!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Erhart_Albe_CSi__MO_903987585848_002 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 = 2.73904800415 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 4.656005012238175e+00 4.656005012238777e+00 6.02185e-13 2.84182e-11 2 2.245485965009747e+00 2.245485965011966e+00 2.21867e-12 4.62563e-11 3 4.843987465750883e+00 4.843987465751095e+00 2.11386e-13 1.19629e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -3.240984834649429e+00 -3.240984834654689e+00 5.26024e-12 7.57061e-11 2 1.868060163220392e+00 1.868060163222899e+00 2.50688e-12 1.02412e-10 3 -4.898656183222306e-02 -4.898656184160358e-02 9.38052e-12 1.30467e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 6.849838506532913e+00 6.849838506531500e+00 1.41309e-12 3.13731e-11 2 -6.267667733438659e+00 -6.267667733433395e+00 5.26335e-12 7.46869e-11 3 -7.231110696392887e+00 -7.231110696401704e+00 8.81695e-12 4.24203e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.683460474942704e+00 -3.683460474963192e+00 2.04872e-11 6.48099e-11 2 1.210404916371792e+01 1.210404916371622e+01 1.70353e-12 3.08855e-11 3 -6.047482396542861e+00 -6.047482396550130e+00 7.26885e-12 4.82894e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.925286498811287e+00 -1.925286498817884e+00 6.59739e-12 3.24649e-11 2 1.834328196488779e+00 1.834328196474436e+00 1.43434e-11 3.69729e-11 3 2.293878373380995e+00 2.293878373409541e+00 2.85456e-11 3.11022e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.355828259414548e+00 -1.355828259413799e+00 7.49623e-13 1.45697e-11 2 -4.001382642240374e+00 -4.001382642240636e+00 2.62013e-13 5.44098e-12 3 1.306964970857970e+00 1.306964970863510e+00 5.54001e-12 5.49989e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.667098110664047e+00 -1.667098110666773e+00 2.72560e-12 2.67935e-11 2 -6.181506345204285e+00 -6.181506345210391e+00 6.10534e-12 3.88347e-11 3 -1.257192103023369e+01 -1.257192103023602e+01 2.33236e-12 3.84155e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.637829118548815e+00 -2.637829118537041e+00 1.17737e-11 2.50377e-11 2 2.631332247765818e+00 2.631332247770765e+00 4.94760e-12 1.42122e-11 3 6.333157871672241e+00 6.333157871660406e+00 1.18350e-11 2.59812e-10 * ----------------------------------------------------------------------------------------------------- 9 C 1 -1.079354458916252e+00 -1.079354458925411e+00 9.15978e-12 2.87446e-11 2 -3.745731400833190e+00 -3.745731400837359e+00 4.16955e-12 2.84950e-11 3 3.046883388879160e+00 3.046883388883651e+00 4.49107e-12 1.86096e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.029410785873912e+00 -4.029410785869567e+00 4.34497e-12 1.97122e-11 2 8.804346408814184e-01 8.804346408817247e-01 3.06311e-13 1.70919e-11 3 -2.429547796433498e+00 -2.429547796429604e+00 3.89466e-12 1.69535e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -6.608884219732565e-01 -6.608884219754853e-01 2.22877e-12 2.66979e-11 2 -1.377065134038647e+01 -1.377065134039235e+01 5.87796e-12 6.38245e-11 3 -6.283995316604382e+00 -6.283995316601128e+00 3.25340e-12 5.23164e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.540049415309783e+00 -1.540049415316338e+00 6.55564e-12 2.36333e-11 2 1.772488456988393e+00 1.772488456991091e+00 2.69806e-12 2.02827e-11 3 -5.216682536718150e-01 -5.216682536720817e-01 2.66676e-13 1.58944e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -4.240427326388855e+00 -4.240427326392562e+00 3.70726e-12 3.22862e-11 2 -3.118823690808170e+00 -3.118823690809036e+00 8.65974e-13 1.40310e-11 3 -1.153084433503166e+01 -1.153084433503152e+01 1.31450e-13 2.99654e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 2.708129386576240e+00 2.708129386575896e+00 3.44169e-13 4.20264e-11 2 2.873778049027800e-01 2.873778049042741e-01 1.49414e-12 9.30545e-12 3 -2.292413274335284e+00 -2.292413274336413e+00 1.12932e-12 9.98401e-12 ----------------------------------------------------------------------------------------------------- 15 C 1 1.053410688532446e+01 1.053410688531757e+01 6.89582e-12 1.75042e-11 2 2.167899322623453e+00 2.167899322624116e+00 6.63025e-13 1.10430e-10 3 4.940953644486719e+00 4.940953644487819e+00 1.10045e-12 1.02434e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.824188989014704e-01 -5.824188989020975e-01 6.27165e-13 4.59667e-11 2 7.358126375216512e+00 7.358126375216211e+00 3.00204e-13 6.62910e-11 3 4.216431049325785e+00 4.216431049321363e+00 4.42224e-12 3.45928e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -6.300009085683175e+00 -6.300009085684587e+00 1.41132e-12 4.79616e-12 2 -2.916541750196918e+00 -2.916541750198250e+00 1.33227e-12 1.75975e-11 3 -1.840539132435007e+00 -1.840539132442489e+00 7.48157e-12 7.21809e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 2.499477892977831e+00 2.499477892973325e+00 4.50573e-12 3.11307e-11 2 7.084495235680436e+00 7.084495235670113e+00 1.03233e-11 1.49472e-11 3 -4.095641844707509e+00 -4.095641844696685e+00 1.08242e-11 2.29265e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.014959301854776e+01 1.014959301853486e+01 1.29035e-11 4.88871e-11 2 -2.867380306354528e+00 -2.867380306352426e+00 2.10187e-12 8.69260e-12 3 3.205196988502297e+00 3.205196988502674e+00 3.77032e-13 1.96888e-10 * ----------------------------------------------------------------------------------------------------- 20 C 1 -7.208305867997425e-01 -7.208305867978898e-01 1.85274e-12 1.48481e-11 2 9.032337740050557e-01 9.032337740035026e-01 1.55309e-12 1.22846e-12 3 1.138470365916466e+00 1.138470365917634e+00 1.16751e-12 6.20770e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 -6.326196110720776e+00 -6.326196110719114e+00 1.66178e-12 1.08039e-10 2 -3.571465329837297e+00 -3.571465329836184e+00 1.11289e-12 2.39724e-11 3 6.759809632124758e+00 6.759809632113105e+00 1.16529e-11 5.54721e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 3.419649453252032e+00 3.419649453252491e+00 4.59188e-13 4.94449e-11 2 4.422919077742670e+00 4.422919077745346e+00 2.67608e-12 1.72635e-11 3 9.307033364610959e+00 9.307033364615361e+00 4.40181e-12 2.70362e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.822378908274271e+00 -2.822378908271857e+00 2.41451e-12 5.70690e-11 2 2.547541635220921e+00 2.547541635218050e+00 2.87104e-12 1.88991e-11 3 -2.454115272543845e+00 -2.454115272543236e+00 6.08402e-13 1.48810e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 6.927772956424082e+00 6.927772956429888e+00 5.80602e-12 1.14826e-10 2 5.095731498162479e+00 5.095731498168802e+00 6.32294e-12 1.44373e-11 3 -1.530458042863101e+00 -1.530458042868013e+00 4.91229e-12 1.79908e-10 * ----------------------------------------------------------------------------------------------------- 25 C 1 -2.445581146191018e-01 -2.445581146252517e-01 6.14986e-12 9.39147e-11 2 -4.068959111734009e+00 -4.068959111750194e+00 1.61844e-11 1.30655e-10 3 -2.110905230690800e+00 -2.110905230694847e+00 4.04654e-12 3.28670e-12 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.025267968272110e+00 -1.025267968268488e+00 3.62133e-12 4.71994e-11 2 4.717767538145844e+00 4.717767538151000e+00 5.15676e-12 2.37206e-11 3 2.231962648427305e+00 2.231962648424629e+00 2.67564e-12 7.00728e-12 ----------------------------------------------------------------------------------------------------- 27 C 1 5.836290914798157e+00 5.836290914807003e+00 8.84626e-12 2.99440e-11 2 -4.810953027191503e+00 -4.810953027187139e+00 4.36362e-12 5.62661e-12 3 2.803414068154852e+00 2.803414068142952e+00 1.19003e-11 2.48805e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.394668411310890e+00 -7.394668411318852e+00 7.96163e-12 1.34293e-11 2 5.593176157532961e+00 5.593176157535926e+00 2.96474e-12 1.28457e-11 3 3.012358118745880e-01 3.012358118705776e-01 4.01046e-12 1.44108e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 7.590992670061323e-01 7.590992670020574e-01 4.07485e-12 2.60025e-11 2 -4.767615581535095e+00 -4.767615581532665e+00 2.43006e-12 1.23404e-11 3 -1.215616216227432e+00 -1.215616216226576e+00 8.55760e-13 2.92424e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 1.996115199278612e+00 1.996115199282327e+00 3.71414e-12 1.23647e-10 2 2.719437586411187e-01 2.719437586400835e-01 1.03528e-12 7.00763e-11 3 -1.247642291241536e+00 -1.247642291244347e+00 2.81086e-12 6.73817e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.610524063993370e+00 -5.610524063984399e+00 8.97149e-12 3.01092e-12 2 -5.323819875286915e+00 -5.323819875299860e+00 1.29452e-11 2.88551e-11 3 5.451881919994532e+00 5.451881919995115e+00 5.82645e-13 1.67031e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 7.513913611114109e-01 7.513913611295021e-01 1.80912e-11 2.13419e-11 2 1.626107123100727e+00 1.626107123100934e+00 2.06946e-13 1.68107e-10 * 3 5.271626127828013e+00 5.271626127826067e+00 1.94511e-12 7.47722e-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 = 2, direction = 3: |F_model - F_numer| error = --------------------------------- = 1.91492e-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 = 3.84633159637 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 5.120228101542434e+00 5.120228101541583e+00 8.50875e-13 8.63309e-12 2 3.393276701829114e+00 3.393276701828386e+00 7.27862e-13 6.58984e-12 3 7.166916026352627e+00 7.166916026352144e+00 4.83169e-13 3.95666e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.319794633861930e+00 -4.319794633859185e+00 2.74536e-12 1.89164e-11 2 6.778729509997690e-01 6.778729509972088e-01 2.56017e-12 1.56078e-11 3 1.210930928180556e+00 1.210930928170852e+00 9.70424e-12 1.49305e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.311238562823195e+00 -3.311238562844084e+00 2.08891e-11 3.35985e-11 2 1.767538326347312e+00 1.767538326348184e+00 8.71969e-13 5.00395e-11 3 -3.372786151738972e+00 -3.372786151741418e+00 2.44604e-12 5.52682e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 3.253108951815377e+00 3.253108951818077e+00 2.70006e-12 3.80043e-11 2 9.138613240048199e-01 9.138613240186749e-01 1.38550e-11 5.78380e-11 3 3.277580016496260e+00 3.277580016502563e+00 6.30296e-12 3.07629e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 5.138793606882930e+00 5.138793606882892e+00 3.81917e-14 5.77582e-12 2 3.987408671932647e+00 3.987408671934326e+00 1.67910e-12 1.12221e-12 3 6.768210195901148e+00 6.768210195899513e+00 1.63425e-12 1.95941e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -4.097705283998379e+00 -4.097705284011208e+00 1.28288e-11 1.01457e-11 2 -2.640829895487648e+00 -2.640829895487633e+00 1.42109e-14 6.14309e-12 3 3.615053971407729e+00 3.615053971407383e+00 3.46390e-13 4.42304e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -2.577972054465119e+00 -2.577972054462230e+00 2.88880e-12 4.81748e-12 2 3.485233497210941e+00 3.485233497213568e+00 2.62679e-12 1.54332e-10 3 -2.290945757187005e+00 -2.290945757190385e+00 3.37996e-12 1.40692e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.382287037615340e+00 -1.382287037624536e+00 9.19553e-12 3.74137e-10 * 2 1.210098497532958e-02 1.210098497396014e-02 1.36944e-12 1.12132e-10 3 -4.549195058561045e-01 -4.549195058766837e-01 2.05792e-11 2.32327e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 5.307644572263404e+00 5.307644572263992e+00 5.87974e-13 2.93747e-11 2 1.621423263354513e+00 1.621423263359147e+00 4.63407e-12 1.13285e-11 3 3.242218557069962e+00 3.242218557062849e+00 7.11387e-12 1.48699e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.758917851459133e+00 -3.758917851460889e+00 1.75548e-12 5.53455e-11 2 -5.561909586165673e+00 -5.561909586163896e+00 1.77725e-12 5.02762e-11 3 6.201846955656680e+00 6.201846955661101e+00 4.42135e-12 3.06768e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.260728464901294e+00 -5.260728464889486e+00 1.18074e-11 8.45892e-11 2 2.731999226748954e+00 2.731999226740443e+00 8.51141e-12 5.03322e-11 3 -2.899232832979736e+00 -2.899232832992463e+00 1.27267e-11 1.44447e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 7.087336623516578e+00 7.087336623512270e+00 4.30767e-12 1.45635e-11 2 -6.327038939233573e+00 -6.327038939240706e+00 7.13296e-12 1.70015e-11 3 -4.486303028589572e+00 -4.486303028587254e+00 2.31815e-12 4.75575e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -7.897728093148447e+00 -7.897728093151449e+00 3.00204e-12 1.28259e-10 2 4.720610143740531e-01 4.720610143807533e-01 6.70020e-12 2.02963e-11 3 -3.424633101104232e+00 -3.424633101103049e+00 1.18261e-12 6.18128e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.100575504364668e+00 -1.100575504365616e+00 9.47686e-13 1.31923e-11 2 -1.166142504014309e-01 -1.166142504028903e-01 1.45936e-12 9.98646e-13 3 1.177044965756930e+00 1.177044965757035e+00 1.05027e-13 9.82570e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.408514972671296e+00 5.408514972670215e+00 1.08091e-12 1.14878e-10 2 -2.919163684706272e+00 -2.919163684694225e+00 1.20468e-11 4.31659e-11 3 4.556462195280337e+00 4.556462195296080e+00 1.57430e-11 2.27365e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -2.991247545011930e+00 -2.991247545015432e+00 3.50253e-12 5.17616e-10 * 2 3.082685736524030e+00 3.082685736524128e+00 9.85878e-14 1.30114e-11 3 3.292431975413629e-01 3.292431975224152e-01 1.89478e-11 3.68857e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 6.715821560734349e+00 6.715821560737486e+00 3.13705e-12 2.08411e-11 2 6.372852553876662e+00 6.372852553875889e+00 7.72715e-13 7.34985e-11 3 3.718307920573274e-01 3.718307920584187e-01 1.09124e-12 4.78680e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -3.610347070168900e+00 -3.610347070170770e+00 1.87006e-12 2.91092e-11 2 -6.141735258066732e-01 -6.141735258201905e-01 1.35173e-11 4.97195e-11 3 1.010963483356917e+00 1.010963483338369e+00 1.85474e-11 1.12822e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.258449680064497e+00 -4.258449680059357e+00 5.13989e-12 4.93205e-12 2 -2.157374250535053e+00 -2.157374250534224e+00 8.28670e-13 4.65459e-11 3 -2.812043846040755e+00 -2.812043846036748e+00 4.00702e-12 1.12043e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.486193056104767e+00 3.486193056101228e+00 3.53895e-12 1.28098e-11 2 2.785849442523422e+00 2.785849442524471e+00 1.04894e-12 1.65223e-11 3 -5.687845584510588e+00 -5.687845584509128e+00 1.45928e-12 3.12070e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.347818524356927e+00 1.347818524372226e+00 1.52984e-11 1.01033e-10 2 2.490183843477709e+00 2.490183843454894e+00 2.28155e-11 7.61333e-11 3 1.932083839443234e+00 1.932083839445740e+00 2.50644e-12 7.50999e-12 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.563371817459821e-01 1.563371817461225e-01 1.40471e-13 2.74564e-12 2 -6.574787662548992e+00 -6.574787662544738e+00 4.25437e-12 6.38662e-11 3 3.307339909610016e+00 3.307339909623383e+00 1.33666e-11 1.51701e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.588390172335107e+00 -2.588390172335560e+00 4.53415e-13 1.87943e-11 2 5.427053792619379e+00 5.427053792620661e+00 1.28253e-12 2.57785e-11 3 -6.808057334750174e+00 -6.808057334749488e+00 6.85674e-13 1.22151e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 8.419500917244584e-01 8.419500917250594e-01 6.00964e-13 4.31706e-11 2 4.634218407549263e+00 4.634218407549223e+00 3.99680e-14 3.42295e-11 3 -2.354033241436861e+00 -2.354033241466261e+00 2.94000e-11 3.62692e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.505350506099174e+00 4.505350506136358e+00 3.71836e-11 6.54182e-09 * 2 -5.803948460371596e+00 -5.803948460369828e+00 1.76836e-12 2.52101e-11 3 -4.043420370547820e+00 -4.043420370544456e+00 3.36442e-12 1.58078e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -3.629061818574740e+00 -3.629061818567519e+00 7.22089e-12 3.46341e-11 2 1.749303996419028e+00 1.749303996423222e+00 4.19420e-12 1.26070e-10 3 1.391800484262318e+00 1.391800484259130e+00 3.18812e-12 1.46423e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -4.391848132897591e+00 -4.391848132880979e+00 1.66125e-11 1.90555e-10 2 -2.226603210225103e+00 -2.226603210224060e+00 1.04228e-12 4.58806e-11 3 -4.100677594806298e+00 -4.100677594810207e+00 3.90976e-12 2.37810e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.522070175995093e+00 5.522070175994833e+00 2.60236e-13 6.26654e-11 2 -3.989027505616664e+00 -3.989027505618676e+00 2.01261e-12 1.70837e-11 3 -1.731960298193591e+00 -1.731960298189728e+00 3.86335e-12 3.09910e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 3.235136459327066e+00 3.235136459322990e+00 4.07585e-12 7.56994e-11 2 -2.626983972775188e+00 -2.626983972763903e+00 1.12852e-11 1.62314e-10 3 2.507994264235599e-01 2.507994264382613e-01 1.47014e-11 9.43647e-10 * ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.101502813242203e-01 -8.101502813251662e-01 9.45910e-13 3.86341e-11 2 -2.096098428771267e+00 -2.096098428770454e+00 8.13571e-13 1.42548e-10 3 -1.165424914182895e+00 -1.165424914194611e+00 1.17162e-11 9.95986e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -4.228757944919061e+00 -4.228757944918322e+00 7.38964e-13 1.17873e-10 2 -4.392869421563263e-01 -4.392869421604139e-01 4.08756e-12 2.01369e-10 3 -1.300545528140778e+00 -1.300545528172685e+00 3.19074e-11 1.34126e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.088895747153706e+00 3.088895747140573e+00 1.31335e-11 2.75557e-12 2 -1.511083419965492e+00 -1.511083419978257e+00 1.27649e-11 2.18371e-10 3 1.122504145268416e+00 1.122504145272780e+00 4.36406e-12 1.28229e-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 = 2: |F_model - F_numer| error = --------------------------------- = 1.13168e-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 = 3.23755686579 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -4.955141080666041e-01 -4.955141076367170e-01 4.29887e-10 6.30566e-10 2 3.306946657247029e-01 3.306946695963514e-01 3.87165e-09 1.28125e-08 3 -2.355510603702048e+00 -2.355510605622329e+00 1.92028e-09 7.35233e-09 ----------------------------------------------------------------------------------------------------- 2 C 1 -5.008145582073300e+00 -5.008145582635079e+00 5.61779e-10 1.02366e-09 2 3.132263896749791e+00 3.132263897093004e+00 3.43213e-10 4.42435e-09 3 -1.768347673791820e+00 -1.768347673354260e+00 4.37560e-10 4.95213e-09 ----------------------------------------------------------------------------------------------------- 3 Si 1 -6.347305421543442e+00 -6.347305421325401e+00 2.18042e-10 1.68795e-08 2 -2.201354831962496e+01 -2.201354832246560e+01 2.84064e-09 5.72336e-09 3 -2.144448135772110e+01 -2.144448135734275e+01 3.78350e-10 5.60055e-09 ----------------------------------------------------------------------------------------------------- 4 C 1 -2.921650268611003e+00 -2.921650268616563e+00 5.56000e-12 1.33387e-09 2 4.181145874951945e+00 4.181145877513089e+00 2.56114e-09 9.67460e-09 3 -1.008959026391546e+00 -1.008959027244709e+00 8.53163e-10 1.65252e-07 * ----------------------------------------------------------------------------------------------------- 5 C 1 -2.304200735021600e+00 -2.304200735193326e+00 1.71726e-10 8.87770e-09 2 -7.871837981840258e+00 -7.871837982192335e+00 3.52077e-10 6.01394e-09 3 -4.511507877760039e+00 -4.511507877051298e+00 7.08741e-10 2.64384e-08 ----------------------------------------------------------------------------------------------------- 6 Si 1 7.489760681145792e+00 7.489760681227827e+00 8.20348e-11 9.35589e-09 2 4.923075522198176e+00 4.923075521460528e+00 7.37648e-10 2.97590e-10 3 -5.338644442845410e+00 -5.338644443523359e+00 6.77949e-10 9.97070e-09 ----------------------------------------------------------------------------------------------------- 7 Si 1 7.170587484016934e+00 7.170587483440684e+00 5.76250e-10 4.02449e-09 2 -6.213075831512344e+00 -6.213075832495750e+00 9.83406e-10 5.40207e-09 3 -7.028001076437687e+00 -7.028001071488342e+00 4.94934e-09 1.09249e-08 ----------------------------------------------------------------------------------------------------- 8 C 1 -1.195262545254455e+01 -1.195262545392524e+01 1.38069e-09 7.72696e-09 2 1.145228821567685e+01 1.145228821556897e+01 1.07883e-10 6.23929e-09 3 -6.044903445399445e+00 -6.044903445245644e+00 1.53801e-10 7.59328e-09 ----------------------------------------------------------------------------------------------------- 9 Si 1 -7.593377166307860e-01 -7.593377171556117e-01 5.24826e-10 1.31851e-08 2 -7.540451420677152e+00 -7.540451420874041e+00 1.96889e-10 1.48939e-09 3 2.772540842656516e+00 2.772540843015332e+00 3.58816e-10 1.56341e-08 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.363423877002049e+00 1.363423875602280e+00 1.39977e-09 1.90839e-08 2 5.558570264116801e+00 5.558570264020946e+00 9.58549e-11 4.98434e-08 * 3 -1.282940210454734e+00 -1.282940211456721e+00 1.00199e-09 4.31266e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 6.672257477317918e-01 6.672257478697217e-01 1.37930e-10 6.39984e-09 2 -7.116989773018045e+00 -7.116989769886673e+00 3.13137e-09 2.16474e-09 3 2.114593489658090e+00 2.114593489456515e+00 2.01575e-10 4.23460e-09 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.250088911414259e+00 -1.250088909954582e+00 1.45968e-09 3.95086e-09 2 2.457551282839919e+00 2.457551278689738e+00 4.15018e-09 2.34438e-08 3 -1.723568336564033e-01 -1.723568340824051e-01 4.26002e-10 1.77508e-09 ----------------------------------------------------------------------------------------------------- 13 C 1 4.029833028903135e+00 4.029833030165785e+00 1.26265e-09 9.92189e-10 2 -1.115986706163044e+01 -1.115986706349920e+01 1.86876e-09 4.84170e-09 3 -1.051721850811894e+01 -1.051721850836768e+01 2.48738e-10 2.09985e-08 ----------------------------------------------------------------------------------------------------- 14 Si 1 -2.792291483318724e+00 -2.792291483468308e+00 1.49583e-10 4.55890e-09 2 2.038406794016135e+00 2.038406795044264e+00 1.02813e-09 7.23152e-09 3 2.080727785906002e-01 2.080727782469100e-01 3.43690e-10 2.53406e-09 ----------------------------------------------------------------------------------------------------- 15 Si 1 8.767927262572904e+00 8.767927263055832e+00 4.82927e-10 6.59201e-09 2 -8.178901532454933e+00 -8.178901531876516e+00 5.78417e-10 8.26558e-09 3 -2.673515987492395e+00 -2.673515987520453e+00 2.80584e-11 9.28411e-09 ----------------------------------------------------------------------------------------------------- 16 C 1 1.911559880711119e+00 1.911559880207881e+00 5.03239e-10 2.25093e-09 2 1.231176858706143e+01 1.231176858792150e+01 8.60062e-10 7.55985e-09 3 6.555433058778658e+00 6.555433057864197e+00 9.14461e-10 8.26319e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 -2.687999941299388e+00 -2.687999942665664e+00 1.36628e-09 8.25203e-08 * 2 -3.943660996923284e+00 -3.943660996054089e+00 8.69195e-10 1.67012e-09 3 -1.882328418494393e-01 -1.882328400038840e-01 1.84556e-09 4.20026e-09 ----------------------------------------------------------------------------------------------------- 18 Si 1 -8.150949419706132e+00 -8.150949421617579e+00 1.91145e-09 1.86789e-08 2 2.478853820104449e+01 2.478853820054730e+01 4.97195e-10 9.05420e-09 3 1.835892557335786e+01 1.835892557176889e+01 1.58897e-09 3.65428e-08 * ----------------------------------------------------------------------------------------------------- 19 C 1 3.847984197215504e-01 3.847984198902922e-01 1.68742e-10 7.88824e-10 2 1.616036722257860e+00 1.616036722490552e+00 2.32692e-10 5.52944e-10 3 -2.332301361577950e+00 -2.332301361775150e+00 1.97200e-10 2.09955e-09 ----------------------------------------------------------------------------------------------------- 20 C 1 -5.336385056665869e-01 -5.336385057811474e-01 1.14560e-10 2.68782e-09 2 7.446591134228630e+00 7.446591133723436e+00 5.05194e-10 4.96343e-08 * 3 -6.871766782183844e+00 -6.871766783535778e+00 1.35193e-09 1.62255e-09 ----------------------------------------------------------------------------------------------------- 21 Si 1 5.201826712946190e+00 5.201826713106603e+00 1.60413e-10 6.22298e-09 2 -1.155617302766621e+01 -1.155617302782761e+01 1.61400e-10 2.05084e-09 3 1.921553844562623e+01 1.921553844489036e+01 7.35866e-10 3.30758e-09 ----------------------------------------------------------------------------------------------------- 22 C 1 1.424176667845539e+01 1.424176668207982e+01 3.62443e-09 1.29026e-08 2 5.173575213699051e+00 5.173575213689709e+00 9.34186e-12 1.14483e-08 3 8.349044712021691e+00 8.349044709945684e+00 2.07601e-09 2.75900e-09 ----------------------------------------------------------------------------------------------------- 23 Si 1 -5.083289370793251e-01 -5.083289368983080e-01 1.81017e-10 2.61301e-09 2 3.422858055222792e+00 3.422858055851539e+00 6.28747e-10 9.37172e-10 3 2.684021198034100e-01 2.684021195322426e-01 2.71167e-10 4.32438e-09 ----------------------------------------------------------------------------------------------------- 24 C 1 5.821126681883078e+00 5.821126681819026e+00 6.40528e-11 8.30779e-10 2 6.947797931479269e-01 6.947797933351443e-01 1.87217e-10 2.85664e-09 3 7.159900029460901e-01 7.159900032445720e-01 2.98482e-10 4.76545e-09 ----------------------------------------------------------------------------------------------------- 25 C 1 1.689171508708375e+00 1.689171508589542e+00 1.18833e-10 1.96753e-09 2 -6.145532159294662e+00 -6.145532158636972e+00 6.57690e-10 1.57908e-09 3 6.881227912599741e+00 6.881227912407364e+00 1.92377e-10 6.04228e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -1.827913164900041e+01 -1.827913164921766e+01 2.17245e-10 9.99886e-10 2 5.102549572677839e+00 5.102549574989935e+00 2.31210e-09 3.30828e-08 3 -2.373131469180814e+00 -2.373131468905927e+00 2.74887e-10 8.59948e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 -9.232745919954222e-01 -9.232745918346719e-01 1.60750e-10 7.50467e-10 2 -2.093501784157580e+00 -2.093501784239531e+00 8.19509e-11 2.60660e-09 3 1.810175926063347e+00 1.810175926336042e+00 2.72695e-10 1.87430e-09 ----------------------------------------------------------------------------------------------------- 28 C 1 4.413650712889059e+00 4.413650712724338e+00 1.64721e-10 8.30275e-10 2 -7.666513752471735e-02 -7.666513786341475e-02 3.38697e-10 4.27086e-10 3 -3.429191270161012e+00 -3.429191270465654e+00 3.04642e-10 9.99505e-08 * ----------------------------------------------------------------------------------------------------- 29 Si 1 -7.143751639245134e+00 -7.143751639233143e+00 1.19913e-11 1.66633e-08 2 -6.206029979580893e+00 -6.206029981040980e+00 1.46009e-09 9.07466e-08 * 3 -6.548131170730647e-01 -6.548131166705434e-01 4.02521e-10 3.37950e-08 ----------------------------------------------------------------------------------------------------- 30 Si 1 6.067147021817379e+00 6.067147022002350e+00 1.84971e-10 6.50138e-09 2 5.834452728969989e+00 5.834452728910371e+00 5.96181e-11 1.70684e-09 3 1.813837537998961e+00 1.813837537976249e+00 2.27114e-11 8.65602e-08 * ----------------------------------------------------------------------------------------------------- 31 Si 1 -3.554572481422526e+00 -3.554572481082913e+00 3.39613e-10 8.79049e-10 2 -4.440458759530963e+00 -4.440458759340793e+00 1.90170e-10 1.61736e-09 3 1.264769575860923e+00 1.264769575966361e+00 1.05438e-10 1.03144e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 6.393001146134462e+00 6.393001145928937e+00 2.05524e-10 1.32029e-09 2 4.091547240852131e+00 4.091547240480339e+00 3.71792e-10 3.12903e-10 3 9.667271909835581e+00 9.667271909679615e+00 1.55966e-10 1.05947e-09 ----------------------------------------------------------------------------------------------------- * 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 = 1, direction = 2: |F_model - F_numer| error = --------------------------------- = 1.17076e-08 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.17076e-08 Machine precision = 2.22045e-16 Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.17076e-08 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.