!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_FarkasJones_1996_NbTiAl__MO_042691367780_000 Supported species : Al Nb 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 = [3, 47, 31, 0, 28, 33, 39, 48, 61, 12, 16, 30, 9, 27, 24, 59, 10, 44, 45, 38, 41, 51, 37, 35, 14, 62, 32, 13, 4, 40, 11, 2, 26, 5, 46, 23, 42, 22, 19, 6, 29, 20, 36, 57, 17, 18, 34, 1, 7, 56, 54, 21, 55, 58, 50, 52, 49, 43, 53, 15, 63, 8, 25, 60] 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)) = 164.6808135986734 V(r_1,...,r_N) = 164.68081359867332 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 -5.71646679e+00 -3.80472441e+00 -4.94476560e+00 | -5.71646679e+00 -3.80472441e+00 -4.94476560e+00 1 -1.36811243e+01 -4.08475999e+01 3.07243683e+01 | -1.36811243e+01 -4.08475999e+01 3.07243683e+01 2 -2.79595842e+00 1.49798113e+01 -5.29173436e+01 | -2.79595842e+00 1.49798113e+01 -5.29173436e+01 3 2.23320742e+01 2.70251714e+01 2.30971652e+01 | 2.23320742e+01 2.70251714e+01 2.30971652e+01 4 -2.89118993e+00 -7.06686774e+00 -5.70198555e+00 | -2.89118993e+00 -7.06686774e+00 -5.70198555e+00 5 -8.96383140e+00 2.61565569e+01 -1.38568831e+01 | -8.96383140e+00 2.61565569e+01 -1.38568831e+01 6 -3.32697359e+00 -1.96427672e+00 -2.14686495e+00 | -3.32697359e+00 -1.96427672e+00 -2.14686495e+00 7 -3.94785608e+01 9.19759684e+01 -5.22808604e+01 | -3.94785608e+01 9.19759684e+01 -5.22808604e+01 8 -5.51918511e+00 -1.23566505e+00 -5.82674380e+00 | -5.51918511e+00 -1.23566505e+00 -5.82674380e+00 9 -3.31349945e+01 2.26009983e+01 -1.79780032e+01 | -3.31349945e+01 2.26009983e+01 -1.79780032e+01 10 -2.38331775e+01 -2.46501885e+01 -1.07508025e+01 | -2.38331775e+01 -2.46501885e+01 -1.07508025e+01 11 2.31724447e+01 2.50376008e+01 1.10964142e+01 | 2.31724447e+01 2.50376008e+01 1.10964142e+01 12 2.89825628e+01 -3.02221086e+01 1.04365999e+01 | 2.89825628e+01 -3.02221086e+01 1.04365999e+01 13 1.33944565e+01 5.16484807e+00 9.45404215e+00 | 1.33944565e+01 5.16484807e+00 9.45404215e+00 14 2.42992583e+00 7.25300211e+00 -1.11149950e+01 | 2.42992583e+00 7.25300211e+00 -1.11149950e+01 15 2.78759197e+00 4.02326969e+00 1.34950412e+00 | 2.78759197e+00 4.02326969e+00 1.34950412e+00 16 -1.31423138e+00 -2.38201023e+00 -1.99316540e+00 | -1.31423138e+00 -2.38201023e+00 -1.99316540e+00 17 -4.65520132e+00 -6.01320640e+00 1.57246467e+01 | -4.65520132e+00 -6.01320640e+00 1.57246467e+01 18 7.25604629e+00 6.82811562e+00 -1.32731168e+01 | 7.25604629e+00 6.82811562e+00 -1.32731168e+01 19 -6.78484918e+01 4.13070257e+01 -4.58001524e+01 | -6.78484918e+01 4.13070257e+01 -4.58001524e+01 20 -2.49709109e+01 -1.54972478e+01 -2.03075637e+01 | -2.49709109e+01 -1.54972478e+01 -2.03075637e+01 21 3.19029978e+01 2.16255158e+01 1.54486704e+01 | 3.19029978e+01 2.16255158e+01 1.54486704e+01 22 -3.14394160e+00 -1.46756066e+00 -2.35435042e+00 | -3.14394160e+00 -1.46756066e+00 -2.35435042e+00 23 5.65824268e-01 3.91519412e+00 2.10941042e+00 | 5.65824268e-01 3.91519412e+00 2.10941042e+00 24 -3.42751536e-01 -3.24807520e-01 6.09611851e-01 | -3.42751536e-01 -3.24807520e-01 6.09611851e-01 25 -2.31392369e+01 2.46686223e+01 -2.14673600e+01 | -2.31392369e+01 2.46686223e+01 -2.14673600e+01 26 -2.47536335e+00 -6.85532256e-01 -1.38787035e+00 | -2.47536335e+00 -6.85532256e-01 -1.38787035e+00 27 1.77926259e+00 2.45996530e-03 2.13829131e+00 | 1.77926259e+00 2.45996530e-03 2.13829131e+00 28 1.83501768e+01 -3.10027578e+01 1.92718994e+01 | 1.83501768e+01 -3.10027578e+01 1.92718994e+01 29 4.77027834e+00 5.42562037e+00 2.58038348e+00 | 4.77027834e+00 5.42562037e+00 2.58038348e+00 30 6.62140976e+01 -3.97154768e+01 4.21084279e+01 | 6.62140976e+01 -3.97154768e+01 4.21084279e+01 31 -3.12969175e+01 1.31702334e+01 -1.73472780e+01 | -3.12969175e+01 1.31702334e+01 -1.73472780e+01 32 -6.10358943e+00 -4.52685637e-02 -1.16023650e+00 | -6.10358943e+00 -4.52685637e-02 -1.16023650e+00 33 -5.26281577e+00 7.36911352e+00 -4.60543781e+00 | -5.26281577e+00 7.36911352e+00 -4.60543781e+00 34 3.87952556e+01 -9.82790922e+01 5.56204582e+01 | 3.87952556e+01 -9.82790922e+01 5.56204582e+01 35 -5.64002795e+00 -8.67210689e+00 6.82515609e+00 | -5.64002795e+00 -8.67210689e+00 6.82515609e+00 36 7.08215511e+00 -6.61198428e+00 7.10683829e+00 | 7.08215511e+00 -6.61198428e+00 7.10683829e+00 37 -1.02784222e+01 -1.02109159e+01 6.39337496e+00 | -1.02784222e+01 -1.02109159e+01 6.39337496e+00 38 -1.38346142e+01 -8.96133921e+00 -1.09738242e+01 | -1.38346142e+01 -8.96133921e+00 -1.09738242e+01 39 -1.46146583e+01 -1.52142150e+01 2.79442261e+01 | -1.46146583e+01 -1.52142150e+01 2.79442261e+01 40 9.76534006e+00 -2.78034687e+01 2.52386273e+01 | 9.76534006e+00 -2.78034687e+01 2.52386273e+01 41 -3.55734712e+01 4.91824283e+01 -3.33396027e+01 | -3.55734712e+01 4.91824283e+01 -3.33396027e+01 42 -1.54931358e+01 -3.05798708e+01 -1.74461328e+01 | -1.54931358e+01 -3.05798708e+01 -1.74461328e+01 43 2.04338693e+01 3.59261611e+01 1.91682798e+01 | 2.04338693e+01 3.59261611e+01 1.91682798e+01 44 3.15865164e+01 -6.09354209e+01 2.51259439e+01 | 3.15865164e+01 -6.09354209e+01 2.51259439e+01 45 4.07856450e+00 2.79906467e+00 4.93182913e+00 | 4.07856450e+00 2.79906467e+00 4.93182913e+00 46 4.20461445e+00 1.55668859e+01 -6.11237899e-01 | 4.20461445e+00 1.55668859e+01 -6.11237899e-01 47 1.70323626e+00 -1.32017801e+00 6.45473080e-03 | 1.70323626e+00 -1.32017801e+00 6.45473080e-03 48 -9.17718631e+00 -4.99670891e+00 -5.62400909e-01 | -9.17718631e+00 -4.99670891e+00 -5.62400909e-01 49 1.05224351e+01 -2.71521153e+00 3.21919590e+00 | 1.05224351e+01 -2.71521153e+00 3.21919590e+00 50 -8.84236495e+00 -2.22494556e+01 -2.56275984e+01 | -8.84236495e+00 -2.22494556e+01 -2.56275984e+01 51 1.59774804e+01 2.29094867e+01 2.19666562e+01 | 1.59774804e+01 2.29094867e+01 2.19666562e+01 52 2.57916725e+01 2.59048001e+01 -1.67475250e+01 | 2.57916725e+01 2.59048001e+01 -1.67475250e+01 53 -3.09020340e+00 -1.71697117e+00 4.94012833e+00 | -3.09020340e+00 -1.71697117e+00 4.94012833e+00 54 -1.10615454e+01 9.14528574e+00 6.44886728e+00 | -1.10615454e+01 9.14528574e+00 6.44886728e+00 55 3.27158814e-01 -6.94175508e-01 -7.88041079e-01 | 3.27158814e-01 -6.94175508e-01 -7.88041079e-01 56 -2.60060519e-01 -1.31579274e+00 -7.02084828e+00 | -2.60060519e-01 -1.31579274e+00 -7.02084828e+00 57 2.88525805e+01 -4.33946530e+01 -6.44543716e+01 | 2.88525805e+01 -4.33946530e+01 -6.44543716e+01 58 3.34521243e+01 -1.20777083e+01 1.98506895e+01 | 3.34521243e+01 -1.20777083e+01 1.98506895e+01 59 -7.92237875e-01 -8.13044369e-01 6.11964693e-02 | -7.92237875e-01 -8.13044369e-01 6.11964693e-02 60 6.13777070e+00 -5.55677518e+00 2.01446817e+00 | 6.13777070e+00 -5.55677518e+00 2.01446817e+00 61 3.49622797e+00 2.51721447e+00 4.64165421e+00 | 3.49622797e+00 2.51721447e+00 4.64165421e+00 62 -2.78271745e+01 5.87760128e+01 5.73119346e+01 | -2.78271745e+01 5.87760128e+01 5.73119346e+01 63 2.35274582e-01 -2.12080635e-01 -1.78052733e-01 | 2.35274582e-01 -2.12080635e-01 -1.78052733e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Nb (Configuration in file "config-Nb.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [12, 45, 63, 41, 33, 39, 50, 44, 53, 13, 37, 21, 0, 9, 32, 56, 57, 59, 40, 58, 60, 11, 24, 35, 22, 26, 25, 29, 51, 27, 46, 54, 14, 4, 49, 23, 61, 10, 52, 5, 18, 3, 48, 47, 7, 1, 30, 43, 42, 34, 6, 28, 38, 8, 31, 62, 15, 16, 19, 17, 20, 36, 55, 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)) = 54.37054819763525 V(r_1,...,r_N) = 54.370548197635266 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 2.06289997e+00 1.38904453e+00 1.81852044e+00 | 2.06289997e+00 1.38904453e+00 1.81852044e+00 1 -8.52880049e+00 1.21765732e+01 -9.97523911e+00 | -8.52880049e+00 1.21765732e+01 -9.97523911e+00 2 -1.41570850e+00 1.69409103e-01 -7.02238378e-01 | -1.41570850e+00 1.69409103e-01 -7.02238378e-01 3 9.70717338e-01 2.34871381e+00 -5.95447386e-01 | 9.70717338e-01 2.34871381e+00 -5.95447386e-01 4 4.89195338e+00 -1.65137999e+01 6.13944431e+00 | 4.89195338e+00 -1.65137999e+01 6.13944431e+00 5 -1.62412778e+02 -2.10451431e+01 6.49001540e+01 | -1.62412778e+02 -2.10451431e+01 6.49001540e+01 6 -1.15910956e+00 -5.54225564e-01 -1.14489640e+00 | -1.15910956e+00 -5.54225564e-01 -1.14489640e+00 7 -4.50310112e+00 9.19066504e-01 9.61151753e-01 | -4.50310112e+00 9.19066504e-01 9.61151753e-01 8 -2.00098677e+00 -4.69690997e-01 -1.20861936e-01 | -2.00098677e+00 -4.69690997e-01 -1.20861936e-01 9 -3.10582174e+01 -5.63482162e+00 2.80107988e+01 | -3.10582174e+01 -5.63482162e+00 2.80107988e+01 10 2.62678041e+01 -5.33957237e+00 -3.81700640e+01 | 2.62678041e+01 -5.33957237e+00 -3.81700640e+01 11 9.04315576e+00 8.73810054e+00 -1.31635812e+00 | 9.04315576e+00 8.73810054e+00 -1.31635812e+00 12 -1.14801221e+01 -1.13518946e+01 -8.28685178e+00 | -1.14801221e+01 -1.13518946e+01 -8.28685178e+00 13 1.46641457e+01 8.04485345e+00 9.84468855e+00 | 1.46641457e+01 8.04485345e+00 9.84468855e+00 14 1.48235285e+02 4.80758112e+01 -1.00259268e+02 | 1.48235285e+02 4.80758112e+01 -1.00259268e+02 15 -1.87594560e+02 8.67618428e+01 -6.60436333e+01 | -1.87594560e+02 8.67618428e+01 -6.60436333e+01 16 -1.62044658e+01 -4.18118495e+01 -6.89446675e+01 | -1.62044658e+01 -4.18118495e+01 -6.89446675e+01 17 7.46100507e+00 2.20985952e+01 5.19482148e+01 | 7.46100507e+00 2.20985952e+01 5.19482148e+01 18 7.82883870e+00 1.27007736e+00 -3.59925777e+00 | 7.82883870e+00 1.27007736e+00 -3.59925777e+00 19 2.45135553e-02 2.14453721e+00 1.68895220e+00 | 2.45135553e-02 2.14453721e+00 1.68895220e+00 20 7.12941341e+00 -2.56207999e+00 -9.97454109e-01 | 7.12941341e+00 -2.56207999e+00 -9.97454109e-01 21 -6.01940474e+01 3.22303899e+01 -2.45968005e+00 | -6.01940474e+01 3.22303899e+01 -2.45968005e+00 22 -2.83198560e+00 1.77188797e+01 1.65173807e+01 | -2.83198560e+00 1.77188797e+01 1.65173807e+01 23 -8.42974505e+00 5.68655425e+00 -4.89234739e+00 | -8.42974505e+00 5.68655425e+00 -4.89234739e+00 24 4.30419824e-01 4.48476558e-01 2.00663867e-01 | 4.30419824e-01 4.48476558e-01 2.00663867e-01 25 1.29174662e+00 -4.57927379e+00 1.17377618e-01 | 1.29174662e+00 -4.57927379e+00 1.17377618e-01 26 2.18006941e+00 3.23749984e+00 -1.69187246e+00 | 2.18006941e+00 3.23749984e+00 -1.69187246e+00 27 -2.37155373e+00 -1.75914809e+00 -4.04777372e-01 | -2.37155373e+00 -1.75914809e+00 -4.04777372e-01 28 -3.17025672e+00 4.60700073e+00 7.15761736e+00 | -3.17025672e+00 4.60700073e+00 7.15761736e+00 29 4.24762501e+00 -2.46128602e+00 -2.27083711e+00 | 4.24762501e+00 -2.46128602e+00 -2.27083711e+00 30 -3.55013020e+01 -5.28741824e+01 -7.18287115e+01 | -3.55013020e+01 -5.28741824e+01 -7.18287115e+01 31 2.95469159e+01 6.63285668e+01 6.28363398e+01 | 2.95469159e+01 6.63285668e+01 6.28363398e+01 32 -1.03335382e+01 -4.62335569e+00 -1.74388445e+01 | -1.03335382e+01 -4.62335569e+00 -1.74388445e+01 33 -5.28416340e+00 -9.65512874e+00 1.51303037e+01 | -5.28416340e+00 -9.65512874e+00 1.51303037e+01 34 -4.09874094e+00 -2.49241563e+00 5.66763018e+00 | -4.09874094e+00 -2.49241563e+00 5.66763018e+00 35 1.00222457e+01 1.71398425e+01 1.99986341e+00 | 1.00222457e+01 1.71398425e+01 1.99986341e+00 36 -1.49731161e+01 -1.82989906e+01 -3.23438802e+00 | -1.49731161e+01 -1.82989906e+01 -3.23438802e+00 37 -1.14145255e+01 -6.44889775e+01 5.71121530e+01 | -1.14145255e+01 -6.44889775e+01 5.71121530e+01 38 -2.94801542e+01 -1.67487677e+01 -1.87575895e+01 | -2.94801542e+01 -1.67487677e+01 -1.87575895e+01 39 -3.53180738e+01 -2.20118942e+02 1.45051749e+02 | -3.53180738e+01 -2.20118942e+02 1.45051749e+02 40 2.23068756e+01 -3.15467982e+01 2.72385922e+01 | 2.23068756e+01 -3.15467982e+01 2.72385922e+01 41 -9.85661129e+00 -3.41504593e+01 2.39511518e+01 | -9.85661129e+00 -3.41504593e+01 2.39511518e+01 42 1.96411833e+02 -6.46721045e+01 3.57165501e+01 | 1.96411833e+02 -6.46721045e+01 3.57165501e+01 43 1.72601714e+01 1.60792086e+00 6.85158049e+00 | 1.72601714e+01 1.60792086e+00 6.85158049e+00 44 -3.94565083e-01 3.07930509e-01 1.31462342e+00 | -3.94565083e-01 3.07930509e-01 1.31462342e+00 45 -2.21580076e+00 6.01347136e-01 -1.98142150e+00 | -2.21580076e+00 6.01347136e-01 -1.98142150e+00 46 3.65593018e+01 7.48235736e+01 -4.76065392e+01 | 3.65593018e+01 7.48235736e+01 -4.76065392e+01 47 5.97007203e-01 -1.30832608e+00 1.78846203e+00 | 5.97007203e-01 -1.30832608e+00 1.78846203e+00 48 -3.40004824e+01 -3.15253191e+01 -2.63335555e+01 | -3.40004824e+01 -3.15253191e+01 -2.63335555e+01 49 1.42187499e+02 -8.71346906e+01 -1.29594017e+02 | 1.42187499e+02 -8.71346906e+01 -1.29594017e+02 50 -4.54377292e+01 -3.95334524e+01 -3.15283292e+01 | -4.54377292e+01 -3.95334524e+01 -3.15283292e+01 51 4.86441515e+01 4.53882377e+01 3.80188002e+01 | 4.86441515e+01 4.53882377e+01 3.80188002e+01 52 5.79271723e+01 2.42469906e+02 -1.20884451e+02 | 5.79271723e+01 2.42469906e+02 -1.20884451e+02 53 -1.59676637e+01 -9.80642574e+00 8.37326154e+00 | -1.59676637e+01 -9.80642574e+00 8.37326154e+00 54 -1.09867059e+02 1.18651212e+02 1.56623094e+02 | -1.09867059e+02 1.18651212e+02 1.56623094e+02 55 1.56868053e+00 -1.18149154e+00 -1.42381502e+00 | 1.56868053e+00 -1.18149154e+00 -1.42381502e+00 56 5.44414805e+01 -3.80474938e+01 -8.94079259e+00 | 5.44414805e+01 -3.80474938e+01 -8.94079259e+00 57 -1.02416422e+02 -6.99002683e+01 8.98791459e+01 | -1.02416422e+02 -6.99002683e+01 8.98791459e+01 58 9.94770174e+01 1.07222813e+02 -1.04375622e+02 | 9.94770174e+01 1.07222813e+02 -1.04375622e+02 59 -1.27781833e+00 -1.93202195e+00 7.37118789e-02 | -1.27781833e+00 -1.93202195e+00 7.37118789e-02 60 -1.11957260e+00 -3.02644345e+01 3.29902176e+01 | -1.11957260e+00 -3.02644345e+01 3.29902176e+01 61 1.06223921e+00 1.48885784e+00 -6.90965053e-02 | 1.06223921e+00 1.48885784e+00 -6.90965053e-02 62 -1.49519029e+02 -1.36789159e+02 -4.43384395e+01 | -1.49519029e+02 -1.36789159e+02 -4.43384395e+01 63 1.67089623e+02 1.47080358e+02 4.02891706e+01 | 1.67089623e+02 1.47080358e+02 4.02891706e+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 = [33, 2, 1, 38, 63, 20, 49, 59, 26, 52, 19, 47, 28, 31, 24, 55, 17, 16, 23, 10, 5, 46, 51, 18, 14, 45, 8, 53, 12, 60, 32, 13, 30, 0, 50, 58, 56, 44, 3, 61, 42, 57, 40, 62, 37, 25, 21, 11, 54, 6, 34, 22, 9, 27, 48, 15, 36, 41, 35, 7, 29, 39, 43, 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)) = -142.06822673182364 V(r_1,...,r_N) = -142.0682267318237 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 -4.87259022e+00 7.57212451e-01 -4.65881277e+00 | -4.87259022e+00 7.57212451e-01 -4.65881277e+00 1 6.79407370e-01 -3.50858646e+00 -1.45200549e+00 | 6.79407370e-01 -3.50858646e+00 -1.45200549e+00 2 5.04460978e-02 1.42482048e+00 -8.53839210e-01 | 5.04460978e-02 1.42482048e+00 -8.53839210e-01 3 -5.22241709e-01 3.09491803e-01 -9.28828269e-01 | -5.22241709e-01 3.09491803e-01 -9.28828269e-01 4 4.29942765e+00 -2.02494020e+00 4.32566140e+00 | 4.29942765e+00 -2.02494020e+00 4.32566140e+00 5 7.97038782e-01 -2.04120081e+00 -4.55128962e+00 | 7.97038782e-01 -2.04120081e+00 -4.55128962e+00 6 -2.20990463e+00 3.53547739e+00 7.04951777e-01 | -2.20990463e+00 3.53547739e+00 7.04951777e-01 7 -5.68006986e+00 -1.51557391e+00 -6.24788159e+00 | -5.68006986e+00 -1.51557391e+00 -6.24788159e+00 8 -5.22183999e-01 -7.20382900e-01 -2.93280164e-01 | -5.22183999e-01 -7.20382900e-01 -2.93280164e-01 9 -1.06950906e+00 -9.02627462e-02 1.26835889e-02 | -1.06950906e+00 -9.02627462e-02 1.26835889e-02 10 1.19143302e+00 9.81046744e-01 -1.66943885e+00 | 1.19143302e+00 9.81046744e-01 -1.66943885e+00 11 -1.39810841e-01 1.43318971e-01 8.72538619e-01 | -1.39810841e-01 1.43318971e-01 8.72538619e-01 12 -9.35327354e-01 -2.24036640e+00 1.56678293e+00 | -9.35327354e-01 -2.24036640e+00 1.56678293e+00 13 3.08261419e+00 -1.29885983e+00 -1.85272410e+00 | 3.08261419e+00 -1.29885983e+00 -1.85272410e+00 14 -2.11439745e+00 -2.22350615e+00 1.37067570e+00 | -2.11439745e+00 -2.22350615e+00 1.37067570e+00 15 -3.55550373e+00 6.83094382e+00 -2.99134851e+00 | -3.55550373e+00 6.83094382e+00 -2.99134851e+00 16 8.30899622e-01 -6.09957429e-01 1.14030241e+00 | 8.30899622e-01 -6.09957429e-01 1.14030241e+00 17 -8.73871447e+00 -9.07750500e+00 4.47811616e+00 | -8.73871447e+00 -9.07750500e+00 4.47811616e+00 18 8.05214866e+00 7.45238629e+00 -1.20932508e+01 | 8.05214866e+00 7.45238629e+00 -1.20932508e+01 19 6.73329768e-01 2.57780769e+00 2.73698071e+00 | 6.73329768e-01 2.57780769e+00 2.73698071e+00 20 -1.18728241e+01 -9.85075746e-01 -1.17982963e+01 | -1.18728241e+01 -9.85075746e-01 -1.17982963e+01 21 5.04822301e+00 8.30785335e-01 2.83031851e+00 | 5.04822301e+00 8.30785335e-01 2.83031851e+00 22 -3.54599954e+00 -1.89782830e+00 1.15672536e+00 | -3.54599954e+00 -1.89782830e+00 1.15672536e+00 23 1.33980900e+00 1.69413827e+00 1.49797185e+00 | 1.33980900e+00 1.69413827e+00 1.49797185e+00 24 -1.18305147e+00 1.74553475e+00 -3.01536472e+00 | -1.18305147e+00 1.74553475e+00 -3.01536472e+00 25 -3.58890982e+00 -3.63255620e+00 2.58259093e+00 | -3.58890982e+00 -3.63255620e+00 2.58259093e+00 26 6.75532014e+00 5.69210860e+00 -6.22798717e+00 | 6.75532014e+00 5.69210860e+00 -6.22798717e+00 27 -6.88463763e-01 -6.78601710e-01 1.00957800e+00 | -6.88463763e-01 -6.78601710e-01 1.00957800e+00 28 -2.14169258e+00 -4.67293119e+00 -1.01196104e+00 | -2.14169258e+00 -4.67293119e+00 -1.01196104e+00 29 8.60751124e+00 -4.33531773e+00 -3.33565908e+00 | 8.60751124e+00 -4.33531773e+00 -3.33565908e+00 30 -3.37191436e+00 -4.18391528e-01 8.33174022e-01 | -3.37191436e+00 -4.18391528e-01 8.33174022e-01 31 -4.44071775e-03 3.59878197e+00 -1.01538874e+00 | -4.44071775e-03 3.59878197e+00 -1.01538874e+00 32 -8.85068754e+00 -2.74630601e+00 -6.10228771e+00 | -8.85068754e+00 -2.74630601e+00 -6.10228771e+00 33 5.52242830e+00 1.61537978e+00 5.77481936e+00 | 5.52242830e+00 1.61537978e+00 5.77481936e+00 34 -6.93622872e+00 3.69694733e+00 8.72538983e-01 | -6.93622872e+00 3.69694733e+00 8.72538983e-01 35 1.06099867e+01 1.04384109e+00 8.57756105e+00 | 1.06099867e+01 1.04384109e+00 8.57756105e+00 36 9.45134802e-01 -1.12868354e+00 1.35566454e+00 | 9.45134802e-01 -1.12868354e+00 1.35566454e+00 37 -7.64900435e+00 -2.95427504e+00 2.52270569e+00 | -7.64900435e+00 -2.95427504e+00 2.52270569e+00 38 -1.01145070e+01 -3.24350024e+00 -3.41935069e+00 | -1.01145070e+01 -3.24350024e+00 -3.41935069e+00 39 6.66880970e+00 2.34530911e+00 3.19488709e+00 | 6.66880970e+00 2.34530911e+00 3.19488709e+00 40 1.41754752e+00 -2.66905266e+00 8.13038774e-01 | 1.41754752e+00 -2.66905266e+00 8.13038774e-01 41 -1.20242954e+00 -3.59125474e+00 2.06439957e+00 | -1.20242954e+00 -3.59125474e+00 2.06439957e+00 42 7.89836823e+00 -2.71722952e+00 4.74262641e-01 | 7.89836823e+00 -2.71722952e+00 4.74262641e-01 43 6.13860121e+00 -8.31464814e-01 -3.68748550e+00 | 6.13860121e+00 -8.31464814e-01 -3.68748550e+00 44 -1.03623910e+00 8.77394754e-02 -5.71256231e-01 | -1.03623910e+00 8.77394754e-02 -5.71256231e-01 45 1.92024052e-01 1.15351607e+00 -2.95585458e-01 | 1.92024052e-01 1.15351607e+00 -2.95585458e-01 46 2.08910012e+00 -3.88572911e+00 3.23423861e-01 | 2.08910012e+00 -3.88572911e+00 3.23423861e-01 47 -4.61044706e+00 -8.04663678e+00 1.62909388e+01 | -4.61044706e+00 -8.04663678e+00 1.62909388e+01 48 -8.33039889e-01 -5.07519962e-01 -2.50690858e-01 | -8.33039889e-01 -5.07519962e-01 -2.50690858e-01 49 2.81030044e+01 -2.30104028e+01 -1.91338447e+01 | 2.81030044e+01 -2.30104028e+01 -1.91338447e+01 50 3.31509357e+00 8.47049120e-01 -3.72266560e+00 | 3.31509357e+00 8.47049120e-01 -3.72266560e+00 51 1.12793089e+00 1.01871865e+00 6.89182278e-01 | 1.12793089e+00 1.01871865e+00 6.89182278e-01 52 -1.78350661e+01 -1.80383727e+01 -1.51814446e+01 | -1.78350661e+01 -1.80383727e+01 -1.51814446e+01 53 1.30571064e+01 1.33449449e+01 1.91788868e+01 | 1.30571064e+01 1.33449449e+01 1.91788868e+01 54 -3.70102563e+01 1.78150216e+01 1.99458228e+01 | -3.70102563e+01 1.78150216e+01 1.99458228e+01 55 4.16331005e+00 4.76593737e+00 3.58735433e+00 | 4.16331005e+00 4.76593737e+00 3.58735433e+00 56 1.10586393e+01 1.43949542e+00 7.14949840e+00 | 1.10586393e+01 1.43949542e+00 7.14949840e+00 57 -2.65551358e+00 5.35242749e+00 -5.07059917e+00 | -2.65551358e+00 5.35242749e+00 -5.07059917e+00 58 -4.00829091e+00 4.84748389e+00 8.69658916e+00 | -4.00829091e+00 4.84748389e+00 8.69658916e+00 59 2.55175992e-02 -2.45063270e-01 4.08807972e-01 | 2.55175992e-02 -2.45063270e-01 4.08807972e-01 60 1.02115942e+01 8.92971045e+00 -4.37144724e+00 | 1.02115942e+01 8.92971045e+00 -4.37144724e+00 61 6.34281856e-01 1.55879044e+00 3.31624871e-01 | 6.34281856e-01 1.55879044e+00 3.31624871e-01 62 4.40651083e+00 7.63600337e+00 -3.79355835e+00 | 4.40651083e+00 7.63600337e+00 -3.79355835e+00 63 5.06661492e-01 5.15165292e-01 2.26513601e-01 | 5.06661492e-01 5.15165292e-01 2.26513601e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Nb Ti (Configuration in file "config-AlNbTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [39, 28, 37, 15, 35, 55, 58, 57, 34, 43, 13, 47, 17, 10, 41, 3, 61, 12, 63, 49, 42, 30, 52, 44, 26, 38, 24, 45, 1, 33, 21, 46, 50, 29, 8, 4, 40, 2, 25, 0, 36, 14, 20, 9, 23, 27, 31, 11, 51, 19, 32, 48, 22, 62, 54, 5, 59, 7, 6, 56, 60, 16, 53, 18] 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)) = -78.804874987168 V(r_1,...,r_N) = -78.80487498716772 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 -1.70476868e+00 -2.48977214e+00 -2.04731162e+00 | -1.70476868e+00 -2.48977214e+00 -2.04731162e+00 1 -1.48340963e+00 6.50855746e+00 -1.19672359e-01 | -1.48340963e+00 6.50855746e+00 -1.19672359e-01 2 -1.86725123e+00 -1.86640025e+00 -1.79184536e+00 | -1.86725123e+00 -1.86640025e+00 -1.79184536e+00 3 -5.51064301e+00 -3.67014583e+00 6.36825036e+00 | -5.51064301e+00 -3.67014583e+00 6.36825036e+00 4 3.73274087e+00 -3.19333491e+00 3.12091802e+00 | 3.73274087e+00 -3.19333491e+00 3.12091802e+00 5 -2.27956333e+01 -8.84646814e+00 5.02815392e+00 | -2.27956333e+01 -8.84646814e+00 5.02815392e+00 6 -1.81454241e-01 -9.77980366e-01 -1.99075370e+00 | -1.81454241e-01 -9.77980366e-01 -1.99075370e+00 7 -3.24104965e+01 -2.38899518e+01 1.84614320e+01 | -3.24104965e+01 -2.38899518e+01 1.84614320e+01 8 -6.87153493e+00 -1.50842820e+00 -8.89470327e+00 | -6.87153493e+00 -1.50842820e+00 -8.89470327e+00 9 1.12798960e+01 -6.32833759e+00 2.55869489e+01 | 1.12798960e+01 -6.32833759e+00 2.55869489e+01 10 -2.27447837e+00 -3.12195228e+00 -4.28129083e+00 | -2.27447837e+00 -3.12195228e+00 -4.28129083e+00 11 5.58832139e+01 -8.12657698e+01 -4.22480701e+01 | 5.58832139e+01 -8.12657698e+01 -4.22480701e+01 12 -5.96319005e+00 1.02011198e+01 -1.53011533e+01 | -5.96319005e+00 1.02011198e+01 -1.53011533e+01 13 1.27527937e+00 -4.56546681e+00 -1.16128517e+00 | 1.27527937e+00 -4.56546681e+00 -1.16128517e+00 14 1.15169049e+01 5.93861823e+00 -2.47299377e+01 | 1.15169049e+01 5.93861823e+00 -2.47299377e+01 15 8.14688176e+00 9.25545595e+00 7.65188761e+00 | 8.14688176e+00 9.25545595e+00 7.65188761e+00 16 2.09378316e+01 2.46714173e+01 1.15000073e+01 | 2.09378316e+01 2.46714173e+01 1.15000073e+01 17 -2.65032112e+01 -2.80391086e+01 -3.17420385e+00 | -2.65032112e+01 -2.80391086e+01 -3.17420385e+00 18 1.29853671e+00 3.48437099e+00 -7.05260157e-01 | 1.29853671e+00 3.48437099e+00 -7.05260157e-01 19 2.21854646e-01 2.34143862e+00 -3.97071741e+00 | 2.21854646e-01 2.34143862e+00 -3.97071741e+00 20 2.39595443e+01 1.34211915e+01 -2.99241892e+01 | 2.39595443e+01 1.34211915e+01 -2.99241892e+01 21 1.38712589e+01 1.16560986e+01 1.09614781e+01 | 1.38712589e+01 1.16560986e+01 1.09614781e+01 22 3.97907944e+00 -2.75873270e+00 -5.94398335e+00 | 3.97907944e+00 -2.75873270e+00 -5.94398335e+00 23 2.77389167e-01 1.07524638e-01 -1.75069685e-01 | 2.77389167e-01 1.07524638e-01 -1.75069685e-01 24 4.81191234e+00 3.33676947e+00 -6.76967973e+00 | 4.81191234e+00 3.33676947e+00 -6.76967973e+00 25 -1.81658848e+00 -3.36477245e+00 3.93658780e+00 | -1.81658848e+00 -3.36477245e+00 3.93658780e+00 26 -4.98524987e-01 3.53645476e+00 -3.01878437e+00 | -4.98524987e-01 3.53645476e+00 -3.01878437e+00 27 2.29329117e+00 1.48573770e+00 2.61982196e+00 | 2.29329117e+00 1.48573770e+00 2.61982196e+00 28 -5.64919469e+01 8.20243463e+01 4.20512718e+01 | -5.64919469e+01 8.20243463e+01 4.20512718e+01 29 3.29881282e+01 -9.25840288e+00 -3.17863272e+01 | 3.29881282e+01 -9.25840288e+00 -3.17863272e+01 30 -7.87107647e+00 -8.66530773e+00 1.37579682e-01 | -7.87107647e+00 -8.66530773e+00 1.37579682e-01 31 8.39891822e+00 6.70350875e+00 2.63587373e+00 | 8.39891822e+00 6.70350875e+00 2.63587373e+00 32 -4.63021486e+00 -1.29091791e+01 -1.01382449e+00 | -4.63021486e+00 -1.29091791e+01 -1.01382449e+00 33 3.17127798e+00 3.97037308e+00 -6.20569114e+00 | 3.17127798e+00 3.97037308e+00 -6.20569114e+00 34 5.03264002e+00 4.92058759e+00 -4.90706731e+00 | 5.03264002e+00 4.92058759e+00 -4.90706731e+00 35 8.01931148e+00 -6.93182410e+00 -1.24678073e+00 | 8.01931148e+00 -6.93182410e+00 -1.24678073e+00 36 -3.58597365e+00 -1.68301807e+00 -4.70171720e+00 | -3.58597365e+00 -1.68301807e+00 -4.70171720e+00 37 4.21026206e+00 1.70658544e+00 5.52497635e+00 | 4.21026206e+00 1.70658544e+00 5.52497635e+00 38 -3.56964188e+00 -1.14150052e+01 -6.64650381e+00 | -3.56964188e+00 -1.14150052e+01 -6.64650381e+00 39 -3.56650992e+00 1.08234297e+01 1.98189148e+01 | -3.56650992e+00 1.08234297e+01 1.98189148e+01 40 3.54493911e+00 -8.48947576e+00 9.69392364e+00 | 3.54493911e+00 -8.48947576e+00 9.69392364e+00 41 -2.00960899e+01 -2.12094741e+00 -2.55977871e+01 | -2.00960899e+01 -2.12094741e+00 -2.55977871e+01 42 -3.65389254e+00 2.12063943e+00 1.79469257e+00 | -3.65389254e+00 2.12063943e+00 1.79469257e+00 43 1.01834848e+00 2.23835180e+00 5.50512757e-01 | 1.01834848e+00 2.23835180e+00 5.50512757e-01 44 -1.92729218e+01 -3.30846717e+01 -2.00195792e+00 | -1.92729218e+01 -3.30846717e+01 -2.00195792e+00 45 4.45291902e+01 2.71448400e+01 2.57154651e+01 | 4.45291902e+01 2.71448400e+01 2.57154651e+01 46 -3.77216918e+00 1.02939170e+01 8.52330145e-01 | -3.77216918e+00 1.02939170e+01 8.52330145e-01 47 -1.60783459e+00 -2.30689932e-01 -2.76575995e-01 | -1.60783459e+00 -2.30689932e-01 -2.76575995e-01 48 -1.92606031e+01 -2.80039009e+01 -6.49596724e+01 | -1.92606031e+01 -2.80039009e+01 -6.49596724e+01 49 -7.36963642e+00 9.79143060e+00 7.71767689e+01 | -7.36963642e+00 9.79143060e+00 7.71767689e+01 50 2.33722309e+01 2.29128361e+01 -1.11403636e+01 | 2.33722309e+01 2.29128361e+01 -1.11403636e+01 51 -2.05672249e+01 1.93116378e+01 -5.40547052e+00 | -2.05672249e+01 1.93116378e+01 -5.40547052e+00 52 -2.93650388e+00 3.12385421e+00 3.48761808e+00 | -2.93650388e+00 3.12385421e+00 3.48761808e+00 53 -1.66139392e+01 -1.49605394e+01 1.25709457e+01 | -1.66139392e+01 -1.49605394e+01 1.25709457e+01 54 -2.33710336e+00 -1.58595597e+00 -3.27281106e+00 | -2.33710336e+00 -1.58595597e+00 -3.27281106e+00 55 3.22284629e+00 1.67529304e+00 2.46654158e+00 | 3.22284629e+00 1.67529304e+00 2.46654158e+00 56 -1.76147589e+01 -1.68121236e+01 -1.64967429e+01 | -1.76147589e+01 -1.68121236e+01 -1.64967429e+01 57 -4.88214195e+01 8.20963496e+01 1.05336441e+02 | -4.88214195e+01 8.20963496e+01 1.05336441e+02 58 -2.16969688e+01 1.51137678e+01 2.46006770e+01 | -2.16969688e+01 1.51137678e+01 2.46006770e+01 59 -1.44835426e-01 2.56139224e-01 7.47597160e-01 | -1.44835426e-01 2.56139224e-01 7.47597160e-01 60 -4.97289449e+01 -3.53692105e+01 -4.64877493e+01 | -4.97289449e+01 -3.53692105e+01 -4.64877493e+01 61 5.17217252e+01 3.41405554e+01 4.88533821e+01 | 5.17217252e+01 3.41405554e+01 4.88533821e+01 62 8.52646649e+01 -7.35484970e+01 -9.66857908e+01 | 8.52646649e+01 -7.35484970e+01 -9.66857908e+01 63 7.11129666e+00 4.64217310e+00 5.82974633e+00 | 7.11129666e+00 4.64217310e+00 5.82974633e+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.