!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_MEAM_Wagner_2007_SiC__SM_264944083668_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 = 2.91614055634 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 5.215667307821369e+01 5.215667307779004e+01 4.23654e-10 3.20692e-09 2 -9.909374112704175e+01 -9.909374112722114e+01 1.79384e-10 4.35392e-10 3 -2.228028791653219e+02 -2.228028791650707e+02 2.51163e-10 1.04663e-09 ----------------------------------------------------------------------------------------------------- 2 C 1 -2.058412214936521e+02 -2.058412214942872e+02 6.35083e-10 3.68905e-09 2 1.026268843373727e+02 1.026268843375358e+02 1.63055e-10 8.92683e-10 3 -1.028771253305586e+02 -1.028771253307660e+02 2.07450e-10 4.87148e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.240284370911811e+03 -1.240284370911786e+03 2.50111e-11 4.30987e-09 2 -7.804241930707287e+02 -7.804241930700545e+02 6.74277e-10 3.87377e-09 3 1.293226522048351e+03 1.293226522046908e+03 1.44291e-09 5.32805e-09 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.336555080872843e+02 -1.336555080871010e+02 1.83377e-10 4.46136e-10 2 2.740139605141571e+02 2.740139605144851e+02 3.27987e-10 4.77331e-09 3 1.845031147547977e+02 1.845031147550604e+02 2.62673e-10 5.53825e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 1.899140602225673e+02 1.899140602226816e+02 1.14284e-10 4.08099e-09 2 -5.604023209667688e+01 -5.604023209722548e+01 5.48603e-10 2.48173e-09 3 3.912836955186432e+01 3.912836955212950e+01 2.65175e-10 5.39738e-08 * ----------------------------------------------------------------------------------------------------- 6 C 1 -5.890904832459580e+01 -5.890904832360868e+01 9.87121e-10 2.02257e-09 2 3.124784040192826e+01 3.124784040188418e+01 4.40821e-11 4.27804e-10 3 1.234063146864737e+01 1.234063147110130e+01 2.45393e-09 2.23748e-08 ----------------------------------------------------------------------------------------------------- 7 C 1 5.731714303765482e+01 5.731714313992811e+01 1.02273e-07 2.34122e-06 * 2 -2.353318906596890e+02 -2.353318912126794e+02 5.52990e-07 3.42850e-06 * 3 -1.411382923222836e+02 -1.411382924037054e+02 8.14219e-08 9.75461e-07 * ----------------------------------------------------------------------------------------------------- 8 C 1 -6.284987815994416e+02 -6.284987815996182e+02 1.76556e-10 1.98671e-08 2 -9.411957527182540e+02 -9.411957527179984e+02 2.55568e-10 2.24736e-09 3 3.779464362365509e+02 3.779464362364860e+02 6.49152e-11 1.98531e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 9.112470051204454e+00 9.112470051131988e+00 7.24665e-11 1.19107e-09 2 -1.170173668514250e+02 -1.170173668510630e+02 3.61965e-10 4.60038e-09 3 -2.742958794578012e+01 -2.742958794571941e+01 6.07123e-11 6.84619e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.580639144937779e+02 -1.580639144935378e+02 2.40135e-10 2.55653e-09 2 7.385227277581497e+01 7.385227277576287e+01 5.20970e-11 1.44401e-09 3 3.764548913144473e+00 3.764548913492175e+00 3.47702e-10 2.64608e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 8.288096036855232e+01 8.288096036834079e+01 2.11529e-10 3.21968e-09 2 -8.528337337601862e+01 -8.528337337622187e+01 2.03258e-10 1.53115e-08 3 8.823390127922200e+01 8.823390127904530e+01 1.76698e-10 5.15860e-09 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.799758141768871e+01 -1.799758141747567e+01 2.13035e-10 4.62395e-09 2 6.535174239800097e+01 6.535174239793544e+01 6.55263e-11 1.44237e-09 3 1.680685810256403e+01 1.680685810256410e+01 6.75016e-14 6.20798e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 -2.601986697240855e+03 -2.601986697240378e+03 4.77030e-10 6.78428e-08 * 2 -1.186118401574587e+03 -1.186118401574767e+03 1.79625e-10 8.99240e-09 3 -1.125378600528836e+03 -1.125378600529444e+03 6.08225e-10 2.76827e-09 ----------------------------------------------------------------------------------------------------- 14 C 1 1.455567424460062e+03 1.455567424459549e+03 5.13182e-10 1.56833e-08 2 -5.525150759852838e+02 -5.525150759851479e+02 1.35969e-10 1.66176e-09 3 1.746192449851633e+03 1.746192449853485e+03 1.85196e-09 9.72591e-09 ----------------------------------------------------------------------------------------------------- 15 C 1 1.953693810078294e+03 1.953693810079114e+03 8.19455e-10 1.45988e-08 2 2.768718749716026e+03 2.768718749715784e+03 2.42380e-10 1.76196e-08 3 -5.919870060550400e+02 -5.919870060553593e+02 3.19346e-10 1.30115e-09 ----------------------------------------------------------------------------------------------------- 16 C 1 8.192342165745819e+01 8.192342165734622e+01 1.11967e-10 3.01416e-09 2 3.250567051431672e+02 3.250567051430678e+02 9.94191e-11 2.82796e-10 3 -1.798257148237803e+02 -1.798257148241572e+02 3.76872e-10 3.38395e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.348277785801104e+03 -1.348277785800768e+03 3.35831e-10 3.22188e-09 2 -3.505989470707211e+02 -3.505989470702856e+02 4.35477e-10 1.45596e-08 3 -1.991688489160116e+03 -1.991688489160634e+03 5.17502e-10 5.05679e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 1.206027529304542e+03 1.206027529305023e+03 4.81123e-10 6.33918e-09 2 1.519009175625398e+03 1.519009175625602e+03 2.03272e-10 8.76685e-09 3 3.367045711688821e+02 3.367045711688609e+02 2.12026e-11 4.60420e-09 ----------------------------------------------------------------------------------------------------- 19 C 1 2.132450331361971e+03 2.132450331361536e+03 4.34738e-10 1.90080e-08 2 -3.288695072029464e+02 -3.288695072029379e+02 8.52651e-12 1.05013e-09 3 8.761106725666915e+02 8.761106725662283e+02 4.63160e-10 3.83739e-09 ----------------------------------------------------------------------------------------------------- 20 C 1 -5.753160037723874e+02 -5.753160037726032e+02 2.15778e-10 1.05024e-09 2 -3.300820198159452e+01 -3.300820198126533e+01 3.29187e-10 1.42345e-09 3 -5.808642985246260e+02 -5.808642985247732e+02 1.47224e-10 1.10208e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.530427279831315e+02 -3.530427279892990e+02 6.16745e-09 5.12448e-07 * 2 -2.419545027581337e+02 -2.419545028407007e+02 8.25669e-08 1.39967e-06 * 3 -6.834847583150723e+02 -6.834847591355814e+02 8.20509e-07 1.26069e-06 * ----------------------------------------------------------------------------------------------------- 22 C 1 -1.802844536367606e+02 -1.802844577414459e+02 4.10469e-06 6.65608e-06 * 2 1.855981594783913e+02 1.855981594005947e+02 7.77966e-08 1.63330e-06 * 3 -1.721032863303716e+01 -1.721032854110202e+01 9.19351e-08 5.50593e-07 * ----------------------------------------------------------------------------------------------------- 23 C 1 1.720751913985410e+01 1.720751913984857e+01 5.52447e-12 1.50131e-09 2 3.440609537412277e+02 3.440609537413135e+02 8.58336e-11 2.81091e-10 3 5.123217106331811e+02 5.123217106342347e+02 1.05365e-09 2.23349e-09 ----------------------------------------------------------------------------------------------------- 24 C 1 2.633429644978340e+02 2.633429644978165e+02 1.75078e-11 1.50453e-09 2 -1.192410808364966e+02 -1.192410808359668e+02 5.29880e-10 1.93333e-09 3 2.101766087423095e+02 2.101766087422529e+02 5.65876e-11 8.74621e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.720775607416134e+02 -2.720775607413419e+02 2.71484e-10 2.72593e-09 2 6.183797397608798e+02 6.183797397603729e+02 5.06930e-10 3.03680e-09 3 1.003157660683619e+03 1.003157660684671e+03 1.05160e-09 5.43685e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -2.799035080805867e+02 -2.799035080808084e+02 2.21746e-10 2.55366e-08 2 2.300812613521094e+02 2.300812613521360e+02 2.66880e-11 4.09671e-10 3 2.093898467938778e+02 2.093898467937097e+02 1.68086e-10 4.33010e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 2.915119579239542e+03 2.915119579238850e+03 6.91671e-10 9.84983e-09 2 -2.044982514917313e+03 -2.044982514916827e+03 4.86580e-10 8.50264e-09 3 3.569681180456106e+02 3.569681180430027e+02 2.60786e-09 2.35658e-08 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.673831482920384e+03 -2.673831482919787e+03 5.97538e-10 4.45607e-09 2 1.321105329895327e+03 1.321105329894825e+03 5.02496e-10 1.15808e-08 3 -1.219078072933065e+03 -1.219078072932107e+03 9.58607e-10 5.03883e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 2.324641212472640e+02 2.324641212477349e+02 4.70919e-10 8.86700e-10 2 -7.059710488949368e+02 -7.059710488952535e+02 3.16732e-10 7.94455e-09 3 -1.864447150404621e+02 -1.864447150404630e+02 8.52651e-13 3.32815e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 7.346535365430869e+01 7.346535365422005e+01 8.86331e-11 9.23706e-11 2 -4.669495832299524e+01 -4.669495832342733e+01 4.32088e-10 4.76408e-09 3 -1.352960955053335e+02 -1.352960955050006e+02 3.32903e-10 7.15630e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.836177929347140e+01 -2.836177929367804e+01 2.06640e-10 7.05001e-10 2 -1.444035528992474e+01 -1.444035529007048e+01 1.45734e-10 8.51289e-10 3 -1.986459660021560e+01 -1.986459660036026e+01 1.44659e-10 5.32767e-09 ----------------------------------------------------------------------------------------------------- 32 C 1 3.368906439922527e+01 3.368906439889890e+01 3.26374e-10 7.30175e-10 2 7.967836959496714e+01 7.967836959473738e+01 2.29761e-10 2.21794e-09 3 -4.160145995741862e+01 -4.160145995733888e+01 7.97442e-11 1.72322e-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 = 6, direction = 3: |F_model - F_numer| error = ----------------------- = 1.98850e-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 = 4.19901847839 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.643552321468374e+01 -1.643552321466949e+01 1.42464e-11 7.18572e-11 2 -2.674559015565253e+00 -2.674559015552754e+00 1.24989e-11 6.71543e-11 3 1.390237044834556e+01 1.390237044831829e+01 2.72689e-11 1.54619e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 2.475050569160999e+01 2.475050569156377e+01 4.62279e-11 7.54952e-12 2 1.937356254484513e+01 1.937356254485268e+01 7.55307e-12 1.52227e-10 3 -1.535872343804913e+01 -1.535872343805459e+01 5.46230e-12 1.64674e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 5.218472205685618e+00 5.218472205678236e+00 7.38254e-12 6.53042e-11 2 -1.073759958383420e+01 -1.073759958384422e+01 1.00204e-11 7.35909e-11 3 3.067218390123311e+00 3.067218390142151e+00 1.88405e-11 2.45768e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.075818703895875e+01 -1.075818703895152e+01 7.22800e-12 4.11298e-11 2 -6.586045290560857e+00 -6.586045290575601e+00 1.47446e-11 1.63855e-10 3 -5.857896698529135e+00 -5.857896698456822e+00 7.23128e-11 1.45199e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.092480018889388e+01 -1.092480018889131e+01 2.57394e-12 3.75309e-11 2 -3.002115577301042e+00 -3.002115577306103e+00 5.06084e-12 4.96865e-11 3 -4.558441863493861e+00 -4.558441863487039e+00 6.82210e-12 7.73603e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.448709253857858e+00 2.448709253851237e+00 6.62093e-12 2.10389e-10 2 -1.350430897932775e+01 -1.350430897931480e+01 1.29514e-11 2.67617e-10 3 -5.883566955515209e+00 -5.883566955557635e+00 4.24256e-11 1.41691e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 6.872315878904135e+00 6.872315878908303e+00 4.16822e-12 1.31946e-10 2 5.943140392069806e+00 5.943140392089321e+00 1.95151e-11 9.05436e-11 3 1.412712199472450e+00 1.412712199468662e+00 3.78875e-12 1.53720e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.255408899174180e-01 3.255408899172860e-01 1.32006e-13 1.37946e-10 2 8.460185122312566e+00 8.460185122325871e+00 1.33049e-11 9.47757e-11 3 5.190188768225995e+00 5.190188768224841e+00 1.15374e-12 9.20686e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 1.396027977333040e+00 1.396027977345844e+00 1.28049e-11 3.51305e-10 2 -3.408562744208976e-01 -3.408562744127304e-01 8.16719e-12 1.31686e-10 3 5.827668270499189e-01 5.827668270498843e-01 3.46390e-14 5.19660e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.646397438255043e+00 -1.646397438256787e+00 1.74438e-12 2.05408e-10 2 2.153477488479985e+00 2.153477488465069e+00 1.49156e-11 4.56200e-11 3 -4.009666561886041e+00 -4.009666561882276e+00 3.76499e-12 3.53984e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 2.692588944073505e+00 2.692588944063308e+00 1.01976e-11 5.59141e-10 2 -8.088110776588598e+00 -8.088110776572355e+00 1.62430e-11 3.14653e-10 3 4.749155718011461e+00 4.749155718003609e+00 7.85239e-12 5.89263e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.776595165490662e+00 -2.776595165464045e+00 2.66178e-11 1.06037e-10 2 3.221632911393127e+00 3.221632911422712e+00 2.95852e-11 8.41212e-11 3 -3.512263526858952e+00 -3.512263526862406e+00 3.45368e-12 2.83311e-09 * ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.426381137427086e+01 -1.426381137426881e+01 2.04636e-12 5.46656e-10 2 -7.933271391973758e+00 -7.933271391932885e+00 4.08731e-11 1.59720e-10 3 -9.344351058105399e+00 -9.344351058125719e+00 2.03197e-11 8.55884e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.619569700064288e+00 7.619569700063401e+00 8.86402e-13 1.06464e-10 2 -2.099204387335893e-01 -2.099204387330547e-01 5.34656e-13 1.12563e-10 3 3.903431310963229e+00 3.903431310913676e+00 4.95533e-11 1.24035e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 7.479979748503020e+00 7.479979748517106e+00 1.40865e-11 1.45984e-10 2 1.681155916438582e+01 1.681155916441418e+01 2.83578e-11 8.44018e-11 3 1.509730641279815e+01 1.509730641280959e+01 1.14468e-11 2.36692e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -6.013451601478241e-01 -6.013451601942935e-01 4.64694e-11 1.17685e-10 2 4.797012837555418e+00 4.797012837558229e+00 2.81108e-12 7.39675e-12 3 5.816954444521606e+00 5.816954444518324e+00 3.28182e-12 1.71545e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.249805385551446e+00 1.249805385591440e+00 3.99942e-11 8.79514e-11 2 -3.183177860317201e+00 -3.183177860309032e+00 8.16902e-12 8.32343e-11 3 4.490115150982308e+00 4.490115150970865e+00 1.14424e-11 1.62601e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.031761088782843e+00 2.031761088787371e+00 4.52793e-12 1.75531e-10 2 1.204208062364317e+01 1.204208062367503e+01 3.18643e-11 1.76094e-10 3 -1.214923357073173e+00 -1.214923357127683e+00 5.45106e-11 2.01120e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.597755395857630e+00 -4.597755395869067e+00 1.14371e-11 1.88454e-10 2 -3.553560426882064e+00 -3.553560426888059e+00 5.99476e-12 6.09131e-11 3 1.094483049716388e+00 1.094483049705729e+00 1.06590e-11 3.85616e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -4.936290325158073e-01 -4.936290325234227e-01 7.61535e-12 2.82956e-10 2 4.593560777863369e-02 4.593560775661309e-02 2.20206e-11 6.22325e-11 3 -1.309224323631288e-01 -1.309224323663662e-01 3.23733e-12 4.23638e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 4.607723848111270e-01 4.607723848145697e-01 3.44269e-12 1.09725e-09 * 2 -1.110320932614098e+01 -1.110320932614247e+01 1.49747e-12 6.81215e-11 3 5.045701057389962e+00 5.045701057402497e+00 1.25349e-11 8.64988e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 8.622011941876771e+00 8.622011941869552e+00 7.21911e-12 8.24745e-11 2 9.372564098463315e+00 9.372564098470763e+00 7.44826e-12 1.47722e-10 3 -1.459443242854570e+01 -1.459443242851056e+01 3.51417e-11 3.63443e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.278298530437819e+00 -2.278298530382541e+00 5.52784e-11 5.09122e-11 2 -9.387273351560980e+00 -9.387273351536066e+00 2.49134e-11 2.49340e-10 3 6.090303175810129e-01 6.090303175789996e-01 2.01328e-12 1.64878e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -9.011890185935037e+00 -9.011890185943709e+00 8.67217e-12 2.58309e-10 2 2.784019255678842e+00 2.784019255640764e+00 3.80784e-11 4.16946e-10 3 8.309886037396460e+00 8.309886037417801e+00 2.13412e-11 1.46477e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -4.874296390620022e+00 -4.874296390611741e+00 8.28049e-12 5.70362e-11 2 -4.420384788625229e+00 -4.420384788612540e+00 1.26894e-11 8.19827e-10 * 3 1.889339641978028e+00 1.889339641950131e+00 2.78968e-11 5.67204e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 6.460239948338598e+00 6.460239948290454e+00 4.81446e-11 5.04237e-11 2 4.173907782404745e+00 4.173907782377626e+00 2.71196e-11 1.79724e-10 3 -3.833964275284115e+00 -3.833964275300564e+00 1.64495e-11 1.42286e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.446229768630782e-01 -1.446229768980829e-01 3.50047e-11 2.62946e-10 2 -7.268736657849795e+00 -7.268736657847425e+00 2.36966e-12 2.39373e-10 3 2.524723447855426e+00 2.524723447890305e+00 3.48788e-11 5.65314e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.804772868368591e+00 -2.804772868296918e+00 7.16729e-11 7.52993e-11 2 -3.115085008304477e-01 -3.115085008233077e-01 7.13996e-12 2.75714e-11 3 2.312680695695315e+00 2.312680695692824e+00 2.49090e-12 2.07229e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -6.064147181449841e+00 -6.064147181463244e+00 1.34026e-11 1.05353e-10 2 -5.845632734687640e+00 -5.845632734646318e+00 4.13216e-11 2.93701e-10 3 -1.528343656382265e+01 -1.528343656379334e+01 2.93010e-11 7.36691e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 4.276960397062956e+00 4.276960397070821e+00 7.86482e-12 1.11140e-09 * 2 3.799930642249003e+00 3.799930642235855e+00 1.31481e-11 3.03640e-10 3 -3.107959781925874e+00 -3.107959781951038e+00 2.51643e-11 2.36691e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.462923983859817e+00 5.462923983910677e+00 5.08606e-11 2.76229e-10 2 -2.067007669754767e+00 -2.067007669744819e+00 9.94849e-12 6.48939e-11 3 3.174083853962765e+00 3.174083853976250e+00 1.34843e-11 2.47654e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.078867225161570e-01 3.078867225016373e-01 1.45197e-11 3.89528e-11 2 7.238270173695484e+00 7.238270173739006e+00 4.35225e-11 2.42866e-10 3 3.518401169383022e+00 3.518401169346804e+00 3.62181e-11 2.51621e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 20, direction = 2: |F_model - F_numer| error = ----------------------- = 4.79380e-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 = 3.84650732058 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -5.373493768965290e+01 -5.373493768965113e+01 1.76215e-12 7.76197e-11 2 3.300890100237826e+01 3.300890100231378e+01 6.44746e-11 2.43247e-10 3 -2.954858694726251e+01 -2.954858694713973e+01 1.22785e-10 2.12594e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 1.183865878337313e-01 1.183865878300084e-01 3.72291e-12 6.14222e-10 2 -4.139056901764927e+00 -4.139056901667071e+00 9.78559e-11 6.86445e-10 3 -5.048797911754112e+00 -5.048797911822939e+00 6.88276e-11 8.77156e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.196100742550328e+02 1.196100742550247e+02 8.02913e-12 4.75865e-10 2 -4.113007909609986e+01 -4.113007909617077e+01 7.09122e-11 2.28802e-10 3 7.651427418441742e+01 7.651427418432135e+01 9.60654e-11 3.73944e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.839577914175697e+01 -3.839577914180447e+01 4.75069e-11 2.11550e-10 2 5.360187003651921e+00 5.360187003613221e+00 3.87006e-11 7.17408e-11 3 -2.327167852221369e+01 -2.327167852228848e+01 7.47882e-11 4.61043e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 -7.341521277045505e-01 -7.341521278830974e-01 1.78547e-10 5.03162e-10 2 3.572267112074279e+00 3.572267111954819e+00 1.19460e-10 3.23404e-10 3 6.780304418941346e+00 6.780304419026668e+00 8.53220e-11 6.18341e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 1.120417692207497e+01 1.120417692223359e+01 1.58625e-10 8.58762e-11 2 3.515454616638173e+00 3.515454616809278e+00 1.71104e-10 2.60788e-10 3 -1.359528090408784e+01 -1.359528090416008e+01 7.22373e-11 1.90216e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -7.979760783209493e+00 -7.979760783322045e+00 1.12553e-10 5.33147e-11 2 -3.038854903482943e+00 -3.038854903467256e+00 1.56866e-11 3.12212e-10 3 4.822252259186421e+00 4.822252259152779e+00 3.36424e-11 3.55652e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.576741255685300e+01 -1.576741255707812e+01 2.25118e-10 2.04222e-10 2 4.027175437472463e+00 4.027175437397024e+00 7.54392e-11 3.89494e-10 3 1.417541632157321e+01 1.417541632168993e+01 1.16724e-10 3.93753e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 1.913378955662814e+01 1.913378955680422e+01 1.76080e-10 7.56231e-11 2 4.041984267227727e+01 4.041984267236086e+01 8.35954e-11 2.68621e-10 3 -1.541640486299637e+01 -1.541640486287614e+01 1.20227e-10 6.38138e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -5.458008257383204e+01 -5.458008257371993e+01 1.12102e-10 1.37327e-10 2 -3.069350061026855e+01 -3.069350061008349e+01 1.85061e-10 6.66144e-10 3 -5.195540162789582e+01 -5.195540162781622e+01 7.96021e-11 2.58389e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 7.637803509919809e+00 7.637803510063401e+00 1.43592e-10 1.49884e-10 2 -2.064752682147980e+01 -2.064752682136733e+01 1.12472e-10 1.58835e-10 3 2.434929549926938e+01 2.434929549939040e+01 1.21020e-10 3.18991e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 4.740212888166075e+00 4.740212888037744e+00 1.28331e-10 9.26326e-11 2 2.345912518940735e+00 2.345912518780117e+00 1.60617e-10 2.09952e-10 3 1.324983403730131e+01 1.324983403727832e+01 2.29896e-11 1.31275e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 1.925822448328510e+00 1.925822448198656e+00 1.29854e-10 4.14696e-10 2 3.428645357533867e+00 3.428645357486215e+00 4.76525e-11 1.46571e-10 3 1.188990131559777e+00 1.188990131599477e+00 3.97005e-11 4.45924e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.861753731021110e+01 1.861753731027458e+01 6.34799e-11 5.10717e-10 2 -1.401298873711946e+01 -1.401298873710135e+01 1.81100e-11 2.66464e-10 3 -1.208651656644931e+01 -1.208651656641543e+01 3.38840e-11 1.36289e-10 ----------------------------------------------------------------------------------------------------- 15 C 1 1.933107843640335e+00 1.933107843677702e+00 3.73663e-11 1.54376e-10 2 -6.073971626015893e-01 -6.073971625066532e-01 9.49361e-11 2.04014e-10 3 -7.281822707916271e+00 -7.281822707939069e+00 2.27978e-11 7.98760e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 7.974844704032725e+00 7.974844703897610e+00 1.35114e-10 7.65494e-11 2 7.216763409015670e+00 7.216763408961718e+00 5.39524e-11 6.28333e-11 3 5.439838052052242e+01 5.439838052069895e+01 1.76534e-10 2.24404e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -4.545637024130448e+00 -4.545637024008444e+00 1.22004e-10 1.00057e-10 2 2.893421519885463e+00 2.893421520005357e+00 1.19895e-10 2.24748e-10 3 2.007028944449144e+00 2.007028944586776e+00 1.37632e-10 1.39614e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.524756497525923e+01 -1.524756497512923e+01 1.30003e-10 6.75193e-11 2 2.025386841586418e+01 2.025386841604289e+01 1.78709e-10 4.35637e-10 3 -2.638688438257630e+01 -2.638688438255214e+01 2.41585e-11 3.04084e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 1.054667523494316e+01 1.054667523499912e+01 5.59641e-11 3.53104e-10 2 5.498949964392140e-02 5.498949938757210e-02 2.56349e-10 2.08416e-10 3 7.885106149209086e+00 7.885106149139330e+00 6.97566e-11 1.86836e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.882189137194911e+01 -1.882189137203214e+01 8.30340e-11 1.18028e-10 2 -1.124741531766644e+01 -1.124741531778911e+01 1.22672e-10 1.04234e-09 3 -4.364755975480155e+00 -4.364755975578600e+00 9.84448e-11 1.69886e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 6.071584220224305e+01 6.071584220222154e+01 2.15081e-11 5.35380e-10 2 -5.730986784912980e+01 -5.730986784935400e+01 2.24198e-10 1.09966e-09 3 -8.636544714315320e+00 -8.636544714320651e+00 5.33085e-12 3.73561e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 1.128454982064189e+01 1.128454982056800e+01 7.38893e-11 5.35628e-10 2 -4.301297134896112e-01 -4.301297135068805e-01 1.72693e-11 2.76863e-10 3 3.788534895466560e+00 3.788534895361268e+00 1.05293e-10 6.85580e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 1.319487404131408e+00 1.319487403952606e+00 1.78802e-10 2.25710e-10 2 -6.391127259340126e+01 -6.391127259348740e+01 8.61320e-11 2.17284e-10 3 -8.477597830185191e+01 -8.477597830204485e+01 1.92941e-10 3.24334e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 -7.047884245021417e+01 -7.047884245037071e+01 1.56533e-10 4.08093e-10 2 1.132954976903787e+02 1.132954976903068e+02 7.18501e-11 3.89619e-10 3 7.576693360756808e+01 7.576693360755256e+01 1.55183e-11 1.84414e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -1.664704855562214e+00 -1.664704855292418e+00 2.69796e-10 5.16093e-10 2 -4.635577851039014e+00 -4.635577850993836e+00 4.51781e-11 1.31906e-10 3 4.660337346592791e+00 4.660337346468791e+00 1.24000e-10 2.38876e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -1.359042640729556e+02 -1.359042640729172e+02 3.83977e-11 2.35624e-09 * 2 6.914960759244271e+01 6.914960759243134e+01 1.13687e-11 1.40804e-09 * 3 -1.927433898854568e+02 -1.927433898855288e+02 7.19922e-11 9.84102e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.089156228575010e+02 1.089156228574124e+02 8.86331e-11 2.23878e-10 2 9.422859451283441e+01 9.422859451275609e+01 7.83160e-11 3.34772e-09 * 3 7.566187406772302e+01 7.566187406751310e+01 2.09923e-10 3.11161e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 2.809712653796697e+00 2.809712653753320e+00 4.33773e-11 3.33866e-11 2 -1.187800870246282e+00 -1.187800870320672e+00 7.43903e-11 1.37089e-10 3 -3.981186481229577e+00 -3.981186481230285e+00 7.08322e-13 7.47211e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 2.238483482228212e+01 2.238483482228516e+01 3.04823e-12 4.42078e-10 2 -2.946391324277567e+01 -2.946391324283466e+01 5.89893e-11 5.50315e-10 3 -4.334419530482284e+01 -4.334419530481203e+01 1.08074e-11 1.02524e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.475194990848782e+01 -1.475194990845159e+01 3.62306e-11 5.73781e-11 2 9.929493247714566e+00 9.929493247684579e+00 2.99867e-11 2.21185e-10 3 1.345847378570801e+01 1.345847378564027e+01 6.77378e-11 4.39364e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -1.174591109831662e+01 -1.174591109827676e+01 3.98579e-11 5.85310e-09 * 2 5.446686886965969e+00 5.446686886929550e+00 3.64189e-11 1.12342e-10 3 5.912482393063787e+00 5.912482393061192e+00 2.59437e-12 7.95985e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.348040960847658e+01 3.348040960833265e+01 1.43935e-10 4.42924e-10 2 -1.356919268251474e+02 -1.356919268250855e+02 6.19309e-11 1.26434e-09 3 1.378179065337571e+02 1.378179065337534e+02 3.69482e-12 1.40403e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 19, direction = 2: |F_model - F_numer| error = ----------------------- = 4.66179e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.66179e-09 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 4.66179e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.