!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_MEAM_CuiGaoCui_2012_LiSi__SM_562938628131_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 5.355470140923946e-02 5.355470141161948e-02 2.38002e-12 1.77565e-11 2 -4.656082285943704e-02 -4.656082286191666e-02 2.47961e-12 2.36824e-11 3 1.278541750707889e-02 1.278541750765492e-02 5.76034e-13 1.39352e-11 ----------------------------------------------------------------------------------------------------- 2 Li 1 1.561971114440266e-01 1.561971114438148e-01 2.11803e-13 6.23018e-11 2 3.324564076116538e-01 3.324564076078207e-01 3.83310e-12 8.95239e-11 3 1.242007787014008e-01 1.242007787001295e-01 1.27136e-12 3.02156e-11 ----------------------------------------------------------------------------------------------------- 3 Li 1 3.468714749843004e-01 3.468714749823658e-01 1.93462e-12 6.18559e-11 2 1.003150372075101e-01 1.003150372158899e-01 8.37974e-12 8.65658e-12 3 1.392138132259255e-01 1.392138132356732e-01 9.74767e-12 4.32038e-12 ----------------------------------------------------------------------------------------------------- 4 Li 1 1.208427753866691e-01 1.208427754130833e-01 2.64142e-11 5.93610e-11 2 1.546331593665503e-01 1.546331593806204e-01 1.40701e-11 3.19881e-10 * 3 2.746241446576623e-01 2.746241446639811e-01 6.31878e-12 5.60208e-11 ----------------------------------------------------------------------------------------------------- 5 Li 1 -1.119809712319879e-01 -1.119809712149812e-01 1.70067e-11 7.55667e-11 2 -1.755694240800825e-02 -1.755694241083446e-02 2.82621e-12 3.50275e-11 3 1.521751723027225e-02 1.521751723414586e-02 3.87361e-12 3.70531e-11 ----------------------------------------------------------------------------------------------------- 6 Li 1 -8.348987990483811e-02 -8.348987991101271e-02 6.17460e-12 5.67251e-11 2 2.606992285243093e-01 2.606992285022149e-01 2.20943e-11 2.94436e-11 3 1.160331202985460e-01 1.160331202986078e-01 6.18117e-14 4.61364e-11 ----------------------------------------------------------------------------------------------------- 7 Li 1 1.600746846336042e-02 1.600746845576103e-02 7.59939e-12 7.84368e-11 2 -2.505892535503684e-01 -2.505892535373440e-01 1.30244e-11 5.07211e-11 3 -8.839790542249434e-02 -8.839790542159462e-02 8.99725e-13 5.25572e-10 * ----------------------------------------------------------------------------------------------------- 8 Li 1 -3.186276490835099e-01 -3.186276490912625e-01 7.75263e-12 2.77934e-11 2 -1.126869322364336e-02 -1.126869322523266e-02 1.58931e-12 7.06860e-11 3 1.145966527205095e-01 1.145966527306191e-01 1.01096e-11 4.51753e-11 ----------------------------------------------------------------------------------------------------- 9 Li 1 -3.490611305988209e-03 -3.490611299507606e-03 6.48060e-12 8.25825e-11 2 -3.705579946407006e-01 -3.705579946546454e-01 1.39448e-11 4.08330e-11 3 -1.710172057363737e-01 -1.710172057364763e-01 1.02585e-13 1.47292e-11 ----------------------------------------------------------------------------------------------------- 10 Li 1 1.141342619374874e-01 1.141342619395147e-01 2.02735e-12 5.90912e-10 * 2 3.057991769338146e-02 3.057991769161564e-02 1.76582e-12 1.15746e-10 3 -1.078736778225312e-01 -1.078736778149518e-01 7.57942e-12 2.67885e-10 ----------------------------------------------------------------------------------------------------- 11 Li 1 8.864882863865671e-02 8.864882865141786e-02 1.27612e-11 1.69251e-11 2 -2.511343902923585e-01 -2.511343902951352e-01 2.77672e-12 4.44680e-11 3 1.556200711262923e-01 1.556200711238796e-01 2.41274e-12 2.95333e-11 ----------------------------------------------------------------------------------------------------- 12 Li 1 8.454825235383458e-02 8.454825236031642e-02 6.48184e-12 3.09538e-11 2 3.093852451470978e-01 3.093852451436305e-01 3.46728e-12 3.64446e-11 3 3.741281295960037e-01 3.741281295940078e-01 1.99590e-12 2.13208e-11 ----------------------------------------------------------------------------------------------------- 13 Li 1 -2.525945772089360e-01 -2.525945772071042e-01 1.83181e-12 1.11886e-10 2 -3.309784464802309e-01 -3.309784464778649e-01 2.36600e-12 3.81687e-10 * 3 -1.923038719907227e-01 -1.923038719900330e-01 6.89671e-13 1.05124e-10 ----------------------------------------------------------------------------------------------------- 14 Li 1 3.120571875137933e-03 3.120571881860582e-03 6.72265e-12 3.24450e-11 2 9.162154104251805e-02 9.162154104269749e-02 1.79440e-13 2.77205e-11 3 2.171147832632417e-02 2.171147833305789e-02 6.73371e-12 3.44128e-11 ----------------------------------------------------------------------------------------------------- 15 Li 1 1.275361891934951e-01 1.275361891944391e-01 9.44050e-13 1.01765e-10 2 -3.658985439188880e-01 -3.658985439194569e-01 5.68878e-13 6.95747e-11 3 2.501223416848147e-01 2.501223416776247e-01 7.18997e-12 6.41787e-12 ----------------------------------------------------------------------------------------------------- 16 Li 1 8.820790068154233e-02 8.820790066781406e-02 1.37283e-11 3.92799e-10 * 2 8.000898140555730e-02 8.000898140048326e-02 5.07404e-12 4.15237e-11 3 1.856298279239213e-01 1.856298279298423e-01 5.92096e-12 3.95797e-11 ----------------------------------------------------------------------------------------------------- 17 Li 1 -2.120406394925647e-01 -2.120406394923688e-01 1.95843e-13 1.95913e-11 2 4.793170955806750e-02 4.793170955969302e-02 1.62553e-12 4.63676e-11 3 -1.833773822514554e-01 -1.833773822536583e-01 2.20299e-12 1.02982e-11 ----------------------------------------------------------------------------------------------------- 18 Li 1 1.459618824935105e-01 1.459618824866753e-01 6.83520e-12 4.12862e-10 * 2 2.743375104438135e-01 2.743375104523972e-01 8.58369e-12 4.62361e-11 3 -8.767418136958924e-02 -8.767418137006507e-02 4.75828e-13 3.49536e-11 ----------------------------------------------------------------------------------------------------- 19 Li 1 1.783281239926313e-01 1.783281240060599e-01 1.34286e-11 3.83009e-11 2 1.229412222276888e-01 1.229412222208056e-01 6.88327e-12 3.19707e-11 3 3.793828434859989e-02 3.793828435204502e-02 3.44513e-12 1.50248e-10 ----------------------------------------------------------------------------------------------------- 20 Li 1 7.581194152100108e-02 7.581194152335363e-02 2.35255e-12 1.89766e-11 2 2.216568423467655e-01 2.216568423490897e-01 2.32414e-12 8.28086e-11 3 -1.391550315019167e-01 -1.391550315026598e-01 7.43045e-13 1.03528e-11 ----------------------------------------------------------------------------------------------------- 21 Li 1 -2.265237377935909e-01 -2.265237377941330e-01 5.42177e-13 5.82883e-11 2 8.973696421918842e-02 8.973696420221700e-02 1.69714e-11 2.00843e-11 3 -2.357781705955326e-01 -2.357781706056699e-01 1.01373e-11 2.74184e-11 ----------------------------------------------------------------------------------------------------- 22 Li 1 -2.702634574480366e-02 -2.702634574316105e-02 1.64261e-12 9.31360e-11 2 4.159478258225127e-01 4.159478258198923e-01 2.62040e-12 5.37242e-11 3 9.960583550337776e-02 9.960583549782194e-02 5.55582e-12 4.39091e-11 ----------------------------------------------------------------------------------------------------- 23 Li 1 -7.508332185729427e-02 -7.508332185447530e-02 2.81897e-12 3.43373e-11 2 1.141025340238525e-01 1.141025340233859e-01 4.66516e-13 3.29444e-11 3 -3.744104260158428e-02 -3.744104260195706e-02 3.72785e-13 9.78247e-11 ----------------------------------------------------------------------------------------------------- 24 Li 1 -9.675456333330494e-02 -9.675456331264264e-02 2.06623e-11 7.74227e-11 2 1.760554003716453e-01 1.760554003554314e-01 1.62139e-11 4.10634e-10 * 3 -1.022699825106853e-01 -1.022699824983453e-01 1.23400e-11 3.83891e-11 ----------------------------------------------------------------------------------------------------- 25 Li 1 3.027809139910246e-02 3.027809139656203e-02 2.54042e-12 4.54495e-11 2 -3.319003854349927e-01 -3.319003854297151e-01 5.27761e-12 2.04002e-10 3 2.287324535710205e-01 2.287324535654086e-01 5.61190e-12 5.25970e-11 ----------------------------------------------------------------------------------------------------- 26 Li 1 -1.222727890216360e-01 -1.222727889679179e-01 5.37182e-11 1.75999e-10 2 9.445575308524200e-02 9.445575310980608e-02 2.45641e-11 1.48820e-10 3 -2.252929749056075e-01 -2.252929750137524e-01 1.08145e-10 4.38806e-10 * ----------------------------------------------------------------------------------------------------- 27 Li 1 2.575435596616648e-01 2.575435596498531e-01 1.18117e-11 4.90646e-11 2 -6.749358290308380e-01 -6.749358290164327e-01 1.44054e-11 1.75548e-10 3 -1.052772279402975e-01 -1.052772279382259e-01 2.07159e-12 1.49311e-10 ----------------------------------------------------------------------------------------------------- 28 Li 1 -8.797356299496978e-02 -8.797356298963649e-02 5.33329e-12 8.67544e-11 2 1.133980882430771e-01 1.133980882534115e-01 1.03344e-11 2.22596e-11 3 -2.378422570678573e-01 -2.378422570663327e-01 1.52461e-12 4.07069e-11 ----------------------------------------------------------------------------------------------------- 29 Li 1 -2.565238694399218e-01 -2.565238694407340e-01 8.12128e-13 4.84054e-11 2 -3.239921294110708e-01 -3.239921293734550e-01 3.76159e-11 1.40127e-09 * 3 -2.668421251966572e-01 -2.668421253113457e-01 1.14688e-10 1.35610e-08 * ----------------------------------------------------------------------------------------------------- 30 Li 1 -1.586888564837338e-01 -1.586888564863158e-01 2.58202e-12 8.99643e-11 2 1.122280250101949e-01 1.122280250108718e-01 6.76931e-13 2.88718e-11 3 -1.396793212129302e-01 -1.396793212090714e-01 3.85877e-12 5.99147e-10 * ----------------------------------------------------------------------------------------------------- 31 Li 1 1.763089407045778e-01 1.763089406852449e-01 1.93329e-11 9.37672e-11 2 -2.902473282412633e-01 -2.902473283180301e-01 7.67668e-11 6.04095e-10 * 3 9.420878381288135e-02 9.420878380214692e-02 1.07344e-11 1.21927e-10 ----------------------------------------------------------------------------------------------------- 32 Li 1 -3.083070124315809e-02 -3.083070126162517e-02 1.84671e-11 1.14319e-10 2 1.231293661411737e-01 1.231293661445943e-01 3.42067e-12 8.75845e-11 3 7.585370789160382e-02 7.585370789212809e-02 5.24261e-13 5.40358e-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 = 14, direction = 1: |F_model - F_numer| error = ----------------------- = 2.15430e-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 1.213150243781522e+00 1.213150243771136e+00 1.03855e-11 1.43609e-09 2 -7.160749589451760e-01 -7.160749589363230e-01 8.85303e-12 3.73002e-11 3 1.352752074053082e+00 1.352752074054627e+00 1.54454e-12 6.67468e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.263339162142796e+00 -1.263339162188194e+00 4.53979e-11 1.05573e-09 2 3.025516608101817e+00 3.025516608165905e+00 6.40883e-11 5.16895e-10 3 -1.771517865754543e+00 -1.771517865760871e+00 6.32849e-12 1.43284e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 4.060120981240988e+00 4.060120981158251e+00 8.27374e-11 3.69721e-10 2 -2.549944774986994e+00 -2.549944775091459e+00 1.04465e-10 1.11766e-10 3 -2.319153819111606e+00 -2.319153819061280e+00 5.03264e-11 1.70920e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.460209817047352e+00 -1.460209817022700e+00 2.46516e-11 1.73645e-10 2 -8.821912438677599e-01 -8.821912438534686e-01 1.42913e-11 8.98592e-11 3 2.840829103529530e+00 2.840829103502135e+00 2.73950e-11 1.22422e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 6.879421414736090e-01 6.879421414933964e-01 1.97874e-11 7.77203e-10 2 -3.163293822439986e-01 -3.163293822209313e-01 2.30674e-11 1.86890e-10 3 1.455057853682997e+00 1.455057853652871e+00 3.01261e-11 1.78634e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -1.408529116272407e+00 -1.408529116293477e+00 2.10705e-11 2.16618e-10 2 -8.483901987841817e-02 -8.483901988732759e-02 8.90941e-12 1.67196e-10 3 2.096318927954328e+00 2.096318927950811e+00 3.51674e-12 2.72729e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -1.607659742341152e+00 -1.607659742361244e+00 2.00919e-11 1.16462e-09 2 1.752762672856688e+00 1.752762672843922e+00 1.27662e-11 2.19909e-10 3 -1.199098149454143e+00 -1.199098149457430e+00 3.28737e-12 5.57940e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.859373440874607e-01 -1.859373440276018e-01 5.98589e-11 3.04702e-10 2 2.806210068140910e+00 2.806210068146751e+00 5.84066e-12 1.11629e-10 3 2.199260517853842e+00 2.199260517854591e+00 7.48734e-13 1.21888e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.256029127573880e+00 2.256029127509100e+00 6.47793e-11 9.09748e-11 2 1.920592620235265e+00 1.920592620220611e+00 1.46541e-11 4.56857e-11 3 4.715511478307931e-02 4.715511480825735e-02 2.51780e-11 1.11389e-08 * ----------------------------------------------------------------------------------------------------- 10 Si 1 2.570703859021393e-01 2.570703858863999e-01 1.57395e-11 5.47476e-11 2 -1.537203172070152e+00 -1.537203172065679e+00 4.47331e-12 8.67477e-11 3 2.255357103017322e+00 2.255357103013409e+00 3.91287e-12 2.83497e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 3.340435198481354e+00 3.340435198539998e+00 5.86442e-11 6.38262e-10 2 -2.028562378453050e+00 -2.028562378484583e+00 3.15326e-11 4.14816e-10 3 -6.680790960354552e-02 -6.680790956989677e-02 3.36488e-11 1.46890e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 9.086858809557273e-01 9.086858809396363e-01 1.60910e-11 5.08327e-10 2 4.060063763212247e-01 4.060063764637160e-01 1.42491e-10 1.39020e-10 3 -1.272466380623179e+00 -1.272466380595612e+00 2.75671e-11 6.39697e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.309540436328097e+00 -2.309540436336806e+00 8.70903e-12 1.60588e-10 2 8.769009169317091e-01 8.769009169999925e-01 6.82834e-11 4.76138e-10 3 -7.048890867815447e-01 -7.048890867932612e-01 1.17165e-11 3.76847e-09 * ----------------------------------------------------------------------------------------------------- 14 Si 1 4.737554726028128e-01 4.737554726020289e-01 7.83928e-13 1.04906e-10 2 -6.022916413269785e-01 -6.022916413393773e-01 1.23987e-11 6.47614e-11 3 9.728399077251907e-01 9.728399077272605e-01 2.06979e-12 2.03334e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.548325070490405e+00 1.548325070453775e+00 3.66307e-11 6.25739e-09 * 2 -2.153462939072547e+00 -2.153462939073617e+00 1.06937e-12 4.31363e-10 3 1.544486627197744e+00 1.544486627194713e+00 3.03046e-12 2.08500e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -4.196994649474977e+00 -4.196994649492103e+00 1.71259e-11 1.75387e-10 2 2.336005923085485e+00 2.336005923073052e+00 1.24327e-11 8.56050e-10 3 -4.786127342128545e+00 -4.786127342119480e+00 9.06475e-12 6.85082e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.725396145059627e+00 -2.725396145048399e+00 1.12284e-11 1.58478e-09 2 6.636303138645534e-01 6.636303139074409e-01 4.28875e-11 3.06778e-10 3 3.144259829719492e+00 3.144259829711862e+00 7.63034e-12 2.86134e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 7.240240966991968e-01 7.240240968223060e-01 1.23109e-10 3.50631e-10 2 2.567681834955529e+00 2.567681834956433e+00 9.04610e-13 6.37101e-10 3 -1.608344811973374e+00 -1.608344811984627e+00 1.12532e-11 7.06762e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -1.622446011095948e+00 -1.622446011110341e+00 1.43925e-11 1.92779e-10 2 1.160452390243568e+00 1.160452390253966e+00 1.03979e-11 5.31108e-11 3 -2.427198334781523e+00 -2.427198334778525e+00 2.99760e-12 1.77021e-09 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.231926018003187e+00 2.231926017984005e+00 1.91815e-11 3.59383e-10 2 8.447975245649784e-01 8.447975245740170e-01 9.03866e-12 2.41648e-09 * 3 -2.722064686512774e+00 -2.722064686524188e+00 1.14144e-11 5.97358e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 -2.038938465540820e+00 -2.038938465556541e+00 1.57212e-11 2.03814e-10 2 -2.076327492228683e+00 -2.076327492216953e+00 1.17297e-11 2.01366e-10 3 3.017929593779413e-01 3.017929593988763e-01 2.09350e-11 8.00619e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 9.302065903741441e-01 9.302065903975262e-01 2.33821e-11 5.83816e-09 * 2 2.037428873762349e+00 2.037428873748715e+00 1.36340e-11 9.94823e-09 * 3 -4.815617868554395e-01 -4.815617868404986e-01 1.49410e-11 3.54668e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 5.180343877674929e-01 5.180343877647092e-01 2.78366e-12 2.59698e-10 2 1.741409222808102e+00 1.741409222809789e+00 1.68709e-12 3.10697e-10 3 -4.075583900316397e-01 -4.075583900467831e-01 1.51433e-11 2.02207e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.157641877750510e+00 1.157641877792719e+00 4.22091e-11 4.24468e-10 2 6.559397571363415e-01 6.559397571254519e-01 1.08895e-11 4.02120e-09 * 3 1.321884124263540e+00 1.321884124111608e+00 1.51932e-10 5.77146e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.243520781531057e+00 -2.243520781329056e+00 2.02001e-10 3.03448e-10 2 -2.197058029376874e+00 -2.197058029398451e+00 2.15770e-11 3.41256e-10 3 -6.418707118263336e-01 -6.418707115873606e-01 2.38973e-10 1.68328e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 5.406800178624048e-01 5.406800174727575e-01 3.89647e-10 9.43154e-10 2 2.394095779597686e+00 2.394095779573651e+00 2.40341e-11 4.44458e-10 3 -2.425217857101462e+00 -2.425217857011365e+00 9.00964e-11 2.42612e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 2.174719806958466e+00 2.174719806882027e+00 7.64393e-11 3.15887e-10 2 -1.188336467760998e+00 -1.188336467615768e+00 1.45230e-10 2.56002e-10 3 4.122645107960423e+00 4.122645108075963e+00 1.15540e-10 3.56257e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 1.406252036027704e-01 1.406252035892820e-01 1.34884e-11 1.03839e-09 2 -7.901002786710957e-01 -7.901002787176358e-01 4.65401e-11 1.71433e-10 3 6.726086179687953e-01 6.726086179896094e-01 2.08140e-11 2.47883e-09 * ----------------------------------------------------------------------------------------------------- 29 Si 1 -4.268630678948205e+00 -4.268630678963182e+00 1.49765e-11 1.18903e-08 * 2 -5.839019703839259e+00 -5.839019703862397e+00 2.31379e-11 9.06109e-10 3 -1.228790650768887e+00 -1.228790650827076e+00 5.81895e-11 1.72495e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 4.586922218582989e+00 4.586922218451333e+00 1.31656e-10 2.11793e-08 * 2 3.098983867213905e+00 3.098983867205437e+00 8.46834e-12 3.35786e-10 3 -5.584238163352245e-02 -5.584238160338716e-02 3.01353e-11 3.83274e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -9.416242727874617e-01 -9.416242727724689e-01 1.49929e-11 2.21364e-10 2 -3.080985729940038e+00 -3.080985729930823e+00 9.21485e-12 2.86768e-10 3 9.331082306516442e-01 9.331082306209595e-01 3.06847e-11 2.61854e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.477528097446241e+00 -1.477528097472363e+00 2.61218e-11 5.17294e-10 2 -2.245687537158089e+00 -2.245687537140733e+00 1.73555e-11 1.18201e-10 3 -1.141845934796891e+00 -1.141845934787361e+00 9.52993e-12 4.04231e-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 = 26, direction = 1: |F_model - F_numer| error = ----------------------- = 7.20662e-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 -1.790517284912614e+00 1.54965e-12 1.46166e-10 2 -1.264522078783539e+00 -1.264522078813901e+00 3.03626e-11 1.36872e-10 3 1.582899946383983e-01 1.582899946739960e-01 3.55977e-11 7.00973e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.158112414786004e+00 3.158112414846419e+00 6.04152e-11 1.93304e-10 2 4.521628068689461e+00 4.521628068697598e+00 8.13749e-12 2.59913e-10 3 -3.427818028634122e+00 -3.427818028744400e+00 1.10278e-10 1.08046e-09 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.357404069814833e+00 2.357404069857993e+00 4.31593e-11 3.57777e-10 2 -3.540715619774512e+00 -3.540715619734156e+00 4.03553e-11 3.00415e-10 3 3.130085686317926e+00 3.130085686323970e+00 6.04361e-12 5.66303e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.717699268514920e+00 -2.717699268736133e+00 2.21213e-10 4.81704e-10 2 1.208855285643488e+00 1.208855285628584e+00 1.49045e-11 8.89727e-10 3 2.426416151404607e+00 2.426416151443131e+00 3.85243e-11 1.58598e-10 ----------------------------------------------------------------------------------------------------- 5 Li 1 -6.142243393995269e-01 -6.142243393844015e-01 1.51255e-11 2.07847e-09 * 2 1.753278331116308e+00 1.753278331133876e+00 1.75684e-11 8.74398e-11 3 1.005018384708473e+00 1.005018384700967e+00 7.50533e-12 1.37752e-09 ----------------------------------------------------------------------------------------------------- 6 Si 1 4.873689998050659e-01 4.873689998081636e-01 3.09763e-12 3.03412e-09 * 2 -1.272234512822947e+00 -1.272234512837451e+00 1.45033e-11 3.85598e-11 3 4.231672409396293e-01 4.231672409622038e-01 2.25744e-11 1.09553e-09 ----------------------------------------------------------------------------------------------------- 7 Li 1 -1.136125730842701e+00 -1.136125730829315e+00 1.33853e-11 3.27076e-11 2 1.215896532976825e+00 1.215896532988034e+00 1.12093e-11 2.98749e-10 3 1.044081215873234e-01 1.044081215708248e-01 1.64986e-11 3.97963e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 1.164282886330614e+01 1.164282886340698e+01 1.00840e-10 8.32429e-10 2 -2.734438390842484e+00 -2.734438390863922e+00 2.14389e-11 1.16284e-10 3 -8.025525578710267e+00 -8.025525578652983e+00 5.72840e-11 6.70894e-11 ----------------------------------------------------------------------------------------------------- 9 Li 1 4.659671179116908e-01 4.659671179522165e-01 4.05257e-11 8.86524e-11 2 -6.280461548126517e-01 -6.280461548108078e-01 1.84386e-12 8.63164e-11 3 6.735231351185516e-01 6.735231351117136e-01 6.83797e-12 7.86518e-11 ----------------------------------------------------------------------------------------------------- 10 Li 1 2.127265567619299e-01 2.127265567753157e-01 1.33858e-11 9.35269e-11 2 -4.606023776068714e-01 -4.606023775972767e-01 9.59471e-12 1.16769e-09 3 8.761171512018091e-02 8.761171512162375e-02 1.44283e-12 2.79708e-10 ----------------------------------------------------------------------------------------------------- 11 Li 1 -2.266851337490645e+00 -2.266851337464750e+00 2.58944e-11 5.86957e-11 2 4.061744256482186e+00 4.061744256481729e+00 4.56524e-13 3.21781e-10 3 -1.136808873478877e+00 -1.136808873489031e+00 1.01537e-11 1.29197e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.520679371545610e-01 2.520679371554486e-01 8.87623e-13 5.44715e-10 2 1.013785853613682e+00 1.013785853608935e+00 4.74687e-12 8.51272e-11 3 -2.227525823352680e+00 -2.227525823313777e+00 3.89031e-11 1.10939e-08 * ----------------------------------------------------------------------------------------------------- 13 Si 1 -3.548750539208618e+00 -3.548750539228842e+00 2.02238e-11 2.40584e-10 2 -3.226343792614360e+00 -3.226343792549423e+00 6.49369e-11 2.51248e-10 3 -2.570912604711050e+00 -2.570912604696644e+00 1.44054e-11 3.16033e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.986917687036516e-01 7.986917686969011e-01 6.75049e-12 1.68323e-10 2 2.259304775111507e+00 2.259304775101722e+00 9.78506e-12 4.64847e-10 3 -1.671718616318330e+00 -1.671718616378266e+00 5.99363e-11 1.26566e-10 ----------------------------------------------------------------------------------------------------- 15 Li 1 1.748401550173066e+00 1.748401550197046e+00 2.39795e-11 1.36971e-10 2 -1.455349499753727e+00 -1.455349499789815e+00 3.60876e-11 6.90712e-11 3 2.361263691556973e+00 2.361263691547746e+00 9.22729e-12 4.96105e-11 ----------------------------------------------------------------------------------------------------- 16 Li 1 -9.659819568927196e-01 -9.659819569021669e-01 9.44733e-12 1.37569e-10 2 8.555108243366268e-01 8.555108244381214e-01 1.01495e-10 1.31026e-10 3 1.389903388093579e+00 1.389903388018865e+00 7.47142e-11 1.73115e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.390546287823680e+00 -1.390546287863922e+00 4.02420e-11 6.19585e-10 2 -1.095249577985551e+00 -1.095249578036066e+00 5.05149e-11 4.04913e-10 3 -1.966971567183694e+00 -1.966971567184339e+00 6.44818e-13 1.45902e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 -7.340744560211424e+00 -7.340744560295484e+00 8.40599e-11 8.43565e-11 2 4.390913445917645e-01 4.390913446078782e-01 1.61137e-11 2.82495e-10 3 1.030484808040541e+01 1.030484808034142e+01 6.39826e-11 8.90328e-09 * ----------------------------------------------------------------------------------------------------- 19 Li 1 6.567845864994956e-01 6.567845865007981e-01 1.30251e-12 9.05307e-10 2 1.028462021608506e-01 1.028462021709153e-01 1.00647e-11 2.33760e-10 3 -9.877123960678619e-01 -9.877123961054166e-01 3.75547e-11 8.52977e-10 ----------------------------------------------------------------------------------------------------- 20 Li 1 7.062568047015522e-03 7.062568050188306e-03 3.17278e-12 1.94319e-11 2 4.058933139724325e-01 4.058933139630093e-01 9.42324e-12 1.22295e-10 3 -7.746764416386949e-01 -7.746764416553373e-01 1.66425e-11 1.72672e-09 * ----------------------------------------------------------------------------------------------------- 21 Si 1 -5.230449966255638e+00 -5.230449966293540e+00 3.79012e-11 3.17473e-10 2 -3.413976386004729e+00 -3.413976385993492e+00 1.12377e-11 7.46391e-10 3 -4.060222465881954e+00 -4.060222465850033e+00 3.19211e-11 3.47149e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.763881185196786e+00 2.763881185170722e+00 2.60640e-11 9.91123e-11 2 2.824876051867696e+00 2.824876051836319e+00 3.13771e-11 1.19654e-09 3 -2.108090275077661e+00 -2.108090275130023e+00 5.23612e-11 1.16243e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 4.166662310614381e+00 4.166662310628752e+00 1.43707e-11 7.13268e-10 2 -7.924210127651332e-01 -7.924210127597571e-01 5.37614e-12 7.99693e-11 3 3.555484814206442e+00 3.555484814197578e+00 8.86446e-12 9.58003e-11 ----------------------------------------------------------------------------------------------------- 24 Li 1 -2.476206479950052e+00 -2.476206479962301e+00 1.22489e-11 2.57128e-10 2 2.113612690681224e+00 2.113612690685330e+00 4.10605e-12 1.87323e-10 3 2.106101560261518e+00 2.106101560236137e+00 2.53815e-11 2.55548e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.197524432816697e+00 -1.197524432825144e+00 8.44746e-12 1.50294e-10 2 -3.238154437744121e+00 -3.238154437763833e+00 1.97127e-11 1.83998e-10 3 3.250987610077400e-01 3.250987610146824e-01 6.94239e-12 1.01630e-10 ----------------------------------------------------------------------------------------------------- 26 Li 1 8.979683569333144e-01 8.979683569224981e-01 1.08163e-11 9.13452e-10 2 1.332309335973540e+00 1.332309335967609e+00 5.93103e-12 5.01208e-11 3 -8.244758042017628e-01 -8.244758042121784e-01 1.04156e-11 5.58609e-10 ----------------------------------------------------------------------------------------------------- 27 Li 1 -4.156248118964799e-01 -4.156248118920911e-01 4.38877e-12 5.97924e-10 2 -1.805755282992109e+00 -1.805755282993912e+00 1.80300e-12 8.77098e-10 3 5.575072924208335e-01 5.575072924269021e-01 6.06859e-12 6.86556e-11 ----------------------------------------------------------------------------------------------------- 28 Li 1 -2.968615478553406e-01 -2.968615479031443e-01 4.78037e-11 1.94944e-10 2 4.690823951235272e-01 4.690823951238506e-01 3.23352e-13 1.62589e-09 3 1.214211098230122e+00 1.214211098205468e+00 2.46541e-11 1.30250e-10 ----------------------------------------------------------------------------------------------------- 29 Li 1 2.041352810626589e-01 2.041352810474795e-01 1.51793e-11 3.30396e-10 2 -1.032473661596966e+00 -1.032473661564606e+00 3.23599e-11 2.00898e-10 3 -1.156645488613181e+00 -1.156645488599325e+00 1.38560e-11 1.00999e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 2.012240508967111e-01 2.012240508740737e-01 2.26373e-11 1.63498e-10 2 1.909273912933136e+00 1.909273912993226e+00 6.00899e-11 3.30202e-10 3 -6.806797192331731e-01 -6.806797192192910e-01 1.38820e-11 1.52475e-10 ----------------------------------------------------------------------------------------------------- 31 Li 1 8.508015462439001e-01 8.508015462719370e-01 2.80369e-11 2.27380e-11 2 -1.740131697779272e+00 -1.740131697814081e+00 3.48097e-11 2.30585e-10 3 1.074622997720812e+00 1.074622997712787e+00 8.02491e-12 2.57921e-10 ----------------------------------------------------------------------------------------------------- 32 Li 1 5.160193801613957e-01 5.160193801846317e-01 2.32360e-11 5.82975e-11 2 1.213425308604720e+00 1.213425308599047e+00 5.67302e-12 2.09487e-10 3 7.222215693647906e-01 7.222215693526778e-01 1.21129e-11 8.89997e-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 = 20, direction = 1: |F_model - F_numer| error = ----------------------- = 4.49239e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.15430e-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 2.15430e-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.