!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MaiselKoZhang_2017_VNiTi__MO_744610363128_001 Supported species : Ni Ti V random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [26, 42, 60, 8, 54, 13, 51, 17, 3, 14, 50, 39, 62, 5, 9, 30, 40, 7, 29, 20, 19, 34, 53, 31, 25, 24, 0, 28, 27, 18, 15, 23, 43, 55, 21, 44, 59, 58, 41, 11, 16, 38, 1, 32, 35, 57, 48, 52, 46, 56, 10, 6, 47, 22, 4, 33, 49, 45, 37, 36, 2, 63, 12, 61] 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)) = -22.167028804951364 V(r_1,...,r_N) = -22.16702880495137 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 -1.48476912e+00 -1.04639753e+00 -1.27685785e+00 | -1.48476912e+00 -1.04639753e+00 -1.27685785e+00 1 -6.49414133e+00 -1.73661762e+01 1.23454511e+01 | -6.49414133e+00 -1.73661762e+01 1.23454511e+01 2 -4.67084173e-01 6.50707802e+00 -2.10714017e+01 | -4.67084173e-01 6.50707802e+00 -2.10714017e+01 3 8.04807928e+00 1.16796844e+01 9.29422150e+00 | 8.04807928e+00 1.16796844e+01 9.29422150e+00 4 -1.33743787e+00 2.98303962e-01 6.64273126e-01 | -1.33743787e+00 2.98303962e-01 6.64273126e-01 5 3.67357825e-01 -1.48367097e+01 5.51249071e+00 | 3.67357825e-01 -1.48367097e+01 5.51249071e+00 6 -6.63788767e-01 -3.64272627e-01 -4.59291962e-01 | -6.63788767e-01 -3.64272627e-01 -4.59291962e-01 7 -1.52486879e+01 4.51438157e+01 -2.93670779e+01 | -1.52486879e+01 4.51438157e+01 -2.93670779e+01 8 -1.73253792e+00 4.24390801e-01 -1.29709296e+00 | -1.73253792e+00 4.24390801e-01 -1.29709296e+00 9 7.17164518e-01 1.97585763e+00 9.94231585e-01 | 7.17164518e-01 1.97585763e+00 9.94231585e-01 10 -5.53315148e-01 8.70834074e-03 7.12420564e-01 | -5.53315148e-01 8.70834074e-03 7.12420564e-01 11 3.14533187e+00 -6.18885369e+00 -5.20713101e+00 | 3.14533187e+00 -6.18885369e+00 -5.20713101e+00 12 -6.07145292e+00 -6.42868457e+00 -9.64725734e-01 | -6.07145292e+00 -6.42868457e+00 -9.64725734e-01 13 2.10625917e+01 -4.50925120e+00 -9.79852107e+00 | 2.10625917e+01 -4.50925120e+00 -9.79852107e+00 14 -7.19516516e+00 1.30340335e+01 -9.65162570e+00 | -7.19516516e+00 1.30340335e+01 -9.65162570e+00 15 7.23236654e+00 2.48084971e+00 3.65114801e+00 | 7.23236654e+00 2.48084971e+00 3.65114801e+00 16 -1.62582405e+00 -3.95265264e+00 -1.04597840e+00 | -1.62582405e+00 -3.95265264e+00 -1.04597840e+00 17 -3.37389316e+00 -2.86172067e+00 5.82204357e+00 | -3.37389316e+00 -2.86172067e+00 5.82204357e+00 18 5.72981813e+00 6.15093518e+00 -3.32547302e+00 | 5.72981813e+00 6.15093518e+00 -3.32547302e+00 19 -3.15173957e+01 1.85669030e+01 -2.13953024e+01 | -3.15173957e+01 1.85669030e+01 -2.13953024e+01 20 -9.87448832e+00 -7.55743542e+00 -8.29170674e+00 | -9.87448832e+00 -7.55743542e+00 -8.29170674e+00 21 1.34916223e+01 8.79174189e+00 7.31573906e+00 | 1.34916223e+01 8.79174189e+00 7.31573906e+00 22 -3.76152029e+00 -2.17833403e+00 -7.31789613e+00 | -3.76152029e+00 -2.17833403e+00 -7.31789613e+00 23 2.69007310e+00 4.33638783e+00 4.73580006e+00 | 2.69007310e+00 4.33638783e+00 4.73580006e+00 24 -6.69705609e+00 -3.64991082e+00 -8.45256029e+00 | -6.69705609e+00 -3.64991082e+00 -8.45256029e+00 25 -2.87371703e+00 1.53978750e+01 8.65228457e-01 | -2.87371703e+00 1.53978750e+01 8.65228457e-01 26 -3.55894011e-01 -1.21564994e+00 9.14662558e-01 | -3.55894011e-01 -1.21564994e+00 9.14662558e-01 27 -1.12631692e+00 -7.75652556e-01 5.85275174e-01 | -1.12631692e+00 -7.75652556e-01 5.85275174e-01 28 3.55449273e+00 -6.93696630e+00 1.11721508e+01 | 3.55449273e+00 -6.93696630e+00 1.11721508e+01 29 2.02302819e+00 2.21402407e+00 2.75541290e+00 | 2.02302819e+00 2.21402407e+00 2.75541290e+00 30 3.05591975e+01 -1.85135324e+01 2.00342066e+01 | 3.05591975e+01 -1.85135324e+01 2.00342066e+01 31 -1.75682511e+01 1.29832438e+00 -9.29610339e+00 | -1.75682511e+01 1.29832438e+00 -9.29610339e+00 32 -3.20221150e+01 -2.80456962e+01 -2.09988132e+01 | -3.20221150e+01 -2.80456962e+01 -2.09988132e+01 33 3.22453280e+01 2.87635928e+01 1.96797263e+01 | 3.22453280e+01 2.87635928e+01 1.96797263e+01 34 2.03565487e+01 -4.93406674e+01 2.76739063e+01 | 2.03565487e+01 -4.93406674e+01 2.76739063e+01 35 -3.14623897e+00 -5.89124972e+00 1.45522997e+00 | -3.14623897e+00 -5.89124972e+00 1.45522997e+00 36 1.43130621e+00 4.71524883e-01 7.02941640e-01 | 1.43130621e+00 4.71524883e-01 7.02941640e-01 37 -2.19461987e+00 -2.11546877e+00 7.73298926e-01 | -2.19461987e+00 -2.11546877e+00 7.73298926e-01 38 -5.16904814e+01 -4.15726307e+01 -4.58747733e+01 | -5.16904814e+01 -4.15726307e+01 -4.58747733e+01 39 4.05375471e+01 3.11311360e+01 5.13447206e+01 | 4.05375471e+01 3.11311360e+01 5.13447206e+01 40 -2.72848830e+00 -1.74971229e-01 5.07097705e-01 | -2.72848830e+00 -1.74971229e-01 5.07097705e-01 41 -1.19705171e+01 2.53343732e+01 -1.46054865e+01 | -1.19705171e+01 2.53343732e+01 -1.46054865e+01 42 -1.84981819e+01 5.49251142e+00 6.39244382e+00 | -1.84981819e+01 5.49251142e+00 6.39244382e+00 43 4.62997602e+00 3.75415152e+00 4.55574692e+00 | 4.62997602e+00 3.75415152e+00 4.55574692e+00 44 1.56666667e+01 -2.60202322e+01 1.29436931e+01 | 1.56666667e+01 -2.60202322e+01 1.29436931e+01 45 -2.57918425e-01 1.03762466e+00 2.97302906e-01 | -2.57918425e-01 1.03762466e+00 2.97302906e-01 46 2.31465896e-01 1.89210229e+00 -1.10446898e+00 | 2.31465896e-01 1.89210229e+00 -1.10446898e+00 47 2.01079181e+00 -1.06778414e+00 -8.95072480e-01 | 2.01079181e+00 -1.06778414e+00 -8.95072480e-01 48 -5.32271398e+00 2.67046278e+00 3.87228724e+00 | -5.32271398e+00 2.67046278e+00 3.87228724e+00 49 2.57882278e+00 -5.29471724e+00 -4.51100959e+00 | 2.57882278e+00 -5.29471724e+00 -4.51100959e+00 50 -3.25317128e+00 -1.03808396e+01 -8.17703529e+00 | -3.25317128e+00 -1.03808396e+01 -8.17703529e+00 51 6.72251827e+00 8.61609717e+00 8.78038458e+00 | 6.72251827e+00 8.61609717e+00 8.78038458e+00 52 1.18846158e+01 1.08805061e+01 -6.73805923e+00 | 1.18846158e+01 1.08805061e+01 -6.73805923e+00 53 -1.81986695e+00 1.67030808e+00 -5.56942125e-01 | -1.81986695e+00 1.67030808e+00 -5.56942125e-01 54 -9.68656463e+00 -3.37979270e-01 -1.05775168e-02 | -9.68656463e+00 -3.37979270e-01 -1.05775168e-02 55 6.64329451e+00 4.18649780e+00 5.76970412e+00 | 6.64329451e+00 4.18649780e+00 5.76970412e+00 56 -9.38612868e+00 -8.88483538e+00 -4.11912913e+00 | -9.38612868e+00 -8.88483538e+00 -4.11912913e+00 57 2.62044869e+01 -1.01475481e+01 -2.57631974e+01 | 2.62044869e+01 -1.01475481e+01 -2.57631974e+01 58 1.82183326e+01 -2.73811257e+00 1.06055115e+01 | 1.82183326e+01 -2.73811257e+00 1.06055115e+01 59 -1.21351582e+00 -7.62225198e-01 2.19429146e-01 | -1.21351582e+00 -7.62225198e-01 2.19429146e-01 60 -1.30417085e+00 1.45265195e+00 3.53909581e-01 | -1.30417085e+00 1.45265195e+00 3.53909581e-01 61 -8.21754939e-01 1.10003954e+00 4.20742194e-01 | -8.21754939e-01 1.10003954e+00 4.20742194e-01 62 -1.32622297e+01 2.53038005e+01 2.86987303e+01 | -1.32622297e+01 2.53038005e+01 2.86987303e+01 63 6.18589791e-01 -9.09136304e-01 -8.48251559e-01 | 6.18589791e-01 -9.09136304e-01 -8.48251559e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [44, 26, 17, 15, 45, 40, 29, 14, 13, 61, 36, 47, 52, 8, 7, 3, 50, 2, 49, 54, 24, 35, 51, 42, 20, 55, 1, 33, 41, 6, 48, 59, 53, 27, 58, 21, 10, 38, 37, 46, 5, 28, 23, 57, 0, 4, 39, 11, 30, 18, 16, 22, 12, 32, 19, 25, 62, 43, 34, 31, 63, 9, 56, 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)) = 75.76678021941643 V(r_1,...,r_N) = 75.76678021941649 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 -3.75652445e-01 -7.91504611e-01 2.22387058e-02 | -3.75652445e-01 -7.91504611e-01 2.22387058e-02 1 -3.94452112e+00 7.01908352e+00 -5.87861876e+00 | -3.94452112e+00 7.01908352e+00 -5.87861876e+00 2 -4.61710713e+00 -4.54822195e+00 -9.83759015e+00 | -4.61710713e+00 -4.54822195e+00 -9.83759015e+00 3 3.16603428e-01 6.04103177e+00 9.62429124e+00 | 3.16603428e-01 6.04103177e+00 9.62429124e+00 4 7.00889302e+00 -7.60658970e+00 5.95973576e+00 | 7.00889302e+00 -7.60658970e+00 5.95973576e+00 5 -1.06554095e+01 -1.54822813e+01 1.96029606e+01 | -1.06554095e+01 -1.54822813e+01 1.96029606e+01 6 -5.61555924e+00 7.16326225e-01 -1.83987555e+00 | -5.61555924e+00 7.16326225e-01 -1.83987555e+00 7 6.86633748e+00 -9.92429180e-01 -5.58778174e+00 | 6.86633748e+00 -9.92429180e-01 -5.58778174e+00 8 -2.57282882e+00 -1.65137441e+00 -1.81005863e+00 | -2.57282882e+00 -1.65137441e+00 -1.81005863e+00 9 6.83507864e+00 -4.86219150e+00 -6.38406234e+00 | 6.83507864e+00 -4.86219150e+00 -6.38406234e+00 10 -2.58012204e+00 -4.55865917e+00 -1.09223512e+01 | -2.58012204e+00 -4.55865917e+00 -1.09223512e+01 11 5.02844571e+00 6.79722266e+00 8.87184003e+00 | 5.02844571e+00 6.79722266e+00 8.87184003e+00 12 -1.88234845e+01 -2.30447479e+01 -1.50120343e+01 | -1.88234845e+01 -2.30447479e+01 -1.50120343e+01 13 1.87023570e+01 1.81909024e+01 1.22636097e+01 | 1.87023570e+01 1.81909024e+01 1.22636097e+01 14 -5.30485616e+00 1.44717502e+01 -1.19836952e+01 | -5.30485616e+00 1.44717502e+01 -1.19836952e+01 15 5.55093544e+00 8.85256375e+00 6.91479144e+00 | 5.55093544e+00 8.85256375e+00 6.91479144e+00 16 9.84216670e-01 -1.18198236e-01 9.86862863e-01 | 9.84216670e-01 -1.18198236e-01 9.86862863e-01 17 -3.20149099e+00 -5.06177674e+00 -1.00401118e+01 | -3.20149099e+00 -5.06177674e+00 -1.00401118e+01 18 4.15355382e+00 3.62009842e+00 -8.38892380e+00 | 4.15355382e+00 3.62009842e+00 -8.38892380e+00 19 -7.05805630e-01 1.51260681e-03 -3.81604256e-03 | -7.05805630e-01 1.51260681e-03 -3.81604256e-03 20 -8.19873775e+00 -1.16322292e+01 -7.88197663e+00 | -8.19873775e+00 -1.16322292e+01 -7.88197663e+00 21 1.82680743e+01 9.16759697e+00 1.89788210e+01 | 1.82680743e+01 9.16759697e+00 1.89788210e+01 22 -7.06952876e+00 7.00105960e+00 2.65002562e+00 | -7.06952876e+00 7.00105960e+00 2.65002562e+00 23 -2.12323767e+01 1.15530017e+01 -1.90549254e+01 | -2.12323767e+01 1.15530017e+01 -1.90549254e+01 24 2.58229913e+00 2.46049688e+00 -2.90329629e+00 | 2.58229913e+00 2.46049688e+00 -2.90329629e+00 25 -2.75949998e+01 9.61302064e+00 -4.42428017e+01 | -2.75949998e+01 9.61302064e+00 -4.42428017e+01 26 -1.54108745e+00 -4.54710957e-01 -1.00319042e+00 | -1.54108745e+00 -4.54710957e-01 -1.00319042e+00 27 -6.78017100e-01 -8.74901418e-01 2.37607171e+00 | -6.78017100e-01 -8.74901418e-01 2.37607171e+00 28 2.34160058e+01 -1.57109976e+01 4.05348743e+01 | 2.34160058e+01 -1.57109976e+01 4.05348743e+01 29 6.16133376e+00 8.63228449e-01 3.18729483e+00 | 6.16133376e+00 8.63228449e-01 3.18729483e+00 30 -2.22075218e+00 -7.57600106e+00 -3.24985925e+00 | -2.22075218e+00 -7.57600106e+00 -3.24985925e+00 31 6.15912377e-01 9.76731350e+00 7.67905991e+00 | 6.15912377e-01 9.76731350e+00 7.67905991e+00 32 -1.73954065e-01 -2.57536369e+00 -5.31205145e+00 | -1.73954065e-01 -2.57536369e+00 -5.31205145e+00 33 5.77751497e+00 -1.48684399e+01 -8.62138645e+00 | 5.77751497e+00 -1.48684399e+01 -8.62138645e+00 34 3.17699592e+00 -6.28024946e+00 9.27076886e+00 | 3.17699592e+00 -6.28024946e+00 9.27076886e+00 35 -1.46121209e+01 1.39245689e+01 -1.23356249e+01 | -1.46121209e+01 1.39245689e+01 -1.23356249e+01 36 -6.48406376e-02 -7.30817206e+00 -3.63563336e+00 | -6.48406376e-02 -7.30817206e+00 -3.63563336e+00 37 1.78875589e+00 -8.01394022e-02 9.12572646e+00 | 1.78875589e+00 -8.01394022e-02 9.12572646e+00 38 -1.19740072e+01 1.90972219e+01 5.86811996e+00 | -1.19740072e+01 1.90972219e+01 5.86811996e+00 39 4.59195337e+00 5.51890373e-01 6.74702552e+00 | 4.59195337e+00 5.51890373e-01 6.74702552e+00 40 -4.70125729e+00 -7.47402784e+00 -5.51701275e+00 | -4.70125729e+00 -7.47402784e+00 -5.51701275e+00 41 -9.67681875e-01 1.58911151e+01 -1.70937213e-01 | -9.67681875e-01 1.58911151e+01 -1.70937213e-01 42 -1.80517263e+00 4.18617877e+00 4.60582307e+00 | -1.80517263e+00 4.18617877e+00 4.60582307e+00 43 1.40593276e+00 -1.58046175e+01 -1.35872823e+01 | 1.40593276e+00 -1.58046175e+01 -1.35872823e+01 44 5.91028185e+00 -8.82390968e+00 4.43664698e+00 | 5.91028185e+00 -8.82390968e+00 4.43664698e+00 45 1.34261720e-01 1.42461922e+00 2.17193302e-01 | 1.34261720e-01 1.42461922e+00 2.17193302e-01 46 1.14263074e+01 -2.22187347e+01 1.86481607e+01 | 1.14263074e+01 -2.22187347e+01 1.86481607e+01 47 -2.22361485e+00 -1.84256840e+00 2.79348965e+00 | -2.22361485e+00 -1.84256840e+00 2.79348965e+00 48 -2.00440974e+00 4.52451366e+00 2.64887492e+00 | -2.00440974e+00 4.52451366e+00 2.64887492e+00 49 1.86135295e+00 -1.12773209e+00 -1.54435381e+00 | 1.86135295e+00 -1.12773209e+00 -1.54435381e+00 50 2.24346815e+01 -6.05670346e+00 1.28030987e+01 | 2.24346815e+01 -6.05670346e+00 1.28030987e+01 51 -3.82853777e+00 2.86373940e+00 -4.29454644e+00 | -3.82853777e+00 2.86373940e+00 -4.29454644e+00 52 -4.57498642e-01 -6.64734909e+00 6.41099655e+00 | -4.57498642e-01 -6.64734909e+00 6.41099655e+00 53 -1.36944109e+00 -4.18146785e+00 1.20404565e+00 | -1.36944109e+00 -4.18146785e+00 1.20404565e+00 54 -8.58971038e+00 -3.57575877e+00 -1.13550469e+01 | -8.58971038e+00 -3.57575877e+00 -1.13550469e+01 55 9.90654835e+00 2.60900185e+00 9.52663089e+00 | 9.90654835e+00 2.60900185e+00 9.52663089e+00 56 4.17185524e-01 1.08115851e+01 -1.03013348e+01 | 4.17185524e-01 1.08115851e+01 -1.03013348e+01 57 -2.06802748e+00 -3.89021270e-01 -1.96958803e+00 | -2.06802748e+00 -3.89021270e-01 -1.96958803e+00 58 -8.90673517e+00 -5.12651746e+00 -5.59470490e+00 | -8.90673517e+00 -5.12651746e+00 -5.59470490e+00 59 1.23294690e+01 8.44540614e+00 5.93245570e+00 | 1.23294690e+01 8.44540614e+00 5.93245570e+00 60 -1.35021613e+01 4.92026901e+00 -9.29614935e+00 | -1.35021613e+01 4.92026901e+00 -9.29614935e+00 61 9.55005811e+00 1.42594186e+01 1.85566311e+01 | 9.55005811e+00 1.42594186e+01 1.85566311e+01 62 3.37250350e+00 -1.13321173e+01 -1.51435407e+01 | 3.37250350e+00 -1.13321173e+01 -1.51435407e+01 63 3.60765904e+00 1.10339676e+01 1.62559969e+01 | 3.60765904e+00 1.10339676e+01 1.62559969e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = V (Configuration in file "config-V.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [15, 53, 41, 21, 16, 46, 14, 47, 50, 38, 27, 23, 29, 62, 6, 0, 4, 32, 40, 63, 30, 3, 37, 11, 36, 51, 59, 10, 34, 12, 20, 54, 17, 42, 28, 48, 24, 22, 9, 45, 18, 2, 33, 56, 55, 39, 5, 7, 35, 61, 8, 25, 58, 1, 31, 44, 43, 60, 52, 26, 57, 49, 13, 19] 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)) = -138.36872627300195 V(r_1,...,r_N) = -138.36872627300204 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 -1.32089907e+00 -1.74430608e-01 -1.03506487e+00 | -1.32089907e+00 -1.74430608e-01 -1.03506487e+00 1 4.96553019e+00 -2.68968531e-01 -4.34221379e+00 | 4.96553019e+00 -2.68968531e-01 -4.34221379e+00 2 6.63628087e-01 3.22753455e-01 3.68136309e-01 | 6.63628087e-01 3.22753455e-01 3.68136309e-01 3 -3.51323786e+00 7.55793246e+00 -1.66090240e+00 | -3.51323786e+00 7.55793246e+00 -1.66090240e+00 4 3.76435732e+00 -2.30980061e+00 3.76968940e+00 | 3.76435732e+00 -2.30980061e+00 3.76968940e+00 5 -9.04897208e-01 5.96309870e+00 -4.49616001e-01 | -9.04897208e-01 5.96309870e+00 -4.49616001e-01 6 -7.32793522e+00 4.16685352e+00 2.16305352e+00 | -7.32793522e+00 4.16685352e+00 2.16305352e+00 7 -6.55098236e-01 2.25980905e+00 -7.42033741e+00 | -6.55098236e-01 2.25980905e+00 -7.42033741e+00 8 5.54577904e-01 1.36591690e+00 1.06630197e+00 | 5.54577904e-01 1.36591690e+00 1.06630197e+00 9 4.36479549e+00 -4.56667805e+00 -2.20459857e+00 | 4.36479549e+00 -4.56667805e+00 -2.20459857e+00 10 -5.56609420e-01 -1.03929573e-01 1.18555852e-01 | -5.56609420e-01 -1.03929573e-01 1.18555852e-01 11 4.83306442e+00 -3.48621003e+00 -4.76726388e+00 | 4.83306442e+00 -3.48621003e+00 -4.76726388e+00 12 -8.52343393e-01 1.41305615e+00 1.56185455e-01 | -8.52343393e-01 1.41305615e+00 1.56185455e-01 13 1.34691590e+01 -5.47321124e+00 -4.68713544e+00 | 1.34691590e+01 -5.47321124e+00 -4.68713544e+00 14 -1.40073760e+00 -3.32830677e+00 4.24982997e+00 | -1.40073760e+00 -3.32830677e+00 4.24982997e+00 15 1.05164254e+00 5.78348651e-01 1.60266608e+00 | 1.05164254e+00 5.78348651e-01 1.60266608e+00 16 2.29799571e+00 4.42017360e-01 1.23347249e+00 | 2.29799571e+00 4.42017360e-01 1.23347249e+00 17 -7.50684895e-01 1.15007843e+01 7.84094854e-02 | -7.50684895e-01 1.15007843e+01 7.84094854e-02 18 1.50100189e+00 -2.39211265e-01 -4.26791449e+00 | 1.50100189e+00 -2.39211265e-01 -4.26791449e+00 19 -4.80323653e-01 1.11804777e+00 -3.22262104e-01 | -4.80323653e-01 1.11804777e+00 -3.22262104e-01 20 -9.31003318e-01 -1.28425269e+01 3.84164523e+00 | -9.31003318e-01 -1.28425269e+01 3.84164523e+00 21 -3.47714410e+00 5.85119803e+00 -3.44669264e+00 | -3.47714410e+00 5.85119803e+00 -3.44669264e+00 22 -3.43945622e+00 -6.53134466e+00 -1.94643720e+00 | -3.43945622e+00 -6.53134466e+00 -1.94643720e+00 23 3.52991247e+00 6.33143955e+00 2.30048953e+00 | 3.52991247e+00 6.33143955e+00 2.30048953e+00 24 3.49089881e-02 -5.23060253e-01 -9.84336488e-01 | 3.49089881e-02 -5.23060253e-01 -9.84336488e-01 25 -8.32265922e+00 -3.81456808e+00 2.24882314e+00 | -8.32265922e+00 -3.81456808e+00 2.24882314e+00 26 1.02194081e+01 4.62270849e+00 -3.52984878e+00 | 1.02194081e+01 4.62270849e+00 -3.52984878e+00 27 -1.62753571e+00 -1.66952908e+00 -1.82898860e-02 | -1.62753571e+00 -1.66952908e+00 -1.82898860e-02 28 -6.59963637e+00 2.49034478e+00 5.64177750e+00 | -6.59963637e+00 2.49034478e+00 5.64177750e+00 29 2.49228425e+00 -1.00162994e+01 -6.38543302e+00 | 2.49228425e+00 -1.00162994e+01 -6.38543302e+00 30 1.38511062e+00 1.45308743e+00 -9.32901519e-01 | 1.38511062e+00 1.45308743e+00 -9.32901519e-01 31 -3.92191018e-01 -7.05209263e-01 1.34369545e+00 | -3.92191018e-01 -7.05209263e-01 1.34369545e+00 32 -7.09597319e-01 1.31041053e-01 -6.02128821e-01 | -7.09597319e-01 1.31041053e-01 -6.02128821e-01 33 4.19690531e+00 -5.36476666e+00 1.69354586e+00 | 4.19690531e+00 -5.36476666e+00 1.69354586e+00 34 2.38276586e+00 1.57720632e+00 4.40109143e+00 | 2.38276586e+00 1.57720632e+00 4.40109143e+00 35 1.53303440e+00 3.60848576e+00 -1.72497488e-01 | 1.53303440e+00 3.60848576e+00 -1.72497488e-01 36 3.32133368e-01 -4.41346439e-02 -5.25079883e-01 | 3.32133368e-01 -4.41346439e-02 -5.25079883e-01 37 -4.49193260e+00 7.47420365e-01 5.59461033e+00 | -4.49193260e+00 7.47420365e-01 5.59461033e+00 38 -3.57226596e+00 2.10806159e+00 7.13314219e-01 | -3.57226596e+00 2.10806159e+00 7.13314219e-01 39 5.01165355e-01 -4.15894227e-01 -1.12637775e+00 | 5.01165355e-01 -4.15894227e-01 -1.12637775e+00 40 6.74425347e-01 -6.42840693e+00 1.84460325e+00 | 6.74425347e-01 -6.42840693e+00 1.84460325e+00 41 1.42877851e+00 5.56957000e-02 -2.82762675e-01 | 1.42877851e+00 5.56957000e-02 -2.82762675e-01 42 -1.30780025e+01 3.66297892e+00 3.10177892e+00 | -1.30780025e+01 3.66297892e+00 3.10177892e+00 43 -1.87919799e-01 1.67081557e+00 4.85313819e-01 | -1.87919799e-01 1.67081557e+00 4.85313819e-01 44 -1.03644396e+01 -8.61248603e+00 -5.50352498e+00 | -1.03644396e+01 -8.61248603e+00 -5.50352498e+00 45 9.92081460e+00 9.61432600e+00 4.86252952e+00 | 9.92081460e+00 9.61432600e+00 4.86252952e+00 46 3.05490124e+00 -3.79288620e+00 -4.50021870e+00 | 3.05490124e+00 -3.79288620e+00 -4.50021870e+00 47 -1.01458317e-01 -4.75452918e-01 7.38825546e-02 | -1.01458317e-01 -4.75452918e-01 7.38825546e-02 48 -1.33063284e+00 5.08088422e-01 1.58257081e+00 | -1.33063284e+00 5.08088422e-01 1.58257081e+00 49 -4.82945962e-01 2.02160175e-01 -5.73306474e+00 | -4.82945962e-01 2.02160175e-01 -5.73306474e+00 50 -7.21553205e-01 2.50636037e+00 -1.99759751e+00 | -7.21553205e-01 2.50636037e+00 -1.99759751e+00 51 1.05075979e-01 9.91732057e-01 -8.81922205e-01 | 1.05075979e-01 9.91732057e-01 -8.81922205e-01 52 9.78794534e-01 -6.32716835e+00 5.59720782e+00 | 9.78794534e-01 -6.32716835e+00 5.59720782e+00 53 -1.08687968e+00 -2.49303909e+00 3.70664827e+00 | -1.08687968e+00 -2.49303909e+00 3.70664827e+00 54 -2.00389069e+00 2.37968475e-01 1.52626538e+00 | -2.00389069e+00 2.37968475e-01 1.52626538e+00 55 1.35591320e+00 2.31669561e+00 9.42521659e-02 | 1.35591320e+00 2.31669561e+00 9.42521659e-02 56 2.72514868e+00 -8.39332487e+00 5.02665919e+00 | 2.72514868e+00 -8.39332487e+00 5.02665919e+00 57 3.52165498e+00 -2.13371363e+00 -6.65215175e+00 | 3.52165498e+00 -2.13371363e+00 -6.65215175e+00 58 -2.94611448e+00 1.03164141e+01 7.18604369e+00 | -2.94611448e+00 1.03164141e+01 7.18604369e+00 59 -3.12008359e+00 -1.92085407e+00 1.31585148e-01 | -3.12008359e+00 -1.92085407e+00 1.31585148e-01 60 2.47212446e+00 -9.07810083e-01 1.84292960e+00 | 2.47212446e+00 -9.07810083e-01 1.84292960e+00 61 -7.01758252e-01 1.46072213e-01 -9.16586591e-01 | -7.01758252e-01 1.46072213e-01 -9.16586591e-01 62 -3.92149794e+00 6.69865984e+00 9.33751256e-04 | -3.92149794e+00 6.69865984e+00 9.33751256e-04 63 1.06235238e+00 -1.17435712e+00 -2.35333552e+00 | 1.06235238e+00 -1.17435712e+00 -2.35333552e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ni Ti V (Configuration in file "config-NiTiV.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [41, 31, 32, 37, 10, 7, 35, 5, 63, 25, 4, 61, 23, 24, 38, 59, 45, 19, 36, 17, 33, 40, 43, 12, 13, 9, 47, 30, 39, 60, 27, 1, 2, 20, 57, 6, 18, 3, 14, 28, 21, 0, 48, 22, 44, 16, 53, 26, 42, 51, 52, 49, 50, 46, 62, 56, 55, 34, 58, 15, 29, 11, 54, 8] 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)) = 219.75849720411932 V(r_1,...,r_N) = 219.75849720411935 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -2.12939302e+01 -2.25646603e+01 -1.21924784e+01 | -2.12939302e+01 -2.25646603e+01 -1.21924784e+01 1 2.06136504e+01 2.21616511e+01 1.43245670e+01 | 2.06136504e+01 2.21616511e+01 1.43245670e+01 2 -4.72098832e-02 4.04793849e-01 -8.25864704e-01 | -4.72098832e-02 4.04793849e-01 -8.25864704e-01 3 -1.05137997e+01 -3.69636588e+01 5.04671584e+00 | -1.05137997e+01 -3.69636588e+01 5.04671584e+00 4 4.38804059e+00 1.00010990e+00 -2.33208543e+00 | 4.38804059e+00 1.00010990e+00 -2.33208543e+00 5 -1.91578886e+02 -1.77838218e+02 1.80210600e+02 | -1.91578886e+02 -1.77838218e+02 1.80210600e+02 6 -7.26157912e+01 -1.47288845e+02 -1.13260533e+02 | -7.26157912e+01 -1.47288845e+02 -1.13260533e+02 7 7.18285029e+01 1.44526197e+02 1.13122187e+02 | 7.18285029e+01 1.44526197e+02 1.13122187e+02 8 -4.03933013e-02 -1.40094029e+00 -5.45248117e-01 | -4.03933013e-02 -1.40094029e+00 -5.45248117e-01 9 2.43874413e+01 -1.07917234e+01 -3.15707150e+01 | 2.43874413e+01 -1.07917234e+01 -3.15707150e+01 10 -5.28071559e+00 -4.59536988e+00 -7.41718673e-01 | -5.28071559e+00 -4.59536988e+00 -7.41718673e-01 11 3.84931499e+00 5.19399266e+00 2.76701142e+00 | 3.84931499e+00 5.19399266e+00 2.76701142e+00 12 -1.60837328e+01 -5.98402657e+00 -2.01606481e+01 | -1.60837328e+01 -5.98402657e+00 -2.01606481e+01 13 1.38501930e+01 7.29308551e+00 2.01083836e+01 | 1.38501930e+01 7.29308551e+00 2.01083836e+01 14 1.64453503e+02 1.88720019e+02 -1.49519318e+02 | 1.64453503e+02 1.88720019e+02 -1.49519318e+02 15 -9.84651622e+00 -2.42205616e+01 4.87249224e+00 | -9.84651622e+00 -2.42205616e+01 4.87249224e+00 16 1.57240539e+00 -6.81007106e-01 1.15782436e+00 | 1.57240539e+00 -6.81007106e-01 1.15782436e+00 17 -7.43433156e+01 6.00196247e+01 -2.86858921e+01 | -7.43433156e+01 6.00196247e+01 -2.86858921e+01 18 9.88407533e-03 -1.24585428e+00 -8.04060183e-01 | 9.88407533e-03 -1.24585428e+00 -8.04060183e-01 19 -1.05753329e+01 1.13649280e+01 -1.17291094e+00 | -1.05753329e+01 1.13649280e+01 -1.17291094e+00 20 6.74969925e+01 -6.15585278e+01 1.55984196e+01 | 6.74969925e+01 -6.15585278e+01 1.55984196e+01 21 8.72442114e+00 3.29168734e+00 1.45665870e+01 | 8.72442114e+00 3.29168734e+00 1.45665870e+01 22 -1.61536006e+01 -4.70339532e+00 -1.31421737e+01 | -1.61536006e+01 -4.70339532e+00 -1.31421737e+01 23 -1.40964803e+00 2.18749418e+01 -7.45388139e+00 | -1.40964803e+00 2.18749418e+01 -7.45388139e+00 24 6.37613008e+00 3.03419013e+01 -7.55974131e+00 | 6.37613008e+00 3.03419013e+01 -7.55974131e+00 25 1.12855512e+02 -6.47379281e+01 -4.99037148e+01 | 1.12855512e+02 -6.47379281e+01 -4.99037148e+01 26 -1.50947940e+00 -2.38057720e+00 -2.91263720e+00 | -1.50947940e+00 -2.38057720e+00 -2.91263720e+00 27 1.25059566e+00 1.50022248e+00 3.63438922e+00 | 1.25059566e+00 1.50022248e+00 3.63438922e+00 28 1.38273014e+01 2.59658658e+01 -5.64431346e+00 | 1.38273014e+01 2.59658658e+01 -5.64431346e+00 29 8.49653930e-01 -5.92553119e-01 -1.76057650e+00 | 8.49653930e-01 -5.92553119e-01 -1.76057650e+00 30 -9.79106636e+01 5.58732761e+01 5.78510905e+01 | -9.79106636e+01 5.58732761e+01 5.78510905e+01 31 9.61057629e-01 4.26279865e+00 1.80383819e+00 | 9.61057629e-01 4.26279865e+00 1.80383819e+00 32 -3.63078965e+00 4.20026233e-01 6.70006933e-01 | -3.63078965e+00 4.20026233e-01 6.70006933e-01 33 1.72617304e+01 -1.75947441e+01 -5.56533490e+00 | 1.72617304e+01 -1.75947441e+01 -5.56533490e+00 34 5.31821817e-02 4.91306797e-01 3.75846849e-01 | 5.31821817e-02 4.91306797e-01 3.75846849e-01 35 -3.94732760e+00 3.63519834e+00 -1.38794671e+00 | -3.94732760e+00 3.63519834e+00 -1.38794671e+00 36 4.46973411e+00 -1.89279796e+00 6.75064294e-01 | 4.46973411e+00 -1.89279796e+00 6.75064294e-01 37 -9.32284690e-01 -2.45211906e+00 3.26880327e+00 | -9.32284690e-01 -2.45211906e+00 3.26880327e+00 38 -1.91145726e+01 2.19896033e+01 5.37813185e+00 | -1.91145726e+01 2.19896033e+01 5.37813185e+00 39 -3.95546313e+01 -9.33074054e+00 2.85041986e+00 | -3.95546313e+01 -9.33074054e+00 2.85041986e+00 40 -2.93456081e+00 -3.20658166e+00 -9.92808537e-01 | -2.93456081e+00 -3.20658166e+00 -9.92808537e-01 41 -1.37955618e+01 8.22821853e+00 -4.20629100e+00 | -1.37955618e+01 8.22821853e+00 -4.20629100e+00 42 1.33249176e+00 2.48466416e-02 -7.23394568e+00 | 1.33249176e+00 2.48466416e-02 -7.23394568e+00 43 8.00141009e+00 4.52646459e+00 2.70418480e+00 | 8.00141009e+00 4.52646459e+00 2.70418480e+00 44 1.04376423e+01 -1.12594870e+01 8.86298726e+00 | 1.04376423e+01 -1.12594870e+01 8.86298726e+00 45 -1.97860549e+00 4.47333944e-01 -2.16713936e+00 | -1.97860549e+00 4.47333944e-01 -2.16713936e+00 46 -1.02966375e+00 2.56207603e-01 -1.94521387e+00 | -1.02966375e+00 2.56207603e-01 -1.94521387e+00 47 -2.50927468e+01 -7.72623193e+00 -4.54267047e+00 | -2.50927468e+01 -7.72623193e+00 -4.54267047e+00 48 1.04462573e+00 -3.39551379e-02 -1.66023575e+00 | 1.04462573e+00 -3.39551379e-02 -1.66023575e+00 49 2.56343346e+00 -8.59266168e-01 7.05782452e-01 | 2.56343346e+00 -8.59266168e-01 7.05782452e-01 50 1.37128514e+01 -1.73118649e+01 1.47412917e+01 | 1.37128514e+01 -1.73118649e+01 1.47412917e+01 51 5.60911454e-02 2.03246969e+00 2.88775796e-01 | 5.60911454e-02 2.03246969e+00 2.88775796e-01 52 3.66317711e+01 6.19439525e+00 -2.74335755e+00 | 3.66317711e+01 6.19439525e+00 -2.74335755e+00 53 1.04312313e+00 -5.99521914e-01 1.07945172e+00 | 1.04312313e+00 -5.99521914e-01 1.07945172e+00 54 -6.87601488e+00 -5.03420017e+00 -7.75192569e+00 | -6.87601488e+00 -5.03420017e+00 -7.75192569e+00 55 7.64507837e+00 4.85408224e+00 7.45932741e+00 | 7.64507837e+00 4.85408224e+00 7.45932741e+00 56 -9.42508432e-01 -5.10195682e-01 -6.43751935e-01 | -9.42508432e-01 -5.10195682e-01 -6.43751935e-01 57 7.77210110e+00 -3.16806914e-01 -2.16481570e+00 | 7.77210110e+00 -3.16806914e-01 -2.16481570e+00 58 -6.40501635e+00 -6.71751198e+00 -5.04280652e+00 | -6.40501635e+00 -6.71751198e+00 -5.04280652e+00 59 4.57161734e+00 6.67974866e+00 5.54212026e+00 | 4.57161734e+00 6.67974866e+00 5.54212026e+00 60 2.18279986e+01 -1.03380371e+01 7.85396861e+00 | 2.18279986e+01 -1.03380371e+01 7.85396861e+00 61 3.47953582e+00 1.19404261e+01 5.60038882e-01 | 3.47953582e+00 1.19404261e+01 5.60038882e-01 62 -4.42289566e+00 7.24671653e+00 1.69302673e-01 | -4.42289566e+00 7.24671653e+00 1.69302673e-01 63 6.61176631e-01 -3.02301483e-02 -1.28567475e-02 | 6.61176631e-01 -3.02301483e-02 -1.28567475e-02 ------------------------------------------------------------------------------------------------------------------------- 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.