!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = [52, 49, 63, 28, 26, 37, 47, 10, 19, 16, 7, 29, 27, 61, 23, 59, 9, 33, 30, 8, 62, 24, 31, 14, 21, 35, 4, 12, 3, 11, 18, 22, 34, 17, 32, 25, 44, 5, 41, 42, 55, 38, 39, 46, 36, 54, 43, 6, 60, 1, 56, 57, 0, 58, 45, 40, 50, 51, 53, 15, 48, 13, 20, 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)) = 164.680813599 V(r_1,...,r_N) = 164.680813599 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 = [6, 43, 23, 35, 7, 61, 0, 4, 22, 44, 42, 29, 21, 41, 31, 17, 26, 15, 19, 18, 59, 12, 8, 2, 33, 60, 16, 51, 62, 11, 47, 14, 39, 24, 36, 3, 34, 53, 55, 32, 56, 13, 10, 1, 9, 63, 54, 30, 57, 58, 52, 27, 50, 37, 46, 38, 40, 48, 49, 20, 25, 5, 28, 45] 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)) = -230.157183357 V(r_1,...,r_N) = -230.157183357 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 8.93135977e-01 1.19492214e+00 1.10816750e+00 | 8.93135977e-01 1.19492214e+00 1.10816750e+00 1 -5.19559794e+00 -5.57320829e+00 2.75023190e+00 | -5.19559794e+00 -5.57320829e+00 2.75023190e+00 2 -5.33313307e-01 1.25969350e+00 -1.04575651e+01 | -5.33313307e-01 1.25969350e+00 -1.04575651e+01 3 8.66583251e+00 -1.35106273e+00 -3.33961818e+00 | 8.66583251e+00 -1.35106273e+00 -3.33961818e+00 4 -6.86847328e+00 -6.61404171e+00 -8.02011431e+00 | -6.86847328e+00 -6.61404171e+00 -8.02011431e+00 5 -1.88259175e+01 2.18721574e+01 -6.07024816e+00 | -1.88259175e+01 2.18721574e+01 -6.07024816e+00 6 -3.87726590e-01 -6.22193163e-01 2.79669150e-02 | -3.87726590e-01 -6.22193163e-01 2.79669150e-02 7 -2.33003264e+01 -3.81009206e+01 8.13499761e+00 | -2.33003264e+01 -3.81009206e+01 8.13499761e+00 8 -1.20247507e+00 1.01837897e+00 1.01236314e+00 | -1.20247507e+00 1.01837897e+00 1.01236314e+00 9 -4.76472280e+00 -1.61417794e+00 1.97336992e+00 | -4.76472280e+00 -1.61417794e+00 1.97336992e+00 10 -2.07832465e+00 -1.64386334e+00 -8.84120831e+00 | -2.07832465e+00 -1.64386334e+00 -8.84120831e+00 11 1.01218228e+01 7.19786021e-01 1.28180904e+00 | 1.01218228e+01 7.19786021e-01 1.28180904e+00 12 -5.70656013e+00 -7.80981283e+00 -6.61924148e+00 | -5.70656013e+00 -7.80981283e+00 -6.61924148e+00 13 8.21795459e+00 5.39089181e+00 7.08191937e+00 | 8.21795459e+00 5.39089181e+00 7.08191937e+00 14 1.00530929e+00 -1.93155438e+00 -2.80199066e+00 | 1.00530929e+00 -1.93155438e+00 -2.80199066e+00 15 3.52748589e+00 -3.22496278e+01 -1.41836612e+01 | 3.52748589e+00 -3.22496278e+01 -1.41836612e+01 16 -4.36181884e-02 -1.52714189e+00 3.70946300e-01 | -4.36181884e-02 -1.52714189e+00 3.70946300e-01 17 -5.22366240e+00 4.62141513e+00 -6.21880370e+00 | -5.22366240e+00 4.62141513e+00 -6.21880370e+00 18 -6.73982687e+00 -7.49395136e+00 -1.19303841e+01 | -6.73982687e+00 -7.49395136e+00 -1.19303841e+01 19 4.33000439e+00 1.11291079e+01 7.94616568e+00 | 4.33000439e+00 1.11291079e+01 7.94616568e+00 20 3.24153223e+01 2.94759065e+01 -2.49097579e+01 | 3.24153223e+01 2.94759065e+01 -2.49097579e+01 21 -8.29380232e+00 6.02348553e+00 -7.97312932e+00 | -8.29380232e+00 6.02348553e+00 -7.97312932e+00 22 5.04826249e-02 6.51913681e-01 1.20034216e+00 | 5.04826249e-02 6.51913681e-01 1.20034216e+00 23 -1.66362504e+00 3.35926395e-01 -1.84636706e+00 | -1.66362504e+00 3.35926395e-01 -1.84636706e+00 24 -5.76649101e+00 -1.06154969e+00 -5.66019888e+00 | -5.76649101e+00 -1.06154969e+00 -5.66019888e+00 25 4.78556211e+00 4.37525578e+00 5.82633386e-01 | 4.78556211e+00 4.37525578e+00 5.82633386e-01 26 -3.82189407e+00 -2.24849689e+00 -3.78857901e+00 | -3.82189407e+00 -2.24849689e+00 -3.78857901e+00 27 3.31924418e+00 2.81324776e+00 4.70223153e+00 | 3.31924418e+00 2.81324776e+00 4.70223153e+00 28 1.17220686e+01 9.77211599e+00 -1.27403897e+01 | 1.17220686e+01 9.77211599e+00 -1.27403897e+01 29 1.44094128e+01 -2.07175340e+00 -5.60054839e+00 | 1.44094128e+01 -2.07175340e+00 -5.60054839e+00 30 -1.13499053e+01 -1.42668600e+01 -1.55138055e+01 | -1.13499053e+01 -1.42668600e+01 -1.55138055e+01 31 -8.13134095e+00 3.89097072e+01 -4.28647575e+00 | -8.13134095e+00 3.89097072e+01 -4.28647575e+00 32 -9.08153426e+00 -9.93317064e+00 -8.03224650e+00 | -9.08153426e+00 -9.93317064e+00 -8.03224650e+00 33 1.02221786e+01 -5.72828162e+00 6.56306956e+00 | 1.02221786e+01 -5.72828162e+00 6.56306956e+00 34 9.33047023e+00 -3.97497689e+00 -8.87379002e-02 | 9.33047023e+00 -3.97497689e+00 -8.87379002e-02 35 4.43776272e+00 -3.40657608e+00 6.57316916e-01 | 4.43776272e+00 -3.40657608e+00 6.57316916e-01 36 -2.94999075e+00 -3.66564908e+00 -2.76930879e+00 | -2.94999075e+00 -3.66564908e+00 -2.76930879e+00 37 -1.03120004e+01 -3.54290845e+00 1.14134025e+01 | -1.03120004e+01 -3.54290845e+00 1.14134025e+01 38 -9.09649890e+00 7.01051719e+00 8.40928035e+00 | -9.09649890e+00 7.01051719e+00 8.40928035e+00 39 -7.62804695e+00 -6.83832684e+00 9.53747508e+00 | -7.62804695e+00 -6.83832684e+00 9.53747508e+00 40 2.37025470e+01 -2.21231854e+01 1.85032758e+01 | 2.37025470e+01 -2.21231854e+01 1.85032758e+01 41 1.25782366e+01 -1.29494036e+01 -1.46365253e+01 | 1.25782366e+01 -1.29494036e+01 -1.46365253e+01 42 -5.98718926e+00 -1.09107473e+01 -1.19804099e+01 | -5.98718926e+00 -1.09107473e+01 -1.19804099e+01 43 1.62973298e+01 6.81098198e+00 1.29425805e+01 | 1.62973298e+01 6.81098198e+00 1.29425805e+01 44 3.39806484e+00 -1.94924591e+00 1.71321308e+00 | 3.39806484e+00 -1.94924591e+00 1.71321308e+00 45 -1.86147684e+00 3.09203725e-01 -1.77945830e+00 | -1.86147684e+00 3.09203725e-01 -1.77945830e+00 46 -7.98917859e+00 1.58727139e+01 5.29878386e+00 | -7.98917859e+00 1.58727139e+01 5.29878386e+00 47 1.94748896e+00 4.11914337e+00 4.04360629e+00 | 1.94748896e+00 4.11914337e+00 4.04360629e+00 48 -2.03578287e+01 1.77299948e+01 1.74595430e+01 | -2.03578287e+01 1.77299948e+01 1.74595430e+01 49 1.47107580e+01 -1.14566871e+01 -1.53313996e+01 | 1.47107580e+01 -1.14566871e+01 -1.53313996e+01 50 -9.19322056e+00 -5.09877893e+00 -9.71386198e+00 | -9.19322056e+00 -5.09877893e+00 -9.71386198e+00 51 -1.17656450e+01 2.99648538e+01 -7.60375413e+00 | -1.17656450e+01 2.99648538e+01 -7.60375413e+00 52 7.04919516e+00 7.02916666e+00 -3.58499347e+00 | 7.04919516e+00 7.02916666e+00 -3.58499347e+00 53 -1.93318066e+00 -1.97537435e+00 3.61028358e+00 | -1.93318066e+00 -1.97537435e+00 3.61028358e+00 54 -1.92488530e+01 1.30896412e+01 1.15083653e+01 | -1.92488530e+01 1.30896412e+01 1.15083653e+01 55 3.57491561e+00 1.63398027e+00 2.44964862e+00 | 3.57491561e+00 1.63398027e+00 2.44964862e+00 56 -1.34583996e+01 1.81503060e+01 3.18186885e+01 | -1.34583996e+01 1.81503060e+01 3.18186885e+01 57 -6.03184512e+00 -7.77624905e+00 1.32483700e+01 | -6.03184512e+00 -7.77624905e+00 1.32483700e+01 58 2.61216239e+01 -6.27869730e+00 1.69139031e+01 | 2.61216239e+01 -6.27869730e+00 1.69139031e+01 59 -1.28406761e+00 -1.35144542e+00 -1.37551843e-02 | -1.28406761e+00 -1.35144542e+00 -1.37551843e-02 60 -1.07727490e+01 -1.00061823e+01 -1.09440734e+01 | -1.07727490e+01 -1.00061823e+01 -1.09440734e+01 61 1.22129501e+01 1.17223136e+01 1.30434266e+01 | 1.22129501e+01 1.17223136e+01 1.30434266e+01 62 1.41105536e+01 -2.06425254e+01 1.62108666e+01 | 1.41105536e+01 -2.06425254e+01 1.62108666e+01 63 5.69159598e+00 2.78189966e+00 3.76236768e+00 | 5.69159598e+00 2.78189966e+00 3.76236768e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [21, 6, 50, 57, 47, 17, 1, 39, 9, 8, 22, 25, 43, 42, 40, 24, 41, 5, 54, 59, 35, 0, 10, 38, 15, 11, 60, 28, 27, 51, 32, 58, 30, 53, 36, 20, 34, 63, 23, 7, 14, 16, 13, 12, 48, 55, 56, 4, 44, 52, 2, 29, 49, 33, 18, 45, 46, 3, 31, 19, 26, 62, 61, 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)) = -137.700515026 V(r_1,...,r_N) = -137.700515026 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 -1.66462855e+00 -1.31451486e+00 -1.47341999e+00 | -1.66462855e+00 -1.31451486e+00 -1.47341999e+00 1 3.20744182e+00 -6.39459218e+00 -9.03374537e-01 | 3.20744182e+00 -6.39459218e+00 -9.03374537e-01 2 7.67921802e-01 1.31949964e+00 -2.78625254e+00 | 7.67921802e-01 1.31949964e+00 -2.78625254e+00 3 3.39113139e+00 -3.81940863e+00 -3.06936027e+00 | 3.39113139e+00 -3.81940863e+00 -3.06936027e+00 4 -1.90823985e+00 -1.74349137e+00 -2.27316173e+00 | -1.90823985e+00 -1.74349137e+00 -2.27316173e+00 5 -2.95491407e+00 -1.20294876e+00 2.74589551e+00 | -2.95491407e+00 -1.20294876e+00 2.74589551e+00 6 -4.22425294e+00 5.28129272e+00 3.70602873e+00 | -4.22425294e+00 5.28129272e+00 3.70602873e+00 7 -2.85051423e+00 8.66223105e-01 4.49338754e+00 | -2.85051423e+00 8.66223105e-01 4.49338754e+00 8 -9.03282860e-01 -5.17501464e-01 -1.62794337e+00 | -9.03282860e-01 -5.17501464e-01 -1.62794337e+00 9 -3.20466265e+00 3.51314441e-01 4.10989970e-02 | -3.20466265e+00 3.51314441e-01 4.10989970e-02 10 4.68353488e-01 1.67921172e+00 -7.52593870e-01 | 4.68353488e-01 1.67921172e+00 -7.52593870e-01 11 -9.29432599e-01 -3.71000899e-01 2.50430094e-01 | -9.29432599e-01 -3.71000899e-01 2.50430094e-01 12 5.81062494e+00 -3.79432825e+00 9.28641120e-02 | 5.81062494e+00 -3.79432825e+00 9.28641120e-02 13 1.04403703e+01 -1.32971612e+01 -1.08659153e+01 | 1.04403703e+01 -1.32971612e+01 -1.08659153e+01 14 -6.71140315e+00 -3.96898716e+00 -8.16868492e+00 | -6.71140315e+00 -3.96898716e+00 -8.16868492e+00 15 6.92584153e+00 5.83555891e+00 4.74421298e+00 | 6.92584153e+00 5.83555891e+00 4.74421298e+00 16 -7.06065854e-01 -1.71736198e+00 2.51925806e-04 | -7.06065854e-01 -1.71736198e+00 2.51925806e-04 17 -2.31236796e+01 -2.24881451e+01 1.72050734e+01 | -2.31236796e+01 -2.24881451e+01 1.72050734e+01 18 2.07620255e+01 2.45442891e+01 -2.10455526e+01 | 2.07620255e+01 2.45442891e+01 -2.10455526e+01 19 2.59690391e+00 1.75897885e+00 2.78039211e+00 | 2.59690391e+00 1.75897885e+00 2.78039211e+00 20 -4.10056036e-01 4.65304958e+00 -6.17503711e-01 | -4.10056036e-01 4.65304958e+00 -6.17503711e-01 21 -1.91778388e+01 -7.39520069e+00 5.10528916e+00 | -1.91778388e+01 -7.39520069e+00 5.10528916e+00 22 -5.88490584e+00 -1.52128448e+00 -5.60429231e+00 | -5.88490584e+00 -1.52128448e+00 -5.60429231e+00 23 -4.70921992e-01 1.59084047e+00 2.62602763e+00 | -4.70921992e-01 1.59084047e+00 2.62602763e+00 24 -3.10670049e+00 -5.12264224e+00 -2.53098169e+00 | -3.10670049e+00 -5.12264224e+00 -2.53098169e+00 25 1.21769975e+00 2.41158837e+00 3.28728870e+00 | 1.21769975e+00 2.41158837e+00 3.28728870e+00 26 2.28515932e+00 1.87023691e+00 -2.47101369e+00 | 2.28515932e+00 1.87023691e+00 -2.47101369e+00 27 -6.03228400e-02 -1.41663458e-01 1.15005111e+00 | -6.03228400e-02 -1.41663458e-01 1.15005111e+00 28 4.16414323e+00 2.87112176e+00 -2.44704855e+00 | 4.16414323e+00 2.87112176e+00 -2.44704855e+00 29 2.04931819e+01 -4.22672679e+00 -4.38881552e+00 | 2.04931819e+01 -4.22672679e+00 -4.38881552e+00 30 1.58975920e+01 1.14119951e+01 -7.10646215e+00 | 1.58975920e+01 1.14119951e+01 -7.10646215e+00 31 5.75627721e-01 3.11032927e+00 -6.80111402e-01 | 5.75627721e-01 3.11032927e+00 -6.80111402e-01 32 -8.92877196e-01 -2.24740517e+00 -1.20246264e+00 | -8.92877196e-01 -2.24740517e+00 -1.20246264e+00 33 -7.25380555e+00 -4.59350797e+00 2.36330162e+01 | -7.25380555e+00 -4.59350797e+00 2.36330162e+01 34 5.32951995e+00 6.80087669e+00 -2.04307502e+01 | 5.32951995e+00 6.80087669e+00 -2.04307502e+01 35 -7.45214832e-01 -1.99023736e+00 1.29257769e+00 | -7.45214832e-01 -1.99023736e+00 1.29257769e+00 36 -1.94007378e+00 -2.95007817e+00 -8.32117093e+00 | -1.94007378e+00 -2.95007817e+00 -8.32117093e+00 37 7.14590953e-01 1.41261490e+00 1.03533142e+01 | 7.14590953e-01 1.41261490e+00 1.03533142e+01 38 2.23914127e-01 -7.63793335e-01 -7.83671880e-01 | 2.23914127e-01 -7.63793335e-01 -7.83671880e-01 39 -4.53705088e+00 -2.77881763e+00 3.74939057e+00 | -4.53705088e+00 -2.77881763e+00 3.74939057e+00 40 -2.26519339e+00 -8.94096910e+00 -7.17932079e+00 | -2.26519339e+00 -8.94096910e+00 -7.17932079e+00 41 5.23678054e+00 4.49400674e+00 7.75735017e+00 | 5.23678054e+00 4.49400674e+00 7.75735017e+00 42 -1.54075035e+01 2.55874283e+00 4.35432011e+00 | -1.54075035e+01 2.55874283e+00 4.35432011e+00 43 7.25775649e+00 9.75151768e+00 8.06764677e+00 | 7.25775649e+00 9.75151768e+00 8.06764677e+00 44 -5.84331199e-01 -8.56398746e-01 -4.13887957e-01 | -5.84331199e-01 -8.56398746e-01 -4.13887957e-01 45 1.27354810e+00 6.58779332e-01 -1.08295603e-01 | 1.27354810e+00 6.58779332e-01 -1.08295603e-01 46 -1.02365541e+01 -5.92935244e+00 1.63785680e+00 | -1.02365541e+01 -5.92935244e+00 1.63785680e+00 47 1.09582538e+01 5.39116241e+00 3.70876485e+00 | 1.09582538e+01 5.39116241e+00 3.70876485e+00 48 4.20375464e-01 -1.62969914e+00 -7.18341261e-01 | 4.20375464e-01 -1.62969914e+00 -7.18341261e-01 49 3.44620960e+00 -1.18925469e+00 -1.10225498e+01 | 3.44620960e+00 -1.18925469e+00 -1.10225498e+01 50 4.38589994e+00 -1.69218853e+00 1.15035109e+00 | 4.38589994e+00 -1.69218853e+00 1.15035109e+00 51 1.71621209e+00 1.15331284e+00 2.14041714e+00 | 1.71621209e+00 1.15331284e+00 2.14041714e+00 52 3.08841639e+00 2.83167393e+00 -4.47173262e+00 | 3.08841639e+00 2.83167393e+00 -4.47173262e+00 53 -1.28906151e+00 -1.01256268e+00 4.09790053e+00 | -1.28906151e+00 -1.01256268e+00 4.09790053e+00 54 -6.72488305e+00 -1.74076110e+00 9.13264363e+00 | -6.72488305e+00 -1.74076110e+00 9.13264363e+00 55 4.54275412e+00 4.39848916e+00 1.80097054e+00 | 4.54275412e+00 4.39848916e+00 1.80097054e+00 56 -1.00764638e+00 -2.00255866e+00 9.21947150e-01 | -1.00764638e+00 -2.00255866e+00 9.21947150e-01 57 -8.81263359e+00 4.46117038e+00 -1.20765344e+01 | -8.81263359e+00 4.46117038e+00 -1.20765344e+01 58 -1.72364303e+01 7.15736921e+00 6.40317141e+00 | -1.72364303e+01 7.15736921e+00 6.40317141e+00 59 -7.38900586e-01 -1.39546806e+00 7.05142067e-03 | -7.38900586e-01 -1.39546806e+00 7.05142067e-03 60 1.23628987e+01 -7.63768799e+00 6.81856859e+00 | 1.23628987e+01 -7.63768799e+00 6.81856859e+00 61 1.07219176e+00 1.56338425e+00 8.77104027e-01 | 1.07219176e+00 1.56338425e+00 8.77104027e-01 62 -5.56926559e+00 3.70448803e+00 -2.30804189e+00 | -5.56926559e+00 3.70448803e+00 -2.30804189e+00 63 2.49990709e+00 2.49458199e+00 1.71659326e+00 | 2.49990709e+00 2.49458199e+00 1.71659326e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [17, 7, 63, 49, 56, 52, 18, 1, 57, 13, 36, 44, 28, 9, 23, 41, 35, 0, 6, 55, 61, 50, 32, 14, 26, 59, 24, 58, 12, 42, 60, 37, 22, 39, 43, 16, 10, 31, 51, 33, 45, 15, 29, 34, 11, 40, 62, 48, 47, 3, 21, 38, 5, 53, 54, 19, 4, 8, 27, 25, 30, 20, 46, 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)) = -204.334976566 V(r_1,...,r_N) = -204.334976566 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 1.17660713e+00 1.21725558e+00 1.07165173e+00 | 1.17660713e+00 1.21725558e+00 1.07165173e+00 1 -2.26629364e+00 -3.27626299e+00 2.23845787e+00 | -2.26629364e+00 -3.27626299e+00 2.23845787e+00 2 1.40316130e-01 -5.21306880e+00 -8.09242978e+00 | 1.40316130e-01 -5.21306880e+00 -8.09242978e+00 3 1.14891131e+01 3.86816482e-03 -5.53359301e+00 | 1.14891131e+01 3.86816482e-03 -5.53359301e+00 4 -1.43558524e+01 -1.20312976e+01 -1.01299340e+01 | -1.43558524e+01 -1.20312976e+01 -1.01299340e+01 5 7.79858910e+00 9.14892254e+00 8.71331319e+00 | 7.79858910e+00 9.14892254e+00 8.71331319e+00 6 -1.10398177e+00 7.98654449e-01 -2.39363742e-01 | -1.10398177e+00 7.98654449e-01 -2.39363742e-01 7 -1.83882807e+01 1.08651882e+01 -7.54337513e+00 | -1.83882807e+01 1.08651882e+01 -7.54337513e+00 8 -7.22651666e-01 -9.60322424e-01 -2.54916886e-01 | -7.22651666e-01 -9.60322424e-01 -2.54916886e-01 9 -4.98987339e+00 4.61325907e+00 -8.28257754e+00 | -4.98987339e+00 4.61325907e+00 -8.28257754e+00 10 -8.33524515e+00 -3.42671045e+00 -5.69571392e+00 | -8.33524515e+00 -3.42671045e+00 -5.69571392e+00 11 9.86551279e+00 2.18096585e+00 3.67931161e+00 | 9.86551279e+00 2.18096585e+00 3.67931161e+00 12 1.46780279e+00 -1.18142505e+01 4.54900287e+00 | 1.46780279e+00 -1.18142505e+01 4.54900287e+00 13 9.12220182e+00 1.59470138e+00 3.00094962e-01 | 9.12220182e+00 1.59470138e+00 3.00094962e-01 14 1.33854249e-01 7.03008066e+00 -3.23977741e-01 | 1.33854249e-01 7.03008066e+00 -3.23977741e-01 15 -3.41824084e+00 2.74656716e+00 -1.54631495e+00 | -3.41824084e+00 2.74656716e+00 -1.54631495e+00 16 -2.11303019e+00 -3.71210781e+00 -2.13198873e+00 | -2.11303019e+00 -3.71210781e+00 -2.13198873e+00 17 3.15076231e-01 2.90305157e+00 9.37937010e-01 | 3.15076231e-01 2.90305157e+00 9.37937010e-01 18 -2.78341692e+00 -3.93344218e+00 -5.42249881e+00 | -2.78341692e+00 -3.93344218e+00 -5.42249881e+00 19 -2.65052609e+00 7.73618603e+00 7.12770612e-01 | -2.65052609e+00 7.73618603e+00 7.12770612e-01 20 -6.74032605e+00 4.45094732e+00 6.58079975e+00 | -6.74032605e+00 4.45094732e+00 6.58079975e+00 21 5.25510673e+00 2.32750670e-01 -1.89779481e+00 | 5.25510673e+00 2.32750670e-01 -1.89779481e+00 22 -8.74688953e+00 -4.68675476e+00 -4.24784972e+00 | -8.74688953e+00 -4.68675476e+00 -4.24784972e+00 23 3.52932967e+00 8.99694201e+00 2.45311294e+00 | 3.52932967e+00 8.99694201e+00 2.45311294e+00 24 1.67343908e-01 -4.73722934e-01 -1.20472976e+00 | 1.67343908e-01 -4.73722934e-01 -1.20472976e+00 25 1.30021263e+00 -4.72533948e-01 2.48250887e+00 | 1.30021263e+00 -4.72533948e-01 2.48250887e+00 26 4.33066528e-01 4.67619556e-01 3.27997885e-01 | 4.33066528e-01 4.67619556e-01 3.27997885e-01 27 -2.29716521e+00 -1.95689452e+00 1.43285763e+00 | -2.29716521e+00 -1.95689452e+00 1.43285763e+00 28 -2.26409906e+00 2.27094697e+00 1.81946347e+00 | -2.26409906e+00 2.27094697e+00 1.81946347e+00 29 1.72645164e+00 -2.37531637e+00 -1.58734992e+00 | 1.72645164e+00 -2.37531637e+00 -1.58734992e+00 30 7.15839799e+00 -3.80517385e+00 3.71476666e+00 | 7.15839799e+00 -3.80517385e+00 3.71476666e+00 31 -5.03686994e+00 5.70887358e+00 -6.14739086e+00 | -5.03686994e+00 5.70887358e+00 -6.14739086e+00 32 -3.17350082e+00 -2.58779278e+00 -3.94436968e+00 | -3.17350082e+00 -2.58779278e+00 -3.94436968e+00 33 4.76871707e+00 2.07648038e+00 -8.20267041e+00 | 4.76871707e+00 2.07648038e+00 -8.20267041e+00 34 1.54038727e+01 -1.35864386e+01 1.00621019e+01 | 1.54038727e+01 -1.35864386e+01 1.00621019e+01 35 6.76010968e+00 -5.31612161e+00 3.48674764e+00 | 6.76010968e+00 -5.31612161e+00 3.48674764e+00 36 1.03385473e+00 -6.34648141e+00 2.03962748e+00 | 1.03385473e+00 -6.34648141e+00 2.03962748e+00 37 -2.44668495e+00 -8.45936409e-01 5.75444927e+00 | -2.44668495e+00 -8.45936409e-01 5.75444927e+00 38 -9.03950509e+00 -2.94012173e-01 8.16349103e-01 | -9.03950509e+00 -2.94012173e-01 8.16349103e-01 39 3.67996624e+00 5.01954414e+00 6.03243473e+00 | 3.67996624e+00 5.01954414e+00 6.03243473e+00 40 -1.50282292e+00 -6.38260837e+00 -2.52790870e+00 | -1.50282292e+00 -6.38260837e+00 -2.52790870e+00 41 4.69061886e+00 9.21055789e-01 3.82003588e-01 | 4.69061886e+00 9.21055789e-01 3.82003588e-01 42 -3.64739135e+00 -1.44823982e+00 -1.64020503e+00 | -3.64739135e+00 -1.44823982e+00 -1.64020503e+00 43 4.03238796e+00 3.91853864e+00 4.90187877e+00 | 4.03238796e+00 3.91853864e+00 4.90187877e+00 44 -5.23542132e+00 -6.80501592e+00 -7.53774191e+00 | -5.23542132e+00 -6.80501592e+00 -7.53774191e+00 45 4.51162342e+00 7.49482918e+00 7.29511560e+00 | 4.51162342e+00 7.49482918e+00 7.29511560e+00 46 9.50899931e-01 -7.09195629e-01 -5.93008136e+00 | 9.50899931e-01 -7.09195629e-01 -5.93008136e+00 47 3.36737632e+00 7.44192774e+00 7.16023311e+00 | 3.36737632e+00 7.44192774e+00 7.16023311e+00 48 -1.22360303e+00 5.51242958e-01 6.98570273e-02 | -1.22360303e+00 5.51242958e-01 6.98570273e-02 49 3.55216015e+00 -6.35796663e+00 -6.96483547e+00 | 3.55216015e+00 -6.35796663e+00 -6.96483547e+00 50 -2.91180481e+00 -6.80540687e-01 4.77827267e+00 | -2.91180481e+00 -6.80540687e-01 4.77827267e+00 51 2.92738119e+00 3.91286559e+00 3.33625787e+00 | 2.92738119e+00 3.91286559e+00 3.33625787e+00 52 -7.60506226e+00 5.44099729e+00 1.36772642e+00 | -7.60506226e+00 5.44099729e+00 1.36772642e+00 53 -3.64222474e-01 -2.45864676e+00 2.21849498e+00 | -3.64222474e-01 -2.45864676e+00 2.21849498e+00 54 -7.87079532e+00 -1.77011618e+00 -1.54797037e-01 | -7.87079532e+00 -1.77011618e+00 -1.54797037e-01 55 6.28814587e+00 6.40411279e+00 5.58912323e+00 | 6.28814587e+00 6.40411279e+00 5.58912323e+00 56 5.55690301e+00 6.92306000e-02 -3.70836758e+00 | 5.55690301e+00 6.92306000e-02 -3.70836758e+00 57 -6.67909852e+00 -4.28348123e+00 -6.12372813e-01 | -6.67909852e+00 -4.28348123e+00 -6.12372813e-01 58 1.38284872e+00 -5.66694942e+00 -8.54098500e-01 | 1.38284872e+00 -5.66694942e+00 -8.54098500e-01 59 4.92380855e+00 5.63781877e+00 5.10622142e+00 | 4.92380855e+00 5.63781877e+00 5.10622142e+00 60 -1.64414863e+00 -9.65151847e+00 -4.79210726e+00 | -1.64414863e+00 -9.65151847e+00 -4.79210726e+00 61 5.52917890e+00 6.79866652e+00 5.82500055e+00 | 5.52917890e+00 6.79866652e+00 5.82500055e+00 62 -4.59766194e+00 1.18461935e+00 -2.63377203e+00 | -4.59766194e+00 1.18461935e+00 -2.63377203e+00 63 3.71563026e+00 3.49021074e+00 2.54918465e+00 | 3.71563026e+00 3.49021074e+00 2.54918465e+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.