!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_PlummerTucker_2019_TiSiC__MO_751442731010_000 Supported species : C Si Ti random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = C (Configuration in file "config-C.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [11, 49, 9, 46, 14, 10, 45, 35, 56, 2, 5, 0, 26, 36, 4, 25, 17, 16, 30, 33, 23, 27, 37, 20, 47, 15, 12, 21, 55, 39, 18, 63, 54, 19, 40, 7, 13, 22, 62, 29, 34, 61, 57, 48, 50, 6, 3, 24, 43, 1, 44, 53, 58, 51, 32, 28, 8, 42, 52, 60, 59, 41, 38, 31] 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)) = 3212.421305237555 V(r_1,...,r_N) = 3212.421305237558 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 -7.64404213e+02 -8.37777991e+02 -3.31454330e+02 | -7.64404213e+02 -8.37777991e+02 -3.31454330e+02 1 6.28974454e+02 6.87475134e+02 3.24351398e+02 | 6.28974454e+02 6.87475134e+02 3.24351398e+02 2 1.35126686e+02 1.33468104e+02 -2.87172581e+01 | 1.35126686e+02 1.33468104e+02 -2.87172581e+01 3 -2.60995723e+02 5.23481619e+01 -4.75977708e+02 | -2.60995723e+02 5.23481619e+01 -4.75977708e+02 4 -8.32066530e+01 -1.54200227e+02 -2.89915592e+01 | -8.32066530e+01 -1.54200227e+02 -2.89915592e+01 5 1.25571024e+02 1.04816033e+02 3.19937913e+01 | 1.25571024e+02 1.04816033e+02 3.19937913e+01 6 -9.00451323e+01 1.14165499e+01 -3.83446068e+01 | -9.00451323e+01 1.14165499e+01 -3.83446068e+01 7 -1.71278792e-01 1.91291285e+02 6.26053599e+00 | -1.71278792e-01 1.91291285e+02 6.26053599e+00 8 -4.85358605e+02 -9.28216531e+01 -3.59663581e+02 | -4.85358605e+02 -9.28216531e+01 -3.59663581e+02 9 4.52790728e+02 -5.18157867e+00 3.15393775e+02 | 4.52790728e+02 -5.18157867e+00 3.15393775e+02 10 -1.10151265e+02 -4.06190650e+01 -7.49305729e+01 | -1.10151265e+02 -4.06190650e+01 -7.49305729e+01 11 1.46870068e+02 8.08872707e+01 1.82235332e+01 | 1.46870068e+02 8.08872707e+01 1.82235332e+01 12 -3.54448482e+01 -1.23456131e+02 -5.86330146e+00 | -3.54448482e+01 -1.23456131e+02 -5.86330146e+00 13 1.59114246e+02 8.03678134e+01 -1.34928938e+02 | 1.59114246e+02 8.03678134e+01 -1.34928938e+02 14 2.21145173e+02 -2.67540369e+02 -1.04924031e+02 | 2.21145173e+02 -2.67540369e+02 -1.04924031e+02 15 7.44155168e+00 -3.67295278e+01 6.31150211e+01 | 7.44155168e+00 -3.67295278e+01 6.31150211e+01 16 -3.19878171e+02 9.87272557e+01 -2.64022066e+02 | -3.19878171e+02 9.87272557e+01 -2.64022066e+02 17 2.38898600e+02 -1.55577830e+02 2.59372885e+02 | 2.38898600e+02 -1.55577830e+02 2.59372885e+02 18 2.66062430e+01 5.97318627e+01 -5.86418634e+01 | 2.66062430e+01 5.97318627e+01 -5.86418634e+01 19 -1.27811567e+03 -1.32269129e+02 -2.86382761e+02 | -1.27811567e+03 -1.32269129e+02 -2.86382761e+02 20 -1.24570737e+02 -1.67234981e+02 3.53020497e+02 | -1.24570737e+02 -1.67234981e+02 3.53020497e+02 21 2.03427368e+02 2.59891549e+02 1.48724543e+02 | 2.03427368e+02 2.59891549e+02 1.48724543e+02 22 -1.87420539e+01 4.06572133e+01 -1.00041286e+01 | -1.87420539e+01 4.06572133e+01 -1.00041286e+01 23 1.17778103e+01 9.54595991e+01 -1.97534372e+02 | 1.17778103e+01 9.54595991e+01 -1.97534372e+02 24 1.22395374e+01 -1.50819169e+01 -7.87367449e+01 | 1.22395374e+01 -1.50819169e+01 -7.87367449e+01 25 -3.22366658e+02 4.54391623e+02 -3.01941643e+02 | -3.22366658e+02 4.54391623e+02 -3.01941643e+02 26 -1.11282811e+02 4.56020027e+01 7.94108802e-02 | -1.11282811e+02 4.56020027e+01 7.94108802e-02 27 1.23877845e+02 -2.31563770e+01 -1.38413659e+01 | 1.23877845e+02 -2.31563770e+01 -1.38413659e+01 28 4.04561840e+02 -4.36479409e+02 2.05460811e+02 | 4.04561840e+02 -4.36479409e+02 2.05460811e+02 29 5.93439098e+01 4.30138005e+01 6.42620343e+01 | 5.93439098e+01 4.30138005e+01 6.42620343e+01 30 1.24828569e+03 3.00667152e+02 2.32893118e+02 | 1.24828569e+03 3.00667152e+02 2.32893118e+02 31 -5.30598121e+01 -1.03777775e+01 -5.25805325e+01 | -5.30598121e+01 -1.03777775e+01 -5.25805325e+01 32 -3.83979652e+01 -6.09434080e+01 -1.80443578e+01 | -3.83979652e+01 -6.09434080e+01 -1.80443578e+01 33 -1.59238025e+01 -6.50508118e+01 3.92622626e+01 | -1.59238025e+01 -6.50508118e+01 3.92622626e+01 34 -8.13116278e+01 -6.02037645e+01 -1.13983945e+02 | -8.13116278e+01 -6.02037645e+01 -1.13983945e+02 35 1.03460175e+02 -1.61084906e+02 1.17482664e+02 | 1.03460175e+02 -1.61084906e+02 1.17482664e+02 36 -3.54605168e+01 -1.15347303e+01 -5.96767096e+00 | -3.54605168e+01 -1.15347303e+01 -5.96767096e+00 37 -1.06770825e+02 -1.45432210e+02 1.15115446e+02 | -1.06770825e+02 -1.45432210e+02 1.15115446e+02 38 -1.18793706e+02 -4.53413696e+01 -4.79294190e+00 | -1.18793706e+02 -4.53413696e+01 -4.79294190e+00 39 -1.93727533e+02 -1.27085308e+02 -4.39285216e+01 | -1.93727533e+02 -1.27085308e+02 -4.39285216e+01 40 -9.28091973e+01 -9.80775900e+00 -1.13933800e+02 | -9.28091973e+01 -9.80775900e+00 -1.13933800e+02 41 5.18641176e+01 1.73308144e+02 -9.91301903e+01 | 5.18641176e+01 1.73308144e+02 -9.91301903e+01 42 -5.27711248e+02 -8.53166396e+02 -2.89951393e+02 | -5.27711248e+02 -8.53166396e+02 -2.89951393e+02 43 5.52849048e+02 9.34534285e+02 4.22965537e+02 | 5.52849048e+02 9.34534285e+02 4.22965537e+02 44 -9.27842932e+01 -3.37219546e+02 -2.35980912e+02 | -9.27842932e+01 -3.37219546e+02 -2.35980912e+02 45 1.68989655e+02 1.59494860e+01 3.76375020e+02 | 1.68989655e+02 1.59494860e+01 3.76375020e+02 46 7.18674269e+01 1.77410270e+02 6.31950434e+01 | 7.18674269e+01 1.77410270e+02 6.31950434e+01 47 1.44230719e+02 -1.25853525e+02 2.53817742e+01 | 1.44230719e+02 -1.25853525e+02 2.53817742e+01 48 -1.00153895e+02 1.75265763e+01 -5.77379819e+01 | -1.00153895e+02 1.75265763e+01 -5.77379819e+01 49 3.50042513e+01 -1.88445422e+02 2.73823611e+01 | 3.50042513e+01 -1.88445422e+02 2.73823611e+01 50 -1.09171081e+02 -3.57926947e+02 -3.73456164e+02 | -1.09171081e+02 -3.57926947e+02 -3.73456164e+02 51 8.06935909e+01 4.01846579e+02 4.02161645e+02 | 8.06935909e+01 4.01846579e+02 4.02161645e+02 52 1.45468958e+02 1.58231230e+02 1.92153750e+02 | 1.45468958e+02 1.58231230e+02 1.92153750e+02 53 -8.96270748e+01 1.48131633e+02 9.52721633e+01 | -8.96270748e+01 1.48131633e+02 9.52721633e+01 54 -3.62735503e+02 6.73371030e+01 2.27248674e+00 | -3.62735503e+02 6.73371030e+01 2.27248674e+00 55 2.58450716e+02 1.09696447e+02 2.66980934e+02 | 2.58450716e+02 1.09696447e+02 2.66980934e+02 56 -1.02405428e+02 -1.47860314e+02 -2.35375097e+01 | -1.02405428e+02 -1.47860314e+02 -2.35375097e+01 57 -3.76940060e+02 -3.66178562e+02 -9.53172032e+02 | -3.76940060e+02 -3.66178562e+02 -9.53172032e+02 58 1.09157527e+02 9.90658804e+01 7.19143213e+00 | 1.09157527e+02 9.90658804e+01 7.19143213e+00 59 1.24185100e+02 2.67064494e+01 -3.54541986e+01 | 1.24185100e+02 2.67064494e+01 -3.54541986e+01 60 3.59561643e+02 -2.91560367e+02 7.59845548e+01 | 3.59561643e+02 -2.91560367e+02 7.59845548e+01 61 2.21525160e+01 -1.09062268e+00 1.88582494e+01 | 2.21525160e+01 -1.09062268e+00 1.88582494e+01 62 1.72827011e+02 7.72646207e+02 8.88734371e+02 | 1.72827011e+02 7.72646207e+02 8.88734371e+02 63 -1.04297845e+02 1.16872342e+01 5.66319324e+01 | -1.04297845e+02 1.16872342e+01 5.66319324e+01 ------------------------------------------------------------------------------------------------------------------------- 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 = [50, 27, 34, 48, 39, 18, 33, 49, 12, 29, 45, 47, 8, 42, 28, 40, 61, 43, 5, 24, 37, 58, 38, 46, 19, 44, 36, 1, 14, 9, 31, 30, 53, 6, 2, 41, 26, 20, 22, 4, 15, 35, 13, 17, 25, 10, 23, 11, 3, 7, 0, 54, 57, 32, 51, 63, 60, 52, 21, 62, 56, 16, 59, 55] 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)) = 157.2608220210476 V(r_1,...,r_N) = 157.26082202104828 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 1.60759012e+00 1.15082984e+00 9.06530509e-01 | 1.60759012e+00 1.15082984e+00 9.06530509e-01 1 -1.40532732e+01 1.39925033e+01 -2.82581495e+01 | -1.40532732e+01 1.39925033e+01 -2.82581495e+01 2 2.07242128e+00 5.01180435e+00 -7.17906584e+00 | 2.07242128e+00 5.01180435e+00 -7.17906584e+00 3 -1.69224823e+01 -5.26628693e+00 4.44709623e-01 | -1.69224823e+01 -5.26628693e+00 4.44709623e-01 4 7.28326208e+00 -3.76330037e+01 1.76692322e+01 | 7.28326208e+00 -3.76330037e+01 1.76692322e+01 5 -2.39342885e+01 -4.89352542e+01 5.24979502e+01 | -2.39342885e+01 -4.89352542e+01 5.24979502e+01 6 -1.00008676e+01 7.64038185e+00 3.66154628e+00 | -1.00008676e+01 7.64038185e+00 3.66154628e+00 7 -2.86412828e+01 3.28387772e+01 -3.88223765e+01 | -2.86412828e+01 3.28387772e+01 -3.88223765e+01 8 -5.22245777e+01 -6.29620329e+01 -1.99332836e+01 | -5.22245777e+01 -6.29620329e+01 -1.99332836e+01 9 4.75883986e+01 6.49687405e+01 1.10006531e+01 | 4.75883986e+01 6.49687405e+01 1.10006531e+01 10 -1.84975740e-01 -1.94615762e+01 -2.37546961e+01 | -1.84975740e-01 -1.94615762e+01 -2.37546961e+01 11 1.12480532e+01 7.59942539e+00 1.37837788e+01 | 1.12480532e+01 7.59942539e+00 1.37837788e+01 12 3.26948855e+00 -9.70281348e+00 1.48779249e+00 | 3.26948855e+00 -9.70281348e+00 1.48779249e+00 13 4.99663218e+00 1.26465209e+00 4.64850557e+00 | 4.99663218e+00 1.26465209e+00 4.64850557e+00 14 2.82300821e+01 3.56880564e+01 -5.96911494e+01 | 2.82300821e+01 3.56880564e+01 -5.96911494e+01 15 1.58903618e+01 1.55864675e+01 8.01783074e+00 | 1.58903618e+01 1.55864675e+01 8.01783074e+00 16 -4.53822880e+00 -4.37913548e+00 -5.15444049e-01 | -4.53822880e+00 -4.37913548e+00 -5.15444049e-01 17 -3.21970761e+01 -4.38007832e+01 2.15662757e+01 | -3.21970761e+01 -4.38007832e+01 2.15662757e+01 18 2.90944753e+01 4.32045456e+01 -3.31041234e+01 | 2.90944753e+01 4.32045456e+01 -3.31041234e+01 19 -1.14284909e-01 1.10312108e+01 -2.32509978e+00 | -1.14284909e-01 1.10312108e+01 -2.32509978e+00 20 -4.12303432e+01 -2.83795080e+01 -3.52560824e+01 | -4.12303432e+01 -2.83795080e+01 -3.52560824e+01 21 4.37835143e+01 2.92867331e+01 5.12701640e+01 | 4.37835143e+01 2.92867331e+01 5.12701640e+01 22 -1.82168257e+00 7.85139317e-01 3.38325506e+00 | -1.82168257e+00 7.85139317e-01 3.38325506e+00 23 -7.16655476e+01 2.62918886e+01 -6.24701395e+01 | -7.16655476e+01 2.62918886e+01 -6.24701395e+01 24 1.41934281e+00 1.14855112e+01 -2.36414452e+01 | 1.41934281e+00 1.14855112e+01 -2.36414452e+01 25 -8.26352627e+01 5.29398971e+01 -1.24121239e+02 | -8.26352627e+01 5.29398971e+01 -1.24121239e+02 26 -2.63544347e+00 -1.31515987e+00 -1.97069079e+00 | -2.63544347e+00 -1.31515987e+00 -1.97069079e+00 27 3.46804002e+00 1.06917807e+00 2.86699298e+00 | 3.46804002e+00 1.06917807e+00 2.86699298e+00 28 8.13349689e+01 -5.17573594e+01 1.26217536e+02 | 8.13349689e+01 -5.17573594e+01 1.26217536e+02 29 1.41596575e+01 6.88574282e+00 1.02600225e+01 | 1.41596575e+01 6.88574282e+00 1.02600225e+01 30 6.30404015e-01 -3.09935435e+00 8.67878212e-01 | 6.30404015e-01 -3.09935435e+00 8.67878212e-01 31 3.30305213e+00 5.81689151e+00 5.08670369e+00 | 3.30305213e+00 5.81689151e+00 5.08670369e+00 32 -1.12047965e+00 -1.18663247e+00 1.89339412e+00 | -1.12047965e+00 -1.18663247e+00 1.89339412e+00 33 1.63939675e+00 -3.69499681e+01 -3.81547844e+01 | 1.63939675e+00 -3.69499681e+01 -3.81547844e+01 34 1.33840920e+01 -2.63568766e+01 4.98197164e+01 | 1.33840920e+01 -2.63568766e+01 4.98197164e+01 35 -6.39639323e+01 5.17434148e+01 -3.20085967e+01 | -6.39639323e+01 5.17434148e+01 -3.20085967e+01 36 8.17025554e+00 -1.03875463e+01 2.13608262e+00 | 8.17025554e+00 -1.03875463e+01 2.13608262e+00 37 3.91036316e+00 -3.80040917e+00 1.76518404e+01 | 3.91036316e+00 -3.80040917e+00 1.76518404e+01 38 -2.04629749e+01 4.29976461e+01 2.47050876e+01 | -2.04629749e+01 4.29976461e+01 2.47050876e+01 39 2.46553064e+00 3.95841522e-01 -5.63612163e-01 | 2.46553064e+00 3.95841522e-01 -5.63612163e-01 40 -1.74870290e+01 -1.63707174e+01 7.25408610e-01 | -1.74870290e+01 -1.63707174e+01 7.25408610e-01 41 1.21271099e+01 1.05079756e+01 5.14055552e-01 | 1.21271099e+01 1.05079756e+01 5.14055552e-01 42 3.84103662e-01 2.15499491e+00 9.15522852e-01 | 3.84103662e-01 2.15499491e+00 9.15522852e-01 43 1.05463427e+01 -2.16032143e+01 -1.07905127e+01 | 1.05463427e+01 -2.16032143e+01 -1.07905127e+01 44 7.46851162e+00 -5.49996328e+00 9.01209324e+00 | 7.46851162e+00 -5.49996328e+00 9.01209324e+00 45 -1.93204649e+00 3.44301932e-01 -1.99584927e+00 | -1.93204649e+00 3.44301932e-01 -1.99584927e+00 46 3.56754036e+01 -6.79692648e+01 5.42546264e+01 | 3.56754036e+01 -6.79692648e+01 5.42546264e+01 47 4.08994160e+00 1.99842564e+00 2.66130383e+00 | 4.08994160e+00 1.99842564e+00 2.66130383e+00 48 -5.02087880e+00 -1.96531238e+00 -4.71849977e+00 | -5.02087880e+00 -1.96531238e+00 -4.71849977e+00 49 -1.09807326e+00 -9.76331972e+00 1.08549217e+01 | -1.09807326e+00 -9.76331972e+00 1.08549217e+01 50 6.68374407e+01 -2.05173510e+01 4.12270071e+01 | 6.68374407e+01 -2.05173510e+01 4.12270071e+01 51 1.30857256e+01 3.48199885e+00 1.00719212e+01 | 1.30857256e+01 3.48199885e+00 1.00719212e+01 52 3.80148442e-01 -3.49695873e+00 1.41558227e+00 | 3.80148442e-01 -3.49695873e+00 1.41558227e+00 53 -1.65221621e+00 -1.63235613e+00 3.54971631e+00 | -1.65221621e+00 -1.63235613e+00 3.54971631e+00 54 -1.40781577e+01 -2.64443139e+00 -1.18181305e+01 | -1.40781577e+01 -2.64443139e+00 -1.18181305e+01 55 8.56701607e+00 6.28408158e+00 1.51705296e+01 | 8.56701607e+00 6.28408158e+00 1.51705296e+01 56 3.28499349e+01 2.78745600e+01 -3.06836148e+01 | 3.28499349e+01 2.78745600e+01 -3.06836148e+01 57 -7.41677536e-01 2.23554325e+00 -2.87942342e+00 | -7.41677536e-01 2.23554325e+00 -2.87942342e+00 58 -4.64957494e+01 -2.08193163e+01 -1.46580502e+01 | -4.64957494e+01 -2.08193163e+01 -1.46580502e+01 59 4.36237865e+01 2.47737847e+01 1.06569236e+01 | 4.36237865e+01 2.47737847e+01 1.06569236e+01 60 -1.13723712e+01 1.17543207e+01 1.24409826e+01 | -1.13723712e+01 1.17543207e+01 1.24409826e+01 61 4.56569091e+00 2.45725378e+00 3.69627492e+00 | 4.56569091e+00 2.45725378e+00 3.69627492e+00 62 -2.71145419e+00 -1.82394041e+01 -3.19704439e+01 | -2.71145419e+00 -1.82394041e+01 -3.19704439e+01 63 1.78611885e+00 2.23527902e+01 3.22741551e+01 | 1.78611885e+00 2.23527902e+01 3.22741551e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ti (Configuration in file "config-Ti.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [49, 22, 39, 16, 62, 43, 29, 36, 19, 51, 13, 35, 42, 10, 32, 58, 3, 21, 30, 8, 61, 17, 1, 45, 27, 57, 31, 24, 34, 6, 18, 26, 14, 48, 28, 11, 7, 47, 50, 2, 60, 56, 12, 5, 63, 23, 53, 37, 33, 0, 38, 9, 54, 46, 52, 59, 41, 25, 15, 55, 40, 20, 4, 44] 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)) = -29.055281282118397 V(r_1,...,r_N) = -29.055281282118315 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 1.52593541e+00 1.38337708e-01 7.88708873e-01 | 1.52593541e+00 1.38337708e-01 7.88708873e-01 1 1.16928562e+01 1.05798699e-01 -1.31306738e+01 | 1.16928562e+01 1.05798699e-01 -1.31306738e+01 2 -6.46480899e-01 1.16896751e+00 -8.22594585e-01 | -6.46480899e-01 1.16896751e+00 -8.22594585e-01 3 -1.86161702e+00 1.54799531e+00 3.48395330e+00 | -1.86161702e+00 1.54799531e+00 3.48395330e+00 4 -1.76290825e+00 -1.27220332e+00 -5.64596688e-01 | -1.76290825e+00 -1.27220332e+00 -5.64596688e-01 5 1.50740743e+01 -2.26251508e+00 -1.06076408e+01 | 1.50740743e+01 -2.26251508e+00 -1.06076408e+01 6 -1.03450705e+01 7.95062508e-01 1.57965155e+01 | -1.03450705e+01 7.95062508e-01 1.57965155e+01 7 7.08529626e+00 -1.24830942e+01 -8.83879777e+00 | 7.08529626e+00 -1.24830942e+01 -8.83879777e+00 8 1.45360822e+00 -2.35027125e+00 -1.71674020e+00 | 1.45360822e+00 -2.35027125e+00 -1.71674020e+00 9 5.13321393e-01 -7.09287341e+00 -8.26517288e+00 | 5.13321393e-01 -7.09287341e+00 -8.26517288e+00 10 -5.15111873e+00 -4.41059571e+00 -1.18542504e+01 | -5.15111873e+00 -4.41059571e+00 -1.18542504e+01 11 5.62510544e+00 5.60263229e+00 1.21276310e+01 | 5.62510544e+00 5.60263229e+00 1.21276310e+01 12 8.52276393e+00 -1.56886868e+01 6.70170727e+00 | 8.52276393e+00 -1.56886868e+01 6.70170727e+00 13 -2.07021086e-01 9.43504586e-01 -1.79305627e-01 | -2.07021086e-01 9.43504586e-01 -1.79305627e-01 14 -9.65251695e+00 2.11395564e+01 2.73527183e+00 | -9.65251695e+00 2.11395564e+01 2.73527183e+00 15 5.95852582e+00 -5.64208161e+00 -5.29333713e+00 | 5.95852582e+00 -5.64208161e+00 -5.29333713e+00 16 -1.60405377e+01 -5.53341646e+00 -6.20313129e+00 | -1.60405377e+01 -5.53341646e+00 -6.20313129e+00 17 1.38229552e+01 7.73669991e+00 -2.72646831e+00 | 1.38229552e+01 7.73669991e+00 -2.72646831e+00 18 -9.42170025e+00 -1.53685324e+01 -6.73656755e+00 | -9.42170025e+00 -1.53685324e+01 -6.73656755e+00 19 8.39772947e+00 1.63720365e+01 4.37440497e+00 | 8.39772947e+00 1.63720365e+01 4.37440497e+00 20 3.92281137e+00 5.84879628e-01 7.54490943e+00 | 3.92281137e+00 5.84879628e-01 7.54490943e+00 21 -2.73819375e+00 -1.21513948e+01 7.88894749e+00 | -2.73819375e+00 -1.21513948e+01 7.88894749e+00 22 1.11115500e+00 -6.96928247e-01 -7.17601598e-03 | 1.11115500e+00 -6.96928247e-01 -7.17601598e-03 23 -5.80498912e+00 5.70087282e+00 -6.25992583e+00 | -5.80498912e+00 5.70087282e+00 -6.25992583e+00 24 1.37166486e+00 -1.04337390e-01 -1.98804868e+00 | 1.37166486e+00 -1.04337390e-01 -1.98804868e+00 25 -9.69293374e+00 -1.11757716e+00 -1.21870569e+00 | -9.69293374e+00 -1.11757716e+00 -1.21870569e+00 26 3.08875519e+00 -1.85321179e+00 -8.00190053e+00 | 3.08875519e+00 -1.85321179e+00 -8.00190053e+00 27 3.68099309e+00 3.74218399e+00 4.88307617e+00 | 3.68099309e+00 3.74218399e+00 4.88307617e+00 28 -9.67025610e+00 -6.13798393e+00 -1.51735361e+01 | -9.67025610e+00 -6.13798393e+00 -1.51735361e+01 29 1.73915517e+01 6.18140656e+00 1.23741854e+01 | 1.73915517e+01 6.18140656e+00 1.23741854e+01 30 1.55371442e+00 1.26404807e+01 -3.89526165e+00 | 1.55371442e+00 1.26404807e+01 -3.89526165e+00 31 -9.80068096e+00 1.70654826e+01 -2.18897215e+01 | -9.80068096e+00 1.70654826e+01 -2.18897215e+01 32 -8.63174896e-01 -1.23709360e+00 -1.24355040e+00 | -8.63174896e-01 -1.23709360e+00 -1.24355040e+00 33 3.20138506e+00 8.89471111e-01 -2.65047661e+00 | 3.20138506e+00 8.89471111e-01 -2.65047661e+00 34 -1.52869414e+01 4.58204380e+00 9.22790412e+00 | -1.52869414e+01 4.58204380e+00 9.22790412e+00 35 -2.16036627e+01 -2.97171067e+01 2.57558694e+01 | -2.16036627e+01 -2.97171067e+01 2.57558694e+01 36 1.44518861e+00 -1.51449637e+00 -2.84495205e-01 | 1.44518861e+00 -1.51449637e+00 -2.84495205e-01 37 -1.50343445e+00 -1.14351550e+00 2.33887913e+00 | -1.50343445e+00 -1.14351550e+00 2.33887913e+00 38 -4.30422269e+00 2.73195711e+00 3.70600420e+00 | -4.30422269e+00 2.73195711e+00 3.70600420e+00 39 -1.90352335e+01 -1.05466918e+01 2.66055791e+00 | -1.90352335e+01 -1.05466918e+01 2.66055791e+00 40 -9.87241391e+00 -7.87167121e+00 -6.36144575e+00 | -9.87241391e+00 -7.87167121e+00 -6.36144575e+00 41 1.19600861e+01 -5.90525838e+00 1.67489837e+00 | 1.19600861e+01 -5.90525838e+00 1.67489837e+00 42 5.18461697e+00 -9.89172018e-01 -1.70583375e+01 | 5.18461697e+00 -9.89172018e-01 -1.70583375e+01 43 7.53215382e+00 3.63670632e+00 3.08625978e+00 | 7.53215382e+00 3.63670632e+00 3.08625978e+00 44 -3.79265033e+00 -5.54396863e+00 -4.73244486e+00 | -3.79265033e+00 -5.54396863e+00 -4.73244486e+00 45 4.27250569e+00 5.42866154e+00 4.66911317e+00 | 4.27250569e+00 5.42866154e+00 4.66911317e+00 46 -1.36172524e+01 -9.88139444e-01 1.16552746e+01 | -1.36172524e+01 -9.88139444e-01 1.16552746e+01 47 -6.81178539e+00 2.41877789e+00 9.28865549e+00 | -6.81178539e+00 2.41877789e+00 9.28865549e+00 48 -1.09435576e+01 8.82821288e+00 8.58215830e+00 | -1.09435576e+01 8.82821288e+00 8.58215830e+00 49 2.16275066e+00 -5.51764295e+00 -9.04915919e-01 | 2.16275066e+00 -5.51764295e+00 -9.04915919e-01 50 -5.05429676e+00 -1.28705201e+01 8.62380099e-01 | -5.05429676e+00 -1.28705201e+01 8.62380099e-01 51 9.06985503e+00 1.40326698e+01 -8.14805088e+00 | 9.06985503e+00 1.40326698e+01 -8.14805088e+00 52 1.98702247e+01 1.09765055e+01 -4.82500688e+00 | 1.98702247e+01 1.09765055e+01 -4.82500688e+00 53 1.09673682e+00 -2.90243899e+00 2.83222742e+00 | 1.09673682e+00 -2.90243899e+00 2.83222742e+00 54 -6.01021104e+00 3.07435698e+00 1.19502221e+00 | -6.01021104e+00 3.07435698e+00 1.19502221e+00 55 1.51342632e+00 1.26147747e+00 2.54462042e+00 | 1.51342632e+00 1.26147747e+00 2.54462042e+00 56 5.50987976e+00 2.48165258e+01 -2.45921011e+01 | 5.50987976e+00 2.48165258e+01 -2.45921011e+01 57 6.02599995e+00 7.15770772e+00 6.38497814e+00 | 6.02599995e+00 7.15770772e+00 6.38497814e+00 58 6.12841767e+00 -1.65924316e+01 2.03358479e+01 | 6.12841767e+00 -1.65924316e+01 2.03358479e+01 59 1.35075419e+00 4.40380133e-01 2.69966293e+00 | 1.35075419e+00 4.40380133e-01 2.69966293e+00 60 7.42511071e+00 7.56107347e+00 -9.53114127e-02 | 7.42511071e+00 7.56107347e+00 -9.53114127e-02 61 2.61816436e-01 5.70922104e-02 -4.51963090e-01 | 2.61816436e-01 5.70922104e-02 -4.51963090e-01 62 4.23880507e+00 -1.90215068e+00 9.27363315e+00 | 4.23880507e+00 -1.90215068e+00 9.27363315e+00 63 1.45233131e+00 4.84839349e-02 -7.51605228e-01 | 1.45233131e+00 4.84839349e-02 -7.51605228e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = C Si Ti (Configuration in file "config-CSiTi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [52, 11, 26, 43, 35, 23, 27, 63, 30, 18, 21, 1, 37, 32, 20, 45, 53, 29, 9, 50, 14, 10, 31, 5, 54, 62, 2, 6, 39, 17, 8, 22, 13, 51, 58, 4, 48, 12, 61, 28, 56, 60, 49, 3, 44, 15, 59, 55, 36, 42, 19, 33, 0, 16, 24, 47, 40, 57, 34, 46, 41, 38, 25, 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)) = 183.49587427754048 V(r_1,...,r_N) = 183.49587427754065 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 -1.95963520e+00 -1.75688406e+00 -1.10994064e+00 | -1.95963520e+00 -1.75688406e+00 -1.10994064e+00 1 -2.50163369e+01 1.83727907e+01 -6.83163339e+00 | -2.50163369e+01 1.83727907e+01 -6.83163339e+00 2 1.22695228e+01 1.01415852e+00 -1.46268042e+01 | 1.22695228e+01 1.01415852e+00 -1.46268042e+01 3 -1.76528147e+00 1.17422867e+01 1.31925343e+00 | -1.76528147e+00 1.17422867e+01 1.31925343e+00 4 1.41691709e+01 -2.46725318e+01 1.83814543e+01 | 1.41691709e+01 -2.46725318e+01 1.83814543e+01 5 -1.66026352e+01 1.52457335e+01 -1.91720202e+01 | -1.66026352e+01 1.52457335e+01 -1.91720202e+01 6 -1.42077752e+01 -5.72814864e+00 -1.46133256e+01 | -1.42077752e+01 -5.72814864e+00 -1.46133256e+01 7 1.52352542e+01 7.75612799e+00 1.21218572e+01 | 1.52352542e+01 7.75612799e+00 1.21218572e+01 8 -3.04276874e+00 -1.01281082e+00 -1.55564595e+00 | -3.04276874e+00 -1.01281082e+00 -1.55564595e+00 9 1.03087890e+00 6.44390038e+00 5.30796529e-01 | 1.03087890e+00 6.44390038e+00 5.30796529e-01 10 -1.60143931e+00 -2.04541555e+00 1.92054896e+00 | -1.60143931e+00 -2.04541555e+00 1.92054896e+00 11 -1.30836713e+00 1.35144099e+00 -1.42634448e+00 | -1.30836713e+00 1.35144099e+00 -1.42634448e+00 12 1.51030717e-01 -8.18321207e-03 1.37651534e-01 | 1.51030717e-01 -8.18321207e-03 1.37651534e-01 13 -4.61320535e+00 5.37096755e+00 2.56061597e+00 | -4.61320535e+00 5.37096755e+00 2.56061597e+00 14 4.09976375e+00 -8.74156369e+00 -1.07641756e+00 | 4.09976375e+00 -8.74156369e+00 -1.07641756e+00 15 -7.02735606e+01 4.70793069e+00 -1.03310915e+02 | -7.02735606e+01 4.70793069e+00 -1.03310915e+02 16 8.78451400e-01 -2.56764948e+00 2.74352471e+00 | 8.78451400e-01 -2.56764948e+00 2.74352471e+00 17 -7.45616495e-01 -7.57038255e+00 6.39575266e+00 | -7.45616495e-01 -7.57038255e+00 6.39575266e+00 18 -1.08062423e+00 -6.15429810e+00 -1.43155601e+01 | -1.08062423e+00 -6.15429810e+00 -1.43155601e+01 19 8.23357762e+00 1.04871881e+01 7.05992885e+00 | 8.23357762e+00 1.04871881e+01 7.05992885e+00 20 -2.15575083e+00 4.02759851e-01 -6.77371445e-02 | -2.15575083e+00 4.02759851e-01 -6.77371445e-02 21 -2.28772917e+01 2.40070374e+01 -1.26560316e+01 | -2.28772917e+01 2.40070374e+01 -1.26560316e+01 22 2.00901359e-01 2.11649078e-01 7.11569852e-01 | 2.00901359e-01 2.11649078e-01 7.11569852e-01 23 -1.26573080e-01 -1.40683397e-01 -8.67698308e-01 | -1.26573080e-01 -1.40683397e-01 -8.67698308e-01 24 -3.18050778e+00 2.40424399e+00 3.76302497e+00 | -3.18050778e+00 2.40424399e+00 3.76302497e+00 25 -2.45070110e+01 1.26892577e+01 -8.95151942e+00 | -2.45070110e+01 1.26892577e+01 -8.95151942e+00 26 2.36051995e+01 2.47632809e+00 -1.83137704e+01 | 2.36051995e+01 2.47632809e+00 -1.83137704e+01 27 -1.06925068e+00 -1.03098308e+00 4.39560385e-01 | -1.06925068e+00 -1.03098308e+00 4.39560385e-01 28 1.63834045e+01 -1.88025361e+01 1.19850843e+01 | 1.63834045e+01 -1.88025361e+01 1.19850843e+01 29 6.91905004e+00 -1.55007811e+00 -5.30918256e+00 | 6.91905004e+00 -1.55007811e+00 -5.30918256e+00 30 -5.89989756e+00 7.80200001e+00 9.51603971e+00 | -5.89989756e+00 7.80200001e+00 9.51603971e+00 31 1.38981570e+00 -1.07203920e+01 1.89954187e+00 | 1.38981570e+00 -1.07203920e+01 1.89954187e+00 32 1.26193395e+00 -2.00984179e-01 1.10137372e+00 | 1.26193395e+00 -2.00984179e-01 1.10137372e+00 33 -5.29338816e+02 3.21469053e+02 -4.79331468e+02 | -5.29338816e+02 3.21469053e+02 -4.79331468e+02 34 -1.78672672e+01 -1.45204133e+01 -9.87218017e+00 | -1.78672672e+01 -1.45204133e+01 -9.87218017e+00 35 1.81332394e+01 1.50908025e+01 -7.10797480e-01 | 1.81332394e+01 1.50908025e+01 -7.10797480e-01 36 5.30453151e+02 -3.27730161e+02 4.79844701e+02 | 5.30453151e+02 -3.27730161e+02 4.79844701e+02 37 1.53514523e+00 1.88340779e+00 -2.10507379e+00 | 1.53514523e+00 1.88340779e+00 -2.10507379e+00 38 5.86449564e-01 6.96808610e+00 -4.46674547e+00 | 5.86449564e-01 6.96808610e+00 -4.46674547e+00 39 -7.97763945e-01 -1.64273417e-01 6.07144216e-01 | -7.97763945e-01 -1.64273417e-01 6.07144216e-01 40 4.29902928e+00 -9.56065446e+00 1.95023158e+01 | 4.29902928e+00 -9.56065446e+00 1.95023158e+01 41 -1.15814684e+01 1.21831407e+01 -2.69207768e+00 | -1.15814684e+01 1.21831407e+01 -2.69207768e+00 42 8.08946556e+01 -1.15505915e+01 9.83809559e+01 | 8.08946556e+01 -1.15505915e+01 9.83809559e+01 43 2.18050173e+00 -3.62795821e+00 4.30998272e+00 | 2.18050173e+00 -3.62795821e+00 4.30998272e+00 44 1.53794418e+01 -1.13426914e+01 1.07253172e+01 | 1.53794418e+01 -1.13426914e+01 1.07253172e+01 45 -1.50248059e+00 7.61071959e-01 -3.45842466e+00 | -1.50248059e+00 7.61071959e-01 -3.45842466e+00 46 -6.78577496e+01 -1.42657196e+02 -1.00870815e+02 | -6.78577496e+01 -1.42657196e+02 -1.00870815e+02 47 6.95854121e+01 1.41139205e+02 1.03263137e+02 | 6.95854121e+01 1.41139205e+02 1.03263137e+02 48 2.37131087e+00 -5.49848073e+00 5.81624162e+00 | 2.37131087e+00 -5.49848073e+00 5.81624162e+00 49 2.42332678e+00 -7.48734201e+00 -2.59001165e+00 | 2.42332678e+00 -7.48734201e+00 -2.59001165e+00 50 2.13443679e+00 -9.17322804e-01 1.14552107e+00 | 2.13443679e+00 -9.17322804e-01 1.14552107e+00 51 -1.77364353e+01 8.30550807e+01 -6.04806700e+01 | -1.77364353e+01 8.30550807e+01 -6.04806700e+01 52 -1.63787530e+00 3.81807278e+00 3.44127677e+00 | -1.63787530e+00 3.81807278e+00 3.44127677e+00 53 -3.84536065e+00 -3.24653475e+00 4.03206510e+00 | -3.84536065e+00 -3.24653475e+00 4.03206510e+00 54 -4.49950985e-01 2.97053537e+00 3.38668202e+00 | -4.49950985e-01 2.97053537e+00 3.38668202e+00 55 -2.97787462e+00 3.36538567e-01 8.81801398e-02 | -2.97787462e+00 3.36538567e-01 8.81801398e-02 56 1.00984735e+01 -1.74739620e+01 1.78386427e+01 | 1.00984735e+01 -1.74739620e+01 1.78386427e+01 57 -3.97001914e+01 2.01183196e+01 -9.91708508e+01 | -3.97001914e+01 2.01183196e+01 -9.91708508e+01 58 -1.10115284e+01 9.55787279e+00 4.21810693e+00 | -1.10115284e+01 9.55787279e+00 4.21810693e+00 59 0.00000000e+00 0.00000000e+00 0.00000000e+00 | 0.00000000e+00 0.00000000e+00 0.00000000e+00 60 -9.90082266e+01 -6.70156030e+01 -2.02832572e+01 | -9.90082266e+01 -6.70156030e+01 -2.02832572e+01 61 1.46447675e+02 4.13613726e+01 1.16562570e+02 | 1.46447675e+02 4.13613726e+01 1.16562570e+02 62 1.47316667e+01 -7.78478952e+01 5.43016716e+01 | 1.47316667e+01 -7.78478952e+01 5.43016716e+01 63 2.64647466e-01 1.46243534e-01 1.84828350e-01 | 2.64647466e-01 1.46243534e-01 1.84828350e-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.