!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_1989_SiC__MO_171585019474_003 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 = 2.7275753021240234 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 8.848466019191613e-01 8.848466019197041e-01 5.42788e-13 1.65583e-11 2 3.020762132855734e-02 3.020762132664570e-02 1.91164e-12 3.34498e-11 3 7.987180025485516e-01 7.987180025459442e-01 2.60747e-12 6.57219e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.328177597915319e+00 -1.328177597914848e+00 4.71179e-13 1.80032e-09 * 2 -7.269360632777567e-01 -7.269360632796663e-01 1.90958e-12 7.46470e-12 3 4.461160113534051e-01 4.461160113520796e-01 1.32555e-12 4.86825e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 1.558840549747592e+00 1.558840549789347e+00 4.17548e-11 1.31290e-10 2 -1.927874124534257e+00 -1.927874124526882e+00 7.37432e-12 7.07296e-11 3 -2.641932405264888e+00 -2.641932405233968e+00 3.09202e-11 1.28785e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -2.700306502933675e+00 -2.700306502935167e+00 1.49258e-12 3.33982e-11 2 8.201676760002504e+00 8.201676760002513e+00 8.88178e-15 2.48601e-11 3 -7.618853084291858e+00 -7.618853084299391e+00 7.53264e-12 5.72671e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 3.394549166178603e+00 3.394549166161019e+00 1.75846e-11 1.86937e-10 2 1.613847833455893e+00 1.613847833454455e+00 1.43818e-12 1.08042e-11 3 -5.592226709805299e-01 -5.592226709810431e-01 5.13145e-13 1.53174e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.491476390975837e+00 -1.491476390976273e+00 4.36540e-13 1.88021e-11 2 -5.047560876234032e+00 -5.047560876233185e+00 8.47322e-13 1.90248e-12 3 4.204931917028929e+00 4.204931917035249e+00 6.31939e-12 3.94014e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -2.188505658466267e+00 -2.188505658477597e+00 1.13292e-11 2.14087e-11 2 -7.743623518584196e+00 -7.743623518586301e+00 2.10587e-12 4.75788e-11 3 -1.881205092367486e+01 -1.881205092368626e+01 1.13971e-11 6.30820e-10 * ----------------------------------------------------------------------------------------------------- 8 C 1 -3.516823323528813e+00 -3.516823323529190e+00 3.76588e-13 6.96021e-12 2 6.488509395217680e+00 6.488509395215114e+00 2.56595e-12 7.46434e-11 3 2.872062282305679e+00 2.872062282306954e+00 1.27542e-12 2.52730e-09 * ----------------------------------------------------------------------------------------------------- 9 C 1 -4.564128411073055e+00 -4.564128411075401e+00 2.34657e-12 2.40474e-11 2 -1.907256729271524e+01 -1.907256729272866e+01 1.34222e-11 3.50930e-10 * 3 -1.562948200795887e+00 -1.562948200795906e+00 1.84297e-14 6.23466e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.348240609235110e+00 -1.348240609227350e+00 7.75957e-12 7.01799e-11 2 6.840770030497199e+00 6.840770030498833e+00 1.63336e-12 3.51985e-11 3 -7.239038138805808e+00 -7.239038138801891e+00 3.91776e-12 4.31308e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 1.328742044054668e+00 1.328742044043747e+00 1.09206e-11 1.28444e-10 2 -1.833080373832840e+01 -1.833080373830375e+01 2.46416e-11 1.06294e-10 3 -3.848488688358900e+00 -3.848488688363757e+00 4.85700e-12 8.49796e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -7.143300036998403e+00 -7.143300036998172e+00 2.30926e-13 2.57714e-11 2 1.414625601191174e+01 1.414625601192389e+01 1.21521e-11 3.51683e-11 3 7.410185157802760e+00 7.410185157779142e+00 2.36184e-11 3.77884e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -3.284390538123625e+00 -3.284390538120875e+00 2.75069e-12 9.37219e-11 2 -3.739667066832424e+00 -3.739667066839229e+00 6.80433e-12 1.88152e-11 3 -1.440597203157944e+01 -1.440597203157882e+01 6.23501e-13 9.24771e-12 ----------------------------------------------------------------------------------------------------- 14 C 1 1.432105009377367e+00 1.432105009377610e+00 2.42251e-13 4.34430e-12 2 7.392685845444642e-01 7.392685845440277e-01 4.36540e-13 7.63767e-12 3 -1.684459449727564e+00 -1.684459449728365e+00 8.00471e-13 3.97549e-12 ----------------------------------------------------------------------------------------------------- 15 C 1 1.318847129908692e+01 1.318847129907003e+01 1.68843e-11 2.32731e-10 2 -4.039453233575516e-01 -4.039453233613467e-01 3.79513e-12 9.26770e-12 3 5.283063544605683e+00 5.283063544608807e+00 3.12461e-12 2.71427e-12 ----------------------------------------------------------------------------------------------------- 16 C 1 2.344121124025274e+00 2.344121124026428e+00 1.15419e-12 3.75738e-10 * 2 1.133643789700407e+01 1.133643789699648e+01 7.59748e-12 1.39428e-10 3 7.264816813757237e+00 7.264816813747896e+00 9.34097e-12 5.84235e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -5.671293596550813e+00 -5.671293596543229e+00 7.58327e-12 2.44933e-11 2 -9.165289694451955e-01 -9.165289694432023e-01 1.99318e-12 1.42543e-11 3 3.358800682671100e+00 3.358800682668918e+00 2.18225e-12 2.44591e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.433414927881338e+00 5.433414927878769e+00 2.56861e-12 7.16817e-10 * 2 1.239102322707885e+01 1.239102322708362e+01 4.77485e-12 1.36641e-10 3 3.438476294298142e+00 3.438476294297951e+00 1.90958e-13 6.97518e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 9.469979177955073e+00 9.469979177937603e+00 1.74705e-11 8.17746e-11 2 -8.875596872205181e+00 -8.875596872203090e+00 2.09077e-12 1.35101e-10 3 6.885221682486156e-02 6.885221682630488e-02 1.44332e-12 1.10482e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 -8.849195344927465e-01 -8.849195344922468e-01 4.99711e-13 5.29887e-12 2 -1.127612369653294e+00 -1.127612369654049e+00 7.54952e-13 1.01303e-11 3 -2.374134264750617e+00 -2.374134264752152e+00 1.53522e-12 3.26779e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -7.494115560956953e+00 -7.494115560952787e+00 4.16556e-12 5.49409e-11 2 -7.185361993183792e+00 -7.185361993214867e+00 3.10756e-11 3.25748e-11 3 1.135078004562850e+01 1.135078004564296e+01 1.44578e-11 6.47020e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 6.269010904366777e+00 6.269010904368121e+00 1.34470e-12 1.27695e-10 2 5.945062426549497e+00 5.945062426544286e+00 5.21094e-12 1.18660e-10 3 1.310393448494685e+01 1.310393448493697e+01 9.88010e-12 1.40208e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -4.438738317130912e+00 -4.438738317122728e+00 8.18456e-12 3.83169e-11 2 3.388893138401708e+00 3.388893138400590e+00 1.11822e-12 8.54286e-11 3 -7.083236070738850e+00 -7.083236070743578e+00 4.72866e-12 1.08065e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 4.447250490011039e+00 4.447250489991607e+00 1.94325e-11 4.30544e-11 2 1.012712518420084e+01 1.012712518419081e+01 1.00258e-11 6.12470e-11 3 -6.969494282544327e+00 -6.969494282547293e+00 2.96652e-12 1.15331e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -7.036724545519933e-01 -7.036724545520515e-01 5.81757e-14 2.66779e-11 2 -3.460486237473942e+00 -3.460486237480097e+00 6.15508e-12 5.49267e-11 3 -3.636753623937129e+00 -3.636753623939287e+00 2.15827e-12 2.96425e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 2.553707061217861e+00 2.553707061226413e+00 8.55183e-12 2.60951e-11 2 7.978089472554926e+00 7.978089472553896e+00 1.02940e-12 6.89981e-11 3 -2.293105899406929e+00 -2.293105899426628e+00 1.96985e-11 4.61529e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 4.959266949139494e+00 4.959266949141624e+00 2.13074e-12 3.04965e-11 2 -7.878664658962433e+00 -7.878664658960225e+00 2.20801e-12 4.73230e-11 3 3.597603983987514e+00 3.597603983993690e+00 6.17639e-12 2.02848e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 -1.139985653871083e+01 -1.139985653871936e+01 8.52118e-12 7.59499e-11 2 6.914404597455134e+00 6.914404597454904e+00 2.30038e-13 2.27054e-11 3 4.608963403014166e+00 4.608963403018017e+00 3.85114e-12 1.17133e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 -3.378042098631245e+00 -3.378042098634310e+00 3.06510e-12 6.59064e-11 2 -8.362608987515685e+00 -8.362608987506318e+00 9.36673e-12 1.82157e-10 3 -4.151154246398571e+00 -4.151154246398328e+00 2.43361e-13 1.41309e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 3.989905164547748e+00 3.989905164488439e+00 5.93090e-11 2.14652e-10 2 1.068074911883012e+00 1.068074911880423e+00 2.58904e-12 1.30111e-11 3 2.438161945398292e+00 2.438161945381088e+00 1.72045e-11 1.89608e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 1.338376514548215e+00 1.338376514536909e+00 1.13065e-11 3.82963e-11 2 -9.177850461817355e+00 -9.177850461817100e+00 2.55795e-13 1.63839e-10 3 5.661568149193458e+00 5.661568149193768e+00 3.10862e-13 1.04512e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 -1.056599813781524e+00 -1.056599813779701e+00 1.82254e-12 1.63825e-11 2 6.768041462034689e+00 6.768041462024109e+00 1.05800e-11 6.67999e-11 3 8.973809045891025e+00 8.973809045895369e+00 4.34319e-12 7.12213e-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 discontinuities. Maximum error obtained for particle = 1, direction = 2: |F_model - F_numer| error = ----------------------- = 6.32835e-11 max{|F_numer|, 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 = 3.8974828720092773 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.116624805627700e+00 1.116624805627336e+00 3.63265e-13 1.94089e-11 2 1.234268599389540e+00 1.234268599406720e+00 1.71794e-11 6.33591e-11 3 7.976498550378962e-01 7.976498550489550e-01 1.10588e-11 3.60869e-05 * ----------------------------------------------------------------------------------------------------- 2 Si 1 1.936252753039972e+00 1.936252753031529e+00 8.44214e-12 5.30831e-11 2 -1.364165837043280e+00 -1.364165837051192e+00 7.91123e-12 5.74680e-11 3 -2.412149645632890e+00 -2.412149645637729e+00 4.83880e-12 2.32707e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.461021129244756e+00 2.461021129247406e+00 2.64944e-12 1.54381e-10 2 3.756826320468458e-01 3.756826320316832e-01 1.51625e-11 1.51070e-10 3 2.606144638508629e+00 2.606144638494307e+00 1.43219e-11 2.92725e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.401301021235113e+00 -1.401301021240354e+00 5.24136e-12 8.20275e-11 2 -3.670783479193473e+00 -3.670783479198529e+00 5.05507e-12 8.95350e-11 3 2.684450919141926e+00 2.684450919146484e+00 4.55813e-12 1.08143e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -3.500776482024829e-02 -3.500776481281056e-02 7.43773e-12 4.33539e-11 2 2.081433553376296e+00 2.081433553392946e+00 1.66498e-11 1.76854e-11 3 2.113421134315622e+00 2.113421134316099e+00 4.77840e-13 2.94089e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.735211098828715e+00 -2.735211098825605e+00 3.10996e-12 6.28999e-11 2 1.238242083003477e+00 1.238242083000121e+00 3.35665e-12 4.61988e-11 3 1.326581797669916e+00 1.326581797660115e+00 9.80038e-12 1.37507e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -6.796174766624759e+00 -6.796174766613084e+00 1.16751e-11 2.18261e-11 2 7.845915803101274e+00 7.845915803096028e+00 5.24647e-12 5.85620e-11 3 6.672739094669494e+00 6.672739094668541e+00 9.52127e-13 1.19273e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.120323647038529e+00 3.120323647032023e+00 6.50546e-12 1.70108e-10 2 -4.125038475128463e+00 -4.125038475130033e+00 1.57030e-12 5.58451e-11 3 2.037814763981693e+00 2.037814763983650e+00 1.95755e-12 1.15832e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.236544411597086e+00 -3.236544411594630e+00 2.45581e-12 3.18940e-11 2 4.591823430821439e+00 4.591823430819373e+00 2.06590e-12 2.43707e-11 3 -5.024288368143831e+00 -5.024288368150939e+00 7.10809e-12 4.66915e-12 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.995696981187357e+00 -3.995696981179764e+00 7.59304e-12 3.68634e-11 2 -4.949147084516424e+00 -4.949147084514053e+00 2.37055e-12 1.50768e-11 3 6.922039877297946e+00 6.922039877305110e+00 7.16405e-12 1.35817e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 6.704816690506579e+00 6.704816690509745e+00 3.16636e-12 5.67097e-10 * 2 3.403975239089554e-01 3.403975239203376e-01 1.13821e-11 1.07806e-10 3 5.243976834782169e+00 5.243976834784341e+00 2.17248e-12 2.25571e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 3.627000620891039e+00 3.627000620888067e+00 2.97229e-12 1.65548e-11 2 -2.111352860563411e+00 -2.111352860551587e+00 1.18239e-11 2.31598e-10 3 -1.019828007214803e+00 -1.019828007211604e+00 3.19855e-12 5.61826e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.942846136746071e+00 -2.942846136753960e+00 7.88880e-12 2.97020e-11 2 -4.845990759262693e+00 -4.845990759257612e+00 5.08127e-12 2.38704e-10 3 -2.307872337510691e+00 -2.307872337511651e+00 9.60121e-13 2.60578e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.393685567685936e+00 4.393685567703433e+00 1.74971e-11 1.31303e-10 2 4.558436804405036e+00 4.558436804406533e+00 1.49658e-12 3.76330e-11 3 -1.336591102019287e+00 -1.336591102024538e+00 5.25113e-12 2.19085e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.050701795559685e+00 1.050701795560479e+00 7.94476e-13 3.85154e-11 2 -5.650238531700444e+00 -5.650238531685100e+00 1.53433e-11 4.12017e-11 3 7.457631033041792e-01 7.457631033220142e-01 1.78351e-11 9.73028e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -3.766931401948999e+00 -3.766931401963862e+00 1.48628e-11 1.00882e-10 2 1.547390392702404e+00 1.547390392693679e+00 8.72502e-12 1.20408e-11 3 -6.210863024100662e-01 -6.210863024094473e-01 6.18949e-13 5.00875e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.361657624520519e-01 1.361657624550352e-01 2.98331e-12 6.12087e-11 2 6.775020739166996e-01 6.775020739178595e-01 1.15996e-12 4.30186e-11 3 -2.005591829904537e+00 -2.005591829907662e+00 3.12461e-12 3.27800e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.543202617698183e+00 1.543202617712557e+00 1.43738e-11 1.68376e-10 2 1.920823302644490e-01 1.920823302740580e-01 9.60906e-12 2.83193e-10 3 -2.274693053899661e+00 -2.274693053894169e+00 5.49250e-12 6.63438e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.044775944499974e+00 1.044775944505428e+00 5.45408e-12 4.34914e-11 2 -6.408505738470028e-01 -6.408505738454071e-01 1.59572e-12 3.96873e-11 3 1.363565973780186e-01 1.363565973569446e-01 2.10740e-11 1.84510e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.998195477321940e+00 2.998195477319947e+00 1.99307e-12 5.93281e-11 2 6.600813122713397e+00 6.600813122727915e+00 1.45173e-11 1.85299e-10 3 -4.399976354043209e-01 -4.399976354131510e-01 8.83016e-12 8.76243e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 2.671244386375376e+00 2.671244386265040e+00 1.10337e-10 2.88233e-10 2 3.090183275459970e+00 3.090183275453818e+00 6.15197e-12 5.15761e-11 3 -6.534377498307123e+00 -6.534377498300305e+00 6.81766e-12 2.37138e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 -2.903381593192840e+00 -2.903381593192791e+00 4.88498e-14 5.09748e-11 2 -1.855498763685119e+00 -1.855498763678900e+00 6.21858e-12 3.31639e-10 3 -2.561358699950699e+00 -2.561358699950260e+00 4.38760e-13 1.04804e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 8.002089411726609e-01 8.002089410887950e-01 8.38659e-11 3.63835e-10 2 -1.018100807600886e+00 -1.018100807604571e+00 3.68527e-12 1.13798e-11 3 -7.119356129175829e-01 -7.119356129426885e-01 2.51056e-11 1.81534e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.259161408016870e+00 -2.259161408024904e+00 8.03446e-12 2.61240e-11 2 1.424255787156228e-01 1.424255787200599e-01 4.43706e-12 2.87839e-11 3 -6.792792172798255e-01 -6.792792172898521e-01 1.00265e-11 1.59810e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 1.630985556435685e+00 1.630985556424224e+00 1.14608e-11 2.87976e-10 2 2.309452645453869e+00 2.309452645445637e+00 8.23208e-12 1.75599e-10 3 -1.181610772507671e+00 -1.181610772510358e+00 2.68718e-12 1.05648e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -2.647900281488520e+00 -2.647900281503859e+00 1.53393e-11 1.91027e-10 2 -2.395354664235661e-01 -2.395354663092064e-01 1.14360e-10 3.76113e-09 * 3 1.182704929500053e+00 1.182704929564121e+00 6.40683e-11 2.48058e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -2.820548450458301e+00 -2.820548450449837e+00 8.46434e-12 2.87712e-10 2 -2.742055530176247e+00 -2.742055530206675e+00 3.04281e-11 6.06625e-10 * 3 -1.574248489373372e+00 -1.574248489452933e+00 7.95610e-11 7.16076e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 3.024865102109899e+00 3.024865102113105e+00 3.20632e-12 4.80189e-11 2 -7.153547840129176e-01 -7.153547840109572e-01 1.96043e-12 7.95641e-12 3 -2.674280885226124e+00 -2.674280885227124e+00 1.00009e-12 2.02498e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -2.701686116171557e+00 -2.701686116164720e+00 6.83720e-12 1.29757e-10 2 -2.608470492313528e+00 -2.608470492321818e+00 8.28981e-12 7.49569e-11 3 2.916867987390045e+00 2.916867987374414e+00 1.56311e-11 2.03718e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.312499495086464e+00 1.312499495133853e+00 4.73890e-11 1.13317e-10 2 2.042188071121632e+00 2.042188071112666e+00 8.96572e-12 5.91056e-11 3 1.395078890047025e+00 1.395078890049928e+00 2.90346e-12 6.71241e-12 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.358773891253686e+00 -2.358773891260470e+00 6.78391e-12 1.11421e-10 2 -6.716525329116756e-02 -6.716525328846150e-02 2.70606e-12 1.19085e-10 3 -4.535400047608824e+00 -4.535400047607379e+00 1.44418e-12 4.12568e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 1.028595030823694e+00 1.028595030804702e+00 1.89917e-11 5.28630e-11 2 -2.264489221642310e+00 -2.264489221638666e+00 3.64464e-12 4.07279e-11 3 1.112999082286703e+00 1.112999082279161e+00 7.54263e-12 2.96525e-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 discontinuities. Maximum error obtained for particle = 5, direction = 1: |F_model - F_numer| error = ----------------------- = 2.12459e-10 max{|F_numer|, 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 = 3.310415666619064 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -5.035589192883178e+00 -5.035589192881521e+00 1.65645e-12 5.14380e-11 2 -4.987665396745586e+00 -4.987665396724282e+00 2.13047e-11 1.33431e-11 3 -2.423660718175003e+00 -2.423660718174298e+00 7.05214e-13 2.44973e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.313402718812057e+00 3.313402718813976e+00 1.91847e-12 1.86566e-11 2 9.885675310016845e+00 9.885675310035834e+00 1.89893e-11 1.80981e-10 3 -5.643027668161388e+00 -5.643027668162881e+00 1.49303e-12 5.81606e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 5.795522166803935e+00 5.795522166805117e+00 1.18217e-12 2.64071e-10 2 -9.513251437238946e+00 -9.513251437249053e+00 1.01075e-11 6.69331e-11 3 -3.139562363638477e+00 -3.139562363637154e+00 1.32339e-12 1.60865e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.118923547208971e+01 -1.118923547209338e+01 3.66107e-12 2.27381e-10 2 2.150325600481987e+00 2.150325600472316e+00 9.67137e-12 2.29186e-10 3 -5.744364990304159e+00 -5.744364990318324e+00 1.41656e-11 2.71320e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 7.999278294132206e-01 7.999278293681514e-01 4.50692e-11 8.49746e-11 2 2.253545897674988e+00 2.253545897671215e+00 3.77387e-12 5.37081e-11 3 4.475649360896884e-01 4.475649360930034e-01 3.31501e-12 2.63392e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 7.585757836111532e+00 7.585757836109799e+00 1.73284e-12 9.96891e-11 2 -1.727896932514163e+01 -1.727896932510215e+01 3.94778e-11 4.73797e-10 3 -6.939246433325066e+00 -6.939246433328266e+00 3.19922e-12 2.19012e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -6.257292133921585e-01 -6.257292133960710e-01 3.91254e-12 5.28917e-11 2 6.411010926787477e+00 6.411010926777516e+00 9.96092e-12 1.11848e-11 3 5.220373232400993e+00 5.220373232403355e+00 2.36167e-12 3.88409e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 1.869174616744062e+00 1.869174616716770e+00 2.72922e-11 2.94625e-10 2 -1.715467045336837e+00 -1.715467045345288e+00 8.45057e-12 5.04977e-10 3 -2.441327233181548e+00 -2.441327233211751e+00 3.02034e-11 1.12181e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 4.518312284616036e+00 4.518312284612756e+00 3.28004e-12 4.62137e-11 2 -9.422415959530916e-01 -9.422415959533090e-01 2.17382e-13 7.06444e-11 3 3.536729793408770e+00 3.536729793404356e+00 4.41425e-12 8.64251e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 6.276398020445199e+00 6.276398020445002e+00 1.97176e-13 5.44889e-11 2 -6.064449205026407e+00 -6.064449205050107e+00 2.37002e-11 2.50869e-10 3 1.112603535736476e+00 1.112603535619785e+00 1.16691e-10 1.58087e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -4.811059180501648e+00 -4.811059180529488e+00 2.78391e-11 6.32516e-11 2 4.619798620307366e+00 4.619798620328673e+00 2.13074e-11 9.05487e-10 * 3 -3.539457158465879e+00 -3.539457158519929e+00 5.40501e-11 3.18388e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 6.246942177671818e+00 6.246942177690190e+00 1.83720e-11 2.99023e-11 2 -1.613339704228590e+00 -1.613339704227748e+00 8.42659e-13 1.91472e-10 3 -2.437455104755558e+00 -2.437455104771249e+00 1.56914e-11 9.53952e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.981938537456360e+01 -1.981938537455682e+01 6.77502e-12 3.32594e-10 2 2.300843767343070e+01 2.300843767343313e+01 2.42650e-12 2.36213e-10 3 2.949203806271500e-01 2.949203806092480e-01 1.79020e-11 6.06448e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 3.533002954367402e+00 3.533002954356381e+00 1.10210e-11 2.93475e-10 2 3.097670328084988e+00 3.097670328089620e+00 4.63229e-12 2.43663e-11 3 -7.764828159412589e-01 -7.764828159494365e-01 8.17757e-12 8.17512e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 2.551425735220744e+00 2.551425735233223e+00 1.24785e-11 6.45159e-11 2 7.653646334775990e+00 7.653646334785139e+00 9.14913e-12 3.35558e-10 3 8.011447860211247e+00 8.011447860225985e+00 1.47384e-11 1.04070e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 6.714074346852085e+00 6.714074346861971e+00 9.88631e-12 8.82290e-11 2 -3.315088895161627e+00 -3.315088895174006e+00 1.23794e-11 2.09952e-11 3 3.670031123427164e+00 3.670031123413184e+00 1.39799e-11 7.15459e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -6.436509881773254e+00 -6.436509881885272e+00 1.12018e-10 1.75421e-10 2 -9.744046264906588e+00 -9.744046264929452e+00 2.28635e-11 1.09836e-10 3 1.200993789351122e+01 1.200993789351332e+01 2.09788e-12 1.07359e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 8.127575706312289e+00 8.127575706286569e+00 2.57199e-11 1.62103e-10 2 1.176223805770617e+01 1.176223805768837e+01 1.78080e-11 3.76684e-10 3 1.549070912309202e+01 1.549070912309453e+01 2.51354e-12 1.30031e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 -1.095253877473131e+00 -1.095253877539852e+00 6.67206e-11 1.08341e-10 2 -6.067830991862172e-01 -6.067830991752966e-01 1.09206e-11 4.86307e-11 3 -3.313735585387895e+00 -3.313735585388236e+00 3.40616e-13 7.62350e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 2.424054905017600e-01 2.424054905060536e-01 4.29365e-12 1.23800e-10 2 2.557778746283343e+00 2.557778746306774e+00 2.34310e-11 5.08891e-11 3 -7.115721647220947e+00 -7.115721647235628e+00 1.46816e-11 2.90168e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -1.425978590243322e+01 -1.425978590242484e+01 8.37730e-12 2.74056e-11 2 -1.031540217295995e+01 -1.031540217296989e+01 9.93161e-12 7.72875e-11 3 -4.675510887489057e+00 -4.675510887481647e+00 7.40918e-12 4.99671e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.140395376847426e+01 1.140395376845362e+01 2.06342e-11 1.98529e-10 2 5.826177250280197e+00 5.826177250265379e+00 1.48184e-11 2.70752e-11 3 -3.300857328747059e+00 -3.300857328724380e+00 2.26783e-11 1.56825e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 1.032530870347981e+01 1.032530870348013e+01 3.21521e-13 1.28132e-10 2 -2.289001347746731e+00 -2.289001347767500e+00 2.07687e-11 2.99876e-11 3 1.290130310799888e+01 1.290130310800160e+01 2.72138e-12 1.92717e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -2.733226837082785e+00 -2.733226837102886e+00 2.01013e-11 1.23115e-10 2 2.713954642192516e+00 2.713954642213616e+00 2.11005e-11 1.71973e-10 3 -8.076304694589634e-01 -8.076304694665944e-01 7.63101e-12 1.08646e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.851767901389509e+00 -1.851767901473683e+00 8.41738e-11 1.30477e-10 2 4.386736925399520e+00 4.386736925384827e+00 1.46931e-11 2.75595e-10 3 1.655372089286576e+01 1.655372089286854e+01 2.77467e-12 1.85192e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 -3.365425982095511e+00 -3.365425982111960e+00 1.64491e-11 7.13467e-06 * 2 -3.662284199269716e+00 -3.662284199273513e+00 3.79741e-12 1.52617e-10 3 6.579930574828001e-01 6.579930574393190e-01 4.34811e-11 1.74104e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 1.251534816576350e+01 1.251534816573801e+01 2.54872e-11 2.40734e-10 2 1.129062370609466e+01 1.129062370609456e+01 1.04805e-13 1.10417e-04 * 3 -6.690669850385389e+00 -6.690669850386855e+00 1.46549e-12 9.03402e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -4.130761941552885e-01 -4.130761941507508e-01 4.53770e-12 1.80758e-11 2 -5.535887922492963e+00 -5.535887922492479e+00 4.84057e-13 1.00236e-10 3 -6.028281631462553e+00 -6.028281631453552e+00 9.00080e-12 7.72094e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 -2.072650153236824e+00 -2.072650153227188e+00 9.63674e-12 2.04605e-11 2 -7.993542874226928e-01 -7.993542874210366e-01 1.65612e-12 6.88144e-11 3 3.426765610751378e+00 3.426765610752440e+00 1.06226e-12 5.86526e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.050503242436362e+01 -1.050503242439255e+01 2.89280e-11 2.90418e-10 2 -5.775221528302321e+00 -5.775221528297375e+00 4.94627e-12 1.33273e-10 3 -1.090043073167609e+01 -1.090043073169663e+01 2.05365e-11 1.04652e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -8.968597117226209e-01 -8.968597117190823e-01 3.53861e-12 1.92854e-11 2 -5.162354672455614e+00 -5.162354672452492e+00 3.12195e-12 4.51168e-11 3 -4.885389775094559e+00 -4.885389775117322e+00 2.27631e-11 5.14930e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 -6.707945222433696e+00 -6.707945222435288e+00 1.59162e-12 2.70148e-11 2 -8.296811919941232e+00 -8.296811919939483e+00 1.74971e-12 5.13616e-11 3 -2.531288154732727e+00 -2.531288154736476e+00 3.74945e-12 4.01243e-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 discontinuities. Maximum error obtained for particle = 10, direction = 3: |F_model - F_numer| error = ----------------------- = 1.04881e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.12459e-10 Machine precision = 2.22045e-16 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. Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 2.12459e-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.