!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ZhouJohnsonWadley_2004NISTretabulation_CuAgAu__MO_318213562153_000 Supported species : Ag Au Cu random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ag (Configuration in file "config-Ag.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [36, 48, 6, 16, 13, 25, 2, 24, 62, 20, 59, 28, 23, 4, 61, 19, 3, 26, 29, 15, 9, 27, 41, 12, 7, 5, 17, 21, 11, 18, 35, 37, 53, 34, 33, 30, 0, 31, 43, 52, 60, 22, 55, 38, 56, 57, 58, 63, 1, 51, 54, 49, 39, 32, 50, 42, 44, 45, 46, 10, 40, 14, 8, 47] 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)) = 160.376506102 V(r_1,...,r_N) = 160.376506102 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 -5.22402105e+00 -3.55411105e+00 -4.50354779e+00 | -5.22402105e+00 -3.55411105e+00 -4.50354779e+00 1 -1.20066534e+01 -3.52038754e+01 2.60134967e+01 | -1.20066534e+01 -3.52038754e+01 2.60134967e+01 2 -2.16945611e+00 1.31783979e+01 -4.54201172e+01 | -2.16945611e+00 1.31783979e+01 -4.54201172e+01 3 1.67935450e+01 2.29032250e+01 1.78422313e+01 | 1.67935450e+01 2.29032250e+01 1.78422313e+01 4 -1.66052244e+00 -6.83805086e+00 -4.67011894e+00 | -1.66052244e+00 -6.83805086e+00 -4.67011894e+00 5 7.98149573e+00 7.14250745e+00 4.49296419e-01 | 7.98149573e+00 7.14250745e+00 4.49296419e-01 6 -4.05254948e+00 -2.55416324e+00 -3.21803369e+00 | -4.05254948e+00 -2.55416324e+00 -3.21803369e+00 7 -3.34139463e+01 8.78141994e+01 -5.22789576e+01 | -3.34139463e+01 8.78141994e+01 -5.22789576e+01 8 -5.80121714e+00 -1.48487553e+00 -5.39899918e+00 | -5.80121714e+00 -1.48487553e+00 -5.39899918e+00 9 -1.43947882e+01 1.05948944e+01 -6.73894413e+00 | -1.43947882e+01 1.05948944e+01 -6.73894413e+00 10 -1.22813553e+01 -1.19987248e+01 -1.13531135e+01 | -1.22813553e+01 -1.19987248e+01 -1.13531135e+01 11 1.33664461e+01 1.35768005e+01 9.38350791e+00 | 1.33664461e+01 1.35768005e+01 9.38350791e+00 12 1.30252995e+01 -1.76077510e+01 1.03118669e+01 | 1.30252995e+01 -1.76077510e+01 1.03118669e+01 13 4.14933614e+01 -4.91947197e+00 -3.12549967e+01 | 4.14933614e+01 -4.91947197e+00 -3.12549967e+01 14 -2.21546951e+00 -1.64192315e+00 -4.29623435e+00 | -2.21546951e+00 -1.64192315e+00 -4.29623435e+00 15 1.92415850e+00 1.38139075e+00 6.03771722e+00 | 1.92415850e+00 1.38139075e+00 6.03771722e+00 16 -3.09923204e+01 -1.10752879e+01 -2.95147523e+01 | -3.09923204e+01 -1.10752879e+01 -2.95147523e+01 17 2.92072858e+01 7.45884308e+00 3.18909580e+01 | 2.92072858e+01 7.45884308e+00 3.18909580e+01 18 7.17224794e-01 1.82810146e+00 -3.01588493e+00 | 7.17224794e-01 1.82810146e+00 -3.01588493e+00 19 -6.09487679e+01 3.86673174e+01 -4.08949892e+01 | -6.09487679e+01 3.86673174e+01 -4.08949892e+01 20 -2.06186621e+01 -1.15708466e+01 -1.71262321e+01 | -2.06186621e+01 -1.15708466e+01 -1.71262321e+01 21 2.70402394e+01 1.91243915e+01 9.45011030e+00 | 2.70402394e+01 1.91243915e+01 9.45011030e+00 22 -6.96646588e+00 -1.11905342e+01 -1.98564342e+01 | -6.96646588e+00 -1.11905342e+01 -1.98564342e+01 23 7.28128643e+00 1.10085079e+01 2.03761115e+01 | 7.28128643e+00 1.10085079e+01 2.03761115e+01 24 -5.24063063e+00 -4.65259403e+00 -5.56403862e+00 | -5.24063063e+00 -4.65259403e+00 -5.56403862e+00 25 -1.61526304e+01 2.09420154e+01 -1.03509032e+01 | -1.61526304e+01 2.09420154e+01 -1.03509032e+01 26 -6.20421526e+00 9.63733585e-01 -7.37028057e+00 | -6.20421526e+00 9.63733585e-01 -7.37028057e+00 27 6.93550714e+00 3.37977536e+00 5.18891517e+00 | 6.93550714e+00 3.37977536e+00 5.18891517e+00 28 1.74703638e+01 -2.48250103e+01 1.39213423e+01 | 1.74703638e+01 -2.48250103e+01 1.39213423e+01 29 5.41794181e+00 4.69900789e+00 2.55204492e+00 | 5.41794181e+00 4.69900789e+00 2.55204492e+00 30 5.98872679e+01 -3.58036795e+01 3.78594106e+01 | 5.98872679e+01 -3.58036795e+01 3.78594106e+01 31 -2.64215176e+01 1.16612058e+01 -1.43902035e+01 | -2.64215176e+01 1.16612058e+01 -1.43902035e+01 32 -6.31232671e+00 -4.00524961e-01 -1.55813223e+00 | -6.31232671e+00 -4.00524961e-01 -1.55813223e+00 33 -1.11622590e+01 9.55559515e+00 -4.79136023e+00 | -1.11622590e+01 9.55559515e+00 -4.79136023e+00 34 3.63136664e+01 -9.56449798e+01 5.14125513e+01 | 3.63136664e+01 -9.56449798e+01 5.14125513e+01 35 -4.88249984e-01 -7.38797126e+00 6.27953572e+00 | -4.88249984e-01 -7.38797126e+00 6.27953572e+00 36 1.07997898e+01 -9.56208743e+00 8.44141323e+00 | 1.07997898e+01 -9.56208743e+00 8.44141323e+00 37 -7.73952541e+00 -6.88744289e+00 3.44772112e+00 | -7.73952541e+00 -6.88744289e+00 3.44772112e+00 38 -1.33852794e+01 -7.65795154e+00 -1.00297173e+01 | -1.33852794e+01 -7.65795154e+00 -1.00297173e+01 39 -1.17618549e+01 -1.26458155e+01 2.52675917e+01 | -1.17618549e+01 -1.26458155e+01 2.52675917e+01 40 1.43745552e+00 -2.13240092e+00 2.26642677e+00 | 1.43745552e+00 -2.13240092e+00 2.26642677e+00 41 -2.98468767e+01 4.73717999e+01 -3.11624899e+01 | -2.98468767e+01 4.73717999e+01 -3.11624899e+01 42 -3.75922400e+01 4.38358760e+00 2.83825172e+01 | -3.75922400e+01 4.38358760e+00 2.83825172e+01 43 3.91175552e+00 6.84387946e+00 6.38829881e+00 | 3.91175552e+00 6.84387946e+00 6.38829881e+00 44 3.14794037e+01 -5.26752015e+01 2.57758236e+01 | 3.14794037e+01 -5.26752015e+01 2.57758236e+01 45 1.09143404e-01 1.06160500e+00 6.60587695e-01 | 1.09143404e-01 1.06160500e+00 6.60587695e-01 46 4.68852392e+00 8.78519256e+00 1.08787710e+00 | 4.68852392e+00 8.78519256e+00 1.08787710e+00 47 2.27944227e+01 -1.98048367e+01 1.88171455e+00 | 2.27944227e+01 -1.98048367e+01 1.88171455e+00 48 -1.66677939e+01 -1.29559435e+01 -9.14634515e+00 | -1.66677939e+01 -1.29559435e+01 -9.14634515e+00 49 9.07378102e+00 1.69622403e+01 1.38611327e+01 | 9.07378102e+00 1.69622403e+01 1.38611327e+01 50 -1.53292193e+01 -1.76375529e+01 -1.80349044e+01 | -1.53292193e+01 -1.76375529e+01 -1.80349044e+01 51 1.28068845e+01 1.97387038e+01 1.83183798e+01 | 1.28068845e+01 1.97387038e+01 1.83183798e+01 52 1.99348093e+01 2.41795375e+01 -1.41318872e+01 | 1.99348093e+01 2.41795375e+01 -1.41318872e+01 53 -1.91449476e+01 2.30998560e+01 8.69246713e-01 | -1.91449476e+01 2.30998560e+01 8.69246713e-01 54 -3.90633349e-01 1.34493005e+00 1.20177811e+00 | -3.90633349e-01 1.34493005e+00 1.20177811e+00 55 2.09821998e-01 -6.34984402e-01 -7.12750206e-01 | 2.09821998e-01 -6.34984402e-01 -7.12750206e-01 56 1.71392259e+00 -1.66045943e+00 -7.77320037e-01 | 1.71392259e+00 -1.66045943e+00 -7.77320037e-01 57 2.97207584e+01 -4.50349773e+01 -5.37246959e+01 | 2.97207584e+01 -4.50349773e+01 -5.37246959e+01 58 2.88588871e+01 -9.83841023e+00 1.70494347e+01 | 2.88588871e+01 -9.83841023e+00 1.70494347e+01 59 -9.12731566e-01 -7.31171096e-01 3.78055690e-01 | -9.12731566e-01 -7.31171096e-01 3.78055690e-01 60 -2.35978860e+00 -5.46133605e+00 -1.20395956e+01 | -2.35978860e+00 -5.46133605e+00 -1.20395956e+01 61 3.18419695e+00 6.37335635e+00 1.29444025e+01 | 3.18419695e+00 6.37335635e+00 1.29444025e+01 62 -2.62194947e+01 4.83390781e+01 5.67220841e+01 | -2.62194947e+01 4.83390781e+01 5.67220841e+01 63 4.99764096e-01 -6.88729401e-01 -5.87602766e-01 | 4.99764096e-01 -6.88729401e-01 -5.87602766e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Au (Configuration in file "config-Au.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [4, 11, 54, 25, 0, 53, 41, 42, 27, 39, 32, 1, 37, 61, 18, 24, 59, 60, 14, 55, 56, 23, 49, 21, 15, 3, 29, 8, 57, 26, 40, 45, 10, 47, 36, 50, 34, 12, 62, 9, 30, 6, 7, 48, 51, 31, 52, 33, 43, 22, 35, 44, 46, 5, 2, 19, 20, 28, 63, 16, 17, 13, 38, 58] 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)) = 193.961454976 V(r_1,...,r_N) = 193.961454976 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 -3.20580481e+00 -2.11097725e+00 -4.26320339e+00 | -3.20580481e+00 -2.11097725e+00 -4.26320339e+00 1 -4.73756952e+00 -2.16524446e+01 1.67367015e+01 | -4.73756952e+00 -2.16524446e+01 1.67367015e+01 2 1.25666686e+01 1.73071474e+01 -1.92905742e+01 | 1.25666686e+01 1.73071474e+01 -1.92905742e+01 3 3.10874560e-01 -7.22343000e+00 -2.35337586e+00 | 3.10874560e-01 -7.22343000e+00 -2.35337586e+00 4 -1.49516087e-01 -7.59134372e+00 -2.77755123e+00 | -1.49516087e-01 -7.59134372e+00 -2.77755123e+00 5 1.44781790e+01 -5.55910798e-01 -5.51755519e+00 | 1.44781790e+01 -5.55910798e-01 -5.51755519e+00 6 -1.08494505e+01 2.48925053e+00 -1.96723482e+00 | -1.08494505e+01 2.48925053e+00 -1.96723482e+00 7 -2.16915618e+00 8.62255980e+00 -5.66472394e+00 | -2.16915618e+00 8.62255980e+00 -5.66472394e+00 8 -1.39251753e+01 -1.05488871e+01 -4.97508151e+00 | -1.39251753e+01 -1.05488871e+01 -4.97508151e+00 9 4.48731021e+00 -1.74643089e+01 1.63348900e+01 | 4.48731021e+00 -1.74643089e+01 1.63348900e+01 10 1.73550476e+01 2.05116519e+01 -2.30266286e+01 | 1.73550476e+01 2.05116519e+01 -2.30266286e+01 11 -7.32617367e-01 3.08051655e-02 7.90362956e-01 | -7.32617367e-01 3.08051655e-02 7.90362956e-01 12 -8.42774569e+01 -5.72848852e+01 -7.74669726e+01 | -8.42774569e+01 -5.72848852e+01 -7.74669726e+01 13 8.62646238e+01 5.52796076e+01 7.83562458e+01 | 8.62646238e+01 5.52796076e+01 7.83562458e+01 14 -8.14431392e+00 8.69737586e+00 9.43885168e+00 | -8.14431392e+00 8.69737586e+00 9.43885168e+00 15 -1.14587011e+01 9.81468496e+00 -4.07801710e+01 | -1.14587011e+01 9.81468496e+00 -4.07801710e+01 16 6.43700815e-01 -1.38749357e-01 8.74239445e-01 | 6.43700815e-01 -1.38749357e-01 8.74239445e-01 17 -4.02251943e+00 9.63095515e+00 -9.10835887e+00 | -4.02251943e+00 9.63095515e+00 -9.10835887e+00 18 -2.18358518e+01 -8.79899232e+00 -2.74937485e+01 | -2.18358518e+01 -8.79899232e+00 -2.74937485e+01 19 -1.29943287e+01 4.50125006e+01 -7.25138084e+00 | -1.29943287e+01 4.50125006e+01 -7.25138084e+00 20 -1.27518501e+01 -2.30584886e+01 -6.47385779e+00 | -1.27518501e+01 -2.30584886e+01 -6.47385779e+00 21 2.55684243e+01 2.15106558e+00 1.04792640e+01 | 2.55684243e+01 2.15106558e+00 1.04792640e+01 22 -4.12783552e+00 -1.52876422e+00 1.47043768e+00 | -4.12783552e+00 -1.52876422e+00 1.47043768e+00 23 8.51757190e-02 3.12438324e+00 -4.21016372e-01 | 8.51757190e-02 3.12438324e+00 -4.21016372e-01 24 4.52155635e+00 4.70472897e+00 -5.10496474e+00 | 4.52155635e+00 4.70472897e+00 -5.10496474e+00 25 1.04548085e+01 -2.03301442e+01 -4.59648283e+00 | 1.04548085e+01 -2.03301442e+01 -4.59648283e+00 26 -4.34749760e+01 -2.25107415e+01 -3.79054937e+01 | -4.34749760e+01 -2.25107415e+01 -3.79054937e+01 27 4.31047596e+01 2.21354252e+01 3.82985107e+01 | 4.31047596e+01 2.21354252e+01 3.82985107e+01 28 -4.54123594e+00 -9.24011205e+00 -1.24433658e+01 | -4.54123594e+00 -9.24011205e+00 -1.24433658e+01 29 1.40941441e+01 9.46020228e+00 7.12581935e+00 | 1.40941441e+01 9.46020228e+00 7.12581935e+00 30 2.10550739e+01 -1.24972841e+01 3.20836767e+01 | 2.10550739e+01 -1.24972841e+01 3.20836767e+01 31 -9.48733794e+00 2.12632592e+01 -1.23731637e+01 | -9.48733794e+00 2.12632592e+01 -1.23731637e+01 32 1.09981438e+00 9.93435648e-01 -1.38345480e-01 | 1.09981438e+00 9.93435648e-01 -1.38345480e-01 33 -4.56832554e+00 -3.88235864e+01 5.04426187e+01 | -4.56832554e+00 -3.88235864e+01 5.04426187e+01 34 -1.81923601e+00 3.46227302e+01 -3.12072736e+01 | -1.81923601e+00 3.46227302e+01 -3.12072736e+01 35 -3.26693311e+01 -2.41380075e+01 2.62830856e+01 | -3.26693311e+01 -2.41380075e+01 2.62830856e+01 36 -7.54926890e-01 -2.53875992e+00 -2.96212065e-01 | -7.54926890e-01 -2.53875992e+00 -2.96212065e-01 37 -2.95135326e+00 -5.84386404e-01 1.79310338e+00 | -2.95135326e+00 -5.84386404e-01 1.79310338e+00 38 -1.60691555e+02 -1.39807463e+02 -2.92097067e+02 | -1.60691555e+02 -1.39807463e+02 -2.92097067e+02 39 1.58731412e+02 1.40377830e+02 2.93051661e+02 | 1.58731412e+02 1.40377830e+02 2.93051661e+02 40 -3.44290107e-02 1.06312132e+00 -2.82040388e-01 | -3.44290107e-02 1.06312132e+00 -2.82040388e-01 41 -3.28697153e+00 -3.93762345e+00 2.30032243e+00 | -3.28697153e+00 -3.93762345e+00 2.30032243e+00 42 -1.13101815e+01 -6.73381214e+01 4.15690928e+00 | -1.13101815e+01 -6.73381214e+01 4.15690928e+00 43 2.62046416e+01 5.37688202e+01 3.73043451e+01 | 2.62046416e+01 5.37688202e+01 3.73043451e+01 44 -1.00463843e+01 -1.09681402e+01 -1.02474417e+01 | -1.00463843e+01 -1.09681402e+01 -1.02474417e+01 45 9.62871831e+00 1.13849001e+01 9.90574203e+00 | 9.62871831e+00 1.13849001e+01 9.90574203e+00 46 -6.24710086e+01 -8.95784529e+00 -2.66341799e+01 | -6.24710086e+01 -8.95784529e+00 -2.66341799e+01 47 6.68793331e+01 5.73875078e+00 2.90769174e+01 | 6.68793331e+01 5.73875078e+00 2.90769174e+01 48 -3.28097788e+00 3.54345973e+00 2.96923946e+00 | -3.28097788e+00 3.54345973e+00 2.96923946e+00 49 -1.53585934e+01 4.23167438e+00 -2.20626042e+01 | -1.53585934e+01 4.23167438e+00 -2.20626042e+01 50 -1.19830843e+01 1.15117113e+01 1.05660017e+01 | -1.19830843e+01 1.15117113e+01 1.05660017e+01 51 -3.32124345e-01 1.17124526e+00 1.49476826e+00 | -3.32124345e-01 1.17124526e+00 1.49476826e+00 52 -3.94142619e+00 -4.28101478e+01 -5.26155036e+00 | -3.94142619e+00 -4.28101478e+01 -5.26155036e+00 53 1.41459436e+01 3.93418006e+01 3.43651805e+01 | 1.41459436e+01 3.93418006e+01 3.43651805e+01 54 1.23328806e+00 2.46410582e-01 -2.09324322e-01 | 1.23328806e+00 2.46410582e-01 -2.09324322e-01 55 4.33505095e-01 -1.25698821e+00 -1.32086069e+00 | 4.33505095e-01 -1.25698821e+00 -1.32086069e+00 56 1.35331201e+01 -4.27155685e+00 -4.68699048e+01 | 1.35331201e+01 -4.27155685e+00 -4.68699048e+01 57 1.96937011e+01 2.09978432e+01 1.75171589e+01 | 1.96937011e+01 2.09978432e+01 1.75171589e+01 58 8.86183938e+00 -1.07831246e+01 1.67063988e+01 | 8.86183938e+00 -1.07831246e+01 1.67063988e+01 59 -2.36992438e-01 -4.29840819e-01 9.63686401e-01 | -2.36992438e-01 -4.29840819e-01 9.63686401e-01 60 -7.99640362e+00 -3.21061327e-01 -1.31795429e+00 | -7.99640362e+00 -3.21061327e-01 -1.31795429e+00 61 9.31150844e+00 6.81228336e+00 1.14211540e+00 | 9.31150844e+00 6.81228336e+00 1.14211540e+00 62 1.74283317e+00 4.83814695e+00 -1.95388949e+00 | 1.74283317e+00 4.83814695e+00 -1.95388949e+00 63 1.28996749e-01 -1.37765037e+00 -8.74700945e-01 | 1.28996749e-01 -1.37765037e+00 -8.74700945e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [16, 31, 32, 46, 17, 22, 50, 24, 15, 44, 30, 43, 62, 61, 54, 8, 0, 4, 63, 53, 35, 59, 5, 27, 7, 34, 45, 23, 33, 49, 10, 1, 2, 28, 25, 20, 48, 39, 56, 37, 51, 47, 60, 11, 9, 26, 3, 41, 36, 29, 6, 40, 55, 19, 14, 52, 38, 58, 57, 21, 42, 13, 12, 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)) = 32.5704797833 V(r_1,...,r_N) = 32.5704797833 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 -1.11984301e+00 -2.94030982e+00 -9.87146430e-01 | -1.11984301e+00 -2.94030982e+00 -9.87146430e-01 1 -2.88795351e+01 -2.44012597e+00 3.80660400e+01 | -2.88795351e+01 -2.44012597e+00 3.80660400e+01 2 3.67015488e+01 4.81892070e+00 -4.20188632e+01 | 3.67015488e+01 4.81892070e+00 -4.20188632e+01 3 5.69617290e+00 -1.35848219e+01 -1.29649354e+01 | 5.69617290e+00 -1.35848219e+01 -1.29649354e+01 4 -7.88556544e+00 -5.04481558e+00 -3.65696766e+00 | -7.88556544e+00 -5.04481558e+00 -3.65696766e+00 5 5.78214543e+00 6.42078996e+00 2.44793399e+00 | 5.78214543e+00 6.42078996e+00 2.44793399e+00 6 -8.93588011e+00 -1.85646941e+00 2.87279866e+00 | -8.93588011e+00 -1.85646941e+00 2.87279866e+00 7 9.43893606e-01 4.49526356e+00 3.18921513e-01 | 9.43893606e-01 4.49526356e+00 3.18921513e-01 8 -1.57281932e-01 9.43977678e-01 1.20591266e+00 | -1.57281932e-01 9.43977678e-01 1.20591266e+00 9 -1.32220377e+01 -2.96584968e+01 7.96836560e+00 | -1.32220377e+01 -2.96584968e+01 7.96836560e+00 10 1.68660761e+01 2.77829642e+01 -1.94654744e+01 | 1.68660761e+01 2.77829642e+01 -1.94654744e+01 11 -1.36677686e+00 -8.56508168e-02 7.83550351e-01 | -1.36677686e+00 -8.56508168e-02 7.83550351e-01 12 4.70607651e+00 -5.57754434e+00 5.33539677e+00 | 4.70607651e+00 -5.57754434e+00 5.33539677e+00 13 7.73047781e+00 -4.93293314e+00 -3.27437967e+00 | 7.73047781e+00 -4.93293314e+00 -3.27437967e+00 14 -7.34261500e+00 9.52161908e+00 6.49524666e+00 | -7.34261500e+00 9.52161908e+00 6.49524666e+00 15 -9.36853656e+00 -2.69213528e+00 -7.01130404e-01 | -9.36853656e+00 -2.69213528e+00 -7.01130404e-01 16 -4.26192983e-01 -2.04581569e+00 -1.35359380e+00 | -4.26192983e-01 -2.04581569e+00 -1.35359380e+00 17 1.95845135e+01 -1.87919802e+01 -7.07453141e+00 | 1.95845135e+01 -1.87919802e+01 -7.07453141e+00 18 1.03575071e+01 8.40294459e+00 -6.89388742e+00 | 1.03575071e+01 8.40294459e+00 -6.89388742e+00 19 -1.20900753e+01 5.48080848e-01 -7.41341018e+00 | -1.20900753e+01 5.48080848e-01 -7.41341018e+00 20 -7.76274304e+00 1.12694114e+01 1.17694314e+01 | -7.76274304e+00 1.12694114e+01 1.17694314e+01 21 2.64911782e-01 1.45542459e+00 1.75787748e+00 | 2.64911782e-01 1.45542459e+00 1.75787748e+00 22 -2.77008788e+01 1.14901250e+01 1.75692673e+01 | -2.77008788e+01 1.14901250e+01 1.75692673e+01 23 -1.44789091e+01 1.45200443e+01 3.56537678e+00 | -1.44789091e+01 1.45200443e+01 3.56537678e+00 24 2.21002957e+00 1.01242619e+00 -1.04407177e+00 | 2.21002957e+00 1.01242619e+00 -1.04407177e+00 25 -3.44547801e+00 -1.17753792e+01 1.01259529e+01 | -3.44547801e+00 -1.17753792e+01 1.01259529e+01 26 2.38923347e+00 1.32496332e+01 -1.75874991e+01 | 2.38923347e+00 1.32496332e+01 -1.75874991e+01 27 -8.40728796e-01 -8.34297665e-01 3.42610737e-01 | -8.40728796e-01 -8.34297665e-01 3.42610737e-01 28 -8.79582726e+00 -6.06745804e+00 -1.09327031e+01 | -8.79582726e+00 -6.06745804e+00 -1.09327031e+01 29 1.53170472e+01 1.26650583e+01 1.39273619e+01 | 1.53170472e+01 1.26650583e+01 1.39273619e+01 30 -2.67507565e+00 -6.10453032e+00 1.19286950e+00 | -2.67507565e+00 -6.10453032e+00 1.19286950e+00 31 1.24894073e+01 5.24308292e+00 8.52899947e+00 | 1.24894073e+01 5.24308292e+00 8.52899947e+00 32 -2.13329310e-01 -7.76961015e-01 -1.87283758e+00 | -2.13329310e-01 -7.76961015e-01 -1.87283758e+00 33 7.59683309e+00 -1.49464916e+01 -8.40590108e+00 | 7.59683309e+00 -1.49464916e+01 -8.40590108e+00 34 4.17423892e+00 -2.29613753e+00 2.89869856e+00 | 4.17423892e+00 -2.29613753e+00 2.89869856e+00 35 -3.62100084e+01 -1.85861744e+01 1.30403669e+01 | -3.62100084e+01 -1.85861744e+01 1.30403669e+01 36 2.08078165e-01 1.42680933e+00 -4.68323247e-01 | 2.08078165e-01 1.42680933e+00 -4.68323247e-01 37 -1.48028925e-01 -6.19528630e-02 -8.10182159e-01 | -1.48028925e-01 -6.19528630e-02 -8.10182159e-01 38 -1.74117724e+01 1.44419235e+01 -1.37730649e+01 | -1.74117724e+01 1.44419235e+01 -1.37730649e+01 39 1.11364112e+01 1.56118350e+00 2.38168797e+01 | 1.11364112e+01 1.56118350e+00 2.38168797e+01 40 5.71842877e-01 -3.40894733e-01 1.92616131e+00 | 5.71842877e-01 -3.40894733e-01 1.92616131e+00 41 1.68381062e+00 -1.88496325e+00 -9.96122282e-01 | 1.68381062e+00 -1.88496325e+00 -9.96122282e-01 42 -3.87994960e+00 -1.61435079e+00 7.41059477e+00 | -3.87994960e+00 -1.61435079e+00 7.41059477e+00 43 -1.14716256e+00 9.15893083e-02 5.21299041e-02 | -1.14716256e+00 9.15893083e-02 5.21299041e-02 44 -1.36779717e+01 -2.15266309e+01 -6.14972098e+00 | -1.36779717e+01 -2.15266309e+01 -6.14972098e+00 45 1.26321367e+01 2.26909245e+01 5.08949768e+00 | 1.26321367e+01 2.26909245e+01 5.08949768e+00 46 1.29851197e+01 -1.22101331e+01 1.12251101e+01 | 1.29851197e+01 -1.22101331e+01 1.12251101e+01 47 -9.60005995e-01 -2.89029044e-01 -3.01035269e-01 | -9.60005995e-01 -2.89029044e-01 -3.01035269e-01 48 1.34617456e+00 -2.59683157e-03 1.13815438e-01 | 1.34617456e+00 -2.59683157e-03 1.13815438e-01 49 -6.87155140e+00 1.00363075e+01 -1.55132290e+01 | -6.87155140e+00 1.00363075e+01 -1.55132290e+01 50 1.40734983e+01 -1.39186872e+01 -3.51821388e+00 | 1.40734983e+01 -1.39186872e+01 -3.51821388e+00 51 -7.53595707e-01 -4.10234718e-01 -8.94916953e-01 | -7.53595707e-01 -4.10234718e-01 -8.94916953e-01 52 -3.68756921e+00 -2.46420018e+01 8.34568801e+00 | -3.68756921e+00 -2.46420018e+01 8.34568801e+00 53 1.36372792e+01 1.23111825e+01 3.25232995e+00 | 1.36372792e+01 1.23111825e+01 3.25232995e+00 54 -7.96322384e+00 -2.99508807e+00 -6.52927668e-01 | -7.96322384e+00 -2.99508807e+00 -6.52927668e-01 55 6.07075766e+00 4.28127299e+00 2.31388504e+00 | 6.07075766e+00 4.28127299e+00 2.31388504e+00 56 2.13282590e+01 3.20530124e+01 -2.33106192e+01 | 2.13282590e+01 3.20530124e+01 -2.33106192e+01 57 -7.85602241e+00 5.68752183e+00 -7.13962394e+00 | -7.85602241e+00 5.68752183e+00 -7.13962394e+00 58 -1.19337781e+01 -1.02096467e+01 -3.11739653e+00 | -1.19337781e+01 -1.02096467e+01 -3.11739653e+00 59 1.23030976e+01 1.15595005e+01 2.44536265e+00 | 1.23030976e+01 1.15595005e+01 2.44536265e+00 60 5.73881540e+00 -1.02769613e+01 3.84389426e+00 | 5.73881540e+00 -1.02769613e+01 3.84389426e+00 61 1.99659543e+00 2.23048334e+00 1.87205451e+00 | 1.99659543e+00 2.23048334e+00 1.87205451e+00 62 -4.58418514e+01 -6.58324516e+01 -4.66652758e+01 | -4.58418514e+01 -6.58324516e+01 -4.66652758e+01 63 4.65278118e+01 6.50426739e+01 4.70376018e+01 | 4.65278118e+01 6.50426739e+01 4.70376018e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ag Au Cu (Configuration in file "config-AgAuCu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [21, 49, 36, 62, 19, 25, 30, 56, 16, 12, 59, 41, 9, 14, 13, 46, 8, 57, 58, 4, 53, 0, 33, 61, 27, 5, 63, 24, 31, 42, 6, 28, 45, 22, 44, 39, 2, 55, 48, 35, 51, 11, 29, 50, 34, 32, 15, 60, 38, 1, 43, 40, 52, 20, 54, 37, 7, 17, 18, 10, 47, 23, 3, 26] 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)) = 215.413785353 V(r_1,...,r_N) = 215.413785353 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 3.38943686e-01 4.42348092e-01 2.44819538e-01 | 3.38943686e-01 4.42348092e-01 2.44819538e-01 1 4.84663150e+00 3.33847099e+01 -3.75363256e+01 | 4.84663150e+00 3.33847099e+01 -3.75363256e+01 2 2.07161122e+00 2.99337752e+00 -5.23744172e+00 | 2.07161122e+00 2.99337752e+00 -5.23744172e+00 3 -3.08181652e+01 3.02333181e+01 -4.91009257e+01 | -3.08181652e+01 3.02333181e+01 -4.91009257e+01 4 2.32272454e+01 -5.90413752e+01 2.45954188e+01 | 2.32272454e+01 -5.90413752e+01 2.45954188e+01 5 -9.28008526e+00 -1.18659250e+01 8.33927950e+00 | -9.28008526e+00 -1.18659250e+01 8.33927950e+00 6 -3.42907334e+01 1.96206131e+01 1.49004466e+01 | -3.42907334e+01 1.96206131e+01 1.49004466e+01 7 -2.86050895e+00 -4.11602033e-01 -5.56263026e-01 | -2.86050895e+00 -4.11602033e-01 -5.56263026e-01 8 -8.43932818e-01 1.50647258e-01 -1.96623207e-01 | -8.43932818e-01 1.50647258e-01 -1.96623207e-01 9 9.42679441e+00 -1.53845585e+01 -1.20477243e+01 | 9.42679441e+00 -1.53845585e+01 -1.20477243e+01 10 -5.36755121e+00 -3.04542528e+00 -4.30361876e+00 | -5.36755121e+00 -3.04542528e+00 -4.30361876e+00 11 6.06012533e+01 -4.12889149e+01 -6.30187269e+01 | 6.06012533e+01 -4.12889149e+01 -6.30187269e+01 12 -2.64302122e-02 -5.59524100e-01 7.20055278e-01 | -2.64302122e-02 -5.59524100e-01 7.20055278e-01 13 -6.07223442e-02 9.00774307e-01 5.07327524e-01 | -6.07223442e-02 9.00774307e-01 5.07327524e-01 14 3.67125298e+01 -7.53286579e+00 5.44484381e+01 | 3.67125298e+01 -7.53286579e+00 5.44484381e+01 15 1.32296605e+01 -3.32816298e+00 -2.04560477e+01 | 1.32296605e+01 -3.32816298e+00 -2.04560477e+01 16 2.45211134e-02 -8.45773528e-01 -4.21622697e-01 | 2.45211134e-02 -8.45773528e-01 -4.21622697e-01 17 8.10729775e+01 -6.97551637e+01 -7.35171184e+01 | 8.10729775e+01 -6.97551637e+01 -7.35171184e+01 18 8.15632894e-01 3.55960742e-01 -4.18132881e-01 | 8.15632894e-01 3.55960742e-01 -4.18132881e-01 19 -3.88517135e+00 1.69039318e+00 -3.79493952e+00 | -3.88517135e+00 1.69039318e+00 -3.79493952e+00 20 5.71982919e+00 -1.85081867e+00 -9.56716256e-01 | 5.71982919e+00 -1.85081867e+00 -9.56716256e-01 21 -1.91647566e+00 1.23048623e+00 -8.80733842e-01 | -1.91647566e+00 1.23048623e+00 -8.80733842e-01 22 -8.62710701e+01 7.48351349e+01 7.37675653e+01 | -8.62710701e+01 7.48351349e+01 7.37675653e+01 23 -3.69966363e+01 6.55879619e+01 -5.84934784e+01 | -3.69966363e+01 6.55879619e+01 -5.84934784e+01 24 -7.92632483e+00 -1.57620410e+01 -1.10875694e+01 | -7.92632483e+00 -1.57620410e+01 -1.10875694e+01 25 9.38476582e+00 1.75863292e+01 9.49203215e+00 | 9.38476582e+00 1.75863292e+01 9.49203215e+00 26 -2.26786217e+00 -2.03460597e+00 -2.53348781e+00 | -2.26786217e+00 -2.03460597e+00 -2.53348781e+00 27 1.25366512e+00 1.18302077e+00 3.64055030e+00 | 1.25366512e+00 1.18302077e+00 3.64055030e+00 28 -5.42631066e+01 4.40857669e+01 6.69331437e+01 | -5.42631066e+01 4.40857669e+01 6.69331437e+01 29 4.82248978e+01 -3.08390143e+01 -2.98331961e+01 | 4.82248978e+01 -3.08390143e+01 -2.98331961e+01 30 -6.05732612e+01 -1.20133844e+02 -7.88085489e+01 | -6.05732612e+01 -1.20133844e+02 -7.88085489e+01 31 6.18345153e+01 1.19061418e+02 8.10794576e+01 | 6.18345153e+01 1.19061418e+02 8.10794576e+01 32 -1.77701573e+01 -2.28782224e+01 1.59584049e+00 | -1.77701573e+01 -2.28782224e+01 1.59584049e+00 33 1.68388157e+01 2.34850598e+01 -2.59918578e+00 | 1.68388157e+01 2.34850598e+01 -2.59918578e+00 34 -7.13962373e-01 1.50863533e+00 3.99111259e+00 | -7.13962373e-01 1.50863533e+00 3.99111259e+00 35 1.79018740e+01 -1.66085591e+01 -1.39524762e+01 | 1.79018740e+01 -1.66085591e+01 -1.39524762e+01 36 1.01609049e+00 2.46631054e-01 1.23209673e+00 | 1.01609049e+00 2.46631054e-01 1.23209673e+00 37 -2.20821651e+00 -2.10264103e+00 7.72209532e-01 | -2.20821651e+00 -2.10264103e+00 7.72209532e-01 38 1.29679396e-01 -8.84725339e-01 -8.63393428e-01 | 1.29679396e-01 -8.84725339e-01 -8.63393428e-01 39 8.28379640e-01 2.77788382e-01 4.81647375e-01 | 8.28379640e-01 2.77788382e-01 4.81647375e-01 40 -2.87866410e+01 -1.59743928e+01 -2.06286316e+01 | -2.87866410e+01 -1.59743928e+01 -2.06286316e+01 41 2.17540742e+01 -2.31456097e+00 2.71844062e+01 | 2.17540742e+01 -2.31456097e+00 2.71844062e+01 42 6.08084679e+00 1.91991009e+01 -7.54811941e+00 | 6.08084679e+00 1.91991009e+01 -7.54811941e+00 43 7.19467396e+01 -4.99500466e+01 -4.70264902e+01 | 7.19467396e+01 -4.99500466e+01 -4.70264902e+01 44 8.63256368e-01 -3.52323867e-01 6.34292149e-01 | 8.63256368e-01 -3.52323867e-01 6.34292149e-01 45 -2.83811408e-01 3.36441019e-01 -2.68470326e-01 | -2.83811408e-01 3.36441019e-01 -2.68470326e-01 46 -4.24640569e+00 -1.93467582e+00 -4.22568578e+00 | -4.24640569e+00 -1.93467582e+00 -4.22568578e+00 47 6.45264006e+00 4.14638422e+00 2.46501903e+00 | 6.45264006e+00 4.14638422e+00 2.46501903e+00 48 -1.33316114e+00 2.79576018e-01 1.60263210e-01 | -1.33316114e+00 2.79576018e-01 1.60263210e-01 49 1.57021427e+00 -2.24658067e+00 -2.05160214e+00 | 1.57021427e+00 -2.24658067e+00 -2.05160214e+00 50 3.66817434e+01 -6.48533248e+01 5.87859485e+01 | 3.66817434e+01 -6.48533248e+01 5.87859485e+01 51 -6.43495306e+01 9.18701344e+01 -1.29355979e+02 | -6.43495306e+01 9.18701344e+01 -1.29355979e+02 52 -1.63363511e+01 1.50060847e+01 1.24577515e+01 | -1.63363511e+01 1.50060847e+01 1.24577515e+01 53 -1.24120558e+00 -1.02874520e+00 3.79009307e+00 | -1.24120558e+00 -1.02874520e+00 3.79009307e+00 54 -4.44504921e+01 -4.38797421e+00 -3.15511140e+01 | -4.44504921e+01 -4.38797421e+00 -3.15511140e+01 55 4.25347879e+01 9.05250559e+00 3.42789500e+01 | 4.25347879e+01 9.05250559e+00 3.42789500e+01 56 -1.02916106e+01 3.77309591e+00 2.23857282e+01 | -1.02916106e+01 3.77309591e+00 2.23857282e+01 57 -4.15988398e+00 3.72333835e+00 -6.61101901e-01 | -4.15988398e+00 3.72333835e+00 -6.61101901e-01 58 -4.65476637e+01 2.86775819e+01 3.14642323e+01 | -4.65476637e+01 2.86775819e+01 3.14642323e+01 59 -1.07087416e-01 -2.44280682e-01 1.27139541e-01 | -1.07087416e-01 -2.44280682e-01 1.27139541e-01 60 -6.70158686e+01 4.49907414e+01 4.80024526e+01 | -6.70158686e+01 4.49907414e+01 4.80024526e+01 61 -8.66582882e-01 -3.29386220e-01 -8.83595297e-01 | -8.66582882e-01 -3.29386220e-01 -8.83595297e-01 62 6.19049738e+01 -9.13345874e+01 1.23086914e+02 | 6.19049738e+01 -9.13345874e+01 1.23086914e+02 63 3.06707965e+00 1.18928359e+00 3.25045361e+00 | 3.06707965e+00 1.18928359e+00 3.25045361e+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.