!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_001 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 8.848466019190320e-01 8.848466019230544e-01 4.02245e-12 1.45844e-11 2 3.020762132846854e-02 3.020762132937007e-02 9.01532e-13 1.94589e-11 3 7.987180025485469e-01 7.987180025485248e-01 2.20934e-14 3.89166e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.328177597915059e+00 -1.328177597920190e+00 5.13056e-12 5.86680e-11 2 -7.269360632777718e-01 -7.269360632740521e-01 3.71969e-12 2.96780e-11 3 4.461160113534511e-01 4.461160113534279e-01 2.32592e-14 1.47086e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 1.558840549747586e+00 1.558840549744977e+00 2.60947e-12 9.44253e-07 * 2 -1.927874124534103e+00 -1.927874124532970e+00 1.13354e-12 1.94711e-11 3 -2.641932405264930e+00 -2.641932405277528e+00 1.25979e-11 8.24008e-12 ----------------------------------------------------------------------------------------------------- 4 C 1 -2.700306502933617e+00 -2.700306502938406e+00 4.78906e-12 1.00073e-10 2 8.201676760002364e+00 8.201676760003298e+00 9.34364e-13 4.64286e-11 3 -7.618853084291846e+00 -7.618853084294970e+00 3.12372e-12 9.00879e-12 ----------------------------------------------------------------------------------------------------- 5 C 1 3.394549166178635e+00 3.394549166172407e+00 6.22835e-12 4.22551e-11 2 1.613847833455960e+00 1.613847833453104e+00 2.85594e-12 3.69116e-11 3 -5.592226709804693e-01 -5.592226709814635e-01 9.94205e-13 4.70539e-08 * ----------------------------------------------------------------------------------------------------- 6 C 1 -1.491476390975863e+00 -1.491476390977529e+00 1.66644e-12 1.20026e-11 2 -5.047560876234063e+00 -5.047560876227366e+00 6.69687e-12 1.50671e-11 3 4.204931917028975e+00 4.204931917030134e+00 1.15907e-12 1.62306e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -2.188505658466276e+00 -2.188505658493389e+00 2.71125e-11 4.26232e-11 2 -7.743623518584158e+00 -7.743623518585665e+00 1.50724e-12 8.67573e-12 3 -1.881205092367497e+01 -1.881205092368148e+01 6.50502e-12 1.07434e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -3.516823323528913e+00 -3.516823323533866e+00 4.95293e-12 5.99130e-11 2 6.488509395217677e+00 6.488509395224621e+00 6.94378e-12 3.53566e-11 3 2.872062282305553e+00 2.872062282326610e+00 2.10565e-11 1.69768e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -4.564128411073085e+00 -4.564128411070699e+00 2.38565e-12 4.20224e-11 2 -1.907256729271526e+01 -1.907256729271106e+01 4.19931e-12 3.25713e-11 3 -1.562948200795924e+00 -1.562948200794019e+00 1.90581e-12 1.12563e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.348240609235078e+00 -1.348240609236005e+00 9.27258e-13 1.61873e-11 2 6.840770030497247e+00 6.840770030500314e+00 3.06777e-12 2.41052e-11 3 -7.239038138805819e+00 -7.239038138806881e+00 1.06226e-12 5.10223e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 1.328742044054704e+00 1.328742044057355e+00 2.65188e-12 2.22351e-11 2 -1.833080373832830e+01 -1.833080373834493e+01 1.66231e-11 1.06525e-10 3 -3.848488688358716e+00 -3.848488688353550e+00 5.16609e-12 2.59512e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -7.143300036998395e+00 -7.143300036992096e+00 6.29896e-12 6.13767e-11 2 1.414625601191180e+01 1.414625601190745e+01 4.35740e-12 1.91189e-11 3 7.410185157802696e+00 7.410185157848844e+00 4.61489e-11 2.51550e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -3.284390538123716e+00 -3.284390538124192e+00 4.76508e-13 3.26166e-11 2 -3.739667066832470e+00 -3.739667066832726e+00 2.56239e-13 3.13594e-11 3 -1.440597203157965e+01 -1.440597203157996e+01 3.01981e-13 5.36282e-12 ----------------------------------------------------------------------------------------------------- 14 C 1 1.432105009377425e+00 1.432105009377586e+00 1.61648e-13 8.57669e-12 2 7.392685845445455e-01 7.392685845444559e-01 8.95950e-14 1.66474e-11 3 -1.684459449727628e+00 -1.684459449727926e+00 2.97984e-13 4.56728e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 1.318847129908685e+01 1.318847129908621e+01 6.39488e-13 2.32561e-11 2 -4.039453233575444e-01 -4.039453233585717e-01 1.02729e-12 1.59706e-11 3 5.283063544605842e+00 5.283063544607592e+00 1.74971e-12 2.95408e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 2.344121124025278e+00 2.344121124030860e+00 5.58176e-12 9.11333e-10 * 2 1.133643789700396e+01 1.133643789701257e+01 8.60645e-12 1.20062e-10 3 7.264816813757286e+00 7.264816813756754e+00 5.32019e-13 1.63026e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -5.671293596550789e+00 -5.671293596555299e+00 4.51017e-12 1.20455e-11 2 -9.165289694450832e-01 -9.165289694459205e-01 8.37330e-13 1.36618e-11 3 3.358800682671480e+00 3.358800682663957e+00 7.52287e-12 4.35252e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.433414927881163e+00 5.433414927875049e+00 6.11422e-12 1.06068e-10 2 1.239102322707887e+01 1.239102322708390e+01 5.03064e-12 5.28768e-11 3 3.438476294298090e+00 3.438476294298214e+00 1.23901e-13 3.19691e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 9.469979177954798e+00 9.469979177953769e+00 1.02851e-12 6.14495e-11 2 -8.875596872205099e+00 -8.875596872213764e+00 8.66507e-12 2.29427e-10 * 3 6.885221682479400e-02 6.885221682132163e-02 3.47238e-12 1.63240e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 -8.849195344926407e-01 -8.849195344925839e-01 5.68434e-14 2.09553e-11 2 -1.127612369653505e+00 -1.127612369651738e+00 1.76681e-12 5.11169e-12 3 -2.374134264750870e+00 -2.374134264750771e+00 9.94760e-14 1.91154e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -7.494115560956875e+00 -7.494115560978233e+00 2.13571e-11 1.06200e-10 2 -7.185361993183863e+00 -7.185361993179591e+00 4.27125e-12 4.63780e-11 3 1.135078004562848e+01 1.135078004561892e+01 9.56213e-12 7.06724e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 6.269010904366761e+00 6.269010904367592e+00 8.31335e-13 6.68141e-11 2 5.945062426549505e+00 5.945062426543545e+00 5.96057e-12 4.94333e-11 3 1.310393448494683e+01 1.310393448494601e+01 8.18901e-13 2.85283e-12 ----------------------------------------------------------------------------------------------------- 23 C 1 -4.438738317130947e+00 -4.438738317132112e+00 1.16529e-12 3.03011e-11 2 3.388893138401737e+00 3.388893138401597e+00 1.39888e-13 1.25819e-11 3 -7.083236070738820e+00 -7.083236070739249e+00 4.28990e-13 7.25908e-12 ----------------------------------------------------------------------------------------------------- 24 C 1 4.447250490011169e+00 4.447250490011158e+00 1.06581e-14 2.76748e-11 2 1.012712518420081e+01 1.012712518419940e+01 1.41043e-12 1.02188e-10 3 -6.969494282544225e+00 -6.969494282555822e+00 1.15978e-11 1.14354e-09 * ----------------------------------------------------------------------------------------------------- 25 C 1 -7.036724545519852e-01 -7.036724545477607e-01 4.22451e-12 5.08837e-11 2 -3.460486237474092e+00 -3.460486237474314e+00 2.22045e-13 2.40017e-11 3 -3.636753623937093e+00 -3.636753623926482e+00 1.06106e-11 1.41582e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 2.553707061217941e+00 2.553707061230257e+00 1.23159e-11 1.23175e-10 2 7.978089472554962e+00 7.978089472552360e+00 2.60236e-12 6.52358e-11 3 -2.293105899406976e+00 -2.293105899399062e+00 7.91456e-12 1.60165e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 4.959266949139709e+00 4.959266949140844e+00 1.13509e-12 3.52500e-11 2 -7.878664658962565e+00 -7.878664658960851e+00 1.71418e-12 5.39302e-12 3 3.597603983987559e+00 3.597603984002610e+00 1.50511e-11 2.18119e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -1.139985653871101e+01 -1.139985653871688e+01 5.86198e-12 6.48406e-11 2 6.914404597455280e+00 6.914404597459522e+00 4.24194e-12 7.11253e-12 3 4.608963403014177e+00 4.608963403016826e+00 2.64944e-12 8.35528e-10 * ----------------------------------------------------------------------------------------------------- 29 C 1 -3.378042098631174e+00 -3.378042098629995e+00 1.17950e-12 2.09517e-10 2 -8.362608987515650e+00 -8.362608987499311e+00 1.63389e-11 9.06493e-11 3 -4.151154246398564e+00 -4.151154246405047e+00 6.48370e-12 3.99938e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 3.989905164547747e+00 3.989905164552027e+00 4.28058e-12 6.03857e-05 * 2 1.068074911882982e+00 1.068074911874253e+00 8.72924e-12 2.50124e-11 3 2.438161945398301e+00 2.438161945395832e+00 2.46869e-12 1.12276e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 1.338376514548137e+00 1.338376514540323e+00 7.81375e-12 1.00285e-10 2 -9.177850461817330e+00 -9.177850461836632e+00 1.93019e-11 2.39719e-11 3 5.661568149193427e+00 5.661568149221594e+00 2.81668e-11 2.52713e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 -1.056599813781538e+00 -1.056599813781028e+00 5.10036e-13 1.62452e-11 2 6.768041462034651e+00 6.768041462034762e+00 1.11022e-13 3.02363e-11 3 8.973809045891013e+00 8.973809045874761e+00 1.62519e-11 2.91145e-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 = 19, direction = 3: |F_model - F_numer| error = --------------------------------- = 5.04323e-11 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 1.116624805627634e+00 1.116624805617112e+00 1.05218e-11 6.34026e-11 2 1.234268599389451e+00 1.234268599352194e+00 3.72573e-11 3.30598e-11 3 7.976498550378663e-01 7.976498550372776e-01 5.88751e-13 7.40600e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.936252753040026e+00 1.936252753049800e+00 9.77440e-12 5.48803e-11 2 -1.364165837043186e+00 -1.364165837046901e+00 3.71458e-12 6.34652e-11 3 -2.412149645632956e+00 -2.412149645616069e+00 1.68874e-11 7.92628e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.461021129244771e+00 2.461021129269859e+00 2.50884e-11 5.57518e-11 2 3.756826320468061e-01 3.756826320487545e-01 1.94844e-12 1.52888e-10 3 2.606144638508705e+00 2.606144638515523e+00 6.81810e-12 1.90994e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.401301021235105e+00 -1.401301021241898e+00 6.79301e-12 3.48346e-11 2 -3.670783479193463e+00 -3.670783479141682e+00 5.17804e-11 7.93490e-10 * 3 2.684450919141984e+00 2.684450919124447e+00 1.75366e-11 3.28972e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -3.500776482024590e-02 -3.500776482030745e-02 6.15549e-14 1.69524e-09 * 2 2.081433553376282e+00 2.081433553361665e+00 1.46176e-11 8.92242e-11 3 2.113421134315610e+00 2.113421134312046e+00 3.56426e-12 1.01426e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.735211098828620e+00 -2.735211098844772e+00 1.61515e-11 6.72014e-11 2 1.238242083003326e+00 1.238242083013185e+00 9.85900e-12 1.55465e-10 3 1.326581797669926e+00 1.326581797659689e+00 1.02363e-11 6.17080e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -6.796174766624655e+00 -6.796174766632207e+00 7.55218e-12 2.57625e-11 2 7.845915803101346e+00 7.845915803103478e+00 2.13163e-12 7.21645e-12 3 6.672739094669403e+00 6.672739094662243e+00 7.15961e-12 4.76117e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.120323647038584e+00 3.120323647032509e+00 6.07470e-12 6.62670e-12 2 -4.125038475128452e+00 -4.125038475106040e+00 2.24123e-11 6.35927e-11 3 2.037814763981699e+00 2.037814763967773e+00 1.39262e-11 1.75318e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.236544411597038e+00 -3.236544411597747e+00 7.09655e-13 9.29745e-12 2 4.591823430821525e+00 4.591823430825732e+00 4.20730e-12 5.47811e-11 3 -5.024288368143861e+00 -5.024288368151393e+00 7.53175e-12 4.16795e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.995696981187426e+00 -3.995696981192669e+00 5.24292e-12 5.39266e-11 2 -4.949147084516458e+00 -4.949147084516192e+00 2.65565e-13 2.70663e-11 3 6.922039877297957e+00 6.922039877308305e+00 1.03482e-11 1.68470e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 6.704816690506618e+00 6.704816690495031e+00 1.15872e-11 4.65112e-11 2 3.403975239089412e-01 3.403975238854038e-01 2.35373e-11 2.23443e-10 3 5.243976834782233e+00 5.243976834764273e+00 1.79599e-11 4.80105e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 3.627000620891080e+00 3.627000620901450e+00 1.03699e-11 1.35978e-10 2 -2.111352860563511e+00 -2.111352860554393e+00 9.11760e-12 1.04922e-10 3 -1.019828007214765e+00 -1.019828007229171e+00 1.44060e-11 1.57153e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.942846136746227e+00 -2.942846136746283e+00 5.68434e-14 2.60252e-10 2 -4.845990759262590e+00 -4.845990759262596e+00 6.21725e-15 3.14824e-11 3 -2.307872337510696e+00 -2.307872337520420e+00 9.72422e-12 1.76557e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.393685567685908e+00 4.393685567677346e+00 8.56204e-12 6.55183e-11 2 4.558436804405096e+00 4.558436804393911e+00 1.11848e-11 2.13509e-11 3 -1.336591102019242e+00 -1.336591101995982e+00 2.32598e-11 1.68249e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.050701795559692e+00 1.050701795558113e+00 1.57852e-12 3.50280e-11 2 -5.650238531700483e+00 -5.650238531704272e+00 3.78986e-12 3.31601e-11 3 7.457631033042083e-01 7.457631033070343e-01 2.82607e-12 1.37649e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -3.766931401948955e+00 -3.766931401954594e+00 5.63816e-12 6.58700e-11 2 1.547390392702411e+00 1.547390392697953e+00 4.45777e-12 2.32991e-11 3 -6.210863024101512e-01 -6.210863023937049e-01 1.64463e-11 3.73923e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.361657624520418e-01 1.361657624583340e-01 6.29219e-12 2.61417e-11 2 6.775020739167209e-01 6.775020739069455e-01 9.77540e-12 3.18321e-11 3 -2.005591829904542e+00 -2.005591829906017e+00 1.47526e-12 3.00993e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.543202617698169e+00 1.543202617699859e+00 1.68909e-12 4.14778e-10 2 1.920823302645033e-01 1.920823302704425e-01 5.93925e-12 2.09158e-10 3 -2.274693053899669e+00 -2.274693053896444e+00 3.22542e-12 1.31918e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.044775944500111e+00 1.044775944504666e+00 4.55480e-12 2.12188e-11 2 -6.408505738470534e-01 -6.408505738637863e-01 1.67329e-11 1.61079e-11 3 1.363565973779381e-01 1.363565973778739e-01 6.42819e-14 1.04067e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.998195477321921e+00 2.998195477325304e+00 3.38352e-12 4.92862e-10 * 2 6.600813122713408e+00 6.600813122702401e+00 1.10072e-11 9.79590e-11 3 -4.399976354043597e-01 -4.399976354184818e-01 1.41221e-11 3.74490e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 2.671244386375140e+00 2.671244386399423e+00 2.42832e-11 3.03269e-11 2 3.090183275459947e+00 3.090183275415987e+00 4.39604e-11 7.55676e-11 3 -6.534377498306876e+00 -6.534377498301536e+00 5.33973e-12 6.42068e-10 * ----------------------------------------------------------------------------------------------------- 22 Si 1 -2.903381593192873e+00 -2.903381593195347e+00 2.47447e-12 2.19314e-10 2 -1.855498763685077e+00 -1.855498763690247e+00 5.16964e-12 6.90967e-11 3 -2.561358699950727e+00 -2.561358699972263e+00 2.15352e-11 2.62212e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 8.002089411726195e-01 8.002089411748702e-01 2.25064e-12 4.01716e-11 2 -1.018100807600888e+00 -1.018100807585187e+00 1.57012e-11 1.26077e-10 3 -7.119356129176333e-01 -7.119356129764604e-01 5.88271e-11 9.06306e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.259161408016887e+00 -2.259161408015010e+00 1.87628e-12 4.47233e-11 2 1.424255787156427e-01 1.424255787186687e-01 3.02602e-12 4.04947e-11 3 -6.792792172798388e-01 -6.792792172829210e-01 3.08220e-12 4.54117e-10 * ----------------------------------------------------------------------------------------------------- 25 Si 1 1.630985556435658e+00 1.630985556419547e+00 1.61113e-11 1.61403e-10 2 2.309452645453923e+00 2.309452645435318e+00 1.86042e-11 7.28542e-11 3 -1.181610772507693e+00 -1.181610772518822e+00 1.11289e-11 2.49529e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -2.647900281488541e+00 -2.647900281495814e+00 7.27240e-12 8.67293e-11 2 -2.395354664236209e-01 -2.395354665061259e-01 8.25051e-11 2.03790e-10 3 1.182704929500163e+00 1.182704929624778e+00 1.24615e-10 1.35432e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -2.820548450458278e+00 -2.820548450501454e+00 4.31761e-11 9.43099e-11 2 -2.742055530176243e+00 -2.742055530203156e+00 2.69123e-11 2.91708e-10 3 -1.574248489373393e+00 -1.574248489433997e+00 6.06037e-11 8.78852e-10 * ----------------------------------------------------------------------------------------------------- 28 Si 1 3.024865102109971e+00 3.024865102108252e+00 1.71907e-12 1.46070e-11 2 -7.153547840129183e-01 -7.153547840077439e-01 5.17442e-12 4.93352e-11 3 -2.674280885226231e+00 -2.674280885209136e+00 1.70943e-11 7.54246e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 -2.701686116171598e+00 -2.701686116150086e+00 2.15126e-11 1.65299e-10 2 -2.608470492313577e+00 -2.608470492294370e+00 1.92073e-11 3.78842e-10 3 2.916867987389998e+00 2.916867987475811e+00 8.58131e-11 1.09912e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.312499495086505e+00 1.312499495093598e+00 7.09255e-12 2.76827e-11 2 2.042188071121707e+00 2.042188071125486e+00 3.77876e-12 5.55080e-11 3 1.395078890047023e+00 1.395078890063952e+00 1.69291e-11 8.79283e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.358773891253673e+00 -2.358773891253042e+00 6.30607e-13 2.27280e-11 2 -6.716525329122054e-02 -6.716525329958993e-02 8.36939e-12 2.16221e-11 3 -4.535400047608798e+00 -4.535400047604028e+00 4.76952e-12 7.41540e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 1.028595030823685e+00 1.028595030827248e+00 3.56293e-12 4.24052e-11 2 -2.264489221642295e+00 -2.264489221631344e+00 1.09517e-11 5.12967e-11 3 1.112999082286722e+00 1.112999082286754e+00 3.21965e-14 1.92177e-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 = 26, direction = 2: |F_model - F_numer| error = --------------------------------- = 3.44438e-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. MIXED STRUCTURE -- Species = C Si | a0 = 3.22505243498 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 4.942908593668699e-03 4.942908593518695e-03 1.50003e-13 7.74783e-12 2 3.205123987659852e-01 3.205123987563284e-01 9.65678e-12 7.83670e-11 3 -2.240853948936281e+00 -2.240853948941386e+00 5.10569e-12 9.97105e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 9.866407835214840e+00 9.866407835225887e+00 1.10472e-11 5.08162e-11 2 -1.872877066910960e+01 -1.872877066911126e+01 1.65201e-12 3.52209e-10 3 -1.447325307729457e+01 -1.447325307728750e+01 7.07523e-12 1.29823e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 4.210571357136282e+00 4.210571357126594e+00 9.68825e-12 5.09432e-11 2 -3.179934194469494e+00 -3.179934194497384e+00 2.78897e-11 1.66526e-10 3 4.367787950536204e-01 4.367787950533353e-01 2.85105e-13 1.87102e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.529178167238424e+00 -3.529178167220409e+00 1.80154e-11 5.57603e-11 2 1.217115917410327e+00 1.217115917457331e+00 4.70037e-11 2.71945e-10 3 6.023886194152343e-02 6.023886196889667e-02 2.73732e-11 6.97866e-10 * ----------------------------------------------------------------------------------------------------- 5 C 1 -5.403852967966730e+00 -5.403852967960387e+00 6.34248e-12 8.00844e-11 2 1.145533422969826e+00 1.145533422969571e+00 2.54685e-13 7.61728e-11 3 -2.854185187226074e+00 -2.854185187217814e+00 8.26006e-12 1.27951e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 1.502953730516653e+00 1.502953730524298e+00 7.64566e-12 4.76714e-11 2 1.321784315031476e+01 1.321784315030432e+01 1.04432e-11 4.73257e-11 3 -1.195477106009116e+01 -1.195477106009835e+01 7.18181e-12 1.27489e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 5.709194700735956e+00 5.709194700733553e+00 2.40252e-12 4.08171e-11 2 -2.135210696369124e+01 -2.135210696367364e+01 1.75966e-11 1.99705e-10 3 1.459231849413363e+01 1.459231849414254e+01 8.91198e-12 1.49353e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.944441982300002e-01 -1.944441982417169e-01 1.17167e-11 3.60956e-10 2 -8.386543261250470e+00 -8.386543261229313e+00 2.11564e-11 4.00355e-11 3 1.155358583546048e+01 1.155358583542501e+01 3.54650e-11 4.10569e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 -1.287946386049531e+01 -1.287946386050310e+01 7.78755e-12 6.79368e-11 2 1.298328884085055e+01 1.298328884085153e+01 9.84102e-13 3.72378e-11 3 -9.652723868300956e-01 -9.652723868413866e-01 1.12910e-11 8.46910e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.042424965786464e+00 -4.042424965791899e+00 5.43565e-12 3.94085e-12 2 -1.292368053344363e+00 -1.292368053332765e+00 1.15981e-11 6.78873e-11 3 4.356315426912979e+00 4.356315426927047e+00 1.40679e-11 3.30260e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 6.010745999809434e+00 6.010745999813561e+00 4.12648e-12 6.80549e-11 2 2.315243520509522e+01 2.315243520501744e+01 7.77796e-11 3.65947e-10 3 6.220963220224376e+00 6.220963220220870e+00 3.50564e-12 2.07921e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 7.137913948365721e+00 7.137913948365189e+00 5.32019e-13 3.14682e-11 2 -3.657607331261969e+00 -3.657607331253771e+00 8.19833e-12 3.87730e-11 3 -1.214935046405673e+00 -1.214935046404874e+00 7.98916e-13 3.17806e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 2.058818490977170e+00 2.058818490962362e+00 1.48073e-11 3.80857e-10 2 2.261472810321889e+00 2.261472810318527e+00 3.36176e-12 9.00737e-11 3 -2.863262594773854e+00 -2.863262594769064e+00 4.78995e-12 3.19651e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 7.745976464885050e-01 7.745976464884259e-01 7.91589e-14 7.06397e-11 2 -6.332277107489869e+00 -6.332277107492651e+00 2.78177e-12 7.10365e-12 3 5.769632515584322e+00 5.769632515586983e+00 2.66098e-12 5.43432e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 4.427353695571549e+00 4.427353695563909e+00 7.64011e-12 1.44806e-10 2 1.417904054238605e+01 1.417904054238166e+01 4.38760e-12 1.98115e-10 3 -1.120462688048083e+01 -1.120462688041208e+01 6.87468e-11 2.46366e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -3.496103242099785e-01 -3.496103242061455e-01 3.83299e-12 4.13997e-10 2 -4.854609569848357e+00 -4.854609569849555e+00 1.19815e-12 3.33236e-11 3 1.723170423234630e+00 1.723170423234205e+00 4.24771e-13 9.42060e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.969820098780201e+00 -1.969820098762556e+00 1.76454e-11 2.29649e-10 2 -3.960051765848098e+00 -3.960051765770918e+00 7.71805e-11 9.48089e-10 * 3 1.019969480216476e+01 1.019969480213083e+01 3.39320e-11 5.30491e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 -1.771733508770730e+00 -1.771733508776638e+00 5.90816e-12 1.53396e-10 2 9.592919694604654e-01 9.592919694860007e-01 2.55354e-11 1.73463e-10 3 3.177398209524963e-01 3.177398209254048e-01 2.70914e-11 6.16897e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.774315608286428e+00 1.774315608313064e+00 2.66360e-11 2.57709e-11 2 6.519757479583348e+00 6.519757479586117e+00 2.76934e-12 6.67244e-11 3 -5.580276143442385e-01 -5.580276143534904e-01 9.25182e-12 3.59798e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 2.423154452688834e-01 2.423154452654648e-01 3.41863e-12 3.01902e-11 2 3.004028072482291e+00 3.004028072489269e+00 6.97797e-12 8.33897e-11 3 -3.228838283043023e+00 -3.228838283027645e+00 1.53779e-11 3.26512e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -2.454841916513040e+00 -2.454841916476575e+00 3.64646e-11 2.77307e-10 2 3.290736302767650e+00 3.290736302790447e+00 2.27964e-11 1.06031e-11 3 -5.504295310359595e+00 -5.504295310359629e+00 3.46390e-14 3.35467e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 -1.896870121889648e+00 -1.896870121891849e+00 2.20091e-12 7.22764e-11 2 2.553013737879648e+00 2.553013737941958e+00 6.23102e-11 4.75433e-11 3 -7.702119495441168e-01 -7.702119495370645e-01 7.05225e-12 2.96780e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 2.317260610037016e+00 2.317260610038490e+00 1.47393e-12 1.85066e-10 2 9.897761134945511e-01 9.897761134602054e-01 3.43456e-11 4.52696e-10 3 3.220618730069905e+00 3.220618730068388e+00 1.51701e-12 1.29434e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 -5.685630128980249e+00 -5.685630128887659e+00 9.25908e-11 1.14253e-09 * 2 -1.468945594722742e+01 -1.468945594716443e+01 6.29878e-11 4.25873e-10 3 -7.945572956392932e-01 -7.945572956889946e-01 4.97014e-11 2.57413e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -3.039250553620012e+00 -3.039250553619970e+00 4.13003e-14 1.11583e-10 2 -1.059246434957991e+01 -1.059246434959470e+01 1.47899e-11 2.43245e-10 3 1.195080856682810e+00 1.195080856628531e+00 5.42790e-11 2.36620e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 2.096763505032264e+00 2.096763505032399e+00 1.35447e-13 9.13776e-11 2 5.271694312631041e+00 5.271694312631347e+00 3.05533e-13 3.41522e-11 3 -9.586612240379365e+00 -9.586612240356590e+00 2.27747e-11 2.32736e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -8.598472918812634e+00 -8.598472918710014e+00 1.02620e-10 1.82066e-10 2 -2.870210040086487e+00 -2.870210040069613e+00 1.68741e-11 1.10298e-11 3 3.783301976356746e+00 3.783301976417138e+00 6.03917e-11 1.64754e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -4.512642159869045e+00 -4.512642159873322e+00 4.27747e-12 1.82672e-11 2 2.862655765444543e+00 2.862655765450356e+00 5.81268e-12 1.25477e-11 3 5.906290515136871e+00 5.906290515138284e+00 1.41309e-12 4.55707e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 -4.251292366916323e+00 -4.251292366915523e+00 8.00249e-13 1.05811e-10 2 -1.035548515331442e+00 -1.035548515362454e+00 3.10114e-11 5.72498e-11 3 2.410580847213684e-02 2.410580846255748e-02 9.57935e-12 7.28707e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 2.613568041107279e+00 2.613568041146107e+00 3.88285e-11 1.14332e-10 2 8.143351383136993e+00 8.143351383139885e+00 2.89191e-12 2.90150e-11 3 -6.433280861256947e+00 -6.433280861261596e+00 4.64961e-12 2.04512e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 1.319164699199938e+01 1.319164699202214e+01 2.27569e-11 1.61723e-10 2 -9.973833894653632e+00 -9.973833894622414e+00 3.12177e-11 1.01037e-10 3 1.628736452771974e+00 1.628736452767448e+00 4.52594e-12 3.47540e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -3.359842257062217e+00 -3.359842257061820e+00 3.97016e-13 3.23688e-11 2 8.834234238197253e+00 8.834234238188792e+00 8.46079e-12 5.21339e-10 3 3.658411201451858e+00 3.658411201461084e+00 9.22595e-12 4.31664e-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 = 29, direction = 3: |F_model - F_numer| error = --------------------------------- = 3.97388e-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 = 3.97388e-10 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 3.97388e-10 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.