!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_JelinekGrohHorstemeyer_2012_AlSiMgCuFe__MO_262519520678_001 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)) = 474.1027841225862 V(r_1,...,r_N) = 474.10278412258594 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 -1.96153012e+01 -1.05154395e+01 -3.06596947e+01 | -1.96153012e+01 -1.05154395e+01 -3.06596947e+01 1 1.54798056e+01 1.11593083e+01 2.74967893e+01 | 1.54798056e+01 1.11593083e+01 2.74967893e+01 2 2.25086228e+00 3.49578327e+00 -9.52194833e-01 | 2.25086228e+00 3.49578327e+00 -9.52194833e-01 3 -3.68864866e+00 -5.85210380e+00 4.29960900e+00 | -3.68864866e+00 -5.85210380e+00 4.29960900e+00 4 -6.73904733e+01 -4.14682997e+01 3.00733001e+00 | -6.73904733e+01 -4.14682997e+01 3.00733001e+00 5 3.89106502e+01 3.46983395e-01 2.11320974e+01 | 3.89106502e+01 3.46983395e-01 2.11320974e+01 6 9.50774282e-01 -1.61700216e+00 5.53737939e-01 | 9.50774282e-01 -1.61700216e+00 5.53737939e-01 7 -7.92617678e+00 5.49345081e+01 -4.89784076e+01 | -7.92617678e+00 5.49345081e+01 -4.89784076e+01 8 -1.25629028e+00 3.64290322e-01 8.26359426e-01 | -1.25629028e+00 3.64290322e-01 8.26359426e-01 9 6.38717869e+00 -3.09200412e+00 -2.61708386e+00 | 6.38717869e+00 -3.09200412e+00 -2.61708386e+00 10 -6.97101471e+01 -2.24346635e+01 -4.10130014e+01 | -6.97101471e+01 -2.24346635e+01 -4.10130014e+01 11 6.87186770e+01 2.38550154e+01 4.34350338e+01 | 6.87186770e+01 2.38550154e+01 4.34350338e+01 12 -2.96530807e+01 -4.56732364e+01 -4.91150698e+01 | -2.96530807e+01 -4.56732364e+01 -4.91150698e+01 13 3.35375220e+01 4.59098522e+01 4.54406236e+01 | 3.35375220e+01 4.59098522e+01 4.54406236e+01 14 -2.92207496e+00 2.23165033e+01 -5.13216505e+01 | -2.92207496e+00 2.23165033e+01 -5.13216505e+01 15 2.50946260e+01 2.52541502e+01 3.91508302e+01 | 2.50946260e+01 2.52541502e+01 3.91508302e+01 16 -7.87274804e+00 -5.93568918e+00 -8.35043723e+00 | -7.87274804e+00 -5.93568918e+00 -8.35043723e+00 17 -5.38963789e+01 2.60714633e+01 -3.41458785e+01 | -5.38963789e+01 2.60714633e+01 -3.41458785e+01 18 -2.25333305e+00 -1.59020473e+00 -7.14257501e+00 | -2.25333305e+00 -1.59020473e+00 -7.14257501e+00 19 -7.24400093e+01 -5.96129983e+00 -1.86976715e+01 | -7.24400093e+01 -5.96129983e+00 -1.86976715e+01 20 5.77504360e+01 -2.36724106e+01 2.64402026e+01 | 5.77504360e+01 -2.36724106e+01 2.64402026e+01 21 6.33580993e+00 9.68543780e+00 -7.09706949e+00 | 6.33580993e+00 9.68543780e+00 -7.09706949e+00 22 -1.04174862e+01 -1.55970633e+01 -2.70611272e+01 | -1.04174862e+01 -1.55970633e+01 -2.70611272e+01 23 1.06728054e+01 1.59595675e+01 2.70571676e+01 | 1.06728054e+01 1.59595675e+01 2.70571676e+01 24 -1.25522713e+01 -7.53511982e+00 -1.93590761e+01 | -1.25522713e+01 -7.53511982e+00 -1.93590761e+01 25 9.51623613e+00 2.37524926e+01 5.87847716e+00 | 9.51623613e+00 2.37524926e+01 5.87847716e+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 -1.55489732e+00 -2.14096801e+01 9.15908521e-02 | -1.55489732e+00 -2.14096801e+01 9.15908521e-02 29 1.26782684e+01 6.40255870e+00 1.03118534e+01 | 1.26782684e+01 6.40255870e+00 1.03118534e+01 30 7.05041977e+01 1.92822150e+00 1.74360434e+01 | 7.05041977e+01 1.92822150e+00 1.74360434e+01 31 -1.85406348e+02 1.38171894e+02 -8.92366613e+01 | -1.85406348e+02 1.38171894e+02 -8.92366613e+01 32 -1.27341762e+01 -1.29931910e+01 -2.06357817e+01 | -1.27341762e+01 -1.29931910e+01 -2.06357817e+01 33 1.02378855e+01 1.52134697e+01 1.78650707e+01 | 1.02378855e+01 1.52134697e+01 1.78650707e+01 34 1.50227820e+01 -5.86718096e+01 5.45542060e+01 | 1.50227820e+01 -5.86718096e+01 5.45542060e+01 35 5.83427252e-01 -2.07814905e+01 2.81596237e-01 | 5.83427252e-01 -2.07814905e+01 2.81596237e-01 36 3.11723745e+00 -9.44323782e-01 2.52393993e+00 | 3.11723745e+00 -9.44323782e-01 2.52393993e+00 37 -1.87437091e+00 -9.48590089e+00 1.57054243e+01 | -1.87437091e+00 -9.48590089e+00 1.57054243e+01 38 -4.06422374e+01 -1.65677262e+01 -8.48151344e+00 | -4.06422374e+01 -1.65677262e+01 -8.48151344e+00 39 6.15308594e+00 -1.03040081e+01 2.72617273e+01 | 6.15308594e+00 -1.03040081e+01 2.72617273e+01 40 7.20245046e-01 -1.11841117e-01 -1.87701719e+00 | 7.20245046e-01 -1.11841117e-01 -1.87701719e+00 41 -4.51884541e+01 7.76524296e+01 -8.39701397e-01 | -4.51884541e+01 7.76524296e+01 -8.39701397e-01 42 -5.42372072e+01 -1.41989410e+02 -8.82479066e+01 | -5.42372072e+01 -1.41989410e+02 -8.82479066e+01 43 7.36846545e+01 1.55621255e+02 6.43183873e+01 | 7.36846545e+01 1.55621255e+02 6.43183873e+01 44 2.32604703e+01 -9.15073680e+01 2.35710645e+01 | 2.32604703e+01 -9.15073680e+01 2.35710645e+01 45 -1.72488669e-02 9.06218646e-01 1.31734712e+00 | -1.72488669e-02 9.06218646e-01 1.31734712e+00 46 2.11323021e+00 -2.69870564e+00 -9.97030790e+00 | 2.11323021e+00 -2.69870564e+00 -9.97030790e+00 47 2.59578675e-01 1.61895874e+00 -3.30220386e-01 | 2.59578675e-01 1.61895874e+00 -3.30220386e-01 48 -7.39000954e+00 1.91036074e+00 4.74988246e+00 | -7.39000954e+00 1.91036074e+00 4.74988246e+00 49 7.12905554e-01 -1.11894456e+01 -1.25492621e+01 | 7.12905554e-01 -1.11894456e+01 -1.25492621e+01 50 4.86403134e+00 3.38467013e+00 -5.02460599e+00 | 4.86403134e+00 3.38467013e+00 -5.02460599e+00 51 -2.70304899e+00 1.04878283e+01 1.64556195e+00 | -2.70304899e+00 1.04878283e+01 1.64556195e+00 52 2.18723333e+01 4.14498482e+01 -1.46333049e+01 | 2.18723333e+01 4.14498482e+01 -1.46333049e+01 53 3.96148037e-01 -5.38682745e-02 3.66334114e-01 | 3.96148037e-01 -5.38682745e-02 3.66334114e-01 54 -1.26315718e+01 3.13338274e+00 1.35940255e+01 | -1.26315718e+01 3.13338274e+00 1.35940255e+01 55 4.96002632e+00 2.09716520e+00 -4.29193788e-01 | 4.96002632e+00 2.09716520e+00 -4.29193788e-01 56 1.21905402e+01 1.07293024e+01 -1.51592678e+00 | 1.21905402e+01 1.07293024e+01 -1.51592678e+00 57 -6.26793046e+00 9.39944937e-01 -8.05679539e+01 | -6.26793046e+00 9.39944937e-01 -8.05679539e+01 58 1.82577472e+02 -1.31424380e+02 9.92059691e+01 | 1.82577472e+02 -1.31424380e+02 9.92059691e+01 59 -4.05992234e-01 -1.24879303e+00 8.15926580e-02 | -4.05992234e-01 -1.24879303e+00 8.15926580e-02 60 5.98958003e+01 -4.75119064e+01 6.06878383e+01 | 5.98958003e+01 -4.75119064e+01 6.06878383e+01 61 -3.46039104e-01 9.79830066e-01 -3.17446346e-01 | -3.46039104e-01 9.79830066e-01 -3.17446346e-01 62 -4.61023417e+01 3.69521047e+01 2.07851382e+01 | -4.61023417e+01 3.69521047e+01 2.07851382e+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)) = 230.37921598049573 V(r_1,...,r_N) = 230.37921598049567 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 -9.15359504e+00 -5.67667439e+00 -8.11103766e+00 | -9.15359504e+00 -5.67667439e+00 -8.11103766e+00 1 -1.63965462e+02 -2.74712865e+02 8.17531998e+01 | -1.63965462e+02 -2.74712865e+02 8.17531998e+01 2 1.65456835e+02 2.95871990e+02 -1.07472761e+02 | 1.65456835e+02 2.95871990e+02 -1.07472761e+02 3 -1.17766606e+02 1.17470742e+01 -2.08271102e+02 | -1.17766606e+02 1.17470742e+01 -2.08271102e+02 4 4.16456575e+00 -1.50881627e+01 3.46447458e+01 | 4.16456575e+00 -1.50881627e+01 3.46447458e+01 5 1.96977279e+00 -3.06822224e+00 -2.36276752e+00 | 1.96977279e+00 -3.06822224e+00 -2.36276752e+00 6 1.80030474e+00 -5.15778895e-01 -4.11983341e-01 | 1.80030474e+00 -5.15778895e-01 -4.11983341e-01 7 -3.78580993e+00 -6.30828187e+00 -3.59032889e+00 | -3.78580993e+00 -6.30828187e+00 -3.59032889e+00 8 -1.80179657e-01 8.26918538e-01 5.75493364e-01 | -1.80179657e-01 8.26918538e-01 5.75493364e-01 9 -2.17312612e-01 -4.00471248e+00 2.84178128e+00 | -2.17312612e-01 -4.00471248e+00 2.84178128e+00 10 -7.88188829e+01 -4.47028670e+01 -2.43348661e+01 | -7.88188829e+01 -4.47028670e+01 -2.43348661e+01 11 7.68878126e+01 4.93282685e+01 2.33411655e+01 | 7.68878126e+01 4.93282685e+01 2.33411655e+01 12 -7.79774462e+01 -1.06442296e+02 -3.79475241e+01 | -7.79774462e+01 -1.06442296e+02 -3.79475241e+01 13 7.80737251e+01 1.06834898e+02 3.70133140e+01 | 7.80737251e+01 1.06834898e+02 3.70133140e+01 14 1.19535352e+02 -1.28885533e+01 2.07589356e+02 | 1.19535352e+02 -1.28885533e+01 2.07589356e+02 15 -9.90629716e-01 -8.45533012e+00 1.21457338e+01 | -9.90629716e-01 -8.45533012e+00 1.21457338e+01 16 -6.32180419e+00 -6.85977200e+00 -3.39484274e+00 | -6.32180419e+00 -6.85977200e+00 -3.39484274e+00 17 -2.55831267e+01 3.79477053e+01 -7.37530726e+01 | -2.55831267e+01 3.79477053e+01 -7.37530726e+01 18 -2.82499796e+00 -4.28038098e+00 -1.62418839e+00 | -2.82499796e+00 -4.28038098e+00 -1.62418839e+00 19 2.38017162e+00 4.40166845e+00 1.52497023e+00 | 2.38017162e+00 4.40166845e+00 1.52497023e+00 20 2.51629074e+01 -2.42592787e+01 7.09702075e+01 | 2.51629074e+01 -2.42592787e+01 7.09702075e+01 21 5.24126327e+00 4.37310549e+00 2.46419075e+00 | 5.24126327e+00 4.37310549e+00 2.46419075e+00 22 -2.10368814e+00 -2.85128032e+00 -2.16242352e+00 | -2.10368814e+00 -2.85128032e+00 -2.16242352e+00 23 3.11141292e+00 1.33204634e+00 2.85156398e+00 | 3.11141292e+00 1.33204634e+00 2.85156398e+00 24 -4.18223274e+01 1.29639898e+01 -5.58070609e+01 | -4.18223274e+01 1.29639898e+01 -5.58070609e+01 25 3.98751211e+01 -1.02222275e+01 5.04699304e+01 | 3.98751211e+01 -1.02222275e+01 5.04699304e+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 4.80470588e+00 7.16609746e+00 -5.52426736e+00 | 4.80470588e+00 7.16609746e+00 -5.52426736e+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 -1.03089224e+02 1.54189421e+02 -6.00751744e+01 | -1.03089224e+02 1.54189421e+02 -6.00751744e+01 32 9.30545339e-01 6.56201167e-01 -1.42812769e-02 | 9.30545339e-01 6.56201167e-01 -1.42812769e-02 33 -1.05205733e+02 1.16210656e+02 -1.45649368e+02 | -1.05205733e+02 1.16210656e+02 -1.45649368e+02 34 6.87613701e-02 -4.65254964e+00 5.80821549e+00 | 6.87613701e-02 -4.65254964e+00 5.80821549e+00 35 5.54758238e+00 -1.40104774e+01 -2.19393783e+01 | 5.54758238e+00 -1.40104774e+01 -2.19393783e+01 36 1.04606305e+02 -1.17399200e+02 1.44146455e+02 | 1.04606305e+02 -1.17399200e+02 1.44146455e+02 37 -8.88712280e+01 -3.65441859e+01 5.40119505e+01 | -8.88712280e+01 -3.65441859e+01 5.40119505e+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 -1.79344163e+02 2.42746530e+02 -1.89881752e+02 | -1.79344163e+02 2.42746530e+02 -1.89881752e+02 42 -4.03874436e+00 -8.65553364e+00 -3.73266643e+00 | -4.03874436e+00 -8.65553364e+00 -3.73266643e+00 43 3.35990532e+00 8.32835998e+00 4.40022700e+00 | 3.35990532e+00 8.32835998e+00 4.40022700e+00 44 1.65488395e+02 -2.54761835e+02 1.76126025e+02 | 1.65488395e+02 -2.54761835e+02 1.76126025e+02 45 1.25398578e+01 1.23018366e+01 1.30640921e+01 | 1.25398578e+01 1.23018366e+01 1.30640921e+01 46 8.79471573e+01 3.56016869e+01 -5.53748336e+01 | 8.79471573e+01 3.56016869e+01 -5.53748336e+01 47 -2.06134672e+01 -1.15088076e+01 9.14040175e+00 | -2.06134672e+01 -1.15088076e+01 9.14040175e+00 48 -1.65160979e+00 -2.87471245e+00 -2.20129365e+00 | -1.65160979e+00 -2.87471245e+00 -2.20129365e+00 49 -8.58579651e+01 -5.10106241e+01 3.45834756e+01 | -8.58579651e+01 -5.10106241e+01 3.45834756e+01 50 8.57402023e+01 4.32158286e+01 -3.77130574e+01 | 8.57402023e+01 4.32158286e+01 -3.77130574e+01 51 4.84930932e+00 7.68784181e+00 3.59317413e+00 | 4.84930932e+00 7.68784181e+00 3.59317413e+00 52 -5.79807426e+00 1.14787479e+01 2.89448276e+01 | -5.79807426e+00 1.14787479e+01 2.89448276e+01 53 -8.03875441e+00 -3.32656812e+00 3.70569751e+00 | -8.03875441e+00 -3.32656812e+00 3.70569751e+00 54 -1.04181310e+00 2.43142745e+00 1.32797644e+00 | -1.04181310e+00 2.43142745e+00 1.32797644e+00 55 -3.76052492e-01 1.25144399e-01 -4.01849425e-01 | -3.76052492e-01 1.25144399e-01 -4.01849425e-01 56 3.38062909e+00 5.61590778e+00 -3.82604936e+00 | 3.38062909e+00 5.61590778e+00 -3.82604936e+00 57 2.94004178e+00 -5.07601522e-01 -3.11394153e-01 | 2.94004178e+00 -5.07601522e-01 -3.11394153e-01 58 1.00826435e+02 -1.52477312e+02 6.03413013e+01 | 1.00826435e+02 -1.52477312e+02 6.03413013e+01 59 -9.90572601e-01 -9.73761120e-01 -1.91170354e-01 | -9.90572601e-01 -9.73761120e-01 -1.91170354e-01 60 2.09598530e+01 1.46144567e+01 -8.84758599e+00 | 2.09598530e+01 1.46144567e+01 -8.84758599e+00 61 -8.48765132e-01 1.52178848e-01 -4.84131194e-01 | -8.48765132e-01 1.52178848e-01 -4.84131194e-01 62 7.48264411e+00 4.98839988e+00 -3.31525214e+00 | 7.48264411e+00 4.98839988e+00 -3.31525214e+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)) = 264.89379341474574 V(r_1,...,r_N) = 264.8937934147458 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 -3.33857400e+01 4.61678911e+01 -4.14416439e+01 | -3.33857400e+01 4.61678911e+01 -4.14416439e+01 2 -7.85794889e-01 -4.06664869e+00 -3.38139687e+00 | -7.85794889e-01 -4.06664869e+00 -3.38139687e+00 3 1.24600656e+01 -3.33514367e+00 -1.08054818e+01 | 1.24600656e+01 -3.33514367e+00 -1.08054818e+01 4 3.67995535e+01 -3.81159839e+01 4.44924523e+01 | 3.67995535e+01 -3.81159839e+01 4.44924523e+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 -1.04008885e+02 -7.79993029e+01 2.92657839e+01 | -1.04008885e+02 -7.79993029e+01 2.92657839e+01 8 -2.21138814e-01 -2.58944909e-02 3.99721388e-01 | -2.21138814e-01 -2.58944909e-02 3.99721388e-01 9 -6.94735724e+01 1.24736413e+02 -7.50403450e+01 | -6.94735724e+01 1.24736413e+02 -7.50403450e+01 10 -5.23462339e+01 -6.92623455e+01 -8.49686228e+01 | -5.23462339e+01 -6.92623455e+01 -8.49686228e+01 11 5.04516133e+01 6.96547086e+01 8.58069220e+01 | 5.04516133e+01 6.96547086e+01 8.58069220e+01 12 7.75813085e+01 -1.34449516e+02 7.08034984e+01 | 7.75813085e+01 -1.34449516e+02 7.08034984e+01 13 -1.52884308e+00 7.62818308e-01 -1.69216896e-01 | -1.52884308e+00 7.62818308e-01 -1.69216896e-01 14 -1.90373631e+01 -4.59766507e-01 -1.13285004e+01 | -1.90373631e+01 -4.59766507e-01 -1.13285004e+01 15 -4.88502593e+01 -1.01986072e+02 6.78607593e+01 | -4.88502593e+01 -1.01986072e+02 6.78607593e+01 16 8.09776710e-01 4.44028268e-01 1.79504657e+00 | 8.09776710e-01 4.44028268e-01 1.79504657e+00 17 -1.52721671e+01 -1.72147529e+01 2.35416147e+01 | -1.52721671e+01 -1.72147529e+01 2.35416147e+01 18 1.29333701e+01 1.50233044e+01 -2.64875460e+01 | 1.29333701e+01 1.50233044e+01 -2.64875460e+01 19 -8.21368897e+00 2.79687072e+00 -8.62757747e-01 | -8.21368897e+00 2.79687072e+00 -8.62757747e-01 20 8.92667150e+01 8.25104589e+01 -9.42395353e+00 | 8.92667150e+01 8.25104589e+01 -9.42395353e+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 -1.19047052e+01 1.00637452e+01 -1.12498520e+01 | -1.19047052e+01 1.00637452e+01 -1.12498520e+01 24 -1.03643209e+02 -1.67247387e+02 -7.68554562e+01 | -1.03643209e+02 -1.67247387e+02 -7.68554562e+01 25 9.18953730e+01 1.52543378e+02 8.05464553e+01 | 9.18953730e+01 1.52543378e+02 8.05464553e+01 26 1.54777375e+01 1.60813841e+01 -6.43840499e+00 | 1.54777375e+01 1.60813841e+01 -6.43840499e+00 27 -9.13668163e-01 -9.08146281e-01 3.38161892e-01 | -9.13668163e-01 -9.08146281e-01 3.38161892e-01 28 6.07059632e+01 1.13202307e+02 -5.18606562e+01 | 6.07059632e+01 1.13202307e+02 -5.18606562e+01 29 -1.64783058e+00 2.39450601e-01 3.19951132e-01 | -1.64783058e+00 2.39450601e-01 3.19951132e-01 30 1.59376856e+01 -2.29231152e+01 -1.27466561e+02 | 1.59376856e+01 -2.29231152e+01 -1.27466561e+02 31 -7.74872940e+00 2.13672961e+01 1.31930391e+02 | -7.74872940e+00 2.13672961e+01 1.31930391e+02 32 6.79730324e-01 2.20457778e-01 -3.02186221e-01 | 6.79730324e-01 2.20457778e-01 -3.02186221e-01 33 -9.92544478e+01 5.68284014e+01 -1.78199092e+01 | -9.92544478e+01 5.68284014e+01 -1.78199092e+01 34 -8.73851668e+01 -8.03116190e+01 -5.57363498e+01 | -8.73851668e+01 -8.03116190e+01 -5.57363498e+01 35 9.47425645e+01 8.60049835e+01 5.10385812e+01 | 9.47425645e+01 8.60049835e+01 5.10385812e+01 36 9.52132406e+01 -7.20227598e+01 2.01809637e+01 | 9.52132406e+01 -7.20227598e+01 2.01809637e+01 37 -1.10414380e+00 -4.86200828e-01 9.75137738e-01 | -1.10414380e+00 -4.86200828e-01 9.75137738e-01 38 -1.77174318e+01 -4.21638191e+00 -3.86218109e+01 | -1.77174318e+01 -4.21638191e+00 -3.86218109e+01 39 -2.96033189e+00 -8.13682586e+00 5.42036475e+01 | -2.96033189e+00 -8.13682586e+00 5.42036475e+01 40 -9.46993871e+00 -7.29183127e+00 -6.43412988e+00 | -9.46993871e+00 -7.29183127e+00 -6.43412988e+00 41 2.32118906e+00 4.83940866e+01 -4.15338836e+01 | 2.32118906e+00 4.83940866e+01 -4.15338836e+01 42 1.02588518e+01 2.16076219e+01 -1.22177704e+01 | 1.02588518e+01 2.16076219e+01 -1.22177704e+01 43 -7.36693731e-02 9.23568130e-01 8.83184695e-01 | -7.36693731e-02 9.23568130e-01 8.83184695e-01 44 -4.02450764e+00 -6.21060036e+01 6.13296468e+01 | -4.02450764e+00 -6.21060036e+01 6.13296468e+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 -2.68881742e+01 -4.15206712e+01 3.84312130e+01 | -2.68881742e+01 -4.15206712e+01 3.84312130e+01 48 -2.49926611e+00 -7.73331848e+00 -1.00475466e+00 | -2.49926611e+00 -7.73331848e+00 -1.00475466e+00 49 3.16303066e+01 -2.59941173e+01 -1.00652289e+02 | 3.16303066e+01 -2.59941173e+01 -1.00652289e+02 50 4.91514185e+00 -5.09366736e+00 1.49532412e+01 | 4.91514185e+00 -5.09366736e+00 1.49532412e+01 51 -4.11696008e+01 9.20843380e+01 -6.30580714e+01 | -4.11696008e+01 9.20843380e+01 -6.30580714e+01 52 1.58517029e+01 1.98641308e+01 -1.42747376e+01 | 1.58517029e+01 1.98641308e+01 -1.42747376e+01 53 -1.93735297e+01 -2.19013437e+01 3.75564924e+01 | -1.93735297e+01 -2.19013437e+01 3.75564924e+01 54 -2.70702391e+01 3.30621361e+01 1.02011050e+02 | -2.70702391e+01 3.30621361e+01 1.02011050e+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 -1.19139520e+01 2.48685385e+01 -3.44979744e+01 | -1.19139520e+01 2.48685385e+01 -3.44979744e+01 58 -3.74589565e+01 -3.80106194e+01 -4.29506744e+01 | -3.74589565e+01 -3.80106194e+01 -4.29506744e+01 59 3.96899789e+01 3.60224065e+01 4.47135374e+01 | 3.96899789e+01 3.60224065e+01 4.47135374e+01 60 4.56842319e+01 2.32441493e+01 3.22515732e+00 | 4.56842319e+01 2.32441493e+01 3.22515732e+00 61 -5.83245112e-01 -4.10059953e-01 -8.55464910e-01 | -5.83245112e-01 -4.10059953e-01 -8.55464910e-01 62 6.04742847e+01 -7.06816829e+01 2.52991787e+01 | 6.04742847e+01 -7.06816829e+01 2.52991787e+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)) = 150.63579571158027 V(r_1,...,r_N) = 150.63579571158027 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 -3.67169000e-01 -8.59071002e-01 -7.64046662e-01 | -3.67169000e-01 -8.59071002e-01 -7.64046662e-01 1 1.58828744e+01 -4.92653478e+01 -1.96668261e+01 | 1.58828744e+01 -4.92653478e+01 -1.96668261e+01 2 -1.63835161e+00 -1.40945679e+00 -3.97818994e+00 | -1.63835161e+00 -1.40945679e+00 -3.97818994e+00 3 2.91018143e+00 1.90410712e+00 1.36481048e+00 | 2.91018143e+00 1.90410712e+00 1.36481048e+00 4 4.30170083e-01 -1.05993641e+00 2.07238624e-01 | 4.30170083e-01 -1.05993641e+00 2.07238624e-01 5 -1.60923454e+01 -9.53314277e+00 2.18774014e+01 | -1.60923454e+01 -9.53314277e+00 2.18774014e+01 6 -2.03471986e+01 4.83120752e+01 1.76222409e+01 | -2.03471986e+01 4.83120752e+01 1.76222409e+01 7 -4.27976126e+00 4.70824635e-01 -5.00252605e+00 | -4.27976126e+00 4.70824635e-01 -5.00252605e+00 8 -4.06777574e+00 -2.40451894e+00 -2.98330326e+00 | -4.06777574e+00 -2.40451894e+00 -2.98330326e+00 9 -7.05369989e+00 -4.94997161e+00 -1.06738373e+00 | -7.05369989e+00 -4.94997161e+00 -1.06738373e+00 10 6.21424931e+00 -2.42663749e-02 -9.80735644e+00 | 6.21424931e+00 -2.42663749e-02 -9.80735644e+00 11 3.79546704e+00 5.39939630e+00 -7.79105438e-01 | 3.79546704e+00 5.39939630e+00 -7.79105438e-01 12 -3.84839297e+00 -1.29647898e+01 1.20662197e+00 | -3.84839297e+00 -1.29647898e+01 1.20662197e+00 13 7.87900886e+00 1.07426693e+01 7.69236176e+00 | 7.87900886e+00 1.07426693e+01 7.69236176e+00 14 1.51653322e+01 9.16248134e+00 -2.40616324e+01 | 1.51653322e+01 9.16248134e+00 -2.40616324e+01 15 1.23723450e-01 -8.34332038e+00 -7.91635719e+00 | 1.23723450e-01 -8.34332038e+00 -7.91635719e+00 16 -9.26891620e+00 -1.46556882e+01 -5.37593051e+00 | -9.26891620e+00 -1.46556882e+01 -5.37593051e+00 17 8.59773494e+00 1.29031066e+01 4.91200081e+00 | 8.59773494e+00 1.29031066e+01 4.91200081e+00 18 -1.11257448e+01 -1.12349602e+01 -1.38027966e+01 | -1.11257448e+01 -1.12349602e+01 -1.38027966e+01 19 1.16873010e+01 1.27585759e+01 1.22901461e+01 | 1.16873010e+01 1.27585759e+01 1.22901461e+01 20 -5.90673480e+00 -8.87235317e+00 -1.00220093e+01 | -5.90673480e+00 -8.87235317e+00 -1.00220093e+01 21 3.87883622e+00 3.27984559e+00 9.68065374e+00 | 3.87883622e+00 3.27984559e+00 9.68065374e+00 22 -2.75260361e+00 -4.59312602e-01 -8.68389826e-01 | -2.75260361e+00 -4.59312602e-01 -8.68389826e-01 23 -2.64110045e-01 3.33721650e+00 -2.08721025e+00 | -2.64110045e-01 3.33721650e+00 -2.08721025e+00 24 -1.03105137e-01 2.06610697e-01 -6.89665820e-01 | -1.03105137e-01 2.06610697e-01 -6.89665820e-01 25 -2.00303002e+00 5.54331725e+00 -2.14759346e+00 | -2.00303002e+00 5.54331725e+00 -2.14759346e+00 26 -2.23072112e+00 -1.16140552e+01 -5.83961847e+00 | -2.23072112e+00 -1.16140552e+01 -5.83961847e+00 27 2.18125665e+00 1.16846482e+01 5.84732554e+00 | 2.18125665e+00 1.16846482e+01 5.84732554e+00 28 4.65882050e+00 1.29296342e+00 1.08368839e+00 | 4.65882050e+00 1.29296342e+00 1.08368839e+00 29 1.05153442e+00 -9.21163789e-01 -8.37520225e-01 | 1.05153442e+00 -9.21163789e-01 -8.37520225e-01 30 3.77987308e+00 5.00841343e+00 -5.77412870e+00 | 3.77987308e+00 5.00841343e+00 -5.77412870e+00 31 -1.82339230e+00 2.05551700e+00 -2.45203221e+00 | -1.82339230e+00 2.05551700e+00 -2.45203221e+00 32 -7.32480737e-01 -9.12548961e-01 -1.89987460e+00 | -7.32480737e-01 -9.12548961e-01 -1.89987460e+00 33 -2.00559465e+01 1.26184317e+01 -1.66635589e+01 | -2.00559465e+01 1.26184317e+01 -1.66635589e+01 34 -4.02874145e+00 -1.76098704e+00 -1.15747852e+00 | -4.02874145e+00 -1.76098704e+00 -1.15747852e+00 35 -3.39338922e+01 3.15572014e+01 2.88408854e+00 | -3.39338922e+01 3.15572014e+01 2.88408854e+00 36 2.14771262e+01 -1.36858106e+01 1.79192792e+01 | 2.14771262e+01 -1.36858106e+01 1.79192792e+01 37 -7.18943083e-02 -1.10206389e+00 2.34948673e+00 | -7.18943083e-02 -1.10206389e+00 2.34948673e+00 38 -1.40624338e+01 -3.01623308e+01 -1.23623454e+01 | -1.40624338e+01 -3.01623308e+01 -1.23623454e+01 39 5.80300543e+00 2.43187485e+01 1.93460924e+01 | 5.80300543e+00 2.43187485e+01 1.93460924e+01 40 -2.57471216e+00 -8.22625862e+00 -3.45343914e+00 | -2.57471216e+00 -8.22625862e+00 -3.45343914e+00 41 7.17112660e+00 -1.01246603e+01 1.39555009e+00 | 7.17112660e+00 -1.01246603e+01 1.39555009e+00 42 -1.17580618e+01 -1.23042334e+01 -3.82294809e+00 | -1.17580618e+01 -1.23042334e+01 -3.82294809e+00 43 2.56431248e+01 1.37843068e+01 8.93587411e+00 | 2.56431248e+01 1.37843068e+01 8.93587411e+00 44 2.26274210e+00 -3.38837851e+00 1.36069424e+00 | 2.26274210e+00 -3.38837851e+00 1.36069424e+00 45 1.51339358e+00 9.24514733e-01 1.24612845e+00 | 1.51339358e+00 9.24514733e-01 1.24612845e+00 46 2.93400867e+01 -1.76861265e+01 1.10832853e+01 | 2.93400867e+01 -1.76861265e+01 1.10832853e+01 47 -4.83099148e-01 -4.48038380e-01 1.06564160e+00 | -4.83099148e-01 -4.48038380e-01 1.06564160e+00 48 -1.66979147e+00 -4.51158502e-01 -5.80414492e-01 | -1.66979147e+00 -4.51158502e-01 -5.80414492e-01 49 -3.35336361e+01 -1.67262748e+01 7.94308463e+00 | -3.35336361e+01 -1.67262748e+01 7.94308463e+00 50 2.89796460e+01 1.02093923e+01 -6.03530365e+00 | 2.89796460e+01 1.02093923e+01 -6.03530365e+00 51 5.35603326e+00 1.07690144e+01 4.86440060e+00 | 5.35603326e+00 1.07690144e+01 4.86440060e+00 52 6.51375764e+00 5.85239191e+00 -3.41662698e+00 | 6.51375764e+00 5.85239191e+00 -3.41662698e+00 53 -4.64551768e+00 -3.47848328e+00 4.76937043e+00 | -4.64551768e+00 -3.47848328e+00 4.76937043e+00 54 -2.02747284e+00 -5.31058267e-01 1.27813065e-01 | -2.02747284e+00 -5.31058267e-01 1.27813065e-01 55 8.42832985e-01 1.18141170e+00 9.61823059e-01 | 8.42832985e-01 1.18141170e+00 9.61823059e-01 56 -8.78612614e+00 6.36786107e+00 1.47504122e+00 | -8.78612614e+00 6.36786107e+00 1.47504122e+00 57 -9.33159767e+00 2.86937977e+00 -1.03114662e+00 | -9.33159767e+00 2.86937977e+00 -1.03114662e+00 58 -1.10327698e+01 -5.17434768e+00 -3.17892614e+00 | -1.10327698e+01 -5.17434768e+00 -3.17892614e+00 59 1.54038420e+01 8.94988133e+00 3.22323611e+00 | 1.54038420e+01 8.94988133e+00 3.22323611e+00 60 3.59397180e+00 -7.16543061e+00 1.50265405e+00 | 3.59397180e+00 -7.16543061e+00 1.50265405e+00 61 5.51774933e+00 3.59954873e+00 5.78631895e+00 | 5.51774933e+00 3.59954873e+00 5.78631895e+00 62 2.46923324e+00 3.56277175e+00 -3.99894629e+00 | 2.46923324e+00 3.56277175e+00 -3.99894629e+00 63 1.77719086e+00 1.27292081e+00 1.50027876e+00 | 1.77719086e+00 1.27292081e+00 1.50027876e+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)) = 451.2050169957002 V(r_1,...,r_N) = 451.2050169957 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 -4.79529681e+01 -7.39444774e+01 -5.69900955e+01 | -4.79529681e+01 -7.39444774e+01 -5.69900955e+01 1 5.36927508e+01 7.27225647e+01 5.61391272e+01 | 5.36927508e+01 7.27225647e+01 5.61391272e+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 -4.02004801e+01 -6.17345670e+01 -1.66274232e+01 | -4.02004801e+01 -6.17345670e+01 -1.66274232e+01 5 -2.70021740e+01 -1.95055552e+01 1.85409934e+01 | -2.70021740e+01 -1.95055552e+01 1.85409934e+01 6 -5.03253538e+00 -1.58336349e+00 -1.79127646e+00 | -5.03253538e+00 -1.58336349e+00 -1.79127646e+00 7 -1.31544339e+02 -1.72520086e+02 1.00774745e+02 | -1.31544339e+02 -1.72520086e+02 1.00774745e+02 8 -4.18105822e+00 -9.69643219e+00 -1.30329770e+01 | -4.18105822e+00 -9.69643219e+00 -1.30329770e+01 9 -1.82686518e+02 1.11611763e+02 -9.84133624e+01 | -1.82686518e+02 1.11611763e+02 -9.84133624e+01 10 3.68257195e-01 3.08493359e-01 4.34331348e+00 | 3.68257195e-01 3.08493359e-01 4.34331348e+00 11 7.07335262e+01 -6.74673247e+01 -7.06227676e+01 | 7.07335262e+01 -6.74673247e+01 -7.06227676e+01 12 1.88121921e+02 -9.69383997e+01 1.13163852e+02 | 1.88121921e+02 -9.69383997e+01 1.13163852e+02 13 4.03898420e+01 -3.66603226e+01 -4.29288032e+01 | 4.03898420e+01 -3.66603226e+01 -4.29288032e+01 14 6.66552106e+01 4.43936022e+01 -1.37818586e+01 | 6.66552106e+01 4.43936022e+01 -1.37818586e+01 15 -5.78864647e+01 -2.64920466e+01 7.20722910e+01 | -5.78864647e+01 -2.64920466e+01 7.20722910e+01 16 -1.57135022e+02 -2.47386906e+02 -1.86453652e+02 | -1.57135022e+02 -2.47386906e+02 -1.86453652e+02 17 1.71846616e+02 2.41708305e+02 1.95142224e+02 | 1.71846616e+02 2.41708305e+02 1.95142224e+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 1.36926407e+02 1.76333346e+02 -1.05120365e+02 | 1.36926407e+02 1.76333346e+02 -1.05120365e+02 21 4.35369253e+01 -3.04592934e+01 -4.37936946e+01 | 4.35369253e+01 -3.04592934e+01 -4.37936946e+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 9.55044508e+01 -3.96957802e+01 -2.17997240e+01 | 9.55044508e+01 -3.96957802e+01 -2.17997240e+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 9.91834029e+00 1.05070319e+02 8.42451943e+00 | 9.91834029e+00 1.05070319e+02 8.42451943e+00 29 1.66364526e+01 -2.95303961e+01 -2.31143628e+01 | 1.66364526e+01 -2.95303961e+01 -2.31143628e+01 30 -9.46546307e+01 4.14421215e+01 2.00223672e+01 | -9.46546307e+01 4.14421215e+01 2.00223672e+01 31 -1.84220575e+02 1.67080408e+02 -8.59110183e+01 | -1.84220575e+02 1.67080408e+02 -8.59110183e+01 32 -2.70394146e+01 -7.25888503e+01 -7.72442935e+01 | -2.70394146e+01 -7.25888503e+01 -7.72442935e+01 33 -2.17702651e+01 8.47830478e+01 3.39585276e+01 | -2.17702651e+01 8.47830478e+01 3.39585276e+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 5.77148379e+01 -2.93033214e+01 3.05172034e+01 | 5.77148379e+01 -2.93033214e+01 3.05172034e+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 4.04897361e+01 4.13993306e+01 | -4.65309059e+01 4.04897361e+01 4.13993306e+01 43 6.15131275e-01 -2.27957823e+00 -2.41708419e+00 | 6.15131275e-01 -2.27957823e+00 -2.41708419e+00 44 -5.44376796e+01 -6.24847960e+01 -1.99992744e+01 | -5.44376796e+01 -6.24847960e+01 -1.99992744e+01 45 5.63060226e+01 6.11888729e+01 2.10138574e+01 | 5.63060226e+01 6.11888729e+01 2.10138574e+01 46 -4.92706412e+01 -5.37651098e+01 -7.02514622e+01 | -4.92706412e+01 -5.37651098e+01 -7.02514622e+01 47 6.01435522e+00 2.37093218e+01 9.83188319e+01 | 6.01435522e+00 2.37093218e+01 9.83188319e+01 48 -1.05268239e+02 -1.11161167e+02 -1.27024245e+02 | -1.05268239e+02 -1.11161167e+02 -1.27024245e+02 49 1.02277643e+02 1.10694204e+02 1.28072839e+02 | 1.02277643e+02 1.10694204e+02 1.28072839e+02 50 -4.83632581e+01 1.95046028e+01 2.77442560e+01 | -4.83632581e+01 1.95046028e+01 2.77442560e+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 1.62329732e+02 -1.48209269e+02 1.08190629e+02 | 1.62329732e+02 -1.48209269e+02 1.08190629e+02 59 -1.84818589e-01 1.65260527e+00 2.70287991e+00 | -1.84818589e-01 1.65260527e+00 2.70287991e+00 60 4.24838678e+01 3.26138353e+01 -3.17603592e+01 | 4.24838678e+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)) = 162.78657969222806 V(r_1,...,r_N) = 162.786579692228 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 -5.36255119e+01 -3.71427579e+01 5.63078463e+01 | -5.36255119e+01 -3.71427579e+01 5.63078463e+01 2 5.63260402e+01 4.04638837e+01 -6.55236966e+01 | 5.63260402e+01 4.04638837e+01 -6.55236966e+01 3 -3.00632743e+01 -1.68746468e+00 3.02664593e+01 | -3.00632743e+01 -1.68746468e+00 3.02664593e+01 4 -6.22455924e-01 -7.06040082e+00 2.63880913e+00 | -6.22455924e-01 -7.06040082e+00 2.63880913e+00 5 1.18355024e+00 1.09160903e+00 1.03214586e+00 | 1.18355024e+00 1.09160903e+00 1.03214586e+00 6 -1.36976983e+01 -1.90284430e+01 -3.43093616e+00 | -1.36976983e+01 -1.90284430e+01 -3.43093616e+00 7 9.12779332e+00 1.82613740e+01 1.03279211e+01 | 9.12779332e+00 1.82613740e+01 1.03279211e+01 8 -7.75085953e+00 -9.30330776e-01 -7.24652358e+00 | -7.75085953e+00 -9.30330776e-01 -7.24652358e+00 9 6.14858460e+00 2.82206285e+00 4.30736492e+00 | 6.14858460e+00 2.82206285e+00 4.30736492e+00 10 -3.62531261e+00 -4.28196132e+00 -4.29805698e+00 | -3.62531261e+00 -4.28196132e+00 -4.29805698e+00 11 3.43293304e+00 2.79130072e+00 3.87415905e+00 | 3.43293304e+00 2.79130072e+00 3.87415905e+00 12 1.55665447e+00 -3.64743134e-01 3.63903234e+00 | 1.55665447e+00 -3.64743134e-01 3.63903234e+00 13 4.86405552e+00 -8.82145660e+00 -3.58251565e+01 | 4.86405552e+00 -8.82145660e+00 -3.58251565e+01 14 3.92639794e+00 1.24074798e+00 -5.97125654e-01 | 3.92639794e+00 1.24074798e+00 -5.97125654e-01 15 5.32928751e+00 -2.45686424e+00 -7.65177744e-01 | 5.32928751e+00 -2.45686424e+00 -7.65177744e-01 16 2.53925549e-01 -6.68197142e-01 1.07260558e-01 | 2.53925549e-01 -6.68197142e-01 1.07260558e-01 17 -2.65763743e+01 -4.42658929e+01 5.62400394e+01 | -2.65763743e+01 -4.42658929e+01 5.62400394e+01 18 3.49340967e+01 3.85923191e+01 -6.74862568e+01 | 3.49340967e+01 3.85923191e+01 -6.74862568e+01 19 -9.92434031e+01 4.69069282e+01 -2.12172120e+01 | -9.92434031e+01 4.69069282e+01 -2.12172120e+01 20 -2.96150824e-01 2.48942610e+00 6.35136939e-01 | -2.96150824e-01 2.48942610e+00 6.35136939e-01 21 -1.74500731e+00 -1.53543571e+01 1.58694172e+01 | -1.74500731e+00 -1.53543571e+01 1.58694172e+01 22 -1.10186572e+01 4.90464773e+00 9.04038985e+00 | -1.10186572e+01 4.90464773e+00 9.04038985e+00 23 -1.04802997e+00 -8.82972456e-01 -1.03076259e-01 | -1.04802997e+00 -8.82972456e-01 -1.03076259e-01 24 3.12924365e+01 1.87813088e+00 -3.10888368e+01 | 3.12924365e+01 1.87813088e+00 -3.10888368e+01 25 -9.06868003e+01 -3.61258183e+01 8.28648237e+01 | -9.06868003e+01 -3.61258183e+01 8.28648237e+01 26 8.92843292e+01 3.10409219e+01 -8.51601658e+01 | 8.92843292e+01 3.10409219e+01 -8.51601658e+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 1.00645398e+02 -2.82852231e+01 9.20766269e+00 | 1.00645398e+02 -2.82852231e+01 9.20766269e+00 31 -7.99712710e+00 6.02135628e+00 -9.07266320e+00 | -7.99712710e+00 6.02135628e+00 -9.07266320e+00 32 -9.36663406e+00 -1.48245068e+01 -1.58758357e+01 | -9.36663406e+00 -1.48245068e+01 -1.58758357e+01 33 1.10479262e+02 -9.48713893e+01 -7.47150363e+01 | 1.10479262e+02 -9.48713893e+01 -7.47150363e+01 34 -5.35034973e+01 -7.16025582e+01 -5.05781290e+01 | -5.35034973e+01 -7.16025582e+01 -5.05781290e+01 35 5.30704630e+01 6.01077354e+01 3.15135734e+01 | 5.30704630e+01 6.01077354e+01 3.15135734e+01 36 -6.63307962e+00 -5.36983223e+00 -1.13974479e+01 | -6.63307962e+00 -5.36983223e+00 -1.13974479e+01 37 7.57567882e+00 4.37661138e+00 1.29590825e+01 | 7.57567882e+00 4.37661138e+00 1.29590825e+01 38 -1.05892299e+02 1.11713295e+02 8.86819566e+01 | -1.05892299e+02 1.11713295e+02 8.86819566e+01 39 3.22624038e+00 -1.08053146e+00 9.18696780e-01 | 3.22624038e+00 -1.08053146e+00 9.18696780e-01 40 -3.26583915e+00 -3.22160147e+00 -1.19053267e+00 | -3.26583915e+00 -3.22160147e+00 -1.19053267e+00 41 2.34398456e+01 -3.88976578e+01 -3.41554043e+01 | 2.34398456e+01 -3.88976578e+01 -3.41554043e+01 42 -5.00442802e+00 7.31342472e+00 3.53051797e+01 | -5.00442802e+00 7.31342472e+00 3.53051797e+01 43 1.23015016e+01 -1.37591578e+01 -7.06404184e+00 | 1.23015016e+01 -1.37591578e+01 -7.06404184e+00 44 -4.88100725e+00 -7.56445868e+00 -8.61038082e+00 | -4.88100725e+00 -7.56445868e+00 -8.61038082e+00 45 8.71055850e+00 4.50834805e+00 1.07904253e+01 | 8.71055850e+00 4.50834805e+00 1.07904253e+01 46 -5.77733596e+01 -2.67294683e+00 2.17308408e+01 | -5.77733596e+01 -2.67294683e+00 2.17308408e+01 47 3.47830092e+01 4.54407988e+01 1.38548551e+01 | 3.47830092e+01 4.54407988e+01 1.38548551e+01 48 2.08128694e+00 1.05210601e+00 9.92041257e-01 | 2.08128694e+00 1.05210601e+00 9.92041257e-01 49 -4.42258793e+01 -1.14444392e+02 7.36720750e+01 | -4.42258793e+01 -1.14444392e+02 7.36720750e+01 50 6.32326855e+01 1.04400940e+02 -9.71279428e+01 | 6.32326855e+01 1.04400940e+02 -9.71279428e+01 51 -4.01830477e+00 2.89634494e+01 -1.65381810e+01 | -4.01830477e+00 2.89634494e+01 -1.65381810e+01 52 -2.33667496e+00 3.05582847e+00 2.45885058e+00 | -2.33667496e+00 3.05582847e+00 2.45885058e+00 53 -2.95392634e+00 6.62591788e+00 1.43245740e+01 | -2.95392634e+00 6.62591788e+00 1.43245740e+01 54 -2.17643438e+01 2.91105087e-01 1.68346485e+01 | -2.17643438e+01 2.91105087e-01 1.68346485e+01 55 2.81104074e+00 4.80901609e+00 3.91616069e+00 | 2.81104074e+00 4.80901609e+00 3.91616069e+00 56 -7.17000263e+00 5.12143948e+00 -9.54086140e-03 | -7.17000263e+00 5.12143948e+00 -9.54086140e-03 57 -2.35662442e+01 5.95583395e+00 -1.32743620e+01 | -2.35662442e+01 5.95583395e+00 -1.32743620e+01 58 -2.34749448e+00 -1.17674327e+01 -4.34269492e+00 | -2.34749448e+00 -1.17674327e+01 -4.34269492e+00 59 9.79189867e+00 4.18936510e+00 1.31323072e+01 | 9.79189867e+00 4.18936510e+00 1.31323072e+01 60 1.10319127e+01 9.36095287e+00 1.79750880e+01 | 1.10319127e+01 9.36095287e+00 1.79750880e+01 61 3.74199384e-01 1.70995331e+00 3.44294510e-01 | 3.74199384e-01 1.70995331e+00 3.44294510e-01 62 8.42173345e+00 -2.41096069e+01 1.63506340e+01 | 8.42173345e+00 -2.41096069e+01 1.63506340e+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.