!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_JangSeolLee_2019_CaZnMg__MO_708495328010_000 Supported species : Ca Mg Zn random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ca (Configuration in file "config-Ca.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [12, 17, 24, 39, 40, 46, 37, 62, 32, 58, 27, 59, 0, 16, 56, 51, 13, 1, 36, 26, 35, 28, 47, 44, 2, 33, 19, 10, 21, 50, 45, 53, 8, 25, 55, 20, 18, 6, 41, 3, 4, 38, 52, 49, 23, 30, 5, 22, 54, 43, 29, 15, 42, 31, 48, 34, 14, 60, 9, 11, 57, 63, 7, 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)) = 474.0001971897114 V(r_1,...,r_N) = 474.0001971897113 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 -1.16815207e+01 -5.92706978e+00 -1.45562428e+00 | -1.16815207e+01 -5.92706978e+00 -1.45562428e+00 1 -7.90642536e+00 -1.47982699e+01 2.57464858e+00 | -7.90642536e+00 -1.47982699e+01 2.57464858e+00 2 4.90245051e+00 1.78820705e+01 -2.32937944e+01 | 4.90245051e+00 1.78820705e+01 -2.32937944e+01 3 -1.87264894e-01 8.71015586e+00 -1.07805248e+01 | -1.87264894e-01 8.71015586e+00 -1.07805248e+01 4 -8.39153488e+00 -1.99270252e+01 7.73636491e+00 | -8.39153488e+00 -1.99270252e+01 7.73636491e+00 5 1.35587590e+01 1.40753489e+00 6.17040075e+00 | 1.35587590e+01 1.40753489e+00 6.17040075e+00 6 -5.66590142e+00 -1.26234038e+00 -5.35799610e+00 | -5.66590142e+00 -1.26234038e+00 -5.35799610e+00 7 -1.56237136e+01 3.89064511e+01 -2.60800802e+01 | -1.56237136e+01 3.89064511e+01 -2.60800802e+01 8 -1.04334177e+01 -6.23732407e+00 -9.39158713e+00 | -1.04334177e+01 -6.23732407e+00 -9.39158713e+00 9 -5.89381011e+00 5.11259974e+00 -1.73682421e+00 | -5.89381011e+00 5.11259974e+00 -1.73682421e+00 10 -3.95640931e+00 -3.37635487e+00 -1.76141491e+01 | -3.95640931e+00 -3.37635487e+00 -1.76141491e+01 11 1.52041811e+01 8.14361782e+00 6.49901159e+00 | 1.52041811e+01 8.14361782e+00 6.49901159e+00 12 4.63802601e+00 -1.76857600e+01 9.28904911e+00 | 4.63802601e+00 -1.76857600e+01 9.28904911e+00 13 2.87357839e+01 -1.06437665e+01 -1.04938246e+01 | 2.87357839e+01 -1.06437665e+01 -1.04938246e+01 14 1.47131949e+00 -3.07208262e+00 -6.14408617e+00 | 1.47131949e+00 -3.07208262e+00 -6.14408617e+00 15 7.92537690e+00 -2.83155451e+00 3.52767444e+00 | 7.92537690e+00 -2.83155451e+00 3.52767444e+00 16 -5.93116982e+00 -7.00210478e+00 -5.86349313e+00 | -5.93116982e+00 -7.00210478e+00 -5.86349313e+00 17 -6.30875066e-01 -3.81423664e+00 6.65156941e+00 | -6.30875066e-01 -3.81423664e+00 6.65156941e+00 18 5.52741429e+00 1.92892184e+00 -1.32353184e+01 | 5.52741429e+00 1.92892184e+00 -1.32353184e+01 19 -3.61807470e+01 2.58222859e+01 -2.36913714e+01 | -3.61807470e+01 2.58222859e+01 -2.36913714e+01 20 -1.83397736e+01 -3.34012519e-01 -9.83036508e+00 | -1.83397736e+01 -3.34012519e-01 -9.83036508e+00 21 2.32035205e+01 1.06756993e+01 9.44806836e+00 | 2.32035205e+01 1.06756993e+01 9.44806836e+00 22 -1.25685182e+01 4.78734575e-01 -6.77921994e+00 | -1.25685182e+01 4.78734575e-01 -6.77921994e+00 23 2.44831829e+00 1.43232757e+01 1.20792187e+01 | 2.44831829e+00 1.43232757e+01 1.20792187e+01 24 -4.32662183e-01 -5.95655973e-01 -5.13938654e+00 | -4.32662183e-01 -5.95655973e-01 -5.13938654e+00 25 -1.28057462e+01 1.01851332e+01 -7.19364780e+00 | -1.28057462e+01 1.01851332e+01 -7.19364780e+00 26 1.23388861e+00 9.17470081e+00 -1.13896656e+01 | 1.23388861e+00 9.17470081e+00 -1.13896656e+01 27 2.11052814e+00 2.12431117e+00 -4.03099202e-01 | 2.11052814e+00 2.12431117e+00 -4.03099202e-01 28 4.38909156e+00 -1.98960474e+01 1.00590255e+01 | 4.38909156e+00 -1.98960474e+01 1.00590255e+01 29 1.31260694e+01 4.09768293e+00 1.01838634e+01 | 1.31260694e+01 4.09768293e+00 1.01838634e+01 30 3.08860883e+01 -1.76954880e+01 1.88437998e+01 | 3.08860883e+01 -1.76954880e+01 1.88437998e+01 31 -2.28668134e+01 9.07495982e+00 -1.34334029e+01 | -2.28668134e+01 9.07495982e+00 -1.34334029e+01 32 -4.63657809e+00 -4.46893656e+00 -2.31929363e+00 | -4.63657809e+00 -4.46893656e+00 -2.31929363e+00 33 -4.11619056e+00 1.63782076e+01 -1.58751809e+01 | -4.11619056e+00 1.63782076e+01 -1.58751809e+01 34 2.00337984e+01 -4.63111866e+01 2.54907488e+01 | 2.00337984e+01 -4.63111866e+01 2.54907488e+01 35 -8.61400779e+00 -1.01621436e+01 9.16391452e+00 | -8.61400779e+00 -1.01621436e+01 9.16391452e+00 36 3.88408811e+00 -2.22130116e+01 1.94650327e+01 | 3.88408811e+00 -2.22130116e+01 1.94650327e+01 37 -9.86147937e+00 -1.54353729e+01 1.32882017e+01 | -9.86147937e+00 -1.54353729e+01 1.32882017e+01 38 -1.58914718e+01 -9.16585794e+00 -9.69406283e+00 | -1.58914718e+01 -9.16585794e+00 -9.69406283e+00 39 -7.88980064e+00 -8.80464607e+00 2.42560578e+01 | -7.88980064e+00 -8.80464607e+00 2.42560578e+01 40 -9.06669211e+00 -8.11220047e+00 -4.60696312e+00 | -9.06669211e+00 -8.11220047e+00 -4.60696312e+00 41 -7.89037873e+00 3.33499635e+01 -1.51382129e+01 | -7.89037873e+00 3.33499635e+01 -1.51382129e+01 42 -3.17240442e+01 -3.80238045e+00 -6.33128076e+00 | -3.17240442e+01 -3.80238045e+00 -6.33128076e+00 43 2.01453710e+01 2.22446901e+01 2.41433412e+01 | 2.01453710e+01 2.22446901e+01 2.41433412e+01 44 1.97326081e+01 -3.76475668e+01 1.47313245e+01 | 1.97326081e+01 -3.76475668e+01 1.47313245e+01 45 2.45445776e+00 2.47850271e+00 4.02736934e+00 | 2.45445776e+00 2.47850271e+00 4.02736934e+00 46 4.16209118e+00 5.90541908e+00 -9.93893588e+00 | 4.16209118e+00 5.90541908e+00 -9.93893588e+00 47 8.56094247e+00 8.52394830e+00 9.62742471e+00 | 8.56094247e+00 8.52394830e+00 9.62742471e+00 48 -1.87480814e+01 4.60196037e+00 1.99046389e+00 | -1.87480814e+01 4.60196037e+00 1.99046389e+00 49 4.18962392e-01 -4.05080961e-01 1.23718203e+00 | 4.18962392e-01 -4.05080961e-01 1.23718203e+00 50 -7.48411383e+00 -1.77293813e+01 -1.43416669e+01 | -7.48411383e+00 -1.77293813e+01 -1.43416669e+01 51 8.72961380e+00 2.06887188e+01 1.47738935e+01 | 8.72961380e+00 2.06887188e+01 1.47738935e+01 52 3.39590464e+00 1.61169406e+01 -1.46998798e+01 | 3.39590464e+00 1.61169406e+01 -1.46998798e+01 53 1.29536756e+01 7.72728085e+00 1.20950310e+01 | 1.29536756e+01 7.72728085e+00 1.20950310e+01 54 -6.04540684e+00 4.39910479e+00 2.00032593e+00 | -6.04540684e+00 4.39910479e+00 2.00032593e+00 55 1.57691697e+00 9.32023801e-01 2.40261233e+00 | 1.57691697e+00 9.32023801e-01 2.40261233e+00 56 7.57399461e+00 2.85687514e+00 -5.22097820e+00 | 7.57399461e+00 2.85687514e+00 -5.22097820e+00 57 -3.66078185e+00 -1.65082568e+01 -4.94440531e+01 | -3.66078185e+00 -1.65082568e+01 -4.94440531e+01 58 2.79078363e+01 -2.78569834e+00 1.60787103e+01 | 2.79078363e+01 -2.78569834e+00 1.60787103e+01 59 2.83190026e+00 1.55909759e+00 8.30151006e-01 | 2.83190026e+00 1.55909759e+00 8.30151006e-01 60 2.12248909e+01 -7.24803953e+00 1.60828545e+01 | 2.12248909e+01 -7.24803953e+00 1.60828545e+01 61 2.32977313e+00 -3.50542361e-01 3.77783138e+00 | 2.32977313e+00 -3.50542361e-01 3.77783138e+00 62 -1.26012763e+01 2.69466240e+01 3.42033794e+01 | -1.26012763e+01 2.69466240e+01 3.42033794e+01 63 4.48965272e-01 3.49190306e+00 4.18942383e+00 | 4.48965272e-01 3.49190306e+00 4.18942383e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Mg (Configuration in file "config-Mg.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [49, 20, 4, 8, 2, 26, 37, 21, 3, 43, 59, 14, 45, 54, 11, 19, 55, 41, 35, 15, 1, 7, 30, 50, 52, 60, 5, 61, 42, 44, 22, 58, 39, 51, 47, 18, 48, 6, 62, 32, 56, 17, 28, 9, 29, 12, 53, 34, 36, 0, 23, 33, 24, 46, 13, 16, 40, 63, 31, 10, 25, 27, 38, 57] 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)) = 134.03717719694856 V(r_1,...,r_N) = 134.0371771969485 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 -6.20718888e+00 -8.39636653e+00 -1.96934696e+00 | -6.20718888e+00 -8.39636653e+00 -1.96934696e+00 1 -3.91646049e+00 2.36343761e+00 1.20358024e+00 | -3.91646049e+00 2.36343761e+00 1.20358024e+00 2 7.14005146e+00 5.27018269e+00 -4.58536092e+00 | 7.14005146e+00 5.27018269e+00 -4.58536092e+00 3 1.27114974e+01 -8.54460593e+00 -8.40543349e+00 | 1.27114974e+01 -8.54460593e+00 -8.40543349e+00 4 -2.38152385e-01 -2.46296914e+00 -4.33343717e-01 | -2.38152385e-01 -2.46296914e+00 -4.33343717e-01 5 1.94049871e+00 -1.20901965e+01 -3.08023539e+01 | 1.94049871e+00 -1.20901965e+01 -3.08023539e+01 6 -1.85357508e+00 -1.21232168e+00 -7.92288978e-01 | -1.85357508e+00 -1.21232168e+00 -7.92288978e-01 7 6.45098813e-01 1.05880367e+00 2.84745158e+00 | 6.45098813e-01 1.05880367e+00 2.84745158e+00 8 -3.14186991e-02 -7.73730996e-01 -9.91462627e-01 | -3.14186991e-02 -7.73730996e-01 -9.91462627e-01 9 -2.32806769e+00 2.55810644e+00 -3.05367329e+00 | -2.32806769e+00 2.55810644e+00 -3.05367329e+00 10 -1.05937090e+00 -6.31723746e-01 -1.93829787e+00 | -1.05937090e+00 -6.31723746e-01 -1.93829787e+00 11 1.37755175e+01 -7.67664257e+00 -1.02589323e+01 | 1.37755175e+01 -7.67664257e+00 -1.02589323e+01 12 1.82240430e+00 -7.11199814e+00 1.61524474e+00 | 1.82240430e+00 -7.11199814e+00 1.61524474e+00 13 2.53491883e+00 1.03570705e-01 3.97625838e-01 | 2.53491883e+00 1.03570705e-01 3.97625838e-01 14 4.67385497e+00 -6.18606806e+00 3.90569810e+00 | 4.67385497e+00 -6.18606806e+00 3.90569810e+00 15 -1.09230374e+01 4.56888660e+00 -5.91139581e+00 | -1.09230374e+01 4.56888660e+00 -5.91139581e+00 16 -2.18092622e+00 -2.71573992e+00 -1.56861441e+00 | -2.18092622e+00 -2.71573992e+00 -1.56861441e+00 17 -7.51488808e+00 -1.75192498e+01 1.73964149e+01 | -7.51488808e+00 -1.75192498e+01 1.73964149e+01 18 8.68147169e+00 1.83943595e+01 -1.85361779e+01 | 8.68147169e+00 1.83943595e+01 -1.85361779e+01 19 1.15811880e+00 1.73828634e+00 1.41890824e+00 | 1.15811880e+00 1.73828634e+00 1.41890824e+00 20 -2.33166875e+01 6.44618907e+00 9.01476738e+00 | -2.33166875e+01 6.44618907e+00 9.01476738e+00 21 -3.92452240e+00 5.44620344e+00 -6.78600173e+00 | -3.92452240e+00 5.44620344e+00 -6.78600173e+00 22 -3.73690298e+00 1.35988804e-01 -4.84807420e+00 | -3.73690298e+00 1.35988804e-01 -4.84807420e+00 23 7.11884942e-01 2.53162727e+00 3.08904558e+00 | 7.11884942e-01 2.53162727e+00 3.08904558e+00 24 -1.08391071e+00 5.05887257e-01 -1.19605766e+01 | -1.08391071e+00 5.05887257e-01 -1.19605766e+01 25 8.83460262e+00 -8.19623961e+00 -1.69012115e+01 | 8.83460262e+00 -8.19623961e+00 -1.69012115e+01 26 8.39132453e+00 2.87466829e-01 -1.10359994e+01 | 8.39132453e+00 2.87466829e-01 -1.10359994e+01 27 2.05635187e+00 4.00892339e+00 2.58376795e+00 | 2.05635187e+00 4.00892339e+00 2.58376795e+00 28 -1.76190077e+01 1.39680926e+00 6.49831134e+00 | -1.76190077e+01 1.39680926e+00 6.49831134e+00 29 8.30463522e+00 5.00805220e+00 4.82979277e+00 | 8.30463522e+00 5.00805220e+00 4.82979277e+00 30 -1.38584990e+01 1.16706648e+01 2.52583763e+01 | -1.38584990e+01 1.16706648e+01 2.52583763e+01 31 1.10897928e-01 1.34888314e+00 7.38026313e-01 | 1.10897928e-01 1.34888314e+00 7.38026313e-01 32 -2.25422450e+00 -2.35188142e+00 -2.06704684e+00 | -2.25422450e+00 -2.35188142e+00 -2.06704684e+00 33 1.58309031e-02 7.08790848e-01 -7.09198394e-01 | 1.58309031e-02 7.08790848e-01 -7.09198394e-01 34 -1.38374235e+01 2.42280146e+01 1.98692223e+01 | -1.38374235e+01 2.42280146e+01 1.98692223e+01 35 -4.22957004e+00 -7.87404667e+00 4.25645892e+00 | -4.22957004e+00 -7.87404667e+00 4.25645892e+00 36 4.71824448e-01 -5.50528220e-01 4.05187223e-01 | 4.71824448e-01 -5.50528220e-01 4.05187223e-01 37 -9.73541161e-01 -3.32814989e+00 1.06493287e+01 | -9.73541161e-01 -3.32814989e+00 1.06493287e+01 38 -2.52498938e+00 -2.76801881e-01 2.34375728e+00 | -2.52498938e+00 -2.76801881e-01 2.34375728e+00 39 -6.69171416e-01 -1.91443950e+00 3.39493898e+00 | -6.69171416e-01 -1.91443950e+00 3.39493898e+00 40 1.29187282e+01 -1.29093452e+01 9.08781586e+00 | 1.29187282e+01 -1.29093452e+01 9.08781586e+00 41 -3.11906920e+00 2.98558945e+00 -8.81108653e+00 | -3.11906920e+00 2.98558945e+00 -8.81108653e+00 42 1.06760404e+01 -3.45456973e+00 5.07793412e+00 | 1.06760404e+01 -3.45456973e+00 5.07793412e+00 43 1.94223376e+00 2.49462267e-01 1.08590019e+00 | 1.94223376e+00 2.49462267e-01 1.08590019e+00 44 8.47355051e+00 -6.54658926e+00 7.98585319e+00 | 8.47355051e+00 -6.54658926e+00 7.98585319e+00 45 5.31522612e-01 6.59664796e-01 6.27312449e-01 | 5.31522612e-01 6.59664796e-01 6.27312449e-01 46 -2.60492772e+00 4.16466098e+00 -6.20683194e+00 | -2.60492772e+00 4.16466098e+00 -6.20683194e+00 47 -1.35769785e+00 -2.44585054e+00 1.56914925e+00 | -1.35769785e+00 -2.44585054e+00 1.56914925e+00 48 -2.82478036e+00 -1.17831210e+00 1.06853923e+00 | -2.82478036e+00 -1.17831210e+00 1.06853923e+00 49 -5.25555717e+00 -2.20888295e+00 1.15894592e-01 | -5.25555717e+00 -2.20888295e+00 1.15894592e-01 50 5.72713432e+00 3.30418184e+00 -1.39028428e+00 | 5.72713432e+00 3.30418184e+00 -1.39028428e+00 51 -1.38003126e+01 1.16604473e+01 -6.79724380e+00 | -1.38003126e+01 1.16604473e+01 -6.79724380e+00 52 1.37856988e+00 -1.81344437e+00 -3.43235069e+00 | 1.37856988e+00 -1.81344437e+00 -3.43235069e+00 53 3.81604443e+00 -4.50162765e+00 5.91830203e+00 | 3.81604443e+00 -4.50162765e+00 5.91830203e+00 54 -5.00785033e+00 6.48264644e-01 7.69930643e-02 | -5.00785033e+00 6.48264644e-01 7.69930643e-02 55 -2.34846311e+00 6.76958592e+00 5.55777468e+00 | -2.34846311e+00 6.76958592e+00 5.55777468e+00 56 1.06974313e+01 5.98677442e+00 2.86884601e+00 | 1.06974313e+01 5.98677442e+00 2.86884601e+00 57 -1.26734645e+01 2.65932994e+00 7.94860240e+00 | -1.26734645e+01 2.65932994e+00 7.94860240e+00 58 1.21657808e+01 -3.45570826e+00 -8.99095641e+00 | 1.21657808e+01 -3.45570826e+00 -8.99095641e+00 59 1.24148529e+00 1.81238511e+00 7.32806979e-01 | 1.24148529e+00 1.81238511e+00 7.32806979e-01 60 -6.48171897e+00 1.73103858e+00 -7.62594568e+00 | -6.48171897e+00 1.73103858e+00 -7.62594568e+00 61 9.35825586e+00 -5.12200106e-01 8.78744907e+00 | 9.35825586e+00 -5.12200106e-01 8.78744907e+00 62 1.41357872e+01 -4.50411811e+00 4.35654061e+00 | 1.41357872e+01 -4.50411811e+00 4.35654061e+00 63 2.71202834e+00 9.33828838e-01 2.22787169e+00 | 2.71202834e+00 9.33828838e-01 2.22787169e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Zn (Configuration in file "config-Zn.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [34, 33, 9, 48, 27, 52, 28, 55, 41, 2, 43, 26, 37, 21, 44, 35, 40, 36, 32, 45, 29, 13, 47, 59, 51, 60, 11, 4, 6, 20, 31, 30, 18, 1, 0, 15, 17, 12, 63, 56, 16, 8, 57, 10, 14, 19, 58, 22, 3, 62, 61, 24, 5, 54, 53, 7, 39, 42, 46, 23, 25, 50, 49, 38] 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)) = 289.8325366881743 V(r_1,...,r_N) = 289.8325366881742 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 -6.13459731e+00 -5.16428093e+00 -4.36523726e+00 | -6.13459731e+00 -5.16428093e+00 -4.36523726e+00 1 6.81265395e+00 3.68852148e+00 4.17733442e+00 | 6.81265395e+00 3.68852148e+00 4.17733442e+00 2 6.91899888e-01 -5.11830684e+00 -4.36615378e+00 | 6.91899888e-01 -5.11830684e+00 -4.36615378e+00 3 5.29072119e-01 -4.42289497e+00 -2.21073674e+01 | 5.29072119e-01 -4.42289497e+00 -2.21073674e+01 4 -3.26420306e-02 -3.69273450e-02 4.84417783e-02 | -3.26420306e-02 -3.69273450e-02 4.84417783e-02 5 -4.24270218e+00 1.41414830e+01 -4.89279358e+00 | -4.24270218e+00 1.41414830e+01 -4.89279358e+00 6 -1.01289778e+00 1.09761329e+00 6.61117039e-01 | -1.01289778e+00 1.09761329e+00 6.61117039e-01 7 -1.15622922e+02 -7.72992196e+01 4.17334344e+01 | -1.15622922e+02 -7.72992196e+01 4.17334344e+01 8 -6.67803879e-01 2.84086807e-02 -1.73025740e-01 | -6.67803879e-01 2.84086807e-02 -1.73025740e-01 9 -2.45128902e+01 -1.98703913e+01 2.70610948e+01 | -2.45128902e+01 -1.98703913e+01 2.70610948e+01 10 2.31289235e+01 2.15762885e+01 -2.82750449e+01 | 2.31289235e+01 2.15762885e+01 -2.82750449e+01 11 2.68010212e-01 4.04775380e-01 2.46941802e-01 | 2.68010212e-01 4.04775380e-01 2.46941802e-01 12 -5.01373572e+00 -4.34630564e+01 -3.01201507e+01 | -5.01373572e+00 -4.34630564e+01 -3.01201507e+01 13 6.78045642e+00 4.12719513e+01 3.09580164e+01 | 6.78045642e+00 4.12719513e+01 3.09580164e+01 14 2.00468447e+00 -4.98266117e-01 -8.63313532e-01 | 2.00468447e+00 -4.98266117e-01 -8.63313532e-01 15 -1.36522811e+01 1.15704423e+01 -8.54080730e+00 | -1.36522811e+01 1.15704423e+01 -8.54080730e+00 16 -2.89429827e+01 -4.51382226e+01 -7.59197418e+01 | -2.89429827e+01 -4.51382226e+01 -7.59197418e+01 17 2.84803607e+01 4.36165424e+01 7.47904840e+01 | 2.84803607e+01 4.36165424e+01 7.47904840e+01 18 -6.22886992e+00 -4.57366337e+00 -1.49146012e+00 | -6.22886992e+00 -4.57366337e+00 -1.49146012e+00 19 6.84629762e+00 4.94636422e+00 1.43874659e+00 | 6.84629762e+00 4.94636422e+00 1.43874659e+00 20 1.22056164e+02 7.73173331e+01 -3.01432927e+01 | 1.22056164e+02 7.73173331e+01 -3.01432927e+01 21 -3.33825656e+01 -3.38753832e+01 2.87484341e+01 | -3.33825656e+01 -3.38753832e+01 2.87484341e+01 22 -3.72579875e+01 -6.63665521e+01 -2.58385335e+01 | -3.72579875e+01 -6.63665521e+01 -2.58385335e+01 23 3.38155208e+01 6.87834910e+01 2.36482152e+01 | 3.38155208e+01 6.87834910e+01 2.36482152e+01 24 -2.11710536e+01 -1.05688077e+01 -2.00769880e+01 | -2.11710536e+01 -1.05688077e+01 -2.00769880e+01 25 -5.80543960e+01 5.06181637e+01 -5.96548315e+01 | -5.80543960e+01 5.06181637e+01 -5.96548315e+01 26 -2.99517792e+00 -1.90034159e+00 -2.97841038e+00 | -2.99517792e+00 -1.90034159e+00 -2.97841038e+00 27 2.93824570e+00 2.44441298e+00 2.47943978e+00 | 2.93824570e+00 2.44441298e+00 2.47943978e+00 28 4.70440688e+01 -6.21668170e+01 5.28426366e+01 | 4.70440688e+01 -6.21668170e+01 5.28426366e+01 29 3.21104078e+01 1.93057608e+01 2.69558778e+01 | 3.21104078e+01 1.93057608e+01 2.69558778e+01 30 1.06411653e+01 2.11213236e+01 -4.26040139e+01 | 1.06411653e+01 2.11213236e+01 -4.26040139e+01 31 2.12069950e+01 1.76495221e+01 1.01646831e+01 | 2.12069950e+01 1.76495221e+01 1.01646831e+01 32 -1.11444675e+01 -3.23316115e+01 -3.68178913e+01 | -1.11444675e+01 -3.23316115e+01 -3.68178913e+01 33 2.74686625e+01 -5.22869780e-01 1.40634488e+01 | 2.74686625e+01 -5.22869780e-01 1.40634488e+01 34 -1.69652732e+01 -1.15765780e+01 -1.28684983e+01 | -1.69652732e+01 -1.15765780e+01 -1.28684983e+01 35 1.78883315e+01 1.26147981e+01 1.20383322e+01 | 1.78883315e+01 1.26147981e+01 1.20383322e+01 36 -5.99165643e+00 -4.60959580e+00 -6.07914854e+00 | -5.99165643e+00 -4.60959580e+00 -6.07914854e+00 37 1.10346814e+00 -2.87269068e+00 9.49309119e+00 | 1.10346814e+00 -2.87269068e+00 9.49309119e+00 38 -1.79319232e+01 3.22893820e+01 2.23953372e+01 | -1.79319232e+01 3.22893820e+01 2.23953372e+01 39 7.99860756e-02 -7.48475184e-02 -3.32647508e-01 | 7.99860756e-02 -7.48475184e-02 -3.32647508e-01 40 4.04851025e+00 -1.44706802e+01 6.65380854e+00 | 4.04851025e+00 -1.44706802e+01 6.65380854e+00 41 2.69058192e+01 -2.26488634e+01 -3.65028517e+01 | 2.69058192e+01 -2.26488634e+01 -3.65028517e+01 42 -5.56458121e+00 -4.26739132e+01 -2.44108417e+01 | -5.56458121e+00 -4.26739132e+01 -2.44108417e+01 43 2.22799576e+01 2.72973892e+01 3.21370447e+01 | 2.22799576e+01 2.72973892e+01 3.21370447e+01 44 -8.93571187e-01 -7.79657273e-01 -7.28487853e-01 | -8.93571187e-01 -7.79657273e-01 -7.28487853e-01 45 8.09130541e-01 9.47753902e-01 6.20322732e-01 | 8.09130541e-01 9.47753902e-01 6.20322732e-01 46 -2.16371175e+01 2.81491513e+01 3.27798056e+01 | -2.16371175e+01 2.81491513e+01 3.27798056e+01 47 3.62052297e-02 1.29503701e+00 1.53463473e+00 | 3.62052297e-02 1.29503701e+00 1.53463473e+00 48 -1.03665719e+01 7.31791751e+00 1.17406836e+01 | -1.03665719e+01 7.31791751e+00 1.17406836e+01 49 2.54072839e+00 -1.09885350e+01 -7.81544036e+00 | 2.54072839e+00 -1.09885350e+01 -7.81544036e+00 50 -4.04749670e+01 -2.61784805e+01 -3.29489151e+01 | -4.04749670e+01 -2.61784805e+01 -3.29489151e+01 51 4.12541267e+01 2.73260123e+01 3.83118466e+01 | 4.12541267e+01 2.73260123e+01 3.83118466e+01 52 -8.29556134e+01 -7.69968670e+01 -1.00560136e+02 | -8.29556134e+01 -7.69968670e+01 -1.00560136e+02 53 8.10830433e+01 7.59288426e+01 1.02312975e+02 | 8.10830433e+01 7.59288426e+01 1.02312975e+02 54 -2.12561720e+01 5.24970281e+00 -3.46980636e+01 | -2.12561720e+01 5.24970281e+00 -3.46980636e+01 55 1.86944218e+01 6.08937883e+00 4.25387472e+01 | 1.86944218e+01 6.08937883e+00 4.25387472e+01 56 9.88194881e-01 -1.64575992e+00 2.26593589e+00 | 9.88194881e-01 -1.64575992e+00 2.26593589e+00 57 2.40660523e+01 -7.40726633e+00 -4.10209376e+01 | 2.40660523e+01 -7.40726633e+00 -4.10209376e+01 58 -1.31654737e+00 -3.28153018e+00 -6.60832941e+00 | -1.31654737e+00 -3.28153018e+00 -6.60832941e+00 59 2.95107337e+00 4.68898661e+00 8.55793197e+00 | 2.95107337e+00 4.68898661e+00 8.55793197e+00 60 2.08706116e+01 -2.34929492e+01 6.20323998e+00 | 2.08706116e+01 -2.34929492e+01 6.20323998e+00 61 1.50067460e+01 -7.83931081e+00 1.11712584e+00 | 1.50067460e+01 -7.83931081e+00 1.11712584e+00 62 -4.90327511e+01 2.86389818e+01 2.94564807e+01 | -4.90327511e+01 2.86389818e+01 2.94564807e+01 63 -8.97327687e+00 1.34394055e+01 3.62766410e+00 | -8.97327687e+00 1.34394055e+01 3.62766410e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ca Mg Zn (Configuration in file "config-CaMgZn.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [23, 58, 14, 22, 15, 34, 26, 45, 21, 33, 28, 43, 38, 39, 2, 4, 53, 49, 41, 20, 19, 8, 3, 0, 60, 54, 6, 31, 10, 59, 48, 27, 55, 9, 5, 40, 52, 42, 12, 13, 35, 18, 37, 11, 46, 7, 44, 47, 30, 17, 51, 50, 36, 16, 25, 32, 57, 56, 1, 29, 24, 62, 61, 63] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 217.55650208842522 V(r_1,...,r_N) = 217.5565020884253 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 6.91039429e-02 -1.37898867e-01 6.53888669e-02 | 6.91039429e-02 -1.37898867e-01 6.53888669e-02 1 -2.16450965e-02 -8.33181630e-01 2.51941125e+00 | -2.16450965e-02 -8.33181630e-01 2.51941125e+00 2 1.62513197e-01 -4.72348323e+00 -5.30080761e+00 | 1.62513197e-01 -4.72348323e+00 -5.30080761e+00 3 1.79176382e+00 7.75880986e-01 -4.91821060e+00 | 1.79176382e+00 7.75880986e-01 -4.91821060e+00 4 -1.09897484e+00 -9.64021597e-01 -2.16632709e+00 | -1.09897484e+00 -9.64021597e-01 -2.16632709e+00 5 1.39985633e+01 -1.24551248e+01 -1.71363812e+01 | 1.39985633e+01 -1.24551248e+01 -1.71363812e+01 6 -5.91716685e+01 -3.79166757e+01 -2.29670129e+01 | -5.91716685e+01 -3.79166757e+01 -2.29670129e+01 7 5.85935324e+01 3.30484109e+01 1.73708700e+01 | 5.85935324e+01 3.30484109e+01 1.73708700e+01 8 -1.03650417e+00 -3.57394157e+00 -1.05428223e+00 | -1.03650417e+00 -3.57394157e+00 -1.05428223e+00 9 -1.06445549e+01 -4.83139057e+00 5.24193237e+00 | -1.06445549e+01 -4.83139057e+00 5.24193237e+00 10 -6.73160246e+00 -1.10773223e+01 -2.08027901e+01 | -6.73160246e+00 -1.10773223e+01 -2.08027901e+01 11 1.99660185e+01 1.67046892e+01 1.43660155e+01 | 1.99660185e+01 1.67046892e+01 1.43660155e+01 12 -1.88343143e+00 -4.29388064e+00 -5.75011093e+00 | -1.88343143e+00 -4.29388064e+00 -5.75011093e+00 13 1.56659092e+01 -8.53668487e+00 -3.34838735e+00 | 1.56659092e+01 -8.53668487e+00 -3.34838735e+00 14 1.44093392e-01 8.48391538e-01 1.28027077e-01 | 1.44093392e-01 8.48391538e-01 1.28027077e-01 15 -1.64147090e+01 8.95799521e+00 -4.25542970e+00 | -1.64147090e+01 8.95799521e+00 -4.25542970e+00 16 -1.33235531e+00 -8.87860717e-01 -1.88698243e-01 | -1.33235531e+00 -8.87860717e-01 -1.88698243e-01 17 1.79278286e+00 -4.67091227e+00 1.49138393e+00 | 1.79278286e+00 -4.67091227e+00 1.49138393e+00 18 -3.14710008e+00 -5.46501659e+00 -1.45226294e+01 | -3.14710008e+00 -5.46501659e+00 -1.45226294e+01 19 5.50520064e+00 8.67211007e+00 7.26397972e+00 | 5.50520064e+00 8.67211007e+00 7.26397972e+00 20 -1.39897984e+00 8.09659277e+00 4.71141773e+00 | -1.39897984e+00 8.09659277e+00 4.71141773e+00 21 -7.92871282e+00 1.10843661e+01 -1.33584393e+01 | -7.92871282e+00 1.10843661e+01 -1.33584393e+01 22 -1.04189376e+01 1.05957121e+00 -6.55072903e-02 | -1.04189376e+01 1.05957121e+00 -6.55072903e-02 23 -1.29554675e+00 1.51829377e+01 -9.07918951e+00 | -1.29554675e+00 1.51829377e+01 -9.07918951e+00 24 -3.58410636e+00 -8.20984065e+00 -1.36270956e+01 | -3.58410636e+00 -8.20984065e+00 -1.36270956e+01 25 5.54924057e+00 3.53275179e+00 9.40959603e+00 | 5.54924057e+00 3.53275179e+00 9.40959603e+00 26 1.04321302e+00 8.54821217e-01 -9.97755054e-01 | 1.04321302e+00 8.54821217e-01 -9.97755054e-01 27 -4.63915430e-02 -2.38309472e-01 -4.53632472e-02 | -4.63915430e-02 -2.38309472e-01 -4.53632472e-02 28 -4.15065877e+01 -4.81292071e+01 -3.91153424e+01 | -4.15065877e+01 -4.81292071e+01 -3.91153424e+01 29 6.74328917e+01 2.38882479e+01 1.78287659e+01 | 6.74328917e+01 2.38882479e+01 1.78287659e+01 30 -2.01156223e+01 -2.59450419e+01 -1.00081149e+01 | -2.01156223e+01 -2.59450419e+01 -1.00081149e+01 31 1.90950036e+01 2.94182225e+01 1.54882498e+01 | 1.90950036e+01 2.94182225e+01 1.54882498e+01 32 -2.15978362e+01 -1.15174330e-02 -2.02257213e+01 | -2.15978362e+01 -1.15174330e-02 -2.02257213e+01 33 1.51855951e+01 2.73893467e-02 1.64336123e+01 | 1.51855951e+01 2.73893467e-02 1.64336123e+01 34 -1.34925856e+01 1.16012122e+01 1.49996477e+01 | -1.34925856e+01 1.16012122e+01 1.49996477e+01 35 3.16015324e+00 -1.61688573e+01 -2.70774703e+01 | 3.16015324e+00 -1.61688573e+01 -2.70774703e+01 36 3.29722337e+00 -8.60060505e+00 4.91418786e-01 | 3.29722337e+00 -8.60060505e+00 4.91418786e-01 37 4.33545979e-01 2.34871548e+00 4.39884932e+00 | 4.33545979e-01 2.34871548e+00 4.39884932e+00 38 -2.87625552e+00 1.85246518e-01 -7.55105932e-02 | -2.87625552e+00 1.85246518e-01 -7.55105932e-02 39 8.64076398e-01 1.66383835e+00 2.62263981e+00 | 8.64076398e-01 1.66383835e+00 2.62263981e+00 40 -9.29398417e+00 -3.32909783e+00 -4.16506546e+00 | -9.29398417e+00 -3.32909783e+00 -4.16506546e+00 41 6.94037457e-01 1.38465877e+01 -5.67966141e-02 | 6.94037457e-01 1.38465877e+01 -5.67966141e-02 42 9.33524509e+00 6.51341197e+00 5.79904468e+00 | 9.33524509e+00 6.51341197e+00 5.79904468e+00 43 9.53524996e-01 -5.48086125e-02 -1.34079994e-01 | 9.53524996e-01 -5.48086125e-02 -1.34079994e-01 44 7.28603277e+00 -1.87600565e+01 9.91217416e+00 | 7.28603277e+00 -1.87600565e+01 9.91217416e+00 45 7.94973025e-01 8.43836115e-01 5.11821804e-01 | 7.94973025e-01 8.43836115e-01 5.11821804e-01 46 -3.11237173e+00 -1.09324208e+01 -1.00716139e+01 | -3.11237173e+00 -1.09324208e+01 -1.00716139e+01 47 7.35853985e+00 9.22770892e+00 1.26514998e+01 | 7.35853985e+00 9.22770892e+00 1.26514998e+01 48 -3.82948744e+00 1.66202443e+00 4.95496797e+00 | -3.82948744e+00 1.66202443e+00 4.95496797e+00 49 -1.31067736e+00 3.30381495e-01 9.42061737e-01 | -1.31067736e+00 3.30381495e-01 9.42061737e-01 50 -1.71987992e+00 -1.81651944e+01 9.83643071e+00 | -1.71987992e+00 -1.81651944e+01 9.83643071e+00 51 6.77267216e+00 6.81775867e+00 3.21861087e+00 | 6.77267216e+00 6.81775867e+00 3.21861087e+00 52 -2.01645581e+01 1.03489760e+01 3.38313626e+01 | -2.01645581e+01 1.03489760e+01 3.38313626e+01 53 6.02792223e-01 5.04569845e+00 7.26041217e+00 | 6.02792223e-01 5.04569845e+00 7.26041217e+00 54 -2.69416583e+01 -2.13791961e+01 -6.24711326e+00 | -2.69416583e+01 -2.13791961e+01 -6.24711326e+00 55 2.60805922e+01 2.26221075e+01 6.97819738e+00 | 2.60805922e+01 2.26221075e+01 6.97819738e+00 56 1.15542414e+01 -6.98562171e+00 -2.89739950e-02 | 1.15542414e+01 -6.98562171e+00 -2.89739950e-02 57 3.52444832e-01 5.22034318e+00 -5.61209703e+00 | 3.52444832e-01 5.22034318e+00 -5.61209703e+00 58 -2.70535633e+01 2.17039811e+01 1.70950145e+01 | -2.70535633e+01 2.17039811e+01 1.70950145e+01 59 3.47415944e+00 3.25326386e+00 3.40640230e+00 | 3.47415944e+00 3.25326386e+00 3.40640230e+00 60 -5.68170024e-01 -9.90972745e+00 5.71668662e+00 | -5.68170024e-01 -9.90972745e+00 5.71668662e+00 61 8.28601039e+00 8.84898357e+00 4.36653126e+00 | 8.28601039e+00 8.84898357e+00 4.36653126e+00 62 2.24418251e+00 -2.14973195e+01 -1.07073366e+00 | 2.24418251e+00 -2.14973195e+01 -1.07073366e+00 63 1.98585899e-01 2.44477633e+01 2.16062603e+00 | 1.98585899e-01 2.44477633e+01 2.16062603e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.