!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_CuiGaoCui_2012_LiSi__MO_557492625287_001 Supported species : Li 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 = Li | a0 = 4.350019454956055 | (Configuration in file "config-Li.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Li 1 5.355470140923003e-02 5.355470141169270e-02 2.46266e-12 9.61153e-12 2 -4.656082285943406e-02 -4.656082286198447e-02 2.55041e-12 2.34313e-11 3 1.278541750708488e-02 1.278541750764450e-02 5.59620e-13 1.38210e-11 ----------------------------------------------------------------------------------------------------- 2 Li 1 1.561971114440072e-01 1.561971114415873e-01 2.41990e-12 5.42070e-11 2 3.324564076116588e-01 3.324564075998645e-01 1.17943e-11 4.50962e-11 3 1.242007787013894e-01 1.242007787045915e-01 3.20211e-12 1.04576e-10 ----------------------------------------------------------------------------------------------------- 3 Li 1 3.468714749843162e-01 3.468714749862823e-01 1.96615e-12 6.80787e-11 2 1.003150372074664e-01 1.003150371968957e-01 1.05707e-11 3.87182e-11 3 1.392138132259322e-01 1.392138132240015e-01 1.93071e-12 4.07311e-11 ----------------------------------------------------------------------------------------------------- 4 Li 1 1.208427753866624e-01 1.208427753862687e-01 3.93685e-13 2.18022e-11 2 1.546331593665565e-01 1.546331593454777e-01 2.10788e-11 6.55901e-11 3 2.746241446576435e-01 2.746241446597656e-01 2.12214e-12 3.84979e-11 ----------------------------------------------------------------------------------------------------- 5 Li 1 -1.119809712319715e-01 -1.119809712345755e-01 2.60404e-12 3.48032e-11 2 -1.755694240802323e-02 -1.755694240528546e-02 2.73777e-12 4.16170e-11 3 1.521751723027794e-02 1.521751723300361e-02 2.72567e-12 3.57375e-11 ----------------------------------------------------------------------------------------------------- 6 Li 1 -8.348987990482147e-02 -8.348987991027428e-02 5.45280e-12 1.01450e-11 2 2.606992285242964e-01 2.606992285247322e-01 4.35763e-13 3.50173e-11 3 1.160331202985559e-01 1.160331202984753e-01 8.05606e-14 5.12442e-11 ----------------------------------------------------------------------------------------------------- 7 Li 1 1.600746846332706e-02 1.600746845545344e-02 7.87361e-12 2.87059e-11 2 -2.505892535503862e-01 -2.505892535447229e-01 5.66336e-12 5.84190e-11 3 -8.839790542246556e-02 -8.839790542114664e-02 1.31892e-12 9.97069e-12 ----------------------------------------------------------------------------------------------------- 8 Li 1 -3.186276490835117e-01 -3.186276490706529e-01 1.28587e-11 3.47485e-11 2 -1.126869322365194e-02 -1.126869322226486e-02 1.38708e-12 8.15146e-11 3 1.145966527205206e-01 1.145966527227318e-01 2.21113e-12 6.20358e-11 ----------------------------------------------------------------------------------------------------- 9 Li 1 -3.490611306021596e-03 -3.490611307313606e-03 1.29201e-12 1.38229e-11 2 -3.705579946407026e-01 -3.705579946436952e-01 2.99255e-12 1.10044e-11 3 -1.710172057363940e-01 -1.710172057372404e-01 8.46462e-13 9.03419e-12 ----------------------------------------------------------------------------------------------------- 10 Li 1 1.141342619374674e-01 1.141342619447479e-01 7.28044e-12 5.86139e-10 * 2 3.057991769339562e-02 3.057991768667099e-02 6.72464e-12 4.02292e-11 3 -1.078736778225684e-01 -1.078736778192027e-01 3.36567e-12 8.72889e-11 ----------------------------------------------------------------------------------------------------- 11 Li 1 8.864882863864382e-02 8.864882861458757e-02 2.40562e-11 8.03459e-11 2 -2.511343902923751e-01 -2.511343902974859e-01 5.11075e-12 6.58040e-11 3 1.556200711263216e-01 1.556200711359143e-01 9.59260e-12 2.83376e-11 ----------------------------------------------------------------------------------------------------- 12 Li 1 8.454825235385119e-02 8.454825234480394e-02 9.04725e-12 9.89562e-11 2 3.093852451471015e-01 3.093852451473557e-01 2.54186e-13 5.68774e-11 3 3.741281295959916e-01 3.741281295898082e-01 6.18339e-12 1.79747e-10 ----------------------------------------------------------------------------------------------------- 13 Li 1 -2.525945772089582e-01 -2.525945772092802e-01 3.22020e-13 9.37069e-11 2 -3.309784464802445e-01 -3.309784464771910e-01 3.05350e-12 4.05737e-10 * 3 -1.923038719907438e-01 -1.923038719962176e-01 5.47382e-12 1.84019e-11 ----------------------------------------------------------------------------------------------------- 14 Li 1 3.120571875152498e-03 3.120571884379451e-03 9.22695e-12 2.96488e-11 2 9.162154104254397e-02 9.162154104220027e-02 3.43697e-13 3.26068e-10 * 3 2.171147832631648e-02 2.171147832456968e-02 1.74680e-12 1.62270e-11 ----------------------------------------------------------------------------------------------------- 15 Li 1 1.275361891935049e-01 1.275361891965656e-01 3.06069e-12 4.40997e-11 2 -3.658985439188729e-01 -3.658985439157619e-01 3.11101e-12 2.59792e-11 3 2.501223416848604e-01 2.501223416784327e-01 6.42769e-12 4.87480e-11 ----------------------------------------------------------------------------------------------------- 16 Li 1 8.820790068154589e-02 8.820790067867516e-02 2.87073e-12 3.34427e-11 2 8.000898140557583e-02 8.000898140777828e-02 2.20245e-12 1.45834e-10 3 1.856298279239478e-01 1.856298279172617e-01 6.68612e-12 1.60897e-11 ----------------------------------------------------------------------------------------------------- 17 Li 1 -2.120406394925668e-01 -2.120406395039524e-01 1.13857e-11 3.48798e-11 2 4.793170955805557e-02 4.793170955387897e-02 4.17660e-12 2.44532e-10 3 -1.833773822514745e-01 -1.833773822529534e-01 1.47893e-12 7.74381e-12 ----------------------------------------------------------------------------------------------------- 18 Li 1 1.459618824934955e-01 1.459618824928823e-01 6.13204e-13 2.71714e-11 2 2.743375104438457e-01 2.743375104233595e-01 2.04862e-11 5.16086e-11 3 -8.767418136958940e-02 -8.767418136345292e-02 6.13648e-12 1.07663e-10 ----------------------------------------------------------------------------------------------------- 19 Li 1 1.783281239926267e-01 1.783281239865604e-01 6.06631e-12 2.33323e-11 2 1.229412222276765e-01 1.229412222161261e-01 1.15504e-11 7.88986e-11 3 3.793828434859702e-02 3.793828434815730e-02 4.39718e-13 3.78998e-11 ----------------------------------------------------------------------------------------------------- 20 Li 1 7.581194152100976e-02 7.581194152060894e-02 4.00818e-13 3.58343e-11 2 2.216568423467726e-01 2.216568423479942e-01 1.22158e-12 3.21750e-11 3 -1.391550315019423e-01 -1.391550315016707e-01 2.71588e-13 2.56877e-10 ----------------------------------------------------------------------------------------------------- 21 Li 1 -2.265237377935797e-01 -2.265237377932449e-01 3.34816e-13 4.60428e-11 2 8.973696421916430e-02 8.973696421182838e-02 7.33592e-12 1.79529e-11 3 -2.357781705955809e-01 -2.357781705946627e-01 9.18182e-13 4.62331e-11 ----------------------------------------------------------------------------------------------------- 22 Li 1 -2.702634574482361e-02 -2.702634573810515e-02 6.71846e-12 2.30806e-10 2 4.159478258225711e-01 4.159478258154942e-01 7.07684e-12 3.97991e-10 * 3 9.960583550334175e-02 9.960583550173623e-02 1.60552e-12 1.76221e-10 ----------------------------------------------------------------------------------------------------- 23 Li 1 -7.508332185726269e-02 -7.508332183974918e-02 1.75135e-11 2.05072e-11 2 1.141025340237784e-01 1.141025340239917e-01 2.13315e-13 1.75194e-11 3 -3.744104260154443e-02 -3.744104262598098e-02 2.44366e-11 2.91400e-11 ----------------------------------------------------------------------------------------------------- 24 Li 1 -9.675456333329750e-02 -9.675456332678072e-02 6.51679e-12 4.21131e-11 2 1.760554003716569e-01 1.760554003642381e-01 7.41882e-12 3.45095e-11 3 -1.022699825106731e-01 -1.022699825068844e-01 3.78866e-12 5.48182e-11 ----------------------------------------------------------------------------------------------------- 25 Li 1 3.027809139909422e-02 3.027809139309094e-02 6.00328e-12 2.12225e-11 2 -3.319003854350137e-01 -3.319003854435557e-01 8.54200e-12 4.44885e-11 3 2.287324535710573e-01 2.287324535734696e-01 2.41226e-12 3.76102e-12 ----------------------------------------------------------------------------------------------------- 26 Li 1 -1.222727890216316e-01 -1.222727889697792e-01 5.18524e-11 3.14512e-10 * 2 9.445575308526856e-02 9.445575312331922e-02 3.80507e-11 5.20109e-10 * 3 -2.252929749055594e-01 -2.252929752269037e-01 3.21344e-10 6.27999e-10 * ----------------------------------------------------------------------------------------------------- 27 Li 1 2.575435596616916e-01 2.575435596335477e-01 2.81439e-11 5.00233e-11 2 -6.749358290307825e-01 -6.749358290463611e-01 1.55785e-11 7.60603e-11 3 -1.052772279403152e-01 -1.052772279432792e-01 2.96399e-12 2.95235e-11 ----------------------------------------------------------------------------------------------------- 28 Li 1 -8.797356299496904e-02 -8.797356302617261e-02 3.12036e-11 3.36338e-11 2 1.133980882430739e-01 1.133980882389422e-01 4.13161e-12 3.27342e-10 * 3 -2.378422570678516e-01 -2.378422570657710e-01 2.08056e-12 2.12860e-10 ----------------------------------------------------------------------------------------------------- 29 Li 1 -2.565238694398854e-01 -2.565238694382324e-01 1.65301e-12 2.88427e-11 2 -3.239921294111027e-01 -3.239921297983413e-01 3.87239e-10 1.43893e-08 * 3 -2.668421251966646e-01 -2.668421251036813e-01 9.29833e-11 1.35705e-08 * ----------------------------------------------------------------------------------------------------- 30 Li 1 -1.586888564837155e-01 -1.586888564893476e-01 5.63208e-12 1.07133e-10 2 1.122280250102169e-01 1.122280250053234e-01 4.89343e-12 2.07042e-11 3 -1.396793212129487e-01 -1.396793212167570e-01 3.80829e-12 7.24637e-11 ----------------------------------------------------------------------------------------------------- 31 Li 1 1.763089407045654e-01 1.763089406614381e-01 4.31273e-11 2.53963e-10 2 -2.902473282412496e-01 -2.902473282051453e-01 3.61043e-11 3.21950e-10 * 3 9.420878381291169e-02 9.420878376804573e-02 4.48660e-11 8.45353e-11 ----------------------------------------------------------------------------------------------------- 32 Li 1 -3.083070124317547e-02 -3.083070123743377e-02 5.74171e-12 6.90126e-11 2 1.231293661411637e-01 1.231293661372483e-01 3.91541e-12 1.62805e-11 3 7.585370789156563e-02 7.585370789052927e-02 1.03637e-12 3.08636e-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 = 14, direction = 1: |F_model - F_numer| error = ----------------------- = 2.95681e-09 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 = 3.9545106887817383 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.213150243781496e+00 1.213150243780144e+00 1.35247e-12 1.17761e-10 2 -7.160749589451474e-01 -7.160749589587039e-01 1.35565e-11 2.11081e-11 3 1.352752074053140e+00 1.352752074023846e+00 2.92941e-11 1.25832e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.263339162142688e+00 -1.263339162127361e+00 1.53273e-11 7.21589e-10 2 3.025516608101957e+00 3.025516608067167e+00 3.47899e-11 5.55631e-11 3 -1.771517865754617e+00 -1.771517865758216e+00 3.59890e-12 2.07452e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 4.060120981241000e+00 4.060120981258799e+00 1.77991e-11 6.20721e-11 2 -2.549944774986975e+00 -2.549944774991686e+00 4.71090e-12 3.73191e-10 3 -2.319153819111474e+00 -2.319153819177646e+00 6.61720e-11 2.67825e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.460209817047393e+00 -1.460209817024005e+00 2.33882e-11 6.22802e-10 2 -8.821912438678809e-01 -8.821912438498045e-01 1.80764e-11 3.64502e-10 3 2.840829103529573e+00 2.840829103557888e+00 2.83151e-11 5.16231e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 6.879421414736850e-01 6.879421414602157e-01 1.34693e-11 1.24393e-10 2 -3.163293822439430e-01 -3.163293822376614e-01 6.28159e-12 2.06223e-11 3 1.455057853683059e+00 1.455057853693891e+00 1.08322e-11 1.41591e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -1.408529116272459e+00 -1.408529116347268e+00 7.48097e-11 1.69107e-10 2 -8.483901987851616e-02 -8.483901984876686e-02 2.97493e-11 1.04338e-10 3 2.096318927954329e+00 2.096318928119562e+00 1.65233e-10 4.56921e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -1.607659742341176e+00 -1.607659742321110e+00 2.00666e-11 2.02310e-09 * 2 1.752762672856702e+00 1.752762672859140e+00 2.43805e-12 1.22035e-09 3 -1.199098149454261e+00 -1.199098149460248e+00 5.98743e-12 5.87814e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.859373440873930e-01 -1.859373441651468e-01 7.77539e-11 4.55865e-11 2 2.806210068140897e+00 2.806210068132293e+00 8.60334e-12 2.16491e-10 3 2.199260517853864e+00 2.199260517841716e+00 1.21485e-11 3.65123e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.256029127573835e+00 2.256029127616034e+00 4.21987e-11 3.47272e-10 2 1.920592620235226e+00 1.920592620240265e+00 5.03841e-12 2.04312e-09 * 3 4.715511478304106e-02 4.715511479959225e-02 1.65512e-11 1.11293e-08 * ----------------------------------------------------------------------------------------------------- 10 Si 1 2.570703859022186e-01 2.570703858988515e-01 3.36708e-12 9.32794e-10 2 -1.537203172070209e+00 -1.537203172072382e+00 2.17315e-12 2.40019e-11 3 2.255357103017415e+00 2.255357103046466e+00 2.90510e-11 4.37985e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 3.340435198481406e+00 3.340435198498029e+00 1.66227e-11 2.18604e-10 2 -2.028562378452957e+00 -2.028562378466448e+00 1.34910e-11 1.12711e-08 * 3 -6.680790960358600e-02 -6.680790960528186e-02 1.69587e-12 1.07199e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 9.086858809557286e-01 9.086858809750130e-01 1.92845e-11 2.79147e-10 2 4.060063763212431e-01 4.060063763272745e-01 6.03140e-12 1.19999e-10 3 -1.272466380623235e+00 -1.272466380674113e+00 5.08780e-11 9.91422e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.309540436328148e+00 -2.309540436362623e+00 3.44742e-11 8.04561e-11 2 8.769009169317015e-01 8.769009169884857e-01 5.67842e-11 3.21725e-10 3 -7.048890867814441e-01 -7.048890867882601e-01 6.81599e-12 2.99061e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.737554726028045e-01 4.737554726059798e-01 3.17529e-12 3.72692e-11 2 -6.022916413269365e-01 -6.022916413264485e-01 4.87943e-13 8.10554e-10 3 9.728399077251482e-01 9.728399077319339e-01 6.78568e-12 1.99344e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.548325070490425e+00 1.548325070468364e+00 2.20615e-11 6.21889e-09 * 2 -2.153462939072662e+00 -2.153462939099897e+00 2.72351e-11 5.04889e-10 3 1.544486627197808e+00 1.544486627181789e+00 1.60192e-11 3.55243e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -4.196994649475032e+00 -4.196994649488398e+00 1.33662e-11 4.24867e-10 2 2.336005923085515e+00 2.336005922955927e+00 1.29587e-10 5.12312e-09 * 3 -4.786127342128678e+00 -4.786127342115429e+00 1.32490e-11 6.81961e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.725396145059650e+00 -2.725396145095650e+00 3.59992e-11 1.52107e-09 2 6.636303138645726e-01 6.636303139248634e-01 6.02908e-11 2.94530e-10 3 3.144259829719442e+00 3.144259829823807e+00 1.04366e-10 1.59607e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 7.240240966992953e-01 7.240240967259407e-01 2.66454e-11 1.47496e-10 2 2.567681834955591e+00 2.567681835035599e+00 8.00080e-11 5.48050e-10 3 -1.608344811973426e+00 -1.608344811928719e+00 4.47069e-11 9.06618e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -1.622446011095863e+00 -1.622446011124173e+00 2.83100e-11 6.96073e-09 * 2 1.160452390243494e+00 1.160452390246450e+00 2.95564e-12 4.81722e-10 3 -2.427198334781584e+00 -2.427198334800974e+00 1.93903e-11 6.97473e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.231926018003173e+00 2.231926017990202e+00 1.29705e-11 4.15086e-10 2 8.447975245651193e-01 8.447975244561133e-01 1.09006e-10 2.54650e-09 * 3 -2.722064686512820e+00 -2.722064686566449e+00 5.36287e-11 4.66076e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -2.038938465540925e+00 -2.038938465541420e+00 4.94271e-13 2.67990e-10 2 -2.076327492228767e+00 -2.076327492266448e+00 3.76810e-11 1.01458e-08 * 3 3.017929593779864e-01 3.017929594210256e-01 4.30392e-11 4.50847e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 9.302065903741565e-01 9.302065903439680e-01 3.01885e-11 2.86430e-11 2 2.037428873762479e+00 2.037428873801058e+00 3.85780e-11 3.11214e-10 3 -4.815617868554475e-01 -4.815617868456630e-01 9.78456e-12 5.53433e-07 * ----------------------------------------------------------------------------------------------------- 23 Si 1 5.180343877674587e-01 5.180343877671495e-01 3.09197e-13 3.38342e-10 2 1.741409222808099e+00 1.741409222762147e+00 4.59515e-11 3.82827e-10 3 -4.075583900316354e-01 -4.075583900365801e-01 4.94477e-12 1.52644e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.157641877750484e+00 1.157641877783600e+00 3.31155e-11 3.71984e-10 2 6.559397571364363e-01 6.559397571609243e-01 2.44881e-11 3.37468e-09 * 3 1.321884124263561e+00 1.321884124350736e+00 8.71749e-11 4.17976e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.243520781530973e+00 -2.243520781386809e+00 1.44164e-10 1.52601e-10 2 -2.197058029376874e+00 -2.197058029505959e+00 1.29085e-10 4.13965e-10 3 -6.418707118261653e-01 -6.418707116090131e-01 2.17152e-10 3.19035e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 5.406800178622847e-01 5.406800178603158e-01 1.96887e-12 3.60610e-10 2 2.394095779597693e+00 2.394095779558490e+00 3.92024e-11 4.34730e-10 3 -2.425217857101362e+00 -2.425217856979844e+00 1.21518e-10 1.77948e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 2.174719806958462e+00 2.174719806997549e+00 3.90870e-11 1.13292e-09 2 -1.188336467761070e+00 -1.188336467810054e+00 4.89835e-11 5.85226e-10 3 4.122645107960270e+00 4.122645107991723e+00 3.14531e-11 3.57305e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 1.406252036027286e-01 1.406252036705715e-01 6.78429e-11 2.35087e-10 2 -7.901002786711180e-01 -7.901002787238951e-01 5.27771e-11 3.90245e-10 3 6.726086179687865e-01 6.726086179780255e-01 9.23905e-12 4.18031e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 -4.268630678948170e+00 -4.268630679003419e+00 5.52491e-11 1.19776e-10 2 -5.839019703839345e+00 -5.839019703806056e+00 3.32889e-11 1.14658e-08 * 3 -1.228790650768912e+00 -1.228790650650232e+00 1.18680e-10 2.68790e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 4.586922218582949e+00 4.586922218560584e+00 2.23652e-11 3.44151e-11 2 3.098983867213855e+00 3.098983867231191e+00 1.73368e-11 3.06834e-10 3 -5.584238163352798e-02 -5.584238161347352e-02 2.00545e-11 3.92201e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -9.416242727875165e-01 -9.416242727862103e-01 1.30618e-12 2.49827e-10 2 -3.080985729940035e+00 -3.080985729979874e+00 3.98384e-11 5.71068e-10 3 9.331082306516288e-01 9.331082306544805e-01 2.85161e-12 1.05523e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.477528097446207e+00 -1.477528097274504e+00 1.71703e-10 6.63007e-11 2 -2.245687537158144e+00 -2.245687537167415e+00 9.27169e-12 2.50819e-09 * 3 -1.141845934796879e+00 -1.141845934759792e+00 3.70874e-11 2.97868e-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 = 28, direction = 1: |F_model - F_numer| error = ----------------------- = 4.82438e-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 = Li Si | a0 = 3.7567454455916036 | (Configuration in file "config-LiSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.790517284914164e+00 -1.790517284922107e+00 7.94254e-12 3.28630e-10 2 -1.264522078783577e+00 -1.264522078786756e+00 3.17923e-12 2.67631e-10 3 1.582899946383685e-01 1.582899946589980e-01 2.06294e-11 1.12880e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.158112414785887e+00 3.158112414645051e+00 1.40836e-10 4.68442e-10 2 4.521628068689511e+00 4.521628068710784e+00 2.12736e-11 3.00808e-10 3 -3.427818028634169e+00 -3.427818028830181e+00 1.96012e-10 3.03491e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.357404069814879e+00 2.357404069850853e+00 3.59734e-11 1.08584e-10 2 -3.540715619774599e+00 -3.540715619810289e+00 3.56906e-11 1.69514e-10 3 3.130085686317801e+00 3.130085686312326e+00 5.47429e-12 5.25057e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.717699268514877e+00 -2.717699268499249e+00 1.56279e-11 1.30556e-09 2 1.208855285643590e+00 1.208855285667308e+00 2.37188e-11 8.62099e-10 3 2.426416151404646e+00 2.426416151450542e+00 4.58953e-11 2.22830e-10 ----------------------------------------------------------------------------------------------------- 5 Li 1 -6.142243393995063e-01 -6.142243393926500e-01 6.85629e-12 2.07627e-09 * 2 1.753278331116231e+00 1.753278331120391e+00 4.16045e-12 1.09160e-10 3 1.005018384708459e+00 1.005018384687921e+00 2.05376e-11 1.06711e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 4.873689998050291e-01 4.873689998190321e-01 1.40031e-11 1.16552e-10 2 -1.272234512822888e+00 -1.272234512823903e+00 1.01519e-12 6.39750e-11 3 4.231672409396043e-01 4.231672409455632e-01 5.95890e-12 5.09467e-11 ----------------------------------------------------------------------------------------------------- 7 Li 1 -1.136125730842689e+00 -1.136125730861361e+00 1.86720e-11 3.40477e-10 2 1.215896532976795e+00 1.215896532991618e+00 1.48233e-11 1.62455e-10 3 1.044081215873552e-01 1.044081215658820e-01 2.14733e-11 1.12149e-09 ----------------------------------------------------------------------------------------------------- 8 Si 1 1.164282886330633e+01 1.164282886328238e+01 2.39506e-11 1.38796e-07 * 2 -2.734438390842544e+00 -2.734438390841537e+00 1.00675e-12 8.16100e-09 * 3 -8.025525578710303e+00 -8.025525578719559e+00 9.25660e-12 2.05944e-10 ----------------------------------------------------------------------------------------------------- 9 Li 1 4.659671179117119e-01 4.659671178619820e-01 4.97299e-11 4.80670e-10 2 -6.280461548126368e-01 -6.280461547815906e-01 3.10462e-11 3.36223e-10 3 6.735231351185951e-01 6.735231351027664e-01 1.58287e-11 2.96819e-11 ----------------------------------------------------------------------------------------------------- 10 Li 1 2.127265567620119e-01 2.127265567660871e-01 4.07527e-12 1.84248e-09 * 2 -4.606023776068873e-01 -4.606023776073859e-01 4.98546e-13 1.18120e-09 3 8.761171512021274e-02 8.761171511913424e-02 1.07850e-12 7.55023e-11 ----------------------------------------------------------------------------------------------------- 11 Li 1 -2.266851337490819e+00 -2.266851337481895e+00 8.92397e-12 1.25227e-10 2 4.061744256482274e+00 4.061744256467151e+00 1.51230e-11 1.66246e-10 3 -1.136808873478833e+00 -1.136808873541266e+00 6.24327e-11 8.95310e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.520679371546201e-01 2.520679371636521e-01 9.03200e-12 1.23080e-10 2 1.013785853613723e+00 1.013785853603361e+00 1.03610e-11 3.60094e-11 3 -2.227525823352852e+00 -2.227525823369070e+00 1.62181e-11 1.31898e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -3.548750539208489e+00 -3.548750539198156e+00 1.03331e-11 2.58819e-10 2 -3.226343792614232e+00 -3.226343792609365e+00 4.86722e-12 7.45581e-11 3 -2.570912604711006e+00 -2.570912604739069e+00 2.80629e-11 8.34444e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.986917687035550e-01 7.986917687066311e-01 3.07609e-12 1.28065e-10 2 2.259304775111421e+00 2.259304775109494e+00 1.92690e-12 1.86950e-10 3 -1.671718616318311e+00 -1.671718616286348e+00 3.19629e-11 9.02447e-11 ----------------------------------------------------------------------------------------------------- 15 Li 1 1.748401550173001e+00 1.748401550189534e+00 1.65326e-11 1.06681e-09 2 -1.455349499753689e+00 -1.455349499779519e+00 2.58302e-11 2.14593e-10 3 2.361263691556849e+00 2.361263691566898e+00 1.00484e-11 1.09674e-10 ----------------------------------------------------------------------------------------------------- 16 Li 1 -9.659819568927389e-01 -9.659819569160214e-01 2.32825e-11 3.50771e-10 2 8.555108243365719e-01 8.555108242674994e-01 6.90725e-11 2.33376e-10 3 1.389903388093617e+00 1.389903388094541e+00 9.24150e-13 2.98799e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.390546287823689e+00 -1.390546287767265e+00 5.64238e-11 1.51361e-10 2 -1.095249577985515e+00 -1.095249577963647e+00 2.18683e-11 1.56164e-10 3 -1.966971567183667e+00 -1.966971567201296e+00 1.76290e-11 2.47637e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 -7.340744560211628e+00 -7.340744560156018e+00 5.56106e-11 3.11459e-10 2 4.390913445918037e-01 4.390913445978431e-01 6.03945e-12 1.16254e-09 3 1.030484808040546e+01 1.030484808038208e+01 2.33822e-11 3.54470e-10 ----------------------------------------------------------------------------------------------------- 19 Li 1 6.567845864995783e-01 6.567845864982205e-01 1.35780e-12 1.53675e-10 2 1.028462021608259e-01 1.028462021795984e-01 1.87725e-11 2.33554e-10 3 -9.877123960678241e-01 -9.877123960669257e-01 8.98392e-13 6.65233e-10 ----------------------------------------------------------------------------------------------------- 20 Li 1 7.062568046998022e-03 7.062568045011076e-03 1.98695e-12 3.25863e-10 2 4.058933139724333e-01 4.058933139655173e-01 6.91597e-12 1.28701e-09 3 -7.746764416386438e-01 -7.746764416372263e-01 1.41753e-12 1.69955e-09 * ----------------------------------------------------------------------------------------------------- 21 Si 1 -5.230449966255746e+00 -5.230449966284776e+00 2.90301e-11 1.25721e-10 2 -3.413976386004714e+00 -3.413976386011058e+00 6.34426e-12 5.49317e-09 * 3 -4.060222465881976e+00 -4.060222465881340e+00 6.35936e-13 5.23880e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.763881185196809e+00 2.763881185190691e+00 6.11822e-12 7.30433e-11 2 2.824876051867628e+00 2.824876051882218e+00 1.45901e-11 1.73928e-10 3 -2.108090275077651e+00 -2.108090275094674e+00 1.70224e-11 4.29202e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 4.166662310614454e+00 4.166662310605356e+00 9.09761e-12 9.33689e-11 2 -7.924210127650680e-01 -7.924210127567272e-01 8.34088e-12 1.05136e-10 3 3.555484814206483e+00 3.555484814200851e+00 5.63150e-12 2.28240e-10 ----------------------------------------------------------------------------------------------------- 24 Li 1 -2.476206479950076e+00 -2.476206479984687e+00 3.46105e-11 1.49272e-10 2 2.113612690681208e+00 2.113612690713379e+00 3.21707e-11 2.23996e-10 3 2.106101560261629e+00 2.106101560289058e+00 2.74287e-11 2.29957e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.197524432816632e+00 -1.197524432803766e+00 1.28659e-11 2.28498e-10 2 -3.238154437744249e+00 -3.238154437744574e+00 3.25073e-13 6.05769e-11 3 3.250987610078125e-01 3.250987610159153e-01 8.10280e-12 1.99063e-10 ----------------------------------------------------------------------------------------------------- 26 Li 1 8.979683569333502e-01 8.979683569121614e-01 2.11888e-11 1.80318e-10 2 1.332309335973575e+00 1.332309335972093e+00 1.48281e-12 1.99476e-10 3 -8.244758042017204e-01 -8.244758042279369e-01 2.62165e-11 1.21692e-10 ----------------------------------------------------------------------------------------------------- 27 Li 1 -4.156248118965454e-01 -4.156248119007077e-01 4.16234e-12 5.93943e-10 2 -1.805755282992175e+00 -1.805755282999090e+00 6.91469e-12 9.25335e-10 3 5.575072924207378e-01 5.575072924260702e-01 5.33240e-12 7.31005e-11 ----------------------------------------------------------------------------------------------------- 28 Li 1 -2.968615478553227e-01 -2.968615478706695e-01 1.53468e-11 6.01581e-10 2 4.690823951235348e-01 4.690823951325930e-01 9.05814e-12 1.65136e-09 * 3 1.214211098230123e+00 1.214211098203065e+00 2.70575e-11 9.68943e-11 ----------------------------------------------------------------------------------------------------- 29 Li 1 2.041352810627700e-01 2.041352810548431e-01 7.92688e-12 1.90928e-10 2 -1.032473661596912e+00 -1.032473661626169e+00 2.92570e-11 1.29923e-10 3 -1.156645488613240e+00 -1.156645488627407e+00 1.41678e-11 3.37757e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 2.012240508966336e-01 2.012240508998880e-01 3.25440e-12 1.38450e-10 2 1.909273912933116e+00 1.909273912810544e+00 1.22572e-10 1.97262e-10 3 -6.806797192331735e-01 -6.806797192308176e-01 2.35589e-12 7.16852e-10 ----------------------------------------------------------------------------------------------------- 31 Li 1 8.508015462439086e-01 8.508015462311896e-01 1.27189e-11 6.27497e-10 2 -1.740131697779261e+00 -1.740131697806959e+00 2.76983e-11 5.04896e-10 3 1.074622997720854e+00 1.074622997695104e+00 2.57501e-11 1.54790e-10 ----------------------------------------------------------------------------------------------------- 32 Li 1 5.160193801613948e-01 5.160193801644567e-01 3.06188e-12 7.64655e-11 2 1.213425308604708e+00 1.213425308605100e+00 3.92353e-13 4.74305e-10 3 7.222215693647598e-01 7.222215693478907e-01 1.68691e-11 1.60628e-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 = 20, direction = 1: |F_model - F_numer| error = ----------------------- = 2.81335e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.95681e-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 2.95681e-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.