!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_HuangLiuDuan_2021_HfNbTaTiZr__MO_893505888031_001 Supported species : Hf Nb Ta Ti Zr random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Hf (Configuration in file "config-Hf.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [4, 32, 56, 37, 0, 16, 14, 13, 50, 20, 34, 19, 52, 7, 6, 60, 5, 58, 23, 11, 9, 38, 57, 18, 45, 59, 54, 31, 42, 63, 39, 27, 1, 35, 10, 33, 55, 3, 21, 30, 51, 49, 28, 48, 46, 24, 44, 62, 43, 41, 8, 40, 12, 61, 26, 36, 2, 22, 17, 25, 15, 53, 47, 29] 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)) = -203.5435132715056 V(r_1,...,r_N) = -203.54351327150573 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 -4.11250069e+00 -1.01126023e+00 -7.49210513e-01 | -4.11250069e+00 -1.01126023e+00 -7.49210513e-01 1 1.62221584e+00 -2.16048238e+00 3.72059141e+00 | 1.62221584e+00 -2.16048238e+00 3.72059141e+00 2 -1.10284045e+00 2.03206430e+00 -6.05598244e+00 | -1.10284045e+00 2.03206430e+00 -6.05598244e+00 3 2.24076715e+00 1.79649464e+00 -2.50467940e+00 | 2.24076715e+00 1.79649464e+00 -2.50467940e+00 4 -2.20695977e+00 -1.83056647e+00 -8.92132802e-01 | -2.20695977e+00 -1.83056647e+00 -8.92132802e-01 5 3.09692200e+00 3.14183241e-01 -5.68439461e-01 | 3.09692200e+00 3.14183241e-01 -5.68439461e-01 6 -1.59039919e+00 -3.57765981e-01 -2.65081553e+00 | -1.59039919e+00 -3.57765981e-01 -2.65081553e+00 7 6.63192054e-01 -6.21110028e+00 3.79159625e+00 | 6.63192054e-01 -6.21110028e+00 3.79159625e+00 8 -2.93887741e+00 -6.46753021e-01 -1.72725142e+00 | -2.93887741e+00 -6.46753021e-01 -1.72725142e+00 9 -2.99684581e+00 1.64413936e+00 3.03228510e+00 | -2.99684581e+00 1.64413936e+00 3.03228510e+00 10 -2.94088195e+00 -8.34629319e-01 -5.94110620e+00 | -2.94088195e+00 -8.34629319e-01 -5.94110620e+00 11 4.67312702e+00 1.76846428e+00 2.69271354e+00 | 4.67312702e+00 1.76846428e+00 2.69271354e+00 12 6.31717994e-01 -4.69176076e+00 6.24180304e-01 | 6.31717994e-01 -4.69176076e+00 6.24180304e-01 13 4.41515467e+00 -8.47816412e-01 -1.50647915e-01 | 4.41515467e+00 -8.47816412e-01 -1.50647915e-01 14 -1.73851152e+00 9.98656221e-01 -1.13122282e+00 | -1.73851152e+00 9.98656221e-01 -1.13122282e+00 15 3.78883372e+00 -2.30876781e+00 2.18745076e-01 | 3.78883372e+00 -2.30876781e+00 2.18745076e-01 16 -2.45154018e+00 -3.14978533e+00 -2.07040875e+00 | -2.45154018e+00 -3.14978533e+00 -2.07040875e+00 17 1.54810809e+00 -1.07658750e+00 2.06485613e+00 | 1.54810809e+00 -1.07658750e+00 2.06485613e+00 18 -2.78447063e-01 -3.79898491e-01 -3.06304560e+00 | -2.78447063e-01 -3.79898491e-01 -3.06304560e+00 19 -3.92092028e+00 3.90677205e+00 2.48813773e+00 | -3.92092028e+00 3.90677205e+00 2.48813773e+00 20 2.03717047e-01 8.41088808e-01 9.08027454e-01 | 2.03717047e-01 8.41088808e-01 9.08027454e-01 21 9.51734148e-01 -1.35472553e+00 -2.65169335e+00 | 9.51734148e-01 -1.35472553e+00 -2.65169335e+00 22 -3.53648407e+00 -1.29573412e+00 -5.02439478e+00 | -3.53648407e+00 -1.29573412e+00 -5.02439478e+00 23 2.85394166e+00 3.67469125e+00 4.01340704e+00 | 2.85394166e+00 3.67469125e+00 4.01340704e+00 24 -1.07701169e+00 -1.01082663e+00 -1.98758607e+00 | -1.07701169e+00 -1.01082663e+00 -1.98758607e+00 25 1.98976165e+00 -2.33024371e+00 2.24786350e+00 | 1.98976165e+00 -2.33024371e+00 2.24786350e+00 26 -1.72232535e+00 1.84896688e+00 -3.74941133e+00 | -1.72232535e+00 1.84896688e+00 -3.74941133e+00 27 1.31773444e+00 -1.83166374e-01 2.84507378e+00 | 1.31773444e+00 -1.83166374e-01 2.84507378e+00 28 -4.18407830e-01 -2.23678317e+00 6.33524860e-01 | -4.18407830e-01 -2.23678317e+00 6.33524860e-01 29 2.46608727e+00 8.72015388e-01 2.09066239e+00 | 2.46608727e+00 8.72015388e-01 2.09066239e+00 30 1.80967692e+00 1.97891517e+00 -4.95266661e-01 | 1.80967692e+00 1.97891517e+00 -4.95266661e-01 31 -3.24713437e+00 3.45672635e+00 -1.48427857e+00 | -3.24713437e+00 3.45672635e+00 -1.48427857e+00 32 -4.34915499e+00 -2.33383101e+00 -3.12247055e+00 | -4.34915499e+00 -2.33383101e+00 -3.12247055e+00 33 8.67840605e-01 2.04774421e-01 8.32012817e-01 | 8.67840605e-01 2.04774421e-01 8.32012817e-01 34 2.92456306e+00 6.44299971e+00 -2.20150983e+00 | 2.92456306e+00 6.44299971e+00 -2.20150983e+00 35 -8.40714565e-01 -2.23269955e+00 1.48213319e+00 | -8.40714565e-01 -2.23269955e+00 1.48213319e+00 36 -2.67187315e-01 -3.17487236e-01 1.91191762e+00 | -2.67187315e-01 -3.17487236e-01 1.91191762e+00 37 -1.68584813e+00 -2.83511010e+00 2.63854543e+00 | -1.68584813e+00 -2.83511010e+00 2.63854543e+00 38 -7.54306239e-01 -2.68156974e+00 -3.60390853e+00 | -7.54306239e-01 -2.68156974e+00 -3.60390853e+00 39 2.29021757e+00 3.14198643e+00 3.26571486e+00 | 2.29021757e+00 3.14198643e+00 3.26571486e+00 40 -1.17995327e+00 -1.79543922e+00 2.53318257e+00 | -1.17995327e+00 -1.79543922e+00 2.53318257e+00 41 5.95406993e+00 -4.43532584e+00 5.38266707e+00 | 5.95406993e+00 -4.43532584e+00 5.38266707e+00 42 -3.09635602e+00 3.68873125e+00 -9.64152252e-01 | -3.09635602e+00 3.68873125e+00 -9.64152252e-01 43 2.67043493e+00 5.21339727e-01 1.44917488e+00 | 2.67043493e+00 5.21339727e-01 1.44917488e+00 44 -5.02467600e+00 1.31199280e+00 -8.86196958e+00 | -5.02467600e+00 1.31199280e+00 -8.86196958e+00 45 1.04616173e+00 2.73311380e+00 2.55923029e+00 | 1.04616173e+00 2.73311380e+00 2.55923029e+00 46 8.43409092e-01 5.83588828e-01 -2.07771455e+00 | 8.43409092e-01 5.83588828e-01 -2.07771455e+00 47 1.39913077e+00 8.76769488e-01 1.23515080e+00 | 1.39913077e+00 8.76769488e-01 1.23515080e+00 48 -4.48360505e+00 -2.21486860e+00 -1.68165483e+00 | -4.48360505e+00 -2.21486860e+00 -1.68165483e+00 49 3.84590597e+00 -8.45857037e-01 1.70649976e+00 | 3.84590597e+00 -8.45857037e-01 1.70649976e+00 50 -3.95033552e+00 -1.46611643e+00 -1.26148797e+00 | -3.95033552e+00 -1.46611643e+00 -1.26148797e+00 51 1.51174283e+00 4.20673767e+00 3.28304176e+00 | 1.51174283e+00 4.20673767e+00 3.28304176e+00 52 -4.00918132e+00 1.47583264e+00 -2.05917820e+00 | -4.00918132e+00 1.47583264e+00 -2.05917820e+00 53 1.24930655e+00 1.49832213e+00 2.67226587e+00 | 1.24930655e+00 1.49832213e+00 2.67226587e+00 54 -4.23651211e+00 1.18170329e+00 5.62469210e-01 | -4.23651211e+00 1.18170329e+00 5.62469210e-01 55 3.98377647e+00 -5.03848400e-01 3.76608130e-01 | 3.98377647e+00 -5.03848400e-01 3.76608130e-01 56 -2.09157827e+00 -9.31363072e-01 3.38227733e+00 | -2.09157827e+00 -9.31363072e-01 3.38227733e+00 57 8.13231203e+00 6.60422991e+00 1.73464942e-01 | 8.13231203e+00 6.60422991e+00 1.73464942e-01 58 5.34251960e+00 -2.36159442e+00 9.10111971e-01 | 5.34251960e+00 -2.36159442e+00 9.10111971e-01 59 -1.66042747e+00 -1.10879483e+00 1.26061206e+00 | -1.66042747e+00 -1.10879483e+00 1.26061206e+00 60 5.02861720e-01 1.32079447e+00 -1.63262172e+00 | 5.02861720e-01 1.32079447e+00 -1.63262172e+00 61 9.44028299e-01 2.11349780e+00 1.35436550e+00 | 9.44028299e-01 2.11349780e+00 1.35436550e+00 62 -6.01501968e+00 -3.15240132e+00 -8.84995885e-01 | -6.01501968e+00 -3.15240132e+00 -8.84995885e-01 63 2.14397072e+00 9.53680520e-02 9.06126900e-01 | 2.14397072e+00 9.53680520e-02 9.06126900e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Nb (Configuration in file "config-Nb.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [17, 55, 18, 42, 39, 60, 54, 58, 48, 62, 14, 49, 44, 53, 10, 27, 47, 0, 2, 52, 28, 57, 33, 35, 45, 30, 56, 15, 20, 61, 25, 36, 63, 22, 38, 23, 31, 46, 34, 4, 59, 51, 3, 50, 12, 24, 37, 16, 8, 11, 43, 41, 19, 13, 6, 1, 26, 21, 7, 40, 5, 29, 9, 32] 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)) = -325.3871586820723 V(r_1,...,r_N) = -325.3871586820728 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 9.31721242e-01 1.10643469e+00 5.70006433e-01 | 9.31721242e-01 1.10643469e+00 5.70006433e-01 1 -1.61275157e+00 -2.38082812e+00 1.72104931e-01 | -1.61275157e+00 -2.38082812e+00 1.72104931e-01 2 -1.35852977e+00 -1.14141681e-01 -1.83634199e+00 | -1.35852977e+00 -1.14141681e-01 -1.83634199e+00 3 2.19614876e+00 -5.64805342e-01 -2.69168209e+00 | 2.19614876e+00 -5.64805342e-01 -2.69168209e+00 4 -1.65157713e+00 -2.01197761e+00 3.19131784e-01 | -1.65157713e+00 -2.01197761e+00 3.19131784e-01 5 -1.37773556e+00 -3.80508078e+00 5.35303237e+00 | -1.37773556e+00 -3.80508078e+00 5.35303237e+00 6 7.17290199e-01 4.87278435e-01 -1.71182896e-01 | 7.17290199e-01 4.87278435e-01 -1.71182896e-01 7 -6.61000980e-01 -1.71429924e+00 -4.30674548e+00 | -6.61000980e-01 -1.71429924e+00 -4.30674548e+00 8 -9.99842882e-01 -5.53447381e-02 -7.50646056e-02 | -9.99842882e-01 -5.53447381e-02 -7.50646056e-02 9 4.04362794e+00 -1.40399019e+00 -5.26650338e+00 | 4.04362794e+00 -1.40399019e+00 -5.26650338e+00 10 -5.30906981e-01 7.06262322e-01 -5.87091079e-01 | -5.30906981e-01 7.06262322e-01 -5.87091079e-01 11 5.55021296e+00 -4.53877644e+00 -5.03409712e+00 | 5.55021296e+00 -4.53877644e+00 -5.03409712e+00 12 1.95778528e+00 -2.41553580e+00 1.80462954e+00 | 1.95778528e+00 -2.41553580e+00 1.80462954e+00 13 1.45739792e+00 -1.20448080e-01 -3.54348668e-01 | 1.45739792e+00 -1.20448080e-01 -3.54348668e-01 14 -3.80918054e+00 5.53388803e+00 -3.13224991e+00 | -3.80918054e+00 5.53388803e+00 -3.13224991e+00 15 1.14574882e+00 -1.92192210e+00 5.71972032e-01 | 1.14574882e+00 -1.92192210e+00 5.71972032e-01 16 3.76817694e-02 -7.48755670e-01 5.76981323e-01 | 3.76817694e-02 -7.48755670e-01 5.76981323e-01 17 -2.01760093e+00 -1.00448533e+00 2.38483566e+00 | -2.01760093e+00 -1.00448533e+00 2.38483566e+00 18 3.26760213e+00 1.76689622e+00 -3.04501268e+00 | 3.26760213e+00 1.76689622e+00 -3.04501268e+00 19 -2.58133177e-01 -5.32437920e-01 5.34259669e-01 | -2.58133177e-01 -5.32437920e-01 5.34259669e-01 20 -3.24346110e+00 5.18989148e-01 2.25535583e+00 | -3.24346110e+00 5.18989148e-01 2.25535583e+00 21 -1.49515586e+00 1.96164701e+00 -7.56588243e-01 | -1.49515586e+00 1.96164701e+00 -7.56588243e-01 22 7.85861894e-01 1.27955822e+00 1.82412155e+00 | 7.85861894e-01 1.27955822e+00 1.82412155e+00 23 -6.93695525e-01 -1.93243675e+00 -8.10791632e-01 | -6.93695525e-01 -1.93243675e+00 -8.10791632e-01 24 1.47207037e+00 6.62125059e-01 -6.89200941e-01 | 1.47207037e+00 6.62125059e-01 -6.89200941e-01 25 1.17980617e+00 -2.17924725e+00 -3.13513807e-01 | 1.17980617e+00 -2.17924725e+00 -3.13513807e-01 26 1.86849279e+00 1.67823455e+00 -1.67455859e+00 | 1.86849279e+00 1.67823455e+00 -1.67455859e+00 27 -9.10415652e-01 -5.91654764e-01 7.36024338e-01 | -9.10415652e-01 -5.91654764e-01 7.36024338e-01 28 -1.19529267e+00 5.82526336e+00 8.87960482e-01 | -1.19529267e+00 5.82526336e+00 8.87960482e-01 29 1.54971289e+00 1.76588386e-01 7.90559772e-01 | 1.54971289e+00 1.76588386e-01 7.90559772e-01 30 -1.88027760e+00 3.77576961e+00 -1.05577757e+00 | -1.88027760e+00 3.77576961e+00 -1.05577757e+00 31 -1.75241641e+00 1.86833650e+00 -5.41014614e-01 | -1.75241641e+00 1.86833650e+00 -5.41014614e-01 32 6.29250901e-01 -1.51735476e-01 -1.71904763e-01 | 6.29250901e-01 -1.51735476e-01 -1.71904763e-01 33 -3.62682819e-01 -4.50967678e-01 -2.35779278e+00 | -3.62682819e-01 -4.50967678e-01 -2.35779278e+00 34 -2.56949521e+00 -1.85320665e+00 -1.89664672e+00 | -2.56949521e+00 -1.85320665e+00 -1.89664672e+00 35 -5.65945434e-01 -2.44046028e+00 5.00781002e+00 | -5.65945434e-01 -2.44046028e+00 5.00781002e+00 36 1.14579264e+00 -9.47478675e-01 -3.40928499e-01 | 1.14579264e+00 -9.47478675e-01 -3.40928499e-01 37 9.16958395e-02 1.00122658e-01 -8.71427347e-01 | 9.16958395e-02 1.00122658e-01 -8.71427347e-01 38 -9.28025204e-01 1.39620164e+00 3.93380193e+00 | -9.28025204e-01 1.39620164e+00 3.93380193e+00 39 5.03770820e-01 1.20224025e-03 -1.54561056e+00 | 5.03770820e-01 1.20224025e-03 -1.54561056e+00 40 -4.27907110e-01 -8.45853239e-01 4.34790706e-01 | -4.27907110e-01 -8.45853239e-01 4.34790706e-01 41 -1.80658586e+00 -5.09328669e+00 5.48935706e+00 | -1.80658586e+00 -5.09328669e+00 5.48935706e+00 42 3.02004974e+00 3.55598184e+00 -5.59680306e+00 | 3.02004974e+00 3.55598184e+00 -5.59680306e+00 43 7.38518288e-01 2.86374950e-01 4.80155850e-01 | 7.38518288e-01 2.86374950e-01 4.80155850e-01 44 1.60193745e+00 -6.50267299e-01 2.27543056e+00 | 1.60193745e+00 -6.50267299e-01 2.27543056e+00 45 -2.10428479e+00 2.39300546e-01 -1.44795882e+00 | -2.10428479e+00 2.39300546e-01 -1.44795882e+00 46 -1.17508470e+00 2.42458436e-01 2.45553679e+00 | -1.17508470e+00 2.42458436e-01 2.45553679e+00 47 9.03635105e-01 1.95452483e-01 6.20001638e-01 | 9.03635105e-01 1.95452483e-01 6.20001638e-01 48 -1.38786608e+01 -6.09816894e+00 -2.83483993e+00 | -1.38786608e+01 -6.09816894e+00 -2.83483993e+00 49 1.09051550e+01 8.18009217e+00 5.43164980e+00 | 1.09051550e+01 8.18009217e+00 5.43164980e+00 50 7.95505025e-01 1.71520273e+00 1.98129127e-01 | 7.95505025e-01 1.71520273e+00 1.98129127e-01 51 -8.42695005e-01 -6.49512585e-02 -4.12662914e-01 | -8.42695005e-01 -6.49512585e-02 -4.12662914e-01 52 -4.63993219e-01 1.79681351e-01 1.63104934e+00 | -4.63993219e-01 1.79681351e-01 1.63104934e+00 53 1.43866673e-01 -1.15737455e+00 2.31648050e+00 | 1.43866673e-01 -1.15737455e+00 2.31648050e+00 54 2.89039036e+00 1.99008170e+00 1.88909986e+00 | 2.89039036e+00 1.99008170e+00 1.88909986e+00 55 -1.75768496e+00 -2.44770990e+00 -2.44428467e+00 | -1.75768496e+00 -2.44770990e+00 -2.44428467e+00 56 -1.62304190e-01 4.21421523e+00 2.62410620e+00 | -1.62304190e-01 4.21421523e+00 2.62410620e+00 57 -2.90792913e-01 -2.97603830e+00 1.29700974e-01 | -2.90792913e-01 -2.97603830e+00 1.29700974e-01 58 4.26643377e+00 3.19352139e+00 -2.97848432e+00 | 4.26643377e+00 3.19352139e+00 -2.97848432e+00 59 -8.54997191e-01 -1.24502792e+00 7.65070354e-01 | -8.54997191e-01 -1.24502792e+00 7.65070354e-01 60 1.59197794e+00 -8.05937998e-01 1.20186387e+00 | 1.59197794e+00 -8.05937998e-01 1.20186387e+00 61 -1.37084878e+00 3.00481508e-01 -1.08188433e+00 | -1.37084878e+00 3.00481508e-01 -1.08188433e+00 62 -2.74334531e+00 3.27171825e+00 1.47417777e+00 | -2.74334531e+00 3.27171825e+00 1.47417777e+00 63 3.64167147e-01 -1.14472801e+00 -8.16194024e-01 | 3.64167147e-01 -1.14472801e+00 -8.16194024e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ta (Configuration in file "config-Ta.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [16, 31, 35, 17, 10, 19, 8, 46, 6, 21, 4, 34, 38, 15, 61, 13, 0, 3, 53, 5, 55, 9, 28, 47, 41, 36, 27, 26, 22, 52, 44, 1, 58, 62, 11, 2, 25, 45, 12, 42, 48, 24, 39, 49, 30, 37, 7, 23, 40, 43, 59, 60, 29, 18, 57, 20, 63, 54, 32, 50, 51, 14, 33, 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)) = -200.84394944311254 V(r_1,...,r_N) = -200.8439494431123 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 -3.12198860e+00 -3.38591862e+00 -2.81541846e+00 | -3.12198860e+00 -3.38591862e+00 -2.81541846e+00 1 -3.00147010e+00 -2.01450133e+00 2.29168522e+01 | -3.00147010e+00 -2.01450133e+00 2.29168522e+01 2 -1.86219738e+00 1.79866345e+01 -2.50625471e+01 | -1.86219738e+00 1.79866345e+01 -2.50625471e+01 3 5.51011413e+00 2.67470719e+00 1.51894610e-01 | 5.51011413e+00 2.67470719e+00 1.51894610e-01 4 4.41889664e+00 -1.83734544e+01 3.73393220e+00 | 4.41889664e+00 -1.83734544e+01 3.73393220e+00 5 -1.35726424e+01 1.45606696e+01 -6.05809580e+00 | -1.35726424e+01 1.45606696e+01 -6.05809580e+00 6 -5.40962082e+00 -8.79292131e-01 -6.87658350e-01 | -5.40962082e+00 -8.79292131e-01 -6.87658350e-01 7 -2.65203662e+00 1.29353069e+01 -6.74024860e+00 | -2.65203662e+00 1.29353069e+01 -6.74024860e+00 8 -2.36068114e+00 5.61686659e-01 -1.30355986e+00 | -2.36068114e+00 5.61686659e-01 -1.30355986e+00 9 -5.13453925e+00 1.02683607e+01 -1.18611580e+01 | -5.13453925e+00 1.02683607e+01 -1.18611580e+01 10 -1.35497718e+00 2.48908515e-02 1.09944328e-01 | -1.35497718e+00 2.48908515e-02 1.09944328e-01 11 1.86995444e+01 -2.03479148e+01 -1.14171415e+01 | 1.86995444e+01 -2.03479148e+01 -1.14171415e+01 12 8.20086235e+00 -1.24904590e+01 1.13613409e+01 | 8.20086235e+00 -1.24904590e+01 1.13613409e+01 13 -3.36637858e-01 1.29657808e+00 -1.26487212e-01 | -3.36637858e-01 1.29657808e+00 -1.26487212e-01 14 -7.92576051e-01 3.80608155e+00 -2.46728412e+00 | -7.92576051e-01 3.80608155e+00 -2.46728412e+00 15 -4.22784100e+00 5.71333350e+00 -4.10606034e+00 | -4.22784100e+00 5.71333350e+00 -4.10606034e+00 16 -5.91338452e+00 -6.49644385e+00 -3.76630879e+00 | -5.91338452e+00 -6.49644385e+00 -3.76630879e+00 17 -1.05385934e+01 -9.28091152e+00 4.65207429e+00 | -1.05385934e+01 -9.28091152e+00 4.65207429e+00 18 1.83540466e+01 1.25137339e+01 -9.59946747e+00 | 1.83540466e+01 1.25137339e+01 -9.59946747e+00 19 -7.69007399e+00 6.73032335e+00 -4.95658687e+00 | -7.69007399e+00 6.73032335e+00 -4.95658687e+00 20 4.36232643e+00 6.33286968e+00 -6.17743251e+00 | 4.36232643e+00 6.33286968e+00 -6.17743251e+00 21 4.42769098e+00 -7.99977315e+00 -4.73808902e+00 | 4.42769098e+00 -7.99977315e+00 -4.73808902e+00 22 -6.19878494e+00 -8.28634477e-01 5.63874875e+00 | -6.19878494e+00 -8.28634477e-01 5.63874875e+00 23 2.24349316e+00 4.26525126e+00 -2.46966477e-01 | 2.24349316e+00 4.26525126e+00 -2.46966477e-01 24 -3.87350359e+00 -1.59940982e+00 -5.93481851e+00 | -3.87350359e+00 -1.59940982e+00 -5.93481851e+00 25 3.18637565e+00 1.57533294e+00 3.06875715e+00 | 3.18637565e+00 1.57533294e+00 3.06875715e+00 26 -4.37543808e+00 -4.24342684e+00 -4.60079684e+00 | -4.37543808e+00 -4.24342684e+00 -4.60079684e+00 27 4.25381725e+00 4.28677052e+00 5.01055521e+00 | 4.25381725e+00 4.28677052e+00 5.01055521e+00 28 -1.13623899e+01 1.96557333e+01 8.99491759e+00 | -1.13623899e+01 1.96557333e+01 8.99491759e+00 29 6.74168349e-01 -1.45425703e+00 -2.42776043e+00 | 6.74168349e-01 -1.45425703e+00 -2.42776043e+00 30 5.56497949e+00 -4.58729814e+00 6.37034026e+00 | 5.56497949e+00 -4.58729814e+00 6.37034026e+00 31 9.52723534e-02 4.41107000e-01 2.37550175e-01 | 9.52723534e-02 4.41107000e-01 2.37550175e-01 32 -3.43424873e+00 2.97572279e-01 -2.96218325e+00 | -3.43424873e+00 2.97572279e-01 -2.96218325e+00 33 -1.86374526e+00 5.48109088e+00 -5.54468752e+00 | -1.86374526e+00 5.48109088e+00 -5.54468752e+00 34 1.86716563e+00 -1.62806791e+01 1.42283293e+01 | 1.86716563e+00 -1.62806791e+01 1.42283293e+01 35 2.50097870e+00 -6.73121798e+00 -4.39902304e+00 | 2.50097870e+00 -6.73121798e+00 -4.39902304e+00 36 1.00588966e+00 -1.14418084e+01 6.39948420e+00 | 1.00588966e+00 -1.14418084e+01 6.39948420e+00 37 1.29207993e+00 2.03976093e+00 5.94081313e+00 | 1.29207993e+00 2.03976093e+00 5.94081313e+00 38 -6.32273461e+00 -3.70244642e+00 -5.14287918e+00 | -6.32273461e+00 -3.70244642e+00 -5.14287918e+00 39 7.26308933e+00 3.36748567e+00 3.69574504e+00 | 7.26308933e+00 3.36748567e+00 3.69574504e+00 40 9.97558844e+00 -1.88032868e+01 9.06066817e+00 | 9.97558844e+00 -1.88032868e+01 9.06066817e+00 41 1.21640363e+00 -1.08695375e+01 2.43042784e+00 | 1.21640363e+00 -1.08695375e+01 2.43042784e+00 42 8.24165650e+00 -1.70267809e+00 -9.67875427e-01 | 8.24165650e+00 -1.70267809e+00 -9.67875427e-01 43 3.21183297e+00 -2.79748294e+00 -2.49386392e+00 | 3.21183297e+00 -2.79748294e+00 -2.49386392e+00 44 -1.53005292e+00 -1.69414809e+00 -1.03194529e+00 | -1.53005292e+00 -1.69414809e+00 -1.03194529e+00 45 8.28386008e-01 2.63667485e+00 6.70952133e-01 | 8.28386008e-01 2.63667485e+00 6.70952133e-01 46 -1.21883028e+00 4.27495159e+00 4.08806584e+00 | -1.21883028e+00 4.27495159e+00 4.08806584e+00 47 -1.96271580e+00 -3.52810591e+00 1.29462310e+00 | -1.96271580e+00 -3.52810591e+00 1.29462310e+00 48 -6.46704928e+00 -2.37974980e+00 -2.29795040e+00 | -6.46704928e+00 -2.37974980e+00 -2.29795040e+00 49 -8.70719493e+00 9.72856820e+00 -6.17220659e+00 | -8.70719493e+00 9.72856820e+00 -6.17220659e+00 50 -8.34466488e+00 1.19437490e+01 7.66359659e-01 | -8.34466488e+00 1.19437490e+01 7.66359659e-01 51 -9.86822800e+00 1.14682901e+01 -9.36430359e+00 | -9.86822800e+00 1.14682901e+01 -9.36430359e+00 52 5.67713044e+00 -3.38551083e+00 7.10972264e+00 | 5.67713044e+00 -3.38551083e+00 7.10972264e+00 53 3.47917802e+00 3.44369076e+00 9.16564996e+00 | 3.47917802e+00 3.44369076e+00 9.16564996e+00 54 -5.32016695e+00 -4.15222456e-01 -3.20461105e+00 | -5.32016695e+00 -4.15222456e-01 -3.20461105e+00 55 6.38497224e+00 -5.58461403e-01 2.39544073e+00 | 6.38497224e+00 -5.58461403e-01 2.39544073e+00 56 3.47652071e+00 -3.85726490e+00 3.37111515e+00 | 3.47652071e+00 -3.85726490e+00 3.37111515e+00 57 -1.93632659e+01 -9.62305415e+00 -1.24224908e+00 | -1.93632659e+01 -9.62305415e+00 -1.24224908e+00 58 1.06338069e+01 -7.67973680e-01 -1.73019351e+01 | 1.06338069e+01 -7.67973680e-01 -1.73019351e+01 59 1.08480554e+01 1.56997002e+01 1.94788409e+01 | 1.08480554e+01 1.56997002e+01 1.94788409e+01 60 -1.27111254e+01 9.70895227e-01 -1.79007294e+01 | -1.27111254e+01 9.70895227e-01 -1.79007294e+01 61 1.33260747e+01 5.90495760e+00 2.13323207e+01 | 1.33260747e+01 5.90495760e+00 2.13323207e+01 62 9.51128569e+00 -9.33766164e+00 1.28302643e+01 | 9.51128569e+00 -9.33766164e+00 1.28302643e+01 63 1.61717028e-01 -1.02877348e+00 -1.38540125e+00 | 1.61717028e-01 -1.02877348e+00 -1.38540125e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ti (Configuration in file "config-Ti.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [18, 10, 55, 57, 61, 26, 27, 47, 46, 15, 1, 16, 28, 53, 29, 9, 11, 39, 0, 42, 41, 63, 51, 36, 50, 52, 5, 6, 12, 14, 58, 49, 37, 60, 56, 45, 23, 32, 40, 17, 38, 20, 19, 54, 59, 35, 8, 7, 62, 31, 24, 22, 25, 13, 43, 2, 34, 3, 30, 44, 33, 4, 48, 21] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 14.516111681665253 V(r_1,...,r_N) = 14.516111681665263 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 -1.52315878e+01 -1.18555175e+01 -7.92248311e+00 | -1.52315878e+01 -1.18555175e+01 -7.92248311e+00 1 4.56933356e+00 2.32520921e+00 6.35283509e+00 | 4.56933356e+00 2.32520921e+00 6.35283509e+00 2 1.12450479e+01 6.04657050e+00 -1.29726978e+00 | 1.12450479e+01 6.04657050e+00 -1.29726978e+00 3 3.60878231e+01 -3.26696239e+01 -1.42041546e+01 | 3.60878231e+01 -3.26696239e+01 -1.42041546e+01 4 -1.91337228e+01 -1.05271495e+01 -6.89421099e+00 | -1.91337228e+01 -1.05271495e+01 -6.89421099e+00 5 1.80644333e+01 1.18716834e+01 4.71089979e+00 | 1.80644333e+01 1.18716834e+01 4.71089979e+00 6 -1.84871846e-02 1.60131419e+00 2.33120857e+00 | -1.84871846e-02 1.60131419e+00 2.33120857e+00 7 1.46326937e+00 1.27470026e+01 -6.52091534e+00 | 1.46326937e+00 1.27470026e+01 -6.52091534e+00 8 -1.30629778e+00 -3.67651894e-01 4.00796520e-01 | -1.30629778e+00 -3.67651894e-01 4.00796520e-01 9 9.36766965e-01 -1.96007252e+00 -4.99297184e+00 | 9.36766965e-01 -1.96007252e+00 -4.99297184e+00 10 -6.54100494e-01 -1.74382958e+00 -3.78828814e+00 | -6.54100494e-01 -1.74382958e+00 -3.78828814e+00 11 4.50027520e+00 -3.89839150e+00 9.75245189e-01 | 4.50027520e+00 -3.89839150e+00 9.75245189e-01 12 -4.95807981e+00 -3.74627806e+00 -5.38573196e-01 | -4.95807981e+00 -3.74627806e+00 -5.38573196e-01 13 7.29243923e+00 1.31831917e+00 9.73485951e-01 | 7.29243923e+00 1.31831917e+00 9.73485951e-01 14 1.17751698e+00 2.94055514e+00 2.00666398e+00 | 1.17751698e+00 2.94055514e+00 2.00666398e+00 15 -3.20440495e+00 2.24006142e+00 -6.33757969e+00 | -3.20440495e+00 2.24006142e+00 -6.33757969e+00 16 -1.10335939e+01 -8.30905395e+00 -1.20954139e+01 | -1.10335939e+01 -8.30905395e+00 -1.20954139e+01 17 1.15522115e+01 4.38839695e+00 1.95618804e+01 | 1.15522115e+01 4.38839695e+00 1.95618804e+01 18 6.33266711e+00 6.72046982e+00 -9.29418357e+00 | 6.33266711e+00 6.72046982e+00 -9.29418357e+00 19 -3.68140291e+00 5.53017925e-01 -4.42533003e+00 | -3.68140291e+00 5.53017925e-01 -4.42533003e+00 20 -3.54763567e+01 3.05583466e+01 1.63037498e+01 | -3.54763567e+01 3.05583466e+01 1.63037498e+01 21 -6.44135839e+00 -2.79908390e+00 -1.16309138e+01 | -6.44135839e+00 -2.79908390e+00 -1.16309138e+01 22 -1.16580587e+01 6.35941910e-01 3.10854103e+00 | -1.16580587e+01 6.35941910e-01 3.10854103e+00 23 3.16313758e+00 -1.28043044e+00 -1.99030876e+00 | 3.16313758e+00 -1.28043044e+00 -1.99030876e+00 24 -2.67131305e+00 -1.64026003e+00 -1.90002323e+00 | -2.67131305e+00 -1.64026003e+00 -1.90002323e+00 25 -1.16591477e+01 7.32835302e+00 -4.10211355e+00 | -1.16591477e+01 7.32835302e+00 -4.10211355e+00 26 -1.68385930e-01 1.89399269e+00 1.73537573e-01 | -1.68385930e-01 1.89399269e+00 1.73537573e-01 27 -2.80499443e-01 -2.74157640e-01 -4.55483201e-01 | -2.80499443e-01 -2.74157640e-01 -4.55483201e-01 28 8.50009370e+00 -4.97006342e+00 9.04253798e+00 | 8.50009370e+00 -4.97006342e+00 9.04253798e+00 29 7.67987905e+00 -1.24726362e+00 3.27254795e+00 | 7.67987905e+00 -1.24726362e+00 3.27254795e+00 30 -2.68646085e+01 -1.73619625e+01 -3.58392009e+01 | -2.68646085e+01 -1.73619625e+01 -3.58392009e+01 31 6.90282005e+00 2.94116107e+01 3.07083087e+01 | 6.90282005e+00 2.94116107e+01 3.07083087e+01 32 1.19046886e-01 9.20955252e-02 -1.56480636e-02 | 1.19046886e-01 9.20955252e-02 -1.56480636e-02 33 2.30438779e+00 -2.65441203e+00 1.34393511e+00 | 2.30438779e+00 -2.65441203e+00 1.34393511e+00 34 7.28855926e+00 -1.91058879e+01 1.50565636e+00 | 7.28855926e+00 -1.91058879e+01 1.50565636e+00 35 5.26354398e+00 -6.74479326e+00 -8.92738930e+00 | 5.26354398e+00 -6.74479326e+00 -8.92738930e+00 36 9.05783840e-01 4.43468803e-01 -2.14950767e-01 | 9.05783840e-01 4.43468803e-01 -2.14950767e-01 37 -2.94512670e+00 -1.14773634e+00 7.02577162e-01 | -2.94512670e+00 -1.14773634e+00 7.02577162e-01 38 -4.66617254e+00 -1.52870232e+00 2.82557146e-01 | -4.66617254e+00 -1.52870232e+00 2.82557146e-01 39 -5.56715131e+00 -4.31765665e+00 9.36123712e+00 | -5.56715131e+00 -4.31765665e+00 9.36123712e+00 40 -2.86704263e+00 -1.91430547e+00 -5.49927864e+00 | -2.86704263e+00 -1.91430547e+00 -5.49927864e+00 41 -1.90245005e+01 8.56993179e+00 -7.52214998e+00 | -1.90245005e+01 8.56993179e+00 -7.52214998e+00 42 2.22294694e+00 -1.01514469e+01 3.06204129e+00 | 2.22294694e+00 -1.01514469e+01 3.06204129e+00 43 4.20521349e+00 3.26315967e+00 3.24888049e+00 | 4.20521349e+00 3.26315967e+00 3.24888049e+00 44 1.60744916e+01 -5.26932154e+00 3.20010870e+00 | 1.60744916e+01 -5.26932154e+00 3.20010870e+00 45 7.15224986e+00 2.49572656e-01 1.05629357e+01 | 7.15224986e+00 2.49572656e-01 1.05629357e+01 46 -4.32598056e+00 -9.31555726e+00 -1.99585144e+01 | -4.32598056e+00 -9.31555726e+00 -1.99585144e+01 47 4.76317761e+00 1.10978691e+01 1.66279798e+01 | 4.76317761e+00 1.10978691e+01 1.66279798e+01 48 -6.72801914e+00 7.93055117e+00 2.55949474e+00 | -6.72801914e+00 7.93055117e+00 2.55949474e+00 49 2.49939055e+01 -2.11662386e+01 -2.23007089e+01 | 2.49939055e+01 -2.11662386e+01 -2.23007089e+01 50 -1.12789496e+01 -2.72454538e-01 -2.28644480e+00 | -1.12789496e+01 -2.72454538e-01 -2.28644480e+00 51 5.70287939e+00 6.95398107e+00 6.35377824e+00 | 5.70287939e+00 6.95398107e+00 6.35377824e+00 52 -3.70863515e+00 6.64533974e+00 -2.07936812e+00 | -3.70863515e+00 6.64533974e+00 -2.07936812e+00 53 -9.40024197e+00 -1.46787218e+01 4.52177203e+00 | -9.40024197e+00 -1.46787218e+01 4.52177203e+00 54 -2.67488517e+01 2.22827192e+01 2.33024761e+01 | -2.67488517e+01 2.22827192e+01 2.33024761e+01 55 1.13910724e+00 1.32765068e-01 1.34214934e-01 | 1.13910724e+00 1.32765068e-01 1.34214934e-01 56 5.10954711e+00 -8.72080090e-01 -2.40850294e+00 | 5.10954711e+00 -8.72080090e-01 -2.40850294e+00 57 5.11738963e+00 3.74076933e+00 9.80589641e+00 | 5.11738963e+00 3.74076933e+00 9.80589641e+00 58 1.60098715e+01 -8.62384865e+00 1.15134149e+01 | 1.60098715e+01 -8.62384865e+00 1.15134149e+01 59 6.21241848e-01 -1.75906708e+00 -4.88037892e-01 | 6.21241848e-01 -1.75906708e+00 -4.88037892e-01 60 -1.13764792e+01 -1.57712312e+01 -5.70890914e+00 | -1.13764792e+01 -1.57712312e+01 -5.70890914e+00 61 1.10902095e+01 1.55437815e+01 4.02002060e+00 | 1.10902095e+01 1.55437815e+01 4.02002060e+00 62 1.32707665e+01 2.11488051e+01 2.73813153e-01 | 1.32707665e+01 2.11488051e+01 2.73813153e-01 63 2.56522969e-01 -7.31403339e-01 -6.65708068e-01 | 2.56522969e-01 -7.31403339e-01 -6.65708068e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Zr (Configuration in file "config-Zr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [50, 35, 40, 18, 16, 53, 34, 48, 41, 14, 30, 58, 57, 47, 9, 46, 4, 26, 3, 52, 39, 62, 29, 27, 36, 61, 17, 23, 59, 22, 10, 38, 33, 32, 6, 1, 24, 44, 31, 20, 2, 8, 56, 49, 37, 63, 15, 13, 7, 43, 0, 55, 19, 5, 60, 51, 42, 12, 11, 28, 54, 25, 21, 45] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 42.145430082504426 V(r_1,...,r_N) = 42.14543008250446 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 -1.79691730e+00 -2.18631296e+00 -2.28998386e+00 | -1.79691730e+00 -2.18631296e+00 -2.28998386e+00 1 8.24648575e+00 -2.32816198e+01 -6.96089345e+00 | 8.24648575e+00 -2.32816198e+01 -6.96089345e+00 2 1.15370369e+01 8.41971076e+00 -8.20903540e+00 | 1.15370369e+01 8.41971076e+00 -8.20903540e+00 3 -2.77697511e+01 -1.17949659e+01 3.62023298e+01 | -2.77697511e+01 -1.17949659e+01 3.62023298e+01 4 -2.78470752e-01 -7.38856924e+00 -3.65852932e+00 | -2.78470752e-01 -7.38856924e+00 -3.65852932e+00 5 -4.79081003e+00 -2.49136502e+00 -9.13930108e+00 | -4.79081003e+00 -2.49136502e+00 -9.13930108e+00 6 -1.76340140e+01 1.86118285e+01 1.26101151e+01 | -1.76340140e+01 1.86118285e+01 1.26101151e+01 7 -4.48656358e+01 2.26778030e+01 -4.39329633e+01 | -4.48656358e+01 2.26778030e+01 -4.39329633e+01 8 -8.70532518e+00 -1.55041151e+01 -6.03402422e+00 | -8.70532518e+00 -1.55041151e+01 -6.03402422e+00 9 5.07486405e+00 1.61132774e+01 2.36581293e-01 | 5.07486405e+00 1.61132774e+01 2.36581293e-01 10 1.21307685e+00 1.28262917e-01 2.27887143e-01 | 1.21307685e+00 1.28262917e-01 2.27887143e-01 11 1.28322054e+01 -1.00277491e+01 -9.06004834e+00 | 1.28322054e+01 -1.00277491e+01 -9.06004834e+00 12 -1.23579175e+01 -8.49174802e+00 -9.79720736e+00 | -1.23579175e+01 -8.49174802e+00 -9.79720736e+00 13 1.27828293e+01 1.02369679e+01 8.53696674e+00 | 1.27828293e+01 1.02369679e+01 8.53696674e+00 14 -1.27419819e+01 -1.54882612e+01 -4.58417818e+00 | -1.27419819e+01 -1.54882612e+01 -4.58417818e+00 15 1.32053397e+01 8.11060114e+00 1.34286088e+01 | 1.32053397e+01 8.11060114e+00 1.34286088e+01 16 -5.24302426e+00 -3.12272547e+00 -2.23212902e+00 | -5.24302426e+00 -3.12272547e+00 -2.23212902e+00 17 -2.52996802e+00 -1.51431589e+00 -9.49825505e-01 | -2.52996802e+00 -1.51431589e+00 -9.49825505e-01 18 8.66682852e-01 7.08188317e+00 -1.40120517e+01 | 8.66682852e-01 7.08188317e+00 -1.40120517e+01 19 -1.80369610e+00 -3.90480759e-01 1.23016679e+00 | -1.80369610e+00 -3.90480759e-01 1.23016679e+00 20 7.43428208e+00 -2.22805599e+00 1.29161963e+01 | 7.43428208e+00 -2.22805599e+00 1.29161963e+01 21 -8.61906818e-01 -9.27841898e+00 5.88036356e+00 | -8.61906818e-01 -9.27841898e+00 5.88036356e+00 22 -3.67915787e+00 -6.71858272e+00 -6.13750189e+00 | -3.67915787e+00 -6.71858272e+00 -6.13750189e+00 23 1.14074133e+00 1.39727325e+01 9.24551851e+00 | 1.14074133e+00 1.39727325e+01 9.24551851e+00 24 2.86503311e+01 1.02860745e+01 -4.61912070e+01 | 2.86503311e+01 1.02860745e+01 -4.61912070e+01 25 -1.92464420e+00 -5.65930370e+00 -1.03712080e+00 | -1.92464420e+00 -5.65930370e+00 -1.03712080e+00 26 8.49573612e+00 4.00833848e+00 -1.04080285e+01 | 8.49573612e+00 4.00833848e+00 -1.04080285e+01 27 7.43602607e-01 2.18536081e+00 9.78789842e-01 | 7.43602607e-01 2.18536081e+00 9.78789842e-01 28 -9.59764629e+00 7.06745159e+00 8.10491952e+00 | -9.59764629e+00 7.06745159e+00 8.10491952e+00 29 1.04303229e+01 -5.27367286e+00 -3.67438898e+00 | 1.04303229e+01 -5.27367286e+00 -3.67438898e+00 30 -3.95949349e+00 1.19063405e+01 -4.91225243e+00 | -3.95949349e+00 1.19063405e+01 -4.91225243e+00 31 -6.09095333e+00 1.55315931e+01 -5.87440264e+00 | -6.09095333e+00 1.55315931e+01 -5.87440264e+00 32 -8.89716222e+00 -5.16929335e+00 -1.52476455e+01 | -8.89716222e+00 -5.16929335e+00 -1.52476455e+01 33 5.63149420e+00 3.16368478e+00 8.20566351e+00 | 5.63149420e+00 3.16368478e+00 8.20566351e+00 34 2.83098976e+01 -1.40126343e+01 4.46026992e+01 | 2.83098976e+01 -1.40126343e+01 4.46026992e+01 35 1.33018438e+01 3.04727157e+00 1.08082620e+01 | 1.33018438e+01 3.04727157e+00 1.08082620e+01 36 -2.37385345e+00 -4.78176763e+00 1.72029723e+00 | -2.37385345e+00 -4.78176763e+00 1.72029723e+00 37 -2.13650884e+01 -1.57491532e+01 1.86301073e+01 | -2.13650884e+01 -1.57491532e+01 1.86301073e+01 38 3.70979918e-01 2.21645265e+00 1.08083670e+00 | 3.70979918e-01 2.21645265e+00 1.08083670e+00 39 -1.86062162e+01 1.28990448e+01 1.30596180e+01 | -1.86062162e+01 1.28990448e+01 1.30596180e+01 40 5.98138834e+00 -6.21271200e+00 6.05116013e+00 | 5.98138834e+00 -6.21271200e+00 6.05116013e+00 41 6.34606852e+00 -9.93296734e+00 -1.52540711e+01 | 6.34606852e+00 -9.93296734e+00 -1.52540711e+01 42 -1.63192367e+01 -3.01011971e+01 -3.15481116e+01 | -1.63192367e+01 -3.01011971e+01 -3.15481116e+01 43 2.42558459e+01 2.50069864e+01 2.86485707e+01 | 2.42558459e+01 2.50069864e+01 2.86485707e+01 44 -4.22816212e+00 -9.91131512e+00 -1.52574722e+01 | -4.22816212e+00 -9.91131512e+00 -1.52574722e+01 45 1.03737502e+01 1.32198250e+01 1.19493968e+01 | 1.03737502e+01 1.32198250e+01 1.19493968e+01 46 8.37303762e+00 3.01259825e+01 1.06877970e-01 | 8.37303762e+00 3.01259825e+01 1.06877970e-01 47 -2.30017518e+01 6.19883762e-01 2.09423640e+01 | -2.30017518e+01 6.19883762e-01 2.09423640e+01 48 -1.71530043e+01 -1.92780862e+01 -9.16374048e+00 | -1.71530043e+01 -1.92780862e+01 -9.16374048e+00 49 1.21654049e+01 1.50057340e+01 1.12922627e+01 | 1.21654049e+01 1.50057340e+01 1.12922627e+01 50 -3.40259277e-01 3.66616634e+00 -2.57234253e+00 | -3.40259277e-01 3.66616634e+00 -2.57234253e+00 51 2.83219689e+00 5.81390310e+00 -8.02081141e-01 | 2.83219689e+00 5.81390310e+00 -8.02081141e-01 52 2.49956559e+01 -1.96565430e+01 -1.80859905e+01 | 2.49956559e+01 -1.96565430e+01 -1.80859905e+01 53 -1.28358202e+01 4.60412990e-01 1.03379730e+01 | -1.28358202e+01 4.60412990e-01 1.03379730e+01 54 -3.26313441e+00 1.99719353e+00 5.02710924e+00 | -3.26313441e+00 1.99719353e+00 5.02710924e+00 55 3.00837265e-01 -2.11106263e-01 -2.44783204e-01 | 3.00837265e-01 -2.11106263e-01 -2.44783204e-01 56 2.61340906e+00 -7.24971807e+00 5.85031534e+00 | 2.61340906e+00 -7.24971807e+00 5.85031534e+00 57 -2.23300846e+00 6.02817245e-01 2.02203460e+01 | -2.23300846e+00 6.02817245e-01 2.02203460e+01 58 4.10218967e-01 -7.48454211e+00 -6.25892098e+00 | 4.10218967e-01 -7.48454211e+00 -6.25892098e+00 59 7.62644317e-01 3.92817393e-01 7.29949555e-01 | 7.62644317e-01 3.92817393e-01 7.29949555e-01 60 1.95632787e+01 2.68023015e+00 -1.72144094e+01 | 1.95632787e+01 2.68023015e+00 -1.72144094e+01 61 1.26704927e+00 3.06273909e+00 3.53842068e-01 | 1.26704927e+00 3.06273909e+00 3.53842068e-01 62 6.11731569e+00 -5.39762828e-01 1.00459385e+00 | 6.11731569e+00 -5.39762828e-01 1.00459385e+00 63 6.22157480e-01 8.11689632e-01 5.23952849e-01 | 6.22157480e-01 8.11689632e-01 5.23952849e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Hf Nb Ta Ti Zr (Configuration in file "config-HfNbTaTiZr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [19, 10, 28, 24, 40, 17, 15, 59, 50, 42, 1, 21, 51, 20, 45, 6, 36, 5, 30, 0, 13, 11, 39, 46, 3, 53, 56, 54, 2, 61, 18, 44, 35, 33, 49, 32, 16, 52, 48, 22, 4, 41, 9, 62, 31, 14, 23, 60, 38, 34, 8, 12, 37, 25, 27, 55, 26, 58, 57, 7, 47, 29, 43, 63] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 160.87335425352111 V(r_1,...,r_N) = 160.87335425352114 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 -8.26110203e+00 -6.35469900e+00 -6.63986209e+00 | -8.26110203e+00 -6.35469900e+00 -6.63986209e+00 1 -1.63575601e+00 7.56497744e+00 -4.74916249e+00 | -1.63575601e+00 7.56497744e+00 -4.74916249e+00 2 -5.65380832e-01 5.17150402e-01 -2.17463447e-01 | -5.65380832e-01 5.17150402e-01 -2.17463447e-01 3 -1.67296201e+00 -5.34768846e+00 3.67110068e+00 | -1.67296201e+00 -5.34768846e+00 3.67110068e+00 4 9.35624180e+00 -1.80024937e+00 9.82147583e+00 | 9.35624180e+00 -1.80024937e+00 9.82147583e+00 5 1.01570148e+02 -1.68556746e+02 -1.36404117e+02 | 1.01570148e+02 -1.68556746e+02 -1.36404117e+02 6 2.14924393e-01 8.37843391e-01 1.77201635e-02 | 2.14924393e-01 8.37843391e-01 1.77201635e-02 7 -2.85983664e+01 4.40525607e+00 -8.92815367e+00 | -2.85983664e+01 4.40525607e+00 -8.92815367e+00 8 -1.36093341e+00 -2.18496467e-01 -3.29246925e-01 | -1.36093341e+00 -2.18496467e-01 -3.29246925e-01 9 -3.39145433e+00 3.86051743e+00 -6.28386029e+00 | -3.39145433e+00 3.86051743e+00 -6.28386029e+00 10 -2.03267822e+00 7.70885455e-01 -3.35572608e-01 | -2.03267822e+00 7.70885455e-01 -3.35572608e-01 11 3.01399194e+00 -3.00173148e-01 1.88391118e+00 | 3.01399194e+00 -3.00173148e-01 1.88391118e+00 12 3.18381627e+00 -3.45549871e+00 4.41769332e+00 | 3.18381627e+00 -3.45549871e+00 4.41769332e+00 13 1.06659929e+02 -5.46352438e+01 -1.00985458e+02 | 1.06659929e+02 -5.46352438e+01 -1.00985458e+02 14 4.36988603e+01 3.05705117e+01 -3.19994863e+01 | 4.36988603e+01 3.05705117e+01 -3.19994863e+01 15 1.86112780e+00 -1.83337120e+00 1.66711358e+00 | 1.86112780e+00 -1.83337120e+00 1.66711358e+00 16 -2.10764568e+00 -1.02460603e+01 -1.11994787e+01 | -2.10764568e+00 -1.02460603e+01 -1.11994787e+01 17 4.30684853e+01 -1.72337108e+01 -7.45250826e+00 | 4.30684853e+01 -1.72337108e+01 -7.45250826e+00 18 1.20499518e+00 1.17749906e+00 -2.71761978e+00 | 1.20499518e+00 1.17749906e+00 -2.71761978e+00 19 -5.27123751e+00 5.19191078e+00 -1.31919293e+01 | -5.27123751e+00 5.19191078e+00 -1.31919293e+01 20 1.70510142e+01 -6.73707623e+00 4.19029341e+00 | 1.70510142e+01 -6.73707623e+00 4.19029341e+00 21 1.25482972e+01 -2.46436936e+00 8.62004472e+00 | 1.25482972e+01 -2.46436936e+00 8.62004472e+00 22 -5.70892601e+01 4.18615854e+01 1.51000831e+00 | -5.70892601e+01 4.18615854e+01 1.51000831e+00 23 8.85625559e-01 -9.03857619e-01 1.71441601e-01 | 8.85625559e-01 -9.03857619e-01 1.71441601e-01 24 6.14973615e-02 4.64081386e+00 -5.89428726e+00 | 6.14973615e-02 4.64081386e+00 -5.89428726e+00 25 -7.99118453e+01 -9.48659425e+01 -2.03379776e+01 | -7.99118453e+01 -9.48659425e+01 -2.03379776e+01 26 3.67702636e+01 1.23323311e+02 -4.13270409e+01 | 3.67702636e+01 1.23323311e+02 -4.13270409e+01 27 2.39964137e+00 1.05554431e+00 2.06267984e+00 | 2.39964137e+00 1.05554431e+00 2.06267984e+00 28 3.61185526e+01 -2.62172896e+01 5.41866159e+01 | 3.61185526e+01 -2.62172896e+01 5.41866159e+01 29 7.47957091e+00 2.07218221e+00 2.63582621e+00 | 7.47957091e+00 2.07218221e+00 2.63582621e+00 30 -5.18177855e+00 -1.56566002e+01 1.16194779e+00 | -5.18177855e+00 -1.56566002e+01 1.16194779e+00 31 1.20711806e+01 1.56431447e+01 7.64070253e+00 | 1.20711806e+01 1.56431447e+01 7.64070253e+00 32 -1.04765206e+00 9.57156087e-01 -9.84859506e-01 | -1.04765206e+00 9.57156087e-01 -9.84859506e-01 33 6.52739442e+01 -3.95788455e+01 8.52084661e+01 | 6.52739442e+01 -3.95788455e+01 8.52084661e+01 34 -1.45629210e+02 1.05668593e+02 1.50033509e+02 | -1.45629210e+02 1.05668593e+02 1.50033509e+02 35 1.85165640e+01 1.92814997e+01 1.42907587e+01 | 1.85165640e+01 1.92814997e+01 1.42907587e+01 36 -6.46052148e+01 3.89426958e+01 -8.33580881e+01 | -6.46052148e+01 3.89426958e+01 -8.33580881e+01 37 5.18383949e-01 1.51567341e+00 -3.94025223e-02 | 5.18383949e-01 1.51567341e+00 -3.94025223e-02 38 -3.71969866e+01 -2.97478474e+01 1.84953515e-01 | -3.71969866e+01 -2.97478474e+01 1.84953515e-01 39 3.58779940e+01 2.73456686e+01 -8.18498940e-01 | 3.58779940e+01 2.73456686e+01 -8.18498940e-01 40 8.34449371e+00 -1.68467000e+01 1.44728773e+01 | 8.34449371e+00 -1.68467000e+01 1.44728773e+01 41 -2.40623396e+01 -1.73065734e+01 2.87620463e+01 | -2.40623396e+01 -1.73065734e+01 2.87620463e+01 42 -8.34782745e+01 6.83919481e+01 7.06799335e+01 | -8.34782745e+01 6.83919481e+01 7.06799335e+01 43 2.69375716e+01 -3.36673741e+01 -4.96488394e+01 | 2.69375716e+01 -3.36673741e+01 -4.96488394e+01 44 -3.58283643e+01 -1.70563609e+01 -3.50866356e+01 | -3.58283643e+01 -1.70563609e+01 -3.50866356e+01 45 3.47486402e+01 1.78013433e+01 3.47974187e+01 | 3.47486402e+01 1.78013433e+01 3.47974187e+01 46 -6.56715040e+01 -5.73425739e+01 -8.63688188e+00 | -6.56715040e+01 -5.73425739e+01 -8.63688188e+00 47 6.17627807e+01 5.18947542e+01 2.06155866e+01 | 6.17627807e+01 5.18947542e+01 2.06155866e+01 48 -3.86094500e+01 -1.75963366e+01 -1.25426694e+01 | -3.86094500e+01 -1.75963366e+01 -1.25426694e+01 49 3.91353661e+00 -1.17958431e+00 2.42135875e+01 | 3.91353661e+00 -1.17958431e+00 2.42135875e+01 50 8.44291782e+00 1.54693945e+01 -2.49654616e+01 | 8.44291782e+00 1.54693945e+01 -2.49654616e+01 51 8.76765849e+00 1.92059197e+01 1.01035377e+01 | 8.76765849e+00 1.92059197e+01 1.01035377e+01 52 -2.58477534e+00 -4.80554763e+00 -4.24621321e+00 | -2.58477534e+00 -4.80554763e+00 -4.24621321e+00 53 -1.33845725e+00 -1.28074979e+01 2.00021511e+01 | -1.33845725e+00 -1.28074979e+01 2.00021511e+01 54 -1.40036062e+00 6.31561033e-01 2.90948111e+00 | -1.40036062e+00 6.31561033e-01 2.90948111e+00 55 1.08487796e+00 -9.38863450e-01 -1.03614045e-02 | 1.08487796e+00 -9.38863450e-01 -1.03614045e-02 56 -1.27148944e+01 -9.58385965e-01 -6.44175881e+00 | -1.27148944e+01 -9.58385965e-01 -6.44175881e+00 57 -1.34189729e+01 -1.95968757e+01 1.94174143e+01 | -1.34189729e+01 -1.95968757e+01 1.94174143e+01 58 1.58798576e+01 1.69631408e+01 -1.44469833e+01 | 1.58798576e+01 1.69631408e+01 -1.44469833e+01 59 1.18718487e+00 4.06179849e+00 2.95974127e+00 | 1.18718487e+00 4.06179849e+00 2.95974127e+00 60 -1.77829634e+01 3.47948163e+01 4.65847445e+01 | -1.77829634e+01 3.47948163e+01 4.65847445e+01 61 -8.87804050e-01 2.81627266e+00 -5.19003851e-01 | -8.87804050e-01 2.81627266e+00 -5.19003851e-01 62 -9.92252253e+00 -1.27335491e+01 -4.72332267e+01 | -9.92252253e+00 -1.27335491e+01 -4.72332267e+01 63 2.27855774e+01 2.97546198e+01 3.90773267e+01 | 2.27855774e+01 2.97546198e+01 3.90773267e+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.