02 18 -1.69259370e+02 1.72128717e+02 -2.42777601e+02 | -1.69259370e+02 1.72128717e+02 -2.42777601e+02 19 2.70091607e+02 7.17457578e+01 -4.28759420e+01 | 2.70091607e+02 7.17457578e+01 -4.28759420e+01 20 1.98204705e+01 1.82869209e+02 -8.21479935e+01 | 1.98204705e+01 1.82869209e+02 -8.21479935e+01 21 2.88341341e+01 6.81298682e+01 5.41939983e+01 | 2.88341341e+01 6.81298682e+01 5.41939983e+01 22 1.06901871e+01 3.12029298e+02 -2.43549834e+02 | 1.06901871e+01 3.12029298e+02 -2.43549834e+02 23 1.70416946e+02 3.68933909e+02 -2.08264330e+01 | 1.70416946e+02 3.68933909e+02 -2.08264330e+01 24 1.27508595e+02 5.10509427e+01 -3.16481854e+02 | 1.27508595e+02 5.10509427e+01 -3.16481854e+02 25 8.38552169e+01 -2.24616082e+01 1.42014487e+02 | 8.38552169e+01 -2.24616082e+01 1.42014487e+02 26 3.09134216e-02 1.67477954e+02 -2.64735458e+02 | 3.09134216e-02 1.67477954e+02 -2.64735458e+02 27 6.42591051e+00 6.88317872e+00 1.26976839e+00 | 6.42591051e+00 6.88317872e+00 1.26976839e+00 28 -6.10330965e+01 1.35209294e+02 1.10964633e+02 | -6.10330965e+01 1.35209294e+02 1.10964633e+02 29 2.39699952e+02 -3.93016465e+01 -6.08451972e+01 | 2.39699952e+02 -3.93016465e+01 -6.08451972e+01 30 3.42997498e+01 3.25331008e+01 2.31588050e+01 | 3.42997498e+01 3.25331008e+01 2.31588050e+01 31 -8.38643994e+02 7.28382861e+02 6.09592175e+02 | -8.38643994e+02 7.28382861e+02 6.09592175e+02 32 -4.90229654e+01 -2.04098130e+01 -1.15029117e+01 | -4.90229654e+01 -2.04098130e+01 -1.15029117e+01 33 1.44490736e+01 8.58470180e+00 1.81973821e+01 | 1.44490736e+01 8.58470180e+00 1.81973821e+01 34 -4.61749931e+01 -1.03627984e+02 1.31073175e+02 | -4.61749931e+01 -1.03627984e+02 1.31073175e+02 35 -8.11724508e-01 2.70964644e+01 -5.52802849e+02 | -8.11724508e-01 2.70964644e+01 -5.52802849e+02 36 1.05425352e+00 -6.12419075e+00 3.52088240e+01 | 1.05425352e+00 -6.12419075e+00 3.52088240e+01 37 -6.70289222e-01 -3.96958249e+00 2.43748471e+00 | -6.70289222e-01 -3.96958249e+00 2.43748471e+00 38 -4.15365335e+01 -2.52773174e+01 2.39342375e+01 | -4.15365335e+01 -2.52773174e+01 2.39342375e+01 39 -1.03482618e+01 6.16175455e+00 3.18380862e+01 | -1.03482618e+01 6.16175455e+00 3.18380862e+01 40 -1.98016273e+02 -1.40455563e+02 1.78159140e+01 | -1.98016273e+02 -1.40455563e+02 1.78159140e+01 41 2.59144082e+02 1.30547721e+02 7.75736687e+01 | 2.59144082e+02 1.30547721e+02 7.75736687e+01 42 -2.12407278e+02 3.36088527e+02 -2.47104742e+01 | -2.12407278e+02 3.36088527e+02 -2.47104742e+01 43 5.17804301e+01 -2.94227575e+01 1.94133279e+01 | 5.17804301e+01 -2.94227575e+01 1.94133279e+01 44 3.12382700e+01 -4.07890366e+01 4.76482945e+01 | 3.12382700e+01 -4.07890366e+01 4.76482945e+01 45 -9.36424664e-01 3.63057665e+00 7.27474721e-01 | -9.36424664e-01 3.63057665e+00 7.27474721e-01 46 -8.39738721e+01 -5.92324407e+01 5.20236935e+02 | -8.39738721e+01 -5.92324407e+01 5.20236935e+02 47 1.00900447e+02 5.46106122e+00 1.02274492e+02 | 1.00900447e+02 5.46106122e+00 1.02274492e+02 48 -4.09491874e+02 -6.46551891e+02 -4.94165594e+01 | -4.09491874e+02 -6.46551891e+02 -4.94165594e+01 49 2.91911135e+02 6.41598156e+02 4.97520643e+01 | 2.91911135e+02 6.41598156e+02 4.97520643e+01 50 -1.89181752e+02 -2.57788308e+02 -7.34774287e+01 | -1.89181752e+02 -2.57788308e+02 -7.34774287e+01 51 7.99815727e+02 1.97837208e+02 -8.18365897e+02 | 7.99815727e+02 1.97837208e+02 -8.18365897e+02 52 -1.93130480e+01 -1.26702509e+01 6.63822827e+01 | -1.93130480e+01 -1.26702509e+01 6.63822827e+01 53 -2.52473985e+00 -1.72179587e+01 3.48035871e+01 | -2.52473985e+00 -1.72179587e+01 3.48035871e+01 54 -2.91904511e+01 8.14665490e+00 6.71725891e+01 | -2.91904511e+01 8.14665490e+00 6.71725891e+01 55 -1.34803213e+02 8.54187170e+00 6.69158607e+01 | -1.34803213e+02 8.54187170e+00 6.69158607e+01 56 -5.26356546e+01 2.20453437e+01 1.41518150e+02 | -5.26356546e+01 2.20453437e+01 1.41518150e+02 57 3.03164284e+01 8.19532047e+01 1.07579237e+01 | 3.03164284e+01 8.19532047e+01 1.07579237e+01 58 8.98585474e+02 -6.60504998e+02 -6.78393026e+02 | 8.98585474e+02 -6.60504998e+02 -6.78393026e+02 59 3.25046858e+01 3.14360041e+01 1.28368132e+01 | 3.25046858e+01 3.14360041e+01 1.28368132e+01 60 -4.55464579e+01 -6.02588819e-01 4.04519149e+01 | -4.55464579e+01 -6.02588819e-01 4.04519149e+01 61 2.02447507e+01 -4.93068844e+00 2.15277202e+01 | 2.02447507e+01 -4.93068844e+00 2.15277202e+01 62 -6.98633749e+02 -1.66309943e+02 8.81780467e+02 | -6.98633749e+02 -1.66309943e+02 8.81780467e+02 63 2.11679934e+01 1.24041778e+01 2.81318327e+01 | 2.11679934e+01 1.24041778e+01 2.81318327e+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 = [14, 23, 60, 17, 5, 4, 42, 63, 46, 55, 31, 15, 22, 34, 0, 11, 30, 3, 20, 56, 18, 35, 12, 1, 38, 53, 28, 52, 26, 33, 16, 10, 50, 29, 13, 21, 49, 45, 24, 62, 57, 51, 6, 59, 47, 37, 8, 44, 58, 36, 32, 41, 27, 25, 61, 9, 19, 40, 48, 43, 2, 54, 39, 7] 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)) = -38.115737733203346 V(r_1,...,r_N) = -38.11573773320343 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 -8.88855877e+00 -6.19927618e+00 -7.93480683e+00 | -8.88855877e+00 -6.19927618e+00 -7.93480683e+00 1 8.26272956e+00 4.69067530e+00 1.05859204e+01 | 8.26272956e+00 4.69067530e+00 1.05859204e+01 2 -1.38216079e+01 -4.51478655e+00 -6.25899409e+00 | -1.38216079e+01 -4.51478655e+00 -6.25899409e+00 3 1.48148420e+01 1.43427938e+00 5.16942223e+00 | 1.48148420e+01 1.43427938e+00 5.16942223e+00 4 -4.79063715e+00 -6.60001932e+00 -9.30031826e+00 | -4.79063715e+00 -6.60001932e+00 -9.30031826e+00 5 5.75049183e+00 5.72848014e+00 5.16643840e+00 | 5.75049183e+00 5.72848014e+00 5.16643840e+00 6 -1.00996868e+01 -8.02716107e+00 -6.24119324e+00 | -1.00996868e+01 -8.02716107e+00 -6.24119324e+00 7 1.15913597e+01 7.96659754e+00 4.29573802e+00 | 1.15913597e+01 7.96659754e+00 4.29573802e+00 8 -3.55784337e+00 -2.25348755e+00 -7.08892376e-01 | -3.55784337e+00 -2.25348755e+00 -7.08892376e-01 9 -4.30530813e+00 -2.34596093e+00 6.72762347e+00 | -4.30530813e+00 -2.34596093e+00 6.72762347e+00 10 7.43353332e+00 6.88138924e+00 -1.53087962e+01 | 7.43353332e+00 6.88138924e+00 -1.53087962e+01 11 -8.17021405e-01 -1.80961721e+00 7.41384158e-01 | -8.17021405e-01 -1.80961721e+00 7.41384158e-01 12 3.37546169e+00 -5.69704161e+00 4.58584256e+00 | 3.37546169e+00 -5.69704161e+00 4.58584256e+00 13 7.12375014e+00 -5.95546035e+00 -3.28073437e+00 | 7.12375014e+00 -5.95546035e+00 -3.28073437e+00 14 -8.96402328e+00 -2.83606820e-01 5.19055879e-01 | -8.96402328e+00 -2.83606820e-01 5.19055879e-01 15 -3.87087065e+00 1.81616906e+01 -1.64515778e+01 | -3.87087065e+00 1.81616906e+01 -1.64515778e+01 16 8.34161376e-01 -1.26243376e+00 1.55682897e+00 | 8.34161376e-01 -1.26243376e+00 1.55682897e+00 17 -3.25639972e+00 2.69682311e+00 -2.53737613e+00 | -3.25639972e+00 2.69682311e+00 -2.53737613e+00 18 -6.08700591e-01 -4.69795323e+00 -3.94725601e+00 | -6.08700591e-01 -4.69795323e+00 -3.94725601e+00 19 1.05316703e+00 3.03023211e+00 6.70144668e+00 | 1.05316703e+00 3.03023211e+00 6.70144668e+00 20 2.95472320e+00 -6.95471615e-01 3.36853841e+00 | 2.95472320e+00 -6.95471615e-01 3.36853841e+00 21 5.45856646e+00 -2.81139796e+00 -7.68217171e+00 | 5.45856646e+00 -2.81139796e+00 -7.68217171e+00 22 -1.24179752e+01 -6.44873461e+00 -1.14817262e+01 | -1.24179752e+01 -6.44873461e+00 -1.14817262e+01 23 1.19599410e+01 7.25675815e+00 1.16956134e+01 | 1.19599410e+01 7.25675815e+00 1.16956134e+01 24 -7.48831668e+00 -2.38531965e+00 -8.00044248e+00 | -7.48831668e+00 -2.38531965e+00 -8.00044248e+00 25 -3.80902253e+00 8.65160159e+00 -4.09473845e+00 | -3.80902253e+00 8.65160159e+00 -4.09473845e+00 26 -3.89726852e+00 -5.48804214e+00 -5.44391173e+00 | -3.89726852e+00 -5.48804214e+00 -5.44391173e+00 27 2.30378997e+00 3.24982980e+00 8.03423906e+00 | 2.30378997e+00 3.24982980e+00 8.03423906e+00 28 1.03289102e+01 -6.24765631e+00 7.48880941e+00 | 1.03289102e+01 -6.24765631e+00 7.48880941e+00 29 4.50564225e-01 -1.56386782e+00 5.54212230e-01 | 4.50564225e-01 -1.56386782e+00 5.54212230e-01 30 -1.08739224e+00 3.07081350e+00 4.86687704e-02 | -1.08739224e+00 3.07081350e+00 4.86687704e-02 31 -1.08797102e+01 1.39154600e+01 -4.99411294e+00 | -1.08797102e+01 1.39154600e+01 -4.99411294e+00 32 -1.23669899e+01 -1.82458052e+01 -9.46509838e+00 | -1.23669899e+01 -1.82458052e+01 -9.46509838e+00 33 4.92246394e+00 1.54285403e+01 1.26821601e+01 | 4.92246394e+00 1.54285403e+01 1.26821601e+01 34 7.18734582e+00 4.71086398e+00 -1.03756210e+00 | 7.18734582e+00 4.71086398e+00 -1.03756210e+00 35 -5.62654804e-01 -2.74231089e+00 6.09630925e+00 | -5.62654804e-01 -2.74231089e+00 6.09630925e+00 36 -6.70224348e+00 -4.73004002e+00 -1.27065364e+01 | -6.70224348e+00 -4.73004002e+00 -1.27065364e+01 37 4.35709949e+00 4.47471472e+00 1.24946840e+01 | 4.35709949e+00 4.47471472e+00 1.24946840e+01 38 -1.16198504e+01 -1.39236146e+01 -9.14513456e+00 | -1.16198504e+01 -1.39236146e+01 -9.14513456e+00 39 1.35117540e+01 1.50577873e+01 7.47161230e+00 | 1.35117540e+01 1.50577873e+01 7.47161230e+00 40 -2.29806954e+01 -1.49890970e+01 -3.66473968e+00 | -2.29806954e+01 -1.49890970e+01 -3.66473968e+00 41 1.31504524e+01 2.08676978e+01 -1.10572389e+01 | 1.31504524e+01 2.08676978e+01 -1.10572389e+01 42 4.58945469e+00 -4.72151444e+00 2.51173644e+01 | 4.58945469e+00 -4.72151444e+00 2.51173644e+01 43 -3.12000915e-01 4.53957639e-01 4.05232455e-01 | -3.12000915e-01 4.53957639e-01 4.05232455e-01 44 9.06047825e+00 -8.60796757e+00 1.57742100e+01 | 9.06047825e+00 -8.60796757e+00 1.57742100e+01 45 -5.54297838e-02 8.48720508e-01 -1.07710802e+00 | -5.54297838e-02 8.48720508e-01 -1.07710802e+00 46 9.85035619e-01 -1.24747198e+00 2.20566423e+00 | 9.85035619e-01 -1.24747198e+00 2.20566423e+00 47 -6.54323773e+00 -4.72566283e+00 3.25696298e+00 | -6.54323773e+00 -4.72566283e+00 3.25696298e+00 48 -3.08473225e+01 -3.51833869e+01 -1.32829893e+01 | -3.08473225e+01 -3.51833869e+01 -1.32829893e+01 49 2.75524511e+01 3.38706630e+01 1.18586292e+01 | 2.75524511e+01 3.38706630e+01 1.18586292e+01 50 -9.59298945e+00 6.05172476e+00 5.03221777e+00 | -9.59298945e+00 6.05172476e+00 5.03221777e+00 51 2.22074681e+00 5.76753329e+00 6.51112855e-01 | 2.22074681e+00 5.76753329e+00 6.51112855e-01 52 1.39005337e+00 -2.13918522e+00 1.53115439e-02 | 1.39005337e+00 -2.13918522e+00 1.53115439e-02 53 -3.27528312e+00 -3.70685545e+00 6.67166485e+00 | -3.27528312e+00 -3.70685545e+00 6.67166485e+00 54 -1.42720045e+00 -4.53821744e-01 -6.97678171e+00 | -1.42720045e+00 -4.53821744e-01 -6.97678171e+00 55 2.29785179e+00 3.04120022e-01 5.65920923e+00 | 2.29785179e+00 3.04120022e-01 5.65920923e+00 56 2.25887748e+00 3.43221730e+00 -8.45789131e+00 | 2.25887748e+00 3.43221730e+00 -8.45789131e+00 57 1.31669220e+01 3.04703209e+00 -9.29326400e+00 | 1.31669220e+01 3.04703209e+00 -9.29326400e+00 58 8.16062280e+00 -1.20659799e+01 4.43474596e+00 | 8.16062280e+00 -1.20659799e+01 4.43474596e+00 59 9.31835601e-01 4.10886099e-01 2.61583158e+00 | 9.31835601e-01 4.10886099e-01 2.61583158e+00 60 4.50781120e+00 2.91992608e+00 -4.01178408e+00 | 4.50781120e+00 2.91992608e+00 -4.01178408e+00 61 -8.41321165e-02 1.62825015e+00 -8.53328306e-01 | -8.41321165e-02 1.62825015e+00 -8.53328306e-01 62 -6.20092466e+00 -2.52148198e+00 5.46928590e+00 | -6.20092466e+00 -2.52148198e+00 5.46928590e+00 63 1.18404984e+00 -7.17775000e-01 -4.55485066e-01 | 1.18404984e+00 -7.17775000e-01 -4.55485066e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al C Ti (Configuration in file "config-AlCTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [5, 8, 27, 12, 13, 0, 20, 60, 1, 45, 54, 31, 3, 4, 42, 55, 36, 22, 46, 43, 6, 56, 17, 61, 49, 33, 50, 2, 59, 39, 58, 11, 38, 25, 44, 52, 16, 41, 32, 29, 53, 37, 14, 19, 34, 9, 18, 51, 57, 24, 26, 47, 35, 40, 10, 15, 21, 48, 30, 28, 7, 23, 62, 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)) = -93.00363241037972 V(r_1,...,r_N) = -93.00363241037962 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 -4.24950979e+00 -2.24735641e+00 -4.22668634e+00 | -4.24950979e+00 -2.24735641e+00 -4.22668634e+00 1 1.27954867e+01 -4.88565189e-01 -1.03179141e+01 | 1.27954867e+01 -4.88565189e-01 -1.03179141e+01 2 -4.07387187e+00 -3.73978025e+00 4.83942108e+00 | -4.07387187e+00 -3.73978025e+00 4.83942108e+00 3 -7.62215040e+00 1.00270634e+01 -1.52239356e+01 | -7.62215040e+00 1.00270634e+01 -1.52239356e+01 4 -2.73363538e+00 -2.38534707e+00 -4.86122789e-01 | -2.73363538e+00 -2.38534707e+00 -4.86122789e-01 5 5.15729410e+00 -4.23053890e+00 1.07255770e+01 | 5.15729410e+00 -4.23053890e+00 1.07255770e+01 6 -6.95209832e+00 4.60652699e+00 6.36894336e+00 | -6.95209832e+00 4.60652699e+00 6.36894336e+00 7 -5.56149269e+00 -6.49867163e-01 6.62048753e+00 | -5.56149269e+00 -6.49867163e-01 6.62048753e+00 8 -2.07135840e+01 -2.01580849e+01 -1.25814081e+01 | -2.07135840e+01 -2.01580849e+01 -1.25814081e+01 9 1.53220876e+01 2.49731400e+01 9.27078545e+00 | 1.53220876e+01 2.49731400e+01 9.27078545e+00 10 -7.93311832e-01 -2.00948801e+00 -5.89208594e-01 | -7.93311832e-01 -2.00948801e+00 -5.89208594e-01 11 4.84674979e+00 -9.29755500e+00 -1.08377066e+01 | 4.84674979e+00 -9.29755500e+00 -1.08377066e+01 12 5.35655399e+00 -4.07928257e+00 3.22513522e+00 | 5.35655399e+00 -4.07928257e+00 3.22513522e+00 13 1.23574968e+00 -1.04954038e+00 -2.10203339e+00 | 1.23574968e+00 -1.04954038e+00 -2.10203339e+00 14 1.08612986e+01 -7.79505242e+00 1.05329445e+01 | 1.08612986e+01 -7.79505242e+00 1.05329445e+01 15 -1.86219442e+00 -3.21907960e+00 1.08369812e+00 | -1.86219442e+00 -3.21907960e+00 1.08369812e+00 16 2.86738190e+00 2.87694786e+00 2.98703720e+00 | 2.86738190e+00 2.87694786e+00 2.98703720e+00 17 -1.56084254e+00 -7.46005996e-01 1.02916627e+00 | -1.56084254e+00 -7.46005996e-01 1.02916627e+00 18 -1.05758828e+00 -2.23232399e+00 1.16152551e+00 | -1.05758828e+00 -2.23232399e+00 1.16152551e+00 19 9.09192228e-01 -8.77344587e-01 6.91665357e-01 | 9.09192228e-01 -8.77344587e-01 6.91665357e-01 20 2.27594616e+00 8.58670409e+00 -4.36764331e+00 | 2.27594616e+00 8.58670409e+00 -4.36764331e+00 21 -1.24237607e-01 4.10221117e+00 -1.67655473e+01 | -1.24237607e-01 4.10221117e+00 -1.67655473e+01 22 8.62388481e+00 4.02095444e+00 6.62326268e+00 | 8.62388481e+00 4.02095444e+00 6.62326268e+00 23 -5.74884704e+00 -8.14380400e+00 -9.27468476e+00 | -5.74884704e+00 -8.14380400e+00 -9.27468476e+00 24 -3.46407956e+00 -1.01911452e+00 -5.20899923e+00 | -3.46407956e+00 -1.01911452e+00 -5.20899923e+00 25 9.51999226e+00 -2.50260732e+00 -7.02752436e+00 | 9.51999226e+00 -2.50260732e+00 -7.02752436e+00 26 -1.13558919e+00 -1.21494992e+00 1.79108789e+00 | -1.13558919e+00 -1.21494992e+00 1.79108789e+00 27 0.00000000e+00 0.00000000e+00 0.00000000e+00 | 0.00000000e+00 0.00000000e+00 0.00000000e+00 28 -2.92129263e+00 7.39630455e+00 9.75743661e+00 | -2.92129263e+00 7.39630455e+00 9.75743661e+00 29 -1.50785763e+00 4.73201766e+00 2.97068227e+00 | -1.50785763e+00 4.73201766e+00 2.97068227e+00 30 -5.02006394e-01 2.85782720e+00 5.89652123e+00 | -5.02006394e-01 2.85782720e+00 5.89652123e+00 31 -3.57147055e+00 3.01621867e+00 -2.98321065e+00 | -3.57147055e+00 3.01621867e+00 -2.98321065e+00 32 6.10649136e-01 -8.77544559e-02 9.66616345e-01 | 6.10649136e-01 -8.77544559e-02 9.66616345e-01 33 -2.70988200e+00 1.89156337e+00 -1.23166805e+01 | -2.70988200e+00 1.89156337e+00 -1.23166805e+01 34 -2.94956127e+00 -3.47929493e+00 -1.05657176e+00 | -2.94956127e+00 -3.47929493e+00 -1.05657176e+00 35 -1.39636105e+00 -7.48993582e+00 3.73527647e+00 | 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4.86528386e+00 56 6.65864786e+00 1.01283778e+01 2.60593142e+00 | 6.65864786e+00 1.01283778e+01 2.60593142e+00 57 -3.62597384e+00 2.68090797e+00 2.85923567e+00 | -3.62597384e+00 2.68090797e+00 2.85923567e+00 58 5.02391048e+00 -5.43020141e+00 3.41086201e+00 | 5.02391048e+00 -5.43020141e+00 3.41086201e+00 59 -2.38746704e+00 -2.65417097e+00 -5.42220451e-01 | -2.38746704e+00 -2.65417097e+00 -5.42220451e-01 60 7.51764273e+00 8.57949693e+00 -8.73213516e+00 | 7.51764273e+00 8.57949693e+00 -8.73213516e+00 61 -6.62680938e-01 -1.65433604e+00 -1.45627761e+00 | -6.62680938e-01 -1.65433604e+00 -1.45627761e+00 62 8.32301290e+00 5.07074893e-01 -1.19790969e+01 | 8.32301290e+00 5.07074893e-01 -1.19790969e+01 63 1.18404111e+00 1.81027873e+00 9.34378471e-01 | 1.18404111e+00 1.81027873e+00 9.34378471e-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.