!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Tersoff_LAMMPS_Tersoff_PRB39_1989_CSi__MO_171585019474_000 Supported species : C Si random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = C | a0 = 2.72757530212 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 -6.591566360919283e+00 -6.591566360924320e+00 5.03686e-12 1.57785e-11 2 -6.546469436297915e+00 -6.546469436297941e+00 2.57572e-14 9.66986e-11 3 -4.401832171593576e+00 -4.401832171592622e+00 9.54792e-13 3.56071e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 2.680418590372279e+00 2.680418590353851e+00 1.84279e-11 9.74500e-11 2 8.263983641451656e+00 8.263983641463842e+00 1.21858e-11 6.03269e-11 3 -3.466337566822794e+00 -3.466337566810816e+00 1.19780e-11 1.06852e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 2.819678994396001e+00 2.819678994393125e+00 2.87592e-12 4.72342e-11 2 -5.552646986190846e+00 -5.552646986187951e+00 2.89457e-12 2.99920e-11 3 -1.580668512257959e+00 -1.580668512260280e+00 2.32103e-12 3.19824e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.220743822019951e+00 -3.220743822020940e+00 9.88987e-13 3.39275e-11 2 1.374888420555523e+01 1.374888420555556e+01 3.32179e-13 3.46780e-11 3 9.807974963858366e-01 9.807974963897723e-01 3.93574e-12 2.29519e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 2.548577402016492e+00 2.548577402011131e+00 5.36016e-12 3.93477e-10 * 2 -3.618702554037709e+00 -3.618702554040945e+00 3.23608e-12 8.38982e-11 3 2.705464061744820e+00 2.705464061743398e+00 1.42242e-12 4.21441e-12 ----------------------------------------------------------------------------------------------------- 6 C 1 -6.572613868567720e+00 -6.572613868571191e+00 3.47100e-12 6.00826e-11 2 5.752499579308083e+00 5.752499579307934e+00 1.48326e-13 5.50529e-10 * 3 7.013518760762111e-01 7.013518760810328e-01 4.82170e-12 4.51658e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -9.837295794213187e-01 -9.837295794173485e-01 3.97016e-12 1.47826e-12 2 -1.203798310688042e+01 -1.203798310688246e+01 2.04459e-12 4.24727e-11 3 -1.265185984582280e+01 -1.265185984583152e+01 8.72014e-12 4.34074e-10 * ----------------------------------------------------------------------------------------------------- 8 C 1 -7.304415261199686e+00 -7.304415261185638e+00 1.40483e-11 3.25200e-10 * 2 -2.021865969921545e+00 -2.021865969913482e+00 8.06333e-12 6.45484e-11 3 2.713394605104458e-01 2.713394605123143e-01 1.86845e-12 1.26743e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -6.160876975144660e+00 -6.160876975151121e+00 6.46061e-12 7.07967e-11 2 -1.318477724182868e+01 -1.318477724182628e+01 2.39275e-12 7.61826e-11 3 -8.992909479973759e+00 -8.992909479971352e+00 2.40696e-12 4.35207e-12 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.628077076810213e+00 -1.628077076800881e+00 9.33165e-12 3.05331e-11 2 1.076626728047456e+01 1.076626728046753e+01 7.02727e-12 1.19696e-10 3 -1.000375311872419e+01 -1.000375311872541e+01 1.21680e-12 4.21316e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -1.134277384868917e+00 -1.134277384873100e+00 4.18265e-12 1.76592e-11 2 -1.271959888844338e+01 -1.271959888843030e+01 1.30811e-11 8.78462e-11 3 5.325281981913130e+00 5.325281981906979e+00 6.15064e-12 1.20041e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -3.361228745634271e+00 -3.361228745633402e+00 8.69083e-13 6.94378e-12 2 7.776813729605894e-01 7.776813729625892e-01 1.99984e-12 1.96773e-11 3 1.371021219963457e+01 1.371021219963776e+01 3.19744e-12 4.68958e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 7.509513179500961e+00 7.509513179502013e+00 1.05249e-12 8.21565e-12 2 -7.197583875006495e+00 -7.197583875014551e+00 8.05667e-12 5.70761e-11 3 -1.223933011400493e+01 -1.223933011400481e+01 1.19016e-13 4.94307e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 2.524979404205104e-01 2.524979404206467e-01 1.36280e-13 1.01815e-11 2 3.223059196253976e-01 3.223059196232576e-01 2.14001e-12 6.63686e-12 3 -1.661312827759232e+00 -1.661312827759049e+00 1.83409e-13 1.83402e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 9.729644163438628e+00 9.729644163440316e+00 1.68754e-12 1.25162e-11 2 2.069909191754935e+00 2.069909191756564e+00 1.62892e-12 7.47233e-11 3 1.145712096468690e+00 1.145712096464444e+00 4.24571e-12 1.61493e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 2.972611013664045e+00 2.972611013652516e+00 1.15286e-11 5.21898e-11 2 1.054533731802914e+01 1.054533731804496e+01 1.58149e-11 7.55342e-11 3 4.743593834902855e+00 4.743593834911696e+00 8.84093e-12 2.35492e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.337086911056938e+00 -1.337086911060142e+00 3.20455e-12 7.21601e-12 2 -2.063707196375835e+00 -2.063707196365846e+00 9.98934e-12 4.43801e-11 3 2.593004139965747e+00 2.593004139970805e+00 5.05862e-12 1.00136e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 2.322047712394245e+00 2.322047712400162e+00 5.91704e-12 3.67173e-11 2 1.167272945837481e+01 1.167272945835685e+01 1.79590e-11 1.14541e-10 3 -1.006223607387507e-01 -1.006223607502150e-01 1.14643e-11 1.11563e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 2.649592649445990e+00 2.649592649445827e+00 1.63425e-13 6.24363e-11 2 -4.929193741059586e+00 -4.929193741059838e+00 2.52243e-13 4.36220e-11 3 1.440271816194358e+00 1.440271816194443e+00 8.52651e-14 4.49378e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 4.885737035970040e-01 4.885737035957454e-01 1.25860e-12 3.90922e-11 2 -7.580525575677105e-01 -7.580525575656151e-01 2.09543e-12 5.81917e-11 3 -2.219741246146993e-01 -2.219741246162957e-01 1.59639e-12 5.38107e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -1.399172902559493e+01 -1.399172902560404e+01 9.10561e-12 4.56737e-11 2 -1.216018378854490e+01 -1.216018378853244e+01 1.24523e-11 3.67692e-10 * 3 4.503068691984128e+00 4.503068691989516e+00 5.38858e-12 9.73621e-12 ----------------------------------------------------------------------------------------------------- 22 C 1 1.580359453328576e+01 1.580359453330441e+01 1.86446e-11 2.27473e-10 2 1.574837850716312e+01 1.574837850715658e+01 6.54232e-12 2.32099e-11 3 1.026469815596322e+01 1.026469815597155e+01 8.33467e-12 1.48486e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 2.670090314912756e+00 2.670090314913092e+00 3.35287e-13 2.14446e-11 2 7.851022410845406e-01 7.851022410896346e-01 5.09393e-12 1.23458e-11 3 1.952400742211909e+00 1.952400742212828e+00 9.19709e-13 1.12206e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 -3.671734206749518e+00 -3.671734206739627e+00 9.89120e-12 2.52625e-11 2 2.923816973231427e+00 2.923816973238071e+00 6.64446e-12 2.34830e-11 3 -1.809836702780394e+00 -1.809836702770904e+00 9.48930e-12 9.76610e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 2.731225969207721e+00 2.731225969207584e+00 1.36779e-13 8.48694e-11 2 -1.576186922849275e+00 -1.576186922849083e+00 1.92291e-13 2.67646e-11 3 -8.952117099950122e+00 -8.952117099982807e+00 3.26850e-11 3.80087e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 4.226814280889135e-01 4.226814280880850e-01 8.28448e-13 4.12135e-11 2 7.155086297111066e+00 7.155086297086747e+00 2.43192e-11 3.96764e-10 * 3 2.746875002620377e+00 2.746875002619976e+00 4.01457e-13 4.61742e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 9.271872459930201e+00 9.271872459943260e+00 1.30598e-11 3.84292e-10 * 2 -1.163143447670321e+01 -1.163143447669730e+01 5.91172e-12 8.30642e-11 3 1.757309627685695e+00 1.757309627677768e+00 7.92744e-12 4.29190e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -1.289097388204955e+01 -1.289097388204774e+01 1.80478e-12 1.51470e-11 2 1.124522002854165e+01 1.124522002854350e+01 1.84741e-12 1.43174e-11 3 1.251890751910816e+00 1.251890751912303e+00 1.48637e-12 5.99325e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 -2.011486394585066e+00 -2.011486394583020e+00 2.04636e-12 3.21256e-10 * 2 -1.918219541398761e+01 -1.918219541401261e+01 2.50040e-11 7.76303e-11 3 -5.542793179158004e+00 -5.542793179174171e+00 1.61675e-11 4.64455e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 5.371529221881267e+00 5.371529221885432e+00 4.16467e-12 2.76357e-11 2 4.103801140060304e+00 4.103801140058548e+00 1.75682e-12 8.03748e-11 3 -6.588217592619583e-01 -6.588217592709197e-01 8.96139e-12 3.98570e-10 * ----------------------------------------------------------------------------------------------------- 31 C 1 4.590003842131592e+00 4.590003842128713e+00 2.87947e-12 8.84270e-12 2 1.952243086846962e+00 1.952243086858564e+00 1.16021e-11 2.84304e-11 3 5.552121848322771e+00 5.552121848319492e+00 3.27915e-12 9.57545e-12 ----------------------------------------------------------------------------------------------------- 32 C 1 -3.973613624062346e+00 -3.973613624072075e+00 9.72911e-12 2.57852e-11 2 7.347335914121626e+00 7.347335914131573e+00 9.94760e-12 5.99600e-11 3 1.063877507896761e+01 1.063877507892352e+01 4.40910e-11 2.96852e-10 * ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 18, direction = 3: |F_model - F_numer| error = --------------------------------- = 1.13934e-10 max{(|F_model|+|F_numer|)/2, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Si | a0 = 3.89748287201 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.543085788706563e+00 -1.543085788720879e+00 1.43165e-11 1.91017e-10 2 1.514344231326253e+00 1.514344231300961e+00 2.52918e-11 3.07037e-11 3 3.791263341036459e+00 3.791263341027757e+00 8.70237e-12 2.33629e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.788362902804489e+00 1.788362902826249e+00 2.17604e-11 7.90947e-11 2 4.291730200255137e+00 4.291730200251364e+00 3.77298e-12 8.21512e-11 3 2.752861959468468e+00 2.752861959483419e+00 1.49503e-11 1.63101e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.256798217070103e+00 1.256798217083756e+00 1.36533e-11 2.75427e-10 2 -2.998288015930669e-01 -2.998288015877600e-01 5.30687e-12 2.97635e-11 3 -2.715318271201781e-01 -2.715318271250366e-01 4.85845e-12 3.70482e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.450377321021017e+00 -1.450377321018598e+00 2.41873e-12 5.54190e-11 2 8.089382455566905e-01 8.089382455592361e-01 2.54563e-12 5.56514e-11 3 -4.358143064699298e+00 -4.358143064687722e+00 1.15765e-11 8.59215e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 3.227990375307814e+00 3.227990375301785e+00 6.02896e-12 5.59481e-11 2 2.801398959504158e+00 2.801398959483273e+00 2.08851e-11 1.01066e-11 3 -1.972278662236410e-01 -1.972278662227516e-01 8.89372e-13 2.59222e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -3.139047231993286e+00 -3.139047231994788e+00 1.50280e-12 4.85247e-11 2 -2.973431725545941e+00 -2.973431725550062e+00 4.12026e-12 2.16778e-11 3 3.725940641601460e+00 3.725940641598754e+00 2.70628e-12 2.32246e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 1.889641160066569e-01 1.889641160115591e-01 4.90216e-12 1.00157e-11 2 1.615135758103810e+00 1.615135758107930e+00 4.11937e-12 3.90818e-11 3 -3.357243164951605e+00 -3.357243164958257e+00 6.65201e-12 1.13349e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -4.439888995412526e-03 -4.439888982561823e-03 1.28507e-11 6.27082e-11 2 3.701928785555234e-01 3.701928785605685e-01 5.04513e-12 2.76186e-10 3 5.064689261186328e+00 5.064689261186760e+00 4.31655e-13 2.67007e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 1.042075418522945e-02 1.042075416608186e-02 1.91476e-11 2.18668e-10 2 -1.598999786015309e-01 -1.598999786281000e-01 2.65691e-11 1.17023e-10 3 5.949644609317567e-01 5.949644609280466e-01 3.71014e-12 1.22072e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -2.221758572144851e+00 -2.221758570701752e+00 1.44310e-09 1.22818e-08 * 2 1.750784309896985e+00 1.750784309862438e+00 3.45466e-11 3.08130e-07 * 3 -8.697216874468661e-01 -8.697216872786754e-01 1.68191e-10 3.12440e-09 * ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.798584972016923e+00 -5.798584972013913e+00 3.01004e-12 6.10667e-11 2 -4.722892543690762e+00 -4.722892543704483e+00 1.37215e-11 1.53824e-10 3 1.149952209960232e-01 1.149952209682401e-01 2.77831e-11 8.44518e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 7.359767528241311e-01 7.359767540110653e-01 1.18693e-09 1.95466e-05 * 2 -5.170568956154761e+00 -5.170568956062565e+00 9.21965e-11 3.19023e-07 * 3 3.788164272014197e+00 3.788164272033399e+00 1.92024e-11 4.69981e-09 * ----------------------------------------------------------------------------------------------------- 13 Si 1 1.913774027633320e+00 1.913774027640702e+00 7.38187e-12 3.04348e-11 2 -1.554249094712645e+00 -1.554249094692391e+00 2.02531e-11 1.99627e-10 3 -4.802124170777522e+00 -4.802124170773815e+00 3.70726e-12 1.26511e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -5.755503391890224e-01 -5.755503391945516e-01 5.52913e-12 8.38535e-11 2 1.323439894076720e+00 1.323439894076723e+00 3.33067e-15 2.19793e-11 3 -2.406813224572314e+00 -2.406813224567471e+00 4.84279e-12 5.19362e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 6.901630949599022e-01 6.901630949652432e-01 5.34095e-12 1.53758e-10 2 -8.881460778484810e+00 -8.881460778524762e+00 3.99520e-11 8.64961e-11 3 4.531025644837216e+00 4.531025644831583e+00 5.63283e-12 9.45244e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -2.049341223856856e+00 -2.049341223826446e+00 3.04095e-11 9.18003e-11 2 3.717982738413134e+00 3.717982738434542e+00 2.14082e-11 1.35053e-10 3 5.615237280692123e+00 5.615237280696074e+00 3.95062e-12 1.06892e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.138874594833200e-01 -3.138874594903621e-01 7.04209e-12 4.32202e-11 2 -6.784913148273793e-01 -6.784913148214490e-01 5.93037e-12 6.99924e-10 * 3 3.767936964728538e+00 3.767936964724231e+00 4.30678e-12 9.90341e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.296559236070399e+00 2.296559236054214e+00 1.61857e-11 4.71951e-11 2 -2.051789858407791e+00 -2.051789858375264e+00 3.25278e-11 3.22196e-11 3 -5.269909708255899e+00 -5.269909708238677e+00 1.72218e-11 1.95148e-09 * ----------------------------------------------------------------------------------------------------- 19 Si 1 3.845622812712576e+00 3.845622812707566e+00 5.00977e-12 1.04405e-10 2 3.444496762061578e+00 3.444496762066938e+00 5.36060e-12 1.45111e-10 3 2.753268091054725e-02 2.753268091113910e-02 5.91849e-13 2.66006e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 5.034163177111679e+00 5.034163177118910e+00 7.23066e-12 4.55849e-11 2 4.220195318883737e+00 4.220195318873823e+00 9.91385e-12 6.43228e-11 3 -1.598335606642337e+00 -1.598335606661235e+00 1.88978e-11 7.12290e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 2.946263766015366e-01 2.946263766017688e-01 2.32148e-13 1.61144e-11 2 -1.375125140504719e-01 -1.375125140381058e-01 1.23661e-11 4.47364e-12 3 1.162964608833411e+00 1.162964608831907e+00 1.50391e-12 2.86000e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.421033086097136e+00 -1.421033086091968e+00 5.16787e-12 5.89300e-11 2 4.668275142077761e+00 4.668275142078484e+00 7.22977e-13 2.16298e-11 3 2.273789643417626e+00 2.273789643405860e+00 1.17657e-11 3.11280e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.814050661570814e+00 -1.814050661574817e+00 4.00302e-12 2.90188e-11 2 3.759167705686735e+00 3.759167705685877e+00 8.58424e-13 3.69744e-11 3 -3.573856447106118e+00 -3.573856447118908e+00 1.27898e-11 1.88769e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.620237344824022e+00 -1.620237344827068e+00 3.04623e-12 9.08822e-11 2 -6.531370343368424e+00 -6.531370343318402e+00 5.00222e-11 1.23028e-10 3 7.554434220978657e-01 7.554434221002162e-01 2.35045e-12 3.62677e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.292121115613990e+00 4.292121115618635e+00 4.64517e-12 8.41327e-11 2 1.143779500921756e+01 1.143779500923091e+01 1.33493e-11 6.17852e-11 3 -3.934824353808445e-01 -3.934824353903670e-01 9.52249e-12 5.07099e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -6.130402688085143e+00 -6.130402688075988e+00 9.15445e-12 5.44720e-11 2 -1.863976564371451e+00 -1.863976564391772e+00 2.03206e-11 1.82130e-11 3 4.398250520214748e-01 4.398250520392981e-01 1.78233e-11 2.77071e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -6.069818682551539e+00 -6.069818682553644e+00 2.10587e-12 5.31388e-11 2 -4.647346450515856e+00 -4.647346450520708e+00 4.85212e-12 1.22085e-10 3 2.099833060187659e+00 2.099833060185659e+00 1.99973e-12 1.68686e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 4.862738112508536e+00 4.862738112501688e+00 6.84786e-12 2.25047e-11 2 -5.009370427987434e+00 -5.009370427993400e+00 5.96678e-12 4.32268e-11 3 -1.091061956084754e+01 -1.091061956084501e+01 2.52776e-12 1.34417e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 6.158294236811554e+00 6.158294236824267e+00 1.27134e-11 8.44036e-11 2 2.849308887192703e+00 2.849308887208067e+00 1.53637e-11 5.89573e-11 3 1.346058817727654e+00 1.346058817687223e+00 4.04308e-11 5.62283e-10 * ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.725129742216358e+00 -1.725129742208236e+00 8.12195e-12 1.93563e-11 2 -1.404490954837395e+00 -1.404490954853268e+00 1.58737e-11 1.53317e-10 3 3.694901086704534e+00 3.694901086703736e+00 7.98028e-13 2.63163e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -3.626433021172481e+00 -3.626433021181899e+00 9.41869e-12 4.89364e-11 2 -3.234114716545045e+00 -3.234114716537588e+00 7.45715e-12 8.48375e-11 3 -6.999509991556189e+00 -6.999509991558829e+00 2.64055e-12 5.11466e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 2.906602715702831e+00 2.906602715705307e+00 2.47624e-12 2.81064e-10 2 7.476089828863067e-01 7.476089829070032e-01 2.06964e-11 6.71023e-11 3 -5.389086638129976e-01 -5.389086638211429e-01 8.14526e-12 1.53504e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 8, direction = 1: |F_model - F_numer| error = --------------------------------- = 2.89437e-09 max{(|F_model|+|F_numer|)/2, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = C Si | a0 = 3.26511896941 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 -3.406403169290294e-02 -3.406403169529527e-02 2.39233e-12 5.65566e-12 2 7.303032397245568e-01 7.303032397256916e-01 1.13476e-12 3.91176e-12 3 6.293966161345541e-01 6.293966161330922e-01 1.46194e-12 4.26037e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 -8.037053345815686e+00 -8.037053345812241e+00 3.44436e-12 5.05267e-11 2 2.306804669045454e+00 2.306804669069689e+00 2.42348e-11 1.50386e-09 * 3 -2.953696841152695e+00 -2.953696841135930e+00 1.67648e-11 3.90297e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.066705981518909e-01 -2.066705981516940e-01 1.96926e-13 3.38428e-11 2 5.743825352125643e+00 5.743825352126425e+00 7.82485e-13 2.76446e-11 3 6.500462647439377e+00 6.500462647437132e+00 2.24443e-12 3.98828e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 3.375210223049084e-01 3.375210223275877e-01 2.26793e-11 4.01800e-10 2 7.764156682158786e+00 7.764156682405182e+00 2.46396e-10 2.96146e-10 3 -2.563831485257584e+00 -2.563831485253405e+00 4.17932e-12 7.80433e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 -3.498134167930810e+00 -3.498134167937815e+00 7.00462e-12 1.71198e-10 2 -5.632618231712677e+00 -5.632618231707537e+00 5.13989e-12 8.68798e-11 3 -1.241682131147120e+00 -1.241682131194838e+00 4.77174e-11 8.24101e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 1.343012403869093e+01 1.343012403868237e+01 8.55849e-12 1.00302e-10 2 9.738458908255140e+00 9.738458908280089e+00 2.49489e-11 1.80135e-10 3 -1.816537597078691e+01 -1.816537597073095e+01 5.59659e-11 1.49583e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 6.400131134167938e-01 6.400131134202003e-01 3.40650e-12 5.26332e-11 2 -1.068044790558358e+01 -1.068044790558582e+01 2.24354e-12 1.17003e-10 3 1.111694732745473e+01 1.111694732744946e+01 5.27578e-12 1.11747e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 8.976205707434207e+00 8.976205707459334e+00 2.51266e-11 2.87205e-10 2 -2.435389307235035e+01 -2.435389307232525e+01 2.50964e-11 1.51843e-10 3 1.974750442078501e+01 1.974750442077223e+01 1.27827e-11 3.17829e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.560437636772733e+00 2.560437636769748e+00 2.98428e-12 1.65250e-10 2 -5.925944343553941e+00 -5.925944343552108e+00 1.83320e-12 5.26335e-12 3 4.657260704068438e+00 4.657260704093542e+00 2.51035e-11 1.19148e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -2.337547291876134e-01 -2.337547291923592e-01 4.74570e-12 1.96856e-11 2 -6.019213473978673e-01 -6.019213474164050e-01 1.85377e-11 4.99757e-11 3 4.557906287239840e-01 4.557906287140281e-01 9.95581e-12 2.12199e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -2.199452762146495e+01 -2.199452762139532e+01 6.96261e-11 5.60249e-09 * 2 9.107812332214822e+00 9.107812332336980e+00 1.22158e-10 2.90636e-09 * 3 2.262495823320358e+00 2.262495823322489e+00 2.13163e-12 1.28726e-08 * ----------------------------------------------------------------------------------------------------- 12 C 1 -4.225612654297634e-01 -4.225612654252388e-01 4.52466e-12 1.61962e-11 2 -2.003168518990240e+00 -2.003168518988399e+00 1.84075e-12 3.87290e-12 3 -1.679731744811992e+00 -1.679731744811788e+00 2.04281e-13 1.22671e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.941492046847990e-01 -1.941492046941305e-01 9.33148e-12 2.04257e-11 2 1.244126434543953e+01 1.244126434544891e+01 9.37916e-12 3.91154e-10 3 -3.173572348393289e+01 -3.173572348392023e+01 1.26619e-11 7.12248e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 3.442195160406317e+00 3.442195160407794e+00 1.47704e-12 8.96896e-11 2 2.721262302152011e+00 2.721262302148118e+00 3.89244e-12 1.79501e-11 3 1.955432162108704e+00 1.955432162109894e+00 1.18971e-12 1.20681e-10 ----------------------------------------------------------------------------------------------------- 15 C 1 -5.103475007922148e-01 -5.103475007882320e-01 3.98281e-12 2.98416e-11 2 4.478559969111278e+00 4.478559969113898e+00 2.62013e-12 2.51785e-10 3 2.602506811246130e+00 2.602506811250925e+00 4.79483e-12 7.57976e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -6.032876677466059e-01 -6.032876677325494e-01 1.40565e-11 1.14070e-10 2 4.031698737299720e+00 4.031698737306032e+00 6.31140e-12 9.75220e-12 3 2.176737355788254e+00 2.176737355797755e+00 9.50173e-12 5.99494e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.718036721515199e-02 -1.718036717731474e-02 3.78373e-11 2.08451e-09 * 2 4.126821457544408e+00 4.126821457563016e+00 1.86073e-11 8.93250e-11 3 4.543910732708505e+00 4.543910732709206e+00 7.00773e-13 3.16538e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 8.823176296709498e+00 8.823176296574822e+00 1.34676e-10 8.10580e-10 2 -1.318717022966815e+01 -1.318717022966784e+01 3.07310e-13 1.92010e-09 * 3 -1.601940824815187e+01 -1.601940824822971e+01 7.78400e-11 4.32173e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 2.892886060071026e-01 2.892886060160172e-01 8.91465e-12 9.68444e-11 2 -2.486563363334789e+00 -2.486563363345038e+00 1.02491e-11 5.12181e-11 3 2.570307209217786e+00 2.570307209192554e+00 2.52327e-11 1.83936e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.155337563097218e+01 -1.155337563097515e+01 2.97362e-12 7.47331e-11 2 -7.141176418043957e+00 -7.141176418062555e+00 1.85985e-11 4.90763e-11 3 2.370599308145874e+00 2.370599308173155e+00 2.72808e-11 1.40422e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 -2.507359217196235e+00 -2.507359217207082e+00 1.08469e-11 5.11231e-10 2 -8.024573884154407e-01 -8.024573884108241e-01 4.61653e-12 6.47603e-11 3 -2.134475796707114e+00 -2.134475796685460e+00 2.16538e-11 5.50351e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 3.548136603079662e-01 3.548136603673114e-01 5.93452e-11 9.85226e-11 2 -1.723116346930026e+00 -1.723116346939682e+00 9.65605e-12 3.56026e-11 3 -2.238724254380713e+00 -2.238724254399299e+00 1.85856e-11 9.24234e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 2.049897255532357e+01 2.049897255536856e+01 4.49845e-11 1.81860e-10 2 -3.647131063216835e+01 -3.647131063216590e+01 2.45137e-12 2.21689e-11 3 -1.782122146829057e+00 -1.782122146750716e+00 7.83409e-11 3.36965e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.581723917508837e+01 -2.581723917509082e+01 2.45493e-12 6.00661e-10 2 2.497741763330058e+01 2.497741763342110e+01 1.20519e-10 1.16027e-09 * 3 7.877682926985119e+00 7.877682926943140e+00 4.19789e-11 2.41999e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -3.552002176542558e+00 -3.552002176552175e+00 9.61720e-12 2.46896e-11 2 -4.925219606201811e+00 -4.925219606199821e+00 1.98952e-12 1.19886e-11 3 -3.923203822870300e+00 -3.923203822867605e+00 2.69518e-12 5.83897e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -5.712083595045105e+00 -5.712083595078388e+00 3.32827e-11 2.10116e-10 2 5.697351778728294e+00 5.697351778726852e+00 1.44151e-12 7.40821e-11 3 -8.812342988595596e+00 -8.812342988587769e+00 7.82663e-12 6.67040e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -5.578304589694017e+00 -5.578304589693079e+00 9.38805e-13 3.12483e-10 2 5.371031902421252e+00 5.371031902370798e+00 5.04539e-11 6.47100e-11 3 8.290654332042847e+00 8.290654332038377e+00 4.46931e-12 1.67118e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 4.781470917133998e+00 4.781470917150696e+00 1.66986e-11 2.85963e-10 2 -3.815678824341037e+00 -3.815678824341832e+00 7.94476e-13 1.40319e-11 3 -2.918087248938201e-01 -2.918087249014091e-01 7.58898e-12 5.73391e-12 ----------------------------------------------------------------------------------------------------- 29 Si 1 9.293201965620083e+00 9.293201965620895e+00 8.11795e-13 3.87740e-10 2 6.694262174294875e+00 6.694262174321691e+00 2.68159e-11 1.55538e-11 3 9.509177472530915e+00 9.509177472539388e+00 8.47322e-12 2.02043e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.043575130971745e+00 -1.043575130996901e+00 2.51559e-11 6.92499e-11 2 -4.485678034103253e+00 -4.485678034081046e+00 2.22071e-11 1.60327e-10 3 -3.820812383521974e-02 -3.820812386848473e-02 3.32650e-11 1.40347e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 8.267808940084226e+00 8.267808940075756e+00 8.46967e-12 1.46997e-10 2 1.655686288513177e+01 1.655686288514784e+01 1.60689e-11 3.39984e-10 3 1.338716279612020e+00 1.338716279624100e+00 1.20806e-11 2.96820e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 9.820440395410266e+00 9.820440395488395e+00 7.81295e-11 1.10523e-10 2 1.748469893847339e+00 1.748469893859174e+00 1.18345e-11 2.36595e-11 3 4.974753005040297e+00 4.974753005055048e+00 1.47509e-11 4.92992e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 30, direction = 3: |F_model - F_numer| error = --------------------------------- = 8.70626e-10 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.89437e-09 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 2.89437e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure. Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation.