!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_FarkasCaro_2020_FeNiCrCoAl__MO_820335782779_000 Supported species : Al Co Cr Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Al (Configuration in file "config-Al.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [61, 27, 18, 12, 36, 46, 44, 40, 22, 38, 49, 26, 3, 14, 13, 62, 19, 58, 2, 16, 34, 28, 8, 29, 53, 33, 11, 1, 21, 23, 45, 35, 59, 25, 20, 31, 4, 39, 9, 37, 7, 47, 63, 55, 6, 30, 5, 41, 51, 10, 54, 48, 56, 24, 50, 43, 52, 60, 17, 32, 57, 0, 15, 42] 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)) = -27.75047405715906 V(r_1,...,r_N) = -27.750474057159103 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -4.17820559e+00 -8.66605161e-01 -1.63219855e+00 | -4.17820559e+00 -8.66605161e-01 -1.63219855e+00 1 1.58749588e+00 -1.07052680e+00 6.83615579e-01 | 1.58749588e+00 -1.07052680e+00 6.83615579e-01 2 -1.48419678e+00 9.39470390e-01 -3.69051259e+00 | -1.48419678e+00 9.39470390e-01 -3.69051259e+00 3 3.35798162e-01 5.00172624e+00 -3.62022503e+00 | 3.35798162e-01 5.00172624e+00 -3.62022503e+00 4 -2.86552900e+00 -3.77460804e+00 2.36383189e+00 | -2.86552900e+00 -3.77460804e+00 2.36383189e+00 5 2.09566369e+00 1.52184707e+00 -7.48216611e-01 | 2.09566369e+00 1.52184707e+00 -7.48216611e-01 6 -2.80573050e+00 -3.33495054e+00 -3.70967308e+00 | -2.80573050e+00 -3.33495054e+00 -3.70967308e+00 7 1.29680859e+00 4.01818208e+00 -1.10641563e+00 | 1.29680859e+00 4.01818208e+00 -1.10641563e+00 8 -1.82319583e+00 -9.39533610e-01 -2.48319134e+00 | -1.82319583e+00 -9.39533610e-01 -2.48319134e+00 9 -2.90932831e+00 2.01110580e+00 3.23737628e+00 | -2.90932831e+00 2.01110580e+00 3.23737628e+00 10 -1.94853651e+00 -1.32111618e+00 -5.91215361e+00 | -1.94853651e+00 -1.32111618e+00 -5.91215361e+00 11 4.17864527e+00 1.50078727e+00 1.69724234e+00 | 4.17864527e+00 1.50078727e+00 1.69724234e+00 12 -7.88854559e-01 -4.35801981e+00 -5.91799640e-01 | -7.88854559e-01 -4.35801981e+00 -5.91799640e-01 13 3.80907825e+00 2.22047050e+00 3.24518840e+00 | 3.80907825e+00 2.22047050e+00 3.24518840e+00 14 -4.72471529e-01 -1.18578648e+00 -2.18207968e+00 | -4.72471529e-01 -1.18578648e+00 -2.18207968e+00 15 3.29871141e+00 6.69057062e-01 5.56520207e-01 | 3.29871141e+00 6.69057062e-01 5.56520207e-01 16 -2.63095673e+00 -2.86037921e+00 -2.26349540e+00 | -2.63095673e+00 -2.86037921e+00 -2.26349540e+00 17 3.09477586e+00 -2.90103600e+00 5.37356929e+00 | 3.09477586e+00 -2.90103600e+00 5.37356929e+00 18 1.35182680e+00 2.41157428e+00 -3.81980400e+00 | 1.35182680e+00 2.41157428e+00 -3.81980400e+00 19 -4.70340626e+00 1.18008707e+00 -2.61088737e+00 | -4.70340626e+00 1.18008707e+00 -2.61088737e+00 20 -2.27363778e+00 -6.10139739e-01 -2.98762733e+00 | -2.27363778e+00 -6.10139739e-01 -2.98762733e+00 21 5.12025051e+00 4.26054231e+00 -4.49633249e+00 | 5.12025051e+00 4.26054231e+00 -4.49633249e+00 22 -2.51451035e+00 -7.68494318e-01 -2.87050520e+00 | -2.51451035e+00 -7.68494318e-01 -2.87050520e+00 23 8.31613433e-01 4.99275033e+00 3.14192001e+00 | 8.31613433e-01 4.99275033e+00 3.14192001e+00 24 -1.64227361e+00 -1.24604586e+00 -2.68177658e+00 | -1.64227361e+00 -1.24604586e+00 -2.68177658e+00 25 -1.42906874e+00 2.31214983e+00 2.39470920e+00 | -1.42906874e+00 2.31214983e+00 2.39470920e+00 26 -1.67736767e+00 1.14821846e+00 -2.76649258e+00 | -1.67736767e+00 1.14821846e+00 -2.76649258e+00 27 1.41305921e+00 3.63696543e-01 1.79845179e+00 | 1.41305921e+00 3.63696543e-01 1.79845179e+00 28 -1.26803266e+00 -4.06016238e+00 1.48314522e+00 | -1.26803266e+00 -4.06016238e+00 1.48314522e+00 29 3.39489907e+00 2.11130148e+00 2.39527599e+00 | 3.39489907e+00 2.11130148e+00 2.39527599e+00 30 2.31879080e+00 -1.48887901e+00 -9.29960846e-01 | 2.31879080e+00 -1.48887901e+00 -9.29960846e-01 31 -2.05476474e+00 1.88301618e+00 7.42041690e-01 | -2.05476474e+00 1.88301618e+00 7.42041690e-01 32 -1.65451059e+00 -1.11370645e+00 -2.74611192e+00 | -1.65451059e+00 -1.11370645e+00 -2.74611192e+00 33 -1.16273510e-01 3.07410715e+00 -7.41123327e-02 | -1.16273510e-01 3.07410715e+00 -7.41123327e-02 34 1.72674806e-01 -4.47932571e+00 -1.23612652e+00 | 1.72674806e-01 -4.47932571e+00 -1.23612652e+00 35 1.72906734e+00 -4.15085380e+00 4.24704824e+00 | 1.72906734e+00 -4.15085380e+00 4.24704824e+00 36 9.24269053e-01 -3.82544455e+00 2.35687259e+00 | 9.24269053e-01 -3.82544455e+00 2.35687259e+00 37 -1.30118536e+00 -2.85443291e+00 2.77975018e+00 | -1.30118536e+00 -2.85443291e+00 2.77975018e+00 38 -4.15681100e+00 -9.18440765e-01 -3.30323623e+00 | -4.15681100e+00 -9.18440765e-01 -3.30323623e+00 39 1.92216842e+00 -2.93858866e+00 4.97881934e+00 | 1.92216842e+00 -2.93858866e+00 4.97881934e+00 40 -1.84277163e+00 -3.40040312e+00 3.27417894e+00 | -1.84277163e+00 -3.40040312e+00 3.27417894e+00 41 2.77249770e+00 3.66402864e+00 -3.46273435e+00 | 2.77249770e+00 3.66402864e+00 -3.46273435e+00 42 -1.28504616e+00 -3.17439843e+00 -2.81526090e+00 | -1.28504616e+00 -3.17439843e+00 -2.81526090e+00 43 3.59923551e+00 1.48935806e+00 3.03699998e+00 | 3.59923551e+00 1.48935806e+00 3.03699998e+00 44 1.34806522e+00 -4.69864123e+00 2.38805651e-01 | 1.34806522e+00 -4.69864123e+00 2.38805651e-01 45 6.91577872e-01 1.44834621e+00 1.03995537e+00 | 6.91577872e-01 1.44834621e+00 1.03995537e+00 46 -1.28112604e+00 1.97319149e+00 -1.32412312e+00 | -1.28112604e+00 1.97319149e+00 -1.32412312e+00 47 2.43165189e+00 2.86052672e+00 2.05232849e+00 | 2.43165189e+00 2.86052672e+00 2.05232849e+00 48 -5.21787426e+00 1.00717479e+00 2.47596352e+00 | -5.21787426e+00 1.00717479e+00 2.47596352e+00 49 -3.34524927e-01 -3.63472209e+00 -4.14067381e-01 | -3.34524927e-01 -3.63472209e+00 -4.14067381e-01 50 1.41325971e+00 -2.09620517e+00 -3.94054670e+00 | 1.41325971e+00 -2.09620517e+00 -3.94054670e+00 51 1.09449155e+00 4.30635358e+00 2.10249698e+00 | 1.09449155e+00 4.30635358e+00 2.10249698e+00 52 -2.93449393e+00 5.45524624e+00 -1.79930247e+00 | -2.93449393e+00 5.45524624e+00 -1.79930247e+00 53 2.00190578e+00 7.31365851e-01 3.09898081e+00 | 2.00190578e+00 7.31365851e-01 3.09898081e+00 54 -7.57563216e+00 7.58404984e-01 1.78138985e+00 | -7.57563216e+00 7.58404984e-01 1.78138985e+00 55 5.31952647e+00 1.20027344e+00 2.02730756e+00 | 5.31952647e+00 1.20027344e+00 2.02730756e+00 56 -6.52606713e-01 -1.14468360e+00 3.27206846e+00 | -6.52606713e-01 -1.14468360e+00 3.27206846e+00 57 -3.38897058e-03 2.26760438e-01 -4.27585705e+00 | -3.38897058e-03 2.26760438e-01 -4.27585705e+00 58 4.76895769e+00 -1.01674464e+00 3.48499805e+00 | 4.76895769e+00 -1.01674464e+00 3.48499805e+00 59 -1.12718442e+00 -9.61417021e-01 3.87694090e-01 | -1.12718442e+00 -9.61417021e-01 3.87694090e-01 60 2.72745329e+00 -8.97087417e-01 1.79455628e+00 | 2.72745329e+00 -8.97087417e-01 1.79455628e+00 61 3.70042937e-01 1.46264359e+00 8.16330044e-01 | 3.70042937e-01 1.46264359e+00 8.16330044e-01 62 9.02305633e-01 4.82338383e+00 3.06590907e+00 | 9.02305633e-01 4.82338383e+00 3.06590907e+00 63 6.36929002e-01 -9.35769257e-01 -9.30514851e-01 | 6.36929002e-01 -9.35769257e-01 -9.30514851e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [59, 33, 48, 4, 3, 45, 27, 44, 61, 32, 15, 41, 43, 19, 30, 10, 46, 28, 26, 13, 50, 25, 24, 49, 22, 21, 18, 6, 17, 58, 14, 47, 9, 1, 60, 53, 57, 62, 54, 51, 55, 11, 52, 12, 7, 5, 16, 31, 2, 23, 20, 39, 42, 35, 38, 40, 63, 36, 29, 0, 34, 8, 37, 56] 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)) = -68.88578563233513 V(r_1,...,r_N) = -68.88578563233514 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -8.34140511e-01 -3.01826451e+00 -3.33977332e+00 | -8.34140511e-01 -3.01826451e+00 -3.33977332e+00 1 -4.72646094e-01 -4.22673286e-01 5.82469042e+00 | -4.72646094e-01 -4.22673286e-01 5.82469042e+00 2 -1.15252543e+00 3.62999215e-01 -2.97685025e+00 | -1.15252543e+00 3.62999215e-01 -2.97685025e+00 3 1.95782243e+00 -2.62795904e-01 3.99583074e+00 | 1.95782243e+00 -2.62795904e-01 3.99583074e+00 4 -3.75202488e+00 -1.24903708e+00 -2.86452435e+00 | -3.75202488e+00 -1.24903708e+00 -2.86452435e+00 5 -3.25275970e+00 1.31055218e+01 -3.05056062e+00 | -3.25275970e+00 1.31055218e+01 -3.05056062e+00 6 -2.22430936e+00 -5.87892045e-01 -1.87150956e+00 | -2.22430936e+00 -5.87892045e-01 -1.87150956e+00 7 -1.06247875e+01 2.52895194e+01 -9.85107855e-01 | -1.06247875e+01 2.52895194e+01 -9.85107855e-01 8 -2.55084130e+00 -3.42489326e-01 -3.22526980e-02 | -2.55084130e+00 -3.42489326e-01 -3.22526980e-02 9 1.67600006e+00 -3.39915234e+00 1.54835761e-01 | 1.67600006e+00 -3.39915234e+00 1.54835761e-01 10 9.76961586e-02 9.64223150e-01 -2.39079628e+00 | 9.76961586e-02 9.64223150e-01 -2.39079628e+00 11 1.10820202e+00 2.71439103e+00 1.95915331e+00 | 1.10820202e+00 2.71439103e+00 1.95915331e+00 12 -2.76815691e+00 -3.19193666e+00 -2.79003182e+00 | -2.76815691e+00 -3.19193666e+00 -2.79003182e+00 13 1.31855643e+00 4.86026942e+00 3.74834712e+00 | 1.31855643e+00 4.86026942e+00 3.74834712e+00 14 -2.44446938e+00 1.79227820e+00 3.23257661e+00 | -2.44446938e+00 1.79227820e+00 3.23257661e+00 15 3.11918097e-01 -4.77052911e+00 -1.76789087e+00 | 3.11918097e-01 -4.77052911e+00 -1.76789087e+00 16 1.64625850e+00 -1.10524367e-02 1.71835451e+00 | 1.64625850e+00 -1.10524367e-02 1.71835451e+00 17 1.98506486e+00 1.94721894e+00 -2.19385941e+00 | 1.98506486e+00 1.94721894e+00 -2.19385941e+00 18 -1.56908411e+00 -4.40346449e+00 -2.79101746e+00 | -1.56908411e+00 -4.40346449e+00 -2.79101746e+00 19 2.06021106e+00 4.54808725e+00 -1.01648395e+00 | 2.06021106e+00 4.54808725e+00 -1.01648395e+00 20 1.16485587e+00 -7.72851714e-01 -2.84471054e+00 | 1.16485587e+00 -7.72851714e-01 -2.84471054e+00 21 -1.70471120e+01 3.28521663e+00 -1.56973169e+01 | -1.70471120e+01 3.28521663e+00 -1.56973169e+01 22 -4.67665231e+00 -2.82512892e+00 1.71677155e+00 | -4.67665231e+00 -2.82512892e+00 1.71677155e+00 23 1.04412321e+00 2.75212997e+00 -3.89749579e-01 | 1.04412321e+00 2.75212997e+00 -3.89749579e-01 24 1.27529124e+00 3.18657136e+00 -3.05283067e+00 | 1.27529124e+00 3.18657136e+00 -3.05283067e+00 25 -1.96684259e+00 -6.59984817e-02 5.87373618e-01 | -1.96684259e+00 -6.59984817e-02 5.87373618e-01 26 -4.09550608e-01 4.36672055e-01 9.59968179e-01 | -4.09550608e-01 4.36672055e-01 9.59968179e-01 27 -1.05961708e+00 -7.99336128e-01 -1.12882301e-02 | -1.05961708e+00 -7.99336128e-01 -1.12882301e-02 28 -9.69965884e+00 -7.46463407e+00 -1.96684363e+01 | -9.69965884e+00 -7.46463407e+00 -1.96684363e+01 29 1.19421297e+01 9.72969842e+00 2.08265955e+01 | 1.19421297e+01 9.72969842e+00 2.08265955e+01 30 1.93678553e-01 -4.21842745e+00 3.74006285e+00 | 1.93678553e-01 -4.21842745e+00 3.74006285e+00 31 -1.58006621e-01 3.31012859e+00 -2.09517900e+00 | -1.58006621e-01 3.31012859e+00 -2.09517900e+00 32 -1.91520865e+00 -2.16650809e+00 -3.84190464e+00 | -1.91520865e+00 -2.16650809e+00 -3.84190464e+00 33 4.52519680e+00 3.06897384e+00 2.09910612e+00 | 4.52519680e+00 3.06897384e+00 2.09910612e+00 34 1.35575495e+01 -2.44146823e+01 7.42719550e+00 | 1.35575495e+01 -2.44146823e+01 7.42719550e+00 35 -3.42615859e+00 8.35846444e-01 -3.30553406e+00 | -3.42615859e+00 8.35846444e-01 -3.30553406e+00 36 -1.64142775e+00 -7.09446161e+00 -2.92224037e+00 | -1.64142775e+00 -7.09446161e+00 -2.92224037e+00 37 1.58469644e+00 6.76696522e+00 1.98069753e+00 | 1.58469644e+00 6.76696522e+00 1.98069753e+00 38 -2.63811197e+00 5.45900713e-02 -2.98728050e-01 | -2.63811197e+00 5.45900713e-02 -2.98728050e-01 39 2.33471221e+00 -2.71037346e+00 3.13707281e+00 | 2.33471221e+00 -2.71037346e+00 3.13707281e+00 40 6.66412222e+00 -9.10362321e+00 6.73623349e+00 | 6.66412222e+00 -9.10362321e+00 6.73623349e+00 41 -2.71344622e+00 -2.46765699e+00 1.96209783e+00 | -2.71344622e+00 -2.46765699e+00 1.96209783e+00 42 -1.70354762e+00 5.19660444e-01 -2.61463273e-01 | -1.70354762e+00 5.19660444e-01 -2.61463273e-01 43 2.97815909e+00 2.01726098e+00 3.44736519e-01 | 2.97815909e+00 2.01726098e+00 3.44736519e-01 44 -4.06457704e+00 -2.78605138e+00 -2.05282115e+00 | -4.06457704e+00 -2.78605138e+00 -2.05282115e+00 45 1.31506933e+00 5.67727799e+00 -1.96793846e-01 | 1.31506933e+00 5.67727799e+00 -1.96793846e-01 46 3.62974108e+00 -3.46212732e+00 2.35443535e-01 | 3.62974108e+00 -3.46212732e+00 2.35443535e-01 47 8.19749266e-01 3.24341426e+00 1.38115135e+00 | 8.19749266e-01 3.24341426e+00 1.38115135e+00 48 -7.87805798e-01 -8.39357306e-01 -1.52741922e+00 | -7.87805798e-01 -8.39357306e-01 -1.52741922e+00 49 -1.09421742e+00 1.86487072e+00 -1.42517713e+00 | -1.09421742e+00 1.86487072e+00 -1.42517713e+00 50 2.07514884e+00 5.82671537e-01 -2.25691076e+00 | 2.07514884e+00 5.82671537e-01 -2.25691076e+00 51 -4.28373205e-02 9.36543408e-01 1.25934624e-01 | -4.28373205e-02 9.36543408e-01 1.25934624e-01 52 1.95321464e+00 4.77854244e-01 1.30779667e-01 | 1.95321464e+00 4.77854244e-01 1.30779667e-01 53 -1.61336388e-02 -6.58158526e-01 -1.18232874e+00 | -1.61336388e-02 -6.58158526e-01 -1.18232874e+00 54 -2.28938180e+00 -4.02673162e+00 -3.86547712e+00 | -2.28938180e+00 -4.02673162e+00 -3.86547712e+00 55 3.17374472e+00 2.93903622e+00 2.85086703e+00 | 3.17374472e+00 2.93903622e+00 2.85086703e+00 56 1.31547503e+01 -2.78242899e+00 1.70431360e+01 | 1.31547503e+01 -2.78242899e+00 1.70431360e+01 57 2.57336940e+00 -3.56887915e+00 1.40367152e+00 | 2.57336940e+00 -3.56887915e+00 1.40367152e+00 58 -1.31741449e+00 -1.98931344e+00 -1.15697837e+00 | -1.31741449e+00 -1.98931344e+00 -1.15697837e+00 59 2.19700901e+00 6.74210897e-01 7.43121017e-01 | 2.19700901e+00 6.74210897e-01 7.43121017e-01 60 -2.69446396e+00 -4.47249632e+00 -4.08987464e+00 | -2.69446396e+00 -4.47249632e+00 -4.08987464e+00 61 1.47933416e+00 4.39628364e+00 2.13933123e+00 | 1.47933416e+00 4.39628364e+00 2.13933123e+00 62 1.13000495e+00 -1.17219184e+00 2.57329466e+00 | 1.13000495e+00 -1.17219184e+00 2.57329466e+00 63 8.05373366e-02 -8.19679767e-01 -5.64609587e-01 | 8.05373366e-02 -8.19679767e-01 -5.64609587e-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 = [22, 17, 36, 43, 42, 41, 40, 20, 31, 28, 48, 61, 21, 46, 24, 52, 23, 1, 32, 62, 7, 12, 0, 16, 14, 39, 37, 63, 9, 59, 35, 8, 18, 54, 45, 30, 2, 26, 56, 25, 6, 5, 4, 3, 58, 34, 13, 53, 10, 50, 49, 55, 15, 47, 33, 51, 38, 60, 44, 29, 57, 11, 19, 27] 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)) = -16.22020480410894 V(r_1,...,r_N) = -16.220204804109187 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 7.97148969e-02 -4.37546510e-01 4.39984352e-01 | 7.97148969e-02 -4.37546510e-01 4.39984352e-01 1 -1.28499357e+00 -1.25095289e+00 1.07145422e+00 | -1.28499357e+00 -1.25095289e+00 1.07145422e+00 2 3.08866426e-01 2.35908100e+00 -5.43826403e-01 | 3.08866426e-01 2.35908100e+00 -5.43826403e-01 3 1.38069523e+00 -3.78461495e+00 3.32430147e-01 | 1.38069523e+00 -3.78461495e+00 3.32430147e-01 4 -7.80948206e-01 1.09148322e+00 6.18728677e-01 | -7.80948206e-01 1.09148322e+00 6.18728677e-01 5 -3.81777126e+01 -2.90327324e+01 1.22675856e+01 | -3.81777126e+01 -2.90327324e+01 1.22675856e+01 6 7.82688689e-01 -2.32608128e+00 -2.87279309e-01 | 7.82688689e-01 -2.32608128e+00 -2.87279309e-01 7 3.12589409e+00 2.93272930e-01 -1.79382460e+00 | 3.12589409e+00 2.93272930e-01 -1.79382460e+00 8 -8.67173863e-01 8.14028139e-01 1.11648693e+00 | -8.67173863e-01 8.14028139e-01 1.11648693e+00 9 2.46212456e+00 1.03218519e+00 -1.52014559e+00 | 2.46212456e+00 1.03218519e+00 -1.52014559e+00 10 -4.83561490e+01 -8.17693077e+01 -1.22993356e+02 | -4.83561490e+01 -8.17693077e+01 -1.22993356e+02 11 4.58893372e+01 8.25383561e+01 1.25444174e+02 | 4.58893372e+01 8.25383561e+01 1.25444174e+02 12 -4.79100859e+00 5.34283392e-01 -6.11673405e-01 | -4.79100859e+00 5.34283392e-01 -6.11673405e-01 13 1.52523947e+00 3.52886613e+00 1.67702828e+00 | 1.52523947e+00 3.52886613e+00 1.67702828e+00 14 3.59483972e+01 3.06914576e+01 -1.35805725e+01 | 3.59483972e+01 3.06914576e+01 -1.35805725e+01 15 -3.88186473e+00 -4.52724586e+00 2.97243295e+00 | -3.88186473e+00 -4.52724586e+00 2.97243295e+00 16 3.50062676e-01 -6.14300791e-01 -6.41081585e-01 | 3.50062676e-01 -6.14300791e-01 -6.41081585e-01 17 4.51116660e-01 -4.01435691e+00 3.48259525e+00 | 4.51116660e-01 -4.01435691e+00 3.48259525e+00 18 9.08626415e-01 9.23536167e-01 -1.13148936e+00 | 9.08626415e-01 9.23536167e-01 -1.13148936e+00 19 -3.90877575e-01 -1.54143180e+00 -1.41147923e-01 | -3.90877575e-01 -1.54143180e+00 -1.41147923e-01 20 -1.72303312e+00 1.99184260e-01 1.28970972e-01 | -1.72303312e+00 1.99184260e-01 1.28970972e-01 21 4.72338186e-01 -8.36507213e-02 2.85202576e+00 | 4.72338186e-01 -8.36507213e-02 2.85202576e+00 22 -2.71769331e+00 5.64171442e-01 -2.06969892e+00 | -2.71769331e+00 5.64171442e-01 -2.06969892e+00 23 1.46486462e+00 2.15553803e+00 3.05281661e-01 | 1.46486462e+00 2.15553803e+00 3.05281661e-01 24 4.86927877e-01 -1.03413704e+00 -4.21219862e+00 | 4.86927877e-01 -1.03413704e+00 -4.21219862e+00 25 1.70457195e+00 3.50574530e+00 4.83740139e+00 | 1.70457195e+00 3.50574530e+00 4.83740139e+00 26 -3.48839682e+00 -2.79910353e+00 -1.14390991e+00 | -3.48839682e+00 -2.79910353e+00 -1.14390991e+00 27 2.00711421e+00 1.63772554e+00 2.45592451e+00 | 2.00711421e+00 1.63772554e+00 2.45592451e+00 28 1.25010126e+00 2.04804497e+00 -5.53627134e+00 | 1.25010126e+00 2.04804497e+00 -5.53627134e+00 29 2.57946020e-01 1.66508588e-01 2.26300307e+00 | 2.57946020e-01 1.66508588e-01 2.26300307e+00 30 -1.74865933e+00 4.48120249e-01 -6.66521217e-01 | -1.74865933e+00 4.48120249e-01 -6.66521217e-01 31 2.82737809e+00 -4.87580855e-01 2.03430691e+00 | 2.82737809e+00 -4.87580855e-01 2.03430691e+00 32 1.55845820e+00 8.09713074e-01 -1.12088087e+00 | 1.55845820e+00 8.09713074e-01 -1.12088087e+00 33 6.93269932e+01 -3.35385476e+01 -2.30666244e+01 | 6.93269932e+01 -3.35385476e+01 -2.30666244e+01 34 -1.30984351e+00 -1.38915639e+00 -5.73088562e+00 | -1.30984351e+00 -1.38915639e+00 -5.73088562e+00 35 3.90589072e-01 1.76050024e+00 2.70070445e+00 | 3.90589072e-01 1.76050024e+00 2.70070445e+00 36 3.17237430e-01 -4.02778702e-01 -4.83954342e-01 | 3.17237430e-01 -4.02778702e-01 -4.83954342e-01 37 -3.98353894e-01 1.51269702e+00 -1.71745137e+00 | -3.98353894e-01 1.51269702e+00 -1.71745137e+00 38 -7.00647409e+01 3.57816521e+01 2.52700267e+01 | -7.00647409e+01 3.57816521e+01 2.52700267e+01 39 3.13475046e-01 -1.13151450e+00 -1.71414933e+00 | 3.13475046e-01 -1.13151450e+00 -1.71414933e+00 40 1.31756868e-01 -3.33120492e+00 -1.87781315e-02 | 1.31756868e-01 -3.33120492e+00 -1.87781315e-02 41 2.23988001e+00 3.51302553e+00 3.12805142e+00 | 2.23988001e+00 3.51302553e+00 3.12805142e+00 42 -1.13360253e+00 -2.83539701e+00 -2.28987940e+00 | -1.13360253e+00 -2.83539701e+00 -2.28987940e+00 43 2.07432663e+00 1.98896398e+00 7.41483161e-01 | 2.07432663e+00 1.98896398e+00 7.41483161e-01 44 -1.92676426e+00 -3.43102721e-01 -3.99290954e+00 | -1.92676426e+00 -3.43102721e-01 -3.99290954e+00 45 3.11194077e-01 3.41851252e+00 2.30077212e+00 | 3.11194077e-01 3.41851252e+00 2.30077212e+00 46 2.88275337e-01 -2.20334151e-01 -1.87832485e-01 | 2.88275337e-01 -2.20334151e-01 -1.87832485e-01 47 1.56816726e+00 -1.85078964e+01 1.40301684e+01 | 1.56816726e+00 -1.85078964e+01 1.40301684e+01 48 3.26079733e-01 3.30442616e-01 3.01406792e+00 | 3.26079733e-01 3.30442616e-01 3.01406792e+00 49 5.23168168e-01 -6.98158037e-01 1.20391611e+00 | 5.23168168e-01 -6.98158037e-01 1.20391611e+00 50 2.19793814e+00 -1.33731174e+00 8.56747978e-01 | 2.19793814e+00 -1.33731174e+00 8.56747978e-01 51 -2.29980124e+00 1.64586366e+00 -2.85512213e+00 | -2.29980124e+00 1.64586366e+00 -2.85512213e+00 52 -3.43629227e+00 -7.84307288e+00 -8.35195820e-01 | -3.43629227e+00 -7.84307288e+00 -8.35195820e-01 53 2.56397027e+00 6.21205620e+00 -1.81661771e+00 | 2.56397027e+00 6.21205620e+00 -1.81661771e+00 54 -1.41115270e+00 -3.14024596e+00 -3.16062948e+00 | -1.41115270e+00 -3.14024596e+00 -3.16062948e+00 55 2.65384962e+00 1.92046348e+00 2.31440857e+00 | 2.65384962e+00 1.92046348e+00 2.31440857e+00 56 -1.27716417e+00 -2.58441702e+00 -3.51444768e-01 | -1.27716417e+00 -2.58441702e+00 -3.51444768e-01 57 5.40353619e-01 -2.51046559e+00 1.11890383e+00 | 5.40353619e-01 -2.51046559e+00 1.11890383e+00 58 2.88320026e+00 7.01874578e-01 -4.01620520e-01 | 2.88320026e+00 7.01874578e-01 -4.01620520e-01 59 -1.47930314e+00 -1.87888383e+00 7.83212267e-01 | -1.47930314e+00 -1.87888383e+00 7.83212267e-01 60 -3.41585400e+00 1.99209083e+01 -1.46984971e+01 | -3.41585400e+00 1.99209083e+01 -1.46984971e+01 61 -1.77065233e+00 6.82379508e-02 -1.96864677e+00 | -1.77065233e+00 6.82379508e-02 -1.96864677e+00 62 2.33160007e+00 2.15884090e+00 2.25233628e+00 | 2.33160007e+00 2.15884090e+00 2.25233628e+00 63 1.90751691e+00 -8.79809790e-01 -7.30497733e-01 | 1.90751691e+00 -8.79809790e-01 -7.30497733e-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 = [21, 37, 11, 63, 47, 6, 5, 28, 15, 17, 27, 2, 24, 23, 31, 8, 60, 9, 43, 45, 55, 0, 54, 13, 12, 53, 38, 10, 7, 30, 29, 14, 52, 49, 56, 62, 57, 1, 26, 46, 61, 50, 51, 18, 48, 19, 39, 4, 44, 33, 41, 42, 32, 25, 22, 20, 34, 36, 59, 58, 16, 40, 35, 3] 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)) = 40.38733474109371 V(r_1,...,r_N) = 40.38733474109368 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 9.03945453e-01 1.81753012e+00 2.28860711e-01 | 9.03945453e-01 1.81753012e+00 2.28860711e-01 1 3.34345162e+00 -4.57701410e-01 -7.38382807e-01 | 3.34345162e+00 -4.57701410e-01 -7.38382807e-01 2 -2.58647151e+00 2.88589308e+00 2.87917115e+00 | -2.58647151e+00 2.88589308e+00 2.87917115e+00 3 -3.06156841e+00 -2.32145690e+00 1.98501838e+00 | -3.06156841e+00 -2.32145690e+00 1.98501838e+00 4 -1.06526426e+00 3.50138451e+00 -5.83156896e-01 | -1.06526426e+00 3.50138451e+00 -5.83156896e-01 5 -4.08153448e+00 1.78007652e+00 3.16163762e+00 | -4.08153448e+00 1.78007652e+00 3.16163762e+00 6 3.57459367e-01 -3.49491295e+00 1.02722166e+00 | 3.57459367e-01 -3.49491295e+00 1.02722166e+00 7 -3.41189207e-01 -4.21347551e+00 -8.30302707e-01 | -3.41189207e-01 -4.21347551e+00 -8.30302707e-01 8 -1.42028280e+00 -5.54938921e+00 -3.60150367e+00 | -1.42028280e+00 -5.54938921e+00 -3.60150367e+00 9 6.33778810e+00 5.80660770e+00 7.35173941e+00 | 6.33778810e+00 5.80660770e+00 7.35173941e+00 10 3.58582142e-01 -2.66066867e+00 1.45795238e+00 | 3.58582142e-01 -2.66066867e+00 1.45795238e+00 11 -2.29812024e+00 9.18264670e-01 -2.91878994e-01 | -2.29812024e+00 9.18264670e-01 -2.91878994e-01 12 -5.35822289e+00 4.24656069e+00 -1.50102433e+00 | -5.35822289e+00 4.24656069e+00 -1.50102433e+00 13 -4.26826190e+00 1.92179009e+00 1.36468822e+00 | -4.26826190e+00 1.92179009e+00 1.36468822e+00 14 -3.03144981e+01 -4.16394921e+01 -2.86272156e+01 | -3.03144981e+01 -4.16394921e+01 -2.86272156e+01 15 3.32539523e+01 4.07672408e+01 2.91467116e+01 | 3.32539523e+01 4.07672408e+01 2.91467116e+01 16 5.30839360e+00 3.74148477e+00 3.40324073e+00 | 5.30839360e+00 3.74148477e+00 3.40324073e+00 17 4.11086193e+00 6.86959054e-01 2.88019034e+00 | 4.11086193e+00 6.86959054e-01 2.88019034e+00 18 -2.34415947e+00 1.88726994e+00 3.49847733e+00 | -2.34415947e+00 1.88726994e+00 3.49847733e+00 19 -3.17245840e+00 -1.12370826e+01 5.79829244e+00 | -3.17245840e+00 -1.12370826e+01 5.79829244e+00 20 -2.70495152e+00 -3.05914121e+00 -1.23693495e+00 | -2.70495152e+00 -3.05914121e+00 -1.23693495e+00 21 -6.74602549e+00 3.98053077e+00 -4.55433368e+00 | -6.74602549e+00 3.98053077e+00 -4.55433368e+00 22 9.14803934e-01 -2.50921556e-02 -1.13556374e+00 | 9.14803934e-01 -2.50921556e-02 -1.13556374e+00 23 2.12441181e+00 -3.23378482e+00 -8.68281787e+00 | 2.12441181e+00 -3.23378482e+00 -8.68281787e+00 24 1.90535492e+00 3.26792100e+00 -7.78548194e-01 | 1.90535492e+00 3.26792100e+00 -7.78548194e-01 25 9.46112951e-01 5.12779004e-01 1.44080116e+00 | 9.46112951e-01 5.12779004e-01 1.44080116e+00 26 -1.65910181e+00 -9.59634808e-01 6.82245200e-01 | -1.65910181e+00 -9.59634808e-01 6.82245200e-01 27 -8.33274537e-01 4.69363393e-01 4.57602963e-01 | -8.33274537e-01 4.69363393e-01 4.57602963e-01 28 2.07032130e+00 -7.95783571e-01 -7.48210357e-01 | 2.07032130e+00 -7.95783571e-01 -7.48210357e-01 29 -1.94031499e-01 -2.42550854e+00 3.05292372e+00 | -1.94031499e-01 -2.42550854e+00 3.05292372e+00 30 4.38965512e+00 5.09548802e+00 -3.66288806e+00 | 4.38965512e+00 5.09548802e+00 -3.66288806e+00 31 -2.19526510e+00 -7.23787313e+00 -2.83831532e+00 | -2.19526510e+00 -7.23787313e+00 -2.83831532e+00 32 2.35968440e+00 4.31477433e+00 -2.03047894e+00 | 2.35968440e+00 4.31477433e+00 -2.03047894e+00 33 -1.99654178e+00 -1.93838011e+00 4.10390746e+00 | -1.99654178e+00 -1.93838011e+00 4.10390746e+00 34 -1.28102301e+00 -3.29823679e+00 -2.41396342e+00 | -1.28102301e+00 -3.29823679e+00 -2.41396342e+00 35 1.82339716e+00 3.26485476e+00 3.33695758e+00 | 1.82339716e+00 3.26485476e+00 3.33695758e+00 36 3.89998005e+00 7.43444558e+00 -5.81812891e+00 | 3.89998005e+00 7.43444558e+00 -5.81812891e+00 37 -1.59859951e+01 -1.88409574e+01 2.25908463e+01 | -1.59859951e+01 -1.88409574e+01 2.25908463e+01 38 4.76172581e+00 -1.77887486e+00 -6.91780901e+00 | 4.76172581e+00 -1.77887486e+00 -6.91780901e+00 39 -1.05641633e+00 3.98895112e+00 -3.17837423e+00 | -1.05641633e+00 3.98895112e+00 -3.17837423e+00 40 -3.88698539e+01 -2.59110831e+01 -2.45471132e+01 | -3.88698539e+01 -2.59110831e+01 -2.45471132e+01 41 3.95178817e+01 2.44814500e+01 2.35871492e+01 | 3.95178817e+01 2.44814500e+01 2.35871492e+01 42 -1.72586829e+00 -5.27369542e+00 -4.84506447e-01 | -1.72586829e+00 -5.27369542e+00 -4.84506447e-01 43 3.28835967e+00 1.86547590e+00 6.63674424e-01 | 3.28835967e+00 1.86547590e+00 6.63674424e-01 44 -7.97238328e-01 4.22773899e+00 2.04450258e+00 | -7.97238328e-01 4.22773899e+00 2.04450258e+00 45 -4.44877874e+00 3.91463865e+00 -5.78548519e+00 | -4.44877874e+00 3.91463865e+00 -5.78548519e+00 46 1.05490011e+01 1.23540575e+01 -2.61143109e+01 | 1.05490011e+01 1.23540575e+01 -2.61143109e+01 47 5.39364863e+00 -1.54207929e+00 3.59581797e+00 | 5.39364863e+00 -1.54207929e+00 3.59581797e+00 48 -2.42376228e-01 1.82624831e+00 6.38713714e+00 | -2.42376228e-01 1.82624831e+00 6.38713714e+00 49 1.22137516e+00 1.02536293e+01 -8.45368803e+00 | 1.22137516e+00 1.02536293e+01 -8.45368803e+00 50 2.97614779e+00 1.47684193e+00 4.01191136e+00 | 2.97614779e+00 1.47684193e+00 4.01191136e+00 51 -8.96039368e+00 3.92088754e+01 -3.12002893e+01 | -8.96039368e+00 3.92088754e+01 -3.12002893e+01 52 4.12021312e-01 -1.11273144e+01 5.92628413e+00 | 4.12021312e-01 -1.11273144e+01 5.92628413e+00 53 -4.34203965e+01 -6.07112128e+01 2.16779199e+01 | -4.34203965e+01 -6.07112128e+01 2.16779199e+01 54 -6.32377720e-02 -1.89579370e+00 2.82780582e+00 | -6.32377720e-02 -1.89579370e+00 2.82780582e+00 55 8.17318947e-01 -2.73709413e+00 -3.25138549e+00 | 8.17318947e-01 -2.73709413e+00 -3.25138549e+00 56 4.01784248e+00 -1.17707169e+00 5.46718092e+00 | 4.01784248e+00 -1.17707169e+00 5.46718092e+00 57 8.63805558e-01 3.42782265e+00 1.50525226e+00 | 8.63805558e-01 3.42782265e+00 1.50525226e+00 58 -4.01504343e+00 3.41170046e+00 3.25618203e+00 | -4.01504343e+00 3.41170046e+00 3.25618203e+00 59 -5.41134739e+00 -2.56393120e+00 9.84345047e-01 | -5.41134739e+00 -2.56393120e+00 9.84345047e-01 60 1.98764825e+00 1.62181365e-01 8.43588171e-01 | 1.98764825e+00 1.62181365e-01 8.43588171e-01 61 -5.67611857e+00 4.75438992e+00 -6.01772706e+00 | -5.67611857e+00 4.75438992e+00 -6.01772706e+00 62 5.91214899e+01 2.49127580e+01 1.09796308e+01 | 5.91214899e+01 2.49127580e+01 1.09796308e+01 63 -7.41111794e-01 -1.04612559e+01 -7.58253078e+00 | -7.41111794e-01 -1.04612559e+01 -7.58253078e+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 = [10, 6, 42, 58, 12, 21, 1, 43, 24, 56, 0, 25, 4, 54, 49, 62, 39, 36, 47, 53, 50, 5, 48, 28, 8, 11, 45, 40, 23, 59, 51, 38, 33, 32, 61, 41, 17, 46, 31, 16, 27, 35, 2, 7, 52, 26, 37, 18, 22, 14, 20, 30, 44, 19, 13, 57, 9, 55, 3, 29, 63, 34, 15, 60] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -12.122708621164469 V(r_1,...,r_N) = -12.122708621164556 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 9.25330061e-01 8.78230643e-01 7.43731454e-01 | 9.25330061e-01 8.78230643e-01 7.43731454e-01 1 -6.96334386e+01 -6.86331518e+01 3.09421577e+01 | -6.96334386e+01 -6.86331518e+01 3.09421577e+01 2 6.70751610e+01 6.61412433e+01 -2.88162575e+01 | 6.70751610e+01 6.61412433e+01 -2.88162575e+01 3 4.51280078e+00 4.32976896e-01 -2.40033775e+00 | 4.51280078e+00 4.32976896e-01 -2.40033775e+00 4 -3.81239820e+00 -1.93152666e+00 8.72151915e-01 | -3.81239820e+00 -1.93152666e+00 8.72151915e-01 5 3.80022670e+00 1.54992509e+00 -2.18632345e+00 | 3.80022670e+00 1.54992509e+00 -2.18632345e+00 6 2.22030322e+00 7.21952673e-01 -9.47623340e-01 | 2.22030322e+00 7.21952673e-01 -9.47623340e-01 7 9.28313732e+00 -1.59790824e+01 -4.50083407e+00 | 9.28313732e+00 -1.59790824e+01 -4.50083407e+00 8 2.25288173e-01 3.39144277e-01 1.83617821e+00 | 2.25288173e-01 3.39144277e-01 1.83617821e+00 9 -3.22043972e+00 3.47115866e+00 -1.59888316e+00 | -3.22043972e+00 3.47115866e+00 -1.59888316e+00 10 1.96979355e+00 -1.69053842e+00 1.94483977e+00 | 1.96979355e+00 -1.69053842e+00 1.94483977e+00 11 -1.51562548e+00 -1.56304969e+00 2.29219600e-01 | -1.51562548e+00 -1.56304969e+00 2.29219600e-01 12 -2.66907389e+00 -4.06249275e+00 -2.38911993e+00 | -2.66907389e+00 -4.06249275e+00 -2.38911993e+00 13 3.97463835e+00 1.62415180e+00 -3.98836139e-01 | 3.97463835e+00 1.62415180e+00 -3.98836139e-01 14 -3.28191705e+00 -7.51455716e-02 -2.29159035e-01 | -3.28191705e+00 -7.51455716e-02 -2.29159035e-01 15 1.62363249e-01 2.23062974e+01 -1.40167601e+01 | 1.62363249e-01 2.23062974e+01 -1.40167601e+01 16 -3.91944392e-01 -3.09724132e+00 7.35976303e-01 | -3.91944392e-01 -3.09724132e+00 7.35976303e-01 17 2.72063514e-01 1.74663464e+00 3.10127206e+00 | 2.72063514e-01 1.74663464e+00 3.10127206e+00 18 1.37487514e+00 1.91376765e+00 4.09032209e-01 | 1.37487514e+00 1.91376765e+00 4.09032209e-01 19 -2.94034980e+00 3.64636928e-01 -1.56346503e+00 | -2.94034980e+00 3.64636928e-01 -1.56346503e+00 20 -1.15680953e+00 1.02633541e+00 2.87097767e+00 | -1.15680953e+00 1.02633541e+00 2.87097767e+00 21 -1.67656769e+00 1.69073309e+00 -5.09511194e+00 | -1.67656769e+00 1.69073309e+00 -5.09511194e+00 22 -5.95552182e-01 -1.18539364e+00 -2.44716829e+00 | -5.95552182e-01 -1.18539364e+00 -2.44716829e+00 23 2.19206878e-01 1.35040313e+00 1.26769723e+00 | 2.19206878e-01 1.35040313e+00 1.26769723e+00 24 -1.58287561e+00 -2.83581349e+00 -1.08325853e+00 | -1.58287561e+00 -2.83581349e+00 -1.08325853e+00 25 3.29372950e+01 -2.31863071e+01 -1.66532732e+01 | 3.29372950e+01 -2.31863071e+01 -1.66532732e+01 26 1.47330621e+00 1.58084691e+00 -1.43859294e+00 | 1.47330621e+00 1.58084691e+00 -1.43859294e+00 27 -1.53031499e+00 -9.75984405e-01 6.29995363e-01 | -1.53031499e+00 -9.75984405e-01 6.29995363e-01 28 -2.08012076e+00 -3.47774193e-01 -1.82177431e+00 | -2.08012076e+00 -3.47774193e-01 -1.82177431e+00 29 -6.08270899e-01 -2.39804447e+00 -5.58811440e+00 | -6.08270899e-01 -2.39804447e+00 -5.58811440e+00 30 -2.87759823e+01 2.07795278e+01 2.33259796e+01 | -2.87759823e+01 2.07795278e+01 2.33259796e+01 31 -8.10729029e-01 1.23727175e-01 -1.96454141e+00 | -8.10729029e-01 1.23727175e-01 -1.96454141e+00 32 1.96973711e+00 8.26096539e-01 -3.87086157e-01 | 1.96973711e+00 8.26096539e-01 -3.87086157e-01 33 -1.42578403e-01 1.52507810e+00 4.48172019e-01 | -1.42578403e-01 1.52507810e+00 4.48172019e-01 34 -3.88056268e+00 -1.57383489e+00 3.05068887e-01 | -3.88056268e+00 -1.57383489e+00 3.05068887e-01 35 -6.87745610e+01 -2.52558196e+01 6.20187564e+01 | -6.87745610e+01 -2.52558196e+01 6.20187564e+01 36 -1.84985486e+01 -6.49586916e+01 -2.91108078e+01 | -1.84985486e+01 -6.49586916e+01 -2.91108078e+01 37 1.85612717e+01 6.70372320e+01 2.69150062e+01 | 1.85612717e+01 6.70372320e+01 2.69150062e+01 38 5.71938887e-01 -6.70901488e-01 -1.71704252e+00 | 5.71938887e-01 -6.70901488e-01 -1.71704252e+00 39 4.09324059e-01 -6.44675444e-01 1.07285551e+00 | 4.09324059e-01 -6.44675444e-01 1.07285551e+00 40 -1.42876519e-01 3.18746511e-01 -3.11741129e+00 | -1.42876519e-01 3.18746511e-01 -3.11741129e+00 41 -4.54780513e+00 9.21989805e-01 9.57039271e-02 | -4.54780513e+00 9.21989805e-01 9.57039271e-02 42 1.49811055e+00 -1.70333947e+01 1.58731669e+01 | 1.49811055e+00 -1.70333947e+01 1.58731669e+01 43 -1.57806801e+00 7.74813369e-01 -7.04812573e-01 | -1.57806801e+00 7.74813369e-01 -7.04812573e-01 44 5.22145737e+00 -1.34628319e+00 2.44460815e+00 | 5.22145737e+00 -1.34628319e+00 2.44460815e+00 45 -9.32282671e-01 2.64880550e-01 -1.07447465e+00 | -9.32282671e-01 2.64880550e-01 -1.07447465e+00 46 -2.90875798e+00 -1.52106447e+00 -6.02085725e-01 | -2.90875798e+00 -1.52106447e+00 -6.02085725e-01 47 -7.82619002e-01 2.56377072e+00 1.94183619e+00 | -7.82619002e-01 2.56377072e+00 1.94183619e+00 48 -6.47774384e+00 1.56898929e+01 5.57651136e+00 | -6.47774384e+00 1.56898929e+01 5.57651136e+00 49 -1.14215387e+01 1.67863132e+01 -1.79466533e+01 | -1.14215387e+01 1.67863132e+01 -1.79466533e+01 50 -2.59723192e-01 -2.59197825e+00 2.79714032e+00 | -2.59723192e-01 -2.59197825e+00 2.79714032e+00 51 1.74754447e+00 6.29464190e-02 8.15905097e-01 | 1.74754447e+00 6.29464190e-02 8.15905097e-01 52 1.28989554e+01 -1.62652894e+01 1.52695515e+01 | 1.28989554e+01 -1.62652894e+01 1.52695515e+01 53 1.14284311e-03 -1.34053626e-01 -1.36959439e+00 | 1.14284311e-03 -1.34053626e-01 -1.36959439e+00 54 -8.22600872e-01 -3.05311254e+00 -1.53908195e+00 | -8.22600872e-01 -3.05311254e+00 -1.53908195e+00 55 3.15850360e+00 5.33461372e-01 4.95019628e-01 | 3.15850360e+00 5.33461372e-01 4.95019628e-01 56 7.07218857e+01 2.32032385e+01 -5.90305443e+01 | 7.07218857e+01 2.32032385e+01 -5.90305443e+01 57 1.99865733e+00 4.13916776e+00 7.15058725e-01 | 1.99865733e+00 4.13916776e+00 7.15058725e-01 58 -4.62998717e-01 2.99607929e-01 8.75180965e+00 | -4.62998717e-01 2.99607929e-01 8.75180965e+00 59 1.70575127e-01 6.48690015e-01 7.13019045e-01 | 1.70575127e-01 6.48690015e-01 7.13019045e-01 60 4.47631246e-01 1.69641963e+00 -8.96552510e-01 | 4.47631246e-01 1.69641963e+00 -8.96552510e-01 61 -1.86335610e+00 -5.47442818e-01 -1.07541211e+00 | -1.86335610e+00 -5.47442818e-01 -1.07541211e+00 62 -1.66930444e+00 -2.54381292e+00 -3.01157399e+00 | -1.66930444e+00 -2.54381292e+00 -3.01157399e+00 63 1.64581142e+00 7.67862069e-01 1.56416920e+00 | 1.64581142e+00 7.67862069e-01 1.56416920e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Co Cr Fe Ni (Configuration in file "config-AlCoCrFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [6, 63, 30, 11, 34, 14, 0, 38, 26, 10, 9, 3, 55, 32, 5, 58, 53, 57, 50, 48, 43, 45, 36, 61, 62, 37, 8, 52, 31, 54, 2, 28, 13, 41, 4, 59, 22, 25, 7, 44, 47, 33, 42, 20, 39, 21, 46, 40, 19, 51, 18, 49, 27, 16, 29, 12, 56, 17, 15, 35, 60, 23, 24, 1] 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)) = 113.97281999840855 V(r_1,...,r_N) = 113.97281999840854 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 -1.55932078e+00 -2.08910222e+00 -1.84740757e+00 | -1.55932078e+00 -2.08910222e+00 -1.84740757e+00 1 3.95390907e+00 9.96851606e-01 1.12919097e+00 | 3.95390907e+00 9.96851606e-01 1.12919097e+00 2 -1.20652498e+00 9.39789004e-01 1.86258505e+00 | -1.20652498e+00 9.39789004e-01 1.86258505e+00 3 -7.39164903e+01 4.68690421e+01 -4.60109341e+01 | -7.39164903e+01 4.68690421e+01 -4.60109341e+01 4 -1.14754402e+00 2.47618222e+00 1.15764867e+00 | -1.14754402e+00 2.47618222e+00 1.15764867e+00 5 -1.22970919e-01 -1.48425618e+00 1.59310631e+00 | -1.22970919e-01 -1.48425618e+00 1.59310631e+00 6 -2.36781096e+00 -5.53867214e-01 1.74115187e+00 | -2.36781096e+00 -5.53867214e-01 1.74115187e+00 7 1.72805283e+00 3.11013845e+00 -2.54168005e+00 | 1.72805283e+00 3.11013845e+00 -2.54168005e+00 8 -5.68068811e+00 -1.53957909e+00 -1.60187767e+00 | -5.68068811e+00 -1.53957909e+00 -1.60187767e+00 9 2.63554176e+00 2.17140876e-01 4.17185155e+00 | 2.63554176e+00 2.17140876e-01 4.17185155e+00 10 2.08448376e+00 6.02682770e+00 -1.47250734e+00 | 2.08448376e+00 6.02682770e+00 -1.47250734e+00 11 3.37845766e+01 -1.74252992e+01 -6.41315459e+00 | 3.37845766e+01 -1.74252992e+01 -6.41315459e+00 12 -1.67680975e+00 -3.40217184e+00 7.43792270e-02 | -1.67680975e+00 -3.40217184e+00 7.43792270e-02 13 4.07910554e+01 -1.57427110e+01 -1.04126240e+02 | 4.07910554e+01 -1.57427110e+01 -1.04126240e+02 14 7.35666529e+01 -4.65657650e+01 4.27051493e+01 | 7.35666529e+01 -4.65657650e+01 4.27051493e+01 15 2.81458850e+00 8.47985990e-01 1.55843394e+00 | 2.81458850e+00 8.47985990e-01 1.55843394e+00 16 8.28607059e-01 -1.14853508e+00 -1.27586521e+00 | 8.28607059e-01 -1.14853508e+00 -1.27586521e+00 17 -6.80480821e-01 -2.62506550e-02 4.65473773e+00 | -6.80480821e-01 -2.62506550e-02 4.65473773e+00 18 1.99518586e+00 -2.13494568e-01 2.84861633e+00 | 1.99518586e+00 -2.13494568e-01 2.84861633e+00 19 -1.90536393e+00 -1.46003957e+00 -1.30464365e+00 | -1.90536393e+00 -1.46003957e+00 -1.30464365e+00 20 -1.80298612e-01 9.02974064e-01 -2.28321255e+00 | -1.80298612e-01 9.02974064e-01 -2.28321255e+00 21 -6.52315905e+01 3.21916634e+01 -3.13162853e+01 | -6.52315905e+01 3.21916634e+01 -3.13162853e+01 22 -1.67252750e+01 -3.40965288e+01 -3.84882754e+01 | -1.67252750e+01 -3.40965288e+01 -3.84882754e+01 23 1.91842769e+01 3.19707241e+01 3.64987655e+01 | 1.91842769e+01 3.19707241e+01 3.64987655e+01 24 -3.76686425e+00 -1.88526738e+00 -1.83947844e+00 | -3.76686425e+00 -1.88526738e+00 -1.83947844e+00 25 1.63881402e+01 -1.00892470e+01 -5.11360076e+00 | 1.63881402e+01 -1.00892470e+01 -5.11360076e+00 26 3.10676006e+00 -8.62807436e-01 -3.42603749e+00 | 3.10676006e+00 -8.62807436e-01 -3.42603749e+00 27 -1.07937093e+00 -4.87331422e-01 1.14282551e+00 | -1.07937093e+00 -4.87331422e-01 1.14282551e+00 28 -3.79579768e+01 1.61489244e+01 8.35029874e+00 | -3.79579768e+01 1.61489244e+01 8.35029874e+00 29 -7.70530692e-01 -1.52904553e+00 -1.73841641e+00 | -7.70530692e-01 -1.52904553e+00 -1.73841641e+00 30 -1.60284995e+01 1.02012509e+01 1.35154684e+01 | -1.60284995e+01 1.02012509e+01 1.35154684e+01 31 -4.01084661e+01 4.00018557e+01 -4.58910706e+01 | -4.01084661e+01 4.00018557e+01 -4.58910706e+01 32 -3.83354686e+01 -3.61452783e+01 -8.70891509e+01 | -3.83354686e+01 -3.61452783e+01 -8.70891509e+01 33 4.04474824e+01 3.74896449e+01 8.67308569e+01 | 4.04474824e+01 3.74896449e+01 8.67308569e+01 34 7.75147493e-01 -1.16997241e+00 3.60339735e+00 | 7.75147493e-01 -1.16997241e+00 3.60339735e+00 35 -1.35210333e+00 -3.79214242e+00 3.33762197e+00 | -1.35210333e+00 -3.79214242e+00 3.33762197e+00 36 1.39233983e+00 4.09649791e+00 -1.05553500e+00 | 1.39233983e+00 4.09649791e+00 -1.05553500e+00 37 -3.08966826e+01 -1.19203978e+01 2.97480764e+01 | -3.08966826e+01 -1.19203978e+01 2.97480764e+01 38 3.64432795e-01 -2.33271329e+00 -3.20690836e+00 | 3.64432795e-01 -2.33271329e+00 -3.20690836e+00 39 -6.15487166e-01 2.11460327e+00 9.71269692e-01 | -6.15487166e-01 2.11460327e+00 9.71269692e-01 40 -3.03680685e+01 -2.27187992e+01 -1.99490470e+01 | -3.03680685e+01 -2.27187992e+01 -1.99490470e+01 41 2.89375260e+01 2.66257723e+01 2.39750595e+01 | 2.89375260e+01 2.66257723e+01 2.39750595e+01 42 -3.99473027e+01 1.91271134e+01 1.03290497e+02 | -3.99473027e+01 1.91271134e+01 1.03290497e+02 43 5.19508562e+00 -2.28506174e+00 -2.40523312e+00 | 5.19508562e+00 -2.28506174e+00 -2.40523312e+00 44 -5.59423589e+00 3.16752998e-01 -2.60941481e+00 | -5.59423589e+00 3.16752998e-01 -2.60941481e+00 45 3.32466669e+00 2.38477339e+00 4.10013391e-01 | 3.32466669e+00 2.38477339e+00 4.10013391e-01 46 3.27265053e+01 9.57952465e+00 -3.61338342e+01 | 3.27265053e+01 9.57952465e+00 -3.61338342e+01 47 -8.93069267e+00 -2.51092665e+01 1.88191462e+01 | -8.93069267e+00 -2.51092665e+01 1.88191462e+01 48 -3.73306533e+01 -4.97490480e+01 -2.80558687e+01 | -3.73306533e+01 -4.97490480e+01 -2.80558687e+01 49 3.89784418e+01 5.08332035e+01 2.94699915e+01 | 3.89784418e+01 5.08332035e+01 2.94699915e+01 50 -3.14774878e+00 3.05258698e+00 1.38815830e+00 | -3.14774878e+00 3.05258698e+00 1.38815830e+00 51 -2.06583958e+01 4.92192122e+00 3.37620165e+00 | -2.06583958e+01 4.92192122e+00 3.37620165e+00 52 1.62252474e+00 8.76196217e-01 -1.26785587e+00 | 1.62252474e+00 8.76196217e-01 -1.26785587e+00 53 -8.05539793e-02 2.17278177e+00 -2.34427560e+00 | -8.05539793e-02 2.17278177e+00 -2.34427560e+00 54 -2.90861384e+00 -6.08589018e+00 -2.36689829e+00 | -2.90861384e+00 -6.08589018e+00 -2.36689829e+00 55 8.57704047e+00 8.53144530e-01 -1.84378617e+00 | 8.57704047e+00 8.53144530e-01 -1.84378617e+00 56 6.97890117e+01 -3.31655594e+01 2.46247916e+01 | 6.97890117e+01 -3.31655594e+01 2.46247916e+01 57 8.21174990e+00 -1.94255796e+01 -4.38186559e+00 | 8.21174990e+00 -1.94255796e+01 -4.38186559e+00 58 3.65797789e+01 -4.26513190e+01 4.33943711e+01 | 3.65797789e+01 -4.26513190e+01 4.33943711e+01 59 1.96230338e+00 8.33860122e-01 3.09277601e+00 | 1.96230338e+00 8.33860122e-01 3.09277601e+00 60 -2.57295940e+00 2.42872379e+01 -1.72351536e+01 | -2.57295940e+00 2.42872379e+01 -1.72351536e+01 61 2.89256070e+00 2.20032643e+00 2.32885879e+00 | 2.89256070e+00 2.20032643e+00 2.32885879e+00 62 1.12717710e+01 1.37491645e+01 6.70166666e+00 | 1.12717710e+01 1.37491645e+01 6.70166666e+00 63 -1.05835627e+00 -1.26412914e+00 -1.63144909e+00 | -1.05835627e+00 -1.26412914e+00 -1.63144909e+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.