!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MirazDhariwalMeng_2020_CuNTi__MO_122936827583_001 Supported species : Cu N Ti random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [20, 4, 58, 11, 1, 55, 24, 17, 26, 53, 34, 3, 19, 22, 52, 50, 28, 7, 23, 12, 0, 57, 13, 18, 6, 31, 8, 56, 16, 46, 39, 25, 51, 45, 10, 49, 40, 61, 54, 30, 36, 42, 41, 44, 43, 33, 29, 59, 63, 35, 15, 32, 14, 9, 38, 5, 27, 21, 2, 47, 62, 37, 60, 48] 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)) = 146.93890517774727 V(r_1,...,r_N) = 146.93890517774722 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 -2.10872093e+01 -2.15870924e+01 -1.67697275e+01 | -2.10872093e+01 -2.15870924e+01 -1.67697275e+01 1 1.58220928e+01 1.58854236e+01 1.77467630e+01 | 1.58220928e+01 1.58854236e+01 1.77467630e+01 2 4.00664239e+00 3.63220519e+00 -2.61418706e+00 | 4.00664239e+00 3.63220519e+00 -2.61418706e+00 3 1.90997275e+00 -6.66602474e-01 -4.90141252e+00 | 1.90997275e+00 -6.66602474e-01 -4.90141252e+00 4 -6.77910392e+00 -5.61565058e+00 -5.22185129e+00 | -6.77910392e+00 -5.61565058e+00 -5.22185129e+00 5 6.24246209e+00 4.93471142e+00 5.43856921e+00 | 6.24246209e+00 4.93471142e+00 5.43856921e+00 6 -2.91179784e-01 -1.14271381e-01 -4.73920706e-01 | -2.91179784e-01 -1.14271381e-01 -4.73920706e-01 7 -4.85363114e+01 1.05009662e+02 -6.23772331e+01 | -4.85363114e+01 1.05009662e+02 -6.23772331e+01 8 -1.01083857e+02 -8.00972863e+01 -1.65174179e+02 | -1.01083857e+02 -8.00972863e+01 -1.65174179e+02 9 9.83066356e+01 7.43974090e+01 1.65768727e+02 | 9.83066356e+01 7.43974090e+01 1.65768727e+02 10 2.03580078e+00 4.43175525e+00 -3.02742429e+00 | 2.03580078e+00 4.43175525e+00 -3.02742429e+00 11 6.60601179e+00 -4.74240626e+00 -4.41042806e+00 | 6.60601179e+00 -4.74240626e+00 -4.41042806e+00 12 -6.14577732e+01 -1.63801003e+01 -3.79983179e+01 | -6.14577732e+01 -1.63801003e+01 -3.79983179e+01 13 6.38510622e+01 1.38587545e+01 3.71129628e+01 | 6.38510622e+01 1.38587545e+01 3.71129628e+01 14 -8.46495136e+00 -8.33911765e+00 -1.33022348e+01 | -8.46495136e+00 -8.33911765e+00 -1.33022348e+01 15 8.60012308e+00 7.76609207e+00 1.31329526e+01 | 8.60012308e+00 7.76609207e+00 1.31329526e+01 16 -8.25534628e+00 -8.12216838e+00 -7.18792940e+00 | -8.25534628e+00 -8.12216838e+00 -7.18792940e+00 17 7.60110003e+00 8.75687358e+00 6.21945476e+00 | 7.60110003e+00 8.75687358e+00 6.21945476e+00 18 -2.88103896e-01 -3.61868730e-01 2.03947628e-01 | -2.88103896e-01 -3.61868730e-01 2.03947628e-01 19 -5.32193833e+01 3.33755159e+01 -3.69205548e+01 | -5.32193833e+01 3.33755159e+01 -3.69205548e+01 20 -2.61238469e+01 -1.69122816e+01 -1.07473806e+00 | -2.61238469e+01 -1.69122816e+01 -1.07473806e+00 21 2.81761674e+01 1.97080521e+01 2.94944547e+00 | 2.81761674e+01 1.97080521e+01 2.94944547e+00 22 -1.10553869e+00 -1.24688902e-01 -2.81138896e+00 | -1.10553869e+00 -1.24688902e-01 -2.81138896e+00 23 -1.06076086e+02 4.28088556e+01 -1.57543840e-01 | -1.06076086e+02 4.28088556e+01 -1.57543840e-01 24 -5.16764569e-01 -2.75728779e-02 2.01276323e-02 | -5.16764569e-01 -2.75728779e-02 2.01276323e-02 25 -1.92992074e+02 3.83720951e+02 -3.07540129e+02 | -1.92992074e+02 3.83720951e+02 -3.07540129e+02 26 -1.32542290e+00 3.80042707e-01 -2.90303341e+00 | -1.32542290e+00 3.80042707e-01 -2.90303341e+00 27 1.83477583e+00 1.41329464e+00 1.71024836e+00 | 1.83477583e+00 1.41329464e+00 1.71024836e+00 28 1.87487478e+02 -3.81460514e+02 3.09705404e+02 | 1.87487478e+02 -3.81460514e+02 3.09705404e+02 29 5.89338494e+00 -3.07052733e+00 -7.95025774e-01 | 5.89338494e+00 -3.07052733e+00 -7.95025774e-01 30 5.27560114e+01 -3.05939931e+01 3.39753954e+01 | 5.27560114e+01 -3.05939931e+01 3.39753954e+01 31 -8.47692894e+00 1.20710013e+01 -6.59543627e+00 | -8.47692894e+00 1.20710013e+01 -6.59543627e+00 32 -4.72525345e+00 -4.21026307e+00 -4.69766054e+00 | -4.72525345e+00 -4.21026307e+00 -4.69766054e+00 33 2.77552631e+00 8.30804342e+00 -1.23616520e+00 | 2.77552631e+00 8.30804342e+00 -1.23616520e+00 34 4.73337505e+01 -1.09153799e+02 6.42438098e+01 | 4.73337505e+01 -1.09153799e+02 6.42438098e+01 35 -2.18772868e+00 -1.25991724e+01 2.92632092e-01 | -2.18772868e+00 -1.25991724e+01 2.92632092e-01 36 6.89966980e-01 -6.19444516e+00 6.79714969e+00 | 6.89966980e-01 -6.19444516e+00 6.79714969e+00 37 -1.48251695e+00 -2.09599441e+00 1.40015466e+00 | -1.48251695e+00 -2.09599441e+00 1.40015466e+00 38 -1.26272908e+01 -1.16027776e+01 -7.25036412e+00 | -1.26272908e+01 -1.16027776e+01 -7.25036412e+00 39 9.33434657e+00 1.05239679e+01 9.01970981e+00 | 9.33434657e+00 1.05239679e+01 9.01970981e+00 40 -1.94784586e+00 -2.84703006e-01 -1.19283062e-01 | -1.94784586e+00 -2.84703006e-01 -1.19283062e-01 41 -1.98472647e+01 3.52029396e+01 -1.75070146e+01 | -1.98472647e+01 3.52029396e+01 -1.75070146e+01 42 -3.43044702e+00 -1.02853218e+00 -6.26518522e-01 | -3.43044702e+00 -1.02853218e+00 -6.26518522e-01 43 2.02493907e+00 2.33464106e+00 2.55649974e+00 | 2.02493907e+00 2.33464106e+00 2.55649974e+00 44 2.16564866e+01 -3.48295857e+01 1.89146456e+01 | 2.16564866e+01 -3.48295857e+01 1.89146456e+01 45 -2.23381340e-01 8.87272349e-02 -1.58402978e-01 | -2.23381340e-01 8.87272349e-02 -1.58402978e-01 46 -1.01836895e+00 4.47561917e-01 -4.11262131e+00 | -1.01836895e+00 4.47561917e-01 -4.11262131e+00 47 1.47237209e+00 8.64226852e-01 3.15380201e+00 | 1.47237209e+00 8.64226852e-01 3.15380201e+00 48 -6.56414111e+00 -2.74693843e+00 -3.59068660e+00 | -6.56414111e+00 -2.74693843e+00 -3.59068660e+00 49 3.72278946e+00 2.46859507e+00 3.10549373e+00 | 3.72278946e+00 2.46859507e+00 3.10549373e+00 50 1.02677682e+02 -4.16290129e+01 -1.90735369e+00 | 1.02677682e+02 -4.16290129e+01 -1.90735369e+00 51 3.41761065e+00 3.96240984e+00 3.87219693e+00 | 3.41761065e+00 3.96240984e+00 3.87219693e+00 52 -6.78183919e+00 -7.06248784e-01 -2.07427089e+00 | -6.78183919e+00 -7.06248784e-01 -2.07427089e+00 53 5.33311346e+00 3.88428488e+00 6.62994598e+00 | 5.33311346e+00 3.88428488e+00 6.62994598e+00 54 -1.81181630e+00 2.69005638e+00 3.73017177e+00 | -1.81181630e+00 2.69005638e+00 3.73017177e+00 55 -4.04112851e-01 -4.10595095e-01 -4.08764097e-01 | -4.04112851e-01 -4.10595095e-01 -4.08764097e-01 56 -1.34197465e-01 1.04828689e+00 -5.81043636e+00 | -1.34197465e-01 1.04828689e+00 -5.81043636e+00 57 3.20546628e+01 -3.34656047e+01 -4.39777718e+01 | 3.20546628e+01 -3.34656047e+01 -4.39777718e+01 58 6.50401689e+00 -5.83033144e+00 1.13593777e+01 | 6.50401689e+00 -5.83033144e+00 1.13593777e+01 59 -4.25897884e-01 -4.79091396e-01 7.32106064e-01 | -4.25897884e-01 -4.79091396e-01 7.32106064e-01 60 3.37025798e+00 1.07717946e+00 -7.65870899e-02 | 3.37025798e+00 1.07717946e+00 -7.65870899e-02 61 -1.13251849e+00 9.93126926e-02 -9.37183105e-01 | -1.13251849e+00 9.93126926e-02 -9.37183105e-01 62 -2.35882247e+01 4.08248701e+01 4.74189655e+01 | -2.35882247e+01 4.08248701e+01 4.74189655e+01 63 9.15484197e-01 -4.92465815e-01 -4.62880053e-01 | 9.15484197e-01 -4.92465815e-01 -4.62880053e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = N (Configuration in file "config-N.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [1, 0, 42, 24, 27, 33, 47, 36, 61, 48, 38, 21, 18, 30, 50, 59, 25, 39, 12, 23, 55, 11, 56, 19, 3, 16, 45, 4, 51, 57, 13, 62, 43, 5, 46, 58, 7, 40, 10, 17, 37, 53, 2, 32, 54, 26, 34, 6, 9, 63, 14, 28, 60, 41, 44, 20, 22, 29, 35, 15, 52, 8, 31, 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)) = 42.16193554068776 V(r_1,...,r_N) = 42.16193554068773 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 3.91018243e+00 7.46855474e+00 8.76378282e+00 | 3.91018243e+00 7.46855474e+00 8.76378282e+00 1 -6.17751350e+00 -8.74541588e+00 -9.01377742e+00 | -6.17751350e+00 -8.74541588e+00 -9.01377742e+00 2 4.02351123e+00 3.42757062e+00 -2.39916969e-01 | 4.02351123e+00 3.42757062e+00 -2.39916969e-01 3 -3.15257104e+00 -3.54255008e+00 -1.96176369e+00 | -3.15257104e+00 -3.54255008e+00 -1.96176369e+00 4 8.08693144e-01 -2.61255651e+00 -2.53309162e-02 | 8.08693144e-01 -2.61255651e+00 -2.53309162e-02 5 -2.03778258e+00 7.81902900e-01 8.89363822e+00 | -2.03778258e+00 7.81902900e-01 8.89363822e+00 6 -1.53586083e+00 -3.52333183e-01 -2.57827733e-01 | -1.53586083e+00 -3.52333183e-01 -2.57827733e-01 7 -1.46185415e+00 3.97070229e-01 1.66268985e+00 | -1.46185415e+00 3.97070229e-01 1.66268985e+00 8 4.97528020e+00 3.08297663e+00 1.86464076e+00 | 4.97528020e+00 3.08297663e+00 1.86464076e+00 9 -6.37325045e+00 -5.80693095e+00 -4.63461923e+00 | -6.37325045e+00 -5.80693095e+00 -4.63461923e+00 10 1.07404543e+01 6.84958409e+00 3.91207293e+00 | 1.07404543e+01 6.84958409e+00 3.91207293e+00 11 -7.59986923e+00 -7.64430484e+00 -7.36677344e+00 | -7.59986923e+00 -7.64430484e+00 -7.36677344e+00 12 2.27032480e+00 2.56401916e+00 3.36136346e+00 | 2.27032480e+00 2.56401916e+00 3.36136346e+00 13 7.17502129e-01 -5.37416012e+00 -3.59444811e+00 | 7.17502129e-01 -5.37416012e+00 -3.59444811e+00 14 2.36574304e+00 3.78114361e+00 2.51646532e+00 | 2.36574304e+00 3.78114361e+00 2.51646532e+00 15 -2.53058792e+00 -4.19160216e+00 -2.46144270e+00 | -2.53058792e+00 -4.19160216e+00 -2.46144270e+00 16 -9.02826624e-01 -7.23159332e-02 -6.74408071e-01 | -9.02826624e-01 -7.23159332e-02 -6.74408071e-01 17 1.03594931e+00 -1.98878556e+00 3.44496107e-01 | 1.03594931e+00 -1.98878556e+00 3.44496107e-01 18 2.81051245e-02 8.40920779e-01 -1.80375885e+00 | 2.81051245e-02 8.40920779e-01 -1.80375885e+00 19 2.01114588e+00 -2.61730970e-01 1.66486116e+00 | 2.01114588e+00 -2.61730970e-01 1.66486116e+00 20 -1.68881240e+00 2.30550798e+00 -2.47590282e+00 | -1.68881240e+00 2.30550798e+00 -2.47590282e+00 21 -1.49357036e+00 -2.19567495e-01 -1.88249198e+00 | -1.49357036e+00 -2.19567495e-01 -1.88249198e+00 22 6.98173024e-01 4.85390877e+00 2.56281008e+00 | 6.98173024e-01 4.85390877e+00 2.56281008e+00 23 -2.36439828e+00 -2.94533549e+00 -1.76766923e+00 | -2.36439828e+00 -2.94533549e+00 -1.76766923e+00 24 1.68903800e+00 4.09682750e+00 4.25146598e-01 | 1.68903800e+00 4.09682750e+00 4.25146598e-01 25 -2.23184586e+00 -2.13535277e+00 -3.17375862e+00 | -2.23184586e+00 -2.13535277e+00 -3.17375862e+00 26 4.48371824e-01 8.02075337e-01 -6.48815853e-01 | 4.48371824e-01 8.02075337e-01 -6.48815853e-01 27 -3.19580215e-02 2.49497880e-01 -2.72510087e-01 | -3.19580215e-02 2.49497880e-01 -2.72510087e-01 28 3.29689628e+00 3.92579424e+00 5.52878482e+00 | 3.29689628e+00 3.92579424e+00 5.52878482e+00 29 1.54191287e-01 -4.38933936e+00 -3.94369698e+00 | 1.54191287e-01 -4.38933936e+00 -3.94369698e+00 30 -3.20057525e+00 1.75308866e+00 -2.48740108e+00 | -3.20057525e+00 1.75308866e+00 -2.48740108e+00 31 9.92330642e+00 -5.35055246e+00 4.57769962e+00 | 9.92330642e+00 -5.35055246e+00 4.57769962e+00 32 -6.72677024e-01 -4.86002805e-01 9.73987797e-01 | -6.72677024e-01 -4.86002805e-01 9.73987797e-01 33 -2.56817256e+00 -1.06297251e+00 -1.09481639e+00 | -2.56817256e+00 -1.06297251e+00 -1.09481639e+00 34 -3.28782633e+00 -1.01511944e+00 -1.22892663e+01 | -3.28782633e+00 -1.01511944e+00 -1.22892663e+01 35 2.56101242e+00 -4.02298223e+00 3.26952102e+00 | 2.56101242e+00 -4.02298223e+00 3.26952102e+00 36 1.08500328e+00 -6.68182078e-01 1.19767642e+00 | 1.08500328e+00 -6.68182078e-01 1.19767642e+00 37 6.68438691e-01 -6.84333552e-01 -1.71375452e-01 | 6.68438691e-01 -6.84333552e-01 -1.71375452e-01 38 -4.27899805e-01 4.47131994e-01 9.21044919e-01 | -4.27899805e-01 4.47131994e-01 9.21044919e-01 39 -2.24085738e+00 1.46956356e+00 1.47786105e+00 | -2.24085738e+00 1.46956356e+00 1.47786105e+00 40 3.78744346e-01 -1.53097742e+00 -1.64269660e+00 | 3.78744346e-01 -1.53097742e+00 -1.64269660e+00 41 -5.02676045e-01 -6.44460526e-01 5.68584515e-01 | -5.02676045e-01 -6.44460526e-01 5.68584515e-01 42 5.07805343e+00 6.02647521e+00 5.06667323e+00 | 5.07805343e+00 6.02647521e+00 5.06667323e+00 43 -1.01524886e+00 -4.90874500e+00 -4.14767967e+00 | -1.01524886e+00 -4.90874500e+00 -4.14767967e+00 44 7.41207637e-01 -8.58896465e-01 5.70058558e-01 | 7.41207637e-01 -8.58896465e-01 5.70058558e-01 45 -9.36891907e-03 -2.04050676e-02 -2.86170763e-02 | -9.36891907e-03 -2.04050676e-02 -2.86170763e-02 46 1.23992529e+00 2.24193321e+00 4.11695492e-01 | 1.23992529e+00 2.24193321e+00 4.11695492e-01 47 6.49166027e+00 7.88093106e+00 -7.50691050e+00 | 6.49166027e+00 7.88093106e+00 -7.50691050e+00 48 -7.42153912e-01 -1.17508613e+00 -1.06861570e+00 | -7.42153912e-01 -1.17508613e+00 -1.06861570e+00 49 -5.54270829e-01 3.71815464e-01 4.51384857e-01 | -5.54270829e-01 3.71815464e-01 4.51384857e-01 50 1.31084131e-01 9.79402391e-01 -8.43833998e-02 | 1.31084131e-01 9.79402391e-01 -8.43833998e-02 51 1.37320600e-01 1.00194819e+00 1.20596858e+00 | 1.37320600e-01 1.00194819e+00 1.20596858e+00 52 1.66087732e+00 3.98672438e+00 5.81757643e+00 | 1.66087732e+00 3.98672438e+00 5.81757643e+00 53 -2.20189178e+00 -4.76750857e+00 -1.76912876e+00 | -2.20189178e+00 -4.76750857e+00 -1.76912876e+00 54 -5.69766922e-01 3.09136346e-01 -1.01266259e-01 | -5.69766922e-01 3.09136346e-01 -1.01266259e-01 55 -3.09165750e-01 3.53833369e-01 5.47646675e-01 | -3.09165750e-01 3.53833369e-01 5.47646675e-01 56 2.81413180e+00 1.99574452e+00 2.35745155e+00 | 2.81413180e+00 1.99574452e+00 2.35745155e+00 57 -8.91312615e+00 5.26334604e+00 5.23424248e+00 | -8.91312615e+00 5.26334604e+00 5.23424248e+00 58 -8.49031635e+00 9.65470813e+00 -5.42391998e+00 | -8.49031635e+00 9.65470813e+00 -5.42391998e+00 59 7.80805150e-01 5.44456162e-01 1.25174860e-01 | 7.80805150e-01 5.44456162e-01 1.25174860e-01 60 -6.45943992e+00 -9.63077478e+00 1.14379407e+01 | -6.45943992e+00 -9.63077478e+00 1.14379407e+01 61 1.40855791e+00 2.53353877e-01 7.36271117e-01 | 1.40855791e+00 2.53353877e-01 7.36271117e-01 62 6.95921196e+00 -4.12745032e+00 -5.76887744e+00 | 6.95921196e+00 -4.12745032e+00 -5.76887744e+00 63 5.15232437e-01 1.27578363e+00 1.33465529e+00 | 5.15232437e-01 1.27578363e+00 1.33465529e+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 = [11, 5, 20, 18, 31, 1, 53, 41, 43, 32, 22, 0, 38, 63, 55, 26, 47, 27, 3, 59, 2, 51, 10, 28, 46, 58, 15, 17, 23, 34, 49, 4, 9, 62, 29, 36, 35, 50, 12, 57, 56, 7, 52, 8, 61, 48, 24, 16, 45, 30, 37, 21, 42, 6, 60, 14, 40, 39, 25, 19, 54, 44, 33, 13] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 15.030099677773842 V(r_1,...,r_N) = 15.030099677773816 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 -2.89725015e+00 -3.71216716e+00 -4.45383022e+00 | -2.89725015e+00 -3.71216716e+00 -4.45383022e+00 1 3.91143711e+00 -6.74184409e+00 -1.95457399e-02 | 3.91143711e+00 -6.74184409e+00 -1.95457399e-02 2 1.48806672e+00 2.18287579e+00 -4.10498648e+00 | 1.48806672e+00 2.18287579e+00 -4.10498648e+00 3 -8.00611370e+00 1.41258126e+01 -3.42984704e+01 | -8.00611370e+00 1.41258126e+01 -3.42984704e+01 4 -8.91594638e-01 -8.70889648e-01 -9.52926082e-01 | -8.91594638e-01 -8.70889648e-01 -9.52926082e-01 5 -8.46523357e+00 4.93656127e+00 4.38754749e+00 | -8.46523357e+00 4.93656127e+00 4.38754749e+00 6 -1.22042970e+01 -8.23119562e+00 -4.61705848e+00 | -1.22042970e+01 -8.23119562e+00 -4.61705848e+00 7 -7.27199392e+00 2.44725216e+01 -5.83816360e+00 | -7.27199392e+00 2.44725216e+01 -5.83816360e+00 8 -1.72529197e+00 -2.99196944e-01 -4.93602447e-01 | -1.72529197e+00 -2.99196944e-01 -4.93602447e-01 9 -3.12575192e+00 4.53660278e+00 6.28214619e-01 | -3.12575192e+00 4.53660278e+00 6.28214619e-01 10 2.13714083e-01 -1.35251847e+00 -3.03785883e+00 | 2.13714083e-01 -1.35251847e+00 -3.03785883e+00 11 4.90062287e+01 -6.42937596e+01 -6.37744143e+01 | 4.90062287e+01 -6.42937596e+01 -6.37744143e+01 12 1.41680609e+00 -5.58241174e+00 8.43283525e-01 | 1.41680609e+00 -5.58241174e+00 8.43283525e-01 13 5.38385461e+00 -1.54878903e+00 -3.58356296e+00 | 5.38385461e+00 -1.54878903e+00 -3.58356296e+00 14 1.94066260e+01 -1.21440869e+01 2.32927303e+01 | 1.94066260e+01 -1.21440869e+01 2.32927303e+01 15 -5.60596529e+00 1.19791439e+01 -1.30464973e+01 | -5.60596529e+00 1.19791439e+01 -1.30464973e+01 16 -4.25076642e+00 -1.26671503e+00 -3.10074461e+00 | -4.25076642e+00 -1.26671503e+00 -3.10074461e+00 17 6.12470000e+00 -9.02512620e+00 5.03085251e-01 | 6.12470000e+00 -9.02512620e+00 5.03085251e-01 18 2.28392197e+00 1.61962890e+00 -1.92779825e+00 | 2.28392197e+00 1.61962890e+00 -1.92779825e+00 19 -2.69400015e+01 2.40832077e+01 -2.58557015e+01 | -2.69400015e+01 2.40832077e+01 -2.58557015e+01 20 -1.34403790e+00 4.80945706e+00 5.33181463e+00 | -1.34403790e+00 4.80945706e+00 5.33181463e+00 21 3.88360865e+00 -7.61899285e+00 -4.76403063e+00 | 3.88360865e+00 -7.61899285e+00 -4.76403063e+00 22 -8.98057831e+00 5.49266907e+00 -2.15321775e+00 | -8.98057831e+00 5.49266907e+00 -2.15321775e+00 23 -1.24698481e+00 5.95131748e+00 2.37971781e+00 | -1.24698481e+00 5.95131748e+00 2.37971781e+00 24 -2.67877461e+00 -1.82779255e+00 -2.50750708e+00 | -2.67877461e+00 -1.82779255e+00 -2.50750708e+00 25 -1.31968231e+01 -7.85256015e+00 1.69765059e+01 | -1.31968231e+01 -7.85256015e+00 1.69765059e+01 26 1.65561862e+01 1.01969317e+01 -1.89619678e+01 | 1.65561862e+01 1.01969317e+01 -1.89619678e+01 27 -2.38441650e-01 7.54228341e-01 9.85780562e-01 | -2.38441650e-01 7.54228341e-01 9.85780562e-01 28 -4.67514802e+01 6.43311669e+01 6.81264266e+01 | -4.67514802e+01 6.43311669e+01 6.81264266e+01 29 -4.70356492e-01 1.05232011e+00 -7.70983725e-01 | -4.70356492e-01 1.05232011e+00 -7.70983725e-01 30 2.67612530e+01 -2.21561764e+01 2.45613585e+01 | 2.67612530e+01 -2.21561764e+01 2.45613585e+01 31 2.96026886e-01 1.77371694e+00 -1.28437189e+00 | 2.96026886e-01 1.77371694e+00 -1.28437189e+00 32 -1.27842900e+00 -3.65550953e+00 -2.55602935e+00 | -1.27842900e+00 -3.65550953e+00 -2.55602935e+00 33 1.23669999e+01 -1.82792554e+00 -1.76754397e+01 | 1.23669999e+01 -1.82792554e+00 -1.76754397e+01 34 1.79999570e+01 -1.11694793e+01 8.13762778e+00 | 1.79999570e+01 -1.11694793e+01 8.13762778e+00 35 3.15408076e+00 -4.23395787e+00 -4.68673017e+00 | 3.15408076e+00 -4.23395787e+00 -4.68673017e+00 36 5.03881184e+00 -3.63343499e+00 7.42150607e+00 | 5.03881184e+00 -3.63343499e+00 7.42150607e+00 37 -7.96722688e+00 -1.64362611e+01 6.72874468e+00 | -7.96722688e+00 -1.64362611e+01 6.72874468e+00 38 -1.78366827e+01 7.80673850e+00 1.53668035e+01 | -1.78366827e+01 7.80673850e+00 1.53668035e+01 39 -2.26503279e+01 -8.72476287e+00 7.42653795e+00 | -2.26503279e+01 -8.72476287e+00 7.42653795e+00 40 5.71350529e+00 -1.19353495e+01 3.39827076e+00 | 5.71350529e+00 -1.19353495e+01 3.39827076e+00 41 -1.11549700e+02 -1.52011850e+02 8.58355269e+01 | -1.11549700e+02 -1.52011850e+02 8.58355269e+01 42 1.11925182e+02 1.48130016e+02 -7.55516218e+01 | 1.11925182e+02 1.48130016e+02 -7.55516218e+01 43 5.66878215e+00 -3.71003531e+00 -2.48029689e-01 | 5.66878215e+00 -3.71003531e+00 -2.48029689e-01 44 2.06731746e+00 -3.78806576e+00 4.61105203e+00 | 2.06731746e+00 -3.78806576e+00 4.61105203e+00 45 -1.98153844e-01 5.33744685e-01 -9.83390363e-02 | -1.98153844e-01 5.33744685e-01 -9.83390363e-02 46 -8.63517636e-01 3.42696354e+00 -1.94920810e+01 | -8.63517636e-01 3.42696354e+00 -1.94920810e+01 47 6.44820576e+00 1.19661077e+01 1.22136352e+01 | 6.44820576e+00 1.19661077e+01 1.22136352e+01 48 -1.17721485e+01 -8.24824083e+00 -1.83288198e-01 | -1.17721485e+01 -8.24824083e+00 -1.83288198e-01 49 1.35442890e+01 1.11400606e-01 -2.45435307e-01 | 1.35442890e+01 1.11400606e-01 -2.45435307e-01 50 -8.72234208e+00 -3.84891785e+00 -9.73316330e-01 | -8.72234208e+00 -3.84891785e+00 -9.73316330e-01 51 6.77156039e+00 6.11740741e+00 1.13064812e+01 | 6.77156039e+00 6.11740741e+00 1.13064812e+01 52 5.93851840e+00 2.91170345e-01 -7.11950840e+00 | 5.93851840e+00 2.91170345e-01 -7.11950840e+00 53 5.58332860e+00 8.38786247e+00 1.42516656e+01 | 5.58332860e+00 8.38786247e+00 1.42516656e+01 54 -4.65794067e+00 7.55465293e+00 4.75883228e+00 | -4.65794067e+00 7.55465293e+00 4.75883228e+00 55 8.38383015e-01 2.30052993e+00 1.27901454e+00 | 8.38383015e-01 2.30052993e+00 1.27901454e+00 56 -1.00736073e+01 -5.33197842e+00 -2.59833743e+00 | -1.00736073e+01 -5.33197842e+00 -2.59833743e+00 57 -3.59168416e+00 1.39164519e+01 -1.34582471e+01 | -3.59168416e+00 1.39164519e+01 -1.34582471e+01 58 -6.64335950e+00 -2.45186682e+00 -4.91211281e-01 | -6.64335950e+00 -2.45186682e+00 -4.91211281e-01 59 7.38600550e+00 2.32131569e+00 1.18040862e+00 | 7.38600550e+00 2.32131569e+00 1.18040862e+00 60 5.91857991e+00 -1.56213648e+01 9.76860595e+00 | 5.91857991e+00 -1.56213648e+01 9.76860595e+00 61 4.72453460e+00 7.92223235e+00 8.60889422e+00 | 4.72453460e+00 7.92223235e+00 8.60889422e+00 62 1.43902714e+00 -1.77157229e+00 -1.25912670e+01 | 1.43902714e+00 -1.77157229e+00 -1.25912670e+01 63 4.83735890e+00 9.84003856e+00 7.20604943e+00 | 4.83735890e+00 9.84003856e+00 7.20604943e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Cu N Ti (Configuration in file "config-CuNTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [48, 11, 60, 41, 16, 55, 34, 32, 52, 36, 12, 1, 10, 38, 50, 39, 4, 19, 51, 17, 42, 59, 26, 30, 29, 58, 22, 44, 40, 24, 23, 53, 7, 35, 6, 33, 9, 43, 13, 15, 28, 3, 20, 37, 27, 62, 46, 57, 0, 63, 14, 18, 8, 31, 61, 5, 56, 47, 25, 21, 2, 54, 45, 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)) = -69.91242311221794 V(r_1,...,r_N) = -69.91242311221785 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 -9.86353068e-02 1.83161842e-02 -1.63403228e+00 | -9.86353068e-02 1.83161842e-02 -1.63403228e+00 1 -7.57014833e+00 2.92758756e+00 1.98924514e+00 | -7.57014833e+00 2.92758756e+00 1.98924514e+00 2 -4.40344896e+00 -6.34692475e+00 -5.78967683e+00 | -4.40344896e+00 -6.34692475e+00 -5.78967683e+00 3 -1.59515410e-01 4.10013925e+00 8.96601032e+00 | -1.59515410e-01 4.10013925e+00 8.96601032e+00 4 8.33923339e+00 -3.30807691e+00 -1.04984861e+00 | 8.33923339e+00 -3.30807691e+00 -1.04984861e+00 5 7.62063795e+00 -4.59291747e+00 -3.32602272e+00 | 7.62063795e+00 -4.59291747e+00 -3.32602272e+00 6 -3.02951330e+00 -5.56685928e-01 -3.30457794e+00 | -3.02951330e+00 -5.56685928e-01 -3.30457794e+00 7 7.59321426e+01 -7.95068930e+01 -5.36294348e+01 | 7.59321426e+01 -7.95068930e+01 -5.36294348e+01 8 -1.22660889e+00 -4.65920852e-01 -4.30340413e-01 | -1.22660889e+00 -4.65920852e-01 -4.30340413e-01 9 4.60601913e+00 1.20190421e+00 -2.57561997e+00 | 4.60601913e+00 1.20190421e+00 -2.57561997e+00 10 -2.22710835e+00 2.75864478e-01 4.17100196e+00 | -2.22710835e+00 2.75864478e-01 4.17100196e+00 11 -2.13626256e+00 1.70356320e-01 -4.14746298e-01 | -2.13626256e+00 1.70356320e-01 -4.14746298e-01 12 -1.41031124e+00 1.27087087e+00 1.04525827e+00 | -1.41031124e+00 1.27087087e+00 1.04525827e+00 13 4.25234869e-01 -9.56106202e-01 -2.64783045e+00 | 4.25234869e-01 -9.56106202e-01 -2.64783045e+00 14 -5.11264262e+01 -3.55629070e+01 -1.60138472e+01 | -5.11264262e+01 -3.55629070e+01 -1.60138472e+01 15 5.06478132e+01 3.29810452e+01 2.11455072e+01 | 5.06478132e+01 3.29810452e+01 2.11455072e+01 16 8.06262651e-01 1.92914519e-01 3.20376678e-01 | 8.06262651e-01 1.92914519e-01 3.20376678e-01 17 -8.22386539e+00 -3.32249302e-01 2.07421003e+00 | -8.22386539e+00 -3.32249302e-01 2.07421003e+00 18 2.85719021e+00 2.28682701e+00 -3.91262158e+00 | 2.85719021e+00 2.28682701e+00 -3.91262158e+00 19 4.52047885e+00 -1.73537779e+00 2.60234432e+00 | 4.52047885e+00 -1.73537779e+00 2.60234432e+00 20 2.98554813e+00 -2.64013685e+00 1.02244871e+00 | 2.98554813e+00 -2.64013685e+00 1.02244871e+00 21 -4.75232738e+00 -2.18712434e+00 -7.05309358e-01 | -4.75232738e+00 -2.18712434e+00 -7.05309358e-01 22 5.98239810e+00 1.12235085e+01 2.74188144e+00 | 5.98239810e+00 1.12235085e+01 2.74188144e+00 23 -5.21742366e+00 -1.01564584e+01 -3.27248391e+00 | -5.21742366e+00 -1.01564584e+01 -3.27248391e+00 24 5.40326135e+00 2.56399831e+00 -4.07042623e+00 | 5.40326135e+00 2.56399831e+00 -4.07042623e+00 25 -1.35564476e+01 1.31356689e+01 -1.10660831e+01 | -1.35564476e+01 1.31356689e+01 -1.10660831e+01 26 7.47050185e-01 -3.00539694e+00 -1.05020298e+00 | 7.47050185e-01 -3.00539694e+00 -1.05020298e+00 27 5.00296540e-01 -2.30572069e-01 7.46173520e-01 | 5.00296540e-01 -2.30572069e-01 7.46173520e-01 28 1.41659260e+01 -1.36048365e+01 5.88289580e+00 | 1.41659260e+01 -1.36048365e+01 5.88289580e+00 29 2.97566330e+00 2.72499537e+00 1.27392672e+00 | 2.97566330e+00 2.72499537e+00 1.27392672e+00 30 -4.17520965e+00 3.17869501e+00 1.21755344e-01 | -4.17520965e+00 3.17869501e+00 1.21755344e-01 31 -7.53447024e-01 5.88879280e-01 1.42876494e+00 | -7.53447024e-01 5.88879280e-01 1.42876494e+00 32 -8.89814059e+01 -1.19785440e+02 -6.96334927e+01 | -8.89814059e+01 -1.19785440e+02 -6.96334927e+01 33 8.90177968e+01 1.15497203e+02 7.11142470e+01 | 8.90177968e+01 1.15497203e+02 7.11142470e+01 34 9.20901444e+00 -6.70064694e+00 2.31645748e+00 | 9.20901444e+00 -6.70064694e+00 2.31645748e+00 35 -9.89182332e-01 3.07209567e-01 6.28734416e-01 | -9.89182332e-01 3.07209567e-01 6.28734416e-01 36 1.54536778e+00 6.34129756e-02 2.79540731e+00 | 1.54536778e+00 6.34129756e-02 2.79540731e+00 37 -2.97378994e+00 -2.22410921e+00 -9.39806276e-01 | -2.97378994e+00 -2.22410921e+00 -9.39806276e-01 38 -8.10343383e-01 1.95026148e+00 3.11834146e+00 | -8.10343383e-01 1.95026148e+00 3.11834146e+00 39 -2.38613197e+01 -2.89731347e+01 1.48989335e+01 | -2.38613197e+01 -2.89731347e+01 1.48989335e+01 40 2.80649215e+00 -9.22019296e-01 2.25560236e+00 | 2.80649215e+00 -9.22019296e-01 2.25560236e+00 41 -3.90642365e+00 -1.78748887e-01 -1.28051713e-01 | -3.90642365e+00 -1.78748887e-01 -1.28051713e-01 42 9.34668064e-01 1.74708925e+00 -3.67731389e-01 | 9.34668064e-01 1.74708925e+00 -3.67731389e-01 43 1.86694134e+01 -2.00520617e+01 -1.61263481e+01 | 1.86694134e+01 -2.00520617e+01 -1.61263481e+01 44 -5.82358006e-01 -7.10257696e-01 -1.39534180e-02 | -5.82358006e-01 -7.10257696e-01 -1.39534180e-02 45 7.96305409e-01 9.46509385e-01 1.21943589e+00 | 7.96305409e-01 9.46509385e-01 1.21943589e+00 46 3.30176358e+00 1.19729050e+00 -2.14516340e+00 | 3.30176358e+00 1.19729050e+00 -2.14516340e+00 47 -2.35011725e+00 -1.57934191e+00 3.53099719e-01 | -2.35011725e+00 -1.57934191e+00 3.53099719e-01 48 -8.94265559e+01 9.42570178e+01 4.96708279e+01 | -8.94265559e+01 9.42570178e+01 4.96708279e+01 49 1.89043258e+00 2.92065653e+00 1.47880242e+00 | 1.89043258e+00 2.92065653e+00 1.47880242e+00 50 -6.30798504e-01 -1.28918331e+00 -4.41356892e+00 | -6.30798504e-01 -1.28918331e+00 -4.41356892e+00 51 2.41747062e-02 1.23964999e+00 6.02409047e+00 | 2.41747062e-02 1.23964999e+00 6.02409047e+00 52 2.31680380e+01 2.84557263e+01 -1.44835415e+01 | 2.31680380e+01 2.84557263e+01 -1.44835415e+01 53 -1.05483349e+00 -2.76812292e+00 -5.72649819e-01 | -1.05483349e+00 -2.76812292e+00 -5.72649819e-01 54 1.62890650e+00 -3.69491406e-01 2.31618757e+00 | 1.62890650e+00 -3.69491406e-01 2.31618757e+00 55 -8.97996838e-01 6.56363836e-02 -2.06065159e+00 | -8.97996838e-01 6.56363836e-02 -2.06065159e+00 56 1.10212043e+00 -4.29728816e+00 -4.42521459e+00 | 1.10212043e+00 -4.29728816e+00 -4.42521459e+00 57 7.24528874e+00 -1.12242826e-01 3.21298128e+00 | 7.24528874e+00 -1.12242826e-01 3.21298128e+00 58 -3.48227119e+00 -6.53352150e-01 -5.10974913e+00 | -3.48227119e+00 -6.53352150e-01 -5.10974913e+00 59 4.06459739e+00 1.15021213e+00 3.35466217e+00 | 4.06459739e+00 1.15021213e+00 3.35466217e+00 60 -1.89994630e+01 2.14586732e+01 1.40755044e+01 | -1.89994630e+01 2.14586732e+01 1.40755044e+01 61 1.04592744e-01 6.24354425e-01 -7.77365529e-02 | 1.04592744e-01 6.24354425e-01 -7.77365529e-02 62 -5.19204374e+00 5.28160663e+00 1.54307574e+00 | -5.19204374e+00 5.28160663e+00 1.54307574e+00 63 1.81472965e-01 -2.00055353e-01 -5.17427693e-01 | 1.81472965e-01 -2.00055353e-01 -5.17427693e-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.