!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_Wagner_2007_SiC__MO_430846853065_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 = 2.916140556335449 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 5.215667307821342e+01 5.215667307829363e+01 8.02061e-11 2.61399e-09 2 -9.909374112704583e+01 -9.909374112759636e+01 5.50529e-10 2.73253e-09 3 -2.228028791653233e+02 -2.228028791652950e+02 2.82512e-11 1.54654e-09 ----------------------------------------------------------------------------------------------------- 2 C 1 -2.058412214936497e+02 -2.058412214928480e+02 8.01691e-10 8.25221e-09 2 1.026268843373722e+02 1.026268843375212e+02 1.49015e-10 1.40190e-09 3 -1.028771253305580e+02 -1.028771253302195e+02 3.38460e-10 2.33801e-09 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.240284370911841e+03 -1.240284370912576e+03 7.35554e-10 9.97966e-09 2 -7.804241930707470e+02 -7.804241930703960e+02 3.51065e-10 8.95568e-09 3 1.293226522048368e+03 1.293226522050466e+03 2.09729e-09 1.70739e-08 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.336555080872824e+02 -1.336555080871136e+02 1.68797e-10 4.68702e-09 2 2.740139605141607e+02 2.740139605138903e+02 2.70404e-10 3.78623e-09 3 1.845031147548012e+02 1.845031147551088e+02 3.07665e-10 1.86088e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 1.899140602225654e+02 1.899140602227184e+02 1.52966e-10 2.29912e-08 2 -5.604023209667504e+01 -5.604023209703968e+01 3.64643e-10 2.12842e-09 3 3.912836955186374e+01 3.912836955164415e+01 2.19593e-10 2.73430e-09 ----------------------------------------------------------------------------------------------------- 6 C 1 -5.890904832459915e+01 -5.890904832500156e+01 4.02409e-10 5.05015e-09 2 3.124784040193057e+01 3.124784040194031e+01 9.73444e-12 9.20948e-09 3 1.234063146864923e+01 1.234063146952166e+01 8.72424e-10 1.86684e-09 ----------------------------------------------------------------------------------------------------- 7 C 1 5.731714303766029e+01 5.731714127601581e+01 1.76164e-06 6.02185e-05 * 2 -2.353318906596991e+02 -2.353318907159104e+02 5.62113e-08 7.30769e-06 * 3 -1.411382923222839e+02 -1.411382923717662e+02 4.94822e-08 1.30838e-05 * ----------------------------------------------------------------------------------------------------- 8 C 1 -6.284987815994555e+02 -6.284987816024749e+02 3.01941e-09 2.89346e-08 2 -9.411957527182732e+02 -9.411957527133349e+02 4.93833e-09 1.71035e-08 3 3.779464362365583e+02 3.779464362352793e+02 1.27903e-09 1.19182e-08 ----------------------------------------------------------------------------------------------------- 9 C 1 9.112470051205676e+00 9.112470051265083e+00 5.94067e-11 1.52342e-09 2 -1.170173668514202e+02 -1.170173668517744e+02 3.54149e-10 4.23370e-10 3 -2.742958794577876e+01 -2.742958794557683e+01 2.01929e-10 7.95213e-09 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.580639144937766e+02 -1.580639144939445e+02 1.67859e-10 6.93973e-10 2 7.385227277581458e+01 7.385227277594228e+01 1.27699e-10 1.61688e-09 3 3.764548913143912e+00 3.764548913350240e+00 2.06328e-10 2.04050e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 8.288096036855111e+01 8.288096036741885e+01 1.13226e-09 4.10523e-09 2 -8.528337337602227e+01 -8.528337337676878e+01 7.46510e-10 3.22385e-09 3 8.823390127922511e+01 8.823390127896926e+01 2.55852e-10 1.66072e-09 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.799758141769101e+01 -1.799758141757731e+01 1.13705e-10 2.13120e-10 2 6.535174239799937e+01 6.535174239785212e+01 1.47253e-10 3.56202e-09 3 1.680685810256319e+01 1.680685810265891e+01 9.57279e-11 6.56095e-09 ----------------------------------------------------------------------------------------------------- 13 C 1 -2.601986697240701e+03 -2.601986697236961e+03 3.73984e-09 1.15788e-05 * 2 -1.186118401574529e+03 -1.186118401575699e+03 1.16984e-09 6.72958e-09 3 -1.125378600528776e+03 -1.125378600529139e+03 3.63116e-10 1.07720e-07 * ----------------------------------------------------------------------------------------------------- 14 C 1 1.455567424459981e+03 1.455567424460568e+03 5.87761e-10 3.25313e-08 2 -5.525150759852620e+02 -5.525150759836517e+02 1.61026e-09 6.24459e-09 3 1.746192449851546e+03 1.746192449856237e+03 4.69117e-09 3.28730e-06 * ----------------------------------------------------------------------------------------------------- 15 C 1 1.953693810078237e+03 1.953693810072079e+03 6.15842e-09 3.21634e-08 2 2.768718749715969e+03 2.768718749717206e+03 1.23737e-09 2.66096e-06 * 3 -5.919870060550068e+02 -5.919870060555365e+02 5.29781e-10 1.82021e-07 * ----------------------------------------------------------------------------------------------------- 16 C 1 8.192342165746737e+01 8.192342165752684e+01 5.94724e-11 6.30627e-09 2 3.250567051431736e+02 3.250567051449145e+02 1.74094e-09 2.73548e-09 3 -1.798257148237971e+02 -1.798257148240258e+02 2.28653e-10 9.87967e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.348277785801142e+03 -1.348277785801396e+03 2.53749e-10 1.39378e-08 2 -3.505989470707034e+02 -3.505989470708643e+02 1.60867e-10 1.93371e-08 3 -1.991688489160148e+03 -1.991688489164603e+03 4.45516e-09 2.20736e-07 * ----------------------------------------------------------------------------------------------------- 18 C 1 1.206027529304574e+03 1.206027529309551e+03 4.97698e-09 5.64478e-09 2 1.519009175625428e+03 1.519009175626926e+03 1.49794e-09 3.57005e-07 * 3 3.367045711689022e+02 3.367045711688834e+02 1.88720e-11 1.42583e-08 ----------------------------------------------------------------------------------------------------- 19 C 1 2.132450331362036e+03 2.132450331363004e+03 9.68157e-10 3.48268e-08 2 -3.288695072029667e+02 -3.288695072028339e+02 1.32786e-10 1.70243e-08 3 8.761106725667213e+02 8.761106725660936e+02 6.27665e-10 1.84940e-08 ----------------------------------------------------------------------------------------------------- 20 C 1 -5.753160037724191e+02 -5.753160037732966e+02 8.77549e-10 5.11488e-09 2 -3.300820198160403e+01 -3.300820198150802e+01 9.60156e-11 8.00001e-09 3 -5.808642985246603e+02 -5.808642985245128e+02 1.47452e-10 4.50973e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.530427279831404e+02 -3.530427276634931e+02 3.19647e-07 2.54949e-05 * 2 -2.419545027581482e+02 -2.419545027394695e+02 1.86786e-08 1.60124e-06 * 3 -6.834847583151195e+02 -6.834847600906143e+02 1.77549e-06 1.62535e-04 * ----------------------------------------------------------------------------------------------------- 22 C 1 -1.802844536367680e+02 -1.802844481911359e+02 5.44563e-06 1.01794e-05 * 2 1.855981594783968e+02 1.855981628224753e+02 3.34408e-06 1.95567e-04 * 3 -1.721032863304091e+01 -1.721032859511444e+01 3.79265e-08 4.43611e-07 * ----------------------------------------------------------------------------------------------------- 23 C 1 1.720751913984131e+01 1.720751913966979e+01 1.71521e-10 1.49041e-09 2 3.440609537412570e+02 3.440609537418112e+02 5.54166e-10 6.97497e-09 3 5.123217106332035e+02 5.123217106332437e+02 4.02451e-11 3.12036e-09 ----------------------------------------------------------------------------------------------------- 24 C 1 2.633429644978586e+02 2.633429644971233e+02 7.35326e-10 1.85310e-09 2 -1.192410808365084e+02 -1.192410808360182e+02 4.90218e-10 8.58478e-10 3 2.101766087423277e+02 2.101766087426616e+02 3.33813e-10 1.87657e-09 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.720775607416031e+02 -2.720775607421471e+02 5.43935e-10 1.33463e-09 2 6.183797397608523e+02 6.183797397605275e+02 3.24803e-10 5.60328e-09 3 1.003157660683585e+03 1.003157660684535e+03 9.49854e-10 9.86472e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -2.799035080805894e+02 -2.799035080805699e+02 1.94973e-11 6.08082e-09 2 2.300812613521028e+02 2.300812613523973e+02 2.94506e-10 4.60037e-09 3 2.093898467938897e+02 2.093898467940638e+02 1.74083e-10 3.33907e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 2.915119579239422e+03 2.915119579237820e+03 1.60207e-09 1.08637e-07 * 2 -2.044982514917250e+03 -2.044982514916755e+03 4.94538e-10 1.14576e-08 3 3.569681180456014e+02 3.569681180421052e+02 3.49621e-09 2.00845e-08 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.673831482920285e+03 -2.673831482919417e+03 8.67658e-10 4.66443e-08 2 1.321105329895284e+03 1.321105329896509e+03 1.22441e-09 6.33811e-08 3 -1.219078072933019e+03 -1.219078072930597e+03 2.42198e-09 6.95923e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 2.324641212472599e+02 2.324641212488446e+02 1.58474e-09 7.02246e-09 2 -7.059710488949377e+02 -7.059710488942665e+02 6.71207e-10 1.98947e-08 3 -1.864447150404676e+02 -1.864447150405491e+02 8.14850e-11 2.92573e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 7.346535365431011e+01 7.346535365413159e+01 1.78517e-10 5.65923e-09 2 -4.669495832299501e+01 -4.669495832302064e+01 2.56293e-11 6.11578e-10 3 -1.352960955053360e+02 -1.352960955054966e+02 1.60554e-10 8.33865e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.836177929347280e+01 -2.836177929350801e+01 3.52074e-11 2.89173e-08 2 -1.444035528992494e+01 -1.444035529036659e+01 4.41650e-10 7.74092e-10 3 -1.986459660021652e+01 -1.986459660049809e+01 2.81577e-10 5.48237e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 3.368906439923268e+01 3.368906439943443e+01 2.01752e-10 1.28578e-09 2 7.967836959497166e+01 7.967836959495018e+01 2.14726e-11 3.52661e-09 3 -4.160145995741983e+01 -4.160145995714873e+01 2.71108e-10 5.07265e-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 discontinuities. Maximum error obtained for particle = 6, direction = 3: |F_model - F_numer| error = ----------------------- = 7.06952e-11 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Si | a0 = 4.199018478393555 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.643552321468383e+01 -1.643552321475212e+01 6.82832e-11 1.49154e-09 2 -2.674559015565164e+00 -2.674559015560912e+00 4.25215e-12 1.07681e-10 3 1.390237044834518e+01 1.390237044832039e+01 2.47855e-11 1.23201e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 2.475050569160964e+01 2.475050569145920e+01 1.50436e-10 4.09450e-11 2 1.937356254484495e+01 1.937356254487152e+01 2.65636e-11 2.62324e-09 3 -1.535872343804890e+01 -1.535872343792670e+01 1.22199e-10 1.04443e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 5.218472205685926e+00 5.218472205662402e+00 2.35243e-11 2.53826e-09 2 -1.073759958383422e+01 -1.073759958379711e+01 3.71081e-11 1.19819e-09 3 3.067218390123376e+00 3.067218390098281e+00 2.50955e-11 1.30022e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.075818703895866e+01 -1.075818703890208e+01 5.65858e-11 4.04595e-10 2 -6.586045290560719e+00 -6.586045290565105e+00 4.38583e-12 2.01823e-10 3 -5.857896698529205e+00 -5.857896698525843e+00 3.36264e-12 1.17709e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.092480018889412e+01 -1.092480018893766e+01 4.35474e-11 3.77050e-11 2 -3.002115577301143e+00 -3.002115577298925e+00 2.21778e-12 7.19476e-10 3 -4.558441863494088e+00 -4.558441863495221e+00 1.13332e-12 3.20357e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.448709253857834e+00 2.448709253879860e+00 2.20259e-11 2.38573e-10 2 -1.350430897932780e+01 -1.350430897934331e+01 1.55094e-11 2.49395e-09 3 -5.883566955515202e+00 -5.883566955494439e+00 2.07629e-11 1.92951e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 6.872315878904274e+00 6.872315878930144e+00 2.58700e-11 1.50578e-09 2 5.943140392070005e+00 5.943140392084438e+00 1.44338e-11 8.70699e-10 3 1.412712199472533e+00 1.412712199473710e+00 1.17684e-12 2.06761e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.255408899173093e-01 3.255408899304142e-01 1.31049e-11 1.20025e-09 2 8.460185122312607e+00 8.460185122319286e+00 6.67910e-12 1.29625e-09 3 5.190188768226062e+00 5.190188768195499e+00 3.05631e-11 2.16981e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 1.396027977333077e+00 1.396027977338454e+00 5.37681e-12 3.30493e-11 2 -3.408562744209035e-01 -3.408562744259095e-01 5.00600e-12 2.65037e-11 3 5.827668270499297e-01 5.827668270539038e-01 3.97415e-12 2.93338e-09 * ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.646397438255119e+00 -1.646397438279467e+00 2.43481e-11 4.33247e-11 2 2.153477488480049e+00 2.153477488477283e+00 2.76623e-12 6.96518e-11 3 -4.009666561885898e+00 -4.009666561890640e+00 4.74198e-12 3.63503e-09 * ----------------------------------------------------------------------------------------------------- 11 Si 1 2.692588944073480e+00 2.692588944071619e+00 1.86029e-12 2.96519e-10 2 -8.088110776588870e+00 -8.088110776640212e+00 5.13420e-11 5.61856e-10 3 4.749155718011296e+00 4.749155718022038e+00 1.07425e-11 2.51384e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.776595165490654e+00 -2.776595165472628e+00 1.80265e-11 2.62103e-09 2 3.221632911393170e+00 3.221632911372958e+00 2.02127e-11 2.01667e-10 3 -3.512263526859083e+00 -3.512263526826504e+00 3.25797e-11 1.68263e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.426381137427050e+01 -1.426381137430966e+01 3.91651e-11 3.46802e-10 2 -7.933271391973833e+00 -7.933271391816010e+00 1.57823e-10 5.67724e-11 3 -9.344351058105197e+00 -9.344351058110162e+00 4.96492e-12 1.61069e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.619569700064313e+00 7.619569700067812e+00 3.49942e-12 2.65636e-10 2 -2.099204387337994e-01 -2.099204387347431e-01 9.43690e-13 1.77745e-09 3 3.903431310963278e+00 3.903431310975640e+00 1.23626e-11 2.08805e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 7.479979748502852e+00 7.479979748527145e+00 2.42935e-11 1.38330e-10 2 1.681155916438596e+01 1.681155916444346e+01 5.75007e-11 7.04961e-10 3 1.509730641279804e+01 1.509730641281662e+01 1.85860e-11 3.52588e-09 * ----------------------------------------------------------------------------------------------------- 16 Si 1 -6.013451601479658e-01 -6.013451600966013e-01 5.13645e-11 1.00028e-10 2 4.797012837555463e+00 4.797012837579665e+00 2.42020e-11 7.31126e-10 3 5.816954444521728e+00 5.816954444526483e+00 4.75531e-12 4.01643e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.249805385551536e+00 1.249805385549546e+00 1.99019e-12 1.38288e-10 2 -3.183177860317281e+00 -3.183177860300173e+00 1.71072e-11 1.77216e-10 3 4.490115150982501e+00 4.490115150960947e+00 2.15543e-11 1.03102e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.031761088782921e+00 2.031761088785057e+00 2.13563e-12 6.45382e-11 2 1.204208062364331e+01 1.204208062368201e+01 3.86997e-11 4.91085e-09 * 3 -1.214923357073565e+00 -1.214923357185520e+00 1.11955e-10 1.65221e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.597755395857797e+00 -4.597755395865661e+00 7.86393e-12 4.70735e-11 2 -3.553560426882240e+00 -3.553560426862558e+00 1.96820e-11 1.47921e-10 3 1.094483049716429e+00 1.094483049729794e+00 1.33646e-11 1.47145e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -4.936290325158439e-01 -4.936290325167087e-01 8.64753e-13 2.10398e-09 2 4.593560777868095e-02 4.593560777804565e-02 6.35297e-13 1.23306e-10 3 -1.309224323631654e-01 -1.309224323604992e-01 2.66620e-12 9.26294e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 4.607723848109206e-01 4.607723848077668e-01 3.15381e-12 9.44810e-11 2 -1.110320932614065e+01 -1.110320932615616e+01 1.55183e-11 3.76058e-10 3 5.045701057389729e+00 5.045701057441305e+00 5.15765e-11 2.96903e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 8.622011941876584e+00 8.622011941883102e+00 6.51745e-12 9.59481e-10 2 9.372564098462863e+00 9.372564098516131e+00 5.32676e-11 1.95588e-10 3 -1.459443242854555e+01 -1.459443242840050e+01 1.45045e-10 8.19716e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.278298530437536e+00 -2.278298530441654e+00 4.11760e-12 1.63838e-11 2 -9.387273351560484e+00 -9.387273351544946e+00 1.55378e-11 1.70571e-10 3 6.090303175811728e-01 6.090303175901894e-01 9.01668e-12 2.95000e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -9.011890185934755e+00 -9.011890185942786e+00 8.03091e-12 3.38662e-10 2 2.784019255678630e+00 2.784019255660479e+00 1.81508e-11 6.30362e-11 3 8.309886037396499e+00 8.309886037309628e+00 8.68710e-11 3.07551e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -4.874296390620053e+00 -4.874296390613332e+00 6.72085e-12 8.03583e-10 2 -4.420384788625249e+00 -4.420384788622398e+00 2.85105e-12 1.24622e-10 3 1.889339641978120e+00 1.889339641923564e+00 5.45561e-11 1.53741e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 6.460239948338775e+00 6.460239948338544e+00 2.30926e-13 4.38730e-10 2 4.173907782404680e+00 4.173907782428060e+00 2.33804e-11 1.12062e-10 3 -3.833964275284244e+00 -3.833964275359013e+00 7.47691e-11 1.06014e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.446229768630400e-01 -1.446229768459462e-01 1.70939e-11 1.59638e-10 2 -7.268736657849727e+00 -7.268736657876241e+00 2.65139e-11 4.04524e-10 3 2.524723447855510e+00 2.524723447866760e+00 1.12501e-11 2.47461e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.804772868368629e+00 -2.804772868354208e+00 1.44209e-11 5.21272e-11 2 -3.115085008304330e-01 -3.115085008698901e-01 3.94571e-11 9.55204e-11 3 2.312680695695289e+00 2.312680695683763e+00 1.15259e-11 1.72420e-09 ----------------------------------------------------------------------------------------------------- 29 Si 1 -6.064147181450024e+00 -6.064147181484662e+00 3.46381e-11 1.60230e-09 2 -5.845632734687503e+00 -5.845632734738671e+00 5.11680e-11 6.85565e-10 3 -1.528343656382272e+01 -1.528343656382873e+01 6.01119e-12 4.67433e-09 * ----------------------------------------------------------------------------------------------------- 30 Si 1 4.276960397063030e+00 4.276960397060626e+00 2.40430e-12 1.66475e-10 2 3.799930642249049e+00 3.799930642265453e+00 1.64042e-11 2.54166e-10 3 -3.107959781925892e+00 -3.107959781927640e+00 1.74749e-12 4.58100e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.462923983859818e+00 5.462923983844890e+00 1.49285e-11 4.08267e-10 2 -2.067007669754861e+00 -2.067007669762480e+00 7.61879e-12 1.10803e-09 3 3.174083853962799e+00 3.174083853963971e+00 1.17151e-12 1.81842e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.078867225162497e-01 3.078867225080387e-01 8.21099e-12 1.91401e-10 2 7.238270173695454e+00 7.238270173717937e+00 2.24825e-11 1.19077e-10 3 3.518401169383233e+00 3.518401169345164e+00 3.80691e-11 1.13127e-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 = 28, direction = 2: |F_model - F_numer| error = ----------------------- = 1.26665e-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 = 3.5952494672596913 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -8.414565335439575e+01 -8.414565335425435e+01 1.41398e-10 3.39425e-09 2 -5.972756357091230e+01 -5.972756357114362e+01 2.31324e-10 2.97531e-09 3 4.651022812566715e+01 4.651022812557586e+01 9.12834e-11 1.22128e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.486758637299782e+02 1.486758637297693e+02 2.08928e-10 5.48260e-09 2 3.531088670420192e+01 3.531088670426539e+01 6.34728e-11 3.56948e-10 3 -2.918512041122838e+01 -2.918512041119332e+01 3.50582e-11 2.30536e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.081966987371945e+01 -2.081966987380646e+01 8.70095e-11 2.02050e-10 2 1.798690157341275e+00 1.798690157360628e+00 1.93525e-11 2.20819e-09 3 2.241576992442848e+01 2.241576992449541e+01 6.69296e-11 2.79773e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.416415792337904e+01 -1.416415792335272e+01 2.63203e-11 7.00364e-11 2 -2.660877977705107e+01 -2.660877977679263e+01 2.58442e-10 1.89019e-10 3 -2.396245820712502e+01 -2.396245820722369e+01 9.86695e-11 3.74111e-09 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.256451328049001e+01 -1.256451328051531e+01 2.53007e-11 5.06174e-09 2 1.340999671465358e+01 1.340999671467074e+01 1.71667e-11 1.19609e-10 3 -1.898466957821876e+01 -1.898466957824984e+01 3.10756e-11 1.40382e-09 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.736767283222677e+01 -2.736767283247628e+01 2.49504e-10 1.41813e-09 2 7.746376728729199e+01 7.746376728650517e+01 7.86812e-10 1.28132e-09 3 -6.145689590011566e+01 -6.145689590022947e+01 1.13808e-10 5.12885e-04 * ----------------------------------------------------------------------------------------------------- 7 Si 1 1.900559168638854e+01 1.900559168637275e+01 1.57918e-11 4.91735e-10 2 -4.967521801171225e+01 -4.967521801175999e+01 4.77485e-11 2.26166e-10 3 7.329002634286387e+01 7.329002634312026e+01 2.56392e-10 5.92422e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 5.672649307289639e+00 5.672649307368898e+00 7.92593e-11 2.14173e-09 2 -2.228174857747311e+00 -2.228174857798980e+00 5.16689e-11 5.21363e-10 3 4.396486513385376e-01 4.396486513259966e-01 1.25410e-11 1.99428e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 -3.009196906578623e+01 -3.009196906577982e+01 6.40554e-12 1.18418e-09 2 6.714086696042169e+01 6.714086696046256e+01 4.08704e-11 5.33593e-09 3 3.648941840890526e+01 3.648941840897534e+01 7.00808e-11 7.16774e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 3.058863606937285e+01 3.058863606940149e+01 2.86420e-11 2.38730e-09 2 -5.161845466422199e+00 -5.161845466463816e+00 4.16174e-11 2.60201e-10 3 -1.711807798649271e+01 -1.711807798649325e+01 5.40012e-13 2.16421e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -9.199873225452986e+00 -9.199873225439003e+00 1.39835e-11 2.13728e-10 2 1.750089676612075e+00 1.750089676581579e+00 3.04963e-11 3.62692e-10 3 2.097849170954421e-01 2.097849170571527e-01 3.82893e-11 2.17119e-09 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.383907936358770e+01 -2.383907936352491e+01 6.27907e-11 2.77744e-10 2 -2.624961802243383e+01 -2.624961802241848e+01 1.53548e-11 1.39476e-10 3 8.683018377505890e+00 8.683018377473644e+00 3.22462e-11 1.17435e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 2.076476526812656e+01 2.076476526768062e+01 4.45933e-10 1.32581e-09 2 -2.155963798694734e+01 -2.155963798729208e+01 3.44748e-10 1.21288e-09 3 1.741433801588166e+00 1.741433801635252e+00 4.70863e-11 1.34474e-09 ----------------------------------------------------------------------------------------------------- 14 Si 1 -8.881349713745989e+00 -8.881349713772609e+00 2.66205e-11 5.89365e-10 2 4.746205494699587e+00 4.746205494709013e+00 9.42624e-12 9.53279e-10 3 -4.223525264853266e+00 -4.223525264856638e+00 3.37241e-12 9.59730e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 -5.501586514716097e+00 -5.501586514670489e+00 4.56080e-11 1.05107e-10 2 -1.029491406295364e+01 -1.029491406305834e+01 1.04704e-10 5.30942e-10 3 7.655238116136843e+00 7.655238116040680e+00 9.61631e-11 8.74918e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 4.077522503899229e-01 4.077522503839128e-01 6.01008e-12 5.01321e-10 2 7.378855656449930e-01 7.378855656555636e-01 1.05707e-11 6.04287e-11 3 -8.960883085704550e+00 -8.960883085689767e+00 1.47828e-11 1.62586e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.228031668426988e+01 -3.228031668429103e+01 2.11529e-11 4.47166e-10 2 -2.990522840167930e+01 -2.990522840159498e+01 8.43130e-11 1.28837e-08 * 3 -2.778920983701104e+01 -2.778920983703209e+01 2.10498e-11 1.18711e-09 ----------------------------------------------------------------------------------------------------- 18 Si 1 5.337998421128373e+01 5.337998421149796e+01 2.14229e-10 8.55565e-10 2 4.729366973285983e+01 4.729366973283197e+01 2.78675e-11 6.52413e-10 3 -4.257367751962549e+01 -4.257367751962398e+01 1.50635e-12 8.97764e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 3.236056578418619e+01 3.236056578420335e+01 1.71667e-11 9.49598e-10 2 -4.262182615519691e+01 -4.262182615538674e+01 1.89829e-10 4.01090e-09 3 1.387282332236293e+01 1.387282332230412e+01 5.88098e-11 1.17067e-09 ----------------------------------------------------------------------------------------------------- 20 Si 1 -3.085928475347219e+01 -3.085928475350392e+01 3.17364e-11 3.88713e-10 2 4.691442404243202e+01 4.691442404250281e+01 7.07843e-11 2.50967e-08 * 3 2.823834534862066e+01 2.823834534855029e+01 7.03722e-11 1.50229e-08 * ----------------------------------------------------------------------------------------------------- 21 C 1 -3.172024744431958e+01 -3.172024744443398e+01 1.14394e-10 6.05564e-10 2 -1.606386256253395e+01 -1.606386256259441e+01 6.04530e-11 2.39157e-09 3 -3.968899193840086e+01 -3.968899193834855e+01 5.23102e-11 8.14801e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.012450720472266e+01 -1.012450720473107e+01 8.40572e-12 1.14824e-10 2 -2.818252748094472e+01 -2.818252748093929e+01 5.42855e-12 4.43126e-10 3 -2.612645217414259e+01 -2.612645217427622e+01 1.33635e-10 3.79440e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 9.820818399473671e+00 9.820818399461315e+00 1.23563e-11 1.05581e-10 2 2.037957921159569e+01 2.037957921163732e+01 4.16271e-11 9.55701e-10 3 3.187101655255806e+01 3.187101655255845e+01 3.87246e-13 6.27043e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 2.638124143012486e+01 2.638124143008642e+01 3.84439e-11 1.55168e-10 2 -9.837509838505117e+00 -9.837509838523328e+00 1.82112e-11 3.70418e-10 3 3.470647591603366e+00 3.470647591607838e+00 4.47242e-12 1.55964e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.370809433856260e+00 -2.370809433851176e+00 5.08393e-12 8.20850e-11 2 -5.663169343486070e+00 -5.663169343486804e+00 7.34524e-13 1.33232e-10 3 -1.312621718976524e+01 -1.312621718964193e+01 1.23311e-10 2.79673e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.092198992681916e+00 1.092198992694272e+00 1.23563e-11 1.10054e-10 2 1.798508681274156e+00 1.798508681298262e+00 2.41052e-11 6.59155e-11 3 5.730368957405390e+00 5.730368957437691e+00 3.23013e-11 8.81180e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 7.254717584934132e+00 7.254717584990485e+00 5.63531e-11 1.18135e-08 * 2 -3.511658576209810e+01 -3.511658576216577e+01 6.76650e-11 4.05847e-09 3 -1.513204088509401e+00 -1.513204088567878e+00 5.84768e-11 1.21547e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -1.276535445890259e+01 -1.276535445891619e+01 1.35945e-11 4.30663e-09 2 2.126423433257806e+01 2.126423433258260e+01 4.54037e-12 3.50354e-10 3 4.080714556960897e+00 4.080714556930816e+00 3.00817e-11 3.74625e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 3.249562020851680e+00 3.249562020933210e+00 8.15303e-11 2.60847e-10 2 -9.431354765546450e+00 -9.431354765639348e+00 9.28981e-11 5.09309e-09 3 -5.732915902441024e+00 -5.732915902433202e+00 7.82219e-12 2.28010e-08 * ----------------------------------------------------------------------------------------------------- 30 C 1 -4.511250623969029e-01 -4.511250623811182e-01 1.57847e-11 7.90610e-11 2 6.787758965495907e+00 6.787758965513444e+00 1.75380e-11 6.06946e-11 3 8.949145537657220e+00 8.949145537659023e+00 1.80300e-12 1.56078e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.573085732547425e+00 -5.573085732521923e+00 2.55023e-11 9.98774e-11 2 3.151372422787625e+01 3.151372422793926e+01 6.30109e-11 1.21748e-09 3 3.037998235555442e+01 3.037998235563533e+01 8.09095e-11 2.69839e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.065909186905628e+00 4.065909186891186e+00 1.44427e-11 4.66916e-08 * 2 1.752831119151825e-02 1.752831119972169e-02 8.20343e-12 8.18035e-07 * 3 -3.585311804618613e+00 -3.585311804617453e+00 1.15996e-12 4.90310e-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 = 11, direction = 3: |F_model - F_numer| error = ----------------------- = 1.82517e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.82517e-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 1.82517e-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.