!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_1994_SiC__MO_794973922560_000 Supported species : C Si random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = C | a0 = 2.71713924407959 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 1.010205099847442e+01 1.010205099849123e+01 1.68061e-11 4.99885e-11 2 3.804973144845042e+00 3.804973144844162e+00 8.79741e-13 9.59721e-12 3 6.954364253046006e+00 6.954364253050439e+00 4.43290e-12 6.00195e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -4.690225704615774e+00 -4.690225704613872e+00 1.90159e-12 1.68772e-11 2 1.522616806165802e-01 1.522616806171068e-01 5.26579e-13 2.67059e-11 3 7.110162402203269e-01 7.110162402286420e-01 8.31502e-12 9.02750e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.770750853931500e+00 -2.770750853929087e+00 2.41318e-12 2.77480e-11 2 -2.286546329567458e+00 -2.286546329558181e+00 9.27702e-12 1.24394e-11 3 -9.024097506850270e+00 -9.024097506846767e+00 3.50298e-12 6.96545e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 4.098662700779443e+00 4.098662700776908e+00 2.53575e-12 4.03215e-11 2 8.461733628140433e+00 8.461733628141715e+00 1.28253e-12 3.40563e-11 3 -9.089578739894335e-01 -9.089578739949910e-01 5.55744e-12 1.42737e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 8.759564539675063e-01 8.759564539683645e-01 8.58202e-13 1.20134e-11 2 -2.430669167197923e-01 -2.430669167156289e-01 4.16336e-12 1.43713e-11 3 4.567359902571570e+00 4.567359902576245e+00 4.67537e-12 4.48892e-10 * ----------------------------------------------------------------------------------------------------- 6 C 1 -9.339662467270513e-01 -9.339662467273050e-01 2.53686e-13 3.93857e-11 2 -5.261611031846011e+00 -5.261611031845430e+00 5.81757e-13 4.73870e-11 3 8.316754782326429e+00 8.316754782322935e+00 3.49409e-12 3.61187e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 2.307435333534955e-01 2.307435333602578e-01 6.76229e-12 1.59407e-11 2 -3.992995214351416e+00 -3.992995214352847e+00 1.43086e-12 1.12133e-11 3 -2.110905871921353e+01 -2.110905871921323e+01 3.01981e-13 2.46736e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -6.655264368268843e+00 -6.655264368274326e+00 5.48273e-12 7.07869e-11 2 -4.625027651027085e-01 -4.625027651062669e-01 3.55832e-12 3.15742e-11 3 -8.793394366667743e-01 -8.793394366799098e-01 1.31355e-11 8.39944e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 3.503782772868122e-01 3.503782772921996e-01 5.38736e-12 4.39802e-11 2 -6.746939689277785e+00 -6.746939689277346e+00 4.39648e-13 3.68257e-11 3 2.497357301002711e+00 2.497357300999770e+00 2.94165e-12 1.42206e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -2.887327371932726e+00 -2.887327371937112e+00 4.38627e-12 5.60565e-11 2 2.551501622993965e+00 2.551501623000453e+00 6.48814e-12 4.12834e-11 3 -4.619026132390064e+00 -4.619026132391162e+00 1.09779e-12 2.57359e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -1.242848086695854e+01 -1.242848086695113e+01 7.41274e-12 1.79298e-10 2 -1.296835776212854e+01 -1.296835776212141e+01 7.13385e-12 1.10958e-10 3 3.704066558571027e+00 3.704066558578994e+00 7.96740e-12 6.25295e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -3.817472978751308e+00 -3.817472978760474e+00 9.16645e-12 6.88343e-11 2 -4.048829076388150e-01 -4.048829076388568e-01 4.18554e-14 8.04021e-11 3 9.650458587472427e+00 9.650458587469437e+00 2.98961e-12 2.74447e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -5.557568757732905e+00 -5.557568757731382e+00 1.52234e-12 1.70760e-10 2 -5.463676037393026e+00 -5.463676037399835e+00 6.80878e-12 5.33982e-11 3 -1.583678960487943e+01 -1.583678960488438e+01 4.95071e-12 6.62830e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 6.020772354399270e+00 6.020772354406595e+00 7.32481e-12 3.07674e-11 2 2.573205815413756e+00 2.573205815411825e+00 1.93090e-12 9.11848e-12 3 -5.236558108591337e+00 -5.236558108593656e+00 2.31903e-12 4.42615e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 1.258266862636329e+01 1.258266862634246e+01 2.08331e-11 1.62006e-10 2 4.247557947023321e+00 4.247557947023490e+00 1.69642e-13 3.86631e-10 * 3 1.463380275137025e+01 1.463380275138142e+01 1.11786e-11 1.59122e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -2.125353237359176e+00 -2.125353237354741e+00 4.43512e-12 2.18546e-10 2 1.061966372934406e+01 1.061966372934799e+01 3.92397e-12 4.31690e-11 3 9.164890361395230e+00 9.164890361389277e+00 5.95257e-12 4.49347e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -3.415002998861669e+00 -3.415002998871980e+00 1.03113e-11 1.53295e-11 2 1.115829542845576e-02 1.115829543230656e-02 3.85080e-12 3.02804e-11 3 6.960222987769470e-01 6.960222987773569e-01 4.09894e-13 2.02923e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 6.916971137392878e+00 6.916971137393690e+00 8.11795e-13 9.30003e-11 2 1.295700559538310e+00 1.295700559543689e+00 5.37836e-12 7.93254e-11 3 -6.169199135135409e+00 -6.169199135141843e+00 6.43396e-12 2.24578e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 5.339469467753513e+00 5.339469467754253e+00 7.40741e-13 9.62403e-11 2 7.624472116533826e+00 7.624472116545899e+00 1.20730e-11 1.52390e-10 3 3.417266770945299e+00 3.417266770942124e+00 3.17479e-12 1.18288e-09 * ----------------------------------------------------------------------------------------------------- 20 C 1 1.104989961832770e+00 1.104989961831797e+00 9.72555e-13 1.16687e-11 2 -2.899287965967368e+00 -2.899287965967781e+00 4.12115e-13 3.85922e-11 3 -8.467858917350101e-01 -8.467858917139454e-01 2.10647e-11 3.07993e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -7.280732003575125e+00 -7.280732003573977e+00 1.14753e-12 1.41398e-11 2 2.668502221812970e+00 2.668502221803045e+00 9.92495e-12 2.63727e-11 3 1.448423933339596e+01 1.448423933339258e+01 3.37685e-12 1.92895e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 6.300501280978314e+00 6.300501280971335e+00 6.97931e-12 4.06439e-11 2 4.831634446728256e+00 4.831634446733769e+00 5.51292e-12 7.73976e-11 3 1.226916558903446e+01 1.226916558903697e+01 2.51710e-12 3.76728e-10 * ----------------------------------------------------------------------------------------------------- 23 C 1 -4.214012170503191e+00 -4.214012170502719e+00 4.72511e-13 6.54756e-11 2 4.155241794971403e+00 4.155241794974239e+00 2.83595e-12 4.88853e-12 3 -7.038961927609524e+00 -7.038961927620071e+00 1.05471e-11 2.05009e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 6.575280995986209e-01 6.575280995981916e-01 4.29323e-13 5.36634e-11 2 -9.324203972332977e+00 -9.324203972339456e+00 6.47837e-12 6.34426e-11 3 -8.153189105500523e+00 -8.153189105508009e+00 7.48557e-12 9.98490e-12 ----------------------------------------------------------------------------------------------------- 25 C 1 6.209089949866758e+00 6.209089949866364e+00 3.94351e-13 2.99964e-11 2 7.995911273230554e+00 7.995911273229435e+00 1.11910e-12 6.69145e-11 3 -1.103265919478235e+01 -1.103265919478468e+01 2.32880e-12 1.14037e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 -2.555145094783450e+00 -2.555145094786182e+00 2.73204e-12 3.89062e-11 2 3.520461003093426e+00 3.520461003096829e+00 3.40350e-12 2.24616e-11 3 -4.704901791242015e+00 -4.704901791247257e+00 5.24292e-12 1.30830e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.213735798304036e-01 -4.213735798278428e-01 2.56084e-12 8.78781e-11 2 -9.470619060849454e+00 -9.470619060851519e+00 2.06413e-12 4.11688e-11 3 4.219529285556013e+00 4.219529285568053e+00 1.20401e-11 3.46780e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -8.907502661208470e+00 -8.907502661186282e+00 2.21885e-11 1.13621e-10 2 1.371459644998213e+00 1.371459644998354e+00 1.41664e-13 6.23857e-12 3 -2.658501196657991e+00 -2.658501196654214e+00 3.77698e-12 4.07967e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 1.124850998163929e+00 1.124850998144111e+00 1.98179e-11 1.99778e-11 2 -4.678099411552286e+00 -4.678099411579340e+00 2.70539e-11 5.09096e-05 * 3 3.014266102550348e+00 3.014266102547477e+00 2.87059e-12 3.21427e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 2.272864962550972e+00 2.272864962553720e+00 2.74847e-12 7.59139e-11 2 -3.221919860426425e+00 -3.221919860424947e+00 1.47793e-12 1.14015e-11 3 -4.988457295407768e+00 -4.988457295397801e+00 9.96714e-12 1.00476e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.463256458504922e+00 -2.463256458523198e+00 1.82756e-11 1.29281e-10 2 -2.113902931455585e+00 -2.113902931454827e+00 7.58504e-13 2.42428e-11 3 1.635034659466535e-01 1.635034659547152e-01 8.06175e-12 1.43516e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 6.935936550783057e+00 6.935936550781521e+00 1.53655e-12 1.94822e-11 2 3.653172931897090e+00 3.653172931901466e+00 4.37606e-12 6.85794e-11 3 4.742419336469799e+00 4.742419336472294e+00 2.49578e-12 1.55668e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 17, direction = 2: |F_model - F_numer| error = ----------------------- = 3.45106e-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. 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 -2.722780454535674e-01 -2.722780454431569e-01 1.04105e-11 1.49249e-11 2 -2.936805046331776e+00 -2.936805046330517e+00 1.25899e-12 3.35993e-11 3 -2.806932004694267e+00 -2.806932004694598e+00 3.31291e-13 1.84519e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.520255068576847e+00 1.520255068573842e+00 3.00560e-12 4.02149e-11 2 1.142756646040563e+00 1.142756646051200e+00 1.06373e-11 7.45124e-11 3 -4.202088614081197e+00 -4.202088614074262e+00 6.93490e-12 5.88862e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.732236631631319e+00 2.732236631629342e+00 1.97620e-12 8.46967e-12 2 -4.047522756380330e+00 -4.047522756390684e+00 1.03544e-11 1.79075e-11 3 -8.646128728413017e-01 -8.646128728523439e-01 1.10422e-11 6.84655e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.889720201668419e+00 -2.889720201658057e+00 1.03624e-11 2.02391e-10 2 5.400116535639766e+00 5.400116535608527e+00 3.12390e-11 6.45084e-11 3 1.842536508337387e+00 1.842536508350640e+00 1.32538e-11 2.11314e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -9.899099277720110e-01 -9.899099277637833e-01 8.22775e-12 2.40470e-11 2 3.710259968127945e+00 3.710259968132874e+00 4.92895e-12 1.53055e-11 3 3.968265450276301e+00 3.968265450260057e+00 1.62443e-11 5.44924e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.445992213050674e+00 -2.445992213070077e+00 1.94031e-11 2.82440e-10 2 9.166857321896056e-01 9.166857321762213e-01 1.33843e-11 6.50325e-11 3 -3.386499193288292e-01 -3.386499193385434e-01 9.71428e-12 3.78864e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 -2.887779738011058e+00 -2.887779738010156e+00 9.01945e-13 4.76166e-11 2 -3.494277978742226e-01 -3.494277978786223e-01 4.39970e-12 1.31727e-11 3 3.029252617230420e+00 3.029252617244043e+00 1.36233e-11 3.18288e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -8.318955635059530e-01 -8.318955635275049e-01 2.15520e-11 8.34213e-10 * 2 7.924982275200196e-02 7.924982272332207e-02 2.86799e-11 2.19071e-05 * 3 1.805610546620119e+00 1.805610546617061e+00 3.05800e-12 2.41003e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.434677452665514e+00 4.434677452677261e+00 1.17470e-11 5.51168e-11 2 2.227543405457771e+00 2.227543405457709e+00 6.26166e-14 1.16067e-11 3 5.528483077144782e+00 5.528483077146801e+00 2.01883e-12 1.45929e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.502209591893434e+00 -9.502209591892189e+00 1.24523e-12 3.68262e-10 2 -2.186768937373404e-01 -2.186768937537559e-01 1.64155e-11 5.36815e-11 3 -1.203809323906818e+00 -1.203809323895465e+00 1.13534e-11 5.85159e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -1.470257826878703e+00 -1.470257826869497e+00 9.20619e-12 2.20067e-10 2 6.729463074385463e-01 6.729463074409681e-01 2.42173e-12 2.47621e-10 3 4.228859764624294e+00 4.228859764620585e+00 3.70903e-12 1.26328e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 5.076678418381774e+00 5.076678418390312e+00 8.53806e-12 6.72040e-11 2 -6.024452511428098e+00 -6.024452511401368e+00 2.67306e-11 1.81336e-10 3 4.632847883576642e-01 4.632847883633137e-01 5.64943e-12 1.22728e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 3.807115312309253e+00 3.807115312308229e+00 1.02363e-12 4.88209e-11 2 -1.056443429602117e+01 -1.056443429601834e+01 2.83151e-12 1.26173e-10 3 -5.714989174769741e+00 -5.714989174800470e+00 3.07292e-11 4.17266e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.627969276307249e+00 1.627969276308732e+00 1.48304e-12 2.46685e-11 2 -3.299489266241587e-01 -3.299489266185736e-01 5.58509e-12 2.10015e-11 3 7.416225905160180e-01 7.416225905017445e-01 1.42735e-11 5.20116e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.772526913439606e-01 5.772526913548194e-01 1.08588e-11 4.32332e-12 2 4.212312430029094e+00 4.212312430014079e+00 1.50147e-11 4.81037e-11 3 8.005385228716367e-01 8.005385228830962e-01 1.14595e-11 1.20339e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.038236950594039e+00 3.038236950593729e+00 3.09974e-13 8.84781e-11 2 5.738987789669173e+00 5.738987789674473e+00 5.29976e-12 1.31303e-10 3 8.988024442142288e+00 8.988024442164406e+00 2.21174e-11 1.15460e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.980591731591840e-01 -2.980591731573353e-01 1.84869e-12 2.74538e-11 2 2.421574953277970e+00 2.421574953283384e+00 5.41345e-12 1.98281e-11 3 2.540222185806515e+00 2.540222185804452e+00 2.06279e-12 1.97709e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 5.106972032928726e+00 5.106972032926828e+00 1.89804e-12 7.65414e-11 2 -1.647585183167921e+00 -1.647585183171207e+00 3.28604e-12 1.80861e-10 3 5.910208661758007e+00 5.910208661740828e+00 1.71791e-11 4.85567e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 7.407886766437607e+00 7.407886766433687e+00 3.92042e-12 4.83791e-11 2 4.809292546677304e+00 4.809292546673090e+00 4.21441e-12 8.77387e-11 3 -5.812734821766545e+00 -5.812734821771744e+00 5.19851e-12 1.02690e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 1.108856149790409e+00 1.108856149785152e+00 5.25713e-12 1.19049e-10 2 -3.053247637684276e+00 -3.053247637683390e+00 8.85958e-13 1.44302e-11 3 -3.553142061403578e+00 -3.553142061400015e+00 3.56382e-12 1.59956e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -3.758370989426138e+00 -3.758370989480250e+00 5.41118e-11 7.55351e-11 2 2.143542000760033e+00 2.143542000719679e+00 4.03548e-11 3.40563e-10 3 3.578057439125338e-01 3.578057439121078e-01 4.25993e-13 6.10949e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -7.733176848796297e-01 -7.733176848855545e-01 5.92482e-12 5.55784e-10 * 2 1.465115665020464e+00 1.465115665224734e+00 2.04270e-10 2.91396e-10 3 -2.047933687015151e+00 -2.047933687031064e+00 1.59130e-11 4.35114e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.133393691544147e-01 -1.133393691625832e-01 8.16844e-12 4.60874e-11 2 3.854018029807729e-01 3.854018029652121e-01 1.55607e-11 1.23214e-05 * 3 8.178939585656193e-01 8.178939585614304e-01 4.18887e-12 2.47781e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -4.360432530914008e+00 -4.360432530917936e+00 3.92752e-12 9.26379e-11 2 9.093463844769787e-01 9.093463844853414e-01 8.36275e-12 2.02967e-05 * 3 -3.609370049946425e+00 -3.609370049959086e+00 1.26610e-11 1.05788e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -3.055460105477334e+00 -3.055460105469478e+00 7.85594e-12 9.80416e-12 2 8.668704881484339e-01 8.668704881419942e-01 6.43974e-12 1.05743e-10 3 -4.480424157791679e+00 -4.480424157791600e+00 7.81597e-14 3.65343e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 3.330093172794879e+00 3.330093172778651e+00 1.62288e-11 1.68385e-10 2 1.666975833838491e+00 1.666975833853890e+00 1.53995e-11 4.94448e-10 3 -3.509637012854244e+00 -3.509637012894408e+00 4.01643e-11 5.08349e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 3.417838403454574e+00 3.417838403450963e+00 3.61133e-12 1.15372e-09 * 2 1.354518783285414e+00 1.354518783289695e+00 4.28058e-12 8.43468e-11 3 1.364414342346003e+00 1.364414342129679e+00 2.16325e-10 1.15308e-09 * ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.456665779636368e+00 -2.456665779630236e+00 6.13198e-12 1.05236e-11 2 1.668237644607384e+00 1.668237644619060e+00 1.16755e-11 8.98350e-11 3 1.692609289300373e+00 1.692609289305021e+00 4.64806e-12 2.52872e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -8.369627205392985e-01 -8.369627201146700e-01 4.24629e-10 2.63770e-09 * 2 -2.546339786804677e+00 -2.546339786801214e+00 3.46301e-12 7.87206e-11 3 -3.847576538854864e-01 -3.847576539779998e-01 9.25134e-11 8.52516e-10 * ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.068326673341346e+00 -1.068326673339474e+00 1.87184e-12 4.34022e-11 2 -4.166599369336991e+00 -4.166599369333767e+00 3.22409e-12 1.64027e-10 3 -3.737832218792702e-01 -3.737832218740799e-01 5.19024e-12 4.39977e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.219268826737376e+00 -2.219268826739534e+00 2.15827e-12 3.13380e-11 2 -3.176256051582069e+00 -3.176256051586863e+00 4.79439e-12 3.65432e-11 3 -3.238845355142832e+00 -3.238845355128107e+00 1.47242e-11 5.45564e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -2.955821365717245e+00 -2.955821365727949e+00 1.07039e-11 6.09783e-11 2 -2.730438483444668e+00 -2.730438483445729e+00 1.06137e-12 5.88951e-11 3 -1.937922558502593e+00 -1.937922558509777e+00 7.18492e-12 3.26126e-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 = 22, direction = 2: |F_model - F_numer| error = ----------------------- = 1.39422e-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 = 3.2936292134212635 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -5.325038749857385e+00 -5.325038749867171e+00 9.78595e-12 1.43929e-11 2 -5.318348980093488e+00 -5.318348980095411e+00 1.92379e-12 4.35652e-11 3 -2.614567429943430e+00 -2.614567429943725e+00 2.94431e-13 4.62297e-12 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.170111568117060e+00 3.170111568171637e+00 5.45768e-11 2.48925e-10 2 1.071475991903835e+01 1.071475991904261e+01 4.25793e-12 2.32802e-10 3 -7.643226426634922e+00 -7.643226426639625e+00 4.70290e-12 3.24292e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 5.928209059526988e+00 5.928209059536370e+00 9.38272e-12 1.82603e-09 * 2 -1.044368264889050e+01 -1.044368264888713e+01 3.36797e-12 3.46549e-11 3 -4.438636785703950e+00 -4.438636785704541e+00 5.91527e-13 1.22675e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.314660295763972e+01 -1.314660295765250e+01 1.27791e-11 6.03219e-10 * 2 2.970519504922358e-01 2.970519504939416e-01 1.70586e-12 3.48951e-11 3 -9.042552455927984e+00 -9.042552455935617e+00 7.63301e-12 7.76570e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.373414441814648e-02 -1.373414441530130e-02 2.84519e-12 4.29513e-11 2 1.850974985774959e+00 1.850974985775218e+00 2.58460e-13 2.93454e-12 3 9.772201156497654e-01 9.772201156449345e-01 4.83091e-12 4.62316e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 8.287627184684824e+00 8.287627184686878e+00 2.05347e-12 6.22560e-11 2 -1.776073763116724e+01 -1.776073763117664e+01 9.39693e-12 2.46974e-10 3 -7.475052382758896e+00 -7.475052382759992e+00 1.09601e-12 6.75824e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -3.464649802603876e-01 -3.464649802590913e-01 1.29630e-12 1.16078e-10 2 4.831132264544722e+00 4.831132264541248e+00 3.47455e-12 4.63505e-11 3 3.882003432326893e+00 3.882003432309634e+00 1.72586e-11 1.13902e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.323545342714103e+00 2.323545342726876e+00 1.27729e-11 1.95579e-10 2 -7.180758447348869e-01 -7.180758447013392e-01 3.35477e-11 8.09078e-11 3 -3.073811614285777e+00 -3.073811614315479e+00 2.97016e-11 1.71273e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 2.228815400088254e+00 2.228815400090110e+00 1.85629e-12 3.74643e-11 2 -3.169097188072561e+00 -3.169097188069424e+00 3.13660e-12 3.40816e-11 3 3.381165041421241e-02 3.381165041388617e-02 3.26239e-13 1.37658e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 2.662875463512817e+00 2.662875463511935e+00 8.81517e-13 8.75966e-12 2 -2.808209064764287e+00 -2.808209064766192e+00 1.90470e-12 1.25078e-11 3 1.678161127658410e-01 1.678161127659542e-01 1.13215e-13 4.01645e-12 ----------------------------------------------------------------------------------------------------- 11 C 1 9.168640667587634e-02 9.168640664693366e-02 2.89427e-11 3.06763e-10 2 2.923023960411312e+00 2.923023960394602e+00 1.67106e-11 5.46421e-11 3 -2.346925416378695e+00 -2.346925416378829e+00 1.34559e-13 5.27378e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 1.746071478157777e+00 1.746071478141124e+00 1.66529e-11 2.46383e-11 2 1.619046901567700e+00 1.619046901555402e+00 1.22977e-11 2.06621e-11 3 1.108927636678347e+00 1.108927636668560e+00 9.78684e-12 7.16494e-12 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.389176719821161e+01 -1.389176719821107e+01 5.34683e-13 3.97591e-10 2 1.881510511548779e+01 1.881510511550747e+01 1.96856e-11 1.49729e-10 3 -2.080295378394137e+00 -2.080295378402395e+00 8.25739e-12 2.13056e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.974119562282649e+00 1.974119562287090e+00 4.44111e-12 4.46132e-12 2 1.318319440806518e+00 1.318319440806711e+00 1.92291e-13 1.00282e-10 3 6.338129458826158e-01 6.338129458844535e-01 1.83764e-12 1.75986e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 3.866410756157283e+00 3.866410756177672e+00 2.03890e-11 8.06364e-11 2 7.942783865517629e+00 7.942783865527947e+00 1.03171e-11 7.43352e-11 3 7.781916790151943e+00 7.781916790131746e+00 2.01972e-11 3.67654e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 2.661249743895945e+00 2.661249743879615e+00 1.63300e-11 1.42828e-10 2 -4.024034266927494e+00 -4.024034266919585e+00 7.90923e-12 5.49036e-11 3 1.051190379259037e+01 1.051190379257643e+01 1.39426e-11 1.13088e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.336857802566679e+00 -3.336857802577633e+00 1.09539e-11 3.08362e-10 2 -1.367304826074635e+01 -1.367304826088121e+01 1.34857e-10 1.08372e-09 * 3 1.648648314536313e+01 1.648648314516532e+01 1.97815e-10 9.83697e-10 * ----------------------------------------------------------------------------------------------------- 18 Si 1 1.426332473067070e+01 1.426332473071118e+01 4.04743e-11 6.05187e-11 2 7.260493416650319e+00 7.260493416636368e+00 1.39506e-11 2.27454e-11 3 1.841345220503690e+01 1.841345220503541e+01 1.49214e-12 8.48122e-10 * ----------------------------------------------------------------------------------------------------- 19 C 1 -3.355242735171526e-01 -3.355242735253745e-01 8.22187e-12 4.29600e-11 2 -2.085147390950557e+00 -2.085147390945146e+00 5.41123e-12 1.59304e-10 3 -1.086781440794193e+01 -1.086781440793955e+01 2.37499e-12 4.10321e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.338169208204819e-01 -2.338169207912927e-01 2.91892e-11 4.97918e-05 * 2 1.143229816160694e+00 1.143229816157224e+00 3.46967e-12 9.40217e-10 * 3 -1.285790160538943e+00 -1.285790160526900e+00 1.20428e-11 6.44706e-10 * ----------------------------------------------------------------------------------------------------- 21 Si 1 -1.388969376002794e+01 -1.388969376003409e+01 6.15863e-12 8.31211e-11 2 -8.053608833836757e+00 -8.053608833831825e+00 4.93117e-12 4.73186e-11 3 3.255961101675355e+00 3.255961101688725e+00 1.33697e-11 2.63496e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.107074481439327e+01 1.107074481438768e+01 5.59197e-12 2.57991e-10 2 3.333659908288740e+00 3.333659908317458e+00 2.87184e-11 4.51474e-05 * 3 -4.522331185442547e+00 -4.522331185172819e+00 2.69728e-10 2.55775e-09 * ----------------------------------------------------------------------------------------------------- 23 Si 1 3.251395462126721e+00 3.251395462104464e+00 2.22573e-11 6.38387e-11 2 7.734536337235433e-02 7.734536340135136e-02 2.89970e-11 3.82009e-11 3 1.045742734159856e+01 1.045742734159863e+01 7.10543e-14 1.16103e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -2.822548724452396e-01 -2.822548724476423e-01 2.40274e-12 2.99763e-11 2 -2.575072207853981e+00 -2.575072207853843e+00 1.38556e-13 4.96354e-11 3 -4.282018439023133e+00 -4.282018439019489e+00 3.64420e-12 5.63647e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -3.867150167763016e+00 -3.867150167762276e+00 7.39853e-13 4.11275e-11 2 1.528873128336616e+01 1.528873128337157e+01 5.40545e-12 2.10942e-11 3 9.775762987180983e+00 9.775762987174044e+00 6.93845e-12 7.21379e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -8.820638029091615e+00 -8.820638029124064e+00 3.24487e-11 7.37916e-11 2 -3.858381815542778e+00 -3.858381815541608e+00 1.16973e-12 3.97788e-11 3 5.752310210927504e+00 5.752310210932164e+00 4.65938e-12 1.00103e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 1.234221802704256e+01 1.234221802704856e+01 6.00409e-12 2.34245e-10 2 9.599314063514109e+00 9.599314063516136e+00 2.02682e-12 1.13276e-10 3 -8.539559367448742e+00 -8.539559367438308e+00 1.04343e-11 7.95950e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 4.987118429639070e+00 4.987118429637579e+00 1.49125e-12 3.28209e-11 2 -2.043556386354227e+00 -2.043556386355900e+00 1.67377e-12 4.23612e-11 3 -6.708341118899011e+00 -6.708341118912875e+00 1.38636e-11 2.11360e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 -2.017911780741473e+00 -2.017911780750507e+00 9.03322e-12 1.68058e-10 2 4.492138675046408e+00 4.492138675050860e+00 4.45244e-12 3.62395e-11 3 -2.380535066612442e+00 -2.380535066609882e+00 2.56017e-12 4.10698e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.631666932367958e+00 -8.631666932339888e+00 2.80700e-11 1.86979e-11 2 -7.333739878566143e+00 -7.333739878572431e+00 6.28830e-12 8.27995e-11 3 -8.720812578411504e+00 -8.720812578417389e+00 5.88507e-12 1.22322e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -1.387195018642929e+00 -1.387195018641603e+00 1.32627e-12 3.74802e-11 2 -4.748542336613616e-01 -4.748542336058003e-01 5.55614e-11 5.11153e-05 * 3 -6.707379225665289e-01 -6.707379226514111e-01 8.48822e-11 1.04519e-05 * ----------------------------------------------------------------------------------------------------- 32 C 1 -5.329205841314166e+00 -5.329205841316674e+00 2.50822e-12 3.93108e-12 2 -7.167516297877389e+00 -7.167516297883670e+00 6.28031e-12 3.15028e-11 3 -2.545801331329848e+00 -2.545801331332365e+00 2.51754e-12 2.73230e-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 = 23, direction = 2: |F_model - F_numer| error = ----------------------- = 3.74903e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.74903e-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 3.74903e-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.