!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KimJungLee_2015_NiAlCo__MO_876687166519_000 Supported species : Al Co Ni 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 = [35, 22, 27, 49, 11, 19, 55, 31, 38, 54, 15, 4, 50, 46, 40, 10, 17, 16, 58, 5, 53, 39, 1, 44, 52, 63, 28, 2, 26, 32, 45, 7, 29, 43, 37, 0, 59, 34, 8, 21, 14, 56, 57, 33, 23, 30, 13, 61, 51, 3, 12, 48, 24, 20, 9, 6, 41, 42, 18, 36, 62, 47, 60, 25] 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)) = 16.993340475474298 V(r_1,...,r_N) = 16.993340475474273 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 -2.56177824e+00 -1.67297970e+00 -2.37620819e+00 | -2.56177824e+00 -1.67297970e+00 -2.37620819e+00 1 -1.02035291e+01 -1.41980540e+01 8.03175298e+00 | -1.02035291e+01 -1.41980540e+01 8.03175298e+00 2 -1.16430614e+00 5.99886067e+00 -2.66842746e+01 | -1.16430614e+00 5.99886067e+00 -2.66842746e+01 3 6.28416197e+00 1.47584806e+01 9.75869698e+00 | 6.28416197e+00 1.47584806e+01 9.75869698e+00 4 2.47106016e+00 -5.82637785e+00 6.81015262e+00 | 2.47106016e+00 -5.82637785e+00 6.81015262e+00 5 4.76651785e-01 1.61900590e+00 -9.80801613e-01 | 4.76651785e-01 1.61900590e+00 -9.80801613e-01 6 -1.99370143e+00 -3.83385105e+00 -5.10211433e+00 | -1.99370143e+00 -3.83385105e+00 -5.10211433e+00 7 -9.63005296e+00 4.71880749e+01 -2.55985861e+01 | -9.63005296e+00 4.71880749e+01 -2.55985861e+01 8 -9.37203968e+00 -1.05245412e+01 -1.35594442e+01 | -9.37203968e+00 -1.05245412e+01 -1.35594442e+01 9 6.85601036e+00 5.24870900e+00 1.79878242e+01 | 6.85601036e+00 5.24870900e+00 1.79878242e+01 10 5.65070671e+00 2.91283627e+00 -7.92049432e+00 | 5.65070671e+00 2.91283627e+00 -7.92049432e+00 11 3.02430744e+00 -1.75063440e+00 -7.48824929e-01 | 3.02430744e+00 -1.75063440e+00 -7.48824929e-01 12 -5.00801239e+00 -3.35785822e+00 -5.90898153e+00 | -5.00801239e+00 -3.35785822e+00 -5.90898153e+00 13 2.00608570e+01 -8.77175742e+00 -4.18265451e+00 | 2.00608570e+01 -8.77175742e+00 -4.18265451e+00 14 -9.28341646e-01 -1.31906795e-01 1.31128582e+00 | -9.28341646e-01 -1.31906795e-01 1.31128582e+00 15 1.59914873e+00 -2.33725568e+00 -1.82735659e+00 | 1.59914873e+00 -2.33725568e+00 -1.82735659e+00 16 -2.53052918e+00 -1.53081175e+00 -1.81355743e+00 | -2.53052918e+00 -1.53081175e+00 -1.81355743e+00 17 -4.45994068e+00 -1.57367083e+01 1.93360157e+01 | -4.45994068e+00 -1.57367083e+01 1.93360157e+01 18 4.59725219e+00 1.65853158e+01 -1.96043271e+01 | 4.59725219e+00 1.65853158e+01 -1.96043271e+01 19 -2.95174974e+01 2.03025778e+01 -2.00974272e+01 | -2.95174974e+01 2.03025778e+01 -2.00974272e+01 20 -1.07263328e+01 -9.39033604e+00 -8.49025517e+00 | -1.07263328e+01 -9.39033604e+00 -8.49025517e+00 21 1.76132531e+01 1.18427619e+01 7.60859467e+00 | 1.76132531e+01 1.18427619e+01 7.60859467e+00 22 -2.87297064e+00 -7.75048202e+00 -1.37315385e+01 | -2.87297064e+00 -7.75048202e+00 -1.37315385e+01 23 2.05334831e+00 7.86904304e+00 1.43338449e+01 | 2.05334831e+00 7.86904304e+00 1.43338449e+01 24 -1.00209982e+00 -7.65789607e-01 -9.36782991e-01 | -1.00209982e+00 -7.65789607e-01 -9.36782991e-01 25 -1.03458649e+01 1.37641235e+01 -9.91750345e+00 | -1.03458649e+01 1.37641235e+01 -9.91750345e+00 26 -1.02445389e+00 -3.76869285e-01 -4.98500983e-01 | -1.02445389e+00 -3.76869285e-01 -4.98500983e-01 27 6.04789673e-01 -2.21020566e-01 9.55529589e-01 | 6.04789673e-01 -2.21020566e-01 9.55529589e-01 28 8.83528871e+00 -1.14178441e+01 1.22102683e+01 | 8.83528871e+00 -1.14178441e+01 1.22102683e+01 29 1.71114029e+00 3.24005278e-01 9.67103943e-01 | 1.71114029e+00 3.24005278e-01 9.67103943e-01 30 2.93141050e+01 -1.75928510e+01 1.72826831e+01 | 2.93141050e+01 -1.75928510e+01 1.72826831e+01 31 -1.56201593e+01 6.67345077e+00 -8.37786399e+00 | -1.56201593e+01 6.67345077e+00 -8.37786399e+00 32 -4.71537386e+00 -4.57530840e+00 -2.36985308e+00 | -4.71537386e+00 -4.57530840e+00 -2.36985308e+00 33 -1.91955738e+00 -4.40187825e+00 6.25803643e+00 | -1.91955738e+00 -4.40187825e+00 6.25803643e+00 34 2.49023248e+01 -3.86442922e+01 2.22199772e+01 | 2.49023248e+01 -3.86442922e+01 2.22199772e+01 35 -4.81600309e+00 -6.68787052e+00 4.86466457e+00 | -4.81600309e+00 -6.68787052e+00 4.86466457e+00 36 -5.38110732e+00 4.70299065e-01 2.17951918e+00 | -5.38110732e+00 4.70299065e-01 2.17951918e+00 37 -7.57020201e+00 -2.14641632e+01 1.59233020e+01 | -7.57020201e+00 -2.14641632e+01 1.59233020e+01 38 -6.58153722e+00 -5.36807331e+00 -5.66041675e+00 | -6.58153722e+00 -5.36807331e+00 -5.66041675e+00 39 -7.41420652e+00 -6.84659504e+00 1.37211634e+01 | -7.41420652e+00 -6.84659504e+00 1.37211634e+01 40 4.25022918e+00 -2.44543002e+00 -3.91919855e-01 | 4.25022918e+00 -2.44543002e+00 -3.91919855e-01 41 -1.74359618e+01 2.38654755e+01 -1.17425728e+01 | -1.74359618e+01 2.38654755e+01 -1.17425728e+01 42 -1.55483080e+01 6.74250172e+00 3.83533043e+00 | -1.55483080e+01 6.74250172e+00 3.83533043e+00 43 3.34389393e+00 6.68474621e+00 4.35421145e+00 | 3.34389393e+00 6.68474621e+00 4.35421145e+00 44 1.62623143e+01 -2.55337090e+01 1.34298007e+01 | 1.62623143e+01 -2.55337090e+01 1.34298007e+01 45 -9.25086912e-01 1.10519286e+00 -2.89987249e-01 | -9.25086912e-01 1.10519286e+00 -2.89987249e-01 46 8.87319558e+00 1.99143343e+01 -1.23385300e+01 | 8.87319558e+00 1.99143343e+01 -1.23385300e+01 47 5.04854100e+00 -5.30638301e+00 -1.15679674e+00 | 5.04854100e+00 -5.30638301e+00 -1.15679674e+00 48 -1.10886562e+01 3.85361231e+00 6.04676630e+00 | -1.10886562e+01 3.85361231e+00 6.04676630e+00 49 4.31876685e-01 -1.75748437e+00 -9.89810939e-01 | 4.31876685e-01 -1.75748437e+00 -9.89810939e-01 50 -7.90226814e+00 -1.12036550e+01 -1.15761695e+01 | -7.90226814e+00 -1.12036550e+01 -1.15761695e+01 51 7.68535390e+00 1.18447451e+01 1.08040891e+01 | 7.68535390e+00 1.18447451e+01 1.08040891e+01 52 1.23673779e+01 1.27915624e+01 -7.68805737e+00 | 1.23673779e+01 1.27915624e+01 -7.68805737e+00 53 -3.42481768e+00 4.25570893e+00 1.55882023e+00 | -3.42481768e+00 4.25570893e+00 1.55882023e+00 54 -6.08880449e+00 6.81352377e-01 -1.60084970e+00 | -6.08880449e+00 6.81352377e-01 -1.60084970e+00 55 4.18804277e+00 1.11942627e+00 3.10436873e+00 | 4.18804277e+00 1.11942627e+00 3.10436873e+00 56 7.51408548e-02 5.54190465e+00 -2.64081047e+00 | 7.51408548e-02 5.54190465e+00 -2.64081047e+00 57 1.75173936e+01 -2.38536692e+01 -2.97036954e+01 | 1.75173936e+01 -2.38536692e+01 -2.97036954e+01 58 1.66715544e+01 -5.47723815e+00 1.01979474e+01 | 1.66715544e+01 -5.47723815e+00 1.01979474e+01 59 -3.45249111e-01 -4.43662205e-01 5.15095444e-01 | -3.45249111e-01 -4.43662205e-01 5.15095444e-01 60 -2.17975403e+00 -2.66271098e+00 -3.48390047e+00 | -2.17975403e+00 -2.66271098e+00 -3.48390047e+00 61 3.72067865e+00 3.38344672e+00 4.05947398e+00 | 3.72067865e+00 3.38344672e+00 4.05947398e+00 62 -1.47734909e+01 2.66134919e+01 3.04537823e+01 | -1.47734909e+01 2.66134919e+01 3.04537823e+01 63 5.81995864e-01 -9.49938516e-02 -1.29233659e-01 | 5.81995864e-01 -9.49938516e-02 -1.29233659e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [53, 25, 28, 7, 30, 45, 36, 3, 44, 20, 29, 34, 43, 54, 60, 19, 31, 23, 39, 15, 9, 55, 59, 17, 57, 1, 62, 47, 2, 10, 4, 16, 50, 58, 11, 51, 6, 48, 61, 18, 56, 42, 41, 12, 8, 5, 49, 27, 37, 46, 32, 35, 63, 0, 13, 21, 40, 24, 33, 22, 14, 38, 26, 52] 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)) = -106.76067190110142 V(r_1,...,r_N) = -106.7606719011014 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 -5.15107013e+00 -3.71141574e+00 -5.83429650e+00 | -5.15107013e+00 -3.71141574e+00 -5.83429650e+00 1 2.12211021e+00 -1.69549431e+00 1.13492581e+01 | 2.12211021e+00 -1.69549431e+00 1.13492581e+01 2 6.07467973e-02 1.12179500e+01 -9.52255436e+00 | 6.07467973e-02 1.12179500e+01 -9.52255436e+00 3 -6.08120529e+00 -8.61107270e+00 2.34243679e+00 | -6.08120529e+00 -8.61107270e+00 2.34243679e+00 4 3.45854197e+00 -4.70347146e+00 4.95257661e+00 | 3.45854197e+00 -4.70347146e+00 4.95257661e+00 5 6.68418094e+00 -1.05414621e+01 -1.00596430e+01 | 6.68418094e+00 -1.05414621e+01 -1.00596430e+01 6 -2.74481614e+00 -2.16502295e+00 -2.04755627e+00 | -2.74481614e+00 -2.16502295e+00 -2.04755627e+00 7 -4.56833873e+00 -2.72713921e+01 1.23998348e+01 | -4.56833873e+00 -2.72713921e+01 1.23998348e+01 8 -2.13850471e-01 8.52372322e-01 1.05419878e+00 | -2.13850471e-01 8.52372322e-01 1.05419878e+00 9 -1.61631996e-01 -1.24607228e+00 1.46153074e+00 | -1.61631996e-01 -1.24607228e+00 1.46153074e+00 10 4.35840296e-01 2.32799223e-01 -7.50760524e-01 | 4.35840296e-01 2.32799223e-01 -7.50760524e-01 11 -2.15886862e-01 5.94915896e-01 8.80454074e-01 | -2.15886862e-01 5.94915896e-01 8.80454074e-01 12 -1.95120536e+00 -8.20939593e+00 -3.53654021e+00 | -1.95120536e+00 -8.20939593e+00 -3.53654021e+00 13 1.81493965e+00 5.47280843e+00 -2.20214265e-01 | 1.81493965e+00 5.47280843e+00 -2.20214265e-01 14 -1.68089836e+00 -7.01617038e-01 -1.18952773e+00 | -1.68089836e+00 -7.01617038e-01 -1.18952773e+00 15 -6.53479294e+00 3.78867232e+00 -1.39889680e+00 | -6.53479294e+00 3.78867232e+00 -1.39889680e+00 16 -4.17041168e-02 -8.55508752e-01 -1.01392529e-01 | -4.17041168e-02 -8.55508752e-01 -1.01392529e-01 17 4.22434459e-01 7.97665153e-01 8.15126350e-01 | 4.22434459e-01 7.97665153e-01 8.15126350e-01 18 -2.08241178e-01 -7.37266179e-01 1.03730884e+00 | -2.08241178e-01 -7.37266179e-01 1.03730884e+00 19 -3.00028548e+00 1.84214468e+00 3.77890376e-01 | -3.00028548e+00 1.84214468e+00 3.77890376e-01 20 6.95352453e+00 3.04415395e+01 -1.37683953e+01 | 6.95352453e+00 3.04415395e+01 -1.37683953e+01 21 -3.33209867e+00 3.85196247e+00 -4.55491176e+00 | -3.33209867e+00 3.85196247e+00 -4.55491176e+00 22 8.31856055e-02 -1.12795583e+00 -5.83814835e-01 | 8.31856055e-02 -1.12795583e+00 -5.83814835e-01 23 8.07816429e-01 1.57265828e-01 1.19622231e+00 | 8.07816429e-01 1.57265828e-01 1.19622231e+00 24 5.49259336e+00 8.53091632e+00 3.31981367e-01 | 5.49259336e+00 8.53091632e+00 3.31981367e-01 25 7.81305966e+00 -9.45327099e+00 -6.87174500e+00 | 7.81305966e+00 -9.45327099e+00 -6.87174500e+00 26 -1.85999265e+01 -2.22581645e+01 -1.20471890e+01 | -1.85999265e+01 -2.22581645e+01 -1.20471890e+01 27 1.87611802e+01 2.20004166e+01 1.07676842e+01 | 1.87611802e+01 2.20004166e+01 1.07676842e+01 28 -5.58864112e+00 -5.57033561e+00 -5.75186621e-01 | -5.58864112e+00 -5.57033561e+00 -5.75186621e-01 29 6.04537224e+00 6.64427006e+00 -3.05119566e-01 | 6.04537224e+00 6.64427006e+00 -3.05119566e-01 30 -4.46420942e+00 7.77630614e+00 6.07463225e+00 | -4.46420942e+00 7.77630614e+00 6.07463225e+00 31 -6.70848312e-01 -9.12092018e-01 3.62387392e-01 | -6.70848312e-01 -9.12092018e-01 3.62387392e-01 32 1.34304945e+00 4.20959478e-01 5.16900842e-01 | 1.34304945e+00 4.20959478e-01 5.16900842e-01 33 -3.78803128e+00 1.70271892e+01 -8.32742421e+00 | -3.78803128e+00 1.70271892e+01 -8.32742421e+00 34 -6.91988139e+00 7.86399911e+00 8.27037244e+00 | -6.91988139e+00 7.86399911e+00 8.27037244e+00 35 1.20071380e+00 1.40217750e+00 3.02200906e+00 | 1.20071380e+00 1.40217750e+00 3.02200906e+00 36 3.76458284e+00 -1.64912363e+01 8.22595481e+00 | 3.76458284e+00 -1.64912363e+01 8.22595481e+00 37 -2.46179689e+00 -1.66476350e+00 3.26557126e-02 | -2.46179689e+00 -1.66476350e+00 3.26557126e-02 38 7.09353638e-01 5.59419924e-01 -2.69474405e-01 | 7.09353638e-01 5.59419924e-01 -2.69474405e-01 39 -1.03861964e-01 -5.99565652e-01 -3.42650749e-01 | -1.03861964e-01 -5.99565652e-01 -3.42650749e-01 40 1.96422318e-01 7.55107479e-01 -3.15471139e-01 | 1.96422318e-01 7.55107479e-01 -3.15471139e-01 41 4.47694786e+00 -7.53100227e+00 -1.15591910e+01 | 4.47694786e+00 -7.53100227e+00 -1.15591910e+01 42 4.48880809e+00 2.13833822e-01 7.28520476e+00 | 4.48880809e+00 2.13833822e-01 7.28520476e+00 43 1.19859242e+00 -1.99853171e+00 -1.26297404e+00 | 1.19859242e+00 -1.99853171e+00 -1.26297404e+00 44 -1.59223213e+00 -8.24227773e+00 -1.44814287e+00 | -1.59223213e+00 -8.24227773e+00 -1.44814287e+00 45 2.68680602e+00 7.08422333e+00 2.93665573e+00 | 2.68680602e+00 7.08422333e+00 2.93665573e+00 46 -3.30002312e+00 1.15663668e+01 9.77402879e+00 | -3.30002312e+00 1.15663668e+01 9.77402879e+00 47 -5.36302985e-01 -3.76972745e+00 1.53639714e+00 | -5.36302985e-01 -3.76972745e+00 1.53639714e+00 48 8.33575049e-02 -8.77314231e-01 -1.49618056e+00 | 8.33575049e-02 -8.77314231e-01 -1.49618056e+00 49 2.31021421e+00 6.85182507e-01 5.58801964e-01 | 2.31021421e+00 6.85182507e-01 5.58801964e-01 50 -1.32182011e+00 -1.14110070e+01 -8.93622918e+00 | -1.32182011e+00 -1.14110070e+01 -8.93622918e+00 51 1.43236748e+00 1.07171969e+01 9.33971550e+00 | 1.43236748e+00 1.07171969e+01 9.33971550e+00 52 -2.11957751e+00 -2.62790060e+00 -1.88680893e+00 | -2.11957751e+00 -2.62790060e+00 -1.88680893e+00 53 1.10608720e+00 2.71869785e+00 2.31708599e+00 | 1.10608720e+00 2.71869785e+00 2.31708599e+00 54 -1.02010980e+00 1.36893495e+00 5.74286859e-01 | -1.02010980e+00 1.36893495e+00 5.74286859e-01 55 6.19730911e-01 -9.22720930e-01 -9.67966984e-01 | 6.19730911e-01 -9.22720930e-01 -9.67966984e-01 56 4.82730331e+00 -3.35703657e+00 1.13711466e+00 | 4.82730331e+00 -3.35703657e+00 1.13711466e+00 57 -8.39231563e+00 3.32392319e+00 -8.07827078e+00 | -8.39231563e+00 3.32392319e+00 -8.07827078e+00 58 -6.58877290e+00 -6.96965703e+00 1.28932937e+00 | -6.58877290e+00 -6.96965703e+00 1.28932937e+00 59 5.57257313e+00 4.86249520e+00 7.16846971e-01 | 5.57257313e+00 4.86249520e+00 7.16846971e-01 60 7.10072264e+00 9.80851439e-01 7.72526051e+00 | 7.10072264e+00 9.80851439e-01 7.72526051e+00 61 -4.93916260e-01 1.44694899e-01 -6.21903263e-01 | -4.93916260e-01 1.44694899e-01 -6.21903263e-01 62 6.12580452e-01 3.12753704e-01 -3.25342185e+00 | 6.12580452e-01 3.12753704e-01 -3.25342185e+00 63 -8.37446620e-01 2.37391471e-02 1.47171036e+00 | -8.37446620e-01 2.37391471e-02 1.47171036e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [14, 23, 60, 17, 5, 4, 42, 63, 46, 55, 31, 15, 22, 34, 0, 11, 30, 3, 20, 56, 18, 35, 12, 1, 38, 53, 28, 52, 26, 33, 16, 10, 50, 29, 13, 21, 49, 45, 24, 62, 57, 51, 6, 59, 47, 37, 8, 44, 58, 36, 32, 41, 27, 25, 61, 9, 19, 40, 48, 43, 2, 54, 39, 7] 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)) = -28.05538598941579 V(r_1,...,r_N) = -28.055385989415793 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 -2.28871482e+00 -9.49664422e-01 -4.67958633e+00 | -2.28871482e+00 -9.49664422e-01 -4.67958633e+00 1 -1.22613498e+01 1.30516359e+01 -1.36669721e+01 | -1.22613498e+01 1.30516359e+01 -1.36669721e+01 2 -4.18695302e-01 -9.29806971e-01 8.84972799e-01 | -4.18695302e-01 -9.29806971e-01 8.84972799e-01 3 1.32944639e+01 -2.48169841e+01 -2.07925032e+01 | 1.32944639e+01 -2.48169841e+01 -2.07925032e+01 4 1.92576358e+01 -1.82667061e+01 1.50360859e+01 | 1.92576358e+01 -1.82667061e+01 1.50360859e+01 5 6.79614955e-01 1.52225118e-02 -5.23576881e-01 | 6.79614955e-01 1.52225118e-02 -5.23576881e-01 6 -4.83280019e+00 6.05437122e+00 2.30328598e+00 | -4.83280019e+00 6.05437122e+00 2.30328598e+00 7 1.06394780e+01 -8.99355769e+00 -1.20630023e+01 | 1.06394780e+01 -8.99355769e+00 -1.20630023e+01 8 -1.82154934e+00 -2.53677184e-01 -7.37025268e-01 | -1.82154934e+00 -2.53677184e-01 -7.37025268e-01 9 4.31009330e+00 -2.55082725e+00 -2.10163230e+00 | 4.31009330e+00 -2.55082725e+00 -2.10163230e+00 10 -7.98236586e+00 -8.71447187e+00 -8.22039198e+00 | -7.98236586e+00 -8.71447187e+00 -8.22039198e+00 11 7.46158767e+00 8.59825134e+00 8.61575005e+00 | 7.46158767e+00 8.59825134e+00 8.61575005e+00 12 -6.43611859e+00 -6.58879133e+00 -6.63269659e+00 | -6.43611859e+00 -6.58879133e+00 -6.63269659e+00 13 7.96345229e+00 5.22771906e+00 6.47324347e+00 | 7.96345229e+00 5.22771906e+00 6.47324347e+00 14 -2.05099502e+00 -1.91841922e+00 2.74794491e+00 | -2.05099502e+00 -1.91841922e+00 2.74794491e+00 15 3.75683133e+00 9.89385145e-01 1.94813848e+00 | 3.75683133e+00 9.89385145e-01 1.94813848e+00 16 1.02593864e+00 4.17471720e-02 7.00501499e-01 | 1.02593864e+00 4.17471720e-02 7.00501499e-01 17 -1.38626181e+00 -4.07351546e+00 2.84223608e+00 | -1.38626181e+00 -4.07351546e+00 2.84223608e+00 18 -6.04336132e-01 6.62558930e-01 -8.53964469e+00 | -6.04336132e-01 6.62558930e-01 -8.53964469e+00 19 2.63854930e+00 1.77781007e+00 4.13959646e+00 | 2.63854930e+00 1.77781007e+00 4.13959646e+00 20 -1.76567515e+01 3.02883883e+01 1.78179221e+01 | -1.76567515e+01 3.02883883e+01 1.78179221e+01 21 -1.99753839e+01 2.07569992e+01 -2.20111751e+01 | -1.99753839e+01 2.07569992e+01 -2.20111751e+01 22 -1.06989175e+01 -1.08905428e+01 -1.17325402e+01 | -1.06989175e+01 -1.08905428e+01 -1.17325402e+01 23 9.22050928e+00 1.24614157e+01 1.29337717e+01 | 9.22050928e+00 1.24614157e+01 1.29337717e+01 24 1.73786337e-01 5.93075492e-01 5.36030074e-01 | 1.73786337e-01 5.93075492e-01 5.36030074e-01 25 9.57436667e+00 -4.90774003e+00 -1.42428641e+01 | 9.57436667e+00 -4.90774003e+00 -1.42428641e+01 26 -1.11355915e-01 -3.09966137e-01 5.93740311e-01 | -1.11355915e-01 -3.09966137e-01 5.93740311e-01 27 -8.46147491e-01 -7.36455110e-01 7.59281723e-01 | -8.46147491e-01 -7.36455110e-01 7.59281723e-01 28 5.70635823e+00 -7.12271219e+00 3.83429295e+00 | 5.70635823e+00 -7.12271219e+00 3.83429295e+00 29 3.18822797e+00 -1.18479056e+00 -1.47715767e+00 | 3.18822797e+00 -1.18479056e+00 -1.47715767e+00 30 -1.12778702e+01 1.55685842e+01 6.29222337e+00 | -1.12778702e+01 1.55685842e+01 6.29222337e+00 31 -2.39196876e+00 2.38662010e+01 -1.80058944e+01 | -2.39196876e+00 2.38662010e+01 -1.80058944e+01 32 9.27356039e-01 5.08298549e-01 4.40821174e-01 | 9.27356039e-01 5.08298549e-01 4.40821174e-01 33 -7.57689989e+00 -1.13281367e+01 1.18016180e+01 | -7.57689989e+00 -1.13281367e+01 1.18016180e+01 34 -9.98501100e+00 -4.87664460e+00 -2.44176768e+01 | -9.98501100e+00 -4.87664460e+00 -2.44176768e+01 35 2.33634177e+01 -2.01530078e+00 -7.97637210e+00 | 2.33634177e+01 -2.01530078e+00 -7.97637210e+00 36 -1.72890701e-02 -3.45135859e-01 -3.23019573e-02 | -1.72890701e-02 -3.45135859e-01 -3.23019573e-02 37 -2.24754041e+01 -8.68219200e+00 2.30198484e+01 | -2.24754041e+01 -8.68219200e+00 2.30198484e+01 38 -1.71173520e+00 -2.33005902e+00 -2.95686903e+00 | -1.71173520e+00 -2.33005902e+00 -2.95686903e+00 39 2.41878410e+00 2.14223984e+00 2.13737519e+00 | 2.41878410e+00 2.14223984e+00 2.13737519e+00 40 -2.89609721e-01 5.40778192e-01 -7.35385956e-01 | -2.89609721e-01 5.40778192e-01 -7.35385956e-01 41 -5.06985418e+01 6.00606205e+00 2.45429494e+01 | -5.06985418e+01 6.00606205e+00 2.45429494e+01 42 5.16062789e+01 -5.55512085e+00 -2.53119071e+01 | 5.16062789e+01 -5.55512085e+00 -2.53119071e+01 43 -6.92144307e-01 9.52447484e-01 6.84333248e-01 | -6.92144307e-01 9.52447484e-01 6.84333248e-01 44 -8.35676728e+00 -7.36697980e+00 -1.93447656e+01 | -8.35676728e+00 -7.36697980e+00 -1.93447656e+01 45 8.35925676e+00 6.98316410e+00 2.01327153e+01 | 8.35925676e+00 6.98316410e+00 2.01327153e+01 46 2.11344301e+01 9.08401810e+00 -2.16075552e+01 | 2.11344301e+01 9.08401810e+00 -2.16075552e+01 47 -3.80346293e+00 -7.94105198e+00 4.59412924e+00 | -3.80346293e+00 -7.94105198e+00 4.59412924e+00 48 -1.33954740e+01 5.72627291e+00 1.12433621e+01 | -1.33954740e+01 5.72627291e+00 1.12433621e+01 49 -3.23112084e+01 -3.99546983e+01 1.90232375e+01 | -3.23112084e+01 -3.99546983e+01 1.90232375e+01 50 3.66467468e+01 4.05979072e+01 -1.94425650e+01 | 3.66467468e+01 4.05979072e+01 -1.94425650e+01 51 -2.77248718e-02 -5.51643754e-01 1.12289157e+00 | -2.77248718e-02 -5.51643754e-01 1.12289157e+00 52 -9.31627180e+00 1.55875397e+01 1.57402001e+01 | -9.31627180e+00 1.55875397e+01 1.57402001e+01 53 -1.48806712e+01 -1.32245009e+01 2.03945515e+01 | -1.48806712e+01 -1.32245009e+01 2.03945515e+01 54 -1.84334766e+00 3.06552726e+00 2.20808813e+00 | -1.84334766e+00 3.06552726e+00 2.20808813e+00 55 3.10779952e-01 -8.16372376e-01 -1.13302151e+00 | 3.10779952e-01 -8.16372376e-01 -1.13302151e+00 56 1.69296320e+01 -2.37877459e+01 2.62179634e+01 | 1.69296320e+01 -2.37877459e+01 2.62179634e+01 57 -1.21446648e+00 1.58213494e-01 1.45618186e+00 | -1.21446648e+00 1.58213494e-01 1.45618186e+00 58 8.61992935e-01 -2.13711029e+01 1.77227075e+01 | 8.61992935e-01 -2.13711029e+01 1.77227075e+01 59 -6.84961444e-01 -9.72554903e-01 -5.96178038e-01 | -6.84961444e-01 -9.72554903e-01 -5.96178038e-01 60 1.15441780e+00 5.49776309e+00 -5.47696926e+00 | 1.15441780e+00 5.49776309e+00 -5.47696926e+00 61 3.55650411e+00 1.30889053e+00 3.62127716e-01 | 3.55650411e+00 1.30889053e+00 3.62127716e-01 62 1.63685128e+01 1.69297860e+01 -1.60268901e+01 | 1.63685128e+01 1.69297860e+01 -1.60268901e+01 63 -2.06430327e-01 -7.14404507e-01 -8.18998494e-01 | -2.06430327e-01 -7.14404507e-01 -8.18998494e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Co Ni (Configuration in file "config-AlCoNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [35, 28, 63, 36, 51, 42, 34, 30, 20, 21, 54, 44, 31, 33, 52, 43, 59, 26, 55, 25, 8, 9, 40, 39, 57, 19, 17, 32, 1, 37, 7, 12, 27, 13, 6, 0, 3, 29, 53, 23, 22, 49, 5, 15, 11, 47, 58, 45, 50, 41, 48, 4, 14, 38, 10, 18, 60, 24, 46, 16, 56, 61, 62, 2] 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)) = -60.024509064269964 V(r_1,...,r_N) = -60.024509064269935 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 -5.94274076e+00 -4.21091405e+00 -6.29732614e+00 | -5.94274076e+00 -4.21091405e+00 -6.29732614e+00 1 6.10776732e+00 -4.11984387e+00 -1.63983568e+01 | 6.10776732e+00 -4.11984387e+00 -1.63983568e+01 2 -4.24899632e+00 -1.83275695e+00 -5.41887067e+00 | -4.24899632e+00 -1.83275695e+00 -5.41887067e+00 3 -1.05476485e+01 2.20834452e+01 -2.15104828e+01 | -1.05476485e+01 2.20834452e+01 -2.15104828e+01 4 8.48652027e+00 -5.86517310e+00 5.81144966e+00 | 8.48652027e+00 -5.86517310e+00 5.81144966e+00 5 -8.11752306e+00 -5.78397125e+00 6.85211919e+00 | -8.11752306e+00 -5.78397125e+00 6.85211919e+00 6 -9.33342993e+00 1.23840182e+01 1.83176940e+01 | -9.33342993e+00 1.23840182e+01 1.83176940e+01 7 -2.10909423e+00 -3.93312259e+00 -3.00132878e+00 | -2.10909423e+00 -3.93312259e+00 -3.00132878e+00 8 -2.79329307e+01 -2.79979300e+01 -1.85326548e+01 | -2.79329307e+01 -2.79979300e+01 -1.85326548e+01 9 2.19691553e+01 3.18904837e+01 1.30753578e+01 | 2.19691553e+01 3.18904837e+01 1.30753578e+01 10 -1.15279263e+00 -1.64554698e+00 -3.24778325e+00 | -1.15279263e+00 -1.64554698e+00 -3.24778325e+00 11 1.13170553e+01 -1.25764040e+01 -1.53731821e+01 | 1.13170553e+01 -1.25764040e+01 -1.53731821e+01 12 5.95262773e+00 -4.27393073e+00 5.30468067e+00 | 5.95262773e+00 -4.27393073e+00 5.30468067e+00 13 2.21931075e+00 -2.14957439e+00 -2.40582637e+00 | 2.21931075e+00 -2.14957439e+00 -2.40582637e+00 14 2.13882530e+01 -8.48090220e+00 1.65834500e+01 | 2.13882530e+01 -8.48090220e+00 1.65834500e+01 15 -5.58409199e+00 -8.02319345e+00 2.37546474e+00 | -5.58409199e+00 -8.02319345e+00 2.37546474e+00 16 5.95394183e-01 8.31208041e-01 7.82805900e-01 | 5.95394183e-01 8.31208041e-01 7.82805900e-01 17 1.71566190e+00 -2.59279883e+00 -7.08807058e+00 | 1.71566190e+00 -2.59279883e+00 -7.08807058e+00 18 -2.76366358e-01 -6.91272412e-01 1.23145697e+00 | -2.76366358e-01 -6.91272412e-01 1.23145697e+00 19 1.41863900e-02 -7.31004769e-01 1.02629416e+00 | 1.41863900e-02 -7.31004769e-01 1.02629416e+00 20 4.45634745e+00 3.99751029e-01 1.76765070e-01 | 4.45634745e+00 3.99751029e-01 1.76765070e-01 21 -4.69056484e+00 2.02864831e+00 -1.48999547e+01 | -4.69056484e+00 2.02864831e+00 -1.48999547e+01 22 -2.58916883e+00 5.05599191e+00 4.73119932e+00 | -2.58916883e+00 5.05599191e+00 4.73119932e+00 23 -5.49426453e-02 1.57230459e-01 -8.88138929e-01 | -5.49426453e-02 1.57230459e-01 -8.88138929e-01 24 -1.11626159e+01 -2.64848518e+00 -2.21637751e+01 | -1.11626159e+01 -2.64848518e+00 -2.21637751e+01 25 1.11399786e+01 1.67632794e+00 1.93902622e+01 | 1.11399786e+01 1.67632794e+00 1.93902622e+01 26 1.70610823e-01 -1.41141533e-01 1.12839852e+00 | 1.70610823e-01 -1.41141533e-01 1.12839852e+00 27 -7.41606673e-01 -9.31573050e-01 -3.58806385e-01 | -7.41606673e-01 -9.31573050e-01 -3.58806385e-01 28 -5.16468447e+00 1.67427357e+01 1.54415843e+01 | -5.16468447e+00 1.67427357e+01 1.54415843e+01 29 3.47368556e+00 4.00241883e+00 -1.86082143e-01 | 3.47368556e+00 4.00241883e+00 -1.86082143e-01 30 5.55223450e+00 -1.94561434e+00 -6.61218248e+00 | 5.55223450e+00 -1.94561434e+00 -6.61218248e+00 31 -3.84305568e-01 4.64669376e+00 2.92845626e+00 | -3.84305568e-01 4.64669376e+00 2.92845626e+00 32 -3.66226160e+00 3.00885129e-01 -2.64616863e+00 | -3.66226160e+00 3.00885129e-01 -2.64616863e+00 33 8.15318910e-01 2.28545120e+00 -4.13077768e+00 | 8.15318910e-01 2.28545120e+00 -4.13077768e+00 34 -3.26170837e+00 -3.08029616e+00 -1.17558646e+00 | -3.26170837e+00 -3.08029616e+00 -1.17558646e+00 35 1.22281198e+01 -6.21595404e-01 -6.78246994e+00 | 1.22281198e+01 -6.21595404e-01 -6.78246994e+00 36 2.90338442e+00 -5.66042954e-01 6.84311015e+00 | 2.90338442e+00 -5.66042954e-01 6.84311015e+00 37 -3.32772953e+00 -1.37019602e+00 1.93654599e+00 | -3.32772953e+00 -1.37019602e+00 1.93654599e+00 38 1.31802841e+00 2.13553518e-01 -6.81894303e-01 | 1.31802841e+00 2.13553518e-01 -6.81894303e-01 39 -5.91372055e-01 -6.01173193e-01 3.86050424e-01 | -5.91372055e-01 -6.01173193e-01 3.86050424e-01 40 1.21389801e+00 -4.25003326e+00 1.58157018e+00 | 1.21389801e+00 -4.25003326e+00 1.58157018e+00 41 -5.76315425e+00 4.37140655e+00 -5.60625535e+00 | -5.76315425e+00 4.37140655e+00 -5.60625535e+00 42 -1.40275086e+01 -4.04349797e+00 -1.33284695e+01 | -1.40275086e+01 -4.04349797e+00 -1.33284695e+01 43 1.26171071e+01 6.62818623e+00 1.58122632e+01 | 1.26171071e+01 6.62818623e+00 1.58122632e+01 44 -2.09763489e+00 -1.22991361e+01 1.79095824e+00 | -2.09763489e+00 -1.22991361e+01 1.79095824e+00 45 9.07808237e+00 7.39430784e+00 4.99299587e+00 | 9.07808237e+00 7.39430784e+00 4.99299587e+00 46 2.12329845e+00 -2.06122480e+00 -3.93602375e+00 | 2.12329845e+00 -2.06122480e+00 -3.93602375e+00 47 -7.22230720e+00 2.47708644e+00 9.20484000e+00 | -7.22230720e+00 2.47708644e+00 9.20484000e+00 48 -1.24098975e+01 -6.88583892e+00 3.98315359e+00 | -1.24098975e+01 -6.88583892e+00 3.98315359e+00 49 1.07767766e+01 8.44033616e+00 1.36682456e+00 | 1.07767766e+01 8.44033616e+00 1.36682456e+00 50 -2.44354929e+01 -9.43391967e+00 3.80103580e-01 | -2.44354929e+01 -9.43391967e+00 3.80103580e-01 51 1.35150917e+01 1.71518512e+01 1.10831833e+01 | 1.35150917e+01 1.71518512e+01 1.10831833e+01 52 -9.47611234e+00 3.55422641e+00 9.40375189e+00 | -9.47611234e+00 3.55422641e+00 9.40375189e+00 53 -8.93795295e+00 -1.05715216e+01 7.32505765e+00 | -8.93795295e+00 -1.05715216e+01 7.32505765e+00 54 1.04026315e+00 -5.76983538e-01 -7.04255190e-01 | 1.04026315e+00 -5.76983538e-01 -7.04255190e-01 55 5.24352922e-01 -4.57276910e-01 -5.05831553e-01 | 5.24352922e-01 -4.57276910e-01 -5.05831553e-01 56 7.28107484e+00 -8.28933461e+00 8.18074199e+00 | 7.28107484e+00 -8.28933461e+00 8.18074199e+00 57 -8.35519684e+00 1.08849166e+01 1.64861224e+00 | -8.35519684e+00 1.08849166e+01 1.64861224e+00 58 -6.89687110e+00 -5.34804543e+00 -1.33084247e+01 | -6.89687110e+00 -5.34804543e+00 -1.33084247e+01 59 1.06285640e+01 7.18509423e+00 1.10042775e+01 | 1.06285640e+01 7.18509423e+00 1.10042775e+01 60 1.22302460e+01 -1.24040015e+01 -7.10791627e+00 | 1.22302460e+01 -1.24040015e+01 -7.10791627e+00 61 -9.02034770e-01 5.45197330e-01 -9.56695549e-01 | -9.02034770e-01 5.45197330e-01 -9.56695549e-01 62 1.62756392e+00 5.05382507e+00 -1.01071853e+01 | 1.62756392e+00 5.05382507e+00 -1.01071853e+01 63 6.92077874e+00 5.04999476e+00 3.27929711e+00 | 6.92077874e+00 5.04999476e+00 3.27929711e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.