!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_WuLeeSu_2017_NiCrFe__MO_912636107108_001 Supported species : Cr Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [11, 49, 9, 46, 14, 10, 45, 35, 56, 2, 5, 0, 26, 36, 4, 25, 17, 16, 30, 33, 23, 27, 37, 20, 47, 15, 12, 21, 55, 39, 18, 63, 54, 19, 40, 7, 13, 22, 62, 29, 34, 61, 57, 48, 50, 6, 3, 24, 43, 1, 44, 53, 58, 51, 32, 28, 8, 42, 52, 60, 59, 41, 38, 31] 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)) = 144.96119442805588 V(r_1,...,r_N) = 144.96119442805588 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 -1.69904996e+00 -7.68754654e-01 -2.05028805e+00 | -1.69904996e+00 -7.68754654e-01 -2.05028805e+00 1 -1.56487321e+01 -4.28833682e+01 3.06979901e+01 | -1.56487321e+01 -4.28833682e+01 3.06979901e+01 2 -3.16149587e+00 1.70606890e+01 -5.65392026e+01 | -3.16149587e+00 1.70606890e+01 -5.65392026e+01 3 1.42969633e+01 2.53038472e+01 1.90647449e+01 | 1.42969633e+01 2.53038472e+01 1.90647449e+01 4 7.49293047e-01 9.92038387e-01 9.63211726e-01 | 7.49293047e-01 9.92038387e-01 9.63211726e-01 5 -5.33724771e-01 -6.20298635e-01 -1.16791832e-01 | -5.33724771e-01 -6.20298635e-01 -1.16791832e-01 6 1.47580008e+00 7.43985220e-02 1.30703769e-01 | 1.47580008e+00 7.43985220e-02 1.30703769e-01 7 -4.96640428e+01 1.26989171e+02 -7.98821954e+01 | -4.96640428e+01 1.26989171e+02 -7.98821954e+01 8 -3.86598121e+00 -9.29690176e-01 -3.85511103e+00 | -3.86598121e+00 -9.29690176e-01 -3.85511103e+00 9 -7.89920813e+00 6.60680816e+00 -1.21623439e+01 | -7.89920813e+00 6.60680816e+00 -1.21623439e+01 10 -7.83783884e-01 -5.01093154e-01 4.93636030e-01 | -7.83783884e-01 -5.01093154e-01 4.93636030e-01 11 6.88955623e+00 -9.11453836e+00 -9.36607054e+00 | 6.88955623e+00 -9.11453836e+00 -9.36607054e+00 12 -8.95776623e+01 -5.17183677e+01 -2.93338031e+01 | -8.95776623e+01 -5.17183677e+01 -2.93338031e+01 13 1.06524503e+02 3.90766713e+01 3.68452118e+01 | 1.06524503e+02 3.90766713e+01 3.68452118e+01 14 -2.03810697e+01 -8.14519967e+00 -3.05088084e+01 | -2.03810697e+01 -8.14519967e+00 -3.05088084e+01 15 2.67556246e+01 7.83050564e+00 3.43235349e+01 | 2.67556246e+01 7.83050564e+00 3.43235349e+01 16 -2.23392764e+01 -2.24839633e+01 -2.03516553e+01 | -2.23392764e+01 -2.24839633e+01 -2.03516553e+01 17 2.28968762e+01 2.09899228e+01 1.92913291e+01 | 2.28968762e+01 2.09899228e+01 1.92913291e+01 18 -5.52684896e-01 -9.81439224e-01 -2.42490159e-01 | -5.52684896e-01 -9.81439224e-01 -2.42490159e-01 19 -8.13661034e+01 5.10470216e+01 -5.36972755e+01 | -8.13661034e+01 5.10470216e+01 -5.36972755e+01 20 -2.89636400e+01 -1.82721681e+01 -1.63460158e+01 | -2.89636400e+01 -1.82721681e+01 -1.63460158e+01 21 3.19215777e+01 2.03475884e+01 1.80907986e+01 | 3.19215777e+01 2.03475884e+01 1.80907986e+01 22 -1.82571021e+00 -2.91421118e+00 -3.84809058e+00 | -1.82571021e+00 -2.91421118e+00 -3.84809058e+00 23 2.35452120e+00 3.01518274e+00 5.02963373e+00 | 2.35452120e+00 3.01518274e+00 5.02963373e+00 24 -7.19340618e+00 -3.04852878e+00 -7.27214799e+00 | -7.19340618e+00 -3.04852878e+00 -7.27214799e+00 25 -1.28354149e+01 2.75566690e+01 -1.26172805e+01 | -1.28354149e+01 2.75566690e+01 -1.26172805e+01 26 9.22186677e-02 -3.88952419e-01 1.06892853e+00 | 9.22186677e-02 -3.88952419e-01 1.06892853e+00 27 -1.55404288e+00 -9.64288289e-01 -1.18725534e-02 | -1.55404288e+00 -9.64288289e-01 -1.18725534e-02 28 9.34627812e+00 -2.02736790e+01 2.73404838e+01 | 9.34627812e+00 -2.02736790e+01 2.73404838e+01 29 3.38549676e+00 3.74014391e+00 3.06875013e+00 | 3.38549676e+00 3.74014391e+00 3.06875013e+00 30 7.98107286e+01 -5.07060973e+01 5.19326709e+01 | 7.98107286e+01 -5.07060973e+01 5.19326709e+01 31 -2.68046777e+01 1.34858272e+01 -1.42726540e+01 | -2.68046777e+01 1.34858272e+01 -1.42726540e+01 32 -7.60626639e-02 4.32266874e-01 2.32923693e-01 | -7.60626639e-02 4.32266874e-01 2.32923693e-01 33 -3.12192343e+00 -3.78139162e+00 1.26356190e+00 | -3.12192343e+00 -3.78139162e+00 1.26356190e+00 34 5.80262562e+01 -1.27358130e+02 7.15480654e+01 | 5.80262562e+01 -1.27358130e+02 7.15480654e+01 35 -1.81917378e-01 -1.07030378e+00 2.13828834e+00 | -1.81917378e-01 -1.07030378e+00 2.13828834e+00 36 -2.57980761e-01 -2.81369298e-02 -2.10466462e-01 | -2.57980761e-01 -2.81369298e-02 -2.10466462e-01 37 7.61441163e-01 2.51923340e-01 4.55402793e-01 | 7.61441163e-01 2.51923340e-01 4.55402793e-01 38 -1.39793689e+02 -1.11106481e+02 -1.31542239e+02 | -1.39793689e+02 -1.11106481e+02 -1.31542239e+02 39 1.16362615e+02 8.84753969e+01 1.51246666e+02 | 1.16362615e+02 8.84753969e+01 1.51246666e+02 40 -1.17280241e+00 -5.75005819e-01 3.17340294e-01 | -1.17280241e+00 -5.75005819e-01 3.17340294e-01 41 -3.78634624e+01 6.71439839e+01 -3.65036427e+01 | -3.78634624e+01 6.71439839e+01 -3.65036427e+01 42 -1.56392925e+01 -3.13707899e+00 -2.90988631e+00 | -1.56392925e+01 -3.13707899e+00 -2.90988631e+00 43 9.95347667e+00 1.17941162e+01 1.21336698e+01 | 9.95347667e+00 1.17941162e+01 1.21336698e+01 44 3.92593481e+01 -6.59071572e+01 3.40751028e+01 | 3.92593481e+01 -6.59071572e+01 3.40751028e+01 45 -3.85309298e-01 8.75796282e-01 1.12662071e-02 | -3.85309298e-01 8.75796282e-01 1.12662071e-02 46 -8.87611553e-01 -1.56554134e-01 6.30489127e-01 | -8.87611553e-01 -1.56554134e-01 6.30489127e-01 47 2.70665104e+00 -1.83633250e+00 -4.82083023e-01 | 2.70665104e+00 -1.83633250e+00 -4.82083023e-01 48 -8.31272956e+00 3.02918025e+00 7.43705664e+00 | -8.31272956e+00 3.02918025e+00 7.43705664e+00 49 7.65703731e+00 -9.09937547e+00 -1.34671904e+01 | 7.65703731e+00 -9.09937547e+00 -1.34671904e+01 50 -1.34984055e+01 -1.87129732e+01 -1.93967018e+01 | -1.34984055e+01 -1.87129732e+01 -1.93967018e+01 51 1.45099573e+01 1.89608996e+01 1.90499180e+01 | 1.45099573e+01 1.89608996e+01 1.90499180e+01 52 2.43923288e+01 2.28615436e+01 -2.10068609e+01 | 2.43923288e+01 2.28615436e+01 -2.10068609e+01 53 -2.42983184e+00 2.27441766e+00 -5.70169008e-01 | -2.42983184e+00 2.27441766e+00 -5.70169008e-01 54 -2.28301538e+01 1.95945570e-01 1.11263650e+00 | -2.28301538e+01 1.95945570e-01 1.11263650e+00 55 1.48897024e+01 8.50435461e+00 1.15511260e+01 | 1.48897024e+01 8.50435461e+00 1.15511260e+01 56 -2.94453951e+01 -2.73088482e+01 -4.42753134e+00 | -2.94453951e+01 -2.73088482e+01 -4.42753134e+00 57 6.17674711e+01 -2.49107461e+01 -7.28689313e+01 | 6.17674711e+01 -2.49107461e+01 -7.28689313e+01 58 2.84918716e+01 -1.23904707e+01 1.78219232e+01 | 2.84918716e+01 -1.23904707e+01 1.78219232e+01 59 -1.21842894e+00 -2.75822519e-01 7.39054369e-01 | -1.21842894e+00 -2.75822519e-01 7.39054369e-01 60 6.43263647e+00 -4.46538147e+00 6.39698292e+00 | 6.43263647e+00 -4.46538147e+00 6.39698292e+00 61 -1.36049697e+00 1.90720685e-01 -1.18783910e+00 | -1.36049697e+00 1.90720685e-01 -1.18783910e+00 62 -3.79967666e+01 5.83384626e+01 7.20842572e+01 | -3.79967666e+01 5.83384626e+01 7.20842572e+01 63 1.41173706e+00 -6.10665615e-01 -1.53972081e+00 | 1.41173706e+00 -6.10665615e-01 -1.53972081e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [56, 24, 55, 15, 60, 25, 40, 27, 20, 37, 63, 34, 41, 35, 30, 3, 18, 48, 16, 62, 8, 23, 59, 21, 1, 5, 32, 7, 42, 45, 14, 49, 26, 53, 11, 13, 50, 9, 39, 38, 6, 12, 28, 46, 58, 29, 43, 54, 17, 31, 36, 61, 57, 33, 47, 2, 0, 52, 44, 22, 4, 51, 19, 10] 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)) = 0.7391363808359628 V(r_1,...,r_N) = 0.7391363808359254 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 6.34331783e-01 4.81491187e-01 6.24210158e-01 | 6.34331783e-01 4.81491187e-01 6.24210158e-01 1 5.38328179e+00 -7.58977045e+00 -7.36444188e+00 | 5.38328179e+00 -7.58977045e+00 -7.36444188e+00 2 1.64470278e+00 6.95432039e-01 -1.66095904e-01 | 1.64470278e+00 6.95432039e-01 -1.66095904e-01 3 -5.32690550e+00 -1.95763062e+01 2.60125249e+01 | -5.32690550e+00 -1.95763062e+01 2.60125249e+01 4 4.34075891e+00 -4.88222068e+00 4.38875098e+00 | 4.34075891e+00 -4.88222068e+00 4.38875098e+00 5 -1.34465457e+01 -1.74899896e+01 1.91419221e+01 | -1.34465457e+01 -1.74899896e+01 1.91419221e+01 6 -1.09101879e+01 1.32012737e+01 3.57059583e+00 | -1.09101879e+01 1.32012737e+01 3.57059583e+00 7 -1.37783658e+01 7.44511125e+00 -2.90498557e+01 | -1.37783658e+01 7.44511125e+00 -2.90498557e+01 8 -5.63289205e+00 -5.67148460e+00 -7.41359739e+00 | -5.63289205e+00 -5.67148460e+00 -7.41359739e+00 9 9.13804020e+00 2.99942244e+00 1.77539827e+00 | 9.13804020e+00 2.99942244e+00 1.77539827e+00 10 -1.22530758e+01 4.78284791e+00 -1.79196181e+01 | -1.22530758e+01 4.78284791e+00 -1.79196181e+01 11 1.07146332e+01 -4.85808342e+00 1.90680595e+01 | 1.07146332e+01 -4.85808342e+00 1.90680595e+01 12 5.30162651e-01 -9.35726949e-01 -3.16950067e-01 | 5.30162651e-01 -9.35726949e-01 -3.16950067e-01 13 1.71779193e+00 -3.00545092e+00 -2.08251256e+00 | 1.71779193e+00 -3.00545092e+00 -2.08251256e+00 14 7.78180246e+00 2.04419526e+01 -1.29373893e+01 | 7.78180246e+00 2.04419526e+01 -1.29373893e+01 15 -2.83788003e+00 2.82562299e+00 -1.19602980e+00 | -2.83788003e+00 2.82562299e+00 -1.19602980e+00 16 7.70715194e-01 -2.25830289e-01 6.43664746e-01 | 7.70715194e-01 -2.25830289e-01 6.43664746e-01 17 -8.77963611e+00 -8.08464322e+00 4.61458708e+00 | -8.77963611e+00 -8.08464322e+00 4.61458708e+00 18 7.42162340e+00 8.94988428e+00 -7.85658851e+00 | 7.42162340e+00 8.94988428e+00 -7.85658851e+00 19 -9.61579453e-01 1.74080671e+00 -1.89441248e+00 | -9.61579453e-01 1.74080671e+00 -1.89441248e+00 20 -1.85683696e+01 -1.33736933e+01 -1.76431843e+01 | -1.85683696e+01 -1.33736933e+01 -1.76431843e+01 21 1.93547102e+01 1.18643950e+01 2.15805187e+01 | 1.93547102e+01 1.18643950e+01 2.15805187e+01 22 3.75615491e-01 -9.44805916e-01 -7.16321323e-01 | 3.75615491e-01 -9.44805916e-01 -7.16321323e-01 23 -3.84866628e+01 1.36824142e+01 -3.22302080e+01 | -3.84866628e+01 1.36824142e+01 -3.22302080e+01 24 4.26870351e+00 2.28827451e+01 -2.77258143e+01 | 4.26870351e+00 2.28827451e+01 -2.77258143e+01 25 -4.88675532e+01 2.80654785e+01 -6.87965499e+01 | -4.88675532e+01 2.80654785e+01 -6.87965499e+01 26 -1.12065223e+00 -6.71256063e-01 -5.71934596e-01 | -1.12065223e+00 -6.71256063e-01 -5.71934596e-01 27 2.33578014e-01 -1.10144928e-01 1.54257682e+00 | 2.33578014e-01 -1.10144928e-01 1.54257682e+00 28 4.76975872e+01 -2.95443403e+01 6.79006808e+01 | 4.76975872e+01 -2.95443403e+01 6.79006808e+01 29 1.19687302e+00 1.69590268e+00 5.19726191e-01 | 1.19687302e+00 1.69590268e+00 5.19726191e-01 30 -1.24306765e+01 -3.70391858e+01 -2.07324608e+01 | -1.24306765e+01 -3.70391858e+01 -2.07324608e+01 31 1.35654960e+01 3.45576409e+01 2.27514531e+01 | 1.35654960e+01 3.45576409e+01 2.27514531e+01 32 2.95365114e-01 3.11463054e-01 -8.33536501e-01 | 2.95365114e-01 3.11463054e-01 -8.33536501e-01 33 -3.37298992e-01 -1.58894020e+01 -2.09524632e+01 | -3.37298992e-01 -1.58894020e+01 -2.09524632e+01 34 1.38496773e+01 -8.33173142e+00 2.89053938e+01 | 1.38496773e+01 -8.33173142e+00 2.89053938e+01 35 -1.67535904e+01 3.89352860e+01 -3.32785033e+01 | -1.67535904e+01 3.89352860e+01 -3.32785033e+01 36 1.03524884e+01 -6.04712127e+00 7.45426847e+00 | 1.03524884e+01 -6.04712127e+00 7.45426847e+00 37 -3.04798129e+00 -5.09679070e+00 7.57323403e+00 | -3.04798129e+00 -5.09679070e+00 7.57323403e+00 38 -1.00670094e+01 2.24367798e+01 1.29676635e+01 | -1.00670094e+01 2.24367798e+01 1.29676635e+01 39 -5.46164155e-01 2.17918028e-01 -2.68129055e-01 | -5.46164155e-01 2.17918028e-01 -2.68129055e-01 40 -7.06965356e+00 -9.02746543e+00 -6.51581654e+00 | -7.06965356e+00 -9.02746543e+00 -6.51581654e+00 41 7.94464018e+00 8.08469297e+00 8.03005589e+00 | 7.94464018e+00 8.08469297e+00 8.03005589e+00 42 1.13050280e+00 1.01148944e+00 4.61011407e+00 | 1.13050280e+00 1.01148944e+00 4.61011407e+00 43 -8.11131203e-01 -2.40698189e+00 -2.82552225e+00 | -8.11131203e-01 -2.40698189e+00 -2.82552225e+00 44 -1.45403757e-01 1.12049466e+00 4.59912927e-01 | -1.45403757e-01 1.12049466e+00 4.59912927e-01 45 -7.46695217e-01 -1.20915030e-01 -5.24556932e-01 | -7.46695217e-01 -1.20915030e-01 -5.24556932e-01 46 2.19712460e+01 -3.54719903e+01 2.57905231e+01 | 2.19712460e+01 -3.54719903e+01 2.57905231e+01 47 2.17067474e-01 -4.62645792e-01 -3.39053166e-01 | 2.17067474e-01 -4.62645792e-01 -3.39053166e-01 48 9.64428528e-01 4.08968911e-01 -2.10633656e-01 | 9.64428528e-01 4.08968911e-01 -2.10633656e-01 49 -3.75152614e+00 -5.89713959e+00 4.28627301e-01 | -3.75152614e+00 -5.89713959e+00 4.28627301e-01 50 4.11952683e+01 -6.90513711e+00 2.87141008e+01 | 4.11952683e+01 -6.90513711e+00 2.87141008e+01 51 -1.64309490e+00 1.16057165e+00 -4.26657574e+00 | -1.64309490e+00 1.16057165e+00 -4.26657574e+00 52 1.09224495e+00 -1.87529681e+00 2.62315008e+00 | 1.09224495e+00 -1.87529681e+00 2.62315008e+00 53 -1.08604035e+01 -1.92346526e+01 1.38014641e+01 | -1.08604035e+01 -1.92346526e+01 1.38014641e+01 54 -6.03640748e+00 -4.08109446e+00 -3.03115580e+00 | -6.03640748e+00 -4.08109446e+00 -3.03115580e+00 55 7.00258229e+00 3.32338617e+00 2.23003584e+00 | 7.00258229e+00 3.32338617e+00 2.23003584e+00 56 -9.20044970e+00 -6.50994725e+00 -5.85137300e+00 | -9.20044970e+00 -6.50994725e+00 -5.85137300e+00 57 4.85720238e+00 5.30949102e+00 6.61037641e+00 | 4.85720238e+00 5.30949102e+00 6.61037641e+00 58 -1.06034117e+01 -8.20923722e+00 -3.12863724e+00 | -1.06034117e+01 -8.20923722e+00 -3.12863724e+00 59 1.49695457e+01 1.07050710e+01 1.56575602e+00 | 1.49695457e+01 1.07050710e+01 1.56575602e+00 60 -3.07623542e+00 6.78013986e-01 8.59099130e-01 | -3.07623542e+00 6.78013986e-01 8.59099130e-01 61 8.18838925e-01 2.69815722e+00 1.54586328e+00 | 8.18838925e-01 2.69815722e+00 1.54586328e+00 62 9.95142578e+00 1.09427169e+01 -1.87859365e+01 | 9.95142578e+00 1.09427169e+01 -1.87859365e+01 63 4.71450766e+00 5.91355930e+00 9.12154969e+00 | 4.71450766e+00 5.91355930e+00 9.12154969e+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 = [17, 8, 25, 7, 23, 18, 47, 3, 1, 43, 54, 51, 21, 50, 32, 58, 35, 0, 5, 52, 33, 12, 38, 4, 34, 2, 61, 36, 31, 57, 55, 28, 14, 20, 24, 16, 27, 56, 22, 48, 45, 46, 53, 9, 59, 40, 41, 6, 39, 60, 13, 11, 19, 42, 10, 30, 37, 29, 15, 44, 49, 26, 63, 62] 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)) = 92.29625387850234 V(r_1,...,r_N) = 92.29625387850231 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 7.68142226e-01 6.62202175e-01 1.12834657e+00 | 7.68142226e-01 6.62202175e-01 1.12834657e+00 1 -9.99328680e+00 3.66249908e+00 4.85918938e+01 | -9.99328680e+00 3.66249908e+00 4.85918938e+01 2 9.41141008e+00 -4.00657172e+00 -4.95579984e+01 | 9.41141008e+00 -4.00657172e+00 -4.95579984e+01 3 3.11967653e+01 -4.42422082e+01 -4.24074238e+01 | 3.11967653e+01 -4.42422082e+01 -4.24074238e+01 4 -7.94393725e-01 -8.10633693e-01 -1.86924122e-01 | -7.94393725e-01 -8.10633693e-01 -1.86924122e-01 5 2.44503284e+01 -3.71915476e+00 -2.26583852e+01 | 2.44503284e+01 -3.71915476e+00 -2.26583852e+01 6 5.52802206e-01 -7.30282545e-01 1.27736419e-02 | 5.52802206e-01 -7.30282545e-01 1.27736419e-02 7 -4.54679525e+00 9.71480184e+00 -3.46241339e+00 | -4.54679525e+00 9.71480184e+00 -3.46241339e+00 8 -1.86068723e+01 -5.18917610e+00 -2.13814946e+01 | -1.86068723e+01 -5.18917610e+00 -2.13814946e+01 9 2.46562099e+01 -1.32902860e+01 1.50982663e+01 | 2.46562099e+01 -1.32902860e+01 1.50982663e+01 10 -6.59097802e-01 -5.15002853e-01 9.33268347e-01 | -6.59097802e-01 -5.15002853e-01 9.33268347e-01 11 1.91684268e-02 3.53471744e-01 1.16291185e+00 | 1.91684268e-02 3.53471744e-01 1.16291185e+00 12 4.10597411e-01 7.07660893e-01 3.03158779e-01 | 4.10597411e-01 7.07660893e-01 3.03158779e-01 13 -1.23883550e+00 3.84305300e-01 -5.26057927e-01 | -1.23883550e+00 3.84305300e-01 -5.26057927e-01 14 -6.63115620e+00 1.88935310e+01 6.15781954e+00 | -6.63115620e+00 1.88935310e+01 6.15781954e+00 15 1.40109332e+00 -2.57839812e+01 8.54948090e+00 | 1.40109332e+00 -2.57839812e+01 8.54948090e+00 16 -8.18165470e+00 -7.23995449e+00 -1.17281773e+01 | -8.18165470e+00 -7.23995449e+00 -1.17281773e+01 17 -1.00993806e+01 -1.96715517e+00 2.90617492e+01 | -1.00993806e+01 -1.96715517e+00 2.90617492e+01 18 1.69579709e+01 1.02672400e+01 -1.75245576e+01 | 1.69579709e+01 1.02672400e+01 -1.75245576e+01 19 -1.06930497e+01 2.84765984e+01 -1.96164212e+01 | -1.06930497e+01 2.84765984e+01 -1.96164212e+01 20 -3.20923353e+01 4.28878959e+01 4.35770184e+01 | -3.20923353e+01 4.28878959e+01 4.35770184e+01 21 -8.68864685e+01 7.83277928e+01 -4.87976058e+01 | -8.68864685e+01 7.83277928e+01 -4.87976058e+01 22 -1.08889444e+01 -1.59965816e+01 -2.26954407e+01 | -1.08889444e+01 -1.59965816e+01 -2.26954407e+01 23 1.13456473e+01 1.56310881e+01 2.27234455e+01 | 1.13456473e+01 1.56310881e+01 2.27234455e+01 24 -1.04676464e+01 -4.61173794e+01 -2.49953648e+01 | -1.04676464e+01 -4.61173794e+01 -2.49953648e+01 25 1.34982087e+01 4.43799654e+01 2.14981850e+01 | 1.34982087e+01 4.43799654e+01 2.14981850e+01 26 -4.08410180e+00 -1.14285439e+00 -5.40313874e+00 | -4.08410180e+00 -1.14285439e+00 -5.40313874e+00 27 3.71496571e+00 1.04155244e+00 6.32601517e+00 | 3.71496571e+00 1.04155244e+00 6.32601517e+00 28 9.32549246e-02 2.53591642e+01 -8.41983268e+00 | 9.32549246e-02 2.53591642e+01 -8.41983268e+00 29 -1.01812964e+00 -4.90222981e-01 -3.22261610e-01 | -1.01812964e+00 -4.90222981e-01 -3.22261610e-01 30 9.15811995e+00 -2.60831665e+01 2.18547182e+01 | 9.15811995e+00 -2.60831665e+01 2.18547182e+01 31 5.64641788e-01 -2.19540154e-01 -2.49106763e-01 | 5.64641788e-01 -2.19540154e-01 -2.49106763e-01 32 5.96440902e-01 8.38623116e-01 -8.91485132e-01 | 5.96440902e-01 8.38623116e-01 -8.91485132e-01 33 -5.25979016e+01 -3.85616843e+01 8.07810137e+01 | -5.25979016e+01 -3.85616843e+01 8.07810137e+01 34 3.21008330e+01 3.25783730e+01 -5.42562666e+01 | 3.21008330e+01 3.25783730e+01 -5.42562666e+01 35 6.78086083e+00 -8.28693249e+00 -6.14084214e+00 | 6.78086083e+00 -8.28693249e+00 -6.14084214e+00 36 -2.44880692e+00 -2.54194681e+00 -5.80060290e-01 | -2.44880692e+00 -2.54194681e+00 -5.80060290e-01 37 -5.98901675e+00 -2.97380122e+00 4.87850686e+00 | -5.98901675e+00 -2.97380122e+00 4.87850686e+00 38 -1.16900717e+01 -1.35409890e+01 -4.97973533e+00 | -1.16900717e+01 -1.35409890e+01 -4.97973533e+00 39 9.54909484e+00 1.35868115e+01 7.07821605e+00 | 9.54909484e+00 1.35868115e+01 7.07821605e+00 40 -1.03085606e+00 -1.38907661e-01 -9.05178853e-01 | -1.03085606e+00 -1.38907661e-01 -9.05178853e-01 41 1.53823967e+01 -2.04799460e+01 -2.09757120e+01 | 1.53823967e+01 -2.04799460e+01 -2.09757120e+01 42 8.21338583e-01 -1.15806610e+00 9.54501712e-01 | 8.21338583e-01 -1.15806610e+00 9.54501712e-01 43 3.85603197e-03 5.60823366e-01 2.32433891e-01 | 3.85603197e-03 5.60823366e-01 2.32433891e-01 44 -5.71907076e+00 -4.00958489e+01 -4.83427622e+00 | -5.71907076e+00 -4.00958489e+01 -4.83427622e+00 45 6.67651680e+00 3.80485668e+01 4.06068394e+00 | 6.67651680e+00 3.80485668e+01 4.06068394e+00 46 -5.10855900e+00 2.71927601e+01 1.83168608e+01 | -5.10855900e+00 2.71927601e+01 1.83168608e+01 47 -1.00203246e+01 -4.71788356e+00 3.42377709e+00 | -1.00203246e+01 -4.71788356e+00 3.42377709e+00 48 -1.14349259e+01 -7.60298979e+00 -2.25796337e+00 | -1.14349259e+01 -7.60298979e+00 -2.25796337e+00 49 -1.15170028e+01 1.42923474e+01 -1.88212008e+01 | -1.15170028e+01 1.42923474e+01 -1.88212008e+01 50 5.00959145e+00 9.14653944e+00 -2.99885139e+00 | 5.00959145e+00 9.14653944e+00 -2.99885139e+00 51 -2.83571757e+00 5.10418284e+00 -7.07523417e+00 | -2.83571757e+00 5.10418284e+00 -7.07523417e+00 52 1.04802059e+01 -9.39159766e+00 2.39377223e+01 | 1.04802059e+01 -9.39159766e+00 2.39377223e+01 53 2.62964803e+00 1.88201162e+00 3.08354474e+00 | 2.62964803e+00 1.88201162e+00 3.08354474e+00 54 -3.89693575e+01 -1.08151832e+02 -2.69915346e+01 | -3.89693575e+01 -1.08151832e+02 -2.69915346e+01 55 3.64942831e+01 1.07806949e+02 2.79255084e+01 | 3.64942831e+01 1.07806949e+02 2.79255084e+01 56 8.71179321e+01 -7.80584345e+01 4.76508651e+01 | 8.71179321e+01 -7.80584345e+01 4.76508651e+01 57 -2.11592341e+01 -8.31974870e+00 1.44948255e+01 | -2.11592341e+01 -8.31974870e+00 1.44948255e+01 58 2.36618391e+01 6.35822248e+00 -1.62407184e+01 | 2.36618391e+01 6.35822248e+00 -1.62407184e+01 59 -1.84499918e-01 -7.85366206e-03 7.07459761e-01 | -1.84499918e-01 -7.85366206e-03 7.07459761e-01 60 -1.03903889e+01 -1.00748164e+00 -1.56926865e+01 | -1.03903889e+01 -1.00748164e+00 -1.56926865e+01 61 1.84484877e+01 7.92299618e+00 1.12272140e+01 | 1.84484877e+01 7.92299618e+00 1.12272140e+01 62 -2.83789347e+00 -7.55505114e+00 3.58404917e+00 | -2.83789347e+00 -7.55505114e+00 3.58404917e+00 63 6.86312445e+00 4.06617001e+00 4.25811598e+00 | 6.86312445e+00 4.06617001e+00 4.25811598e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cr Fe Ni (Configuration in file "config-CrFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [40, 46, 51, 39, 14, 7, 26, 5, 62, 28, 24, 22, 43, 25, 4, 44, 53, 45, 42, 21, 34, 19, 11, 54, 10, 13, 6, 59, 9, 31, 32, 29, 30, 56, 20, 52, 60, 50, 47, 3, 0, 57, 18, 12, 15, 17, 1, 38, 55, 63, 37, 2, 35, 16, 23, 48, 33, 41, 58, 27, 36, 61, 8, 49] 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)) = 78.42352003293432 V(r_1,...,r_N) = 78.42352003293425 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 -6.67255703e+01 -4.60551532e+01 -5.11861266e+01 | -6.67255703e+01 -4.60551532e+01 -5.11861266e+01 1 6.57224711e+01 5.19052724e+01 2.97693739e+01 | 6.57224711e+01 5.19052724e+01 2.97693739e+01 2 -1.21204650e+01 -2.10251421e+01 -2.27188155e+01 | -1.21204650e+01 -2.10251421e+01 -2.27188155e+01 3 3.67439744e+00 1.31906285e+01 2.72753515e+01 | 3.67439744e+00 1.31906285e+01 2.72753515e+01 4 6.97846059e+00 -1.01529250e+01 1.91075756e+01 | 6.97846059e+00 -1.01529250e+01 1.91075756e+01 5 -9.20014877e+00 9.32032506e+00 -1.02141263e+01 | -9.20014877e+00 9.32032506e+00 -1.02141263e+01 6 -5.16805206e+00 4.61025297e+00 1.65420666e+00 | -5.16805206e+00 4.61025297e+00 1.65420666e+00 7 1.43972106e+00 -1.24749852e+00 -5.49644895e-01 | 1.43972106e+00 -1.24749852e+00 -5.49644895e-01 8 -8.35179353e+00 -1.09701880e+01 -4.76636579e+00 | -8.35179353e+00 -1.09701880e+01 -4.76636579e+00 9 4.04105718e+01 -1.71487862e+01 -4.21695129e+01 | 4.04105718e+01 -1.71487862e+01 -4.21695129e+01 10 7.24104675e-01 1.61607460e+00 -9.07956156e-02 | 7.24104675e-01 1.61607460e+00 -9.07956156e-02 11 2.70625001e+00 -1.26369736e+00 -4.24067181e+00 | 2.70625001e+00 -1.26369736e+00 -4.24067181e+00 12 -6.61413846e+00 -2.05166143e+01 -1.54080204e+01 | -6.61413846e+00 -2.05166143e+01 -1.54080204e+01 13 9.05134994e+00 1.68653447e+01 1.27921925e+01 | 9.05134994e+00 1.68653447e+01 1.27921925e+01 14 -3.43598940e+01 2.85661130e+01 4.81592416e+01 | -3.43598940e+01 2.85661130e+01 4.81592416e+01 15 2.15726775e+01 -2.68912952e+01 -1.33538986e+01 | 2.15726775e+01 -2.68912952e+01 -1.33538986e+01 16 6.18095947e-01 2.00954901e-01 2.88005531e-01 | 6.18095947e-01 2.00954901e-01 2.88005531e-01 17 -1.54319701e+01 -2.57249616e+01 5.87561418e+00 | -1.54319701e+01 -2.57249616e+01 5.87561418e+00 18 -2.10542140e+01 -2.49259051e+01 -3.43117133e+01 | -2.10542140e+01 -2.49259051e+01 -3.43117133e+01 19 4.39817835e+01 4.12349614e+01 2.36898060e+01 | 4.39817835e+01 4.12349614e+01 2.36898060e+01 20 -4.09640134e+00 -3.19668261e+00 -2.20164322e+00 | -4.09640134e+00 -3.19668261e+00 -2.20164322e+00 21 1.21983958e+01 -1.46720305e+00 -2.17334470e+00 | 1.21983958e+01 -1.46720305e+00 -2.17334470e+00 22 -8.82132926e+00 9.26301430e+00 4.62556593e+00 | -8.82132926e+00 9.26301430e+00 4.62556593e+00 23 -1.07808700e+00 8.38419549e-01 -8.67349240e-01 | -1.07808700e+00 8.38419549e-01 -8.67349240e-01 24 -1.53960038e+02 -1.23384707e+02 -9.82243678e+01 | -1.53960038e+02 -1.23384707e+02 -9.82243678e+01 25 1.62334164e+02 1.29619092e+02 9.55760867e+01 | 1.62334164e+02 1.29619092e+02 9.55760867e+01 26 1.08478458e+00 -1.20171851e-01 8.56973242e-02 | 1.08478458e+00 -1.20171851e-01 8.56973242e-02 27 1.56753581e-01 1.88602410e+00 -1.75146837e+00 | 1.56753581e-01 1.88602410e+00 -1.75146837e+00 28 -3.18753475e+00 2.25057682e+00 1.72201256e+00 | -3.18753475e+00 2.25057682e+00 1.72201256e+00 29 -3.45449598e-01 -1.69080602e+00 1.57357796e+00 | -3.45449598e-01 -1.69080602e+00 1.57357796e+00 30 -1.51913547e+01 -1.10800756e+01 -1.96571770e+01 | -1.51913547e+01 -1.10800756e+01 -1.96571770e+01 31 1.37514488e+01 1.10697735e+01 1.80482160e+01 | 1.37514488e+01 1.10697735e+01 1.80482160e+01 32 -6.73694358e-01 -7.59228218e-01 -1.66242273e+00 | -6.73694358e-01 -7.59228218e-01 -1.66242273e+00 33 -4.15215267e+00 -6.66289795e+00 3.30473146e+00 | -4.15215267e+00 -6.66289795e+00 3.30473146e+00 34 8.05463227e-01 6.85028260e+00 -6.30046393e+00 | 8.05463227e-01 6.85028260e+00 -6.30046393e+00 35 -3.99879762e+01 6.25988268e+01 -2.32186063e+01 | -3.99879762e+01 6.25988268e+01 -2.32186063e+01 36 -7.29113132e-01 -1.64040095e+00 1.25500554e+00 | -7.29113132e-01 -1.64040095e+00 1.25500554e+00 37 1.70476474e+00 1.33200200e-01 9.66803693e-03 | 1.70476474e+00 1.33200200e-01 9.66803693e-03 38 1.50541664e+00 2.65421917e-01 -2.07939624e-01 | 1.50541664e+00 2.65421917e-01 -2.07939624e-01 39 -5.09784137e-01 -2.92292074e-01 1.37024857e+00 | -5.09784137e-01 -2.92292074e-01 1.37024857e+00 40 9.40897604e+00 -9.39277947e+00 1.05467529e+01 | 9.40897604e+00 -9.39277947e+00 1.05467529e+01 41 -3.96768266e+01 -2.15965591e+01 4.54232866e+01 | -3.96768266e+01 -2.15965591e+01 4.54232866e+01 42 4.11857030e+01 2.18600001e+01 -4.42830499e+01 | 4.11857030e+01 2.18600001e+01 -4.42830499e+01 43 -9.10535517e-01 -1.56123448e-01 5.54552316e-02 | -9.10535517e-01 -1.56123448e-01 5.54552316e-02 44 -2.45864496e-01 2.02344200e+00 5.44697192e-01 | -2.45864496e-01 2.02344200e+00 5.44697192e-01 45 -1.48117946e+00 -1.11349082e-01 -1.24256978e+00 | -1.48117946e+00 -1.11349082e-01 -1.24256978e+00 46 4.05699094e+01 -5.83914584e+01 2.80304347e+01 | 4.05699094e+01 -5.83914584e+01 2.80304347e+01 47 -1.52220452e+01 -7.91510853e+00 8.24030928e+00 | -1.52220452e+01 -7.91510853e+00 8.24030928e+00 48 -6.14302414e+01 -3.49190323e+01 -6.34006392e+00 | -6.14302414e+01 -3.49190323e+01 -6.34006392e+00 49 6.09915520e+01 3.56099213e+01 7.37527556e+00 | 6.09915520e+01 3.56099213e+01 7.37527556e+00 50 -1.09664358e+01 4.71584773e+00 3.37451273e+00 | -1.09664358e+01 4.71584773e+00 3.37451273e+00 51 -2.22291380e+00 3.08002720e+00 -1.11569732e+01 | -2.22291380e+00 3.08002720e+00 -1.11569732e+01 52 -1.82607078e+00 1.34795620e+00 -1.44793358e+00 | -1.82607078e+00 1.34795620e+00 -1.44793358e+00 53 -1.90511389e-01 -2.62556186e-01 -8.38340614e-01 | -1.90511389e-01 -2.62556186e-01 -8.38340614e-01 54 7.80039902e-01 -6.57535818e-01 -1.19330784e+00 | 7.80039902e-01 -6.57535818e-01 -1.19330784e+00 55 2.94098370e-01 3.98792858e-03 2.75882973e-01 | 2.94098370e-01 3.98792858e-03 2.75882973e-01 56 -2.07480367e+01 2.46060099e+01 1.34218286e+01 | -2.07480367e+01 2.46060099e+01 1.34218286e+01 57 1.26124934e-01 6.95391493e-01 8.52315967e-01 | 1.26124934e-01 6.95391493e-01 8.52315967e-01 58 -2.25436984e+00 -6.99075705e+00 -5.24975651e+00 | -2.25436984e+00 -6.99075705e+00 -5.24975651e+00 59 4.19160750e+00 4.97891705e+00 8.82953596e+00 | 4.19160750e+00 4.97891705e+00 8.82953596e+00 60 1.46786461e+01 4.82027797e+00 -6.93266601e+00 | 1.46786461e+01 4.82027797e+00 -6.93266601e+00 61 1.99128845e+00 3.66493464e+00 -6.57240665e-01 | 1.99128845e+00 3.66493464e+00 -6.57240665e-01 62 4.26413988e+00 -2.42040950e+00 1.24499029e+01 | 4.26413988e+00 -2.42040950e+00 1.24499029e+01 63 3.10324116e-02 -6.60972436e-01 -9.85991419e-01 | 3.10324116e-02 -6.60972436e-01 -9.85991419e-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.