!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 5.355470140923006e-02 5.355470141169266e-02 2.46260e-12 9.61153e-12 2 -4.656082285943412e-02 -4.656082286198444e-02 2.55032e-12 2.34313e-11 3 1.278541750708485e-02 1.278541750764449e-02 5.59639e-13 1.38210e-11 ----------------------------------------------------------------------------------------------------- 2 Li 1 1.561971114440072e-01 1.561971114415873e-01 2.41990e-12 5.42071e-11 2 3.324564076116588e-01 3.324564075998643e-01 1.17945e-11 4.50963e-11 3 1.242007787013894e-01 1.242007787045914e-01 3.20202e-12 1.04576e-10 ----------------------------------------------------------------------------------------------------- 3 Li 1 3.468714749843162e-01 3.468714749862821e-01 1.96593e-12 6.80788e-11 2 1.003150372074664e-01 1.003150371968957e-01 1.05708e-11 3.87182e-11 3 1.392138132259322e-01 1.392138132240015e-01 1.93076e-12 4.07311e-11 ----------------------------------------------------------------------------------------------------- 4 Li 1 1.208427753866624e-01 1.208427753862687e-01 3.93727e-13 2.18021e-11 2 1.546331593665566e-01 1.546331593454775e-01 2.10791e-11 6.55902e-11 3 2.746241446576435e-01 2.746241446597654e-01 2.12191e-12 3.84973e-11 ----------------------------------------------------------------------------------------------------- 5 Li 1 -1.119809712319715e-01 -1.119809712345754e-01 2.60396e-12 3.48032e-11 2 -1.755694240802323e-02 -1.755694240528545e-02 2.73778e-12 4.16170e-11 3 1.521751723027794e-02 1.521751723300360e-02 2.72566e-12 3.57375e-11 ----------------------------------------------------------------------------------------------------- 6 Li 1 -8.348987990482147e-02 -8.348987991027419e-02 5.45272e-12 1.01450e-11 2 2.606992285242964e-01 2.606992285247320e-01 4.35652e-13 3.50175e-11 3 1.160331202985559e-01 1.160331202984753e-01 8.05050e-14 5.12442e-11 ----------------------------------------------------------------------------------------------------- 7 Li 1 1.600746846332706e-02 1.600746845545343e-02 7.87363e-12 2.87059e-11 2 -2.505892535503862e-01 -2.505892535447228e-01 5.66341e-12 5.84188e-11 3 -8.839790542246556e-02 -8.839790542114657e-02 1.31899e-12 9.97076e-12 ----------------------------------------------------------------------------------------------------- 8 Li 1 -3.186276490835117e-01 -3.186276490706528e-01 1.28589e-11 3.47486e-11 2 -1.126869322365194e-02 -1.126869322226485e-02 1.38709e-12 8.15146e-11 3 1.145966527205206e-01 1.145966527227317e-01 2.21106e-12 6.20358e-11 ----------------------------------------------------------------------------------------------------- 9 Li 1 -3.490611306021596e-03 -3.490611307313604e-03 1.29201e-12 1.38229e-11 2 -3.705579946407026e-01 -3.705579946436948e-01 2.99222e-12 1.10047e-11 3 -1.710172057363940e-01 -1.710172057372404e-01 8.46379e-13 9.03416e-12 ----------------------------------------------------------------------------------------------------- 10 Li 1 1.141342619374674e-01 1.141342619447479e-01 7.28050e-12 5.86139e-10 * 2 3.057991769339562e-02 3.057991768667096e-02 6.72466e-12 4.02292e-11 3 -1.078736778225684e-01 -1.078736778192027e-01 3.36571e-12 8.72888e-11 ----------------------------------------------------------------------------------------------------- 11 Li 1 8.864882863864382e-02 8.864882861458755e-02 2.40563e-11 8.03459e-11 2 -2.511343902923751e-01 -2.511343902974860e-01 5.11086e-12 6.58040e-11 3 1.556200711263216e-01 1.556200711359142e-01 9.59258e-12 2.83376e-11 ----------------------------------------------------------------------------------------------------- 12 Li 1 8.454825235385119e-02 8.454825234480388e-02 9.04730e-12 9.89562e-11 2 3.093852451471015e-01 3.093852451473556e-01 2.54075e-13 5.68775e-11 3 3.741281295959916e-01 3.741281295898083e-01 6.18322e-12 1.79747e-10 ----------------------------------------------------------------------------------------------------- 13 Li 1 -2.525945772089582e-01 -2.525945772092800e-01 3.21854e-13 9.37070e-11 2 -3.309784464802445e-01 -3.309784464771912e-01 3.05334e-12 4.05737e-10 * 3 -1.923038719907438e-01 -1.923038719962175e-01 5.47368e-12 1.84019e-11 ----------------------------------------------------------------------------------------------------- 14 Li 1 3.120571875152498e-03 3.120571884379449e-03 9.22695e-12 2.96488e-11 2 9.162154104254397e-02 9.162154104220030e-02 3.43670e-13 3.26068e-10 * 3 2.171147832631648e-02 2.171147832456967e-02 1.74682e-12 1.62270e-11 ----------------------------------------------------------------------------------------------------- 15 Li 1 1.275361891935049e-01 1.275361891965655e-01 3.06061e-12 4.40997e-11 2 -3.658985439188729e-01 -3.658985439157617e-01 3.11123e-12 2.59792e-11 3 2.501223416848604e-01 2.501223416784329e-01 6.42753e-12 4.87478e-11 ----------------------------------------------------------------------------------------------------- 16 Li 1 8.820790068154589e-02 8.820790067867501e-02 2.87088e-12 3.34428e-11 2 8.000898140557583e-02 8.000898140777825e-02 2.20242e-12 1.45834e-10 3 1.856298279239478e-01 1.856298279172616e-01 6.68621e-12 1.60896e-11 ----------------------------------------------------------------------------------------------------- 17 Li 1 -2.120406394925668e-01 -2.120406395039522e-01 1.13854e-11 3.48797e-11 2 4.793170955805557e-02 4.793170955387899e-02 4.17658e-12 2.44532e-10 3 -1.833773822514745e-01 -1.833773822529533e-01 1.47879e-12 7.74386e-12 ----------------------------------------------------------------------------------------------------- 18 Li 1 1.459618824934955e-01 1.459618824928822e-01 6.13259e-13 2.71713e-11 2 2.743375104438457e-01 2.743375104233591e-01 2.04866e-11 5.16084e-11 3 -8.767418136958940e-02 -8.767418136345287e-02 6.13654e-12 1.07663e-10 ----------------------------------------------------------------------------------------------------- 19 Li 1 1.783281239926267e-01 1.783281239865602e-01 6.06645e-12 2.33322e-11 2 1.229412222276765e-01 1.229412222161261e-01 1.15505e-11 7.88986e-11 3 3.793828434859702e-02 3.793828434815728e-02 4.39739e-13 3.78998e-11 ----------------------------------------------------------------------------------------------------- 20 Li 1 7.581194152100976e-02 7.581194152060887e-02 4.00888e-13 3.58342e-11 2 2.216568423467726e-01 2.216568423479940e-01 1.22144e-12 3.21752e-11 3 -1.391550315019423e-01 -1.391550315016706e-01 2.71672e-13 2.56877e-10 ----------------------------------------------------------------------------------------------------- 21 Li 1 -2.265237377935797e-01 -2.265237377932448e-01 3.34982e-13 4.60428e-11 2 8.973696421916430e-02 8.973696421182834e-02 7.33597e-12 1.79529e-11 3 -2.357781705955809e-01 -2.357781705946626e-01 9.18293e-13 4.62332e-11 ----------------------------------------------------------------------------------------------------- 22 Li 1 -2.702634574482361e-02 -2.702634573810516e-02 6.71845e-12 2.30806e-10 2 4.159478258225711e-01 4.159478258154944e-01 7.07667e-12 3.97991e-10 * 3 9.960583550334175e-02 9.960583550173617e-02 1.60558e-12 1.76221e-10 ----------------------------------------------------------------------------------------------------- 23 Li 1 -7.508332185726269e-02 -7.508332183974914e-02 1.75135e-11 2.05073e-11 2 1.141025340237784e-01 1.141025340239918e-01 2.13371e-13 1.75194e-11 3 -3.744104260154443e-02 -3.744104262598095e-02 2.44365e-11 2.91401e-11 ----------------------------------------------------------------------------------------------------- 24 Li 1 -9.675456333329750e-02 -9.675456332678065e-02 6.51686e-12 4.21131e-11 2 1.760554003716569e-01 1.760554003642380e-01 7.41895e-12 3.45094e-11 3 -1.022699825106731e-01 -1.022699825068844e-01 3.78873e-12 5.48182e-11 ----------------------------------------------------------------------------------------------------- 25 Li 1 3.027809139909422e-02 3.027809139309092e-02 6.00330e-12 2.12225e-11 2 -3.319003854350137e-01 -3.319003854435554e-01 8.54178e-12 4.44885e-11 3 2.287324535710573e-01 2.287324535734695e-01 2.41215e-12 3.76107e-12 ----------------------------------------------------------------------------------------------------- 26 Li 1 -1.222727890216316e-01 -1.222727889697792e-01 5.18525e-11 3.14512e-10 * 2 9.445575308526856e-02 9.445575312331916e-02 3.80506e-11 5.20109e-10 * 3 -2.252929749055594e-01 -2.252929752269036e-01 3.21344e-10 6.27999e-10 * ----------------------------------------------------------------------------------------------------- 27 Li 1 2.575435596616916e-01 2.575435596335475e-01 2.81440e-11 5.00233e-11 2 -6.749358290307825e-01 -6.749358290463608e-01 1.55783e-11 7.60607e-11 3 -1.052772279403152e-01 -1.052772279432791e-01 2.96392e-12 2.95235e-11 ----------------------------------------------------------------------------------------------------- 28 Li 1 -8.797356299496904e-02 -8.797356302617258e-02 3.12035e-11 3.36339e-11 2 1.133980882430739e-01 1.133980882389423e-01 4.13151e-12 3.27342e-10 * 3 -2.378422570678516e-01 -2.378422570657711e-01 2.08045e-12 2.12860e-10 ----------------------------------------------------------------------------------------------------- 29 Li 1 -2.565238694398854e-01 -2.565238694382322e-01 1.65318e-12 2.88427e-11 2 -3.239921294111027e-01 -3.239921297983411e-01 3.87238e-10 1.43893e-08 * 3 -2.668421251966646e-01 -2.668421251036810e-01 9.29836e-11 1.35705e-08 * ----------------------------------------------------------------------------------------------------- 30 Li 1 -1.586888564837155e-01 -1.586888564893477e-01 5.63216e-12 1.07133e-10 2 1.122280250102169e-01 1.122280250053234e-01 4.89349e-12 2.07041e-11 3 -1.396793212129487e-01 -1.396793212167570e-01 3.80826e-12 7.24637e-11 ----------------------------------------------------------------------------------------------------- 31 Li 1 1.763089407045654e-01 1.763089406614380e-01 4.31274e-11 2.53963e-10 2 -2.902473282412496e-01 -2.902473282051451e-01 3.61045e-11 3.21950e-10 * 3 9.420878381291169e-02 9.420878376804570e-02 4.48660e-11 8.45353e-11 ----------------------------------------------------------------------------------------------------- 32 Li 1 -3.083070124317547e-02 -3.083070123743374e-02 5.74173e-12 6.90126e-11 2 1.231293661411637e-01 1.231293661372483e-01 3.91545e-12 1.62807e-11 3 7.585370789156563e-02 7.585370789052930e-02 1.03634e-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 1.213150243780142e+00 1.35381e-12 1.17760e-10 2 -7.160749589451474e-01 -7.160749589587032e-01 1.35558e-11 2.11079e-11 3 1.352752074053140e+00 1.352752074023845e+00 2.92948e-11 1.25833e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.263339162142688e+00 -1.263339162127360e+00 1.53282e-11 7.21589e-10 2 3.025516608101957e+00 3.025516608067164e+00 3.47926e-11 5.55640e-11 3 -1.771517865754617e+00 -1.771517865758215e+00 3.59779e-12 2.07452e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 4.060120981241000e+00 4.060120981258799e+00 1.77991e-11 6.20748e-11 2 -2.549944774986975e+00 -2.549944774991684e+00 4.70912e-12 3.73191e-10 3 -2.319153819111474e+00 -2.319153819177644e+00 6.61706e-11 2.67824e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.460209817047393e+00 -1.460209817024004e+00 2.33891e-11 6.22802e-10 2 -8.821912438678809e-01 -8.821912438498040e-01 1.80770e-11 3.64502e-10 3 2.840829103529573e+00 2.840829103557886e+00 2.83129e-11 5.16233e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 6.879421414736850e-01 6.879421414602152e-01 1.34699e-11 1.24393e-10 2 -3.163293822439430e-01 -3.163293822376610e-01 6.28197e-12 2.06224e-11 3 1.455057853683059e+00 1.455057853693889e+00 1.08298e-11 1.41593e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -1.408529116272459e+00 -1.408529116347268e+00 7.48088e-11 1.69107e-10 2 -8.483901987851616e-02 -8.483901984876682e-02 2.97493e-11 1.04338e-10 3 2.096318927954329e+00 2.096318928119610e+00 1.65281e-10 4.56970e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -1.607659742341176e+00 -1.607659742321110e+00 2.00659e-11 2.02310e-09 * 2 1.752762672856702e+00 1.752762672859141e+00 2.43894e-12 1.22035e-09 3 -1.199098149454261e+00 -1.199098149460248e+00 5.98788e-12 5.87814e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.859373440873930e-01 -1.859373441651467e-01 7.77538e-11 4.55865e-11 2 2.806210068140897e+00 2.806210068132291e+00 8.60512e-12 2.16491e-10 3 2.199260517853864e+00 2.199260517841714e+00 1.21498e-11 3.65124e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.256029127573835e+00 2.256029127616033e+00 4.21982e-11 3.47270e-10 2 1.920592620235226e+00 1.920592620240266e+00 5.03930e-12 2.04312e-09 * 3 4.715511478304106e-02 4.715511479959227e-02 1.65512e-11 1.11293e-08 * ----------------------------------------------------------------------------------------------------- 10 Si 1 2.570703859022186e-01 2.570703858988514e-01 3.36720e-12 9.32794e-10 2 -1.537203172070209e+00 -1.537203172072381e+00 2.17226e-12 2.40017e-11 3 2.255357103017415e+00 2.255357103046466e+00 2.90510e-11 4.37989e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 3.340435198481406e+00 3.340435198498026e+00 1.66200e-11 2.18608e-10 2 -2.028562378452957e+00 -2.028562378466450e+00 1.34923e-11 1.12711e-08 * 3 -6.680790960358600e-02 -6.680790960528182e-02 1.69582e-12 1.07199e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 9.086858809557286e-01 9.086858809750124e-01 1.92838e-11 2.79147e-10 2 4.060063763212431e-01 4.060063763272743e-01 6.03112e-12 1.19999e-10 3 -1.272466380623235e+00 -1.272466380674113e+00 5.08775e-11 9.91422e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.309540436328148e+00 -2.309540436362620e+00 3.44711e-11 8.04588e-11 2 8.769009169317015e-01 8.769009169884854e-01 5.67839e-11 3.21726e-10 3 -7.048890867814441e-01 -7.048890867882598e-01 6.81566e-12 2.99069e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.737554726028045e-01 4.737554726059794e-01 3.17496e-12 3.72692e-11 2 -6.022916413269365e-01 -6.022916413264489e-01 4.87610e-13 8.10554e-10 3 9.728399077251482e-01 9.728399077319341e-01 6.78591e-12 1.99344e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.548325070490425e+00 1.548325070468365e+00 2.20608e-11 6.21889e-09 * 2 -2.153462939072662e+00 -2.153462939099895e+00 2.72338e-11 5.04887e-10 3 1.544486627197808e+00 1.544486627181788e+00 1.60205e-11 3.55244e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -4.196994649475032e+00 -4.196994649488397e+00 1.33653e-11 4.24864e-10 2 2.336005923085515e+00 2.336005922955929e+00 1.29586e-10 5.12312e-09 * 3 -4.786127342128678e+00 -4.786127342115426e+00 1.32516e-11 6.81954e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.725396145059650e+00 -2.725396145095651e+00 3.60001e-11 1.52107e-09 2 6.636303138645726e-01 6.636303139248629e-01 6.02903e-11 2.94531e-10 3 3.144259829719442e+00 3.144259829823805e+00 1.04364e-10 1.59604e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 7.240240966992953e-01 7.240240967259405e-01 2.66451e-11 1.47496e-10 2 2.567681834955591e+00 2.567681835035597e+00 8.00062e-11 5.48051e-10 3 -1.608344811973426e+00 -1.608344811928718e+00 4.47076e-11 9.06617e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -1.622446011095863e+00 -1.622446011124173e+00 2.83109e-11 6.96073e-09 * 2 1.160452390243494e+00 1.160452390246449e+00 2.95497e-12 4.81721e-10 3 -2.427198334781584e+00 -2.427198334800972e+00 1.93885e-11 6.97455e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.231926018003173e+00 2.231926017990201e+00 1.29723e-11 4.15086e-10 2 8.447975245651193e-01 8.447975244561137e-01 1.09006e-10 2.54650e-09 * 3 -2.722064686512820e+00 -2.722064686566450e+00 5.36300e-11 4.66107e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -2.038938465540925e+00 -2.038938465541418e+00 4.92939e-13 2.67989e-10 2 -2.076327492228767e+00 -2.076327492266449e+00 3.76823e-11 1.01458e-08 * 3 3.017929593779864e-01 3.017929594210254e-01 4.30390e-11 4.50846e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 9.302065903741565e-01 9.302065903439674e-01 3.01892e-11 2.86430e-11 2 2.037428873762479e+00 2.037428873801057e+00 3.85771e-11 3.11213e-10 3 -4.815617868554475e-01 -4.815617868456633e-01 9.78428e-12 5.53433e-07 * ----------------------------------------------------------------------------------------------------- 23 Si 1 5.180343877674587e-01 5.180343877671492e-01 3.09530e-13 3.38342e-10 2 1.741409222808099e+00 1.741409222762146e+00 4.59526e-11 3.82827e-10 3 -4.075583900316354e-01 -4.075583900365798e-01 4.94449e-12 1.52644e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.157641877750484e+00 1.157641877783599e+00 3.31146e-11 3.71982e-10 2 6.559397571364363e-01 6.559397571609239e-01 2.44876e-11 3.37468e-09 * 3 1.321884124263561e+00 1.321884124350735e+00 8.71740e-11 4.17975e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.243520781530973e+00 -2.243520781386808e+00 1.44165e-10 1.52603e-10 2 -2.197058029376874e+00 -2.197058029505958e+00 1.29084e-10 4.13966e-10 3 -6.418707118261653e-01 -6.418707116090127e-01 2.17153e-10 3.19035e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 5.406800178622847e-01 5.406800178603153e-01 1.96942e-12 3.60609e-10 2 2.394095779597693e+00 2.394095779558489e+00 3.92042e-11 4.34727e-10 3 -2.425217857101362e+00 -2.425217856979842e+00 1.21520e-10 1.77949e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 2.174719806958462e+00 2.174719806997547e+00 3.90852e-11 1.13292e-09 2 -1.188336467761070e+00 -1.188336467810053e+00 4.89830e-11 5.85227e-10 3 4.122645107960270e+00 4.122645107991721e+00 3.14504e-11 3.57305e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 1.406252036027286e-01 1.406252036705715e-01 6.78428e-11 2.35087e-10 2 -7.901002786711180e-01 -7.901002787238953e-01 5.27773e-11 3.90244e-10 3 6.726086179687865e-01 6.726086179780248e-01 9.23839e-12 4.18031e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 -4.268630678948170e+00 -4.268630679003417e+00 5.52474e-11 1.19783e-10 2 -5.839019703839345e+00 -5.839019703806058e+00 3.32863e-11 1.14658e-08 * 3 -1.228790650768912e+00 -1.228790650650232e+00 1.18681e-10 2.68790e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 4.586922218582949e+00 4.586922218560582e+00 2.23679e-11 3.44107e-11 2 3.098983867213855e+00 3.098983867231190e+00 1.73350e-11 3.06834e-10 3 -5.584238163352798e-02 -5.584238161347338e-02 2.00546e-11 3.92202e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -9.416242727875165e-01 -9.416242727862096e-01 1.30684e-12 2.49827e-10 2 -3.080985729940035e+00 -3.080985729979872e+00 3.98366e-11 5.71070e-10 3 9.331082306516288e-01 9.331082306544800e-01 2.85116e-12 1.05523e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.477528097446207e+00 -1.477528097274504e+00 1.71703e-10 6.63010e-11 2 -2.245687537158144e+00 -2.245687537167417e+00 9.27303e-12 2.50819e-09 * 3 -1.141845934796879e+00 -1.141845934759791e+00 3.70879e-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 = ----------------------- = 4.82437e-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 -1.790517284922106e+00 7.94120e-12 3.28629e-10 2 -1.264522078783577e+00 -1.264522078786755e+00 3.17857e-12 2.67630e-10 3 1.582899946383685e-01 1.582899946589979e-01 2.06293e-11 1.12880e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.158112414785887e+00 3.158112414645050e+00 1.40836e-10 4.68440e-10 2 4.521628068689511e+00 4.521628068710781e+00 2.12701e-11 3.00810e-10 3 -3.427818028634169e+00 -3.427818028830179e+00 1.96010e-10 3.03491e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.357404069814879e+00 2.357404069850851e+00 3.59717e-11 1.08583e-10 2 -3.540715619774599e+00 -3.540715619810290e+00 3.56910e-11 1.69517e-10 3 3.130085686317801e+00 3.130085686312324e+00 5.47651e-12 5.25055e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.717699268514877e+00 -2.717699268499247e+00 1.56297e-11 1.30556e-09 2 1.208855285643590e+00 1.208855285667309e+00 2.37195e-11 8.62099e-10 3 2.426416151404646e+00 2.426416151450540e+00 4.58940e-11 2.22832e-10 ----------------------------------------------------------------------------------------------------- 5 Li 1 -6.142243393995063e-01 -6.142243393926502e-01 6.85607e-12 2.07627e-09 * 2 1.753278331116231e+00 1.753278331120390e+00 4.15934e-12 1.09160e-10 3 1.005018384708459e+00 1.005018384687921e+00 2.05382e-11 1.06711e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 4.873689998050291e-01 4.873689998190319e-01 1.40028e-11 1.16552e-10 2 -1.272234512822888e+00 -1.272234512823902e+00 1.01430e-12 6.39744e-11 3 4.231672409396043e-01 4.231672409455629e-01 5.95862e-12 5.09467e-11 ----------------------------------------------------------------------------------------------------- 7 Li 1 -1.136125730842689e+00 -1.136125730861360e+00 1.86715e-11 3.40478e-10 2 1.215896532976795e+00 1.215896532991617e+00 1.48224e-11 1.62457e-10 3 1.044081215873552e-01 1.044081215658819e-01 2.14733e-11 1.12149e-09 ----------------------------------------------------------------------------------------------------- 8 Si 1 1.164282886330633e+01 1.164282886328238e+01 2.39471e-11 1.38796e-07 * 2 -2.734438390842544e+00 -2.734438390841538e+00 1.00542e-12 8.16099e-09 * 3 -8.025525578710303e+00 -8.025525578719554e+00 9.25127e-12 2.05944e-10 ----------------------------------------------------------------------------------------------------- 9 Li 1 4.659671179117119e-01 4.659671178619817e-01 4.97302e-11 4.80670e-10 2 -6.280461548126368e-01 -6.280461547815903e-01 3.10465e-11 3.36223e-10 3 6.735231351185951e-01 6.735231351027661e-01 1.58290e-11 2.96814e-11 ----------------------------------------------------------------------------------------------------- 10 Li 1 2.127265567620119e-01 2.127265567660872e-01 4.07535e-12 1.84248e-09 * 2 -4.606023776068873e-01 -4.606023776073860e-01 4.98657e-13 1.18120e-09 3 8.761171512021274e-02 8.761171511913415e-02 1.07858e-12 7.55022e-11 ----------------------------------------------------------------------------------------------------- 11 Li 1 -2.266851337490819e+00 -2.266851337481893e+00 8.92575e-12 1.25227e-10 2 4.061744256482274e+00 4.061744256467147e+00 1.51266e-11 1.66242e-10 3 -1.136808873478833e+00 -1.136808873541265e+00 6.24321e-11 8.95313e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.520679371546201e-01 2.520679371636520e-01 9.03189e-12 1.23079e-10 2 1.013785853613723e+00 1.013785853603361e+00 1.03617e-11 3.60090e-11 3 -2.227525823352852e+00 -2.227525823369069e+00 1.62168e-11 1.31895e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -3.548750539208489e+00 -3.548750539198153e+00 1.03353e-11 2.58819e-10 2 -3.226343792614232e+00 -3.226343792609362e+00 4.86988e-12 7.45604e-11 3 -2.570912604711006e+00 -2.570912604739065e+00 2.80593e-11 8.34266e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.986917687035550e-01 7.986917687066306e-01 3.07565e-12 1.28065e-10 2 2.259304775111421e+00 2.259304775109492e+00 1.92824e-12 1.86947e-10 3 -1.671718616318311e+00 -1.671718616286347e+00 3.19640e-11 9.02447e-11 ----------------------------------------------------------------------------------------------------- 15 Li 1 1.748401550173001e+00 1.748401550189532e+00 1.65314e-11 1.06681e-09 2 -1.455349499753689e+00 -1.455349499779518e+00 2.58293e-11 2.14595e-10 3 2.361263691556849e+00 2.361263691566896e+00 1.00471e-11 1.09672e-10 ----------------------------------------------------------------------------------------------------- 16 Li 1 -9.659819568927389e-01 -9.659819569160207e-01 2.32818e-11 3.50771e-10 2 8.555108243365719e-01 8.555108242674988e-01 6.90731e-11 2.33376e-10 3 1.389903388093617e+00 1.389903388094540e+00 9.23261e-13 2.98799e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.390546287823689e+00 -1.390546287767264e+00 5.64249e-11 1.51360e-10 2 -1.095249577985515e+00 -1.095249577963646e+00 2.18687e-11 1.56165e-10 3 -1.966971567183667e+00 -1.966971567201295e+00 1.76277e-11 2.47637e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 -7.340744560211628e+00 -7.340744560156013e+00 5.56151e-11 3.11462e-10 2 4.390913445918037e-01 4.390913445978428e-01 6.03917e-12 1.16254e-09 3 1.030484808040546e+01 1.030484808038207e+01 2.33875e-11 3.54468e-10 ----------------------------------------------------------------------------------------------------- 19 Li 1 6.567845864995783e-01 6.567845864982201e-01 1.35814e-12 1.53675e-10 2 1.028462021608259e-01 1.028462021795983e-01 1.87724e-11 2.33554e-10 3 -9.877123960678241e-01 -9.877123960669253e-01 8.98837e-13 6.65232e-10 ----------------------------------------------------------------------------------------------------- 20 Li 1 7.062568046998022e-03 7.062568045011080e-03 1.98694e-12 3.25863e-10 2 4.058933139724333e-01 4.058933139655175e-01 6.91575e-12 1.28701e-09 3 -7.746764416386438e-01 -7.746764416372267e-01 1.41709e-12 1.69955e-09 * ----------------------------------------------------------------------------------------------------- 21 Si 1 -5.230449966255746e+00 -5.230449966284772e+00 2.90266e-11 1.25721e-10 2 -3.413976386004714e+00 -3.413976386011060e+00 6.34603e-12 5.49317e-09 * 3 -4.060222465881976e+00 -4.060222465881338e+00 6.38600e-13 5.23881e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.763881185196809e+00 2.763881185190690e+00 6.11955e-12 7.30438e-11 2 2.824876051867628e+00 2.824876051882219e+00 1.45910e-11 1.73931e-10 3 -2.108090275077651e+00 -2.108090275094681e+00 1.70304e-11 4.29589e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 4.166662310614454e+00 4.166662310605354e+00 9.09939e-12 9.33698e-11 2 -7.924210127650680e-01 -7.924210127567266e-01 8.34144e-12 1.05136e-10 3 3.555484814206483e+00 3.555484814200849e+00 5.63327e-12 2.28240e-10 ----------------------------------------------------------------------------------------------------- 24 Li 1 -2.476206479950076e+00 -2.476206479984686e+00 3.46092e-11 1.49271e-10 2 2.113612690681208e+00 2.113612690713377e+00 3.21689e-11 2.23997e-10 3 2.106101560261629e+00 2.106101560289056e+00 2.74269e-11 2.29956e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.197524432816632e+00 -1.197524432803765e+00 1.28666e-11 2.28498e-10 2 -3.238154437744249e+00 -3.238154437744571e+00 3.22853e-13 6.05769e-11 3 3.250987610078125e-01 3.250987610159152e-01 8.10263e-12 1.99063e-10 ----------------------------------------------------------------------------------------------------- 26 Li 1 8.979683569333502e-01 8.979683569121609e-01 2.11893e-11 1.80318e-10 2 1.332309335973575e+00 1.332309335972091e+00 1.48415e-12 1.99478e-10 3 -8.244758042017204e-01 -8.244758042279363e-01 2.62159e-11 1.21692e-10 ----------------------------------------------------------------------------------------------------- 27 Li 1 -4.156248118965454e-01 -4.156248119007079e-01 4.16256e-12 5.93943e-10 2 -1.805755282992175e+00 -1.805755282999091e+00 6.91558e-12 9.25334e-10 3 5.575072924207378e-01 5.575072924260699e-01 5.33207e-12 7.31000e-11 ----------------------------------------------------------------------------------------------------- 28 Li 1 -2.968615478553227e-01 -2.968615478706696e-01 1.53469e-11 6.01581e-10 2 4.690823951235348e-01 4.690823951325932e-01 9.05837e-12 1.65136e-09 * 3 1.214211098230123e+00 1.214211098203064e+00 2.70584e-11 9.68934e-11 ----------------------------------------------------------------------------------------------------- 29 Li 1 2.041352810627700e-01 2.041352810548430e-01 7.92699e-12 1.90928e-10 2 -1.032473661596912e+00 -1.032473661626168e+00 2.92566e-11 1.29922e-10 3 -1.156645488613240e+00 -1.156645488627406e+00 1.41660e-11 3.37756e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 2.012240508966336e-01 2.012240508998878e-01 3.25426e-12 1.38450e-10 2 1.909273912933116e+00 1.909273912810544e+00 1.22572e-10 1.97261e-10 3 -6.806797192331735e-01 -6.806797192308169e-01 2.35656e-12 7.16853e-10 ----------------------------------------------------------------------------------------------------- 31 Li 1 8.508015462439086e-01 8.508015462311901e-01 1.27185e-11 6.27497e-10 2 -1.740131697779261e+00 -1.740131697806958e+00 2.76972e-11 5.04896e-10 3 1.074622997720854e+00 1.074622997695103e+00 2.57510e-11 1.54791e-10 ----------------------------------------------------------------------------------------------------- 32 Li 1 5.160193801613948e-01 5.160193801644565e-01 3.06166e-12 7.64649e-11 2 1.213425308604708e+00 1.213425308605101e+00 3.93019e-13 4.74305e-10 3 7.222215693647598e-01 7.222215693478903e-01 1.68695e-11 1.60629e-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 = ----------------------- = 2.81334e-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.