!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_Tersoff_1990_SiC__MO_444207127575_000 Supported species : C Si random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = C | a0 = 2.9289894104003906 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 2.040299296975444e+00 2.040299296975979e+00 5.35127e-13 1.29905e-11 2 -9.189724559849066e-01 -9.189724559804985e-01 4.40814e-12 3.12148e-11 3 -9.323476298226748e-01 -9.323476298207176e-01 1.95721e-12 4.45222e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.766533230615959e+00 -1.766533230616227e+00 2.68008e-13 1.23295e-11 2 9.194588352645869e-01 9.194588352658513e-01 1.26432e-12 3.64756e-11 3 5.451006841219910e-01 5.451006841229527e-01 9.61675e-13 5.54978e-12 ----------------------------------------------------------------------------------------------------- 3 C 1 3.510382671003890e-01 3.510382671000454e-01 3.43559e-13 1.23677e-11 2 -1.917518765552512e+00 -1.917518765557187e+00 4.67448e-12 1.94307e-11 3 -2.038417821096640e+00 -2.038417821095272e+00 1.36868e-12 1.37801e-12 ----------------------------------------------------------------------------------------------------- 4 C 1 5.292512669285501e-01 5.292512669297652e-01 1.21514e-12 4.86000e-12 2 3.480122658329735e+00 3.480122658327617e+00 2.11786e-12 9.08296e-12 3 2.424206920092419e+00 2.424206920094844e+00 2.42562e-12 1.61040e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 1.536049039407131e+00 1.536049039407696e+00 5.64659e-13 9.21974e-12 2 1.175177618754611e+00 1.175177618752238e+00 2.37321e-12 1.07021e-11 3 1.728746787146057e+00 1.728746787148238e+00 2.18114e-12 1.44009e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -2.205025340521189e+00 -2.205025340521157e+00 3.24185e-14 2.71467e-11 2 3.601948995436043e-02 3.601948995358328e-02 7.77142e-13 1.49711e-12 3 2.302615710223070e+00 2.302615710224006e+00 9.36140e-13 7.89457e-12 ----------------------------------------------------------------------------------------------------- 7 C 1 2.142101768246635e+00 2.142101768246349e+00 2.85105e-13 1.55862e-11 2 -3.739494442740118e+00 -3.739494442741158e+00 1.04050e-12 1.38622e-11 3 -5.727964847525314e+00 -5.727964847528676e+00 3.36176e-12 1.88366e-10 * ----------------------------------------------------------------------------------------------------- 8 C 1 -4.517215763242961e+00 -4.517215763245130e+00 2.16982e-12 4.40004e-11 2 -1.575140831342349e+00 -1.575140831345923e+00 3.57447e-12 1.72818e-10 * 3 -1.879641256884393e+00 -1.879641256886620e+00 2.22711e-12 1.09055e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 -4.808390780846962e-01 -4.808390780827982e-01 1.89798e-12 8.56615e-12 2 -1.036423210343164e+00 -1.036423210342676e+00 4.88054e-13 6.48770e-12 3 -3.448196289655436e-01 -3.448196289659246e-01 3.80973e-13 6.82987e-12 ----------------------------------------------------------------------------------------------------- 10 C 1 -2.999987941397968e+00 -2.999987941400803e+00 2.83462e-12 9.55191e-12 2 3.914243357995308e+00 3.914243357995434e+00 1.26121e-13 1.67186e-11 3 -5.566720598767233e+00 -5.566720598759157e+00 8.07621e-12 1.39364e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -2.081602273547293e+00 -2.081602273545943e+00 1.35003e-12 2.49609e-11 2 -5.884756749142439e+00 -5.884756749145368e+00 2.92921e-12 8.32134e-12 3 6.305450275023439e+00 6.305450275023994e+00 5.55112e-13 3.48903e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 1.261053739795529e+00 1.261053739787665e+00 7.86438e-12 2.30576e-11 2 -9.216980888050598e-01 -9.216980888068851e-01 1.82532e-12 1.21867e-11 3 1.479475795656227e+00 1.479475795659928e+00 3.70060e-12 1.06941e-10 * ----------------------------------------------------------------------------------------------------- 13 C 1 -9.774071370560452e-01 -9.774071370591378e-01 3.09264e-12 1.04586e-11 2 -2.868679728679064e+00 -2.868679728679787e+00 7.23421e-13 1.23306e-11 3 -8.378657213782402e+00 -8.378657213783075e+00 6.73239e-13 1.64402e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.162936198471590e+00 -1.162936198471118e+00 4.72067e-13 2.99072e-12 2 -8.119484552889809e-01 -8.119484552899056e-01 9.24705e-13 1.26210e-12 3 9.748755383249307e-01 9.748755383233040e-01 1.62670e-12 3.81972e-12 ----------------------------------------------------------------------------------------------------- 15 C 1 7.276262133219637e+00 7.276262133207156e+00 1.24816e-11 7.57270e-11 * 2 8.789040413878347e-01 8.789040413870726e-01 7.62168e-13 1.91560e-11 3 3.152512013697003e+00 3.152512013701640e+00 4.63718e-12 1.32570e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 3.530589148186329e+00 3.530589148185680e+00 6.48814e-13 1.22755e-11 2 5.258343302518941e+00 5.258343302518309e+00 6.31495e-13 9.89608e-12 3 4.985450531583936e+00 4.985450531584451e+00 5.15143e-13 9.92628e-12 ----------------------------------------------------------------------------------------------------- 17 C 1 1.455090016152632e-01 1.455090016157266e-01 4.63379e-13 1.35472e-11 2 -1.210226610761389e+00 -1.210226610760187e+00 1.20193e-12 7.79088e-12 3 -3.882673484749517e+00 -3.882673484746641e+00 2.87637e-12 8.94884e-12 ----------------------------------------------------------------------------------------------------- 18 C 1 -9.144885291122539e-03 -9.144885292464145e-03 1.34161e-12 8.37472e-12 2 4.111629633170416e+00 4.111629633167889e+00 2.52687e-12 7.88436e-12 3 1.508555223070260e+00 1.508555223066687e+00 3.57248e-12 4.64377e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.622010077140773e+00 1.622010077137294e+00 3.47877e-12 1.15947e-11 2 3.221613781473649e-01 3.221613781522271e-01 4.86217e-12 2.29172e-11 3 1.097061177633543e+00 1.097061177633627e+00 8.34888e-14 2.83917e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 9.205672624590454e-01 9.205672624600089e-01 9.63452e-13 2.54939e-11 2 1.367732716753021e+00 1.367732716756141e+00 3.11950e-12 1.62770e-11 3 1.371040062880956e+00 1.371040062878362e+00 2.59393e-12 1.19402e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.076971170888740e+00 -3.076971170890521e+00 1.78124e-12 9.52602e-11 * 2 -3.869876882124960e-01 -3.869876882068175e-01 5.67851e-12 8.99364e-12 3 3.125030936726167e+00 3.125030936726011e+00 1.56763e-13 7.32214e-12 ----------------------------------------------------------------------------------------------------- 22 C 1 1.380371173848109e+00 1.380371173849571e+00 1.46261e-12 2.69456e-11 2 3.365719002235842e+00 3.365719002235194e+00 6.47926e-13 1.63634e-11 3 3.730445870431942e+00 3.730445870437957e+00 6.01563e-12 2.43672e-12 ----------------------------------------------------------------------------------------------------- 23 C 1 -1.994217816687530e+00 -1.994217816689809e+00 2.27907e-12 2.80886e-12 2 1.491421730468380e+00 1.491421730467867e+00 5.13367e-13 1.09361e-11 3 -1.824691514595504e+00 -1.824691514596740e+00 1.23634e-12 3.38773e-12 ----------------------------------------------------------------------------------------------------- 24 C 1 3.873198831206462e-02 3.873198830960498e-02 2.45964e-12 2.30041e-11 2 -1.017260426660830e+00 -1.017260426659881e+00 9.48797e-13 2.34981e-11 3 -1.592056677980154e+00 -1.592056677982492e+00 2.33857e-12 6.13176e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 -4.008559953715884e-02 -4.008559953673654e-02 4.22301e-13 3.20561e-11 2 3.238478974160001e-01 3.238478974157408e-01 2.59348e-13 1.58085e-12 3 -1.580685957418216e+00 -1.580685957421649e+00 3.43370e-12 8.86642e-10 * ----------------------------------------------------------------------------------------------------- 26 C 1 -2.546600292147343e+00 -2.546600292150307e+00 2.96341e-12 3.95559e-11 2 1.859135005810031e+00 1.859135005809007e+00 1.02407e-12 1.07077e-11 3 -2.361936443526110e+00 -2.361936443531462e+00 5.35172e-12 1.21895e-10 * ----------------------------------------------------------------------------------------------------- 27 C 1 4.061019288489075e+00 4.061019288486202e+00 2.87326e-12 1.36238e-11 2 -5.659753395589989e+00 -5.659753395589252e+00 7.36300e-13 1.38352e-11 3 8.899775382065617e-01 8.899775382007787e-01 5.78293e-12 4.08819e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.540595627703887e+00 -2.540595627702537e+00 1.34959e-12 1.49987e-11 2 2.191609101724291e+00 2.191609101721482e+00 2.80975e-12 2.01990e-11 3 -1.611676859511964e+00 -1.611676859513838e+00 1.87428e-12 5.85776e-12 ----------------------------------------------------------------------------------------------------- 29 C 1 -1.801124919249303e+00 -1.801124919249560e+00 2.57128e-13 8.71081e-12 2 -2.250277135184147e+00 -2.250277135186906e+00 2.75913e-12 7.45093e-12 3 4.641113509158497e-01 4.641113509195014e-01 3.65169e-12 3.31700e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.589001298900984e+00 -1.589001298901266e+00 2.81997e-13 4.53590e-11 2 -1.029549084313158e+00 -1.029549084314707e+00 1.54921e-12 2.34150e-11 3 -6.952983759281479e-01 -6.952983759294787e-01 1.33082e-12 1.18667e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 2.099318649328644e+00 2.099318649331511e+00 2.86748e-12 1.21769e-11 2 -1.879413971617588e+00 -1.879413971616547e+00 1.04095e-12 1.22402e-11 3 8.277769591772036e-01 8.277769591783279e-01 1.12432e-12 2.47692e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 8.551164722911258e-01 8.551164722896092e-01 1.51656e-12 6.94600e-12 2 2.412575270287482e+00 2.412575270289088e+00 1.60671e-12 2.79807e-11 3 1.505154935642264e+00 1.505154935640714e+00 1.54987e-12 4.35953e-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 = 18, direction = 1: |F_model - F_numer| error = ----------------------- = 1.46706e-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. MONOATOMIC STRUCTURE -- Species = Si | a0 = 3.535533905029297 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -3.917629502464801e+00 -3.917629502465241e+00 4.40536e-13 6.86073e-12 2 -5.917346028557222e+00 -5.917346028555385e+00 1.83675e-12 1.06954e-11 3 -3.734984053111009e+00 -3.734984053102580e+00 8.42926e-12 1.00417e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 5.027940613811775e+00 5.027940613806779e+00 4.99600e-12 1.17932e-11 2 3.078298568581060e+00 3.078298568578038e+00 3.02158e-12 1.44498e-11 3 -4.837393684904950e+00 -4.837393684899075e+00 5.87530e-12 4.19416e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 3.751390296466771e-01 3.751390296387443e-01 7.93277e-12 4.13452e-11 2 -6.123302907024200e+00 -6.123302907030031e+00 5.83178e-12 2.80442e-11 3 2.996510952161250e+00 2.996510952164247e+00 2.99671e-12 1.09512e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -5.295599045793806e+00 -5.295599045801864e+00 8.05755e-12 2.62874e-10 * 2 3.154686407232953e+00 3.154686407229450e+00 3.50298e-12 3.96536e-11 3 6.399225509611238e+00 6.399225509601139e+00 1.00995e-11 6.61053e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.188115266580030e+00 -1.188115266576701e+00 3.32978e-12 3.47578e-11 2 -3.988357914292145e+00 -3.988357914303364e+00 1.12186e-11 5.94822e-11 3 -4.864049055482639e+00 -4.864049055481013e+00 1.62537e-12 1.38485e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 5.928671035840579e+00 5.928671035845047e+00 4.46843e-12 3.16671e-11 2 7.523246728525307e+00 7.523246728526668e+00 1.36069e-12 7.80807e-11 3 -9.742783530619118e+00 -9.742783530621278e+00 2.16005e-12 1.93463e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 4.543824144817949e+00 4.543824144810722e+00 7.22622e-12 4.61525e-10 * 2 -1.084287861614211e+01 -1.084287861614061e+01 1.50280e-12 4.27516e-11 3 6.058663037675101e+00 6.058663037684794e+00 9.69269e-12 2.25837e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -3.977628187648329e+00 -3.977628187638496e+00 9.83258e-12 3.29838e-11 2 4.398790554411503e+00 4.398790554396880e+00 1.46230e-11 2.22249e-11 3 5.016386782280488e+00 5.016386782282904e+00 2.41585e-12 1.51584e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 -1.821546211659704e+00 -1.821546211655491e+00 4.21285e-12 4.04465e-11 2 2.891565758997241e+00 2.891565758992036e+00 5.20473e-12 3.93339e-11 3 -7.359683674254245e-01 -7.359683674206812e-01 4.74332e-12 2.85032e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 2 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 3 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 ----------------------------------------------------------------------------------------------------- 11 Si 1 -8.945847271038416e-01 -8.945847271020336e-01 1.80800e-12 2.19310e-11 2 1.761559241777592e+00 1.761559241806435e+00 2.88432e-11 1.94458e-10 * 3 -3.704314036645422e+00 -3.704314036655746e+00 1.03237e-11 3.52336e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.522857662759980e-01 2.522857662847383e-01 8.74023e-12 3.14904e-11 2 2.281164446625964e-01 2.281164446634111e-01 8.14765e-13 1.81361e-11 3 2.417094392638769e-01 2.417094392629110e-01 9.65922e-13 8.23500e-12 ----------------------------------------------------------------------------------------------------- 13 Si 1 2.088381079101304e-01 2.088381079096779e-01 4.52499e-13 3.34935e-11 2 2.331181941543583e+00 2.331181941544355e+00 7.71827e-13 2.09575e-11 3 -2.043570231206228e+00 -2.043570231200251e+00 5.97700e-12 2.32974e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 -9.643870633747200e-01 -9.643870633785023e-01 3.78231e-12 4.94431e-11 2 1.608705369242285e-01 1.608705369255130e-01 1.28453e-12 1.22518e-11 3 5.048031097690917e-01 5.048031097654845e-01 3.60723e-12 8.98370e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 7.338988058262193e+00 7.338988058277423e+00 1.52305e-11 1.32451e-10 2 -6.281404723325617e-01 -6.281404723253490e-01 7.21267e-12 1.55060e-11 3 -7.320011077994607e+00 -7.320011077972587e+00 2.20206e-11 3.03153e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -4.810377763419388e-01 -4.810377763373485e-01 4.59033e-12 7.97334e-12 2 3.367623809361447e+00 3.367623809365430e+00 3.98259e-12 1.97775e-11 3 -6.937454440328576e+00 -6.937454440329500e+00 9.23706e-13 2.27912e-10 * ----------------------------------------------------------------------------------------------------- 17 Si 1 -8.912164571787153e+00 -8.912164571782711e+00 4.44267e-12 4.03304e-11 2 -6.479942233680273e+00 -6.479942233672756e+00 7.51665e-12 2.01297e-11 3 -9.693709570302561e+00 -9.693709570309498e+00 6.93667e-12 6.34959e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 4.711389040582674e+00 4.711389040577279e+00 5.39480e-12 1.10538e-10 2 -1.146123117398922e+00 -1.146123117401348e+00 2.42539e-12 4.62679e-11 3 -5.824904567456484e+00 -5.824904567458974e+00 2.49045e-12 2.41684e-10 * ----------------------------------------------------------------------------------------------------- 19 Si 1 1.045855024470437e+01 1.045855024470161e+01 2.76046e-12 1.20183e-10 2 -6.327921821368706e+00 -6.327921821371556e+00 2.84928e-12 2.42073e-11 3 9.815632171649787e+00 9.815632171650149e+00 3.62377e-13 1.03908e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -6.490393487120968e+00 -6.490393487127517e+00 6.54943e-12 3.17000e-11 2 4.880121932012614e+00 4.880121932011751e+00 8.62421e-13 5.58034e-11 3 5.517324154462406e+00 5.517324154459153e+00 3.25251e-12 3.12603e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -6.373108817097217e+00 -6.373108817095392e+00 1.82521e-12 4.85203e-11 2 -1.317912002566648e+00 -1.317912002560647e+00 6.00120e-12 6.99576e-11 3 -4.431919848464552e+00 -4.431919848468593e+00 4.04121e-12 5.35456e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.457055296527385e+00 1.457055296507066e+00 2.03189e-11 2.32633e-10 * 2 7.899270127723803e-01 7.899270127776274e-01 5.24714e-12 9.17106e-11 3 3.178476882372139e+00 3.178476882362032e+00 1.01075e-11 1.86671e-10 * ----------------------------------------------------------------------------------------------------- 23 Si 1 6.599149468718871e+00 6.599149468717536e+00 1.33493e-12 4.35190e-11 2 -4.501781765964199e-01 -4.501781765935308e-01 2.88913e-12 3.56607e-11 3 5.940381846565266e+00 5.940381846564070e+00 1.19638e-12 4.43636e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.466145263227532e-01 -2.466145263230473e-01 2.94126e-13 1.29111e-12 2 -2.724310057959529e+00 -2.724310057961851e+00 2.32214e-12 1.27391e-11 3 6.238180042053457e-01 6.238180042049948e-01 3.50941e-13 5.40029e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -7.354559314495985e+00 -7.354559314496156e+00 1.71418e-13 1.88045e-11 2 1.706812474430332e-01 1.706812474391171e-01 3.91612e-12 2.12054e-11 3 -4.717163115105354e+00 -4.717163115102220e+00 3.13438e-12 1.10781e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -3.138222884490093e+00 -3.138222884458155e+00 3.19371e-11 2.91855e-10 * 2 1.992363825328597e+00 1.992363825319926e+00 8.67129e-12 1.37018e-10 3 7.585709562033828e-01 7.585709562125826e-01 9.19986e-12 5.54402e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 3.479763154969871e+00 3.479763154973643e+00 3.77165e-12 8.57661e-11 2 2.791614552898924e+00 2.791614552919824e+00 2.09006e-11 5.81539e-11 3 6.004774804738130e+00 6.004774804736980e+00 1.15019e-12 7.47136e-12 ----------------------------------------------------------------------------------------------------- 28 Si 1 -6.755418853810626e-01 -6.755418853821410e-01 1.07836e-12 2.02185e-11 2 4.698552293323624e+00 4.698552293326386e+00 2.76135e-12 1.21938e-11 3 3.314564084031971e+00 3.314564084037617e+00 5.64615e-12 2.97895e-10 * ----------------------------------------------------------------------------------------------------- 29 Si 1 -8.330822183491060e+00 -8.330822183445065e+00 4.59952e-11 2.65722e-10 * 2 -5.571562504196651e+00 -5.571562504181935e+00 1.47162e-11 1.12823e-10 3 7.176363279493335e+00 7.176363279489839e+00 3.49587e-12 5.96696e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 7.247940852526838e+00 7.247940852516796e+00 1.00426e-11 1.15232e-11 2 5.581104287393152e+00 5.581104287384955e+00 8.19700e-12 4.36859e-11 3 5.164102525655118e+00 5.164102525668124e+00 1.30056e-11 2.62768e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 2.034882236279467e+00 2.034882236275204e+00 4.26326e-12 2.40554e-11 2 1.698527867632542e+00 1.698527867640214e+00 7.67164e-12 2.38649e-11 3 2.630705242358945e-02 2.630705242257916e-02 1.01029e-12 2.73734e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.975384002786861e-01 3.975384002869718e-01 8.28571e-12 4.29147e-11 2 1.914284129301713e-02 1.914284129381623e-02 7.99097e-13 5.39116e-12 3 -1.493890135145843e-01 -1.493890135151639e-01 5.79620e-13 3.21761e-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 = 32, direction = 2: |F_model - F_numer| error = ----------------------- = 4.17439e-11 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = C Si | a0 = 3.5355338690034848 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 1.635412496274410e+00 1.635412496276421e+00 2.01128e-12 1.43936e-11 2 2.075458962687431e+00 2.075458962686712e+00 7.18980e-13 3.96794e-11 3 1.072657759101646e+00 1.072657759101415e+00 2.30926e-13 1.14027e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.340539815840371e+00 -1.340539815840550e+00 1.78524e-13 2.65814e-11 2 -1.690869066467046e-01 -1.690869066415003e-01 5.20439e-12 1.13644e-11 3 -1.550955875689276e+00 -1.550955875689626e+00 3.50164e-13 1.58278e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -9.235079752728726e-01 -9.235079752726586e-01 2.14051e-13 2.62772e-11 2 -5.544932386228738e-02 -5.544932386296286e-02 6.75487e-13 6.10607e-12 3 3.113843705697368e+00 3.113843705697489e+00 1.21680e-13 1.73426e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.325244884697569e+00 -1.325244884708927e+00 1.13580e-11 1.96083e-11 2 1.513442856238827e-02 1.513442857178432e-02 9.39605e-12 5.57928e-11 3 -2.137770703539459e+00 -2.137770703536809e+00 2.64988e-12 1.04761e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 -6.959418703460713e+00 -6.959418703453836e+00 6.87717e-12 1.38263e-11 2 1.675965885010473e+00 1.675965885008796e+00 1.67621e-12 1.03937e-11 3 -8.831809284602725e+00 -8.831809284603862e+00 1.13687e-12 1.01412e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.240874558607822e+00 -1.240874558611004e+00 3.18234e-12 4.62341e-12 2 -3.679242517059386e-01 -3.679242516921922e-01 1.37464e-11 2.84074e-10 * 3 9.693586591844945e-01 9.693586591832535e-01 1.24101e-12 3.98304e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 5.877409560258680e+00 5.877409560233024e+00 2.56559e-11 3.83684e-11 2 3.014075610574750e-01 3.014075610619696e-01 4.49457e-12 4.08112e-11 3 1.016240041788138e+01 1.016240041788373e+01 2.34834e-12 5.54135e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.385309577618180e+00 2.385309577616854e+00 1.32605e-12 8.26272e-12 2 -1.462511342899737e+00 -1.462511342905267e+00 5.53046e-12 6.44840e-12 3 -3.043076041349714e+00 -3.043076041340118e+00 9.59588e-12 1.42788e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 2.866869405228154e+00 2.866869405231022e+00 2.86837e-12 5.29363e-11 2 -3.318232147015096e-01 -3.318232147073879e-01 5.87835e-12 6.68077e-12 3 2.904573577084884e-01 2.904573577127295e-01 4.24116e-12 2.48689e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.668341648532785e+00 -1.668341648530229e+00 2.55596e-12 2.36615e-11 2 -2.282222081692283e+00 -2.282222081689588e+00 2.69473e-12 2.99778e-11 3 -6.054323321502201e-01 -6.054323321394688e-01 1.07513e-11 1.99509e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -7.377333505768898e-01 -7.377333505885328e-01 1.16430e-11 2.86136e-10 * 2 4.327941736840940e-01 4.327941736717248e-01 1.23691e-11 7.12763e-12 3 2.486258078933866e-01 2.486258078916129e-01 1.77372e-12 1.01060e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 1.425971288068025e+00 1.425971288070161e+00 2.13651e-12 4.01967e-11 2 3.893420362232883e-01 3.893420362227299e-01 5.58387e-13 3.11625e-11 3 2.263311371306993e+00 2.263311371303276e+00 3.71614e-12 1.13238e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -7.635041397834760e-01 -7.635041397825875e-01 8.88511e-13 7.57916e-12 2 -9.650458211700837e-02 -9.650458211818633e-02 1.17796e-12 1.63902e-11 3 -3.809692201887644e+00 -3.809692201895642e+00 7.99716e-12 2.05214e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -2.220297642162276e+00 -2.220297642162530e+00 2.53575e-13 1.16667e-11 2 -1.601107297585504e+00 -1.601107297589714e+00 4.20997e-12 1.85187e-11 3 1.001467684381282e+00 1.001467684381508e+00 2.26485e-13 2.00793e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 2.314459458712414e+00 2.314459458715675e+00 3.26139e-12 6.28821e-11 2 2.614310441387908e+00 2.614310441380396e+00 7.51221e-12 3.73208e-11 3 4.197995581851344e+00 4.197995581863927e+00 1.25828e-11 1.57874e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 6.267077871436646e-01 6.267077872442615e-01 1.00597e-10 2.58942e-11 2 -1.657872229197150e+00 -1.657872229198633e+00 1.48259e-12 8.04135e-12 3 2.386005841793991e-01 2.386005842095050e-01 3.01059e-11 5.80195e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 2.158841930247871e+00 2.158841930248415e+00 5.44009e-13 3.97415e-12 2 1.424149506842168e-02 1.424149506809883e-02 3.22851e-13 3.62857e-13 3 -1.868806828942249e+00 -1.868806828939478e+00 2.77112e-12 3.10285e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.647451547984202e+00 -1.647451547982944e+00 1.25855e-12 1.19018e-10 2 -2.866454766632753e+00 -2.866454766635372e+00 2.61924e-12 2.18670e-11 3 4.516679910536123e+00 4.516679910539104e+00 2.98161e-12 1.38209e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 -1.807921148743665e+00 -1.807921148745233e+00 1.56741e-12 7.63567e-12 2 3.192345456416341e+00 3.192345456417171e+00 8.30447e-13 6.24523e-12 3 -1.273546257564153e+00 -1.273546257564900e+00 7.47624e-13 1.49265e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 1.674984365571639e+00 1.674984365571071e+00 5.67324e-13 8.60667e-12 2 -1.854476752422084e+00 -1.854476752422410e+00 3.26406e-13 4.82436e-12 3 3.690062435187266e-02 3.690062435201473e-02 1.42067e-13 1.03142e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 1.849825989638602e+00 1.849825989643987e+00 5.38591e-12 1.81175e-10 * 2 -4.046875858585609e-01 -4.046875858623893e-01 3.82838e-12 1.18579e-11 3 -1.791655138805569e+00 -1.791655138799627e+00 5.94214e-12 9.12070e-12 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.942294577783792e+00 2.942294577784508e+00 7.15428e-13 6.58691e-11 2 -5.337837921256979e-01 -5.337837921343190e-01 8.62110e-12 1.48274e-10 * 3 -7.204963997469876e-01 -7.204963997548427e-01 7.85505e-12 5.18873e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.110532048710438e+00 -2.110532048704623e+00 5.81446e-12 9.06697e-12 2 2.132020298909801e+00 2.132020298910726e+00 9.25038e-13 2.06226e-11 3 -2.096408261859016e+00 -2.096408261857961e+00 1.05471e-12 6.02940e-12 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.117669785830146e+00 -2.117669785829335e+00 8.10907e-13 1.30722e-11 2 -5.532719969288118e-01 -5.532719969307143e-01 1.90248e-12 3.60979e-11 3 3.079407508831186e+00 3.079407508825633e+00 5.55334e-12 3.83507e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.307016000662109e+00 -2.307016000658828e+00 3.28049e-12 9.62976e-11 2 1.065997025395013e+00 1.065997025386794e+00 8.21898e-12 4.00582e-11 3 7.252888924734856e-01 7.252888924705612e-01 2.92444e-12 2.13638e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -4.537080540960528e+00 -4.537080540961576e+00 1.04805e-12 7.78986e-11 2 2.107424617066618e+00 2.107424617067260e+00 6.42153e-13 3.10663e-11 3 -9.641435893183716e-01 -9.641435893213945e-01 3.02292e-12 3.06066e-12 ----------------------------------------------------------------------------------------------------- 27 C 1 2.485649290271716e+00 2.485649290272942e+00 1.22657e-12 3.13172e-12 2 3.338449217924293e-01 3.338449217937532e-01 1.32389e-12 5.43052e-11 3 -1.280728329539606e+00 -1.280728329533802e+00 5.80380e-12 1.73357e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 1.513421120770516e+00 1.513421120766328e+00 4.18798e-12 2.17100e-11 2 -1.408773255369822e-01 -1.408773255415299e-01 4.54767e-12 1.02911e-11 3 -1.311939895769270e+00 -1.311939895768462e+00 8.07576e-13 1.36946e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 5.489157468004817e-01 5.489157467934268e-01 7.05491e-12 1.80562e-11 2 -7.749662822518233e-02 -7.749662822247826e-02 2.70407e-12 2.36907e-11 3 -2.861395174161396e-01 -2.861395174182840e-01 2.14434e-12 2.17386e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 -5.674821889302748e-01 -5.674821889527806e-01 2.25058e-11 1.17765e-10 2 -2.442958658409807e+00 -2.442958658411033e+00 1.22613e-12 1.56035e-10 * 3 8.808153054626777e-01 8.808153054609480e-01 1.72973e-12 1.87912e-10 * ----------------------------------------------------------------------------------------------------- 31 Si 1 8.142779538783435e+00 8.142779538781141e+00 2.29328e-12 7.97336e-11 2 -6.405513065289718e+00 -6.405513065283434e+00 6.28386e-12 1.62981e-12 3 -1.644590201710340e+00 -1.644590201714047e+00 3.70703e-12 4.17133e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -6.174236152415436e+00 -6.174236152411542e+00 3.89466e-12 1.57785e-11 2 6.953734498576027e+00 6.953734498578954e+00 2.92744e-12 1.11937e-11 3 4.193796890496071e-01 4.193796890486955e-01 9.11549e-13 2.28157e-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 = 4, direction = 2: |F_model - F_numer| error = ----------------------- = 6.20840e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 6.20840e-10 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 6.20840e-10 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.