!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EDIP_LAMMPS_JiangMorganSzlufarska_2012_SiC__MO_667792548433_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 = 2.905337333679199 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 6.824787398707462e+00 6.824787398684383e+00 2.30793e-11 3.01377e-11 2 9.307021081520057e+00 9.307021081518446e+00 1.61116e-12 1.67120e-11 3 1.601035185503866e+01 1.601035185504912e+01 1.04592e-11 9.34790e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 3.586395816621181e+00 3.586395816612037e+00 9.14380e-12 5.57803e-11 2 -6.074770752159531e+00 -6.074770752165437e+00 5.90550e-12 9.00826e-11 3 8.509463058309439e-01 8.509463058296584e-01 1.28553e-12 3.15769e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -5.742993049261171e+00 -5.742993049270406e+00 9.23439e-12 2.62433e-10 2 8.767499748317609e-01 8.767499748350075e-01 3.24663e-12 1.59713e-11 3 -1.032678854047965e+01 -1.032678854042873e+01 5.09228e-11 2.90782e-09 * ----------------------------------------------------------------------------------------------------- 4 C 1 -5.599166632642756e-01 -5.599166632633139e-01 9.61675e-13 7.02570e-11 2 -1.086736017792041e+01 -1.086736017791174e+01 8.66685e-12 4.44438e-09 * 3 -8.823995807915942e+00 -8.823995807945764e+00 2.98215e-11 1.57472e-09 * ----------------------------------------------------------------------------------------------------- 5 C 1 -1.298703149462245e+01 -1.298703149463486e+01 1.24096e-11 1.17273e-10 2 4.841448738920272e+00 4.841448738912366e+00 7.90656e-12 1.49162e-10 3 7.650592948640747e+00 7.650592948597861e+00 4.28857e-11 1.22041e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.039182469146723e+00 -1.039182469138041e+00 8.68172e-12 8.89648e-11 2 -5.092600654583558e+00 -5.092600654590751e+00 7.19336e-12 5.97717e-11 3 8.352725521195740e+00 8.352725521182535e+00 1.32054e-11 2.77096e-08 * ----------------------------------------------------------------------------------------------------- 7 C 1 -3.694803911238605e+00 -3.694803911227983e+00 1.06226e-11 1.68969e-10 2 7.449526061008061e+00 7.449526061008706e+00 6.44818e-13 3.09202e-11 3 -4.085837294044548e+00 -4.085837294078050e+00 3.35021e-11 1.80878e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 8.795673961509682e+00 8.795673961512390e+00 2.70894e-12 8.94490e-09 * 2 -8.384335398831684e+00 -8.384335398785641e+00 4.60432e-11 3.08331e-10 3 -8.933686562011722e-01 -8.933686561307455e-01 7.04268e-11 5.76026e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 6.437679115965127e+00 6.437679115966644e+00 1.51612e-12 6.56613e-11 2 1.173184447399663e+01 1.173184447394382e+01 5.28129e-11 3.89905e-10 3 1.128900290733121e+01 1.128900290736219e+01 3.09779e-11 1.68344e-09 * ----------------------------------------------------------------------------------------------------- 10 C 1 -7.726012414966176e+00 -7.726012414966553e+00 3.77476e-13 6.77920e-11 2 -7.007147564571299e+00 -7.007147564564651e+00 6.64802e-12 3.29990e-10 3 4.014199252396669e+00 4.014199252393958e+00 2.71161e-12 6.31237e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -1.559297046733325e+01 -1.559297046728777e+01 4.54801e-11 5.71687e-10 2 4.280813678139268e-01 4.280813677847300e-01 2.91968e-11 4.26185e-10 3 -9.925132512519571e+00 -9.925132512520564e+00 9.92983e-13 1.45199e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 4.158803728093470e+00 4.158803728104339e+00 1.08695e-11 1.28176e-10 2 -9.055105409221762e+00 -9.055105409228370e+00 6.60805e-12 2.78682e-10 3 -5.149383246424021e+00 -5.149383246435668e+00 1.16467e-11 7.30909e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 1.632691748251624e+00 1.632691748246859e+00 4.76530e-12 6.13869e-11 2 2.617989948519674e+00 2.617989948514167e+00 5.50671e-12 1.22312e-10 3 -1.002874538097908e+01 -1.002874538098404e+01 4.95426e-12 1.96057e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -4.565496008276341e+00 -4.565496008277396e+00 1.05516e-12 4.67004e-11 2 -8.023279030226071e+00 -8.023279030225840e+00 2.30926e-13 6.93845e-12 3 3.920618300704198e+00 3.920618300700984e+00 3.21432e-12 5.70095e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 9.275119485234361e+00 9.275119485210222e+00 2.41389e-11 2.35682e-10 2 -9.457597411888491e-01 -9.457597411882745e-01 5.74540e-13 3.90518e-10 3 -6.995823281952082e+00 -6.995823281965920e+00 1.38378e-11 2.56883e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 1.454549973550645e+00 1.454549973563528e+00 1.28828e-11 2.54228e-10 2 3.002769175518813e+00 3.002769175507597e+00 1.12159e-11 2.59022e-10 3 -1.317468989628765e+01 -1.317468989627700e+01 1.06510e-11 4.44675e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 1.768007971685014e+01 1.768007971683136e+01 1.87832e-11 2.07560e-10 2 8.903414397527637e+00 8.903414397522058e+00 5.57954e-12 1.02478e-10 3 5.945616029033473e+00 5.945616029030006e+00 3.46656e-12 7.33946e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 -7.094713336566138e+00 -7.094713336593036e+00 2.68976e-11 2.12504e-10 2 -5.255246873043605e+00 -5.255246873014658e+00 2.89466e-11 6.98156e-10 3 1.261838114027045e+01 1.261838114029343e+01 2.29843e-11 3.88004e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 -7.874263743068737e+00 -7.874263743063281e+00 5.45608e-12 7.48256e-09 * 2 1.401029553888538e+01 1.401029553887118e+01 1.42037e-11 1.06635e-10 3 -5.562625736429905e+00 -5.562625736423813e+00 6.09202e-12 1.45727e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 1.155384276434246e+01 1.155384276434123e+01 1.22924e-12 1.27789e-10 2 -1.207773094930541e+01 -1.207773094929993e+01 5.48006e-12 7.71401e-11 3 -1.420399610737696e+01 -1.420399610736339e+01 1.35749e-11 7.93134e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 1.449720333831771e+01 1.449720333836539e+01 4.76827e-11 7.02970e-10 2 7.825533807658944e+00 7.825533807699783e+00 4.08384e-11 7.58657e-10 3 5.929212241248074e+00 5.929212241275251e+00 2.71774e-11 1.15785e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 -5.511324960895736e+00 -5.511324960887758e+00 7.97762e-12 3.18105e-10 2 -8.433090084052779e+00 -8.433090084039140e+00 1.36389e-11 1.18247e-10 3 8.308344971301867e+00 8.308344971300011e+00 1.85629e-12 9.38627e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -7.845279628560484e+00 -7.845279628563201e+00 2.71694e-12 9.37490e-11 2 4.054441267538006e+00 4.054441267540904e+00 2.89813e-12 1.02323e-10 3 -1.701171268963163e+01 -1.701171268963452e+01 2.89191e-12 2.64642e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -6.103699024604613e+00 -6.103699024607312e+00 2.69917e-12 9.06963e-11 2 -7.439686927637151e+00 -7.439686927626443e+00 1.07079e-11 1.55381e-10 3 -7.002153237867402e+00 -7.002153237862680e+00 4.72244e-12 2.50433e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 5.255938902105399e+00 5.255938902118336e+00 1.29372e-11 2.96685e-10 2 9.028947679715152e+00 9.028947679695296e+00 1.98561e-11 6.51902e-10 3 -3.128500245917116e-01 -3.128500245979325e-01 6.22086e-12 1.22781e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.173922168051181e+01 -1.173922168047775e+01 3.40563e-11 5.96465e-11 2 -7.141922851558311e-01 -7.141922851263913e-01 2.94398e-11 3.18914e-09 * 3 1.733170285681504e+01 1.733170285683450e+01 1.94618e-11 5.22167e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 3.794790482864477e-01 3.794790482785129e-01 7.93476e-12 1.94464e-10 2 6.232936825598901e+00 6.232936825605519e+00 6.61782e-12 3.64472e-10 3 -5.097351301473193e+00 -5.097351301468477e+00 4.71623e-12 5.36216e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 3.510488550139264e+00 3.510488550145735e+00 6.47127e-12 7.14291e-11 2 -3.787365138196360e+00 -3.787365138189114e+00 7.24576e-12 6.28999e-11 3 -4.820624951196956e+00 -4.820624951192368e+00 4.58833e-12 1.62544e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 8.964482240453009e+00 8.964482240460821e+00 7.81242e-12 2.88912e-10 2 4.715790401448734e+00 4.715790401460644e+00 1.19105e-11 3.64929e-10 3 2.126472435354764e+01 2.126472435353308e+01 1.45555e-11 3.71863e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 1.755457228200503e+00 1.755457228202379e+00 1.87583e-12 8.01181e-11 2 -3.345180311952711e+00 -3.345180311970703e+00 1.79918e-11 1.64857e-10 3 1.034791543319750e+01 1.034791543318404e+01 1.34666e-11 1.05310e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -7.401914221083914e+00 -7.401914221070505e+00 1.34097e-11 6.00080e-11 2 9.218449236017138e+00 9.218449235964904e+00 5.22338e-11 6.45830e-11 3 -5.755309172923084e+00 -5.755309172918496e+00 4.58833e-12 1.03340e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 -2.838499432280629e-01 -2.838499432336558e-01 5.59286e-12 1.17689e-07 * 2 -7.742388678472084e+00 -7.742388678470199e+00 1.88471e-12 4.14465e-10 3 -4.663946278257647e+00 -4.663946278260927e+00 3.28004e-12 8.21627e-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 = 8, direction = 3: |F_model - F_numer| error = ----------------------- = 7.88328e-11 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Si | a0 = 3.9393434524536133 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.764101478364099e+00 1.764101478357567e+00 6.53211e-12 1.99421e-09 2 2.733589828380034e+00 2.733589828377418e+00 2.61613e-12 2.46856e-11 3 1.366496193482296e+00 1.366496193486336e+00 4.03988e-12 1.01713e-07 * ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.850660796852486e-01 -4.850660796518281e-01 3.34205e-11 1.46116e-07 * 2 -1.174996279001177e+00 -1.174996278991088e+00 1.00890e-11 1.35688e-10 3 -6.708822782864057e-01 -6.708822782979504e-01 1.15448e-11 1.30977e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.068112011406878e+01 1.068112011401054e+01 5.82343e-11 2.62199e-10 2 -1.653788383043305e-01 -1.653788383231373e-01 1.88068e-11 7.33522e-11 3 -2.709873553019833e+00 -2.709873553039733e+00 1.98996e-11 1.17101e-07 * ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.221039661588624e+00 -3.221039661591616e+00 2.99183e-12 5.62475e-11 2 8.234469992931241e-01 8.234469992957930e-01 2.66887e-12 1.27425e-11 3 -4.192856596170505e+00 -4.192856596200622e+00 3.01172e-11 2.28313e-09 * ----------------------------------------------------------------------------------------------------- 5 Si 1 6.963299267631821e+00 6.963299267634695e+00 2.87415e-12 2.11588e-08 * 2 1.250637980447276e+01 1.250637980445603e+01 1.67315e-11 3.78929e-10 3 6.181880213896958e+00 6.181880213873363e+00 2.35953e-11 1.93645e-07 * ----------------------------------------------------------------------------------------------------- 6 Si 1 -8.306693977411591e+00 -8.306693977482198e+00 7.06066e-11 1.54348e-10 2 -1.088841963423688e+01 -1.088841963425150e+01 1.46265e-11 3.16552e-10 3 5.622947785154641e+00 5.622947785180694e+00 2.60529e-11 6.99317e-08 * ----------------------------------------------------------------------------------------------------- 7 Si 1 -8.361848451083484e+00 -8.361848451085841e+00 2.35723e-12 1.25672e-10 2 8.313611740019045e+00 8.313611740008062e+00 1.09832e-11 2.36788e-12 3 2.308672011513428e-01 2.308672011552826e-01 3.93979e-12 1.49483e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.482900921103485e+00 -1.482900921126888e+00 2.34031e-11 3.01827e-09 * 2 -8.633578813542879e+00 -8.633578813557063e+00 1.41842e-11 2.94753e-07 * 3 -5.863127310967448e+00 -5.863127310964177e+00 3.27027e-12 3.68695e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 5.187851254133402e+00 5.187851254105100e+00 2.83018e-11 5.47500e-11 2 5.576895249124938e+00 5.576895249109532e+00 1.54063e-11 4.95445e-10 3 1.926447062644008e+00 1.926447062644295e+00 2.87104e-13 1.46049e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.662257397040911e+00 -9.662257397064405e+00 2.34941e-11 9.07185e-12 2 -8.496478773264633e+00 -8.496478773362242e+00 9.76090e-11 1.39830e-09 3 6.848690658109807e+00 6.848690658114916e+00 5.10880e-12 7.91172e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -2.248663934002326e+00 -2.248663934000315e+00 2.01039e-12 1.41521e-09 2 5.921819020183218e+00 5.921819020208779e+00 2.55609e-11 5.83390e-10 3 -7.086033082464110e+00 -7.086033082459318e+00 4.79172e-12 1.48692e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 7.742116924745956e+00 7.742116924750937e+00 4.98090e-12 4.37899e-11 2 -3.425154944664833e+00 -3.425154944668737e+00 3.90399e-12 8.35274e-11 3 -4.094169109531260e+00 -4.094169109541408e+00 1.01474e-11 1.53215e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 8.577817339505945e+00 8.577817339499648e+00 6.29718e-12 1.74871e-07 * 2 6.122652627230480e+00 6.122652627231085e+00 6.05738e-13 1.40203e-10 3 1.046822831494374e+01 1.046822831493510e+01 8.64198e-12 1.86818e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -7.341384881092864e+00 -7.341384881093349e+00 4.84945e-13 1.99754e-10 2 -5.816186554412154e+00 -5.816186554400871e+00 1.12834e-11 1.49744e-10 3 1.043224101137555e+01 1.043224101138486e+01 9.31699e-12 3.18444e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 -5.753805223439932e+00 -5.753805223587900e+00 1.47968e-10 6.15064e-08 * 2 -5.416774078549637e-01 -5.416774078481439e-01 6.81977e-12 6.14148e-08 * 3 -3.267786589867763e+00 -3.267786589842335e+00 2.54277e-11 4.40743e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 7.373552262156926e+00 7.373552262176637e+00 1.97113e-11 7.55501e-09 * 2 -7.906521515800635e+00 -7.906521515856284e+00 5.56488e-11 2.63444e-10 3 -6.451817430825304e+00 -6.451817430776543e+00 4.87610e-11 1.95350e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 2.723781407089596e-02 2.723781407308099e-02 2.18503e-12 1.80134e-11 2 1.627391870123089e-01 1.627391870170020e-01 4.69311e-12 5.82009e-11 3 1.595062740546845e+01 1.595062740546946e+01 1.00719e-12 1.03546e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 -2.529651304389988e-01 -2.529651304374174e-01 1.58146e-12 6.05178e-11 2 2.475144786996911e+00 2.475144787027571e+00 3.06599e-11 6.40150e-11 3 2.113910344725161e+00 2.113910344724419e+00 7.42073e-13 4.43161e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -1.250141060960949e+01 -1.250141060959546e+01 1.40332e-11 3.82949e-10 2 8.573318369769172e+00 8.573318369771277e+00 2.10498e-12 4.25846e-11 3 -7.958992400908914e+00 -7.958992400901642e+00 7.27240e-12 5.91197e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 7.601804369088989e+00 7.601804369085122e+00 3.86713e-12 3.67770e-10 2 -1.181602093712286e+01 -1.181602093709877e+01 2.40910e-11 3.44763e-09 * 3 -4.516213059157145e+00 -4.516213059208294e+00 5.11484e-11 8.81959e-09 * ----------------------------------------------------------------------------------------------------- 21 Si 1 5.231649295599532e+00 5.231649295548164e+00 5.13687e-11 4.75661e-08 * 2 -2.348915236662374e+00 -2.348915236668650e+00 6.27542e-12 1.56151e-11 3 -5.383757297071251e+00 -5.383757297114586e+00 4.33351e-11 5.97222e-08 * ----------------------------------------------------------------------------------------------------- 22 Si 1 -8.053997867383737e+00 -8.053997867412470e+00 2.87326e-11 5.79892e-10 2 6.710469989638889e+00 6.710469989657924e+00 1.90354e-11 2.24757e-10 3 4.916456812313552e+00 4.916456812315810e+00 2.25864e-12 1.89289e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.911468741730619e+00 -3.911468741745423e+00 1.48042e-11 6.06552e-08 * 2 5.864217103979037e+00 5.864217103956855e+00 2.21823e-11 1.86109e-11 3 -1.550258225453028e+00 -1.550258225411674e+00 4.13545e-11 1.92630e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.257656507198771e+01 1.257656507198358e+01 4.13358e-12 9.24363e-11 2 2.471376612526152e+00 2.471376612525784e+00 3.68150e-13 9.53215e-11 3 -6.999639667394545e+00 -6.999639667398275e+00 3.73035e-12 1.78478e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.938038763579731e-01 -1.938038763642234e-01 6.25036e-12 1.98792e-11 2 5.609811937567634e+00 5.609811937583088e+00 1.54543e-11 1.01990e-10 3 5.928203171257475e+00 5.928203171259817e+00 2.34213e-12 7.94642e-09 * ----------------------------------------------------------------------------------------------------- 26 Si 1 -8.305611892670393e+00 -8.305611892691092e+00 2.06981e-11 5.03722e-11 2 -6.107834453975343e+00 -6.107834453993087e+00 1.77440e-11 9.40679e-11 3 7.930119671300375e+00 7.930119671318587e+00 1.82121e-11 9.66560e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 4.373843162488319e+00 4.373843162517953e+00 2.96341e-11 5.24141e-11 2 7.937476119216164e+00 7.937476119219289e+00 3.12461e-12 4.09843e-10 3 -4.731657838684456e+00 -4.731657838694723e+00 1.02665e-11 2.04810e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 9.524631630616696e+00 9.524631630625173e+00 8.47677e-12 3.98824e-10 2 -1.797863766385956e+00 -1.797863766374382e+00 1.15741e-11 1.22337e-10 3 -6.390138504903348e+00 -6.390138504898434e+00 4.91340e-12 4.67325e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 4.964609961170258e+00 4.964609961168696e+00 1.56231e-12 5.29268e-10 2 1.875270561668292e+00 1.875270561693085e+00 2.47935e-11 5.59958e-10 3 2.383975004903855e+00 2.383975004944700e+00 4.08451e-11 3.48769e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.672282506436883e+00 -8.672282506461531e+00 2.46487e-11 3.20140e-09 * 2 -1.677726935606856e+00 -1.677726935609463e+00 2.60658e-12 2.18847e-11 3 3.620097730821072e+00 3.620097730814824e+00 6.24834e-12 1.06566e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -7.923265658112562e+00 -7.923265658113259e+00 6.97220e-13 1.47045e-10 2 -5.349166538230886e+00 -5.349166538261741e+00 3.08553e-11 6.01803e-11 3 -5.252942132632704e+00 -5.252942132652305e+00 1.96012e-11 2.59819e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.088266863559796e+00 4.088266863521011e+00 3.87850e-11 4.65023e-10 2 -7.532299308011405e+00 -7.532299308020154e+00 8.74945e-12 6.37166e-10 3 -8.801043504210263e+00 -8.801043504253762e+00 4.34994e-11 3.29536e-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 = 3, direction = 2: |F_model - F_numer| error = ----------------------- = 1.13719e-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 = 3.3446998575149336 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 4.870742095005588e+00 4.870742095004114e+00 1.47438e-12 1.66605e-11 2 3.845455399148110e+00 3.845455399150972e+00 2.86127e-12 6.78946e-11 3 3.558171930940980e+00 3.558171930952308e+00 1.13274e-11 5.34556e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 -7.252093099687379e+00 -7.252093099683977e+00 3.40172e-12 9.27551e-11 2 -2.026376557233565e+00 -2.026376557234857e+00 1.29186e-12 1.76525e-09 * 3 5.948135059220769e+00 5.948135059226741e+00 5.97122e-12 4.23519e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -6.740852594852226e+00 -6.740852594867077e+00 1.48512e-11 9.81182e-08 * 2 3.158821424052783e+00 3.158821424060736e+00 7.95231e-12 4.99742e-11 3 5.302526648642003e+00 5.302526648654931e+00 1.29283e-11 8.12046e-07 * ----------------------------------------------------------------------------------------------------- 4 C 1 2.868633566241056e+00 2.868633566269909e+00 2.88525e-11 1.21103e-12 2 6.896047365303078e+00 6.896047365294276e+00 8.80185e-12 1.48796e-10 3 -8.688791215575590e+00 -8.688791215561583e+00 1.40066e-11 9.38112e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.608607789200036e-01 1.608607789174237e-01 2.57994e-12 1.30202e-11 2 -4.733502671683514e+00 -4.733502671681902e+00 1.61204e-12 8.48743e-12 3 7.995019638329439e-01 7.995019638293570e-01 3.58691e-12 4.35931e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.492830625277349e+00 2.492830625269319e+00 8.03002e-12 2.24754e-11 2 -1.177114923097520e+00 -1.177114923097198e+00 3.22409e-13 1.26134e-10 3 3.130557169444776e+00 3.130557169451180e+00 6.40377e-12 1.51787e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -1.681870489902312e+00 -1.681870489910037e+00 7.72515e-12 5.58975e-11 2 1.821829509532497e+00 1.821829509538159e+00 5.66258e-12 1.01335e-10 3 -1.906685540483072e+00 -1.906685540479255e+00 3.81695e-12 5.39082e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 3.266342899500344e+00 3.266342899498767e+00 1.57696e-12 2.27458e-10 2 7.105538705076494e+00 7.105538705100633e+00 2.41389e-11 2.89218e-10 3 2.810142209928188e+00 2.810142209919973e+00 8.21432e-12 8.07123e-09 * ----------------------------------------------------------------------------------------------------- 9 Si 1 -8.096808797178369e-01 -8.096808797244417e-01 6.60483e-12 5.45138e-10 2 -8.638652925749943e+00 -8.638652925738491e+00 1.14522e-11 1.74001e-10 3 3.894709830049023e+00 3.894709830045506e+00 3.51630e-12 3.44591e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 5.505879630252099e+00 5.505879630225624e+00 2.64748e-11 4.45164e-11 2 -5.793638266520010e+00 -5.793638266523928e+00 3.91776e-12 2.22862e-11 3 9.307845800337084e+00 9.307845800311833e+00 2.52509e-11 1.26892e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 1.327934833764858e+01 1.327934833766442e+01 1.58380e-11 1.63988e-10 2 1.455186428320009e+00 1.455186428325186e+00 5.17697e-12 4.51150e-10 3 -9.567979189822218e-01 -9.567979189717551e-01 1.04666e-11 3.68138e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 6.061457545194408e+00 6.061457545198097e+00 3.68949e-12 6.88898e-09 * 2 -1.936831883680211e+00 -1.936831883685781e+00 5.56954e-12 8.82368e-11 3 1.026075579781682e+01 1.026075579779919e+01 1.76268e-11 1.76843e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -5.486850800547519e+00 -5.486850800543866e+00 3.65308e-12 1.24550e-10 2 9.029264872464342e+00 9.029264872456002e+00 8.34000e-12 1.54870e-10 3 1.235246021881247e+01 1.235246021881320e+01 7.35412e-13 2.27068e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 2 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 3 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 ----------------------------------------------------------------------------------------------------- 15 C 1 -5.920425987124742e-01 -5.920425987276989e-01 1.52247e-11 1.17486e-10 2 3.819063482351801e-01 3.819063482440208e-01 8.84071e-12 5.87809e-11 3 4.756566284170261e+00 4.756566284165519e+00 4.74198e-12 2.45558e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -3.284174295207533e+00 -3.284174295207479e+00 5.41789e-14 2.33555e-10 2 -5.206946636931134e+00 -5.206946636912119e+00 1.90150e-11 2.39711e-10 3 -6.026366886791909e+00 -6.026366886792998e+00 1.08891e-12 2.65147e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 2.000938234454916e+01 2.000938234453016e+01 1.90035e-11 2.02606e-09 * 2 5.255047422629704e+00 5.255047422642718e+00 1.30145e-11 2.99683e-08 * 3 3.592891155613076e+00 3.592891155640441e+00 2.73652e-11 2.94206e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 -2.414784907545026e+00 -2.414784907529249e+00 1.57767e-11 5.25399e-09 * 2 -1.134357778552575e+01 -1.134357778551580e+01 9.94937e-12 5.28672e-10 3 2.974397784006529e+00 2.974397784002663e+00 3.86624e-12 1.78382e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 -1.221028202818506e+01 -1.221028202823442e+01 4.93632e-11 3.41150e-08 * 2 5.759554409202123e+00 5.759554409189461e+00 1.26628e-11 1.44392e-10 3 -1.316658524154420e+01 -1.316658524152874e+01 1.54579e-11 5.05498e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 6.178701485640595e+00 6.178701485681294e+00 4.06990e-11 2.38880e-10 2 2.369685918692281e+00 2.369685918693231e+00 9.50351e-13 7.09668e-11 3 -4.820029087875742e+00 -4.820029087913686e+00 3.79439e-11 4.28800e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.410068763609696e+00 -3.410068763610271e+00 5.75096e-13 1.35648e-10 2 -1.828064861689040e+00 -1.828064861682643e+00 6.39777e-12 6.90248e-12 3 -4.363917278166314e+00 -4.363917278168100e+00 1.78613e-12 2.56879e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -3.733974296096023e-01 -3.733974295838243e-01 2.57780e-11 7.94733e-11 2 7.598221814206802e+00 7.598221814217435e+00 1.06333e-11 8.03464e-11 3 -8.377371527193535e+00 -8.377371527194484e+00 9.48575e-13 1.89939e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.436739769002679e+00 -3.436739769005478e+00 2.79909e-12 2.99982e-11 2 1.230183045828007e+00 1.230183045821789e+00 6.21836e-12 7.88696e-11 3 8.050592539656693e+00 8.050592539658865e+00 2.17248e-12 8.49631e-12 ----------------------------------------------------------------------------------------------------- 24 C 1 1.229974463185838e+00 1.229974463189593e+00 3.75544e-12 1.93170e-11 2 -4.919510407931194e+00 -4.919510407941751e+00 1.05569e-11 1.34796e-10 3 -5.966375084023777e+00 -5.966375083999732e+00 2.40448e-11 1.68337e-09 * ----------------------------------------------------------------------------------------------------- 25 C 1 3.197335240956962e+00 3.197335240963815e+00 6.85274e-12 4.18336e-11 2 1.413328542050528e+00 1.413328542048428e+00 2.09965e-12 8.34568e-11 3 -3.107208996287591e+00 -3.107208996279495e+00 8.09530e-12 7.93405e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.107393545155526e+01 -1.107393545156643e+01 1.11715e-11 1.55836e-10 2 -1.957821302877124e+00 -1.957821302877651e+00 5.26690e-13 5.36056e-11 3 5.227303561873002e-01 5.227303561918909e-01 4.59066e-12 7.13201e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 5.635993094150687e+00 5.635993094148584e+00 2.10321e-12 2.32312e-11 2 -6.738317267676008e-01 -6.738317267711593e-01 3.55849e-12 3.14574e-11 3 -8.963824400166237e-01 -8.963824400128229e-01 3.80085e-12 2.02113e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 2.878817990304449e+00 2.878817990309339e+00 4.88987e-12 1.30091e-10 2 4.447772222777129e+00 4.447772222775074e+00 2.05436e-12 1.39840e-10 3 -5.625697071758404e+00 -5.625697071750370e+00 8.03446e-12 1.15183e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 -1.631845531795182e+01 -1.631845531794022e+01 1.16032e-11 3.25127e-10 2 -8.112443223814608e+00 -8.112443223814346e+00 2.62901e-13 2.52856e-10 3 -9.518541097595035e+00 -9.518541097627468e+00 3.24327e-11 8.04009e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 7.306468543430600e-01 7.306468543318740e-01 1.11859e-11 1.51277e-09 * 2 2.522080629321845e+00 2.522080629317488e+00 4.35740e-12 1.46224e-10 3 -1.506959359127483e+01 -1.506959359126344e+01 1.13953e-11 2.87890e-09 * ----------------------------------------------------------------------------------------------------- 31 Si 1 7.512372652437643e+00 7.512372652442819e+00 5.17630e-12 5.33724e-11 2 -1.369607046500001e+01 -1.369607046499624e+01 3.77831e-12 4.13749e-11 3 8.415663978825449e+00 8.415663978834772e+00 9.32232e-12 5.66089e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.079409117752140e+01 -1.079409117752322e+01 1.81544e-12 1.10717e-10 2 7.754459581660314e+00 7.754459581669336e+00 9.02212e-12 2.16795e-11 3 2.812694250084483e+00 2.812694250063675e+00 2.08087e-11 3.91487e-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 = 1: |F_model - F_numer| error = ----------------------- = 6.90363e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.13719e-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 1.13719e-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.