!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_BonnyCastinTerentyev_2013_FeNiCr__MO_763197941039_000 Supported species : Cr Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [1, 0, 38, 31, 63, 55, 27, 51, 22, 52, 13, 49, 44, 10, 32, 57, 23, 47, 30, 62, 41, 39, 8, 16, 29, 61, 46, 6, 42, 24, 18, 3, 14, 50, 54, 36, 35, 48, 2, 21, 45, 20, 28, 53, 12, 40, 26, 17, 37, 11, 33, 7, 9, 43, 34, 5, 58, 15, 56, 60, 59, 25, 19, 4] 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)) = 900.6600135385142 V(r_1,...,r_N) = 900.6600135385152 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 -3.44879608e+01 -1.76035572e+01 -5.78682484e+00 | -3.44879608e+01 -1.76035572e+01 -5.78682484e+00 1 -2.43060311e+01 -1.17012843e+02 8.32594642e+01 | -2.43060311e+01 -1.17012843e+02 8.32594642e+01 2 -1.19345105e+01 6.04714230e+01 -9.66754578e+01 | -1.19345105e+01 6.04714230e+01 -9.66754578e+01 3 6.95633397e+01 7.73576695e+01 1.80800864e+01 | 6.95633397e+01 7.73576695e+01 1.80800864e+01 4 -1.07162692e+02 -5.83257091e+01 -1.29445613e+01 | -1.07162692e+02 -5.83257091e+01 -1.29445613e+01 5 9.99996922e+01 3.90438025e+01 2.21548216e+01 | 9.99996922e+01 3.90438025e+01 2.21548216e+01 6 6.69635980e-01 -7.60787749e-01 -4.43518536e-01 | 6.69635980e-01 -7.60787749e-01 -4.43518536e-01 7 -6.22607904e+01 1.43842896e+02 -9.68930803e+01 | -6.22607904e+01 1.43842896e+02 -9.68930803e+01 8 -2.60463921e+01 -2.00442670e+01 -6.20768657e+01 | -2.60463921e+01 -2.00442670e+01 -6.20768657e+01 9 -1.25259521e+01 5.13370703e+01 2.97665050e+01 | -1.25259521e+01 5.13370703e+01 2.97665050e+01 10 -5.91698163e+01 -5.94345942e+01 -5.33147709e+01 | -5.91698163e+01 -5.94345942e+01 -5.33147709e+01 11 5.89847647e+01 6.00482417e+01 5.36423771e+01 | 5.89847647e+01 6.00482417e+01 5.36423771e+01 12 -2.90707852e+01 -1.03611497e+02 -1.38972757e+01 | -2.90707852e+01 -1.03611497e+02 -1.38972757e+01 13 9.61567163e+01 5.31990724e+01 4.91297166e+00 | 9.61567163e+01 5.31990724e+01 4.91297166e+00 14 -3.51331007e+01 -5.29244013e+00 -4.92436486e+01 | -3.51331007e+01 -5.29244013e+00 -4.92436486e+01 15 4.23201413e+01 2.49581781e+01 4.34228786e+01 | 4.23201413e+01 2.49581781e+01 4.34228786e+01 16 -4.25516121e+01 -2.87664584e+01 -3.49140942e+01 | -4.25516121e+01 -2.87664584e+01 -3.49140942e+01 17 -9.74343084e+00 -1.00155014e+01 7.71986570e+01 | -9.74343084e+00 -1.00155014e+01 7.71986570e+01 18 5.10001076e+01 3.35900182e+01 -4.38655548e+01 | 5.10001076e+01 3.35900182e+01 -4.38655548e+01 19 -1.47330145e+02 9.45276527e+01 -9.78484634e+01 | -1.47330145e+02 9.45276527e+01 -9.78484634e+01 20 -7.64975988e+01 -6.16537281e+01 -9.27011127e+01 | -7.64975988e+01 -6.16537281e+01 -9.27011127e+01 21 1.12237116e+02 8.17547656e+01 5.99129604e+01 | 1.12237116e+02 8.17547656e+01 5.99129604e+01 22 -3.97270217e+01 -5.58691400e+01 -9.93375641e+01 | -3.97270217e+01 -5.58691400e+01 -9.93375641e+01 23 4.09038111e+01 5.51138403e+01 9.97495030e+01 | 4.09038111e+01 5.51138403e+01 9.97495030e+01 24 -4.80230320e+00 -4.04443004e+00 -4.86000176e+00 | -4.80230320e+00 -4.04443004e+00 -4.86000176e+00 25 -8.70853452e+01 8.08556803e+01 -5.44303933e+01 | -8.70853452e+01 8.08556803e+01 -5.44303933e+01 26 5.01110211e+00 1.47610967e+01 -1.73518677e+01 | 5.01110211e+00 1.47610967e+01 -1.73518677e+01 27 -4.92046000e-01 -6.85692642e-01 3.62832029e-01 | -4.92046000e-01 -6.85692642e-01 3.62832029e-01 28 5.67663949e+01 -1.12022160e+02 5.50144201e+01 | 5.67663949e+01 -1.12022160e+02 5.50144201e+01 29 2.83037258e+01 2.06138469e+01 2.43080377e+01 | 2.83037258e+01 2.06138469e+01 2.43080377e+01 30 1.49363496e+02 -9.17648195e+01 1.00364513e+02 | 1.49363496e+02 -9.17648195e+01 1.00364513e+02 31 -1.21957762e+02 4.53603234e+01 -7.19561654e+01 | -1.21957762e+02 4.53603234e+01 -7.19561654e+01 32 4.72922734e-01 5.37405369e-01 -4.28188597e-01 | 4.72922734e-01 5.37405369e-01 -4.28188597e-01 33 -4.39246901e+01 9.41442037e+01 -9.72019278e+01 | -4.39246901e+01 9.41442037e+01 -9.72019278e+01 34 7.43645431e+01 -1.79249524e+02 1.03009328e+02 | 7.43645431e+01 -1.79249524e+02 1.03009328e+02 35 -5.68653795e+01 -7.46364247e+01 5.93113081e+01 | -5.68653795e+01 -7.46364247e+01 5.93113081e+01 36 4.47273042e+01 -9.31760554e+01 9.67503740e+01 | 4.47273042e+01 -9.31760554e+01 9.67503740e+01 37 -6.70801008e+01 -8.27419166e+01 5.32055258e+01 | -6.70801008e+01 -8.27419166e+01 5.32055258e+01 38 -6.82806227e+01 -5.31887838e+01 -5.88081872e+01 | -6.82806227e+01 -5.31887838e+01 -5.88081872e+01 39 -3.34810268e+01 -3.92067611e+01 1.18010151e+02 | -3.34810268e+01 -3.92067611e+01 1.18010151e+02 40 -1.30055004e+00 6.26966538e-01 5.91603188e-01 | -1.30055004e+00 6.26966538e-01 5.91603188e-01 41 -9.55869521e+01 1.24198873e+02 -7.40905534e+01 | -9.55869521e+01 1.24198873e+02 -7.40905534e+01 42 -9.17457176e+01 -9.19969599e+01 -4.19848757e+01 | -9.17457176e+01 -9.19969599e+01 -4.19848757e+01 43 7.73168516e+01 1.28050570e+02 7.11110562e+01 | 7.73168516e+01 1.28050570e+02 7.11110562e+01 44 9.05278164e+01 -1.46846774e+02 7.67527597e+01 | 9.05278164e+01 -1.46846774e+02 7.67527597e+01 45 -5.17264739e-01 2.90392635e-01 -4.71250143e-01 | -5.17264739e-01 2.90392635e-01 -4.71250143e-01 46 5.53504972e+01 9.04766491e+01 -4.37735512e+01 | 5.53504972e+01 9.04766491e+01 -4.37735512e+01 47 6.17868189e-01 1.20859558e+00 -5.78414351e-01 | 6.17868189e-01 1.20859558e+00 -5.78414351e-01 48 -5.28278595e+01 3.24698136e+00 1.77173988e+01 | -5.28278595e+01 3.24698136e+00 1.77173988e+01 49 7.95870635e+00 1.14777663e+01 7.25132487e+00 | 7.95870635e+00 1.14777663e+01 7.25132487e+00 50 -6.54419429e+01 -8.72488367e+01 -8.79825963e+01 | -6.54419429e+01 -8.72488367e+01 -8.79825963e+01 51 6.59976862e+01 8.61071769e+01 8.73453994e+01 | 6.59976862e+01 8.61071769e+01 8.73453994e+01 52 3.83778490e+01 3.97735173e+01 -8.78941169e+01 | 3.83778490e+01 3.97735173e+01 -8.78941169e+01 53 6.38834491e+01 5.28480721e+01 2.62705983e+01 | 6.38834491e+01 5.28480721e+01 2.62705983e+01 54 2.72495555e-01 -1.74884428e-01 -1.75469770e-02 | 2.72495555e-01 -1.74884428e-01 -1.75469770e-02 55 6.37303919e-01 -6.34265667e-01 -6.50498741e-01 | 6.37303919e-01 -6.34265667e-01 -6.50498741e-01 56 4.48890133e+01 6.10970294e+01 -6.38983493e+01 | 4.48890133e+01 6.10970294e+01 -6.38983493e+01 57 -4.75888552e+01 -6.00591588e+01 -2.42784386e+02 | -4.75888552e+01 -6.00591588e+01 -2.42784386e+02 58 1.21819382e+02 -4.64985224e+01 7.34406672e+01 | 1.21819382e+02 -4.64985224e+01 7.34406672e+01 59 -1.12783172e+00 -1.11414452e+00 1.66794338e-02 | -1.12783172e+00 -1.11414452e+00 1.66794338e-02 60 1.54478220e+02 -7.16093277e+01 1.05966181e+02 | 1.54478220e+02 -7.16093277e+01 1.05966181e+02 61 2.27726493e-02 4.13319685e-01 2.76310237e-01 | 2.27726493e-02 4.13319685e-01 2.76310237e-01 62 -9.53648192e+01 1.44734035e+02 1.40595341e+02 | -9.53648192e+01 1.44734035e+02 1.40595341e+02 63 4.24183870e-01 -7.77166161e-01 -6.66370113e-01 | 4.24183870e-01 -7.77166161e-01 -6.66370113e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Fe (Configuration in file "config-Fe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [61, 14, 3, 2, 10, 27, 18, 11, 28, 29, 4, 7, 35, 41, 1, 59, 47, 57, 6, 42, 36, 44, 63, 25, 51, 23, 62, 5, 8, 9, 39, 37, 38, 56, 60, 12, 20, 31, 32, 30, 50, 13, 19, 54, 21, 52, 49, 16, 55, 46, 40, 24, 45, 58, 43, 48, 33, 17, 53, 15, 34, 0, 26, 22] 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)) = 189.25973959009778 V(r_1,...,r_N) = 189.25973959009792 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 -4.07562764e+00 -1.01460842e+01 -7.44112025e+00 | -4.07562764e+00 -1.01460842e+01 -7.44112025e+00 1 4.56717206e+00 1.12542565e+01 5.02083182e+00 | 4.56717206e+00 1.12542565e+01 5.02083182e+00 2 -1.83215505e+01 -2.06526491e+01 -3.09542704e+01 | -1.83215505e+01 -2.06526491e+01 -3.09542704e+01 3 -2.71639727e+00 4.18680423e+01 -3.82529517e+00 | -2.71639727e+00 4.18680423e+01 -3.82529517e+00 4 1.46080462e+00 -1.60540635e+00 3.75160815e+00 | 1.46080462e+00 -1.60540635e+00 3.75160815e+00 5 -1.85205892e+02 1.36989524e+02 -2.80128219e+02 | -1.85205892e+02 1.36989524e+02 -2.80128219e+02 6 -8.13210792e+00 -4.20486160e+00 -1.07412482e+01 | -8.13210792e+00 -4.20486160e+00 -1.07412482e+01 7 9.34448371e+00 4.89163880e+00 1.14323490e+01 | 9.34448371e+00 4.89163880e+00 1.14323490e+01 8 1.12246279e+00 8.23753557e-01 -1.09639467e+00 | 1.12246279e+00 8.23753557e-01 -1.09639467e+00 9 -1.30303874e+01 1.83849648e+01 6.13605954e+00 | -1.30303874e+01 1.83849648e+01 6.13605954e+00 10 -4.16333190e+01 -3.48510551e+01 -2.17441751e+01 | -4.16333190e+01 -3.48510551e+01 -2.17441751e+01 11 4.06971668e+01 3.56588054e+01 2.19881600e+01 | 4.06971668e+01 3.56588054e+01 2.19881600e+01 12 1.44367228e+01 -1.96166556e+01 -5.42399507e+00 | 1.44367228e+01 -1.96166556e+01 -5.42399507e+00 13 -8.79133824e-01 -1.52346066e+00 -1.54376919e+00 | -8.79133824e-01 -1.52346066e+00 -1.54376919e+00 14 3.81089866e+01 -5.67374930e+01 2.37586471e+01 | 3.81089866e+01 -5.67374930e+01 2.37586471e+01 15 -1.97693382e+00 1.06722957e+00 -6.21990508e-01 | -1.97693382e+00 1.06722957e+00 -6.21990508e-01 16 -3.72925443e+00 -5.09928469e+00 -3.02546422e+00 | -3.72925443e+00 -5.09928469e+00 -3.02546422e+00 17 -2.40284586e+01 -5.28882990e+01 5.57538274e+01 | -2.40284586e+01 -5.28882990e+01 5.57538274e+01 18 2.71767691e+01 5.64818625e+01 -5.09414546e+01 | 2.71767691e+01 5.64818625e+01 -5.09414546e+01 19 2.23140031e+00 1.16611168e-01 1.52902993e+00 | 2.23140031e+00 1.16611168e-01 1.52902993e+00 20 -2.98482825e+01 2.04272873e+01 1.44564562e+01 | -2.98482825e+01 2.04272873e+01 1.44564562e+01 21 4.57056974e+00 -1.23324227e+00 -1.33859704e+01 | 4.57056974e+00 -1.23324227e+00 -1.33859704e+01 22 1.14625742e+00 -3.25230678e-01 -1.68997102e-01 | 1.14625742e+00 -3.25230678e-01 -1.68997102e-01 23 -5.46402893e-01 -3.39775210e-01 -1.51098658e+00 | -5.46402893e-01 -3.39775210e-01 -1.51098658e+00 24 -1.24005323e+01 -6.51316342e+00 -1.19513303e+01 | -1.24005323e+01 -6.51316342e+00 -1.19513303e+01 25 3.60682790e+01 -2.89486324e+01 -5.94445862e+01 | 3.60682790e+01 -2.89486324e+01 -5.94445862e+01 26 2.38324610e+01 7.49977286e+00 -1.90728687e+01 | 2.38324610e+01 7.49977286e+00 -1.90728687e+01 27 -6.50893722e-01 7.88414221e-02 1.75179828e+00 | -6.50893722e-01 7.88414221e-02 1.75179828e+00 28 -3.27631055e+01 -1.90033643e+01 -2.47070377e+01 | -3.27631055e+01 -1.90033643e+01 -2.47070377e+01 29 3.40600054e+01 1.84001914e+01 2.77331977e+01 | 3.40600054e+01 1.84001914e+01 2.77331977e+01 30 -4.37322667e+01 3.81121594e+01 8.19599285e+01 | -4.37322667e+01 3.81121594e+01 8.19599285e+01 31 1.02714877e+00 -1.38233423e+00 -5.88299219e-02 | 1.02714877e+00 -1.38233423e+00 -5.88299219e-02 32 6.86447920e-01 1.12965112e+00 -1.15885525e-01 | 6.86447920e-01 1.12965112e+00 -1.15885525e-01 33 7.06715443e-01 -6.02425274e+00 -1.31506441e+01 | 7.06715443e-01 -6.02425274e+00 -1.31506441e+01 34 -1.20398534e+01 1.54617049e+01 9.72228481e+00 | -1.20398534e+01 1.54617049e+01 9.72228481e+00 35 -4.74698503e+00 -2.49561192e+01 -9.78940848e+00 | -4.74698503e+00 -2.49561192e+01 -9.78940848e+00 36 5.78153004e-01 2.08616415e+00 -1.07339770e+00 | 5.78153004e-01 2.08616415e+00 -1.07339770e+00 37 -1.67054588e+01 -9.03089445e+00 2.76699457e+01 | -1.67054588e+01 -9.03089445e+00 2.76699457e+01 38 -6.59110657e-01 5.79278181e+00 1.23516026e+01 | -6.59110657e-01 5.79278181e+00 1.23516026e+01 39 -7.55501083e+00 -7.58026944e+00 1.20989251e+01 | -7.55501083e+00 -7.58026944e+00 1.20989251e+01 40 1.98363174e+02 -1.54015965e+02 2.69028558e+02 | 1.98363174e+02 -1.54015965e+02 2.69028558e+02 41 1.60492754e+01 -1.41371093e+01 -1.87504313e+01 | 1.60492754e+01 -1.41371093e+01 -1.87504313e+01 42 -1.69098384e-01 -8.74176580e-02 1.59051390e+00 | -1.69098384e-01 -8.74176580e-02 1.59051390e+00 43 -1.35965801e-01 1.02349108e+00 6.66310528e-01 | -1.35965801e-01 1.02349108e+00 6.66310528e-01 44 -4.29447323e+01 -6.24244653e+01 -3.21849967e+01 | -4.29447323e+01 -6.24244653e+01 -3.21849967e+01 45 4.24351605e+01 6.35278007e+01 3.18168808e+01 | 4.24351605e+01 6.35278007e+01 3.18168808e+01 46 -2.00838417e-01 2.52365381e+01 -1.07645982e+01 | -2.00838417e-01 2.52365381e+01 -1.07645982e+01 47 2.09128194e-01 -2.67735138e-01 -1.08869374e+00 | 2.09128194e-01 -2.67735138e-01 -1.08869374e+00 48 -1.41079646e+00 1.71801114e+00 1.26541591e+00 | -1.41079646e+00 1.71801114e+00 1.26541591e+00 49 1.24866504e+01 -1.39972024e+01 -3.22507207e+01 | 1.24866504e+01 -1.39972024e+01 -3.22507207e+01 50 -1.63169783e+01 -2.89227792e+01 -1.39727853e+01 | -1.63169783e+01 -2.89227792e+01 -1.39727853e+01 51 1.37029716e+01 3.71852586e+01 2.67622900e+01 | 1.37029716e+01 3.71852586e+01 2.67622900e+01 52 6.00888669e-01 1.25779066e+01 7.03107292e-01 | 6.00888669e-01 1.25779066e+01 7.03107292e-01 53 -3.25253228e+00 5.61968994e-01 3.44636835e+00 | -3.25253228e+00 5.61968994e-01 3.44636835e+00 54 -2.97139750e+01 -8.79469509e+00 7.04196146e+00 | -2.97139750e+01 -8.79469509e+00 7.04196146e+00 55 1.57678264e+01 2.14047441e+01 2.59937447e+01 | 1.57678264e+01 2.14047441e+01 2.59937447e+01 56 1.61654765e+01 1.45429802e+01 -3.12558274e-01 | 1.61654765e+01 1.45429802e+01 -3.12558274e-01 57 -2.72206729e+01 -7.22247795e+00 1.64056543e+01 | -2.72206729e+01 -7.22247795e+00 1.64056543e+01 58 2.43761662e+01 1.98275100e+00 -2.32265514e+01 | 2.43761662e+01 1.98275100e+00 -2.32265514e+01 59 4.34810801e+00 5.79499232e+00 5.49881077e-01 | 4.34810801e+00 5.79499232e+00 5.49881077e-01 60 -1.43734183e+01 6.32184740e+00 -1.16332160e+01 | -1.43734183e+01 6.32184740e+00 -1.16332160e+01 61 1.42617161e+01 -6.91904616e+00 1.32693823e+01 | 1.42617161e+01 -6.91904616e+00 1.32693823e+01 62 8.30636739e-01 2.87130830e+00 1.87427546e+00 | 8.30636739e-01 2.87130830e+00 1.87427546e+00 63 -3.03212414e-01 -1.82342139e+00 -1.42710436e+00 | -3.03212414e-01 -1.82342139e+00 -1.42710436e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [9, 18, 16, 29, 51, 39, 41, 30, 20, 0, 36, 61, 53, 24, 45, 62, 2, 26, 1, 58, 8, 50, 27, 46, 13, 57, 17, 22, 33, 3, 7, 48, 63, 28, 35, 34, 10, 49, 56, 5, 55, 6, 52, 60, 47, 14, 23, 44, 31, 37, 21, 4, 42, 12, 59, 40, 38, 25, 19, 54, 43, 11, 15, 32] 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)) = 913.685291810731 V(r_1,...,r_N) = 913.6852918107309 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 -7.29127211e+00 -7.14187297e+00 -4.96561088e+00 | -7.29127211e+00 -7.14187297e+00 -4.96561088e+00 1 -6.22553448e+01 -1.49573305e+01 2.63643680e+01 | -6.22553448e+01 -1.49573305e+01 2.63643680e+01 2 4.27513275e+01 3.85827943e+01 -4.55446934e+01 | 4.27513275e+01 3.85827943e+01 -4.55446934e+01 3 5.28730464e-01 2.60442141e+00 -1.53239730e-01 | 5.28730464e-01 2.60442141e+00 -1.53239730e-01 4 2.66902072e+01 -1.88622354e+01 2.01831042e+01 | 2.66902072e+01 -1.88622354e+01 2.01831042e+01 5 -2.06096371e+00 -2.62119324e+00 7.43248950e+00 | -2.06096371e+00 -2.62119324e+00 7.43248950e+00 6 -1.16083668e+00 2.64084431e+00 -1.59175202e-01 | -1.16083668e+00 2.64084431e+00 -1.59175202e-01 7 -2.22506365e+02 1.59644594e+02 -1.45754036e+02 | -2.22506365e+02 1.59644594e+02 -1.45754036e+02 8 -1.05207474e+00 4.65406891e-01 4.15406337e-01 | -1.05207474e+00 4.65406891e-01 4.15406337e-01 9 -3.04158828e+00 -3.10336160e-01 -1.55453407e+00 | -3.04158828e+00 -3.10336160e-01 -1.55453407e+00 10 2.32220744e+00 2.87549237e+00 -1.61390019e+00 | 2.32220744e+00 2.87549237e+00 -1.61390019e+00 11 1.84921249e+01 -2.58321040e+01 -3.87453123e+01 | 1.84921249e+01 -2.58321040e+01 -3.87453123e+01 12 4.52390130e-01 -6.80862703e-01 5.19964934e+00 | 4.52390130e-01 -6.80862703e-01 5.19964934e+00 13 -1.48423271e+00 4.27129461e-01 8.36938857e-02 | -1.48423271e+00 4.27129461e-01 8.36938857e-02 14 4.02895862e+00 5.22757158e-01 -4.45473939e+00 | 4.02895862e+00 5.22757158e-01 -4.45473939e+00 15 5.91895171e-01 2.06438091e+00 -5.97221677e+00 | 5.91895171e-01 2.06438091e+00 -5.97221677e+00 16 -3.73906832e+00 -3.25608304e+00 -4.98759397e+00 | -3.73906832e+00 -3.25608304e+00 -4.98759397e+00 17 -1.16320499e+01 -7.39045273e+00 1.27329791e+01 | -1.16320499e+01 -7.39045273e+00 1.27329791e+01 18 1.37878335e+01 1.14658467e+01 -8.43218968e+00 | 1.37878335e+01 1.14658467e+01 -8.43218968e+00 19 6.81628644e-01 -8.34347350e-01 8.30519936e-01 | 6.81628644e-01 -8.34347350e-01 8.30519936e-01 20 4.49173967e+00 6.94513531e-01 8.79158601e-01 | 4.49173967e+00 6.94513531e-01 8.79158601e-01 21 -6.27542310e+00 1.27823042e+01 -1.37438599e+01 | -6.27542310e+00 1.27823042e+01 -1.37438599e+01 22 9.66856383e-01 -9.03661682e-01 3.59490918e-01 | 9.66856383e-01 -9.03661682e-01 3.59490918e-01 23 -1.49113872e+00 4.86908485e-01 -6.56574468e-01 | -1.49113872e+00 4.86908485e-01 -6.56574468e-01 24 -1.20940231e+02 -1.37717617e+02 -9.42579662e+01 | -1.20940231e+02 -1.37717617e+02 -9.42579662e+01 25 1.18243643e+02 1.35566965e+02 9.68645606e+01 | 1.18243643e+02 1.35566965e+02 9.68645606e+01 26 -5.34555979e-01 -2.05757973e+00 -5.51101875e+00 | -5.34555979e-01 -2.05757973e+00 -5.51101875e+00 27 1.83583132e+00 3.47499254e+00 5.36857290e+00 | 1.83583132e+00 3.47499254e+00 5.36857290e+00 28 -2.81817637e+02 -4.98389942e+02 -5.56919646e+02 | -2.81817637e+02 -4.98389942e+02 -5.56919646e+02 29 2.65008756e+02 5.17076218e+02 5.87632216e+02 | 2.65008756e+02 5.17076218e+02 5.87632216e+02 30 3.47873574e+02 -2.15493729e+03 -8.54560601e+02 | 3.47873574e+02 -2.15493729e+03 -8.54560601e+02 31 -3.47646582e+02 2.15354815e+03 8.54238170e+02 | -3.47646582e+02 2.15354815e+03 8.54238170e+02 32 6.63254223e-01 -1.68576849e+00 1.74699215e+00 | 6.63254223e-01 -1.68576849e+00 1.74699215e+00 33 -1.73482358e+01 1.45837570e+02 -6.69034993e+01 | -1.73482358e+01 1.45837570e+02 -6.69034993e+01 34 2.20199955e+02 -1.58398764e+02 1.46014418e+02 | 2.20199955e+02 -1.58398764e+02 1.46014418e+02 35 -3.11120336e+01 -7.75134503e+01 4.46205640e+01 | -3.11120336e+01 -7.75134503e+01 4.46205640e+01 36 1.19336865e+01 -1.47596326e+02 6.17465070e+01 | 1.19336865e+01 -1.47596326e+02 6.17465070e+01 37 5.35649989e+00 2.32617592e+00 5.47157430e+00 | 5.35649989e+00 2.32617592e+00 5.47157430e+00 38 -2.27797565e+01 -8.57897703e+00 -1.57661999e+00 | -2.27797565e+01 -8.57897703e+00 -1.57661999e+00 39 2.17785191e+01 5.00768389e+00 3.42329057e+00 | 2.17785191e+01 5.00768389e+00 3.42329057e+00 40 8.81836563e+00 -6.82720717e+01 -7.88156479e+01 | 8.81836563e+00 -6.82720717e+01 -7.88156479e+01 41 1.72091008e+00 5.73000396e+01 3.36868263e+01 | 1.72091008e+00 5.73000396e+01 3.36868263e+01 42 7.30339661e-01 -4.15506874e+00 7.90087292e-01 | 7.30339661e-01 -4.15506874e+00 7.90087292e-01 43 1.63126960e+02 -9.24478065e+01 -1.60199546e+02 | 1.63126960e+02 -9.24478065e+01 -1.60199546e+02 44 -5.82665479e-01 1.31594341e+00 -2.34742952e-01 | -5.82665479e-01 1.31594341e+00 -2.34742952e-01 45 -9.08600650e-01 2.88810618e-01 -1.01722853e+00 | -9.08600650e-01 2.88810618e-01 -1.01722853e+00 46 -1.18918582e+01 9.70374210e+00 4.34867144e+01 | -1.18918582e+01 9.70374210e+00 4.34867144e+01 47 8.91378120e-01 1.72879853e+00 1.00294670e+00 | 8.91378120e-01 1.72879853e+00 1.00294670e+00 48 -1.31427196e+01 3.88683030e-01 -4.38296337e+00 | -1.31427196e+01 3.88683030e-01 -4.38296337e+00 49 1.01022909e+01 5.47643164e+00 -6.42939085e+00 | 1.01022909e+01 5.47643164e+00 -6.42939085e+00 50 -8.36599272e+01 -1.41540014e+02 -6.23308700e+01 | -8.36599272e+01 -1.41540014e+02 -6.23308700e+01 51 8.32205444e+01 1.42320020e+02 6.57391252e+01 | 8.32205444e+01 1.42320020e+02 6.57391252e+01 52 5.33397406e+00 -3.75218137e+00 6.43391685e+00 | 5.33397406e+00 -3.75218137e+00 6.43391685e+00 53 -3.32063410e+00 -2.59584845e+00 3.25721641e+00 | -3.32063410e+00 -2.59584845e+00 3.25721641e+00 54 1.24896816e+00 -2.15226777e-01 -4.55155628e-01 | 1.24896816e+00 -2.15226777e-01 -4.55155628e-01 55 3.21922015e-01 -7.05830592e-01 -1.16595503e+00 | 3.21922015e-01 -7.05830592e-01 -1.16595503e+00 56 7.99121745e+00 4.48792269e+01 -4.58886938e+01 | 7.99121745e+00 4.48792269e+01 -4.58886938e+01 57 3.03957755e+01 1.59174555e+01 1.27075084e+01 | 3.03957755e+01 1.59174555e+01 1.27075084e+01 58 -4.39640152e+00 6.74167161e+00 7.57501553e+00 | -4.39640152e+00 6.74167161e+00 7.57501553e+00 59 -4.69711047e-01 -6.42305935e-01 5.97105513e-01 | -4.69711047e-01 -6.42305935e-01 5.97105513e-01 60 -1.61034786e+02 9.34640280e+01 1.60173094e+02 | -1.61034786e+02 9.34640280e+01 1.60173094e+02 61 -5.59372729e-01 1.34278167e+00 5.57013897e-01 | -5.59372729e-01 1.34278167e+00 5.57013897e-01 62 3.62445670e+00 4.44397117e+00 -5.35599727e-01 | 3.62445670e+00 4.44397117e+00 -5.35599727e-01 63 -7.06546117e-02 5.85794588e-01 3.08525542e-01 | -7.06546117e-02 5.85794588e-01 3.08525542e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cr Fe Ni (Configuration in file "config-CrFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [50, 49, 35, 13, 20, 53, 59, 21, 25, 36, 39, 42, 28, 3, 18, 26, 63, 60, 14, 32, 4, 7, 23, 22, 41, 8, 15, 45, 12, 61, 37, 55, 19, 34, 33, 2, 9, 30, 54, 10, 43, 24, 11, 40, 46, 27, 44, 57, 56, 1, 0, 58, 52, 5, 38, 31, 48, 47, 51, 6, 17, 29, 62, 16] 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)) = 459.39146410341016 V(r_1,...,r_N) = 459.39146410340976 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 -1.60015369e+01 -2.69768950e+00 -2.27674171e+01 | -1.60015369e+01 -2.69768950e+00 -2.27674171e+01 1 -9.17356510e+01 5.05656014e+01 -1.18817110e+01 | -9.17356510e+01 5.05656014e+01 -1.18817110e+01 2 3.80944718e+00 -5.42546042e+01 -1.38219526e+01 | 3.80944718e+00 -5.42546042e+01 -1.38219526e+01 3 1.00525852e+00 4.07472855e+01 6.41159450e+00 | 1.00525852e+00 4.07472855e+01 6.41159450e+00 4 1.08985120e+02 -4.57867765e+01 3.55952120e+01 | 1.08985120e+02 -4.57867765e+01 3.55952120e+01 5 -5.73769164e+01 4.85752856e+01 -5.36928055e+01 | -5.73769164e+01 4.85752856e+01 -5.36928055e+01 6 -7.44715737e+01 -4.18253250e+01 -1.06807899e+02 | -7.44715737e+01 -4.18253250e+01 -1.06807899e+02 7 5.37187715e+01 5.23990928e+01 7.03136185e+01 | 5.37187715e+01 5.23990928e+01 7.03136185e+01 8 -8.99313463e-02 6.97226736e-01 4.24833624e-01 | -8.99313463e-02 6.97226736e-01 4.24833624e-01 9 -9.30873711e+00 1.30215428e+00 -5.78715019e+00 | -9.30873711e+00 1.30215428e+00 -5.78715019e+00 10 3.32400390e+00 1.02244893e+00 -3.98598737e+00 | 3.32400390e+00 1.02244893e+00 -3.98598737e+00 11 1.41010479e+01 -1.74111829e+01 -7.40724565e+00 | 1.41010479e+01 -1.74111829e+01 -7.40724565e+00 12 -1.97402598e+01 -8.96465651e+00 -1.84010910e+01 | -1.97402598e+01 -8.96465651e+00 -1.84010910e+01 13 2.70030456e+01 4.47485582e+00 2.53258951e+01 | 2.70030456e+01 4.47485582e+00 2.53258951e+01 14 -9.62002225e+01 -5.62682032e+01 -2.81165892e+01 | -9.62002225e+01 -5.62682032e+01 -2.81165892e+01 15 8.59951402e+01 5.19635759e+01 3.33422383e+01 | 8.59951402e+01 5.19635759e+01 3.33422383e+01 16 9.92521392e-01 2.56849407e-01 1.28498227e+00 | 9.92521392e-01 2.56849407e-01 1.28498227e+00 17 -7.77604071e+01 1.11039856e+02 -7.61973051e+01 | -7.77604071e+01 1.11039856e+02 -7.61973051e+01 18 6.90637879e-01 -1.02662087e-01 5.17466674e-01 | 6.90637879e-01 -1.02662087e-01 5.17466674e-01 19 -1.46698572e+01 8.24108186e+01 -2.51671748e+01 | -1.46698572e+01 8.24108186e+01 -2.51671748e+01 20 9.59198761e+01 -1.03591605e+02 6.85735158e+01 | 9.59198761e+01 -1.03591605e+02 6.85735158e+01 21 -3.30655654e+01 -3.07477797e+00 -3.33052102e+01 | -3.30655654e+01 -3.07477797e+00 -3.33052102e+01 22 -2.37795299e+01 4.49531898e+00 1.79713345e+01 | -2.37795299e+01 4.49531898e+00 1.79713345e+01 23 7.32630400e-01 -1.32577284e+00 -4.58937615e-01 | 7.32630400e-01 -1.32577284e+00 -4.58937615e-01 24 5.92960890e-01 3.05979142e-01 1.04594703e+00 | 5.92960890e-01 3.05979142e-01 1.04594703e+00 25 -1.60286314e+01 -1.68569915e+01 2.87253568e+01 | -1.60286314e+01 -1.68569915e+01 2.87253568e+01 26 1.79216054e+01 1.58605752e+01 -4.15503193e+01 | 1.79216054e+01 1.58605752e+01 -4.15503193e+01 27 -9.39823080e-01 2.75824219e-01 -5.58850757e-01 | -9.39823080e-01 2.75824219e-01 -5.58850757e-01 28 -1.42884446e+01 -8.43234638e+00 8.43982973e+00 | -1.42884446e+01 -8.43234638e+00 8.43982973e+00 29 1.72094553e+01 2.09948732e+01 7.78133604e+00 | 1.72094553e+01 2.09948732e+01 7.78133604e+00 30 -1.77912181e+01 -7.22036354e+01 1.31083531e+01 | -1.77912181e+01 -7.22036354e+01 1.31083531e+01 31 1.66563411e+01 3.28693479e-01 1.39630752e+01 | 1.66563411e+01 3.28693479e-01 1.39630752e+01 32 -1.24896605e+02 -1.54616295e+02 -9.07014115e+01 | -1.24896605e+02 -1.54616295e+02 -9.07014115e+01 33 1.24762504e+01 6.81132778e+01 1.55704663e+02 | 1.24762504e+01 6.81132778e+01 1.55704663e+02 34 1.34640221e+02 6.25872532e+01 -2.70472608e+01 | 1.34640221e+02 6.25872532e+01 -2.70472608e+01 35 -3.65996859e-01 -9.38902577e-01 6.80784028e-01 | -3.65996859e-01 -9.38902577e-01 6.80784028e-01 36 -1.33763264e+00 7.67836485e-02 -1.41795192e+00 | -1.33763264e+00 7.67836485e-02 -1.41795192e+00 37 -9.56296808e+00 -6.71961677e+00 1.65988495e+01 | -9.56296808e+00 -6.71961677e+00 1.65988495e+01 38 -6.86345497e-01 -1.04816708e+00 -1.78716742e+00 | -6.86345497e-01 -1.04816708e+00 -1.78716742e+00 39 -4.13730301e+01 -5.53234897e+01 2.56689510e+01 | -4.13730301e+01 -5.53234897e+01 2.56689510e+01 40 7.14980190e+01 -5.73991154e+01 4.46247574e+01 | 7.14980190e+01 -5.73991154e+01 4.46247574e+01 41 -2.35676153e+01 2.68818403e+01 6.72300287e+00 | -2.35676153e+01 2.68818403e+01 6.72300287e+00 42 8.52298628e+00 1.45737118e+01 -2.98135995e+01 | 8.52298628e+00 1.45737118e+01 -2.98135995e+01 43 7.37350195e+01 -7.69973841e+01 -3.28901697e+01 | 7.37350195e+01 -7.69973841e+01 -3.28901697e+01 44 1.47729132e+01 -4.57200555e+01 1.95749319e+01 | 1.47729132e+01 -4.57200555e+01 1.95749319e+01 45 2.20534494e+00 3.44089533e+00 3.01113105e+00 | 2.20534494e+00 3.44089533e+00 3.01113105e+00 46 7.79903844e+00 8.23387035e+00 -1.45411777e+01 | 7.79903844e+00 8.23387035e+00 -1.45411777e+01 47 -1.77931896e+01 -6.19583415e+00 1.50930632e+01 | -1.77931896e+01 -6.19583415e+00 1.50930632e+01 48 -2.89535189e+01 -7.46178216e+00 -2.64659330e+01 | -2.89535189e+01 -7.46178216e+00 -2.64659330e+01 49 1.73148094e+01 3.22512536e+01 3.25093799e+01 | 1.73148094e+01 3.22512536e+01 3.25093799e+01 50 -6.06342413e+00 7.56084001e+00 1.46617077e+00 | -6.06342413e+00 7.56084001e+00 1.46617077e+00 51 -2.10685589e+01 1.43100633e+01 -1.14105022e+01 | -2.10685589e+01 1.43100633e+01 -1.14105022e+01 52 3.35977326e+01 5.28416023e+01 -3.24780199e+01 | 3.35977326e+01 5.28416023e+01 -3.24780199e+01 53 9.86130701e+00 3.01563260e+00 5.49809115e+00 | 9.86130701e+00 3.01563260e+00 5.49809115e+00 54 -3.50295719e+01 -2.82220005e+01 -1.76098571e+01 | -3.50295719e+01 -2.82220005e+01 -1.76098571e+01 55 3.58346120e+01 2.76640052e+01 1.71436988e+01 | 3.58346120e+01 2.76640052e+01 1.71436988e+01 56 3.90694478e+01 -5.34325256e+00 2.77973129e+01 | 3.90694478e+01 -5.34325256e+00 2.77973129e+01 57 5.90149833e+00 -7.48435926e+00 2.58858698e+00 | 5.90149833e+00 -7.48435926e+00 2.58858698e+00 58 -9.87032251e+00 -4.10350860e+00 -3.10789195e+01 | -9.87032251e+00 -4.10350860e+00 -3.10789195e+01 59 1.44846887e+01 9.52872137e+00 2.24395890e+01 | 1.44846887e+01 9.52872137e+00 2.24395890e+01 60 -5.66966835e+01 8.36925456e+01 1.61886239e+01 | -5.66966835e+01 8.36925456e+01 1.61886239e+01 61 -5.82854569e-01 4.91827278e-01 -6.20642866e-01 | -5.82854569e-01 4.91827278e-01 -6.20642866e-01 62 1.05092233e+01 -1.16050054e+01 2.25592890e+01 | 1.05092233e+01 -1.16050054e+01 2.25592890e+01 63 2.15647279e-01 -1.00544039e+00 -9.25205942e-01 | 2.15647279e-01 -1.00544039e+00 -9.25205942e-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.