!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BelandTammMu_2017_FeNiCr__MO_715003088863_000 Supported species : Cr Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [54, 20, 29, 23, 19, 24, 28, 50, 61, 51, 42, 35, 36, 32, 22, 25, 37, 18, 17, 4, 1, 63, 14, 3, 5, 15, 31, 43, 6, 2, 39, 26, 13, 46, 52, 11, 12, 16, 44, 30, 41, 40, 10, 27, 38, 57, 33, 59, 49, 48, 7, 9, 34, 62, 0, 60, 58, 45, 56, 47, 55, 8, 53, 21] 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)) = -60.70368243265883 V(r_1,...,r_N) = -60.70368243265882 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 -2.25991712e+00 -2.05795952e+00 -2.96537678e+00 | -2.25991712e+00 -2.05795952e+00 -2.96537678e+00 1 -5.60380904e-01 -4.57850391e+00 9.16231764e+00 | -5.60380904e-01 -4.57850391e+00 9.16231764e+00 2 1.95060166e+00 8.08094330e+00 -3.76717557e+00 | 1.95060166e+00 8.08094330e+00 -3.76717557e+00 3 -3.52657213e+00 1.09574322e+00 -5.59320122e+00 | -3.52657213e+00 1.09574322e+00 -5.59320122e+00 4 -6.98059742e-01 2.70837202e-01 -1.63931719e+00 | -6.98059742e-01 2.70837202e-01 -1.63931719e+00 5 3.67543071e+00 2.33891752e+00 -1.02222580e+00 | 3.67543071e+00 2.33891752e+00 -1.02222580e+00 6 7.74308805e-01 -6.04253275e-01 -9.09213406e-01 | 7.74308805e-01 -6.04253275e-01 -9.09213406e-01 7 -1.21512328e+01 3.33444161e+01 -1.94491050e+01 | -1.21512328e+01 3.33444161e+01 -1.94491050e+01 8 -7.58470824e-01 -7.13518296e-01 -1.91346597e+00 | -7.58470824e-01 -7.13518296e-01 -1.91346597e+00 9 -1.94121077e+00 2.77085839e+00 -1.38396367e-01 | -1.94121077e+00 2.77085839e+00 -1.38396367e-01 10 -4.59567497e-01 -4.47313503e-02 8.17070037e-01 | -4.59567497e-01 -4.47313503e-02 8.17070037e-01 11 5.04400448e-01 -1.48594529e+00 -1.73525680e+00 | 5.04400448e-01 -1.48594529e+00 -1.73525680e+00 12 -1.91505071e+01 -8.75203491e+00 -5.57027668e+00 | -1.91505071e+01 -8.75203491e+00 -5.57027668e+00 13 2.16611519e+01 8.41279406e+00 7.37309109e+00 | 2.16611519e+01 8.41279406e+00 7.37309109e+00 14 -5.70270190e-01 -2.45751050e+00 3.98244251e-01 | -5.70270190e-01 -2.45751050e+00 3.98244251e-01 15 6.13428973e+00 1.99537391e-01 4.68996259e+00 | 6.13428973e+00 1.99537391e-01 4.68996259e+00 16 -3.51119942e+00 -4.84760959e+00 -3.55802327e+00 | -3.51119942e+00 -4.84760959e+00 -3.55802327e+00 17 4.41152419e+00 4.30879912e+00 4.33851043e+00 | 4.41152419e+00 4.30879912e+00 4.33851043e+00 18 -2.50561070e-01 -7.30817204e-01 6.70755623e-01 | -2.50561070e-01 -7.30817204e-01 6.70755623e-01 19 -1.63056725e+01 9.18753528e+00 -1.05250339e+01 | -1.63056725e+01 9.18753528e+00 -1.05250339e+01 20 -1.74786624e+00 -4.28119541e-01 -1.66116338e+00 | -1.74786624e+00 -4.28119541e-01 -1.66116338e+00 21 4.68838873e+00 1.21897559e+00 1.72133648e+00 | 4.68838873e+00 1.21897559e+00 1.72133648e+00 22 -1.80947762e-01 -4.07492953e+00 -6.77565397e+00 | -1.80947762e-01 -4.07492953e+00 -6.77565397e+00 23 1.39393119e+00 2.58598951e+00 7.07674358e+00 | 1.39393119e+00 2.58598951e+00 7.07674358e+00 24 1.04001208e-01 5.59395223e-01 1.87949589e+00 | 1.04001208e-01 5.59395223e-01 1.87949589e+00 25 -6.42605316e+00 6.51071520e+00 -4.31648525e+00 | -6.42605316e+00 6.51071520e+00 -4.31648525e+00 26 -3.62619670e+00 -1.48867249e+00 -4.33919684e-01 | -3.62619670e+00 -1.48867249e+00 -4.33919684e-01 27 2.38667293e+00 2.27136382e-01 1.55064847e+00 | 2.38667293e+00 2.27136382e-01 1.55064847e+00 28 -5.30160691e+00 -1.04103390e+01 4.06176442e+00 | -5.30160691e+00 -1.04103390e+01 4.06176442e+00 29 8.60841105e+00 5.28867237e+00 3.56044558e+00 | 8.60841105e+00 5.28867237e+00 3.56044558e+00 30 1.61439621e+01 -9.94577480e+00 8.94233719e+00 | 1.61439621e+01 -9.94577480e+00 8.94233719e+00 31 -2.15367598e+00 8.16465900e-01 -5.87657871e-01 | -2.15367598e+00 8.16465900e-01 -5.87657871e-01 32 -2.27486120e+00 1.16766349e+00 1.18080055e+00 | -2.27486120e+00 1.16766349e+00 1.18080055e+00 33 -3.79700614e-01 1.91949350e+00 -1.96746091e+00 | -3.79700614e-01 1.91949350e+00 -1.96746091e+00 34 1.39383885e+01 -3.27292128e+01 1.74271353e+01 | 1.39383885e+01 -3.27292128e+01 1.74271353e+01 35 -3.99490926e-01 -3.10276703e+00 5.01641253e+00 | -3.99490926e-01 -3.10276703e+00 5.01641253e+00 36 1.24874487e+00 -2.96198717e+00 1.33412008e+00 | 1.24874487e+00 -2.96198717e+00 1.33412008e+00 37 -2.91579337e-01 4.24384200e-02 -6.12947836e-02 | -2.91579337e-01 4.24384200e-02 -6.12947836e-02 38 -6.84669871e-01 -1.53699332e-01 -3.93621453e-01 | -6.84669871e-01 -1.53699332e-01 -3.93621453e-01 39 -7.88602887e+00 -7.60412671e+00 5.79299112e+00 | -7.88602887e+00 -7.60412671e+00 5.79299112e+00 40 -1.78075660e+00 -1.00350487e-01 1.61607128e+00 | -1.78075660e+00 -1.00350487e-01 1.61607128e+00 41 -5.33631139e+00 9.77740359e+00 -6.71271473e+00 | -5.33631139e+00 9.77740359e+00 -6.71271473e+00 42 -3.13345837e+00 -2.73419731e+00 -2.30056915e+00 | -3.13345837e+00 -2.73419731e+00 -2.30056915e+00 43 2.01103759e+00 4.86475234e+00 2.74063695e+00 | 2.01103759e+00 4.86475234e+00 2.74063695e+00 44 7.09962729e+00 -1.01565213e+01 6.18674002e+00 | 7.09962729e+00 -1.01565213e+01 6.18674002e+00 45 -1.28239684e+00 -1.53364905e-01 -1.29469398e+00 | -1.28239684e+00 -1.53364905e-01 -1.29469398e+00 46 -9.40510042e-01 1.01448674e+00 1.01534144e+00 | -9.40510042e-01 1.01448674e+00 1.01534144e+00 47 8.54484794e-01 1.56601912e-01 -3.52512359e-01 | 8.54484794e-01 1.56601912e-01 -3.52512359e-01 48 4.99501878e-01 -3.62152062e-02 6.07445855e-01 | 4.99501878e-01 -3.62152062e-02 6.07445855e-01 49 -2.60480910e+00 -9.52586358e-01 1.47391127e+00 | -2.60480910e+00 -9.52586358e-01 1.47391127e+00 50 -2.75939417e-01 -2.47507575e+00 -5.02623602e+00 | -2.75939417e-01 -2.47507575e+00 -5.02623602e+00 51 2.66842723e+00 2.07541121e+00 2.28882194e+00 | 2.66842723e+00 2.07541121e+00 2.28882194e+00 52 7.16408797e+00 8.67738421e+00 -6.86757221e+00 | 7.16408797e+00 8.67738421e+00 -6.86757221e+00 53 9.11609952e-01 3.63607177e-01 -1.98635547e-01 | 9.11609952e-01 3.63607177e-01 -1.98635547e-01 54 -2.33997646e+00 -1.55903203e+00 -1.11932860e+00 | -2.33997646e+00 -1.55903203e+00 -1.11932860e+00 55 2.47340343e+00 1.14656075e+00 1.29490109e+00 | 2.47340343e+00 1.14656075e+00 1.29490109e+00 56 -2.29866595e-01 2.69902399e+00 -4.10850410e+00 | -2.29866595e-01 2.69902399e+00 -4.10850410e+00 57 -2.69677650e+00 -8.69574006e+00 -1.98297243e+01 | -2.69677650e+00 -8.69574006e+00 -1.98297243e+01 58 2.67099158e+00 -2.31986396e+00 9.01569694e-01 | 2.67099158e+00 -2.31986396e+00 9.01569694e-01 59 -7.72077933e-01 -8.68875281e-01 9.10242569e-02 | -7.72077933e-01 -8.68875281e-01 9.10242569e-02 60 8.88675290e+00 -5.17209815e+00 5.12808197e+00 | 8.88675290e+00 -5.17209815e+00 5.12808197e+00 61 -7.87152707e-01 1.66072685e-01 -8.07661637e-01 | -7.87152707e-01 1.66072685e-01 -8.07661637e-01 62 -7.23653384e+00 1.36816392e+01 1.37879516e+01 | -7.23653384e+00 1.36816392e+01 1.37879516e+01 63 4.87327338e-02 -5.73837989e-01 -5.25202358e-01 | 4.87327338e-02 -5.73837989e-01 -5.25202358e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Fe (Configuration in file "config-Fe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [53, 48, 35, 27, 14, 11, 52, 22, 62, 39, 59, 5, 50, 20, 4, 31, 25, 51, 56, 41, 13, 54, 7, 45, 33, 16, 44, 3, 61, 32, 46, 15, 29, 24, 47, 2, 63, 57, 55, 9, 42, 19, 40, 58, 26, 23, 30, 34, 1, 60, 12, 17, 6, 0, 21, 38, 18, 37, 43, 10, 49, 28, 8, 36] 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)) = -98.25283876138208 V(r_1,...,r_N) = -98.2528387613821 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 -2.78102173e+00 -5.78347202e+00 -2.51441986e+00 | -2.78102173e+00 -5.78347202e+00 -2.51441986e+00 1 8.73893912e-01 4.74562020e+00 1.52105377e+00 | 8.73893912e-01 4.74562020e+00 1.52105377e+00 2 -2.33988458e+00 -4.68276412e+00 -2.47136884e+00 | -2.33988458e+00 -4.68276412e+00 -2.47136884e+00 3 -4.90521835e+00 2.89139993e-01 6.13947949e+00 | -4.90521835e+00 2.89139993e-01 6.13947949e+00 4 3.14274129e-02 -2.06269522e-01 5.37795565e-01 | 3.14274129e-02 -2.06269522e-01 5.37795565e-01 5 -3.25685513e+00 -1.25712752e+01 -8.61176559e+00 | -3.25685513e+00 -1.25712752e+01 -8.61176559e+00 6 -2.14186313e+00 -3.20564870e+00 -2.11145321e+00 | -2.14186313e+00 -3.20564870e+00 -2.11145321e+00 7 1.72952682e+01 -1.51528097e+01 -1.75701677e+01 | 1.72952682e+01 -1.51528097e+01 -1.75701677e+01 8 -2.76274643e+00 -2.26797061e+00 -2.63566935e+00 | -2.76274643e+00 -2.26797061e+00 -2.63566935e+00 9 2.95037210e+00 1.96760010e+00 3.16884119e+00 | 2.95037210e+00 1.96760010e+00 3.16884119e+00 10 -4.24219616e+00 -4.75934875e-01 -5.40820808e+00 | -4.24219616e+00 -4.75934875e-01 -5.40820808e+00 11 3.80362236e+00 8.61867509e-01 5.86629701e+00 | 3.80362236e+00 8.61867509e-01 5.86629701e+00 12 -4.15536903e-01 1.00978963e+00 3.38135200e-03 | -4.15536903e-01 1.00978963e+00 3.38135200e-03 13 -6.11280775e-01 -3.58701735e-02 -3.79942652e-01 | -6.11280775e-01 -3.58701735e-02 -3.79942652e-01 14 7.03925560e+00 5.49923247e+00 -5.82372007e-01 | 7.03925560e+00 5.49923247e+00 -5.82372007e-01 15 1.18533409e+01 -1.45036640e+01 -7.27546446e+00 | 1.18533409e+01 -1.45036640e+01 -7.27546446e+00 16 -9.25737751e+00 -1.01042769e+01 -4.08483170e+00 | -9.25737751e+00 -1.01042769e+01 -4.08483170e+00 17 5.65392369e+00 4.20268655e+00 1.02779751e+01 | 5.65392369e+00 4.20268655e+00 1.02779751e+01 18 4.05783433e+00 5.07361157e+00 -4.35186724e+00 | 4.05783433e+00 5.07361157e+00 -4.35186724e+00 19 -4.10603071e+00 6.60199303e+00 -7.39834751e+00 | -4.10603071e+00 6.60199303e+00 -7.39834751e+00 20 1.82078030e+00 -5.00031887e-01 -3.15266895e+00 | 1.82078030e+00 -5.00031887e-01 -3.15266895e+00 21 4.93955650e+00 -9.12018917e-01 -3.19532231e+00 | 4.93955650e+00 -9.12018917e-01 -3.19532231e+00 22 1.43013958e-01 -1.08109851e+00 -5.84565566e-01 | 1.43013958e-01 -1.08109851e+00 -5.84565566e-01 23 7.16325717e-01 -1.96337578e-01 4.62497375e-01 | 7.16325717e-01 -1.96337578e-01 4.62497375e-01 24 9.22994577e+00 6.13875146e+00 -4.40039490e+00 | 9.22994577e+00 6.13875146e+00 -4.40039490e+00 25 4.98541240e+00 -3.07856853e+00 -2.57977511e+00 | 4.98541240e+00 -3.07856853e+00 -2.57977511e+00 26 -1.76421383e+00 -6.96353670e-01 -5.46839161e-01 | -1.76421383e+00 -6.96353670e-01 -5.46839161e-01 27 6.32029773e-01 -2.00411969e-02 1.38768770e+00 | 6.32029773e-01 -2.00411969e-02 1.38768770e+00 28 -1.62177741e+00 -1.44346613e+00 -3.04480457e+00 | -1.62177741e+00 -1.44346613e+00 -3.04480457e+00 29 1.91779261e+01 -1.20099418e+01 -1.19677114e+01 | 1.91779261e+01 -1.20099418e+01 -1.19677114e+01 30 7.80862185e-01 -3.76588227e+00 1.06280508e+01 | 7.80862185e-01 -3.76588227e+00 1.06280508e+01 31 1.49520850e-01 -1.28523827e+00 5.63073966e-01 | 1.49520850e-01 -1.28523827e+00 5.63073966e-01 32 3.51060113e-02 7.90501673e-01 -1.06441193e+00 | 3.51060113e-02 7.90501673e-01 -1.06441193e+00 33 -4.40295812e+00 2.02323018e+00 -3.96192750e+00 | -4.40295812e+00 2.02323018e+00 -3.96192750e+00 34 -4.68962766e+00 6.26798536e+00 1.02734174e+01 | -4.68962766e+00 6.26798536e+00 1.02734174e+01 35 -4.60082641e+00 1.87612395e+00 2.26652082e+00 | -4.60082641e+00 1.87612395e+00 2.26652082e+00 36 5.34733275e+00 -7.22088858e-01 4.29609569e+00 | 5.34733275e+00 -7.22088858e-01 4.29609569e+00 37 -1.56492618e-02 -2.10715654e-01 3.51628928e-01 | -1.56492618e-02 -2.10715654e-01 3.51628928e-01 38 1.45331976e+00 -1.59185510e-02 -5.24140083e-01 | 1.45331976e+00 -1.59185510e-02 -5.24140083e-01 39 -1.98762562e+01 -1.15746080e+01 2.96110258e+01 | -1.98762562e+01 -1.15746080e+01 2.96110258e+01 40 -1.02947182e+00 1.50383684e-01 -7.10596993e-01 | -1.02947182e+00 1.50383684e-01 -7.10596993e-01 41 5.47727381e+00 -7.29015539e+00 -1.25201851e+00 | 5.47727381e+00 -7.29015539e+00 -1.25201851e+00 42 -2.96685702e+00 -3.22410547e-01 -2.49938283e-01 | -2.96685702e+00 -3.22410547e-01 -2.49938283e-01 43 2.17685277e+00 8.73447024e-01 1.57029725e+00 | 2.17685277e+00 8.73447024e-01 1.57029725e+00 44 -3.20431733e-01 -4.83282846e-01 -9.18727427e-01 | -3.20431733e-01 -4.83282846e-01 -9.18727427e-01 45 -6.37625368e-01 1.63493811e+00 -3.07835774e-01 | -6.37625368e-01 1.63493811e+00 -3.07835774e-01 46 -2.78136490e+00 5.46196612e+00 3.13248003e+00 | -2.78136490e+00 5.46196612e+00 3.13248003e+00 47 -7.60343503e+00 -1.48223702e+01 5.16106241e+00 | -7.60343503e+00 -1.48223702e+01 5.16106241e+00 48 -1.70855310e+01 1.68381183e+01 2.32077501e+01 | -1.70855310e+01 1.68381183e+01 2.32077501e+01 49 -1.22313809e+01 -5.50373020e+00 6.69097186e+00 | -1.22313809e+01 -5.50373020e+00 6.69097186e+00 50 8.43457660e+00 9.24823282e+00 -1.27643946e+00 | 8.43457660e+00 9.24823282e+00 -1.27643946e+00 51 -1.49537301e+01 7.01592701e+00 -1.13492585e+01 | -1.49537301e+01 7.01592701e+00 -1.13492585e+01 52 2.04718735e+01 1.02380258e+01 -3.05139268e+01 | 2.04718735e+01 1.02380258e+01 -3.05139268e+01 53 -6.19529287e-01 8.57728660e-02 -6.95335595e-01 | -6.19529287e-01 8.57728660e-02 -6.95335595e-01 54 -6.40895231e+00 -9.39036921e-01 -5.21917808e+00 | -6.40895231e+00 -9.39036921e-01 -5.21917808e+00 55 7.34123168e+00 1.97917947e-01 4.20984613e+00 | 7.34123168e+00 1.97917947e-01 4.20984613e+00 56 -1.09179075e+01 1.57046707e+01 4.77329071e+00 | -1.09179075e+01 1.57046707e+01 4.77329071e+00 57 -2.17011583e+00 -1.16149614e+00 2.48857815e+00 | -2.17011583e+00 -1.16149614e+00 2.48857815e+00 58 -1.50945622e+01 1.73498604e+01 1.07893822e+01 | -1.50945622e+01 1.73498604e+01 1.07893822e+01 59 -1.45533211e+00 -1.28076327e+00 -9.16829165e-02 | -1.45533211e+00 -1.28076327e+00 -9.16829165e-02 60 6.87009296e+00 1.26369064e+01 -6.50131329e+00 | 6.87009296e+00 1.26369064e+01 -6.50131329e+00 61 1.84595704e-01 1.63795621e+00 -1.31790280e-01 | 1.84595704e-01 1.63795621e+00 -1.31790280e-01 62 1.59908419e+01 -7.53102365e+00 1.10967024e+01 | 1.59908419e+01 -7.53102365e+00 1.10967024e+01 63 1.50137853e-01 -5.85722252e-01 -8.38701684e-01 | 1.50137853e-01 -5.85722252e-01 -8.38701684e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [49, 22, 39, 16, 62, 43, 29, 36, 19, 51, 13, 35, 42, 10, 32, 58, 3, 21, 30, 8, 61, 17, 1, 45, 27, 57, 31, 24, 34, 6, 18, 26, 14, 48, 28, 11, 7, 47, 50, 2, 60, 56, 12, 5, 63, 23, 53, 37, 33, 0, 38, 9, 54, 46, 52, 59, 41, 25, 15, 55, 40, 20, 4, 44] 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)) = -58.603255679118476 V(r_1,...,r_N) = -58.60325567911848 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 1.11991211e+00 6.56816001e-01 1.36340490e+00 | 1.11991211e+00 6.56816001e-01 1.36340490e+00 1 -1.01975388e+01 3.47553557e+00 -3.33896323e+00 | -1.01975388e+01 3.47553557e+00 -3.33896323e+00 2 -4.75208728e+00 -5.18819470e+00 -1.56910817e+00 | -4.75208728e+00 -5.18819470e+00 -1.56910817e+00 3 4.29024903e+00 3.64852580e+00 3.39608453e+00 | 4.29024903e+00 3.64852580e+00 3.39608453e+00 4 4.06078332e-01 -1.59716207e+01 -1.27573491e+01 | 4.06078332e-01 -1.59716207e+01 -1.27573491e+01 5 1.01082332e+01 -1.76037705e+01 2.57259774e-01 | 1.01082332e+01 -1.76037705e+01 2.57259774e-01 6 -3.74768145e+00 -1.00764311e+00 -5.60615031e-01 | -3.74768145e+00 -1.00764311e+00 -5.60615031e-01 7 -4.93785212e+00 -3.28385114e+00 3.17369812e+00 | -4.93785212e+00 -3.28385114e+00 3.17369812e+00 8 -4.57541830e-01 7.60345738e-01 6.44984024e-01 | -4.57541830e-01 7.60345738e-01 6.44984024e-01 9 -1.00796986e+01 -2.78658275e+00 2.26045811e+00 | -1.00796986e+01 -2.78658275e+00 2.26045811e+00 10 9.40741513e+00 3.39211201e+00 -6.57899723e-01 | 9.40741513e+00 3.39211201e+00 -6.57899723e-01 11 3.42274431e+01 -9.57725465e+00 -1.90913833e+01 | 3.42274431e+01 -9.57725465e+00 -1.90913833e+01 12 -4.26458984e+00 -2.57682642e+00 -3.94460853e+00 | -4.26458984e+00 -2.57682642e+00 -3.94460853e+00 13 3.75479074e+00 2.22571836e+00 3.72720697e+00 | 3.75479074e+00 2.22571836e+00 3.72720697e+00 14 1.46575814e+01 1.24587458e+01 -5.82805595e+00 | 1.46575814e+01 1.24587458e+01 -5.82805595e+00 15 2.79674920e+01 -1.51537568e+01 -3.31264049e+01 | 2.79674920e+01 -1.51537568e+01 -3.31264049e+01 16 -1.35000840e+00 -3.49648891e-01 -1.35075761e+00 | -1.35000840e+00 -3.49648891e-01 -1.35075761e+00 17 1.02506536e+01 -1.10376144e+01 -2.86432982e+00 | 1.02506536e+01 -1.10376144e+01 -2.86432982e+00 18 5.47046476e-01 2.63082957e-01 1.25251501e+00 | 5.47046476e-01 2.63082957e-01 1.25251501e+00 19 -5.78593760e-01 -1.23598924e+00 -4.66370144e-01 | -5.78593760e-01 -1.23598924e+00 -4.66370144e-01 20 -2.70308703e+00 -1.45379699e+01 -2.03262042e+01 | -2.70308703e+00 -1.45379699e+01 -2.03262042e+01 21 1.22821864e+01 1.82385253e+01 1.87349486e+01 | 1.22821864e+01 1.82385253e+01 1.87349486e+01 22 -8.55974077e+00 1.30963065e+01 4.90070203e+00 | -8.55974077e+00 1.30963065e+01 4.90070203e+00 23 9.25348741e-01 -1.65983406e+00 4.47856575e-01 | 9.25348741e-01 -1.65983406e+00 4.47856575e-01 24 -1.34528423e+01 -1.87667863e+01 -1.56845516e+01 | -1.34528423e+01 -1.87667863e+01 -1.56845516e+01 25 4.16806255e+00 1.42066670e+01 1.54105932e+01 | 4.16806255e+00 1.42066670e+01 1.54105932e+01 26 2.06920658e+01 -1.81092498e+00 -8.52133415e+00 | 2.06920658e+01 -1.81092498e+00 -8.52133415e+00 27 -1.35035842e+00 -1.19987382e+00 1.06944997e+00 | -1.35035842e+00 -1.19987382e+00 1.06944997e+00 28 -3.43156930e+01 1.04821168e+01 1.90914701e+01 | -3.43156930e+01 1.04821168e+01 1.90914701e+01 29 -1.77811747e+00 -2.85654529e-01 -1.79292676e-01 | -1.77811747e+00 -2.85654529e-01 -1.79292676e-01 30 -1.07519806e+01 5.82709758e+00 1.06336094e+01 | -1.07519806e+01 5.82709758e+00 1.06336094e+01 31 -5.45896156e+00 5.19970468e+00 -8.40466992e+00 | -5.45896156e+00 5.19970468e+00 -8.40466992e+00 32 -3.59302353e+00 -2.80846126e+00 -3.45760860e+00 | -3.59302353e+00 -2.80846126e+00 -3.45760860e+00 33 -6.05993599e+00 6.93532256e+00 2.83656610e+00 | -6.05993599e+00 6.93532256e+00 2.83656610e+00 34 -1.27143425e+01 1.72862693e+01 1.85824658e+01 | -1.27143425e+01 1.72862693e+01 1.85824658e+01 35 1.33694408e+01 -9.97849747e+00 -1.48929086e+01 | 1.33694408e+01 -9.97849747e+00 -1.48929086e+01 36 1.00863036e+01 -2.71675374e+00 1.03940715e+00 | 1.00863036e+01 -2.71675374e+00 1.03940715e+00 37 -8.14102341e-01 6.40819333e-01 -4.61074853e-01 | -8.14102341e-01 6.40819333e-01 -4.61074853e-01 38 -3.24890538e+01 -1.57660678e+01 -1.24934744e+01 | -3.24890538e+01 -1.57660678e+01 -1.24934744e+01 39 3.19169757e+01 1.34026931e+01 1.31721893e+01 | 3.19169757e+01 1.34026931e+01 1.31721893e+01 40 5.24284278e-01 1.43845383e+00 4.57672751e-01 | 5.24284278e-01 1.43845383e+00 4.57672751e-01 41 6.03327349e+00 -1.24285283e+01 -2.73307446e+01 | 6.03327349e+00 -1.24285283e+01 -2.73307446e+01 42 -2.91109310e+00 -5.12321811e+00 -9.21510485e+00 | -2.91109310e+00 -5.12321811e+00 -9.21510485e+00 43 2.34212697e+00 6.22600692e+00 1.00843783e+01 | 2.34212697e+00 6.22600692e+00 1.00843783e+01 44 -5.48249095e-01 1.60219645e+00 -5.53220115e-01 | -5.48249095e-01 1.60219645e+00 -5.53220115e-01 45 -7.38449445e-01 -1.46767288e-01 -7.33451189e-01 | -7.38449445e-01 -1.46767288e-01 -7.33451189e-01 46 -1.13196560e+01 8.44155870e+00 1.50911988e+01 | -1.13196560e+01 8.44155870e+00 1.50911988e+01 47 6.40771699e+00 4.31659522e+00 9.82453241e+00 | 6.40771699e+00 4.31659522e+00 9.82453241e+00 48 -1.71446485e+01 -3.16868211e+01 -1.74740621e+01 | -1.71446485e+01 -3.16868211e+01 -1.74740621e+01 49 2.09665307e+01 2.98521700e+01 1.53647322e+01 | 2.09665307e+01 2.98521700e+01 1.53647322e+01 50 3.30898837e-01 -1.44044495e+01 -5.69584301e+00 | 3.30898837e-01 -1.44044495e+01 -5.69584301e+00 51 -1.64831352e+00 1.40473997e+01 6.45224393e+00 | -1.64831352e+00 1.40473997e+01 6.45224393e+00 52 -1.30591035e+01 1.11522597e+01 1.24644909e+01 | -1.30591035e+01 1.11522597e+01 1.24644909e+01 53 9.67081596e-02 2.15651786e+00 -6.88626074e-01 | 9.67081596e-02 2.15651786e+00 -6.88626074e-01 54 -1.29802170e+00 1.67405373e+00 2.75672131e+00 | -1.29802170e+00 1.67405373e+00 2.75672131e+00 55 5.64489876e-01 -1.58341964e+00 -1.60007021e+00 | 5.64489876e-01 -1.58341964e+00 -1.60007021e+00 56 -2.98666637e+01 1.56022166e+01 3.25172236e+01 | -2.98666637e+01 1.56022166e+01 3.25172236e+01 57 -1.39537749e+01 1.91267807e+01 -3.55698850e+01 | -1.39537749e+01 1.91267807e+01 -3.55698850e+01 58 -1.19936362e+01 -1.71269621e+01 -6.90659551e+00 | -1.19936362e+01 -1.71269621e+01 -6.90659551e+00 59 1.83673254e+01 1.08651560e+01 1.42182704e+01 | 1.83673254e+01 1.08651560e+01 1.42182704e+01 60 1.47845357e+01 -1.89979469e+01 3.69262761e+01 | 1.47845357e+01 -1.89979469e+01 3.69262761e+01 61 -1.89691037e+00 -4.26494999e-02 -1.42296356e+00 | -1.89691037e+00 -4.26494999e-02 -1.42296356e+00 62 -2.84311628e+01 -1.55728577e+01 -2.11458009e+01 | -2.84311628e+01 -1.55728577e+01 -2.11458009e+01 63 2.86213453e+01 1.37194275e+01 2.01607213e+01 | 2.86213453e+01 1.37194275e+01 2.01607213e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cr Fe Ni (Configuration in file "config-CrFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [52, 11, 26, 43, 35, 23, 27, 63, 30, 18, 21, 1, 37, 32, 20, 45, 53, 29, 9, 50, 14, 10, 31, 5, 54, 62, 2, 6, 39, 17, 8, 22, 13, 51, 58, 4, 48, 12, 61, 28, 56, 60, 49, 3, 44, 15, 59, 55, 36, 42, 19, 33, 0, 16, 24, 47, 40, 57, 34, 46, 41, 38, 25, 7] 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)) = -5.934628801754157 V(r_1,...,r_N) = -5.934628801754188 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 -2.07937298e+00 -5.17225425e-01 -2.35176389e+00 | -2.07937298e+00 -5.17225425e-01 -2.35176389e+00 1 -9.38022544e+00 -1.59133854e+01 1.08611372e+01 | -9.38022544e+00 -1.59133854e+01 1.08611372e+01 2 1.00785059e+01 1.74004650e+01 -7.57312499e+00 | 1.00785059e+01 1.74004650e+01 -7.57312499e+00 3 1.80185661e+00 3.14911093e-01 -4.06297655e+00 | 1.80185661e+00 3.14911093e-01 -4.06297655e+00 4 -1.16138847e+00 -3.72896796e-01 6.88759511e-01 | -1.16138847e+00 -3.72896796e-01 6.88759511e-01 5 5.56590068e-02 1.09175368e+00 1.07016259e+00 | 5.56590068e-02 1.09175368e+00 1.07016259e+00 6 -1.20124702e-01 -5.87813422e-01 -6.47593529e-01 | -1.20124702e-01 -5.87813422e-01 -6.47593529e-01 7 -1.72834141e+01 2.65506780e+01 -6.20795856e+01 | -1.72834141e+01 2.65506780e+01 -6.20795856e+01 8 -6.19636599e-02 1.06246544e+00 1.13096807e+00 | -6.19636599e-02 1.06246544e+00 1.13096807e+00 9 1.57909277e-01 -3.29114345e-01 -3.06881592e-01 | 1.57909277e-01 -3.29114345e-01 -3.06881592e-01 10 -3.23079600e+00 -2.20861846e+00 -2.85432756e+00 | -3.23079600e+00 -2.20861846e+00 -2.85432756e+00 11 2.20385073e+00 2.92270758e+00 3.73830067e+00 | 2.20385073e+00 2.92270758e+00 3.73830067e+00 12 -7.24399328e-01 8.94333742e-01 -1.35305318e-01 | -7.24399328e-01 8.94333742e-01 -1.35305318e-01 13 2.79344168e-01 -1.85123957e+00 -3.89543774e+00 | 2.79344168e-01 -1.85123957e+00 -3.89543774e+00 14 -1.90160896e+00 -1.13539412e+00 3.90090054e+00 | -1.90160896e+00 -1.13539412e+00 3.90090054e+00 15 2.66231427e+00 -1.00088027e+00 -2.38682032e-01 | 2.66231427e+00 -1.00088027e+00 -2.38682032e-01 16 -1.89583825e+00 -5.07764178e+00 -1.09460601e+00 | -1.89583825e+00 -5.07764178e+00 -1.09460601e+00 17 2.91737708e+00 4.96164038e+00 1.91353023e+00 | 2.91737708e+00 4.96164038e+00 1.91353023e+00 18 -5.85692444e+00 -6.82704318e+00 -3.02937901e+00 | -5.85692444e+00 -6.82704318e+00 -3.02937901e+00 19 5.89448211e+00 5.64600469e+00 4.31624566e+00 | 5.89448211e+00 5.64600469e+00 4.31624566e+00 20 2.26510070e-01 -3.58884775e-01 1.53784305e-01 | 2.26510070e-01 -3.58884775e-01 1.53784305e-01 21 -1.71985636e+01 1.46144596e+01 -5.55391444e+00 | -1.71985636e+01 1.46144596e+01 -5.55391444e+00 22 -4.09021693e-02 -4.19057461e-01 -4.76647174e-01 | -4.09021693e-02 -4.19057461e-01 -4.76647174e-01 23 -1.56992333e+00 1.11642473e+00 -1.74191861e+00 | -1.56992333e+00 1.11642473e+00 -1.74191861e+00 24 3.67730354e-01 8.41193099e-01 5.05006857e-01 | 3.67730354e-01 8.41193099e-01 5.05006857e-01 25 -1.37759230e+01 1.61656679e+00 8.78782355e+00 | -1.37759230e+01 1.61656679e+00 8.78782355e+00 26 1.09534862e+01 3.65113222e+00 -9.58405476e+00 | 1.09534862e+01 3.65113222e+00 -9.58405476e+00 27 -1.38721528e+00 -1.70569292e+00 -9.97907714e-02 | -1.38721528e+00 -1.70569292e+00 -9.97907714e-02 28 3.20650979e+00 -3.96378006e+00 2.14023379e+00 | 3.20650979e+00 -3.96378006e+00 2.14023379e+00 29 5.46299392e+01 -6.35036746e+01 -1.00649639e+02 | 5.46299392e+01 -6.35036746e+01 -1.00649639e+02 30 3.36284940e+00 7.00201504e+00 -6.15523177e+00 | 3.36284940e+00 7.00201504e+00 -6.15523177e+00 31 1.42514060e+00 8.41533400e-01 3.46402585e-01 | 1.42514060e+00 8.41533400e-01 3.46402585e-01 32 1.29425274e+00 1.38354221e+00 -9.42748227e-02 | 1.29425274e+00 1.38354221e+00 -9.42748227e-02 33 -1.42603658e+02 8.78219812e+01 -1.28497713e+02 | -1.42603658e+02 8.78219812e+01 -1.28497713e+02 34 1.54762787e+01 -2.88653600e+01 5.94213915e+01 | 1.54762787e+01 -2.88653600e+01 5.94213915e+01 35 3.17988544e+00 1.77470155e+00 3.10747120e+00 | 3.17988544e+00 1.77470155e+00 3.10747120e+00 36 1.42590932e+02 -8.67203375e+01 1.27444992e+02 | 1.42590932e+02 -8.67203375e+01 1.27444992e+02 37 7.48472372e-01 -6.77159522e-01 -1.28040254e-01 | 7.48472372e-01 -6.77159522e-01 -1.28040254e-01 38 9.29868732e-01 2.17730346e-01 -1.40565445e+00 | 9.29868732e-01 2.17730346e-01 -1.40565445e+00 39 2.65608370e-01 -2.03905470e+00 -5.73565716e-01 | 2.65608370e-01 -2.03905470e+00 -5.73565716e-01 40 -1.08480447e+00 -8.61899554e-02 2.24486856e-01 | -1.08480447e+00 -8.61899554e-02 2.24486856e-01 41 -3.24465195e+00 6.66776588e+00 -8.54631729e+00 | -3.24465195e+00 6.66776588e+00 -8.54631729e+00 42 -3.11576741e+00 -1.73484120e+00 1.83103469e+00 | -3.11576741e+00 -1.73484120e+00 1.83103469e+00 43 3.47628182e+00 3.13064467e+00 1.16467366e+00 | 3.47628182e+00 3.13064467e+00 1.16467366e+00 44 3.30723577e+00 -5.48557254e+00 9.44758015e+00 | 3.30723577e+00 -5.48557254e+00 9.44758015e+00 45 -1.57320238e+00 5.56812698e-01 -1.74271874e+00 | -1.57320238e+00 5.56812698e-01 -1.74271874e+00 46 -1.36477230e+01 -2.54969642e+01 -1.95800602e+01 | -1.36477230e+01 -2.54969642e+01 -1.95800602e+01 47 1.42564242e+01 2.63481467e+01 1.84618232e+01 | 1.42564242e+01 2.63481467e+01 1.84618232e+01 48 3.56596582e-01 -1.04152091e+00 3.27682680e-01 | 3.56596582e-01 -1.04152091e+00 3.27682680e-01 49 9.35932725e+00 -7.16157997e+00 -9.70813970e+00 | 9.35932725e+00 -7.16157997e+00 -9.70813970e+00 50 1.94882237e+00 -4.29896018e-01 2.45416015e+00 | 1.94882237e+00 -4.29896018e-01 2.45416015e+00 51 -5.17644000e+01 3.36758434e+01 -1.02383634e+01 | -5.17644000e+01 3.36758434e+01 -1.02383634e+01 52 -1.97733387e+01 -9.51031269e+00 -1.33579634e+01 | -1.97733387e+01 -9.51031269e+00 -1.33579634e+01 53 1.99708062e+01 1.17193111e+01 1.19089858e+01 | 1.99708062e+01 1.17193111e+01 1.19089858e+01 54 -8.57497611e+00 6.79771455e+00 1.00748168e+01 | -8.57497611e+00 6.79771455e+00 1.00748168e+01 55 6.96846267e-01 -1.19948941e+00 -8.78858875e-01 | 6.96846267e-01 -1.19948941e+00 -8.78858875e-01 56 1.21250470e+01 -2.26473913e+01 1.08079859e+01 | 1.21250470e+01 -2.26473913e+01 1.08079859e+01 57 -4.93614853e+01 6.07260739e+01 -8.54735187e+01 | -4.93614853e+01 6.07260739e+01 -8.54735187e+01 58 -5.60707285e+01 6.29002967e+01 1.00614648e+02 | -5.60707285e+01 6.29002967e+01 1.00614648e+02 59 -6.53894363e-01 -7.33336459e-01 3.80890848e-02 | -6.53894363e-01 -7.33336459e-01 3.80890848e-02 60 3.94730236e+01 -6.16832628e+01 7.70401022e+01 | 3.94730236e+01 -6.16832628e+01 7.70401022e+01 61 8.45565339e+00 1.51510492e+00 8.75743504e+00 | 8.45565339e+00 1.51510492e+00 8.75743504e+00 62 4.69553373e+01 -4.17936631e+01 3.15931997e+00 | 4.69553373e+01 -4.17936631e+01 3.15931997e+00 63 4.04704886e+00 7.31432041e+00 6.91611416e+00 | 4.04704886e+00 7.31432041e+00 6.91611416e+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.