!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_PlummerTucker_2019_TiAlC__MO_736419017411_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 = [44, 31, 53, 14, 19, 52, 35, 55, 10, 43, 8, 59, 42, 33, 3, 21, 36, 40, 56, 4, 28, 15, 26, 29, 50, 60, 22, 63, 20, 23, 45, 1, 37, 13, 54, 6, 16, 32, 57, 41, 17, 39, 12, 9, 0, 30, 62, 51, 49, 48, 24, 47, 5, 2, 34, 7, 18, 38, 58, 11, 25, 61, 46, 27] 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)) = 104.106120461347 V(r_1,...,r_N) = 104.10612046134669 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 -1.62476434e+01 -5.10557234e+00 -1.21063992e+01 | -1.62476434e+01 -5.10557234e+00 -1.21063992e+01 1 1.51744463e+01 7.55330483e+00 4.86817599e+00 | 1.51744463e+01 7.55330483e+00 4.86817599e+00 2 -2.38060250e+00 -3.91523023e-01 1.96132847e+00 | -2.38060250e+00 -3.91523023e-01 1.96132847e+00 3 -5.18714158e+00 1.74586252e+01 -2.44801179e+01 | -5.18714158e+00 1.74586252e+01 -2.44801179e+01 4 -1.00957770e+02 -9.39168632e+01 -1.42236758e+02 | -1.00957770e+02 -9.39168632e+01 -1.42236758e+02 5 1.05665340e+02 9.20625955e+01 1.49627461e+02 | 1.05665340e+02 9.20625955e+01 1.49627461e+02 6 -2.58531598e+00 -4.48359982e+00 6.77289193e-02 | -2.58531598e+00 -4.48359982e+00 6.77289193e-02 7 4.15993798e+00 2.63030994e+00 -8.18808399e+00 | 4.15993798e+00 2.63030994e+00 -8.18808399e+00 8 -8.89407647e+01 -8.89794917e+01 -5.92262582e+01 | -8.89407647e+01 -8.89794917e+01 -5.92262582e+01 9 7.37710884e+01 9.99498989e+01 4.40041450e+01 | 7.37710884e+01 9.99498989e+01 4.40041450e+01 10 -2.57856344e-01 -1.52049111e-01 1.18084560e+00 | -2.57856344e-01 -1.52049111e-01 1.18084560e+00 11 5.29194022e+00 -5.19290053e+00 -1.21323639e+01 | 5.29194022e+00 -5.19290053e+00 -1.21323639e+01 12 1.75800707e+01 -1.12112724e+01 1.36000265e+01 | 1.75800707e+01 -1.12112724e+01 1.36000265e+01 13 2.25163256e+01 -2.84301293e+01 -1.18456988e+01 | 2.25163256e+01 -2.84301293e+01 -1.18456988e+01 14 5.04508775e+00 -1.55624085e+01 2.33972487e+01 | 5.04508775e+00 -1.55624085e+01 2.33972487e+01 15 -2.62908940e+01 -1.58449627e+01 1.20916106e+01 | -2.62908940e+01 -1.58449627e+01 1.20916106e+01 16 6.03313781e-01 1.15984704e+00 1.70665736e+00 | 6.03313781e-01 1.15984704e+00 1.70665736e+00 17 -2.38212687e+00 1.31921975e+00 -2.95741928e+00 | -2.38212687e+00 1.31921975e+00 -2.95741928e+00 18 -1.20149377e+00 -2.07471118e+00 -9.46339424e-01 | -1.20149377e+00 -2.07471118e+00 -9.46339424e-01 19 -2.57970852e+00 1.41246034e+00 6.58592888e+00 | -2.57970852e+00 1.41246034e+00 6.58592888e+00 20 8.38547461e-01 -3.13054293e+00 7.32436551e-01 | 8.38547461e-01 -3.13054293e+00 7.32436551e-01 21 -4.62587675e+00 -1.31617787e+00 5.24978632e-01 | -4.62587675e+00 -1.31617787e+00 5.24978632e-01 22 3.63018171e+00 1.30299857e+00 3.86803873e+00 | 3.63018171e+00 1.30299857e+00 3.86803873e+00 23 -2.56119600e+00 8.17712503e-01 -9.55010749e+00 | -2.56119600e+00 8.17712503e-01 -9.55010749e+00 24 -1.54053035e+01 -9.21361235e+00 -2.26620067e+01 | -1.54053035e+01 -9.21361235e+00 -2.26620067e+01 25 2.00269667e+01 7.77605221e+00 2.41376551e+01 | 2.00269667e+01 7.77605221e+00 2.41376551e+01 26 -3.04516220e+00 -1.87767017e+00 -2.57001433e+00 | -3.04516220e+00 -1.87767017e+00 -2.57001433e+00 27 -2.24550763e+00 2.51970019e-01 1.33306490e+00 | -2.24550763e+00 2.51970019e-01 1.33306490e+00 28 1.95544634e+01 2.13921254e+01 -3.24974014e+00 | 1.95544634e+01 2.13921254e+01 -3.24974014e+00 29 1.05543902e+00 1.05271079e+00 9.10098141e-01 | 1.05543902e+00 1.05271079e+00 9.10098141e-01 30 7.52591785e+00 -4.25516574e+00 -5.73891411e+00 | 7.52591785e+00 -4.25516574e+00 -5.73891411e+00 31 -6.71073387e-01 6.42776791e+00 -4.41751899e+00 | -6.71073387e-01 6.42776791e+00 -4.41751899e+00 32 1.69484425e-01 2.75039065e+00 -2.80777229e+00 | 1.69484425e-01 2.75039065e+00 -2.80777229e+00 33 -5.89486494e+01 4.95035381e+01 -2.04758816e+02 | -5.89486494e+01 4.95035381e+01 -2.04758816e+02 34 -2.56857072e+00 -3.64802036e+00 2.20949728e+00 | -2.56857072e+00 -3.64802036e+00 2.20949728e+00 35 -3.21751522e+01 -3.24491287e+01 -3.49591638e+00 | -3.21751522e+01 -3.24491287e+01 -3.49591638e+00 36 6.01902912e+01 -5.07329597e+01 2.05676152e+02 | 6.01902912e+01 -5.07329597e+01 2.05676152e+02 37 -3.11567436e-01 2.76574174e+00 -3.57576908e+00 | -3.11567436e-01 2.76574174e+00 -3.57576908e+00 38 2.21337747e-01 7.62559564e+00 -2.68395444e+00 | 2.21337747e-01 7.62559564e+00 -2.68395444e+00 39 1.17725482e+00 7.85769218e-01 -5.65681166e-01 | 1.17725482e+00 7.85769218e-01 -5.65681166e-01 40 -3.86054329e+00 -1.31609500e+00 -4.74655267e+00 | -3.86054329e+00 -1.31609500e+00 -4.74655267e+00 41 -1.20379257e+01 6.12041652e+00 -9.68662221e+00 | -1.20379257e+01 6.12041652e+00 -9.68662221e+00 42 -5.81972988e+01 5.84815917e+00 -3.69257947e+01 | -5.81972988e+01 5.84815917e+00 -3.69257947e+01 43 3.64993832e+01 2.11680407e+01 4.90570260e+01 | 3.64993832e+01 2.11680407e+01 4.90570260e+01 44 6.00147648e+00 -1.44289096e+01 3.59993515e+00 | 6.00147648e+00 -1.44289096e+01 3.59993515e+00 45 1.00190901e+01 6.41478754e+00 7.56273155e+00 | 1.00190901e+01 6.41478754e+00 7.56273155e+00 46 -4.29149213e+01 -4.16102720e+01 -2.31700094e+01 | -4.29149213e+01 -4.16102720e+01 -2.31700094e+01 47 3.72221190e+01 4.27638645e+01 2.53046532e+01 | 3.72221190e+01 4.27638645e+01 2.53046532e+01 48 -4.80350671e+00 -2.80281392e+00 1.31907498e+01 | -4.80350671e+00 -2.80281392e+00 1.31907498e+01 49 9.72607136e-02 -2.66034614e-01 3.63744598e+00 | 9.72607136e-02 -2.66034614e-01 3.63744598e+00 50 -4.66135200e+00 -9.06452092e+00 7.05607447e+00 | -4.66135200e+00 -9.06452092e+00 7.05607447e+00 51 3.94835927e+00 9.04917094e+00 1.73863956e+00 | 3.94835927e+00 9.04917094e+00 1.73863956e+00 52 2.28799059e+00 5.69137871e-01 1.50265673e+00 | 2.28799059e+00 5.69137871e-01 1.50265673e+00 53 -1.33226449e+01 -1.00009095e+01 6.58408248e+00 | -1.33226449e+01 -1.00009095e+01 6.58408248e+00 54 9.73896563e-01 -3.81134443e+00 -2.17257683e+00 | 9.73896563e-01 -3.81134443e+00 -2.17257683e+00 55 5.39155539e+00 -2.14985374e+00 -2.39005681e+00 | 5.39155539e+00 -2.14985374e+00 -2.39005681e+00 56 3.77178332e+01 3.88674300e+01 6.33622728e+00 | 3.77178332e+01 3.88674300e+01 6.33622728e+00 57 -5.25670325e+00 7.91527291e+00 -7.65343865e-01 | -5.25670325e+00 7.91527291e+00 -7.65343865e-01 58 1.24477792e+00 -3.92128455e+00 5.78020690e+00 | 1.24477792e+00 -3.92128455e+00 5.78020690e+00 59 -3.88047871e+00 -4.19899384e+00 9.67435849e-01 | -3.88047871e+00 -4.19899384e+00 9.67435849e-01 60 3.32598352e+00 -2.55427568e+00 2.84871594e+00 | 3.32598352e+00 -2.55427568e+00 2.84871594e+00 61 -1.07654352e+00 -5.56554784e-01 -2.59031402e+00 | -1.07654352e+00 -5.56554784e-01 -2.59031402e+00 62 1.25657536e+01 1.10871017e+01 -1.06344855e+01 | 1.25657536e+01 1.10871017e+01 -1.06344855e+01 63 8.83810580e-02 -1.15139196e+00 -3.72253431e-01 | 8.83810580e-02 -1.15139196e+00 -3.72253431e-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.