!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_ChoiJoSohn_2018_CoNiCrFeMn__MO_115454747503_001 Supported species : Co Cr Fe Mn Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [38, 55, 35, 16, 32, 44, 25, 21, 56, 14, 19, 63, 24, 20, 9, 62, 3, 50, 39, 10, 13, 7, 36, 30, 12, 6, 33, 60, 40, 31, 23, 29, 4, 26, 37, 2, 22, 34, 0, 18, 28, 49, 51, 58, 5, 47, 59, 45, 61, 41, 17, 42, 57, 54, 53, 1, 8, 52, 43, 46, 27, 48, 15, 11] 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)) = -99.5603363152471 V(r_1,...,r_N) = -99.56033631524708 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 -5.84753880e-01 -4.18364877e-01 -5.17677401e-01 | -5.84753880e-01 -4.18364877e-01 -5.17677401e-01 1 -3.83720189e+00 -9.94626510e+00 7.38003278e+00 | -3.83720189e+00 -9.94626510e+00 7.38003278e+00 2 -2.71248042e-01 3.47010715e+00 -1.23523448e+01 | -2.71248042e-01 3.47010715e+00 -1.23523448e+01 3 5.10992652e+00 6.78933834e+00 5.99056848e+00 | 5.10992652e+00 6.78933834e+00 5.99056848e+00 4 -1.20318920e+00 9.05767453e-01 9.89413277e-01 | -1.20318920e+00 9.05767453e-01 9.89413277e-01 5 -3.00313270e-01 4.11641742e-01 -2.08232281e+00 | -3.00313270e-01 4.11641742e-01 -2.08232281e+00 6 -5.35144207e-01 -5.86464521e-01 -1.80498189e-01 | -5.35144207e-01 -5.86464521e-01 -1.80498189e-01 7 -9.80957463e+00 2.49464607e+01 -1.52710506e+01 | -9.80957463e+00 2.49464607e+01 -1.52710506e+01 8 -6.79759493e-01 3.48218103e-01 -1.22593386e+00 | -6.79759493e-01 3.48218103e-01 -1.22593386e+00 9 -2.64046853e+00 4.00501256e+00 -1.30290233e+00 | -2.64046853e+00 4.00501256e+00 -1.30290233e+00 10 -4.03835245e-01 1.10455707e-01 1.24743021e+00 | -4.03835245e-01 1.10455707e-01 1.24743021e+00 11 1.59154379e+00 -3.83134934e+00 -3.04740087e+00 | 1.59154379e+00 -3.83134934e+00 -3.04740087e+00 12 3.41812270e+00 -2.13447026e+00 3.14221580e+00 | 3.41812270e+00 -2.13447026e+00 3.14221580e+00 13 5.55079400e+00 -4.51734517e+00 -5.54076789e+00 | 5.55079400e+00 -4.51734517e+00 -5.54076789e+00 14 1.24244115e-01 -2.88371056e-01 -2.97259285e-01 | 1.24244115e-01 -2.88371056e-01 -2.97259285e-01 15 -3.82776807e-02 1.36332162e-01 4.47233956e-01 | -3.82776807e-02 1.36332162e-01 4.47233956e-01 16 -9.02910737e-01 -2.27208810e+00 -3.05298043e-01 | -9.02910737e-01 -2.27208810e+00 -3.05298043e-01 17 -1.49719289e-01 -1.05107149e+00 3.48877388e+00 | -1.49719289e-01 -1.05107149e+00 3.48877388e+00 18 3.15296111e+00 3.54981397e+00 -1.72855884e+00 | 3.15296111e+00 3.54981397e+00 -1.72855884e+00 19 -1.78081084e+01 1.05673248e+01 -1.22606110e+01 | -1.78081084e+01 1.05673248e+01 -1.22606110e+01 20 -7.05192025e+00 -4.65326537e+00 -5.40153299e+00 | -7.05192025e+00 -4.65326537e+00 -5.40153299e+00 21 7.85401358e+00 6.01249777e+00 3.98170190e+00 | 7.85401358e+00 6.01249777e+00 3.98170190e+00 22 -7.62317948e-01 -1.27724529e+00 -2.29815427e+00 | -7.62317948e-01 -1.27724529e+00 -2.29815427e+00 23 1.40176238e+00 -8.31473184e-02 2.37428052e+00 | 1.40176238e+00 -8.31473184e-02 2.37428052e+00 24 -4.04874120e-01 1.01685727e-02 2.77623539e-01 | -4.04874120e-01 1.01685727e-02 2.77623539e-01 25 -6.54748358e+00 6.97037082e+00 -4.05054270e+00 | -6.54748358e+00 6.97037082e+00 -4.05054270e+00 26 -8.71769180e+00 -2.70506941e+00 -1.82854007e+00 | -8.71769180e+00 -2.70506941e+00 -1.82854007e+00 27 8.22639115e+00 1.98905943e+00 2.48762493e+00 | 8.22639115e+00 1.98905943e+00 2.48762493e+00 28 3.00689271e+00 -3.08838683e+00 6.46549881e+00 | 3.00689271e+00 -3.08838683e+00 6.46549881e+00 29 3.49125207e-01 -4.28530771e-02 8.26012512e-01 | 3.49125207e-01 -4.28530771e-02 8.26012512e-01 30 1.81027122e+01 -1.14389037e+01 1.08989487e+01 | 1.81027122e+01 -1.14389037e+01 1.08989487e+01 31 -1.06411599e+01 1.45379226e+00 -5.29378604e+00 | -1.06411599e+01 1.45379226e+00 -5.29378604e+00 32 -7.30762844e-01 -2.70427219e-01 -2.10257611e+00 | -7.30762844e-01 -2.70427219e-01 -2.10257611e+00 33 -2.36626351e+00 3.53530958e+00 -6.12762109e+00 | -2.36626351e+00 3.53530958e+00 -6.12762109e+00 34 1.18880607e+01 -2.75648338e+01 1.63492490e+01 | 1.18880607e+01 -2.75648338e+01 1.63492490e+01 35 -4.11842557e+00 -4.26822299e+00 5.49190695e+00 | -4.11842557e+00 -4.26822299e+00 5.49190695e+00 36 4.28467763e+00 -1.71037970e+00 7.48809307e+00 | 4.28467763e+00 -1.71037970e+00 7.48809307e+00 37 -2.01799381e+00 -2.58590060e+00 1.78418451e+00 | -2.01799381e+00 -2.58590060e+00 1.78418451e+00 38 -6.26245164e-01 -1.76592144e+00 -2.24304315e+00 | -6.26245164e-01 -1.76592144e+00 -2.24304315e+00 39 -4.88879384e+00 -4.25204520e+00 5.40394073e+00 | -4.88879384e+00 -4.25204520e+00 5.40394073e+00 40 -5.26010836e+00 -1.82818745e+00 3.82009239e-01 | -5.26010836e+00 -1.82818745e+00 3.82009239e-01 41 -3.28601832e+00 1.61400423e+01 -5.07154016e+00 | -3.28601832e+00 1.61400423e+01 -5.07154016e+00 42 -1.91668640e+01 -1.15111544e+01 -8.58315617e+00 | -1.91668640e+01 -1.15111544e+01 -8.58315617e+00 43 1.24341206e+01 1.60053735e+01 1.38565708e+01 | 1.24341206e+01 1.60053735e+01 1.38565708e+01 44 9.36471486e+00 -1.37499619e+01 8.70808784e+00 | 9.36471486e+00 -1.37499619e+01 8.70808784e+00 45 -1.01977012e+00 -1.59926950e-01 -1.16456215e+00 | -1.01977012e+00 -1.59926950e-01 -1.16456215e+00 46 2.00214911e+00 2.20891242e+00 -3.79833551e+00 | 2.00214911e+00 2.20891242e+00 -3.79833551e+00 47 -3.47174022e-01 5.82531664e-01 -4.76416785e-01 | -3.47174022e-01 5.82531664e-01 -4.76416785e-01 48 -9.34633328e-01 1.06463325e+00 1.00787617e+00 | -9.34633328e-01 1.06463325e+00 1.00787617e+00 49 -2.69151800e+00 -5.68612152e-01 2.47921129e+00 | -2.69151800e+00 -5.68612152e-01 2.47921129e+00 50 -9.68512623e-01 -4.50823245e+00 -7.09643588e+00 | -9.68512623e-01 -4.50823245e+00 -7.09643588e+00 51 4.32155331e+00 4.48627072e+00 4.32501989e+00 | 4.32155331e+00 4.48627072e+00 4.32501989e+00 52 6.33177374e+00 5.51796459e+00 -4.52460005e+00 | 6.33177374e+00 5.51796459e+00 -4.52460005e+00 53 2.00555989e-01 -5.00556720e-01 -6.99178352e-01 | 2.00555989e-01 -5.00556720e-01 -6.99178352e-01 54 4.85547252e-01 -5.25890730e-01 -5.32269254e-01 | 4.85547252e-01 -5.25890730e-01 -5.32269254e-01 55 9.65224262e-02 2.61573451e-01 -6.52710078e-02 | 9.65224262e-02 2.61573451e-01 -6.52710078e-02 56 3.47414611e+00 4.27104733e+00 -5.95610038e+00 | 3.47414611e+00 4.27104733e+00 -5.95610038e+00 57 9.82714342e+00 -1.20667030e+01 -1.52351952e+01 | 9.82714342e+00 -1.20667030e+01 -1.52351952e+01 58 9.43449111e+00 -2.16506174e+00 6.92452136e+00 | 9.43449111e+00 -2.16506174e+00 6.92452136e+00 59 -7.81412755e-01 -8.15985380e-01 8.77083418e-02 | -7.81412755e-01 -8.15985380e-01 8.77083418e-02 60 -2.37376052e+01 -1.43548594e+01 -1.85905281e+01 | -2.37376052e+01 -1.43548594e+01 -1.85905281e+01 61 2.19060168e+01 1.41369317e+01 1.71601731e+01 | 2.19060168e+01 1.41369317e+01 1.71601731e+01 62 -8.03247021e+00 1.39543410e+01 1.59869958e+01 | -8.03247021e+00 1.39543410e+01 1.59869958e+01 63 3.24561114e-01 -3.33768899e-01 -1.80896195e-01 | 3.24561114e-01 -3.33768899e-01 -1.80896195e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [46, 54, 14, 58, 23, 38, 25, 19, 35, 61, 32, 39, 33, 28, 2, 17, 47, 15, 26, 7, 56, 29, 37, 4, 59, 6, 18, 43, 13, 21, 48, 52, 10, 12, 63, 8, 40, 22, 5, 11, 36, 44, 62, 27, 41, 57, 0, 16, 30, 53, 60, 55, 31, 49, 1, 51, 20, 45, 3, 24, 50, 9, 42, 34] 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)) = 267.71601093624486 V(r_1,...,r_N) = 267.71601093624486 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 -1.28223448e+01 -5.59926112e+00 -1.33459217e+01 | -1.28223448e+01 -5.59926112e+00 -1.33459217e+01 1 1.70346622e+00 1.81341000e+01 -1.50280203e-01 | 1.70346622e+00 1.81341000e+01 -1.50280203e-01 2 -1.23859072e+00 -1.42762086e+00 -1.09584471e-01 | -1.23859072e+00 -1.42762086e+00 -1.09584471e-01 3 -3.72275110e-01 1.58417758e+00 -4.02905044e+00 | -3.72275110e-01 1.58417758e+00 -4.02905044e+00 4 9.57707204e+00 -1.40647725e+01 1.29168227e+01 | 9.57707204e+00 -1.40647725e+01 1.29168227e+01 5 6.20062102e+01 -1.39302511e+02 -1.78861281e+02 | 6.20062102e+01 -1.39302511e+02 -1.78861281e+02 6 -8.17902752e+00 -4.15870316e+00 -1.23884713e+01 | -8.17902752e+00 -4.15870316e+00 -1.23884713e+01 7 -8.20437940e+01 -1.27523091e+02 4.58905825e+01 | -8.20437940e+01 -1.27523091e+02 4.58905825e+01 8 -1.85697659e-01 1.07451039e+00 1.30488801e+00 | -1.85697659e-01 1.07451039e+00 1.30488801e+00 9 -7.91568091e+00 7.73001124e+00 -3.10596090e+00 | -7.91568091e+00 7.73001124e+00 -3.10596090e+00 10 3.39948134e+00 5.14525085e+00 -2.02739585e+00 | 3.39948134e+00 5.14525085e+00 -2.02739585e+00 11 -2.03226613e+00 -5.05528730e-01 -4.61548659e-01 | -2.03226613e+00 -5.05528730e-01 -4.61548659e-01 12 5.79596128e+00 -1.13657824e+01 7.50295597e+00 | 5.79596128e+00 -1.13657824e+01 7.50295597e+00 13 -1.09842952e+00 6.96407685e-01 -4.01822206e-01 | -1.09842952e+00 6.96407685e-01 -4.01822206e-01 14 2.74419052e+01 1.37570815e+01 -1.75252413e+01 | 2.74419052e+01 1.37570815e+01 -1.75252413e+01 15 -8.46267363e+00 1.93770040e+00 -1.51534579e+00 | -8.46267363e+00 1.93770040e+00 -1.51534579e+00 16 -7.17047773e+00 -4.02567526e+00 -5.73025002e+00 | -7.17047773e+00 -4.02567526e+00 -5.73025002e+00 17 5.28100061e+00 3.54642425e+00 4.44842997e+00 | 5.28100061e+00 3.54642425e+00 4.44842997e+00 18 5.40557008e-01 -1.44785835e-01 2.67771185e-01 | 5.40557008e-01 -1.44785835e-01 2.67771185e-01 19 -1.93653886e+01 2.68814896e+01 -2.23200715e+01 | -1.93653886e+01 2.68814896e+01 -2.23200715e+01 20 3.05409600e+01 3.49067070e+01 -1.82821334e+01 | 3.05409600e+01 3.49067070e+01 -1.82821334e+01 21 5.86198339e+01 9.82110740e+01 -1.18995332e+01 | 5.86198339e+01 9.82110740e+01 -1.18995332e+01 22 -7.95057263e+00 -1.34196491e+01 -2.40139278e+01 | -7.95057263e+00 -1.34196491e+01 -2.40139278e+01 23 -1.96608061e+01 4.54647753e+01 1.28404993e+01 | -1.96608061e+01 4.54647753e+01 1.28404993e+01 24 -2.03301515e-01 2.78445125e-01 1.23290387e+00 | -2.03301515e-01 2.78445125e-01 1.23290387e+00 25 -2.38549406e+00 3.83870231e-01 -4.99731084e-01 | -2.38549406e+00 3.83870231e-01 -4.99731084e-01 26 -5.20476096e+01 -5.31401926e+01 -9.46900575e+01 | -5.20476096e+01 -5.31401926e+01 -9.46900575e+01 27 5.35159881e+01 5.48670677e+01 9.35039300e+01 | 5.35159881e+01 5.48670677e+01 9.35039300e+01 28 1.20484448e+00 -2.11060265e+00 2.51663996e+00 | 1.20484448e+00 -2.11060265e+00 2.51663996e+00 29 -9.35533440e-01 -1.25477336e+00 -1.71251737e-01 | -9.35533440e-01 -1.25477336e+00 -1.71251737e-01 30 1.94067506e+01 -2.73610554e+01 2.13152589e+01 | 1.94067506e+01 -2.73610554e+01 2.13152589e+01 31 -1.10056611e+02 1.55134642e+02 -1.39001952e+02 | -1.10056611e+02 1.55134642e+02 -1.39001952e+02 32 5.35112052e-01 4.55998605e-01 -1.53395001e-01 | 5.35112052e-01 4.55998605e-01 -1.53395001e-01 33 2.74455437e+01 -3.94676583e+01 -3.54462770e+01 | 2.74455437e+01 -3.94676583e+01 -3.54462770e+01 34 -8.43890159e+01 1.27093644e+02 1.95837073e+02 | -8.43890159e+01 1.27093644e+02 1.95837073e+02 35 -3.10582796e+01 5.64646465e+01 -3.83529160e+01 | -3.10582796e+01 5.64646465e+01 -3.83529160e+01 36 1.79384628e-01 9.19303839e-01 -4.75087761e-01 | 1.79384628e-01 9.19303839e-01 -4.75087761e-01 37 -3.42256660e+01 -1.27836289e+01 2.80454441e+01 | -3.42256660e+01 -1.27836289e+01 2.80454441e+01 38 -3.08907869e+01 3.75410733e+01 3.25999727e+01 | -3.08907869e+01 3.75410733e+01 3.25999727e+01 39 4.09772967e+00 2.83488392e+00 2.50491655e+00 | 4.09772967e+00 2.83488392e+00 2.50491655e+00 40 1.12709033e+00 -3.11663488e+00 2.51932454e+00 | 1.12709033e+00 -3.11663488e+00 2.51932454e+00 41 -2.52717491e+01 1.64880597e+01 -2.63202135e+01 | -2.52717491e+01 1.64880597e+01 -2.63202135e+01 42 -5.07441626e+00 -2.45502883e+01 -1.57964564e+01 | -5.07441626e+00 -2.45502883e+01 -1.57964564e+01 43 1.29219868e+01 2.19828672e+01 1.63437718e+01 | 1.29219868e+01 2.19828672e+01 1.63437718e+01 44 2.61905511e+01 -1.55632098e+01 2.62205550e+01 | 2.61905511e+01 -1.55632098e+01 2.62205550e+01 45 -5.24316279e-01 1.46330996e-03 -7.43663999e-01 | -5.24316279e-01 1.46330996e-03 -7.43663999e-01 46 6.56005260e+01 -4.39418144e+01 1.05920074e+01 | 6.56005260e+01 -4.39418144e+01 1.05920074e+01 47 -7.79829960e+00 -8.52733365e+00 1.10444907e+01 | -7.79829960e+00 -8.52733365e+00 1.10444907e+01 48 -6.72990452e+00 -1.91420940e+00 -1.48541049e+01 | -6.72990452e+00 -1.91420940e+00 -1.48541049e+01 49 -7.29040306e+00 5.28970013e+00 -4.09701534e+00 | -7.29040306e+00 5.28970013e+00 -4.09701534e+00 50 2.79622561e+01 -3.23518090e+01 1.28722600e+01 | 2.79622561e+01 -3.23518090e+01 1.28722600e+01 51 7.96000016e-02 -1.34846876e+00 2.70736803e-01 | 7.96000016e-02 -1.34846876e+00 2.70736803e-01 52 1.42561558e+01 -4.24706111e+00 1.79353061e+01 | 1.42561558e+01 -4.24706111e+00 1.79353061e+01 53 -1.42737425e+01 -1.25196093e+01 1.99625234e+01 | -1.42737425e+01 -1.25196093e+01 1.99625234e+01 54 -1.56709267e+01 -6.72979998e+00 -2.45283652e+01 | -1.56709267e+01 -6.72979998e+00 -2.45283652e+01 55 1.64189099e+01 6.23522801e+00 2.37817762e+01 | 1.64189099e+01 6.23522801e+00 2.37817762e+01 56 -4.25266359e+01 -1.60212730e+02 -1.79304374e+02 | -4.25266359e+01 -1.60212730e+02 -1.79304374e+02 57 6.79913526e+01 1.14303972e+02 1.08837537e+02 | 6.79913526e+01 1.14303972e+02 1.08837537e+02 58 1.12176702e+02 -1.54354281e+02 1.39151023e+02 | 1.12176702e+02 -1.54354281e+02 1.39151023e+02 59 -4.25312587e-01 -5.62171414e-01 9.34483167e-01 | -4.25312587e-01 -5.62171414e-01 9.34483167e-01 60 2.24175763e+01 -4.76266841e+00 6.69129671e+00 | 2.24175763e+01 -4.76266841e+00 6.69129671e+00 61 -7.97527457e-01 4.67490812e-01 -1.01889152e+00 | -7.97527457e-01 4.67490812e-01 -1.01889152e+00 62 -2.81642891e+01 7.29307092e+01 3.16864628e+01 | -2.81642891e+01 7.29307092e+01 3.16864628e+01 63 8.03338628e-01 -3.85393429e-01 4.99286401e-02 | 8.03338628e-01 -3.85393429e-01 4.99286401e-02 ------------------------------------------------------------------------------------------------------------------------- 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 = [26, 58, 35, 16, 30, 14, 33, 24, 62, 21, 19, 50, 45, 46, 5, 57, 3, 41, 40, 10, 47, 9, 32, 25, 7, 23, 0, 39, 55, 38, 4, 34, 22, 6, 31, 2, 51, 43, 29, 27, 18, 17, 54, 37, 63, 12, 13, 20, 59, 56, 11, 36, 61, 60, 42, 28, 49, 15, 1, 48, 53, 52, 8, 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)) = 105.05196686292068 V(r_1,...,r_N) = 105.05196686292071 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 9.55037715e-01 9.40945126e-01 7.46598633e-01 | 9.55037715e-01 9.40945126e-01 7.46598633e-01 1 -8.67264183e+00 2.65784805e+00 4.43083106e+01 | -8.67264183e+00 2.65784805e+00 4.43083106e+01 2 8.59255699e+00 -2.38383210e+00 -4.31383085e+01 | 8.59255699e+00 -2.38383210e+00 -4.31383085e+01 3 2.99028828e+01 -4.09571727e+01 -4.03876480e+01 | 2.99028828e+01 -4.09571727e+01 -4.03876480e+01 4 -1.01269485e+00 -1.77545885e+00 -1.25993364e+00 | -1.01269485e+00 -1.77545885e+00 -1.25993364e+00 5 1.49457241e+01 -4.93001148e+00 -1.43746544e+01 | 1.49457241e+01 -4.93001148e+00 -1.43746544e+01 6 6.57672480e-01 -1.02538413e+00 -3.11163880e-02 | 6.57672480e-01 -1.02538413e+00 -3.11163880e-02 7 -2.33319355e+00 8.48856328e+00 -3.05482174e+00 | -2.33319355e+00 8.48856328e+00 -3.05482174e+00 8 -1.48553463e+01 -3.69887901e+00 -1.77825526e+01 | -1.48553463e+01 -3.69887901e+00 -1.77825526e+01 9 1.47568673e+01 4.31491598e+00 1.77875977e+01 | 1.47568673e+01 4.31491598e+00 1.77875977e+01 10 -5.94866848e-01 -4.23142560e-01 6.00470983e-01 | -5.94866848e-01 -4.23142560e-01 6.00470983e-01 11 -5.89895283e-01 2.07395648e-01 5.84295703e-01 | -5.89895283e-01 2.07395648e-01 5.84295703e-01 12 -3.82094837e-01 1.10160390e+00 6.35691675e-01 | -3.82094837e-01 1.10160390e+00 6.35691675e-01 13 -8.81286923e-01 3.86368599e-01 -3.29806702e-01 | -8.81286923e-01 3.86368599e-01 -3.29806702e-01 14 -1.63877953e+00 1.18775943e+00 -2.91863555e+00 | -1.63877953e+00 1.18775943e+00 -2.91863555e+00 15 -6.46798911e+00 1.76645161e+00 -1.34136210e+01 | -6.46798911e+00 1.76645161e+00 -1.34136210e+01 16 -1.26758282e+01 -1.76165533e+01 -1.63255473e+01 | -1.26758282e+01 -1.76165533e+01 -1.63255473e+01 17 3.28018381e+00 1.57659169e+01 1.87349199e+01 | 3.28018381e+00 1.57659169e+01 1.87349199e+01 18 5.91821881e+00 4.82500097e+00 -4.56957544e+00 | 5.91821881e+00 4.82500097e+00 -4.56957544e+00 19 -5.41103583e-02 7.81310194e-01 -7.90500647e-01 | -5.41103583e-02 7.81310194e-01 -7.90500647e-01 20 -2.49404214e+01 3.74286495e+01 4.33500583e+01 | -2.49404214e+01 3.74286495e+01 4.33500583e+01 21 -8.16725355e+01 7.11698493e+01 -4.58053455e+01 | -8.16725355e+01 7.11698493e+01 -4.58053455e+01 22 3.92175878e-01 -4.81957281e-01 -1.23658695e-01 | 3.92175878e-01 -4.81957281e-01 -1.23658695e-01 23 2.99142238e-01 -2.19323539e-01 6.63907793e-01 | 2.99142238e-01 -2.19323539e-01 6.63907793e-01 24 -1.12540486e+00 -4.45990108e+00 -3.17822492e+00 | -1.12540486e+00 -4.45990108e+00 -3.17822492e+00 25 3.04116357e+00 -2.13346666e+00 -1.61730815e-01 | 3.04116357e+00 -2.13346666e+00 -1.61730815e-01 26 2.75550464e-01 2.32066543e+00 -2.75139850e+00 | 2.75550464e-01 2.32066543e+00 -2.75139850e+00 27 -1.45361852e-01 -4.45327484e-01 1.48095766e+00 | -1.45361852e-01 -4.45327484e-01 1.48095766e+00 28 -6.09264845e-01 8.61932478e-01 3.42095162e-01 | -6.09264845e-01 8.61932478e-01 3.42095162e-01 29 -8.94873824e-01 -3.31718406e-01 -2.15667964e-01 | -8.94873824e-01 -3.31718406e-01 -2.15667964e-01 30 -3.21951425e+00 7.49496993e-01 6.13505402e+00 | -3.21951425e+00 7.49496993e-01 6.13505402e+00 31 8.21623462e-01 7.60898423e-01 5.73931445e-01 | 8.21623462e-01 7.60898423e-01 5.73931445e-01 32 7.88769032e-01 9.12363579e-01 -6.62326634e-01 | 7.88769032e-01 9.12363579e-01 -6.62326634e-01 33 -4.86927371e+01 -3.55179968e+01 7.61747605e+01 | -4.86927371e+01 -3.55179968e+01 7.61747605e+01 34 3.54049345e+01 3.46549236e+01 -5.64776430e+01 | 3.54049345e+01 3.46549236e+01 -5.64776430e+01 35 5.57645865e+00 -6.34629619e+00 -3.99825730e+00 | 5.57645865e+00 -6.34629619e+00 -3.99825730e+00 36 -1.83308446e+00 -2.32459434e+00 -6.42374468e-01 | -1.83308446e+00 -2.32459434e+00 -6.42374468e-01 37 -5.98313463e+00 -2.08489179e+00 3.87389653e+00 | -5.98313463e+00 -2.08489179e+00 3.87389653e+00 38 -9.39888712e+00 -1.13036642e+01 -4.08879893e+00 | -9.39888712e+00 -1.13036642e+01 -4.08879893e+00 39 7.39210684e+00 1.11685345e+01 5.92712388e+00 | 7.39210684e+00 1.11685345e+01 5.92712388e+00 40 3.64324130e-01 -9.19595496e-01 -7.59678120e-01 | 3.64324130e-01 -9.19595496e-01 -7.59678120e-01 41 1.18278241e+01 -1.67932331e+01 -1.78842068e+01 | 1.18278241e+01 -1.67932331e+01 -1.78842068e+01 42 9.06763496e+00 -1.54650365e+00 1.59509810e+01 | 9.06763496e+00 -1.54650365e+00 1.59509810e+01 43 2.33190102e+00 -4.63844969e-01 -6.37490148e-01 | 2.33190102e+00 -4.63844969e-01 -6.37490148e-01 44 -6.00261595e+00 -3.63079401e+01 -5.15360677e+00 | -6.00261595e+00 -3.63079401e+01 -5.15360677e+00 45 5.54734219e+00 3.70203582e+01 4.50467710e+00 | 5.54734219e+00 3.70203582e+01 4.50467710e+00 46 -3.49955290e+00 2.18128446e+01 1.41510034e+01 | -3.49955290e+00 2.18128446e+01 1.41510034e+01 47 -1.46456468e+01 -7.18341982e+00 1.29772870e+01 | -1.46456468e+01 -7.18341982e+00 1.29772870e+01 48 -6.40632784e+01 -3.68878871e+01 3.74702295e+00 | -6.40632784e+01 -3.68878871e+01 3.74702295e+00 49 6.27716242e+01 3.73932443e+01 -5.94806384e+00 | 6.27716242e+01 3.73932443e+01 -5.94806384e+00 50 -2.08438763e+00 6.84994691e-02 1.70921102e-01 | -2.08438763e+00 6.84994691e-02 1.70921102e-01 51 1.43081122e+00 1.51441209e+00 -1.31164671e+00 | 1.43081122e+00 1.51441209e+00 -1.31164671e+00 52 -3.70812085e+00 3.32903316e+00 -1.15154839e+00 | -3.70812085e+00 3.32903316e+00 -1.15154839e+00 53 2.33017636e+00 2.72264835e+00 3.40109213e+00 | 2.33017636e+00 2.72264835e+00 3.40109213e+00 54 -4.36120809e+01 -2.35585670e+02 -1.72771044e+02 | -4.36120809e+01 -2.35585670e+02 -1.72771044e+02 55 4.39863667e+01 2.35242522e+02 1.72500035e+02 | 4.39863667e+01 2.35242522e+02 1.72500035e+02 56 8.23835034e+01 -7.31311819e+01 4.53929324e+01 | 8.23835034e+01 -7.31311819e+01 4.53929324e+01 57 6.67778375e-01 -9.75694052e+00 -2.49238990e+00 | 6.67778375e-01 -9.75694052e+00 -2.49238990e+00 58 6.05005439e+00 -8.82936615e-02 -6.55579708e+00 | 6.05005439e+00 -8.82936615e-02 -6.55579708e+00 59 -8.40411824e-01 -7.11735084e-01 1.98284096e-01 | -8.40411824e-01 -7.11735084e-01 1.98284096e-01 60 9.62837057e+00 6.95652823e+00 -1.44942975e+01 | 9.62837057e+00 6.95652823e+00 -1.44942975e+01 61 3.02580340e+00 1.12227881e+00 1.11910339e+00 | 3.02580340e+00 1.12227881e+00 1.11910339e+00 62 -7.84804831e+00 8.82510270e+00 1.03739776e+01 | -7.84804831e+00 8.82510270e+00 1.03739776e+01 63 5.63507445e-01 -6.23048209e-01 -7.65069587e-01 | 5.63507445e-01 -6.23048209e-01 -7.65069587e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Mn (Configuration in file "config-Mn.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [36, 51, 62, 58, 55, 18, 34, 60, 28, 15, 29, 42, 27, 63, 40, 9, 26, 45, 5, 20, 19, 41, 54, 43, 49, 30, 16, 12, 8, 10, 25, 52, 57, 59, 6, 44, 0, 38, 37, 53, 14, 21, 11, 23, 35, 17, 48, 50, 46, 24, 47, 1, 31, 39, 22, 4, 61, 32, 3, 33, 7, 56, 2, 13] 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)) = 2.3395417489137795 V(r_1,...,r_N) = 2.339541748913747 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 -3.23451560e+00 -9.26324064e-01 -1.72894509e+00 | -3.23451560e+00 -9.26324064e-01 -1.72894509e+00 1 5.11350067e+00 -4.75445728e-01 2.29707438e+00 | 5.11350067e+00 -4.75445728e-01 2.29707438e+00 2 -3.92486499e+01 -2.24470505e+01 -2.86004220e+01 | -3.92486499e+01 -2.24470505e+01 -2.86004220e+01 3 4.00784719e+01 2.40237990e+01 2.77802821e+01 | 4.00784719e+01 2.40237990e+01 2.77802821e+01 4 -9.47116918e-01 -1.60223449e-01 -1.12258777e+00 | -9.47116918e-01 -1.60223449e-01 -1.12258777e+00 5 -4.74055400e+00 -4.31129707e+01 4.18839541e+01 | -4.74055400e+00 -4.31129707e+01 4.18839541e+01 6 -1.75771939e+00 1.69637098e+00 1.65135520e+00 | -1.75771939e+00 1.69637098e+00 1.65135520e+00 7 3.73912265e+00 1.96096583e+00 -6.07724243e+00 | 3.73912265e+00 1.96096583e+00 -6.07724243e+00 8 4.61008819e-02 7.57965797e-01 9.47071885e-01 | 4.61008819e-02 7.57965797e-01 9.47071885e-01 9 -6.73728938e-01 2.94479994e-01 -1.22364581e+00 | -6.73728938e-01 2.94479994e-01 -1.22364581e+00 10 -6.31783217e-01 -1.97784350e-01 3.64722533e-01 | -6.31783217e-01 -1.97784350e-01 3.64722533e-01 11 9.88604549e-01 -4.93546120e-01 -5.90438356e-01 | 9.88604549e-01 -4.93546120e-01 -5.90438356e-01 12 9.48486879e-01 1.49807986e-01 4.43043228e-01 | 9.48486879e-01 1.49807986e-01 4.43043228e-01 13 6.59116755e-02 -5.84677725e-02 -6.60637421e-01 | 6.59116755e-02 -5.84677725e-02 -6.60637421e-01 14 4.49124986e+00 4.41526228e+01 -3.88270816e+01 | 4.49124986e+00 4.41526228e+01 -3.88270816e+01 15 -1.91564187e+00 -1.66652581e+00 1.12424344e+00 | -1.91564187e+00 -1.66652581e+00 1.12424344e+00 16 7.73316634e-01 -7.29128965e-01 1.03997251e+00 | 7.73316634e-01 -7.29128965e-01 1.03997251e+00 17 1.07764142e+01 -5.21090520e+00 -1.15188520e+01 | 1.07764142e+01 -5.21090520e+00 -1.15188520e+01 18 -6.21342539e-01 -4.62693063e-01 2.49522965e-01 | -6.21342539e-01 -4.62693063e-01 2.49522965e-01 19 -7.42441263e+00 1.82070671e-01 -1.59406612e+00 | -7.42441263e+00 1.82070671e-01 -1.59406612e+00 20 -9.14412599e+00 -7.46396338e+00 -5.35065653e+00 | -9.14412599e+00 -7.46396338e+00 -5.35065653e+00 21 5.39096571e+00 4.02755506e+00 1.05325822e+01 | 5.39096571e+00 4.02755506e+00 1.05325822e+01 22 -1.11888064e+01 2.66114809e+00 1.25686051e+01 | -1.11888064e+01 2.66114809e+00 1.25686051e+01 23 3.78686898e+00 -1.92037189e-01 -7.14540871e-01 | 3.78686898e+00 -1.92037189e-01 -7.14540871e-01 24 8.73519422e-01 2.61855317e-01 6.55326809e-01 | 8.73519422e-01 2.61855317e-01 6.55326809e-01 25 -9.07412915e+00 3.42032226e+00 1.26996729e+01 | -9.07412915e+00 3.42032226e+00 1.26996729e+01 26 8.61602052e+00 -3.21521501e+00 -1.06131148e+01 | 8.61602052e+00 -3.21521501e+00 -1.06131148e+01 27 -6.35556994e-01 -1.54543625e+00 2.45424709e-02 | -6.35556994e-01 -1.54543625e+00 2.45424709e-02 28 -9.92329063e-02 3.98330339e-01 -7.06870895e-01 | -9.92329063e-02 3.98330339e-01 -7.06870895e-01 29 -8.13832208e-02 -2.60939750e-02 -4.16444886e-02 | -8.13832208e-02 -2.60939750e-02 -4.16444886e-02 30 1.21990781e+01 3.31139088e+00 -2.25657750e+00 | 1.21990781e+01 3.31139088e+00 -2.25657750e+00 31 -2.69360966e+01 5.44503476e+00 -1.14669383e+01 | -2.69360966e+01 5.44503476e+00 -1.14669383e+01 32 8.49160381e-01 1.05988306e+00 -3.40370169e-01 | 8.49160381e-01 1.05988306e+00 -3.40370169e-01 33 -5.74023517e+00 6.85446886e-01 -1.66424681e+01 | -5.74023517e+00 6.85446886e-01 -1.66424681e+01 34 -6.11668969e-01 1.32014785e-01 -2.73439151e-01 | -6.11668969e-01 1.32014785e-01 -2.73439151e-01 35 -7.13049727e-01 -1.33822397e+00 1.27657063e-01 | -7.13049727e-01 -1.33822397e+00 1.27657063e-01 36 1.06560239e+01 -7.83721698e+00 7.11080741e+00 | 1.06560239e+01 -7.83721698e+00 7.11080741e+00 37 -7.42805712e-02 3.31581372e+00 1.92903908e+00 | -7.42805712e-02 3.31581372e+00 1.92903908e+00 38 -3.80267607e+00 5.80702726e+00 5.77892538e+00 | -3.80267607e+00 5.80702726e+00 5.77892538e+00 39 2.80501455e-01 1.24178707e-01 -9.41683194e-01 | 2.80501455e-01 1.24178707e-01 -9.41683194e-01 40 -2.41210235e+01 -4.50117568e+01 -3.17858791e+01 | -2.41210235e+01 -4.50117568e+01 -3.17858791e+01 41 1.33169376e+01 3.81646765e+01 3.41086464e+01 | 1.33169376e+01 3.81646765e+01 3.41086464e+01 42 4.96454202e+00 1.79456044e+00 -3.77052183e+00 | 4.96454202e+00 1.79456044e+00 -3.77052183e+00 43 2.48876811e+00 5.49560664e+00 8.91911408e-01 | 2.48876811e+00 5.49560664e+00 8.91911408e-01 44 5.86325439e-01 1.06744552e+00 1.29295465e-01 | 5.86325439e-01 1.06744552e+00 1.29295465e-01 45 -6.82061032e-01 2.14393404e-01 -6.08054838e-01 | -6.82061032e-01 2.14393404e-01 -6.08054838e-01 46 -1.51475649e+01 -9.59881805e+00 -1.03491381e+01 | -1.51475649e+01 -9.59881805e+00 -1.03491381e+01 47 1.61517252e+01 1.00110642e+01 8.69704341e+00 | 1.61517252e+01 1.00110642e+01 8.69704341e+00 48 -2.41045498e+00 -1.03055075e+00 5.51568795e+00 | -2.41045498e+00 -1.03055075e+00 5.51568795e+00 49 -4.43079390e+00 1.46459775e+01 -1.45555495e+01 | -4.43079390e+00 1.46459775e+01 -1.45555495e+01 50 -1.58068321e+01 -7.79706992e+00 -1.09558569e+01 | -1.58068321e+01 -7.79706992e+00 -1.09558569e+01 51 1.53045621e+01 5.90368459e+00 8.86726913e+00 | 1.53045621e+01 5.90368459e+00 8.86726913e+00 52 6.57103922e+00 -1.56385020e+01 1.32505028e+01 | 6.57103922e+00 -1.56385020e+01 1.32505028e+01 53 -6.91451948e+00 -8.22088055e+00 5.57066795e+00 | -6.91451948e+00 -8.22088055e+00 5.57066795e+00 54 -2.09105544e+00 -1.42772674e+00 3.59875568e-01 | -2.09105544e+00 -1.42772674e+00 3.59875568e-01 55 1.64251022e+00 4.62058648e-01 3.71730706e-01 | 1.64251022e+00 4.62058648e-01 3.71730706e-01 56 -9.48300515e+00 -5.20600220e+00 -6.34280757e+00 | -9.48300515e+00 -5.20600220e+00 -6.34280757e+00 57 2.17670600e+00 1.35961970e+01 3.27647607e+00 | 2.17670600e+00 1.35961970e+01 3.27647607e+00 58 2.54614045e+01 -6.63630125e+00 1.31073705e+01 | 2.54614045e+01 -6.63630125e+00 1.31073705e+01 59 -7.10439859e-01 -6.38825299e-01 5.19553300e-03 | -7.10439859e-01 -6.38825299e-01 5.19553300e-03 60 6.49448345e+00 -3.00087322e+00 3.66452324e+00 | 6.49448345e+00 -3.00087322e+00 3.66452324e+00 61 -9.37386071e-01 -4.34995866e-01 -8.75987033e-01 | -9.37386071e-01 -4.34995866e-01 -8.75987033e-01 62 5.02950382e+00 4.54074893e+00 -7.75517120e+00 | 5.02950382e+00 4.54074893e+00 -7.75517120e+00 63 2.17001714e+00 2.43705762e+00 1.26659180e+00 | 2.17001714e+00 2.43705762e+00 1.26659180e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [30, 54, 25, 15, 60, 39, 28, 10, 12, 29, 7, 14, 8, 57, 11, 3, 19, 47, 49, 16, 56, 33, 38, 43, 61, 2, 63, 58, 6, 9, 0, 55, 44, 21, 36, 48, 34, 52, 22, 5, 59, 42, 41, 23, 32, 51, 53, 17, 35, 18, 62, 45, 37, 46, 1, 31, 20, 13, 27, 40, 4, 24, 50, 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)) = -30.814191764240096 V(r_1,...,r_N) = -30.814191764240103 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 -1.81511690e+01 -2.17671498e+01 -2.11823681e+01 | -1.81511690e+01 -2.17671498e+01 -2.11823681e+01 1 2.49070589e+01 1.09962663e+01 1.43988659e+01 | 2.49070589e+01 1.09962663e+01 1.43988659e+01 2 -1.09759685e+01 -1.87959224e+01 -8.39219103e+00 | -1.09759685e+01 -1.87959224e+01 -8.39219103e+00 3 7.66127010e+00 9.73347996e+00 1.09945455e+01 | 7.66127010e+00 9.73347996e+00 1.09945455e+01 4 -2.99316263e+01 -2.74708131e+01 -4.95154694e+00 | -2.99316263e+01 -2.74708131e+01 -4.95154694e+00 5 2.83123705e+01 2.60520094e+01 6.18756498e+00 | 2.83123705e+01 2.60520094e+01 6.18756498e+00 6 -6.67240056e+00 1.08648483e+01 6.67042238e+00 | -6.67240056e+00 1.08648483e+01 6.67042238e+00 7 5.01816275e-01 1.22796517e+00 -1.20661097e-01 | 5.01816275e-01 1.22796517e+00 -1.20661097e-01 8 3.83014660e-02 3.01622509e-01 2.06268920e-01 | 3.83014660e-02 3.01622509e-01 2.06268920e-01 9 -1.72481816e+01 1.26167236e+01 -3.50107439e+01 | -1.72481816e+01 1.26167236e+01 -3.50107439e+01 10 -1.07489476e+01 -1.15869357e+01 -2.43750558e+01 | -1.07489476e+01 -1.15869357e+01 -2.43750558e+01 11 1.10516070e+01 1.08753913e+01 2.33968906e+01 | 1.10516070e+01 1.08753913e+01 2.33968906e+01 12 2.03181110e+01 -1.61101602e+01 3.10686943e+01 | 2.03181110e+01 -1.61101602e+01 3.10686943e+01 13 3.89467752e+00 -5.06863012e+00 -1.57256479e+00 | 3.89467752e+00 -5.06863012e+00 -1.57256479e+00 14 -3.40714489e+00 4.14229787e+00 1.10796922e+00 | -3.40714489e+00 4.14229787e+00 1.10796922e+00 15 -5.12641643e+00 3.17638159e+00 -3.94907510e+00 | -5.12641643e+00 3.17638159e+00 -3.94907510e+00 16 -9.59436909e-01 -6.50827248e-01 -8.23838548e-01 | -9.59436909e-01 -6.50827248e-01 -8.23838548e-01 17 -1.50514934e+00 6.26501047e-01 5.75353655e-01 | -1.50514934e+00 6.26501047e-01 5.75353655e-01 18 -1.21325992e+00 -5.51391606e+00 -3.04485552e+00 | -1.21325992e+00 -5.51391606e+00 -3.04485552e+00 19 1.80748200e+00 6.10039355e+00 2.20313703e+00 | 1.80748200e+00 6.10039355e+00 2.20313703e+00 20 -3.92875451e+00 2.48694563e-01 7.55357191e-01 | -3.92875451e+00 2.48694563e-01 7.55357191e-01 21 -6.26401896e+00 1.11801457e+01 -8.48513417e+00 | -6.26401896e+00 1.11801457e+01 -8.48513417e+00 22 -2.87263476e+00 -2.47137591e+00 -4.84203798e+00 | -2.87263476e+00 -2.47137591e+00 -4.84203798e+00 23 -2.52368438e+00 7.92131273e+00 1.34087443e+00 | -2.52368438e+00 7.92131273e+00 1.34087443e+00 24 6.00377549e+00 6.53416980e+00 -4.98296050e+00 | 6.00377549e+00 6.53416980e+00 -4.98296050e+00 25 2.25371361e+01 -2.32462918e+00 1.78309738e+00 | 2.25371361e+01 -2.32462918e+00 1.78309738e+00 26 -4.35701313e+00 -1.42417069e+00 -6.72865130e+00 | -4.35701313e+00 -1.42417069e+00 -6.72865130e+00 27 4.62509146e+00 2.10892511e+00 4.33281590e+00 | 4.62509146e+00 2.10892511e+00 4.33281590e+00 28 2.83680136e+00 -4.44586329e+00 2.93773786e+00 | 2.83680136e+00 -4.44586329e+00 2.93773786e+00 29 5.24342169e+00 -1.54337811e+01 -8.41960668e+00 | 5.24342169e+00 -1.54337811e+01 -8.41960668e+00 30 -2.66062493e+01 5.21313088e+00 -4.85910298e-01 | -2.66062493e+01 5.21313088e+00 -4.85910298e-01 31 -1.33590339e+00 4.37071151e-01 -4.90936979e-01 | -1.33590339e+00 4.37071151e-01 -4.90936979e-01 32 3.74666515e-01 3.70722799e-01 -6.56234705e-01 | 3.74666515e-01 3.70722799e-01 -6.56234705e-01 33 -5.41038378e+01 3.43842346e+01 -3.37210177e+01 | -5.41038378e+01 3.43842346e+01 -3.37210177e+01 34 -1.66964880e+01 -2.05320475e+01 -1.21043357e+01 | -1.66964880e+01 -2.05320475e+01 -1.21043357e+01 35 1.95837083e+01 2.09428563e+01 7.67776745e+00 | 1.95837083e+01 2.09428563e+01 7.67776745e+00 36 5.39042210e+01 -3.56051706e+01 3.58639300e+01 | 5.39042210e+01 -3.56051706e+01 3.58639300e+01 37 -2.05266514e-01 7.61742633e-01 -1.09853381e+00 | -2.05266514e-01 7.61742633e-01 -1.09853381e+00 38 -2.69111343e+00 -2.46392265e+00 -2.43400484e+00 | -2.69111343e+00 -2.46392265e+00 -2.43400484e+00 39 2.15102534e+00 1.51040454e+00 3.41863187e+00 | 2.15102534e+00 1.51040454e+00 3.41863187e+00 40 -1.79913297e+00 -6.24238702e-01 -7.13866577e-01 | -1.79913297e+00 -6.24238702e-01 -7.13866577e-01 41 -7.35257054e+00 1.73416891e+01 -1.32786191e+01 | -7.35257054e+00 1.73416891e+01 -1.32786191e+01 42 2.41759943e+00 3.81038860e+00 7.15305932e+00 | 2.41759943e+00 3.81038860e+00 7.15305932e+00 43 2.75959088e+00 -1.47091551e+00 -1.58255822e+00 | 2.75959088e+00 -1.47091551e+00 -1.58255822e+00 44 7.96162192e+00 -1.74352318e+01 1.41530907e+01 | 7.96162192e+00 -1.74352318e+01 1.41530907e+01 45 1.67813890e-01 1.12937386e+00 -2.76053373e-02 | 1.67813890e-01 1.12937386e+00 -2.76053373e-02 46 -9.42808289e+00 -7.35323751e+00 -6.89228223e+00 | -9.42808289e+00 -7.35323751e+00 -6.89228223e+00 47 9.00241759e+00 5.81643826e+00 8.32710987e+00 | 9.00241759e+00 5.81643826e+00 8.32710987e+00 48 -8.27579265e+00 -2.81583017e+00 -5.87468982e+00 | -8.27579265e+00 -2.81583017e+00 -5.87468982e+00 49 -2.87036312e+00 -9.30174542e+00 2.02836523e+01 | -2.87036312e+00 -9.30174542e+00 2.02836523e+01 50 1.38199614e+01 1.48457647e+01 -1.76679251e+01 | 1.38199614e+01 1.48457647e+01 -1.76679251e+01 51 -1.12016574e-01 1.49891701e+01 -8.61257319e+00 | -1.12016574e-01 1.49891701e+01 -8.61257319e+00 52 3.05268610e+00 -6.52126298e+00 8.85059537e+00 | 3.05268610e+00 -6.52126298e+00 8.85059537e+00 53 -5.37180467e-01 -4.66290053e-02 -3.36210662e-01 | -5.37180467e-01 -4.66290053e-02 -3.36210662e-01 54 -1.22661727e+01 -8.67417881e+00 -1.27341966e+01 | -1.22661727e+01 -8.67417881e+00 -1.27341966e+01 55 1.30955101e+01 7.84313249e+00 1.22580045e+01 | 1.30955101e+01 7.84313249e+00 1.22580045e+01 56 7.60704041e+00 -1.02318609e+01 1.04333121e+01 | 7.60704041e+00 -1.02318609e+01 1.04333121e+01 57 -1.44296733e+01 2.55515004e+01 -1.24196632e+01 | -1.44296733e+01 2.55515004e+01 -1.24196632e+01 58 -8.08338768e+00 -3.52528723e+00 1.64719841e+00 | -8.08338768e+00 -3.52528723e+00 1.64719841e+00 59 3.93471677e+00 1.80394784e+01 7.88682874e+00 | 3.93471677e+00 1.80394784e+01 7.88682874e+00 60 1.34388684e+01 -2.24025751e+01 1.50114633e+01 | 1.34388684e+01 -2.24025751e+01 1.50114633e+01 61 5.56654606e-01 -3.64604968e-01 -4.25390520e-01 | 5.56654606e-01 -3.64604968e-01 -4.25390520e-01 62 -5.46621903e-01 -1.45079287e+01 8.64752363e+00 | -5.46621903e-01 -1.45079287e+01 8.64752363e+00 63 -3.41363618e-01 -7.53384855e-01 -1.13391663e+00 | -3.41363618e-01 -7.53384855e-01 -1.13391663e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Co Cr Fe Mn Ni (Configuration in file "config-CoCrFeMnNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [12, 23, 30, 57, 34, 11, 31, 24, 38, 42, 39, 5, 0, 55, 52, 33, 50, 37, 44, 62, 63, 46, 40, 1, 7, 29, 35, 61, 41, 25, 2, 6, 56, 15, 4, 26, 36, 17, 8, 10, 22, 28, 9, 47, 18, 45, 21, 43, 58, 53, 16, 54, 14, 49, 51, 13, 32, 3, 48, 59, 60, 27, 19, 20] 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)) = 263.7171970845428 V(r_1,...,r_N) = 263.71719708454293 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 -3.06185183e+01 -5.27553200e+01 -5.86864280e+01 | -3.06185183e+01 -5.27553200e+01 -5.86864280e+01 1 3.89976829e+01 3.58630467e+01 5.37252133e+01 | 3.89976829e+01 3.58630467e+01 5.37252133e+01 2 -2.50613428e+00 2.16061728e+00 1.38732697e+00 | -2.50613428e+00 2.16061728e+00 1.38732697e+00 3 1.62338389e+01 -1.29223866e+01 -1.36873227e+01 | 1.62338389e+01 -1.29223866e+01 -1.36873227e+01 4 -3.61324646e-01 -1.73899609e+00 -7.11650227e-01 | -3.61324646e-01 -1.73899609e+00 -7.11650227e-01 5 -5.03804027e+01 -6.16169623e+00 -1.02589970e+01 | -5.03804027e+01 -6.16169623e+00 -1.02589970e+01 6 -7.87774831e+00 1.60563064e+01 4.57851340e+00 | -7.87774831e+00 1.60563064e+01 4.57851340e+00 7 -4.99938079e+01 -9.46706426e+00 -1.49923661e+01 | -4.99938079e+01 -9.46706426e+00 -1.49923661e+01 8 3.65092249e-01 1.91577047e-01 1.15890941e+00 | 3.65092249e-01 1.91577047e-01 1.15890941e+00 9 -2.16575071e+01 7.06622430e+01 -4.89534576e+01 | -2.16575071e+01 7.06622430e+01 -4.89534576e+01 10 -6.36542403e+01 -5.94172607e+01 -1.39594118e+02 | -6.36542403e+01 -5.94172607e+01 -1.39594118e+02 11 6.48267901e+01 5.52775806e+01 1.34446037e+02 | 6.48267901e+01 5.52775806e+01 1.34446037e+02 12 2.14865784e+01 -6.94886293e+01 4.97828161e+01 | 2.14865784e+01 -6.94886293e+01 4.97828161e+01 13 1.68853379e+00 -1.54041061e+00 -1.08176324e+00 | 1.68853379e+00 -1.54041061e+00 -1.08176324e+00 14 3.50956308e+01 5.89882423e+01 -1.83150010e+01 | 3.50956308e+01 5.89882423e+01 -1.83150010e+01 15 -7.97845747e+00 3.44661583e+01 -1.47447797e+01 | -7.97845747e+00 3.44661583e+01 -1.47447797e+01 16 -1.39683553e+01 -1.95255711e+01 2.84006527e+00 | -1.39683553e+01 -1.95255711e+01 2.84006527e+00 17 -1.20725187e+01 6.97084594e+00 -2.64533217e+00 | -1.20725187e+01 6.97084594e+00 -2.64533217e+00 18 -3.77675012e+01 -6.39960348e+01 -6.53677302e+01 | -3.77675012e+01 -6.39960348e+01 -6.53677302e+01 19 5.96456115e+01 7.58836156e+01 6.39315366e+01 | 5.96456115e+01 7.58836156e+01 6.39315366e+01 20 -1.91507795e+01 6.21393200e+00 1.24666742e+01 | -1.91507795e+01 6.21393200e+00 1.24666742e+01 21 -8.87627419e-01 1.55892277e+00 -1.96626267e-04 | -8.87627419e-01 1.55892277e+00 -1.96626267e-04 22 -1.72485138e-01 -1.63730748e+00 -7.03089496e-01 | -1.72485138e-01 -1.63730748e+00 -7.03089496e-01 23 -2.86699334e+01 2.96534333e+01 -1.91976498e+01 | -2.86699334e+01 2.96534333e+01 -1.91976498e+01 24 -1.53767053e+01 -1.71911483e+00 -8.69007700e+00 | -1.53767053e+01 -1.71911483e+00 -8.69007700e+00 25 1.71633360e+01 5.99564738e+00 8.20039351e+00 | 1.71633360e+01 5.99564738e+00 8.20039351e+00 26 -1.88503279e+02 -2.41511455e+02 -1.44950960e+02 | -1.88503279e+02 -2.41511455e+02 -1.44950960e+02 27 1.89127756e+02 2.42531108e+02 1.44209218e+02 | 1.89127756e+02 2.42531108e+02 1.44209218e+02 28 -5.93094733e-01 3.49004926e+00 4.75625628e+00 | -5.93094733e-01 3.49004926e+00 4.75625628e+00 29 2.99862539e+01 -2.75194369e+01 -1.11904630e+00 | 2.99862539e+01 -2.75194369e+01 -1.11904630e+00 30 4.99327435e+00 -1.62751213e+00 3.28514124e+00 | 4.99327435e+00 -1.62751213e+00 3.28514124e+00 31 -6.91265690e+00 4.59259400e+01 -8.62830203e-01 | -6.91265690e+00 4.59259400e+01 -8.62830203e-01 32 -1.69482638e-01 -1.52004851e+00 -2.34913720e+00 | -1.69482638e-01 -1.52004851e+00 -2.34913720e+00 33 -2.45854277e+01 3.96004021e+01 -4.56817113e+01 | -2.45854277e+01 3.96004021e+01 -4.56817113e+01 34 5.07687134e+01 8.89358782e+00 1.33608254e+01 | 5.07687134e+01 8.89358782e+00 1.33608254e+01 35 -5.68303340e-01 3.63395491e+00 -6.15511951e+00 | -5.68303340e-01 3.63395491e+00 -6.15511951e+00 36 2.71152160e+01 -3.75290922e+01 4.49043564e+01 | 2.71152160e+01 -3.75290922e+01 4.49043564e+01 37 5.23578131e-01 1.09677115e-02 2.54477803e+00 | 5.23578131e-01 1.09677115e-02 2.54477803e+00 38 -2.91011398e+00 -2.50908458e+00 -3.20025994e+00 | -2.91011398e+00 -2.50908458e+00 -3.20025994e+00 39 2.47019719e+00 2.91927253e+00 4.41733814e+00 | 2.47019719e+00 2.91927253e+00 4.41733814e+00 40 1.41347028e+01 -5.04221682e+01 3.15738284e+01 | 1.41347028e+01 -5.04221682e+01 3.15738284e+01 41 7.82387397e-02 1.65704239e+00 -8.33162554e-01 | 7.82387397e-02 1.65704239e+00 -8.33162554e-01 42 4.56074161e+00 -3.36116746e+01 1.63621517e+01 | 4.56074161e+00 -3.36116746e+01 1.63621517e+01 43 -1.35603351e+00 -4.93680363e-01 -1.46559878e-01 | -1.35603351e+00 -4.93680363e-01 -1.46559878e-01 44 -9.76133141e+01 -1.20088882e+02 -2.57642766e+01 | -9.76133141e+01 -1.20088882e+02 -2.57642766e+01 45 9.77742896e+01 1.20060105e+02 2.57382310e+01 | 9.77742896e+01 1.20060105e+02 2.57382310e+01 46 2.74928827e+00 -3.00560377e+00 2.97532360e+00 | 2.74928827e+00 -3.00560377e+00 2.97532360e+00 47 -1.76465739e+00 -2.07491231e+00 1.19459433e+00 | -1.76465739e+00 -2.07491231e+00 1.19459433e+00 48 2.18495765e-01 1.42281319e+00 -8.24864911e-01 | 2.18495765e-01 1.42281319e+00 -8.24864911e-01 49 -1.43072223e-01 -1.91711670e-01 2.05546761e+00 | -1.43072223e-01 -1.91711670e-01 2.05546761e+00 50 2.11515436e+01 -3.72459433e+01 2.65474714e+00 | 2.11515436e+01 -3.72459433e+01 2.65474714e+00 51 8.97497046e+00 8.55765206e+00 1.68116815e+01 | 8.97497046e+00 8.55765206e+00 1.68116815e+01 52 -2.31268224e+01 -3.67595407e+01 -1.20525277e+01 | -2.31268224e+01 -3.67595407e+01 -1.20525277e+01 53 1.97496215e+01 3.62227209e+01 1.38015733e+01 | 1.97496215e+01 3.62227209e+01 1.38015733e+01 54 6.04492664e-01 3.31222603e-01 2.35746818e-01 | 6.04492664e-01 3.31222603e-01 2.35746818e-01 55 -3.32929945e-01 -1.18556381e+00 -1.38183690e+00 | -3.32929945e-01 -1.18556381e+00 -1.38183690e+00 56 -6.51751694e+00 -1.09627873e+01 -8.06916479e+00 | -6.51751694e+00 -1.09627873e+01 -8.06916479e+00 57 2.32380774e+00 1.46248619e+01 9.41944854e+00 | 2.32380774e+00 1.46248619e+01 9.41944854e+00 58 -2.07230207e+01 -1.43213859e+01 -3.06234549e+00 | -2.07230207e+01 -1.43213859e+01 -3.06234549e+00 59 -5.02038751e-01 -3.11260503e+00 1.53357832e+00 | -5.02038751e-01 -3.11260503e+00 1.53357832e+00 60 6.40378859e+00 -5.26756748e+00 3.63395417e+00 | 6.40378859e+00 -5.26756748e+00 3.63395417e+00 61 9.19512646e-01 9.20344765e-01 -3.58946521e+00 | 9.19512646e-01 9.20344765e-01 -3.58946521e+00 62 5.08794518e-01 5.58583716e-02 -4.47275263e-01 | 5.08794518e-01 5.58583716e-02 -4.47275263e-01 63 -1.22456107e+00 5.30376376e-01 1.34776626e-01 | -1.22456107e+00 5.30376376e-01 1.34776626e-01 ------------------------------------------------------------------------------------------------------------------------- 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.