!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyTerentyevPasianot_2011_FeNiCr__MO_677715648236_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 = [49, 41, 15, 24, 14, 6, 5, 19, 58, 23, 13, 17, 33, 10, 4, 2, 50, 11, 62, 7, 34, 54, 29, 9, 3, 57, 45, 48, 35, 22, 36, 32, 31, 12, 20, 28, 30, 53, 39, 38, 55, 1, 59, 46, 47, 26, 43, 44, 27, 0, 16, 63, 61, 37, 21, 40, 60, 25, 8, 42, 56, 52, 18, 51] 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)) = 123.17012353991882 V(r_1,...,r_N) = 123.17012353991888 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 -1.53232831e+00 -7.79983686e-01 -1.52350398e+00 | -1.53232831e+00 -7.79983686e-01 -1.52350398e+00 1 -1.85168482e+01 -4.58511979e+01 2.92269774e+01 | -1.85168482e+01 -4.58511979e+01 2.92269774e+01 2 -1.67423629e+00 1.80968015e+01 -5.37170626e+01 | -1.67423629e+00 1.80968015e+01 -5.37170626e+01 3 1.83559811e+01 2.82667148e+01 2.31498992e+01 | 1.83559811e+01 2.82667148e+01 2.31498992e+01 4 1.18985498e+00 2.64352835e-01 4.87290062e-02 | 1.18985498e+00 2.64352835e-01 4.87290062e-02 5 -1.90483751e-01 -6.21117322e-01 -1.08143052e+00 | -1.90483751e-01 -6.21117322e-01 -1.08143052e+00 6 -1.18909979e+00 -5.64605476e-01 -1.71597960e+00 | -1.18909979e+00 -5.64605476e-01 -1.71597960e+00 7 -3.47412496e+01 1.14219672e+02 -8.17514790e+01 | -3.47412496e+01 1.14219672e+02 -8.17514790e+01 8 -1.58627937e+00 1.02701365e-01 -1.51805699e+00 | -1.58627937e+00 1.02701365e-01 -1.51805699e+00 9 -4.85000742e+00 2.55471712e+00 -4.89811272e+00 | -4.85000742e+00 2.55471712e+00 -4.89811272e+00 10 -3.00592657e-01 2.14243135e-01 6.20532575e-01 | -3.00592657e-01 2.14243135e-01 6.20532575e-01 11 5.21516373e+00 -8.28236903e+00 -7.77659267e+00 | 5.21516373e+00 -8.28236903e+00 -7.77659267e+00 12 -9.52362019e+01 -4.33489319e+01 -3.67728387e+01 | -9.52362019e+01 -4.33489319e+01 -3.67728387e+01 13 1.05141990e+02 3.96518059e+01 3.64308855e+01 | 1.05141990e+02 3.96518059e+01 3.64308855e+01 14 -2.42421154e+01 -5.90977206e+00 -3.29645097e+01 | -2.42421154e+01 -5.90977206e+00 -3.29645097e+01 15 3.27874120e+01 1.55840254e+00 2.67698528e+01 | 3.27874120e+01 1.55840254e+00 2.67698528e+01 16 -2.26612393e+01 -2.36697731e+01 -2.04290926e+01 | -2.26612393e+01 -2.36697731e+01 -2.04290926e+01 17 2.42187725e+01 2.23866365e+01 2.15031531e+01 | 2.42187725e+01 2.23866365e+01 2.15031531e+01 18 -6.16026369e-01 -8.10284868e-01 7.58512608e-01 | -6.16026369e-01 -8.10284868e-01 7.58512608e-01 19 -8.10008285e+01 4.89695972e+01 -5.44503860e+01 | -8.10008285e+01 4.89695972e+01 -5.44503860e+01 20 -2.70289871e+01 -1.77389585e+01 -1.66095748e+01 | -2.70289871e+01 -1.77389585e+01 -1.66095748e+01 21 3.03536897e+01 2.12058788e+01 1.55914506e+01 | 3.03536897e+01 2.12058788e+01 1.55914506e+01 22 3.28705132e-01 -2.07971776e+00 -1.94978469e+00 | 3.28705132e-01 -2.07971776e+00 -1.94978469e+00 23 8.46027650e-01 2.07939240e+00 2.52071704e+00 | 8.46027650e-01 2.07939240e+00 2.52071704e+00 24 -3.54479620e+00 -5.83611965e-03 -2.98913846e+00 | -3.54479620e+00 -5.83611965e-03 -2.98913846e+00 25 -1.79366780e+01 2.52207858e+01 -1.56656060e+01 | -1.79366780e+01 2.52207858e+01 -1.56656060e+01 26 -2.40963458e-01 -1.11243772e+00 1.54326800e+00 | -2.40963458e-01 -1.11243772e+00 1.54326800e+00 27 -1.47072731e+00 -1.46765803e+00 2.44715690e-01 | -1.47072731e+00 -1.46765803e+00 2.44715690e-01 28 1.32780881e+01 -1.75856928e+01 2.60443012e+01 | 1.32780881e+01 -1.75856928e+01 2.60443012e+01 29 2.88462466e+00 1.08007829e+00 1.06141996e+00 | 2.88462466e+00 1.08007829e+00 1.06141996e+00 30 8.01534153e+01 -4.90896856e+01 5.23011539e+01 | 8.01534153e+01 -4.90896856e+01 5.23011539e+01 31 -2.45155357e+01 1.04508756e+01 -1.34147501e+01 | -2.45155357e+01 1.04508756e+01 -1.34147501e+01 32 -8.31367500e+01 -7.18639613e+01 -5.18344719e+01 | -8.31367500e+01 -7.18639613e+01 -5.18344719e+01 33 8.29621900e+01 7.21559309e+01 5.34960706e+01 | 8.29621900e+01 7.21559309e+01 5.34960706e+01 34 5.22074249e+01 -1.22106524e+02 6.99701121e+01 | 5.22074249e+01 -1.22106524e+02 6.99701121e+01 35 -1.13521858e+00 -1.32518960e+00 1.49565029e+00 | -1.13521858e+00 -1.32518960e+00 1.49565029e+00 36 -2.16613403e-01 5.24283654e-01 -1.28685108e+00 | -2.16613403e-01 5.24283654e-01 -1.28685108e+00 37 -2.65905634e+01 -2.42357248e+01 2.43293471e+01 | -2.65905634e+01 -2.42357248e+01 2.43293471e+01 38 -3.72413786e+01 -2.93492987e+01 -3.64465749e+01 | -3.72413786e+01 -2.93492987e+01 -3.64465749e+01 39 1.10795939e+01 4.70423593e+00 5.11655202e+01 | 1.10795939e+01 4.70423593e+00 5.11655202e+01 40 -6.95350568e-01 1.78543104e-01 2.20551389e+00 | -6.95350568e-01 1.78543104e-01 2.20551389e+00 41 -4.24540256e+01 6.39766926e+01 -3.48991515e+01 | -4.24540256e+01 6.39766926e+01 -3.48991515e+01 42 -3.42934667e+00 2.79816379e+00 4.21039707e+00 | -3.42934667e+00 2.79816379e+00 4.21039707e+00 43 4.43033109e-01 2.50289202e+00 1.12237303e+00 | 4.43033109e-01 2.50289202e+00 1.12237303e+00 44 4.18093519e+01 -6.65547738e+01 3.54158561e+01 | 4.18093519e+01 -6.65547738e+01 3.54158561e+01 45 -1.10304219e+00 -1.18930921e-01 -1.03121599e+00 | -1.10304219e+00 -1.18930921e-01 -1.03121599e+00 46 2.57317803e+01 2.54848758e+01 -2.26269656e+01 | 2.57317803e+01 2.54848758e+01 -2.26269656e+01 47 -2.95325763e-01 1.05391809e+00 -8.03736787e-01 | -2.95325763e-01 1.05391809e+00 -8.03736787e-01 48 -1.67332771e+01 7.22963472e+00 1.48381194e+01 | -1.67332771e+01 7.22963472e+00 1.48381194e+01 49 -1.07451553e+01 -3.11096495e+00 7.80055830e+00 | -1.07451553e+01 -3.11096495e+00 7.80055830e+00 50 -2.88828137e+00 -1.63373718e+01 -2.59270561e+01 | -2.88828137e+00 -1.63373718e+01 -2.59270561e+01 51 1.40263721e+01 1.86131050e+01 1.85346120e+01 | 1.40263721e+01 1.86131050e+01 1.85346120e+01 52 1.81899731e+01 2.10668240e+01 -2.10315107e+01 | 1.81899731e+01 2.10668240e+01 -2.10315107e+01 53 8.21985803e+00 4.15493840e+00 3.76113609e+00 | 8.21985803e+00 4.15493840e+00 3.76113609e+00 54 -7.56877360e+00 -3.46481927e+00 -3.74482798e+00 | -7.56877360e+00 -3.46481927e+00 -3.74482798e+00 55 8.65054791e+00 2.63069490e+00 2.34267333e+00 | 8.65054791e+00 2.63069490e+00 2.34267333e+00 56 -3.95821776e+00 5.14988171e+00 5.01819919e+00 | -3.95821776e+00 5.14988171e+00 5.01819919e+00 57 1.85374551e+01 -5.92455616e+01 -8.70295444e+01 | 1.85374551e+01 -5.92455616e+01 -8.70295444e+01 58 2.48445920e+01 -9.90783691e+00 1.63164554e+01 | 2.48445920e+01 -9.90783691e+00 1.63164554e+01 59 -1.24073658e+00 -8.68581398e-01 -3.01839536e-01 | -1.24073658e+00 -8.68581398e-01 -3.01839536e-01 60 1.76537879e+01 -6.71014587e+00 1.24810725e+01 | 1.76537879e+01 -6.71014587e+00 1.24810725e+01 61 5.75542182e-01 1.13365390e+00 9.67505675e-01 | 5.75542182e-01 1.13365390e+00 9.67505675e-01 62 -3.87848010e+01 6.28140624e+01 7.17274815e+01 | -3.87848010e+01 6.28140624e+01 7.17274815e+01 63 1.60685440e+00 1.62272000e+00 1.17742323e+00 | 1.60685440e+00 1.62272000e+00 1.17742323e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [15, 44, 58, 45, 30, 33, 40, 56, 47, 23, 39, 57, 17, 35, 53, 0, 55, 12, 50, 60, 27, 34, 48, 9, 37, 32, 51, 20, 49, 61, 4, 43, 25, 5, 21, 13, 46, 24, 42, 10, 6, 54, 38, 31, 1, 3, 36, 8, 22, 28, 18, 26, 59, 14, 41, 16, 7, 11, 2, 52, 19, 29, 63, 62] 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)) = 139.55562041850706 V(r_1,...,r_N) = 139.55562041850695 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 3.15086009e-01 5.73606653e-01 3.89413246e-01 | 3.15086009e-01 5.73606653e-01 3.89413246e-01 1 2.14613600e+01 -4.04558630e+00 -5.69945897e+01 | 2.14613600e+01 -4.04558630e+00 -5.69945897e+01 2 3.19203371e-01 8.45402258e-01 -1.13004755e-01 | 3.19203371e-01 8.45402258e-01 -1.13004755e-01 3 -3.46641792e+01 2.39495818e+01 -4.01483943e+01 | -3.46641792e+01 2.39495818e+01 -4.01483943e+01 4 -3.09896681e+01 -7.90156649e+01 -3.35125425e+01 | -3.09896681e+01 -7.90156649e+01 -3.35125425e+01 5 3.00103590e+01 7.90351754e+01 3.36047151e+01 | 3.00103590e+01 7.90351754e+01 3.36047151e+01 6 -2.11319028e+01 2.30122561e+00 5.83551629e+01 | -2.11319028e+01 2.30122561e+00 5.83551629e+01 7 -3.27349683e+01 2.26110360e+01 -6.89067706e+01 | -3.27349683e+01 2.26110360e+01 -6.89067706e+01 8 -5.84323388e-01 -2.12575691e+00 -7.97562782e-01 | -5.84323388e-01 -2.12575691e+00 -7.97562782e-01 9 -2.09119300e+00 1.72072964e-01 8.58782884e-01 | -2.09119300e+00 1.72072964e-01 8.58782884e-01 10 -8.58825113e+00 -1.48788315e+01 -7.33628581e+00 | -8.58825113e+00 -1.48788315e+01 -7.33628581e+00 11 1.11592102e+01 1.60806077e+01 6.31373067e+00 | 1.11592102e+01 1.60806077e+01 6.31373067e+00 12 -5.15806773e+00 -3.03756670e+00 -2.91355547e+00 | -5.15806773e+00 -3.03756670e+00 -2.91355547e+00 13 4.55843186e+00 3.44182625e+00 3.14955054e+00 | 4.55843186e+00 3.44182625e+00 3.14955054e+00 14 2.72542728e+01 -2.98033332e+01 3.46843021e+01 | 2.72542728e+01 -2.98033332e+01 3.46843021e+01 15 6.39191932e+01 -4.93311101e+01 -7.10276578e+01 | 6.39191932e+01 -4.93311101e+01 -7.10276578e+01 16 -1.33266828e+01 -7.59960376e+00 -7.86574099e+00 | -1.33266828e+01 -7.59960376e+00 -7.86574099e+00 17 -4.57461917e+00 1.54217481e+00 -5.94735362e+00 | -4.57461917e+00 1.54217481e+00 -5.94735362e+00 18 1.07561575e+00 2.53715679e+01 -2.31782758e+01 | 1.07561575e+00 2.53715679e+01 -2.31782758e+01 19 8.06834511e+00 -1.49097863e-02 1.01654752e+01 | 8.06834511e+00 -1.49097863e-02 1.01654752e+01 20 9.78930939e+00 -2.06187771e+01 2.59734819e+01 | 9.78930939e+00 -2.06187771e+01 2.59734819e+01 21 -4.00669495e+00 2.41791900e+00 -1.78046561e+00 | -4.00669495e+00 2.41791900e+00 -1.78046561e+00 22 -1.39154815e+00 2.69889656e-01 1.10780099e+00 | -1.39154815e+00 2.69889656e-01 1.10780099e+00 23 8.79034763e-01 -2.40553004e-01 -1.91457151e-01 | 8.79034763e-01 -2.40553004e-01 -1.91457151e-01 24 -5.67930671e+01 -5.75632084e+01 -3.04432036e+01 | -5.67930671e+01 -5.75632084e+01 -3.04432036e+01 25 1.23267331e+02 -1.48795150e+01 -8.15993846e+01 | 1.23267331e+02 -1.48795150e+01 -8.15993846e+01 26 4.84644738e+00 2.40695395e+01 -4.12599324e+01 | 4.84644738e+00 2.40695395e+01 -4.12599324e+01 27 2.24921916e+01 8.35037640e+00 1.48033964e+01 | 2.24921916e+01 8.35037640e+00 1.48033964e+01 28 -5.20247297e+00 -2.84560211e+01 -2.03002159e+00 | -5.20247297e+00 -2.84560211e+01 -2.03002159e+00 29 7.10412690e+00 2.78971106e+01 -9.23208041e-01 | 7.10412690e+00 2.78971106e+01 -9.23208041e-01 30 -9.21598176e+01 3.91918707e+01 1.39022722e+02 | -9.21598176e+01 3.91918707e+01 1.39022722e+02 31 -4.46978172e+00 9.80652836e+00 -6.57886238e+00 | -4.46978172e+00 9.80652836e+00 -6.57886238e+00 32 8.39818293e-01 1.11542949e+00 -5.58695612e-02 | 8.39818293e-01 1.11542949e+00 -5.58695612e-02 33 2.10033038e+01 -2.65785847e+01 -2.12062149e+01 | 2.10033038e+01 -2.65785847e+01 -2.12062149e+01 34 7.05292840e+01 -5.14987299e+01 4.36846962e+01 | 7.05292840e+01 -5.14987299e+01 4.36846962e+01 35 -4.46861093e+01 4.35190814e+01 -4.27322297e+01 | -4.46861093e+01 4.35190814e+01 -4.27322297e+01 36 -2.12760765e+00 -3.50703041e+00 -1.42101410e+00 | -2.12760765e+00 -3.50703041e+00 -1.42101410e+00 37 -2.00087108e+01 -4.79701389e+00 1.37616057e+01 | -2.00087108e+01 -4.79701389e+00 1.37616057e+01 38 -2.14454748e+01 2.54805721e+01 1.78952427e+01 | -2.14454748e+01 2.54805721e+01 1.78952427e+01 39 -1.67632109e-01 1.16885202e+00 3.65505690e+00 | -1.67632109e-01 1.16885202e+00 3.65505690e+00 40 1.12535666e-01 7.51037382e-01 -1.71826208e-01 | 1.12535666e-01 7.51037382e-01 -1.71826208e-01 41 -7.04382081e+00 7.40108191e+01 -1.03984312e+02 | -7.04382081e+00 7.40108191e+01 -1.03984312e+02 42 -9.24535661e-01 -1.78550085e+00 4.11445198e-01 | -9.24535661e-01 -1.78550085e+00 4.11445198e-01 43 3.06665819e+01 -1.48039093e+01 -3.18228273e+01 | 3.06665819e+01 -1.48039093e+01 -3.18228273e+01 44 7.44313151e+00 -7.29568111e+01 1.03943112e+02 | 7.44313151e+00 -7.29568111e+01 1.03943112e+02 45 -1.27165641e+00 1.29683917e-01 -1.31513524e+00 | -1.27165641e+00 1.29683917e-01 -1.31513524e+00 46 4.98970056e+01 -8.11075224e+01 7.61122940e+00 | 4.98970056e+01 -8.11075224e+01 7.61122940e+00 47 2.07665286e+01 4.35931921e+01 2.09351300e+01 | 2.07665286e+01 4.35931921e+01 2.09351300e+01 48 -3.81080451e+01 2.70626677e+01 2.13713015e+01 | -3.81080451e+01 2.70626677e+01 2.13713015e+01 49 -4.67526352e+00 3.14191700e+00 1.36701477e+00 | -4.67526352e+00 3.14191700e+00 1.36701477e+00 50 -2.30759057e+01 -1.15925374e+01 -2.71905869e+01 | -2.30759057e+01 -1.15925374e+01 -2.71905869e+01 51 -4.02406356e+00 7.59179215e+01 -9.90598630e+01 | -4.02406356e+00 7.59179215e+01 -9.90598630e+01 52 4.71203992e+00 -6.79026960e-03 5.19690115e-01 | 4.71203992e+00 -6.79026960e-03 5.19690115e-01 53 -3.92221189e-01 -1.02718894e-01 -1.14941116e+00 | -3.92221189e-01 -1.02718894e-01 -1.14941116e+00 54 -3.61044977e+00 -3.64210363e+00 -2.13663493e+00 | -3.61044977e+00 -3.64210363e+00 -2.13663493e+00 55 4.52476170e+00 4.85904155e+00 2.82588652e+00 | 4.52476170e+00 4.85904155e+00 2.82588652e+00 56 -5.52901423e+01 5.45255507e+01 8.02166646e+01 | -5.52901423e+01 5.45255507e+01 8.02166646e+01 57 -5.08143754e+01 -2.97206055e+01 2.85837822e+01 | -5.08143754e+01 -2.97206055e+01 2.85837822e+01 58 5.34196325e+01 2.05939556e+01 -1.67906597e+01 | 5.34196325e+01 2.05939556e+01 -1.67906597e+01 59 -1.01910460e+00 -8.27463580e-01 1.80192543e-01 | -1.01910460e+00 -8.27463580e-01 1.80192543e-01 60 -3.03494321e+01 1.55187065e+01 3.20754525e+01 | -3.03494321e+01 1.55187065e+01 3.20754525e+01 61 -1.12965939e+00 4.99486617e-01 -1.08542257e+00 | -1.12965939e+00 4.99486617e-01 -1.08542257e+00 62 2.68116246e+01 -6.47578159e+01 1.26828778e+02 | 2.68116246e+01 -6.47578159e+01 1.26828778e+02 63 7.85682231e-01 -5.19850732e-01 -6.24537758e-01 | 7.85682231e-01 -5.19850732e-01 -6.24537758e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [38, 10, 24, 47, 39, 61, 15, 62, 56, 57, 1, 35, 52, 20, 49, 6, 23, 55, 28, 34, 13, 45, 25, 16, 2, 22, 46, 58, 18, 53, 42, 43, 40, 51, 19, 11, 59, 63, 0, 4, 32, 60, 30, 31, 50, 21, 26, 3, 54, 14, 44, 33, 12, 29, 48, 17, 8, 9, 27, 36, 41, 5, 7, 37] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -17.98458948658626 V(r_1,...,r_N) = -17.98458948658597 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -2.43375142e+01 -1.64565428e+01 -3.74106064e+01 | -2.43375142e+01 -1.64565428e+01 -3.74106064e+01 1 2.18505349e+01 1.85598233e+01 3.62360982e+01 | 2.18505349e+01 1.85598233e+01 3.62360982e+01 2 -4.22286714e-01 2.81963609e-01 1.83510060e+00 | -4.22286714e-01 2.81963609e-01 1.83510060e+00 3 -1.95685721e+01 3.03433929e+01 -1.03493528e+01 | -1.95685721e+01 3.03433929e+01 -1.03493528e+01 4 2.11401231e+00 -4.89688067e-01 -7.98980739e-02 | 2.11401231e+00 -4.89688067e-01 -7.98980739e-02 5 2.77555539e+01 -4.28373617e+01 -2.85603481e+01 | 2.77555539e+01 -4.28373617e+01 -2.85603481e+01 6 1.73550095e+00 -2.91408342e-01 8.12473269e-04 | 1.73550095e+00 -2.91408342e-01 8.12473269e-04 7 -2.03700869e+01 2.27067911e+01 -1.34410579e+01 | -2.03700869e+01 2.27067911e+01 -1.34410579e+01 8 9.70533143e-02 6.25411838e-01 7.78969241e-01 | 9.70533143e-02 6.25411838e-01 7.78969241e-01 9 -3.84032275e+01 -2.00203186e+01 2.02862611e+01 | -3.84032275e+01 -2.00203186e+01 2.02862611e+01 10 9.34854729e+00 -3.34043243e+01 -5.32900891e+01 | 9.34854729e+00 -3.34043243e+01 -5.32900891e+01 11 2.79543612e+01 5.35469985e+01 3.39895094e+01 | 2.79543612e+01 5.35469985e+01 3.39895094e+01 12 -2.45985005e-01 -2.14873892e-02 -5.63306880e-01 | -2.45985005e-01 -2.14873892e-02 -5.63306880e-01 13 3.10130923e+01 -2.23922928e+01 -4.04934303e+01 | 3.10130923e+01 -2.23922928e+01 -4.04934303e+01 14 1.82791377e+01 -3.18268094e+01 1.01284810e+01 | 1.82791377e+01 -3.18268094e+01 1.01284810e+01 15 3.17028278e+01 -3.29725412e+01 -1.38319536e+01 | 3.17028278e+01 -3.29725412e+01 -1.38319536e+01 16 -2.48002904e+01 -3.13124717e+01 -2.70348616e+01 | -2.48002904e+01 -3.13124717e+01 -2.70348616e+01 17 6.15868353e+00 4.46723623e+01 1.31489026e+01 | 6.15868353e+00 4.46723623e+01 1.31489026e+01 18 7.63906999e-01 -1.87579130e-01 -4.88875991e-01 | 7.63906999e-01 -1.87579130e-01 -4.88875991e-01 19 4.08090669e-02 -1.42733212e-01 1.09844174e+00 | 4.08090669e-02 -1.42733212e-01 1.09844174e+00 20 1.74000631e+01 -1.38874637e+01 1.47365954e+01 | 1.74000631e+01 -1.38874637e+01 1.47365954e+01 21 3.77764898e+01 -1.03999218e+01 -1.12861206e+00 | 3.77764898e+01 -1.03999218e+01 -1.12861206e+00 22 -1.71630914e+01 -2.29483766e+01 -2.05489997e+01 | -1.71630914e+01 -2.29483766e+01 -2.05489997e+01 23 1.79169117e+01 2.25428867e+01 1.97260561e+01 | 1.79169117e+01 2.25428867e+01 1.97260561e+01 24 -5.83251984e-02 -1.88297210e+01 -2.53375800e+01 | -5.83251984e-02 -1.88297210e+01 -2.53375800e+01 25 2.59174648e+00 1.79846208e+01 2.42330674e+01 | 2.59174648e+00 1.79846208e+01 2.42330674e+01 26 -6.24743215e-01 -8.57416364e-01 6.31388496e-01 | -6.24743215e-01 -8.57416364e-01 6.31388496e-01 27 1.07070332e-01 7.77503396e-02 9.42846325e-02 | 1.07070332e-01 7.77503396e-02 9.42846325e-02 28 -3.14243994e+01 -5.43626802e+01 -1.93916424e+01 | -3.14243994e+01 -5.43626802e+01 -1.93916424e+01 29 3.03227866e+01 5.48756639e+01 1.94259033e+01 | 3.03227866e+01 5.48756639e+01 1.94259033e+01 30 1.50914996e-01 -3.40471046e+00 -4.96172313e-02 | 1.50914996e-01 -3.40471046e+00 -4.96172313e-02 31 4.38016770e-01 3.16531452e+00 1.80458059e+00 | 4.38016770e-01 3.16531452e+00 1.80458059e+00 32 1.48280894e+00 1.51964335e+00 7.32590723e-01 | 1.48280894e+00 1.51964335e+00 7.32590723e-01 33 -1.21996736e+01 3.35422970e+01 -2.94437746e+01 | -1.21996736e+01 3.35422970e+01 -2.94437746e+01 34 -1.48646871e+01 2.50110763e+01 3.07145667e+01 | -1.48646871e+01 2.50110763e+01 3.07145667e+01 35 -1.42257426e+00 3.11516279e-01 -7.34476214e-01 | -1.42257426e+00 3.11516279e-01 -7.34476214e-01 36 1.29384249e+01 -3.40937773e+01 2.75371036e+01 | 1.29384249e+01 -3.40937773e+01 2.75371036e+01 37 -6.28594907e-01 -2.47067567e-01 -3.07603447e-01 | -6.28594907e-01 -2.47067567e-01 -3.07603447e-01 38 3.00824268e-01 1.09307807e+00 7.14686427e-01 | 3.00824268e-01 1.09307807e+00 7.14686427e-01 39 -1.32009163e+00 -7.78041773e-01 -3.20784736e-01 | -1.32009163e+00 -7.78041773e-01 -3.20784736e-01 40 7.95506488e+00 -3.84435216e+00 1.36372772e+01 | 7.95506488e+00 -3.84435216e+00 1.36372772e+01 41 -1.48254181e+01 2.12015597e+01 -1.90749555e+01 | -1.48254181e+01 2.12015597e+01 -1.90749555e+01 42 -3.24007226e+01 2.22124915e+01 3.94713352e+01 | -3.24007226e+01 2.22124915e+01 3.94713352e+01 43 2.21064121e-01 1.06211738e+00 1.20408247e+00 | 2.21064121e-01 1.06211738e+00 1.20408247e+00 44 -2.24928749e+01 -6.05289971e+01 4.71339111e-01 | -2.24928749e+01 -6.05289971e+01 4.71339111e-01 45 3.72181626e+01 3.98725287e+01 1.78901126e+01 | 3.72181626e+01 3.98725287e+01 1.78901126e+01 46 2.50937173e+00 -7.94132662e-01 -2.77024204e-01 | 2.50937173e+00 -7.94132662e-01 -2.77024204e-01 47 2.56099931e-01 5.07033055e-01 -1.40977001e+00 | 2.56099931e-01 5.07033055e-01 -1.40977001e+00 48 1.77117724e-01 2.37519941e-01 -1.61880548e+00 | 1.77117724e-01 2.37519941e-01 -1.61880548e+00 49 5.13021271e-02 -2.05358393e+00 8.70385238e-01 | 5.13021271e-02 -2.05358393e+00 8.70385238e-01 50 -3.86851772e+01 9.53996696e+00 1.52268847e+00 | -3.86851772e+01 9.53996696e+00 1.52268847e+00 51 1.10283123e+00 -2.86887977e-01 7.02648152e-01 | 1.10283123e+00 -2.86887977e-01 7.02648152e-01 52 1.07695888e+00 1.54403569e+00 7.37262449e-01 | 1.07695888e+00 1.54403569e+00 7.37262449e-01 53 -1.54779507e+01 -7.79519016e-01 1.42701697e+01 | -1.54779507e+01 -7.79519016e-01 1.42701697e+01 54 -1.32713194e+01 -1.30295772e+01 -1.84652809e+01 | -1.32713194e+01 -1.30295772e+01 -1.84652809e+01 55 1.28750793e+01 1.43862482e+01 1.91717347e+01 | 1.28750793e+01 1.43862482e+01 1.91717347e+01 56 -3.46781159e+01 3.18710857e+01 1.18660424e+01 | -3.46781159e+01 3.18710857e+01 1.18660424e+01 57 -6.40371563e+01 -3.65207709e+01 -8.91994005e+01 | -6.40371563e+01 -3.65207709e+01 -8.91994005e+01 58 1.89011271e+01 7.83140541e+01 -6.80713102e+00 | 1.89011271e+01 7.83140541e+01 -6.80713102e+00 59 -1.65397508e+00 -1.29077233e+00 -3.12739116e-01 | -1.65397508e+00 -1.29077233e+00 -3.12739116e-01 60 4.88303007e+01 -3.92892054e+01 9.81654194e+01 | 4.88303007e+01 -3.92892054e+01 9.81654194e+01 61 -1.60549413e+00 -8.12877354e-01 -1.28283018e+00 | -1.60549413e+00 -8.12877354e-01 -1.28283018e+00 62 1.60456245e+01 1.18347903e+00 -1.56158040e+01 | 1.60456245e+01 1.18347903e+00 -1.56158040e+01 63 -4.77836140e-01 -1.39729933e+00 -9.63284617e-01 | -4.77836140e-01 -1.39729933e+00 -9.63284617e-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 = [35, 51, 57, 34, 36, 10, 46, 22, 26, 13, 5, 30, 48, 9, 55, 20, 28, 54, 45, 25, 15, 24, 7, 63, 21, 19, 8, 39, 16, 43, 11, 42, 53, 60, 3, 0, 4, 62, 50, 27, 58, 44, 31, 29, 41, 18, 6, 52, 12, 59, 38, 1, 47, 32, 17, 14, 56, 2, 40, 49, 33, 61, 37, 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)) = 128.72095192021942 V(r_1,...,r_N) = 128.72095192021942 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 -3.76491939e-01 -1.19293133e+00 -1.02336713e+00 | -3.76491939e-01 -1.19293133e+00 -1.02336713e+00 1 1.28678107e+00 1.68058699e+00 -2.13438100e-01 | 1.28678107e+00 1.68058699e+00 -2.13438100e-01 2 6.22711459e-02 1.05448473e-01 1.44977667e+00 | 6.22711459e-02 1.05448473e-01 1.44977667e+00 3 -5.56215545e+01 5.25922537e+01 -2.51244986e+01 | -5.56215545e+01 5.25922537e+01 -2.51244986e+01 4 -1.59728293e+01 -4.01438657e+00 -2.35531817e+01 | -1.59728293e+01 -4.01438657e+00 -2.35531817e+01 5 -3.57451070e+01 4.14863394e+01 -8.61867005e+00 | -3.57451070e+01 4.14863394e+01 -8.61867005e+00 6 -5.90478778e-01 -1.72247446e+00 7.56147413e-01 | -5.90478778e-01 -1.72247446e+00 7.56147413e-01 7 9.46915216e+01 -1.35450421e+02 -1.08654774e+02 | 9.46915216e+01 -1.35450421e+02 -1.08654774e+02 8 2.11866878e-01 3.82801742e-01 4.90196704e-01 | 2.11866878e-01 3.82801742e-01 4.90196704e-01 9 5.93300344e+01 -6.09426387e+01 -4.01737423e+01 | 5.93300344e+01 -6.09426387e+01 -4.01737423e+01 10 -7.32264571e+00 -5.63230553e+00 -7.07528217e+00 | -7.32264571e+00 -5.63230553e+00 -7.07528217e+00 11 1.87757570e+01 -1.15267367e+00 2.39747907e+00 | 1.87757570e+01 -1.15267367e+00 2.39747907e+00 12 -9.39690350e+01 -6.36264992e+01 -3.31132660e+01 | -9.39690350e+01 -6.36264992e+01 -3.31132660e+01 13 9.78035449e+01 6.01653475e+01 2.85585576e+01 | 9.78035449e+01 6.01653475e+01 2.85585576e+01 14 -7.16945994e+00 7.81162088e+00 6.17822568e+01 | -7.16945994e+00 7.81162088e+00 6.17822568e+01 15 7.84445425e-01 -8.98026033e-01 3.23161550e+00 | 7.84445425e-01 -8.98026033e-01 3.23161550e+00 16 9.19248890e-01 7.35056384e-01 1.29934141e+00 | 9.19248890e-01 7.35056384e-01 1.29934141e+00 17 -4.63065084e+01 1.02105282e+02 -1.03020886e+02 | -4.63065084e+01 1.02105282e+02 -1.03020886e+02 18 4.51022381e-01 -1.00890552e+00 1.40114395e+00 | 4.51022381e-01 -1.00890552e+00 1.40114395e+00 19 -1.99090448e+01 -1.31021599e+00 -2.21051817e+01 | -1.99090448e+01 -1.31021599e+00 -2.21051817e+01 20 3.66850365e+01 -1.10579005e+02 8.68988568e+01 | 3.66850365e+01 -1.10579005e+02 8.68988568e+01 21 1.48878508e+01 1.16965052e+01 8.29130155e+00 | 1.48878508e+01 1.16965052e+01 8.29130155e+00 22 -1.69924029e+00 1.07559775e+00 -4.09521136e-01 | -1.69924029e+00 1.07559775e+00 -4.09521136e-01 23 -4.76275505e-01 9.14906329e-01 -3.30652935e+00 | -4.76275505e-01 9.14906329e-01 -3.30652935e+00 24 -4.68558077e-01 8.24563735e-03 1.41037315e+00 | -4.68558077e-01 8.24563735e-03 1.41037315e+00 25 -3.74571807e+01 -3.83172861e+01 3.83030509e+01 | -3.74571807e+01 -3.83172861e+01 3.83030509e+01 26 2.03384189e+01 1.77192578e+01 -5.94727532e+01 | 2.03384189e+01 1.77192578e+01 -5.94727532e+01 27 1.91964968e+01 1.76687233e+01 1.89258724e+01 | 1.91964968e+01 1.76687233e+01 1.89258724e+01 28 -1.28444272e+01 5.63570345e+00 2.51600645e+00 | -1.28444272e+01 5.63570345e+00 2.51600645e+00 29 1.60066235e+00 -1.66092341e+00 -1.02888322e+00 | 1.60066235e+00 -1.66092341e+00 -1.02888322e+00 30 -6.99419366e+01 -1.13665420e+02 -4.30258899e+01 | -6.99419366e+01 -1.13665420e+02 -4.30258899e+01 31 8.67496594e+01 1.16570187e+02 6.74876830e+01 | 8.67496594e+01 1.16570187e+02 6.74876830e+01 32 8.39707182e-01 8.94915824e-01 -9.18110585e-02 | 8.39707182e-01 8.94915824e-01 -9.18110585e-02 33 -2.75461052e+01 2.08951227e+01 -1.15401092e+01 | -2.75461052e+01 2.08951227e+01 -1.15401092e+01 34 2.95748269e+00 1.42729145e+00 7.94067651e-01 | 2.95748269e+00 1.42729145e+00 7.94067651e-01 35 8.66591495e+00 -7.38050370e+00 -3.07995646e+00 | 8.66591495e+00 -7.38050370e+00 -3.07995646e+00 36 2.55594365e+01 -2.33552438e+01 1.09127656e+01 | 2.55594365e+01 -2.33552438e+01 1.09127656e+01 37 -3.09819460e+01 -2.06444080e+01 2.38472234e+01 | -3.09819460e+01 -2.06444080e+01 2.38472234e+01 38 1.15694971e+00 1.28798413e-01 -7.07442542e-01 | 1.15694971e+00 1.28798413e-01 -7.07442542e-01 39 -7.92899167e-01 -1.89565306e+00 7.32157847e-02 | -7.92899167e-01 -1.89565306e+00 7.32157847e-02 40 5.20582078e+01 -3.49482356e+01 3.32360601e+01 | 5.20582078e+01 -3.49482356e+01 3.32360601e+01 41 7.09176402e+01 -4.48725492e+01 -5.13478358e+01 | 7.09176402e+01 -4.48725492e+01 -5.13478358e+01 42 -3.09804102e+00 4.02808039e+00 5.66854146e+00 | -3.09804102e+00 4.02808039e+00 5.66854146e+00 43 -1.34846223e+00 -5.80403174e-01 1.98650728e-01 | -1.34846223e+00 -5.80403174e-01 1.98650728e-01 44 1.13187722e-02 1.72873085e+00 -1.61095504e-01 | 1.13187722e-02 1.72873085e+00 -1.61095504e-01 45 -1.55944335e+00 3.43136625e-02 -1.01790746e+00 | -1.55944335e+00 3.43136625e-02 -1.01790746e+00 46 -4.74489190e+01 4.86455470e+01 7.18971550e+00 | -4.74489190e+01 4.86455470e+01 7.18971550e+00 47 8.28672298e+00 1.49030371e+01 1.93276106e+01 | 8.28672298e+00 1.49030371e+01 1.93276106e+01 48 -9.98106962e+01 1.32234302e+02 1.11380677e+02 | -9.98106962e+01 1.32234302e+02 1.11380677e+02 49 3.84282800e+00 -1.17602322e+01 2.69230317e+00 | 3.84282800e+00 -1.17602322e+01 2.69230317e+00 50 -2.45538033e+00 -5.77968825e+00 8.03383492e-01 | -2.45538033e+00 -5.77968825e+00 8.03383492e-01 51 3.33224149e+00 2.22831691e+00 2.52976939e+00 | 3.33224149e+00 2.22831691e+00 2.52976939e+00 52 -1.30789879e+01 5.45354147e+00 -3.38187115e+00 | -1.30789879e+01 5.45354147e+00 -3.38187115e+00 53 -2.13473092e+01 -2.46774295e+01 1.91374936e+01 | -2.13473092e+01 -2.46774295e+01 1.91374936e+01 54 -3.63959349e+00 1.39052565e+01 7.15928955e-01 | -3.63959349e+00 1.39052565e+01 7.15928955e-01 55 6.79350261e-02 -8.40887053e-01 -1.27613504e+00 | 6.79350261e-02 -8.40887053e-01 -1.27613504e+00 56 4.86739837e-01 1.07399368e+00 1.76909910e+00 | 4.86739837e-01 1.07399368e+00 1.76909910e+00 57 1.02357383e+01 -1.09191942e+01 -1.62301052e+01 | 1.02357383e+01 -1.09191942e+01 -1.62301052e+01 58 -1.81587468e+00 2.06722270e+00 2.08673084e+00 | -1.81587468e+00 2.06722270e+00 2.08673084e+00 59 3.04180508e-01 2.65292564e-01 7.97355527e-01 | 3.04180508e-01 2.65292564e-01 7.97355527e-01 60 2.17297536e+00 -3.87934332e+00 8.28448448e-01 | 2.17297536e+00 -3.87934332e+00 8.28448448e-01 61 9.91275578e-01 1.05736718e+00 9.74787718e-01 | 9.91275578e-01 1.05736718e+00 9.74787718e-01 62 1.38929288e+01 3.96493736e+01 -5.36745411e+00 | 1.38929288e+01 3.96493736e+01 -5.36745411e+00 63 1.23958945e+00 3.73351626e+00 3.95809999e+00 | 1.23958945e+00 3.73351626e+00 3.95809999e+00 ------------------------------------------------------------------------------------------------------------------------- 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.