!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_MEAM_JelinekGrohHorstemeyer_2012_AlSiMgCuFe__SM_656517352485_000 Supported species : Al Cu Fe Mg Si random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Al (Configuration in file "config-Al.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [34, 29, 28, 11, 53, 49, 43, 16, 25, 37, 21, 3, 47, 50, 15, 14, 7, 46, 52, 51, 58, 10, 38, 61, 33, 8, 31, 36, 2, 1, 41, 26, 44, 24, 0, 59, 27, 9, 22, 55, 63, 30, 60, 6, 32, 56, 17, 12, 62, 5, 13, 19, 18, 4, 57, 39, 45, 54, 20, 35, 42, 23, 48, 40] 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)) = 474.1050481095163 V(r_1,...,r_N) = 474.1050481095155 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 -1.96153244e+01 -1.05154515e+01 -3.06597305e+01 | -1.96153244e+01 -1.05154515e+01 -3.06597305e+01 1 1.54798288e+01 1.11593203e+01 2.74968252e+01 | 1.54798288e+01 1.11593203e+01 2.74968252e+01 2 2.25086232e+00 3.49578340e+00 -9.52194872e-01 | 2.25086232e+00 3.49578340e+00 -9.52194872e-01 3 -3.68864970e+00 -5.85210478e+00 4.29960989e+00 | -3.68864970e+00 -5.85210478e+00 4.29960989e+00 4 -6.73908733e+01 -4.14685470e+01 3.00730352e+00 | -6.73908733e+01 -4.14685470e+01 3.00730352e+00 5 3.89109564e+01 3.47125735e-01 2.11321568e+01 | 3.89109564e+01 3.47125735e-01 2.11321568e+01 6 9.50774282e-01 -1.61700216e+00 5.53737939e-01 | 9.50774282e-01 -1.61700216e+00 5.53737939e-01 7 -7.92622875e+00 5.49348618e+01 -4.89787224e+01 | -7.92622875e+00 5.49348618e+01 -4.89787224e+01 8 -1.25629028e+00 3.64290322e-01 8.26359426e-01 | -1.25629028e+00 3.64290322e-01 8.26359426e-01 9 6.38718307e+00 -3.09200579e+00 -2.61708628e+00 | 6.38718307e+00 -3.09200579e+00 -2.61708628e+00 10 -6.97105757e+01 -2.24348092e+01 -4.10132557e+01 | -6.97105757e+01 -2.24348092e+01 -4.10132557e+01 11 6.87191056e+01 2.38551611e+01 4.34352881e+01 | 6.87191056e+01 2.38551611e+01 4.34352881e+01 12 -2.96532144e+01 -4.56734488e+01 -4.91152967e+01 | -2.96532144e+01 -4.56734488e+01 -4.91152967e+01 13 3.35376557e+01 4.59100647e+01 4.54408505e+01 | 3.35376557e+01 4.59100647e+01 4.54408505e+01 14 -2.92205423e+00 2.23165453e+01 -5.13217649e+01 | -2.92205423e+00 2.23165453e+01 -5.13217649e+01 15 2.50946948e+01 2.52542149e+01 3.91509142e+01 | 2.50946948e+01 2.52542149e+01 3.91509142e+01 16 -7.87275002e+00 -5.93569012e+00 -8.35043924e+00 | -7.87275002e+00 -5.93569012e+00 -8.35043924e+00 17 -5.38966922e+01 2.60715674e+01 -3.41461267e+01 | -5.38966922e+01 2.60715674e+01 -3.41461267e+01 18 -2.25333317e+00 -1.59020480e+00 -7.14257517e+00 | -2.25333317e+00 -1.59020480e+00 -7.14257517e+00 19 -7.24403889e+01 -5.96134705e+00 -1.86978188e+01 | -7.24403889e+01 -5.96134705e+00 -1.86978188e+01 20 5.77507457e+01 -2.36725164e+01 2.64404449e+01 | 5.77507457e+01 -2.36725164e+01 2.64404449e+01 21 6.33581423e+00 9.68544346e+00 -7.09706832e+00 | 6.33581423e+00 9.68544346e+00 -7.09706832e+00 22 -1.04174986e+01 -1.55970803e+01 -2.70611577e+01 | -1.04174986e+01 -1.55970803e+01 -2.70611577e+01 23 1.06728178e+01 1.59595845e+01 2.70571981e+01 | 1.06728178e+01 1.59595845e+01 2.70571981e+01 24 -1.25522802e+01 -7.53512594e+00 -1.93590865e+01 | -1.25522802e+01 -7.53512594e+00 -1.93590865e+01 25 9.51624567e+00 2.37524999e+01 5.87848626e+00 | 9.51624567e+00 2.37524999e+01 5.87848626e+00 26 -1.91717968e+00 -6.09890151e-02 -1.24240145e+00 | -1.91717968e+00 -6.09890151e-02 -1.24240145e+00 27 -3.32840551e-01 -1.82973752e+00 1.68771319e+00 | -3.32840551e-01 -1.82973752e+00 1.68771319e+00 28 -1.55489865e+00 -2.14096819e+01 9.15891754e-02 | -1.55489865e+00 -2.14096819e+01 9.15891754e-02 29 1.26782701e+01 6.40256025e+00 1.03118556e+01 | 1.26782701e+01 6.40256025e+00 1.03118556e+01 30 7.05045772e+01 1.92826874e+00 1.74361907e+01 | 7.05045772e+01 1.92826874e+00 1.74361907e+01 31 -1.85407836e+02 1.38172957e+02 -8.92374400e+01 | -1.85407836e+02 1.38172957e+02 -8.92374400e+01 32 -1.27341843e+01 -1.29931993e+01 -2.06357931e+01 | -1.27341843e+01 -1.29931993e+01 -2.06357931e+01 33 1.02378935e+01 1.52134781e+01 1.78650821e+01 | 1.02378935e+01 1.52134781e+01 1.78650821e+01 34 1.50228392e+01 -5.86721645e+01 5.45545191e+01 | 1.50228392e+01 -5.86721645e+01 5.45545191e+01 35 5.83436648e-01 -2.07815082e+01 2.81594594e-01 | 5.83436648e-01 -2.07815082e+01 2.81594594e-01 36 3.11723745e+00 -9.44323782e-01 2.52393993e+00 | 3.11723745e+00 -9.44323782e-01 2.52393993e+00 37 -1.87437168e+00 -9.48590457e+00 1.57054310e+01 | -1.87437168e+00 -9.48590457e+00 1.57054310e+01 38 -4.06423077e+01 -1.65677554e+01 -8.48152215e+00 | -4.06423077e+01 -1.65677554e+01 -8.48152215e+00 39 6.15307975e+00 -1.03040259e+01 2.72617767e+01 | 6.15307975e+00 -1.03040259e+01 2.72617767e+01 40 7.20245046e-01 -1.11841117e-01 -1.87701719e+00 | 7.20245046e-01 -1.11841117e-01 -1.87701719e+00 41 -4.51887805e+01 7.76535463e+01 -8.39990982e-01 | -4.51887805e+01 7.76535463e+01 -8.39990982e-01 42 -5.42379683e+01 -1.41991083e+02 -8.82486559e+01 | -5.42379683e+01 -1.41991083e+02 -8.82486559e+01 43 7.36854862e+01 1.55622987e+02 6.43190619e+01 | 7.36854862e+01 1.55622987e+02 6.43190619e+01 44 2.32607261e+01 -9.15085439e+01 2.35714287e+01 | 2.32607261e+01 -9.15085439e+01 2.35714287e+01 45 -1.72488669e-02 9.06218646e-01 1.31734712e+00 | -1.72488669e-02 9.06218646e-01 1.31734712e+00 46 2.11323161e+00 -2.69870338e+00 -9.97031406e+00 | 2.11323161e+00 -2.69870338e+00 -9.97031406e+00 47 2.59578675e-01 1.61895874e+00 -3.30220386e-01 | 2.59578675e-01 1.61895874e+00 -3.30220386e-01 48 -7.39001499e+00 1.91036153e+00 4.74988463e+00 | -7.39001499e+00 1.91036153e+00 4.74988463e+00 49 7.12906841e-01 -1.11894462e+01 -1.25492642e+01 | 7.12906841e-01 -1.11894462e+01 -1.25492642e+01 50 4.86402993e+00 3.38466979e+00 -5.02460689e+00 | 4.86402993e+00 3.38466979e+00 -5.02460689e+00 51 -2.70304841e+00 1.04878298e+01 1.64556315e+00 | -2.70304841e+00 1.04878298e+01 1.64556315e+00 52 2.18723979e+01 4.14499069e+01 -1.46333380e+01 | 2.18723979e+01 4.14499069e+01 -1.46333380e+01 53 3.96148037e-01 -5.38682745e-02 3.66334114e-01 | 3.96148037e-01 -5.38682745e-02 3.66334114e-01 54 -1.26315732e+01 3.13338327e+00 1.35940276e+01 | -1.26315732e+01 3.13338327e+00 1.35940276e+01 55 4.96002642e+00 2.09716528e+00 -4.29193751e-01 | 4.96002642e+00 2.09716528e+00 -4.29193751e-01 56 1.21905440e+01 1.07293064e+01 -1.51592741e+00 | 1.21905440e+01 1.07293064e+01 -1.51592741e+00 57 -6.26844943e+00 9.40325260e-01 -8.05687328e+01 | -6.26844943e+00 9.40325260e-01 -8.05687328e+01 58 1.82578960e+02 -1.31425443e+02 9.92067480e+01 | 1.82578960e+02 -1.31425443e+02 9.92067480e+01 59 -4.05992234e-01 -1.24879303e+00 8.15926580e-02 | -4.05992234e-01 -1.24879303e+00 8.15926580e-02 60 5.98966063e+01 -4.75125451e+01 6.06885368e+01 | 5.98966063e+01 -4.75125451e+01 6.06885368e+01 61 -3.46039104e-01 9.79830066e-01 -3.17446346e-01 | -3.46039104e-01 9.79830066e-01 -3.17446346e-01 62 -4.61026283e+01 3.69523627e+01 2.07852188e+01 | -4.61026283e+01 3.69523627e+01 2.07852188e+01 63 -6.33896359e-02 -9.55688095e-01 -3.50421670e-01 | -6.33896359e-02 -9.55688095e-01 -3.50421670e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [63, 13, 23, 20, 35, 48, 14, 33, 16, 39, 15, 32, 43, 1, 6, 10, 8, 37, 19, 18, 3, 29, 52, 2, 61, 34, 51, 55, 60, 21, 46, 36, 11, 7, 25, 4, 31, 17, 42, 9, 45, 47, 38, 12, 58, 40, 30, 41, 5, 53, 56, 26, 22, 49, 62, 27, 50, 59, 44, 57, 28, 24, 54, 0] 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)) = 230.38333837810296 V(r_1,...,r_N) = 230.3833383781043 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 -9.15363409e+00 -5.67670629e+00 -8.11106178e+00 | -9.15363409e+00 -5.67670629e+00 -8.11106178e+00 1 -1.63967960e+02 -2.74717064e+02 8.17545194e+01 | -1.63967960e+02 -2.74717064e+02 8.17545194e+01 2 1.65459356e+02 2.95876412e+02 -1.07474383e+02 | 1.65459356e+02 2.95876412e+02 -1.07474383e+02 3 -1.17768462e+02 1.17472191e+01 -2.08274254e+02 | -1.17768462e+02 1.17472191e+01 -2.08274254e+02 4 4.16458204e+00 -1.50883531e+01 3.46450728e+01 | 4.16458204e+00 -1.50883531e+01 3.46450728e+01 5 1.96977289e+00 -3.06822260e+00 -2.36276779e+00 | 1.96977289e+00 -3.06822260e+00 -2.36276779e+00 6 1.80030474e+00 -5.15778895e-01 -4.11983341e-01 | 1.80030474e+00 -5.15778895e-01 -4.11983341e-01 7 -3.78581480e+00 -6.30828355e+00 -3.59033463e+00 | -3.78581480e+00 -6.30828355e+00 -3.59033463e+00 8 -1.80179657e-01 8.26918538e-01 5.75493364e-01 | -1.80179657e-01 8.26918538e-01 5.75493364e-01 9 -2.17312741e-01 -4.00471317e+00 2.84178156e+00 | -2.17312741e-01 -4.00471317e+00 2.84178156e+00 10 -7.88199214e+01 -4.47035391e+01 -2.43351572e+01 | -7.88199214e+01 -4.47035391e+01 -2.43351572e+01 11 7.68888513e+01 4.93289412e+01 2.33414563e+01 | 7.68888513e+01 4.93289412e+01 2.33414563e+01 12 -7.79785635e+01 -1.06443841e+02 -3.79480706e+01 | -7.79785635e+01 -1.06443841e+02 -3.79480706e+01 13 7.80748425e+01 1.06836443e+02 3.70138604e+01 | 7.80748425e+01 1.06836443e+02 3.70138604e+01 14 1.19537208e+02 -1.28886982e+01 2.07592508e+02 | 1.19537208e+02 -1.28886982e+01 2.07592508e+02 15 -9.90635795e-01 -8.45536367e+00 1.21457704e+01 | -9.90635795e-01 -8.45536367e+00 1.21457704e+01 16 -6.32182129e+00 -6.85978571e+00 -3.39485559e+00 | -6.32182129e+00 -6.85978571e+00 -3.39485559e+00 17 -2.55835622e+01 3.79481016e+01 -7.37540669e+01 | -2.55835622e+01 3.79481016e+01 -7.37540669e+01 18 -2.82499910e+00 -4.28038254e+00 -1.62418931e+00 | -2.82499910e+00 -4.28038254e+00 -1.62418931e+00 19 2.38017276e+00 4.40167001e+00 1.52497116e+00 | 2.38017276e+00 4.40167001e+00 1.52497116e+00 20 2.51633532e+01 -2.42596559e+01 7.09712065e+01 | 2.51633532e+01 -2.42596559e+01 7.09712065e+01 21 5.24126848e+00 4.37310772e+00 2.46419465e+00 | 5.24126848e+00 4.37310772e+00 2.46419465e+00 22 -2.10368838e+00 -2.85128051e+00 -2.16242370e+00 | -2.10368838e+00 -2.85128051e+00 -2.16242370e+00 23 3.11141316e+00 1.33204653e+00 2.85156417e+00 | 3.11141316e+00 1.33204653e+00 2.85156417e+00 24 -4.18228320e+01 1.29641469e+01 -5.58077309e+01 | -4.18228320e+01 1.29641469e+01 -5.58077309e+01 25 3.98756258e+01 -1.02223847e+01 5.04706005e+01 | 3.98756258e+01 -1.02223847e+01 5.04706005e+01 26 -3.90794659e-01 -3.11744622e-01 1.00099923e+00 | -3.90794659e-01 -3.11744622e-01 1.00099923e+00 27 -1.05995035e+00 -7.66797734e-01 1.25295836e-01 | -1.05995035e+00 -7.66797734e-01 1.25295836e-01 28 4.80471195e+00 7.16613102e+00 -5.52430399e+00 | 4.80471195e+00 7.16613102e+00 -5.52430399e+00 29 1.82711980e+00 -2.50961658e+00 -1.92045557e-01 | 1.82711980e+00 -2.50961658e+00 -1.92045557e-01 30 8.39994997e-01 -9.49250679e-01 9.96012734e-01 | 8.39994997e-01 -9.49250679e-01 9.96012734e-01 31 -1.03090759e+02 1.54191733e+02 -6.00760618e+01 | -1.03090759e+02 1.54191733e+02 -6.00760618e+01 32 9.30545339e-01 6.56201167e-01 -1.42812769e-02 | 9.30545339e-01 6.56201167e-01 -1.42812769e-02 33 -1.05207315e+02 1.16212417e+02 -1.45651588e+02 | -1.05207315e+02 1.16212417e+02 -1.45651588e+02 34 6.87667271e-02 -4.65255670e+00 5.80822466e+00 | 6.87667271e-02 -4.65255670e+00 5.80822466e+00 35 5.54761271e+00 -1.40106081e+01 -2.19396162e+01 | 5.54761271e+00 -1.40106081e+01 -2.19396162e+01 36 1.04607886e+02 -1.17400961e+02 1.44148675e+02 | 1.04607886e+02 -1.17400961e+02 1.44148675e+02 37 -8.88724619e+01 -3.65447159e+01 5.40126829e+01 | -8.88724619e+01 -3.65447159e+01 5.40126829e+01 38 6.10750859e-01 -2.43682818e+00 -1.20473925e+00 | 6.10750859e-01 -2.43682818e+00 -1.20473925e+00 39 4.97482343e-01 1.89955231e+00 4.50313493e-01 | 4.97482343e-01 1.89955231e+00 4.50313493e-01 40 -2.02120228e-01 1.63348285e+00 7.99697944e-01 | -2.02120228e-01 1.63348285e+00 7.99697944e-01 41 -1.79346891e+02 2.42750160e+02 -1.89884661e+02 | -1.79346891e+02 2.42750160e+02 -1.89884661e+02 42 -4.03875281e+00 -8.65555360e+00 -3.73267720e+00 | -4.03875281e+00 -8.65555360e+00 -3.73267720e+00 43 3.35991377e+00 8.32837994e+00 4.40023778e+00 | 3.35991377e+00 8.32837994e+00 4.40023778e+00 44 1.65491002e+02 -2.54765547e+02 1.76128807e+02 | 1.65491002e+02 -2.54765547e+02 1.76128807e+02 45 1.25399795e+01 1.23019178e+01 1.30642189e+01 | 1.25399795e+01 1.23019178e+01 1.30642189e+01 46 8.79483912e+01 3.56022169e+01 -5.53755659e+01 | 8.79483912e+01 3.56022169e+01 -5.53755659e+01 47 -2.06136098e+01 -1.15089011e+01 9.14045893e+00 | -2.06136098e+01 -1.15089011e+01 9.14045893e+00 48 -1.65160979e+00 -2.87471245e+00 -2.20129365e+00 | -1.65160979e+00 -2.87471245e+00 -2.20129365e+00 49 -8.58592057e+01 -5.10113367e+01 3.45839084e+01 | -8.58592057e+01 -5.10113367e+01 3.45839084e+01 50 8.57414366e+01 4.32165324e+01 -3.77134932e+01 | 8.57414366e+01 4.32165324e+01 -3.77134932e+01 51 4.84931577e+00 7.68785049e+00 3.59317701e+00 | 4.84931577e+00 7.68785049e+00 3.59317701e+00 52 -5.79811752e+00 1.14788586e+01 2.89450773e+01 | -5.79811752e+00 1.14788586e+01 2.89450773e+01 53 -8.03877358e+00 -3.32657532e+00 3.70570777e+00 | -8.03877358e+00 -3.32657532e+00 3.70570777e+00 54 -1.04181332e+00 2.43142762e+00 1.32797657e+00 | -1.04181332e+00 2.43142762e+00 1.32797657e+00 55 -3.76052492e-01 1.25144399e-01 -4.01849425e-01 | -3.76052492e-01 1.25144399e-01 -4.01849425e-01 56 3.38064294e+00 5.61592926e+00 -3.82605996e+00 | 3.38064294e+00 5.61592926e+00 -3.82605996e+00 57 2.94004178e+00 -5.07601522e-01 -3.11394153e-01 | 2.94004178e+00 -5.07601522e-01 -3.11394153e-01 58 1.00827971e+02 -1.52479624e+02 6.03421887e+01 | 1.00827971e+02 -1.52479624e+02 6.03421887e+01 59 -9.90572601e-01 -9.73761120e-01 -1.91170354e-01 | -9.90572601e-01 -9.73761120e-01 -1.91170354e-01 60 2.09599956e+01 1.46145502e+01 -8.84764317e+00 | 2.09599956e+01 1.46145502e+01 -8.84764317e+00 61 -8.48765132e-01 1.52178848e-01 -4.84131194e-01 | -8.48765132e-01 1.52178848e-01 -4.84131194e-01 62 7.48266328e+00 4.98840708e+00 -3.31526240e+00 | 7.48266328e+00 4.98840708e+00 -3.31526240e+00 63 2.39765452e-02 -6.57331489e-01 -6.27543014e-01 | 2.39765452e-02 -6.57331489e-01 -6.27543014e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Fe (Configuration in file "config-Fe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [28, 2, 1, 41, 26, 33, 31, 24, 9, 8, 42, 49, 25, 30, 46, 20, 32, 36, 61, 40, 15, 44, 34, 37, 7, 12, 4, 47, 0, 51, 13, 6, 16, 5, 22, 55, 17, 23, 54, 50, 19, 3, 10, 63, 21, 53, 14, 27, 56, 11, 39, 29, 58, 45, 38, 35, 48, 59, 52, 57, 62, 18, 60, 43] 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)) = 264.8946927947656 V(r_1,...,r_N) = 264.89469279476566 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 -3.81497270e+00 -6.35901182e+00 -2.29165180e+00 | -3.81497270e+00 -6.35901182e+00 -2.29165180e+00 1 -3.33858029e+01 4.61679558e+01 -4.14417194e+01 | -3.33858029e+01 4.61679558e+01 -4.14417194e+01 2 -7.85794889e-01 -4.06664869e+00 -3.38139687e+00 | -7.85794889e-01 -4.06664869e+00 -3.38139687e+00 3 1.24600679e+01 -3.33514450e+00 -1.08054845e+01 | 1.24600679e+01 -3.33514450e+00 -1.08054845e+01 4 3.67996164e+01 -3.81160487e+01 4.44925278e+01 | 3.67996164e+01 -3.81160487e+01 4.44925278e+01 5 -2.78935084e-02 1.69298874e+00 -2.86679532e-01 | -2.78935084e-02 1.69298874e+00 -2.86679532e-01 6 -1.57240854e+00 -9.08051798e-01 -2.06638646e+00 | -1.57240854e+00 -9.08051798e-01 -2.06638646e+00 7 -1.04009335e+02 -7.79996328e+01 2.92658970e+01 | -1.04009335e+02 -7.79996328e+01 2.92658970e+01 8 -2.21138814e-01 -2.58944909e-02 3.99721388e-01 | -2.21138814e-01 -2.58944909e-02 3.99721388e-01 9 -6.94740587e+01 1.24737251e+02 -7.50407868e+01 | -6.94740587e+01 1.24737251e+02 -7.50407868e+01 10 -5.23464272e+01 -6.92626075e+01 -8.49689411e+01 | -5.23464272e+01 -6.92626075e+01 -8.49689411e+01 11 5.04518066e+01 6.96549706e+01 8.58072402e+01 | 5.04518066e+01 6.96549706e+01 8.58072402e+01 12 7.75817949e+01 -1.34450354e+02 7.08039401e+01 | 7.75817949e+01 -1.34450354e+02 7.08039401e+01 13 -1.52884308e+00 7.62818308e-01 -1.69216896e-01 | -1.52884308e+00 7.62818308e-01 -1.69216896e-01 14 -1.90373645e+01 -4.59767740e-01 -1.13285023e+01 | -1.90373645e+01 -4.59767740e-01 -1.13285023e+01 15 -4.88505250e+01 -1.01986559e+02 6.78609894e+01 | -4.88505250e+01 -1.01986559e+02 6.78609894e+01 16 8.09776710e-01 4.44028268e-01 1.79504657e+00 | 8.09776710e-01 4.44028268e-01 1.79504657e+00 17 -1.52721733e+01 -1.72147599e+01 2.35416235e+01 | -1.52721733e+01 -1.72147599e+01 2.35416235e+01 18 1.29333762e+01 1.50233115e+01 -2.64875548e+01 | 1.29333762e+01 1.50233115e+01 -2.64875548e+01 19 -8.21368897e+00 2.79687072e+00 -8.62757747e-01 | -8.21368897e+00 2.79687072e+00 -8.62757747e-01 20 8.92671632e+01 8.25107897e+01 -9.42406390e+00 | 8.92671632e+01 8.25107897e+01 -9.42406390e+00 21 9.11614366e+00 -4.86160090e+00 -6.53279040e+00 | 9.11614366e+00 -4.86160090e+00 -6.53279040e+00 22 1.36185357e+00 -7.19240832e-01 -1.08585540e-02 | 1.36185357e+00 -7.19240832e-01 -1.08585540e-02 23 -1.19047059e+01 1.00637459e+01 -1.12498526e+01 | -1.19047059e+01 1.00637459e+01 -1.12498526e+01 24 -1.03644678e+02 -1.67249699e+02 -7.68564405e+01 | -1.03644678e+02 -1.67249699e+02 -7.68564405e+01 25 9.18968406e+01 1.52545689e+02 8.05474404e+01 | 9.18968406e+01 1.52545689e+02 8.05474404e+01 26 1.54777393e+01 1.60813861e+01 -6.43840579e+00 | 1.54777393e+01 1.60813861e+01 -6.43840579e+00 27 -9.13668163e-01 -9.08146281e-01 3.38161892e-01 | -9.13668163e-01 -9.08146281e-01 3.38161892e-01 28 6.07062302e+01 1.13202795e+02 -5.18608843e+01 | 6.07062302e+01 1.13202795e+02 -5.18608843e+01 29 -1.64783058e+00 2.39450601e-01 3.19951132e-01 | -1.64783058e+00 2.39450601e-01 3.19951132e-01 30 1.59377090e+01 -2.29232018e+01 -1.27467123e+02 | 1.59377090e+01 -2.29232018e+01 -1.27467123e+02 31 -7.74875279e+00 2.13673828e+01 1.31930953e+02 | -7.74875279e+00 2.13673828e+01 1.31930953e+02 32 6.79730324e-01 2.20457778e-01 -3.02186221e-01 | 6.79730324e-01 2.20457778e-01 -3.02186221e-01 33 -9.92547909e+01 5.68286591e+01 -1.78199829e+01 | -9.92547909e+01 5.68286591e+01 -1.78199829e+01 34 -8.73855892e+01 -8.03120136e+01 -5.57365685e+01 | -8.73855892e+01 -8.03120136e+01 -5.57365685e+01 35 9.47429869e+01 8.60053782e+01 5.10387999e+01 | 9.47429869e+01 8.60053782e+01 5.10387999e+01 36 9.52135836e+01 -7.20230175e+01 2.01810375e+01 | 9.52135836e+01 -7.20230175e+01 2.01810375e+01 37 -1.10414380e+00 -4.86200828e-01 9.75137738e-01 | -1.10414380e+00 -4.86200828e-01 9.75137738e-01 38 -1.77174383e+01 -4.21638730e+00 -3.86218398e+01 | -1.77174383e+01 -4.21638730e+00 -3.86218398e+01 39 -2.96032755e+00 -8.13682315e+00 5.42036788e+01 | -2.96032755e+00 -8.13682315e+00 5.42036788e+01 40 -9.46993874e+00 -7.29183129e+00 -6.43412990e+00 | -9.46993874e+00 -7.29183129e+00 -6.43412990e+00 41 2.32119388e+00 4.83942239e+01 -4.15340218e+01 | 2.32119388e+00 4.83942239e+01 -4.15340218e+01 42 1.02588541e+01 2.16076265e+01 -1.22177731e+01 | 1.02588541e+01 2.16076265e+01 -1.22177731e+01 43 -7.36693731e-02 9.23568130e-01 8.83184695e-01 | -7.36693731e-02 9.23568130e-01 8.83184695e-01 44 -4.02451466e+00 -6.21061455e+01 6.13297876e+01 | -4.02451466e+00 -6.21061455e+01 6.13297876e+01 45 -9.11323268e-01 1.09128775e+00 -1.44388615e+00 | -9.11323268e-01 1.09128775e+00 -1.44388615e+00 46 1.56357690e+00 9.28999692e-01 -1.54181548e+00 | 1.56357690e+00 9.28999692e-01 -1.54181548e+00 47 -2.68882123e+01 -4.15207306e+01 3.84312686e+01 | -2.68882123e+01 -4.15207306e+01 3.84312686e+01 48 -2.49926611e+00 -7.73331848e+00 -1.00475466e+00 | -2.49926611e+00 -7.73331848e+00 -1.00475466e+00 49 3.16303964e+01 -2.59942244e+01 -1.00652618e+02 | 3.16303964e+01 -2.59942244e+01 -1.00652618e+02 50 4.91514256e+00 -5.09366801e+00 1.49532418e+01 | 4.91514256e+00 -5.09366801e+00 1.49532418e+01 51 -4.11697499e+01 9.20846631e+01 -6.30582993e+01 | -4.11697499e+01 9.20846631e+01 -6.30582993e+01 52 1.58517050e+01 1.98641335e+01 -1.42747400e+01 | 1.58517050e+01 1.98641335e+01 -1.42747400e+01 53 -1.93735473e+01 -2.19013636e+01 3.75565260e+01 | -1.93735473e+01 -2.19013636e+01 3.75565260e+01 54 -2.70703289e+01 3.30622432e+01 1.02011379e+02 | -2.70703289e+01 3.30622432e+01 1.02011379e+02 55 1.98164999e-01 -5.47846608e-01 -6.72224705e-01 | 1.98164999e-01 -5.47846608e-01 -6.72224705e-01 56 -3.67951743e+00 -4.48976736e+00 -8.65788694e+00 | -3.67951743e+00 -4.48976736e+00 -8.65788694e+00 57 -1.19139693e+01 2.48685556e+01 -3.44980135e+01 | -1.19139693e+01 2.48685556e+01 -3.44980135e+01 58 -3.74590264e+01 -3.80106825e+01 -4.29507520e+01 | -3.74590264e+01 -3.80106825e+01 -4.29507520e+01 59 3.96900488e+01 3.60224696e+01 4.47136150e+01 | 3.96900488e+01 3.60224696e+01 4.47136150e+01 60 4.56842872e+01 2.32441916e+01 3.22514083e+00 | 4.56842872e+01 2.32441916e+01 3.22514083e+00 61 -5.83245112e-01 -4.10059953e-01 -8.55464910e-01 | -5.83245112e-01 -4.10059953e-01 -8.55464910e-01 62 6.04744515e+01 -7.06819881e+01 2.52993729e+01 | 6.04744515e+01 -7.06819881e+01 2.52993729e+01 63 -8.55790062e-02 -6.35453312e-01 -6.57207028e-01 | -8.55790062e-02 -6.35453312e-01 -6.57207028e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [60, 37, 52, 14, 13, 26, 22, 15, 47, 28, 17, 31, 54, 4, 3, 7, 49, 10, 50, 27, 33, 45, 6, 53, 56, 55, 5, 19, 9, 35, 51, 11, 48, 20, 59, 29, 57, 1, 46, 58, 61, 63, 62, 44, 43, 21, 38, 8, 32, 16, 18, 30, 2, 23, 12, 25, 24, 36, 39, 34, 0, 40, 42, 41] 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)) = 150.6382326506668 V(r_1,...,r_N) = 150.6382326506668 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 -3.67169190e-01 -8.59071378e-01 -7.64047021e-01 | -3.67169190e-01 -8.59071378e-01 -7.64047021e-01 1 1.58831006e+01 -4.92659812e+01 -1.96670948e+01 | 1.58831006e+01 -4.92659812e+01 -1.96670948e+01 2 -1.63836761e+00 -1.40946835e+00 -3.97820667e+00 | -1.63836761e+00 -1.40946835e+00 -3.97820667e+00 3 2.91019843e+00 1.90411952e+00 1.36482581e+00 | 2.91019843e+00 1.90411952e+00 1.36482581e+00 4 4.30170181e-01 -1.05993650e+00 2.07238680e-01 | 4.30170181e-01 -1.05993650e+00 2.07238680e-01 5 -1.60926127e+01 -9.53331094e+00 2.18778142e+01 | -1.60926127e+01 -9.53331094e+00 2.18778142e+01 6 -2.03474455e+01 4.83126945e+01 1.76224821e+01 | -2.03474455e+01 4.83126945e+01 1.76224821e+01 7 -4.27983902e+00 4.70826548e-01 -5.00264400e+00 | -4.27983902e+00 4.70826548e-01 -5.00264400e+00 8 -4.06780820e+00 -2.40453869e+00 -2.98332939e+00 | -4.06780820e+00 -2.40453869e+00 -2.98332939e+00 9 -7.05384043e+00 -4.95007977e+00 -1.06739183e+00 | -7.05384043e+00 -4.95007977e+00 -1.06739183e+00 10 6.21436342e+00 -2.42504589e-02 -9.80749891e+00 | 6.21436342e+00 -2.42504589e-02 -9.80749891e+00 11 3.79551250e+00 5.39949325e+00 -7.79091907e-01 | 3.79551250e+00 5.39949325e+00 -7.79091907e-01 12 -3.84849165e+00 -1.29650447e+01 1.20659462e+00 | -3.84849165e+00 -1.29650447e+01 1.20659462e+00 13 7.87914927e+00 1.07429029e+01 7.69248998e+00 | 7.87914927e+00 1.07429029e+01 7.69248998e+00 14 1.51655973e+01 9.16265198e+00 -2.40620477e+01 | 1.51655973e+01 9.16265198e+00 -2.40620477e+01 15 1.23768818e-01 -8.34349901e+00 -7.91653038e+00 | 1.23768818e-01 -8.34349901e+00 -7.91653038e+00 16 -9.26911262e+00 -1.46559878e+01 -5.37604358e+00 | -9.26911262e+00 -1.46559878e+01 -5.37604358e+00 17 8.59793100e+00 1.29034056e+01 4.91211392e+00 | 8.59793100e+00 1.29034056e+01 4.91211392e+00 18 -1.11260033e+01 -1.12352171e+01 -1.38030846e+01 | -1.11260033e+01 -1.12352171e+01 -1.38030846e+01 19 1.16875596e+01 1.27588338e+01 1.22904331e+01 | 1.16875596e+01 1.27588338e+01 1.22904331e+01 20 -5.90685712e+00 -8.87255429e+00 -1.00222049e+01 | -5.90685712e+00 -8.87255429e+00 -1.00222049e+01 21 3.87894401e+00 3.27994150e+00 9.68088019e+00 | 3.87894401e+00 3.27994150e+00 9.68088019e+00 22 -2.75261204e+00 -4.59316376e-01 -8.68396345e-01 | -2.75261204e+00 -4.59316376e-01 -8.68396345e-01 23 -2.64104650e-01 3.33722466e+00 -2.08720787e+00 | -2.64104650e-01 3.33722466e+00 -2.08720787e+00 24 -1.03105137e-01 2.06610697e-01 -6.89665820e-01 | -1.03105137e-01 2.06610697e-01 -6.89665820e-01 25 -2.00306241e+00 5.54337840e+00 -2.14761789e+00 | -2.00306241e+00 5.54337840e+00 -2.14761789e+00 26 -2.23075957e+00 -1.16142509e+01 -5.83971660e+00 | -2.23075957e+00 -1.16142509e+01 -5.83971660e+00 27 2.18129509e+00 1.16848438e+01 5.84742367e+00 | 2.18129509e+00 1.16848438e+01 5.84742367e+00 28 4.65888288e+00 1.29298302e+00 1.08369387e+00 | 4.65888288e+00 1.29298302e+00 1.08369387e+00 29 1.05153449e+00 -9.21163848e-01 -8.37520290e-01 | 1.05153449e+00 -9.21163848e-01 -8.37520290e-01 30 3.77992131e+00 5.00847772e+00 -5.77422551e+00 | 3.77992131e+00 5.00847772e+00 -5.77422551e+00 31 -1.82340007e+00 2.05552661e+00 -2.45204298e+00 | -1.82340007e+00 2.05552661e+00 -2.45204298e+00 32 -7.32482496e-01 -9.12550780e-01 -1.89987863e+00 | -7.32482496e-01 -9.12550780e-01 -1.89987863e+00 33 -2.00563001e+01 1.26186540e+01 -1.66638520e+01 | -2.00563001e+01 1.26186540e+01 -1.66638520e+01 34 -4.02882488e+00 -1.76101447e+00 -1.15754754e+00 | -4.02882488e+00 -1.76101447e+00 -1.15754754e+00 35 -3.39342886e+01 3.15576218e+01 2.88423962e+00 | -3.39342886e+01 3.15576218e+01 2.88423962e+00 36 2.14774823e+01 -1.36860331e+01 1.79195752e+01 | 2.14774823e+01 -1.36860331e+01 1.79195752e+01 37 -7.18948591e-02 -1.10206435e+00 2.34948825e+00 | -7.18948591e-02 -1.10206435e+00 2.34948825e+00 38 -1.40626078e+01 -3.01627584e+01 -1.23625273e+01 | -1.40626078e+01 -3.01627584e+01 -1.23625273e+01 39 5.80305400e+00 2.43190604e+01 1.93463871e+01 | 5.80305400e+00 2.43190604e+01 1.93463871e+01 40 -2.57473778e+00 -8.22634250e+00 -3.45348218e+00 | -2.57473778e+00 -8.22634250e+00 -3.45348218e+00 41 7.17135046e+00 -1.01249719e+01 1.39553986e+00 | 7.17135046e+00 -1.01249719e+01 1.39553986e+00 42 -1.17582598e+01 -1.23044337e+01 -3.82300142e+00 | -1.17582598e+01 -1.23044337e+01 -3.82300142e+00 43 2.56435472e+01 1.37845482e+01 8.93602265e+00 | 2.56435472e+01 1.37845482e+01 8.93602265e+00 44 2.26275294e+00 -3.38839310e+00 1.36069955e+00 | 2.26275294e+00 -3.38839310e+00 1.36069955e+00 45 1.51339530e+00 9.24515844e-01 1.24612998e+00 | 1.51339530e+00 9.24515844e-01 1.24612998e+00 46 2.93403204e+01 -1.76862206e+01 1.10834577e+01 | 2.93403204e+01 -1.76862206e+01 1.10834577e+01 47 -4.83099161e-01 -4.48038396e-01 1.06564162e+00 | -4.83099161e-01 -4.48038396e-01 1.06564162e+00 48 -1.66979249e+00 -4.51159465e-01 -5.80415252e-01 | -1.66979249e+00 -4.51159465e-01 -5.80415252e-01 49 -3.35341147e+01 -1.67265189e+01 7.94320316e+00 | -3.35341147e+01 -1.67265189e+01 7.94320316e+00 50 2.89800269e+01 1.02095237e+01 -6.03540976e+00 | 2.89800269e+01 1.02095237e+01 -6.03540976e+00 51 5.35609319e+00 1.07691751e+01 4.86445129e+00 | 5.35609319e+00 1.07691751e+01 4.86445129e+00 52 6.51388204e+00 5.85250636e+00 -3.41673291e+00 | 6.51388204e+00 5.85250636e+00 -3.41673291e+00 53 -4.64557091e+00 -3.47852333e+00 4.76942100e+00 | -4.64557091e+00 -3.47852333e+00 4.76942100e+00 54 -2.02747390e+00 -5.31058702e-01 1.27813265e-01 | -2.02747390e+00 -5.31058702e-01 1.27813265e-01 55 8.42833436e-01 1.18141247e+00 9.61823637e-01 | 8.42833436e-01 1.18141247e+00 9.61823637e-01 56 -8.78632181e+00 6.36803842e+00 1.47510768e+00 | -8.78632181e+00 6.36803842e+00 1.47510768e+00 57 -9.33172409e+00 2.86943206e+00 -1.03118046e+00 | -9.33172409e+00 2.86943206e+00 -1.03118046e+00 58 -1.10330649e+01 -5.17451331e+00 -3.17897895e+00 | -1.10330649e+01 -5.17451331e+00 -3.17897895e+00 59 1.54041530e+01 8.95004661e+00 3.22329396e+00 | 1.54041530e+01 8.95004661e+00 3.22329396e+00 60 3.59403156e+00 -7.16550864e+00 1.50265694e+00 | 3.59403156e+00 -7.16550864e+00 1.50265694e+00 61 5.51782134e+00 3.59959152e+00 5.78638941e+00 | 5.51782134e+00 3.59959152e+00 5.78638941e+00 62 2.46928230e+00 3.56281145e+00 -3.99899730e+00 | 2.46928230e+00 3.56281145e+00 -3.99899730e+00 63 1.77719400e+00 1.27292254e+00 1.50028066e+00 | 1.77719400e+00 1.27292254e+00 1.50028066e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Si (Configuration in file "config-Si.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [56, 3, 48, 1, 21, 44, 42, 13, 22, 25, 18, 23, 27, 7, 46, 39, 35, 41, 10, 24, 36, 4, 8, 11, 19, 9, 32, 12, 54, 37, 57, 53, 26, 60, 61, 16, 20, 29, 52, 15, 59, 17, 6, 45, 5, 43, 14, 62, 2, 50, 49, 55, 38, 31, 28, 51, 0, 30, 63, 40, 33, 34, 47, 58] 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)) = 451.2050957456348 V(r_1,...,r_N) = 451.20509574563533 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -4.79529694e+01 -7.39444795e+01 -5.69900972e+01 | -4.79529694e+01 -7.39444795e+01 -5.69900972e+01 1 5.36927521e+01 7.27225668e+01 5.61391289e+01 | 5.36927521e+01 7.27225668e+01 5.61391289e+01 2 -7.65043018e-01 7.53098836e-01 2.99418824e+00 | -7.65043018e-01 7.53098836e-01 2.99418824e+00 3 -2.50603131e+01 -8.10182788e+00 8.84038844e+00 | -2.50603131e+01 -8.10182788e+00 8.84038844e+00 4 -4.02004802e+01 -6.17345671e+01 -1.66274232e+01 | -4.02004802e+01 -6.17345671e+01 -1.66274232e+01 5 -2.70021763e+01 -1.95055577e+01 1.85409936e+01 | -2.70021763e+01 -1.95055577e+01 1.85409936e+01 6 -5.03253538e+00 -1.58336349e+00 -1.79127646e+00 | -5.03253538e+00 -1.58336349e+00 -1.79127646e+00 7 -1.31544396e+02 -1.72520159e+02 1.00774782e+02 | -1.31544396e+02 -1.72520159e+02 1.00774782e+02 8 -4.18105822e+00 -9.69643219e+00 -1.30329770e+01 | -4.18105822e+00 -9.69643219e+00 -1.30329770e+01 9 -1.82686597e+02 1.11611802e+02 -9.84134098e+01 | -1.82686597e+02 1.11611802e+02 -9.84134098e+01 10 3.68257195e-01 3.08493359e-01 4.34331348e+00 | 3.68257195e-01 3.08493359e-01 4.34331348e+00 11 7.07335321e+01 -6.74673291e+01 -7.06227731e+01 | 7.07335321e+01 -6.74673291e+01 -7.06227731e+01 12 1.88121999e+02 -9.69384383e+01 1.13163900e+02 | 1.88121999e+02 -9.69384383e+01 1.13163900e+02 13 4.03898420e+01 -3.66603226e+01 -4.29288033e+01 | 4.03898420e+01 -3.66603226e+01 -4.29288033e+01 14 6.66552130e+01 4.43936048e+01 -1.37818587e+01 | 6.66552130e+01 4.43936048e+01 -1.37818587e+01 15 -5.78864713e+01 -2.64920486e+01 7.20722961e+01 | -5.78864713e+01 -2.64920486e+01 7.20722961e+01 16 -1.57135241e+02 -2.47387245e+02 -1.86453909e+02 | -1.57135241e+02 -2.47387245e+02 -1.86453909e+02 17 1.71846835e+02 2.41708645e+02 1.95142481e+02 | 1.71846835e+02 2.41708645e+02 1.95142481e+02 18 -2.86250561e+01 -3.81862398e+01 -3.61819926e+01 | -2.86250561e+01 -3.81862398e+01 -3.61819926e+01 19 2.70673567e+01 3.62514853e+01 3.21814086e+01 | 2.70673567e+01 3.62514853e+01 3.21814086e+01 20 1.36926465e+02 1.76333420e+02 -1.05120402e+02 | 1.36926465e+02 1.76333420e+02 -1.05120402e+02 21 4.35369253e+01 -3.04592934e+01 -4.37936947e+01 | 4.35369253e+01 -3.04592934e+01 -4.37936947e+01 22 -1.06572740e+01 -8.22157254e-01 6.49631629e+00 | -1.06572740e+01 -8.22157254e-01 6.49631629e+00 23 1.90584230e+00 4.62929431e+00 1.89866179e+00 | 1.90584230e+00 4.62929431e+00 1.89866179e+00 24 1.40318618e+01 1.59871584e+01 -2.04814839e+01 | 1.40318618e+01 1.59871584e+01 -2.04814839e+01 25 9.55044533e+01 -3.96957814e+01 -2.17997243e+01 | 9.55044533e+01 -3.96957814e+01 -2.17997243e+01 26 -3.75589691e+00 -4.65167139e+00 -4.29765071e+00 | -3.75589691e+00 -4.65167139e+00 -4.29765071e+00 27 3.64249997e+00 5.48681860e+00 5.23708239e+00 | 3.64249997e+00 5.48681860e+00 5.23708239e+00 28 9.91834091e+00 1.05070325e+02 8.42451983e+00 | 9.91834091e+00 1.05070325e+02 8.42451983e+00 29 1.66364526e+01 -2.95303961e+01 -2.31143628e+01 | 1.66364526e+01 -2.95303961e+01 -2.31143628e+01 30 -9.46546332e+01 4.14421226e+01 2.00223676e+01 | -9.46546332e+01 4.14421226e+01 2.00223676e+01 31 -1.84220666e+02 1.67080493e+02 -8.59110567e+01 | -1.84220666e+02 1.67080493e+02 -8.59110567e+01 32 -2.70394162e+01 -7.25888550e+01 -7.72442985e+01 | -2.70394162e+01 -7.25888550e+01 -7.72442985e+01 33 -2.17702649e+01 8.47830530e+01 3.39585317e+01 | -2.17702649e+01 8.47830530e+01 3.39585317e+01 34 -1.26282775e+01 9.90508606e+00 1.21387229e+01 | -1.26282775e+01 9.90508606e+00 1.21387229e+01 35 -1.43260170e-01 -1.76839179e+01 -3.00699813e+00 | -1.43260170e-01 -1.76839179e+01 -3.00699813e+00 36 5.77148394e+01 -2.93033218e+01 3.05172043e+01 | 5.77148394e+01 -2.93033218e+01 3.05172043e+01 37 2.97721071e-01 7.94370159e+00 6.76961591e+00 | 2.97721071e-01 7.94370159e+00 6.76961591e+00 38 -1.83622583e+01 4.22401704e+00 -9.92419405e-01 | -1.83622583e+01 4.22401704e+00 -9.92419405e-01 39 4.84763264e+00 2.74992334e-01 9.81475128e+00 | 4.84763264e+00 2.74992334e-01 9.81475128e+00 40 -4.54724928e+00 -2.91414527e+00 -1.17130321e+01 | -4.54724928e+00 -2.91414527e+00 -1.17130321e+01 41 1.67992065e+00 8.60781569e+00 8.59110741e+00 | 1.67992065e+00 8.60781569e+00 8.59110741e+00 42 -4.65309059e+01 4.04897362e+01 4.13993306e+01 | -4.65309059e+01 4.04897362e+01 4.13993306e+01 43 6.15131275e-01 -2.27957823e+00 -2.41708419e+00 | 6.15131275e-01 -2.27957823e+00 -2.41708419e+00 44 -5.44376799e+01 -6.24847964e+01 -1.99992746e+01 | -5.44376799e+01 -6.24847964e+01 -1.99992746e+01 45 5.63060230e+01 6.11888733e+01 2.10138575e+01 | 5.63060230e+01 6.11888733e+01 2.10138575e+01 46 -4.92706436e+01 -5.37651123e+01 -7.02514656e+01 | -4.92706436e+01 -5.37651123e+01 -7.02514656e+01 47 6.01435749e+00 2.37093242e+01 9.83188353e+01 | 6.01435749e+00 2.37093242e+01 9.83188353e+01 48 -1.05268271e+02 -1.11161199e+02 -1.27024281e+02 | -1.05268271e+02 -1.11161199e+02 -1.27024281e+02 49 1.02277674e+02 1.10694236e+02 1.28072874e+02 | 1.02277674e+02 1.10694236e+02 1.28072874e+02 50 -4.83632581e+01 1.95046028e+01 2.77442561e+01 | -4.83632581e+01 1.95046028e+01 2.77442561e+01 51 8.89981956e+00 1.10254674e+01 9.66268557e+00 | 8.89981956e+00 1.10254674e+01 9.66268557e+00 52 -3.80671410e+01 -2.97333752e+00 -2.89132333e+01 | -3.80671410e+01 -2.97333752e+00 -2.89132333e+01 53 3.55361697e+01 1.30551711e+01 3.32628858e+01 | 3.55361697e+01 1.30551711e+01 3.32628858e+01 54 3.10897636e-01 -1.34803645e+00 -2.35175042e+00 | 3.10897636e-01 -1.34803645e+00 -2.35175042e+00 55 9.20301099e-01 9.28696345e-01 1.33648620e+00 | 9.20301099e-01 9.28696345e-01 1.33648620e+00 56 8.51862459e+00 1.27099466e+01 -4.27569968e-01 | 8.51862459e+00 1.27099466e+01 -4.27569968e-01 57 3.25042424e+01 -2.68428839e+01 -3.99038139e+01 | 3.25042424e+01 -2.68428839e+01 -3.99038139e+01 58 1.62329824e+02 -1.48209354e+02 1.08190668e+02 | 1.62329824e+02 -1.48209354e+02 1.08190668e+02 59 -1.84818589e-01 1.65260527e+00 2.70287991e+00 | -1.84818589e-01 1.65260527e+00 2.70287991e+00 60 4.24838679e+01 3.26138353e+01 -3.17603592e+01 | 4.24838679e+01 3.26138353e+01 -3.17603592e+01 61 -1.24599229e+00 3.35900771e-01 -1.89750632e+00 | -1.24599229e+00 3.35900771e-01 -1.89750632e+00 62 -3.96859015e+01 2.04404634e+01 2.98183071e+01 | -3.96859015e+01 2.04404634e+01 2.98183071e+01 63 6.67046977e+00 9.06499606e+00 9.66115410e+00 | 6.67046977e+00 9.06499606e+00 9.66115410e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Cu Fe Mg Si (Configuration in file "config-AlCuFeMgSi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [45, 39, 30, 52, 60, 34, 54, 42, 31, 48, 47, 13, 17, 11, 21, 46, 50, 12, 44, 51, 24, 14, 61, 28, 20, 38, 58, 40, 23, 29, 2, 8, 63, 59, 5, 49, 41, 53, 25, 1, 27, 36, 7, 57, 18, 0, 15, 10, 9, 35, 16, 19, 3, 37, 6, 55, 56, 43, 26, 33, 4, 22, 62, 32] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 162.78792347014127 V(r_1,...,r_N) = 162.78792347014144 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 2.62183050e-01 3.17621385e-01 3.44765364e-01 | 2.62183050e-01 3.17621385e-01 3.44765364e-01 1 -5.36264683e+01 -3.71434198e+01 5.63089119e+01 | -5.36264683e+01 -3.71434198e+01 5.63089119e+01 2 5.63269949e+01 4.04645517e+01 -6.55247678e+01 | 5.63269949e+01 4.04645517e+01 -6.55247678e+01 3 -3.00635449e+01 -1.68747932e+00 3.02667275e+01 | -3.00635449e+01 -1.68747932e+00 3.02667275e+01 4 -6.22454195e-01 -7.06040699e+00 2.63881471e+00 | -6.22454195e-01 -7.06040699e+00 2.63881471e+00 5 1.18355024e+00 1.09160903e+00 1.03214586e+00 | 1.18355024e+00 1.09160903e+00 1.03214586e+00 6 -1.36977939e+01 -1.90286453e+01 -3.43102355e+00 | -1.36977939e+01 -1.90286453e+01 -3.43102355e+00 7 9.12788892e+00 1.82615763e+01 1.03280085e+01 | 9.12788892e+00 1.82615763e+01 1.03280085e+01 8 -7.75086276e+00 -9.30331282e-01 -7.24652634e+00 | -7.75086276e+00 -9.30331282e-01 -7.24652634e+00 9 6.14858783e+00 2.82206336e+00 4.30736768e+00 | 6.14858783e+00 2.82206336e+00 4.30736768e+00 10 -3.62531269e+00 -4.28196143e+00 -4.29805711e+00 | -3.62531269e+00 -4.28196143e+00 -4.29805711e+00 11 3.43293312e+00 2.79130083e+00 3.87415918e+00 | 3.43293312e+00 2.79130083e+00 3.87415918e+00 12 1.55665447e+00 -3.64743134e-01 3.63903234e+00 | 1.55665447e+00 -3.64743134e-01 3.63903234e+00 13 4.86411785e+00 -8.82154989e+00 -3.58255519e+01 | 4.86411785e+00 -8.82154989e+00 -3.58255519e+01 14 3.92639794e+00 1.24074798e+00 -5.97125654e-01 | 3.92639794e+00 1.24074798e+00 -5.97125654e-01 15 5.32930436e+00 -2.45687904e+00 -7.65171597e-01 | 5.32930436e+00 -2.45687904e+00 -7.65171597e-01 16 2.53925549e-01 -6.68197142e-01 1.07260558e-01 | 2.53925549e-01 -6.68197142e-01 1.07260558e-01 17 -2.65765837e+01 -4.42661533e+01 5.62404390e+01 | -2.65765837e+01 -4.42661533e+01 5.62404390e+01 18 3.49343167e+01 3.85925725e+01 -6.74866652e+01 | 3.49343167e+01 3.85925725e+01 -6.74866652e+01 19 -9.92449108e+01 4.69074975e+01 -2.12174162e+01 | -9.92449108e+01 4.69074975e+01 -2.12174162e+01 20 -2.96150824e-01 2.48942610e+00 6.35136939e-01 | -2.96150824e-01 2.48942610e+00 6.35136939e-01 21 -1.74501737e+00 -1.53543738e+01 1.58694356e+01 | -1.74501737e+00 -1.53543738e+01 1.58694356e+01 22 -1.10186677e+01 4.90465474e+00 9.04039868e+00 | -1.10186677e+01 4.90465474e+00 9.04039868e+00 23 -1.04802997e+00 -8.82972456e-01 -1.03076259e-01 | -1.04802997e+00 -8.82972456e-01 -1.03076259e-01 24 3.12927071e+01 1.87814552e+00 -3.10891050e+01 | 3.12927071e+01 1.87814552e+00 -3.10891050e+01 25 -9.06869968e+01 -3.61258966e+01 8.28650071e+01 | -9.06869968e+01 -3.61258966e+01 8.28650071e+01 26 8.92845257e+01 3.10410002e+01 -8.51603492e+01 | 8.92845257e+01 3.10410002e+01 -8.51603492e+01 27 1.68623401e+00 2.83654096e+00 3.29986921e+00 | 1.68623401e+00 2.83654096e+00 3.29986921e+00 28 -2.18398973e+00 -2.28079030e+00 -2.23429976e+00 | -2.18398973e+00 -2.28079030e+00 -2.23429976e+00 29 2.40505772e+00 3.02094211e+00 3.04797447e+00 | 2.40505772e+00 3.02094211e+00 3.04797447e+00 30 1.00646916e+02 -2.82857757e+01 9.20784850e+00 | 1.00646916e+02 -2.82857757e+01 9.20784850e+00 31 -7.99712717e+00 6.02135635e+00 -9.07266328e+00 | -7.99712717e+00 6.02135635e+00 -9.07266328e+00 32 -9.36666354e+00 -1.48245623e+01 -1.58758886e+01 | -9.36666354e+00 -1.48245623e+01 -1.58758886e+01 33 1.10481182e+02 -9.48733716e+01 -7.47165975e+01 | 1.10481182e+02 -9.48733716e+01 -7.47165975e+01 34 -5.35035009e+01 -7.16025634e+01 -5.05781327e+01 | -5.35035009e+01 -7.16025634e+01 -5.05781327e+01 35 5.30704665e+01 6.01077397e+01 3.15135759e+01 | 5.30704665e+01 6.01077397e+01 3.15135759e+01 36 -6.63322364e+00 -5.36991534e+00 -1.13976918e+01 | -6.63322364e+00 -5.36991534e+00 -1.13976918e+01 37 7.57582284e+00 4.37669448e+00 1.29593264e+01 | 7.57582284e+00 4.37669448e+00 1.29593264e+01 38 -1.05894189e+02 1.11715333e+02 8.86835707e+01 | -1.05894189e+02 1.11715333e+02 8.86835707e+01 39 3.22624038e+00 -1.08053146e+00 9.18696780e-01 | 3.22624038e+00 -1.08053146e+00 9.18696780e-01 40 -3.26583925e+00 -3.22160155e+00 -1.19053276e+00 | -3.26583925e+00 -3.22160155e+00 -1.19053276e+00 41 2.34401498e+01 -3.88982704e+01 -3.41559160e+01 | 2.34401498e+01 -3.88982704e+01 -3.41559160e+01 42 -5.00449035e+00 7.31351801e+00 3.53055751e+01 | -5.00449035e+00 7.31351801e+00 3.53055751e+01 43 1.23016047e+01 -1.37592692e+01 -7.06409095e+00 | 1.23016047e+01 -1.37592692e+01 -7.06409095e+00 44 -4.88102650e+00 -7.56450490e+00 -8.61042220e+00 | -4.88102650e+00 -7.56450490e+00 -8.61042220e+00 45 8.71060007e+00 4.50837292e+00 1.07904780e+01 | 8.71060007e+00 4.50837292e+00 1.07904780e+01 46 -5.77740565e+01 -2.67279020e+00 2.17312134e+01 | -5.77740565e+01 -2.67279020e+00 2.17312134e+01 47 3.47833797e+01 4.54412762e+01 1.38549830e+01 | 3.47833797e+01 4.54412762e+01 1.38549830e+01 48 2.08128694e+00 1.05210601e+00 9.92041257e-01 | 2.08128694e+00 1.05210601e+00 9.92041257e-01 49 -4.42258941e+01 -1.14444421e+02 7.36721001e+01 | -4.42258941e+01 -1.14444421e+02 7.36721001e+01 50 6.32327017e+01 1.04400969e+02 -9.71279693e+01 | 6.32327017e+01 1.04400969e+02 -9.71279693e+01 51 -4.01840990e+00 2.89637830e+01 -1.65384145e+01 | -4.01840990e+00 2.89637830e+01 -1.65384145e+01 52 -2.33668038e+00 3.05575808e+00 2.45874408e+00 | -2.33668038e+00 3.05575808e+00 2.45874408e+00 53 -2.95392121e+00 6.62598800e+00 1.43246827e+01 | -2.95392121e+00 6.62598800e+00 1.43246827e+01 54 -2.17643451e+01 2.91105253e-01 1.68346499e+01 | -2.17643451e+01 2.91105253e-01 1.68346499e+01 55 2.81104074e+00 4.80901609e+00 3.91616069e+00 | 2.81104074e+00 4.80901609e+00 3.91616069e+00 56 -7.17001948e+00 5.12145428e+00 -9.54700858e-03 | -7.17001948e+00 5.12145428e+00 -9.54700858e-03 57 -2.35664668e+01 5.95589639e+00 -1.32744731e+01 | -2.35664668e+01 5.95589639e+00 -1.32744731e+01 58 -2.34750034e+00 -1.17674369e+01 -4.34270307e+00 | -2.34750034e+00 -1.17674369e+01 -4.34270307e+00 59 9.79190461e+00 4.18936920e+00 1.31323154e+01 | 9.79190461e+00 4.18936920e+00 1.31323154e+01 60 1.10320315e+01 9.36100065e+00 1.79752467e+01 | 1.10320315e+01 9.36100065e+00 1.79752467e+01 61 3.74199990e-01 1.70995445e+00 3.44296031e-01 | 3.74199990e-01 1.70995445e+00 3.44296031e-01 62 8.42183895e+00 -2.41099394e+01 1.63508666e+01 | 8.42183895e+00 -2.41099394e+01 1.63508666e+01 63 8.93392712e-01 1.47811977e-01 1.22352612e-01 | 8.93392712e-01 1.47811977e-01 1.22352612e-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.