!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MunetohMotookaMoriguchi_2007_SiO__MO_501246546792_000 Supported species : O 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 = O | a0 = 2.683344841003418 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -6.528769061237346e+00 -6.528769061229356e+00 7.99005e-12 4.08829e-12 2 -1.130557424569438e+01 -1.130557424569118e+01 3.19922e-12 9.50351e-12 3 -1.234053591594230e+01 -1.234053591594079e+01 1.50102e-12 6.01442e-10 * ----------------------------------------------------------------------------------------------------- 2 O 1 4.862816647028324e+00 4.862816647034458e+00 6.13465e-12 3.96732e-11 2 6.543083067033409e+00 6.543083067036664e+00 3.25517e-12 3.25242e-11 3 -8.603870777603754e+00 -8.603870777597374e+00 6.38067e-12 5.01998e-11 ----------------------------------------------------------------------------------------------------- 3 O 1 3.481012836606132e+00 3.481012836606935e+00 8.02913e-13 5.71081e-11 2 -1.005022666580888e+01 -1.005022666583237e+01 2.34852e-11 7.09832e-11 3 7.266786106221129e+00 7.266786106236360e+00 1.52314e-11 1.61871e-11 ----------------------------------------------------------------------------------------------------- 4 O 1 -6.749601144679574e+00 -6.749601144675771e+00 3.80318e-12 9.93881e-11 2 1.210887680593912e+01 1.210887680594226e+01 3.14593e-12 1.73310e-10 3 9.853406536214758e+00 9.853406536227929e+00 1.31717e-11 7.84421e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 2.963641514805767e+00 2.963641514806175e+00 4.07674e-13 3.26130e-11 2 -2.594108794681906e+00 -2.594108794684729e+00 2.82263e-12 4.38019e-11 3 -5.664825869018154e+00 -5.664825869015056e+00 3.09797e-12 2.81384e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 -1.699509149299245e+00 -1.699509149300121e+00 8.76188e-13 1.83435e-11 2 -1.061400822177997e-01 -1.061400822183415e-01 5.41747e-13 4.15135e-11 3 -2.513727783791865e+00 -2.513727783788761e+00 3.10330e-12 1.66933e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 1.268846028196353e+00 1.268846028197326e+00 9.72777e-13 1.67526e-11 2 -1.180809942421052e+01 -1.180809942420723e+01 3.28448e-12 1.79261e-10 3 -7.939444033092679e+00 -7.939444033061911e+00 3.07674e-11 1.83678e-10 ----------------------------------------------------------------------------------------------------- 8 O 1 -9.618367894656235e+00 -9.618367894639274e+00 1.69607e-11 3.30047e-12 2 -2.227663746223855e+00 -2.227663746227924e+00 4.06875e-12 4.34008e-12 3 2.462853417604332e+00 2.462853417608000e+00 3.66818e-12 4.79883e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 -1.092484141480762e+00 -1.092484141480960e+00 1.97398e-13 1.06628e-11 2 6.295955017460405e-01 6.295955017461958e-01 1.55320e-13 4.02305e-11 3 -1.971342597161744e+00 -1.971342597160665e+00 1.07936e-12 4.03568e-11 ----------------------------------------------------------------------------------------------------- 10 O 1 -3.697893951261497e+00 -3.697893951259937e+00 1.56009e-12 5.26863e-11 2 5.216046008176595e+00 5.216046008173276e+00 3.31912e-12 6.94342e-11 3 -4.089447022187684e+00 -4.089447022187693e+00 9.76996e-15 3.08340e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -1.148752135562464e+00 -1.148752135550786e+00 1.16780e-11 5.04299e-11 2 -8.215514162291200e+00 -8.215514162288615e+00 2.58460e-12 9.74014e-10 * 3 1.984127614470386e+00 1.984127614465395e+00 4.99156e-12 4.11899e-11 ----------------------------------------------------------------------------------------------------- 12 O 1 -3.703261444753130e+00 -3.703261444753199e+00 6.88338e-14 1.81997e-11 2 2.527881177564868e+00 2.527881177567974e+00 3.10596e-12 1.32201e-11 3 -5.394161963876610e-01 -5.394161963879316e-01 2.70561e-13 2.94997e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 -9.385016049524449e+00 -9.385016049524969e+00 5.20473e-13 6.86757e-11 2 -1.932649585046788e+00 -1.932649585044605e+00 2.18292e-12 7.76512e-12 3 -2.338566949536785e+01 -2.338566949535904e+01 8.80718e-12 1.63531e-11 ----------------------------------------------------------------------------------------------------- 14 O 1 5.780404828090822e+00 5.780404828095034e+00 4.21263e-12 2.38805e-11 2 6.043677074187065e+00 6.043677074180471e+00 6.59384e-12 1.35145e-11 3 -4.531204764914134e+00 -4.531204764916955e+00 2.82174e-12 1.04254e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 2.217359009382562e+01 2.217359009379142e+01 3.42020e-11 2.36206e-10 2 -3.154303492117914e+00 -3.154303492119560e+00 1.64624e-12 4.52927e-12 3 1.441033029215873e+01 1.441033029216841e+01 9.68292e-12 5.43885e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -4.098841832891181e+00 -4.098841832896062e+00 4.88054e-12 9.19913e-11 2 1.190508391831245e+01 1.190508391830370e+01 8.75389e-12 6.94556e-12 3 3.600363476610251e+00 3.600363476598685e+00 1.15667e-11 1.82934e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 -8.380137311945624e+00 -8.380137311951694e+00 6.06981e-12 1.38561e-10 2 -8.772772732831548e+00 -8.772772732831974e+00 4.26326e-13 1.04684e-10 3 -5.070059119502799e+00 -5.070059119500550e+00 2.24976e-12 5.87166e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 8.485281787292459e+00 8.485281787303974e+00 1.15143e-11 1.35246e-10 2 7.273136474415012e+00 7.273136474415397e+00 3.84581e-13 1.10496e-10 3 -2.141699963612688e+00 -2.141699963615676e+00 2.98783e-12 7.27285e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 4.857223293195736e+00 4.857223293205506e+00 9.77085e-12 4.41425e-11 2 -3.327278593158344e+00 -3.327278593152733e+00 5.61151e-12 1.24833e-11 3 4.845437534013420e+00 4.845437534021899e+00 8.47944e-12 1.74376e-11 ----------------------------------------------------------------------------------------------------- 20 O 1 -3.261240601547916e+00 -3.261240601552872e+00 4.95648e-12 4.45493e-11 2 6.071201605185769e+00 6.071201605187531e+00 1.76215e-12 5.41522e-12 3 6.326430439073124e+00 6.326430439065385e+00 7.73870e-12 7.51763e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 -5.444762825812668e+00 -5.444762825813804e+00 1.13598e-12 6.63292e-11 2 -4.901104342609066e+00 -4.901104342612856e+00 3.78986e-12 6.18439e-12 3 7.560746961358882e+00 7.560746961359823e+00 9.40581e-13 9.93872e-12 ----------------------------------------------------------------------------------------------------- 22 O 1 1.279875780354693e+01 1.279875780354732e+01 3.87246e-13 3.79767e-11 2 1.149056674382975e+01 1.149056674382512e+01 4.63629e-12 4.10161e-11 3 6.112873646530782e+00 6.112873646503997e+00 2.67848e-11 1.74950e-10 ----------------------------------------------------------------------------------------------------- 23 O 1 1.098985122989194e-01 1.098985123018002e-01 2.88077e-12 1.25622e-11 2 -3.756161590898149e+00 -3.756161590898192e+00 4.30767e-14 2.46203e-11 3 1.896725126138902e+00 1.896725126139083e+00 1.80744e-13 6.35403e-12 ----------------------------------------------------------------------------------------------------- 24 O 1 -5.531887904124796e-01 -5.531887904057724e-01 6.70719e-12 9.09287e-11 2 2.228089118435284e+00 2.228089118436789e+00 1.50502e-12 1.89631e-11 3 -6.083844266464701e-01 -6.083844266467869e-01 3.16858e-13 1.15938e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -4.611065817266217e+00 -4.611065817272015e+00 5.79803e-12 7.01439e-11 2 -3.778574162611068e+00 -3.778574162610991e+00 7.68274e-14 1.60560e-11 3 -8.206702921857143e+00 -8.206702921857794e+00 6.50147e-13 9.64384e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 3.058964481526331e+00 3.058964481525952e+00 3.79252e-13 2.52594e-11 2 6.556236095467365e+00 6.556236095471760e+00 4.39471e-12 1.16684e-10 3 -7.579290788559621e+00 -7.579290788559176e+00 4.44089e-13 7.17550e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 5.979505158348008e+00 5.979505158349362e+00 1.35358e-12 6.48370e-13 2 -9.513802152129584e+00 -9.513802152126916e+00 2.66809e-12 7.73710e-11 3 5.487684985933033e+00 5.487684985933166e+00 1.33227e-13 1.97211e-11 ----------------------------------------------------------------------------------------------------- 28 O 1 -1.328201104376091e+01 -1.328201104375962e+01 1.29674e-12 1.02723e-10 2 9.393145077739000e+00 9.393145077741753e+00 2.75335e-12 7.77636e-11 3 9.350840928019393e+00 9.350840928022807e+00 3.41416e-12 4.25491e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 -7.687789801201760e-01 -7.687789801173416e-01 2.83440e-12 2.16704e-11 2 -7.489194345462947e+00 -7.489194345453133e+00 9.81437e-12 4.34754e-11 3 3.811274814903664e+00 3.811274814897425e+00 6.23857e-12 2.04015e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 4.396704081153687e+00 4.396704081150549e+00 3.13793e-12 2.81570e-11 2 3.075934926554075e+00 3.075934926554730e+00 6.55032e-13 1.69060e-11 3 8.657330921636563e-02 8.657330921363858e-02 2.72705e-12 3.66381e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 -2.255168482922431e-01 -2.255168482931551e-01 9.12076e-13 5.96981e-12 2 -2.379694692236863e+00 -2.379694692241871e+00 5.00799e-12 1.34439e-11 3 2.755937929316917e+00 2.755937929315815e+00 1.10223e-12 1.58673e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 4.032551958588998e+00 4.032551958587759e+00 1.23901e-12 1.44329e-11 2 4.250309215644995e+00 4.250309215643964e+00 1.03118e-12 1.62066e-11 3 7.373228557862466e+00 7.373228557858182e+00 4.28368e-12 1.33222e-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 = 30, direction = 3: |F_model - F_numer| error = ----------------------- = 3.14999e-11 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Si | a0 = 3.695751190185547 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 3.349196892902566e+00 3.349196892898594e+00 3.97149e-12 2.15156e-10 2 1.669800641990166e+00 1.669800641979067e+00 1.10993e-11 3.46894e-11 3 2.017537130923642e+00 2.017537130897880e+00 2.57621e-11 1.01863e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 -7.764796469782076e+00 -7.764796469792929e+00 1.08527e-11 3.39240e-11 2 6.573416781888383e-01 6.573416781892280e-01 3.89688e-13 4.62224e-10 3 -4.176900138597210e+00 -4.176900138606078e+00 8.86757e-12 2.51416e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 -2.103354747295130e+00 -2.103354747271949e+00 2.31815e-11 5.53375e-11 2 -1.480744219093465e+00 -1.480744219111296e+00 1.78302e-11 1.06861e-10 3 -1.885470339520362e+00 -1.885470339494027e+00 2.63352e-11 2.96370e-05 * ----------------------------------------------------------------------------------------------------- 4 Si 1 -6.360331248666768e+00 -6.360331248657331e+00 9.43778e-12 3.20741e-10 2 1.512895560230927e+00 1.512895560255606e+00 2.46791e-11 1.06428e-10 3 -9.836365633274449e+00 -9.836365633238559e+00 3.58895e-11 2.89404e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 3.639839692966349e+00 3.639839692973428e+00 7.07923e-12 2.69789e-11 2 -7.842315829295750e+00 -7.842315829297908e+00 2.15827e-12 2.79227e-10 3 -2.526184383200342e+00 -2.526184383191217e+00 9.12470e-12 3.20980e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 6.350321429506315e-01 6.350321429518218e-01 1.19027e-12 4.29912e-11 2 1.871084272054061e+00 1.871084272041231e+00 1.28306e-11 1.48838e-10 3 -1.379787030126916e+00 -1.379787030130916e+00 3.99969e-12 5.36735e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -6.293803937679876e+00 -6.293803937678321e+00 1.55520e-12 8.28626e-11 2 1.431335972401395e+00 1.431335972403897e+00 2.50244e-12 1.67434e-10 3 4.252720542477810e+00 4.252720542474080e+00 3.73035e-12 6.00853e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.962802596284765e+00 3.962802596278183e+00 6.58140e-12 4.02808e-10 2 -2.722989476706259e+00 -2.722989476664721e+00 4.15388e-11 2.28368e-09 * 3 1.177331823731740e+01 1.177331823732815e+01 1.07416e-11 2.79142e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.730086456275996e+00 -3.730086456275772e+00 2.24265e-13 3.87699e-11 2 -1.799385002242848e-01 -1.799385002231431e-01 1.14170e-12 5.93733e-10 3 -4.104247851699993e+00 -4.104247851698831e+00 1.16263e-12 8.78337e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 6.289234232708123e+00 6.289234232714923e+00 6.80078e-12 1.62046e-10 2 -3.332864588921488e+00 -3.332864588917286e+00 4.20197e-12 5.77039e-10 3 3.080147891323756e+00 3.080147891321002e+00 2.75424e-12 3.84404e-12 ----------------------------------------------------------------------------------------------------- 11 Si 1 6.225215925057396e+00 6.225215925057213e+00 1.82077e-13 1.42755e-10 2 1.382721449872943e+00 1.382721449875451e+00 2.50755e-12 5.13762e-11 3 4.105492451645035e+00 4.105492451674380e+00 2.93454e-11 1.10425e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -5.633631872103998e-01 -5.633631871907183e-01 1.96815e-11 1.93921e-10 2 -4.419795025833339e-02 -4.419795024932332e-02 9.01007e-12 1.49581e-11 3 3.961142568178342e+00 3.961142568207177e+00 2.88343e-11 1.76180e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 8.953929729481565e-01 8.953929729403535e-01 7.80298e-12 2.33874e-11 2 1.428919473119057e+01 1.428919473119886e+01 8.28493e-12 2.15222e-10 3 -2.914964599789336e+00 -2.914964599785808e+00 3.52784e-12 2.09141e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -4.357590442080946e+00 -4.357590442100970e+00 2.00240e-11 7.67697e-11 2 -3.759767221800477e+00 -3.759767221804341e+00 3.86446e-12 3.61045e-11 3 2.365325022801043e+00 2.365325022801618e+00 5.74651e-13 8.08864e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 -5.415234260583021e-01 -5.415234260577653e-01 5.36793e-13 3.58576e-10 2 5.213701015792346e+00 5.213701015788907e+00 3.43903e-12 4.13252e-11 3 4.033872202455125e+00 4.033872202455544e+00 4.18332e-13 1.22274e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 1.503081396021285e+00 1.503081396013693e+00 7.59193e-12 5.74416e-10 2 -4.435628736211749e+00 -4.435628736220319e+00 8.57003e-12 6.17346e-11 3 -9.630506227724949e+00 -9.630506227702702e+00 2.22471e-11 4.43716e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.901292999740847e+00 -1.901292999740929e+00 8.21565e-14 2.91087e-11 2 -8.736039000203810e+00 -8.736039000201606e+00 2.20446e-12 1.45288e-11 3 2.841802855783353e+00 2.841802855787593e+00 4.23972e-12 1.32470e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.491232134737511e+01 1.491232134740575e+01 3.06333e-11 1.13868e-10 2 -8.210605953993038e+00 -8.210605954003057e+00 1.00187e-11 4.43983e-10 3 2.369279445639325e+00 2.369279445661622e+00 2.22973e-11 1.38455e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -2.919868101780437e+00 -2.919868101776757e+00 3.67972e-12 1.35474e-12 2 5.003120646068928e+00 5.003120646067868e+00 1.06049e-12 1.00894e-10 3 -2.969334433412478e+00 -2.969334433411152e+00 1.32649e-12 7.76295e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 -2.143225769471243e+00 -2.143225769467241e+00 4.00258e-12 6.24731e-11 2 -2.248482855187253e+00 -2.248482855176990e+00 1.02633e-11 1.69600e-10 3 5.391507825462884e+00 5.391507825473987e+00 1.11031e-11 5.81775e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 2.977426198695477e+00 2.977426198694115e+00 1.36247e-12 9.01186e-11 2 4.734994737147301e+00 4.734994737147132e+00 1.68754e-13 5.57634e-11 3 -1.610355468267527e+00 -1.610355468260205e+00 7.32148e-12 3.17692e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 5.493770555738934e+00 5.493770555736664e+00 2.27018e-12 3.47580e-11 2 -1.157145906821565e+01 -1.157145906819667e+01 1.89733e-11 3.06724e-11 3 -2.662796904527791e-01 -2.662796904450603e-01 7.71883e-12 9.29486e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.698981145223981e+00 -2.698981145225733e+00 1.75238e-12 4.59708e-11 2 8.954338089788582e+00 8.954338089786575e+00 2.00728e-12 1.14841e-10 3 -5.269082465167611e+00 -5.269082465164088e+00 3.52340e-12 2.73239e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.664859755075907e+00 -1.664859755074627e+00 1.27964e-12 3.14884e-10 2 -9.331515806013082e+00 -9.331515805982086e+00 3.09957e-11 3.06414e-10 3 2.824150191794547e+00 2.824150191783491e+00 1.10560e-11 1.97473e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -4.098502901299191e+00 -4.098502901317881e+00 1.86899e-11 9.39009e-11 2 1.199661466568486e+01 1.199661466567455e+01 1.03153e-11 7.33724e-11 3 4.820302282709664e+00 4.820302282693881e+00 1.57829e-11 1.17144e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 2.256531834224294e+00 2.256531834223011e+00 1.28253e-12 7.25285e-10 2 -8.498975885447398e-01 -8.498975885321670e-01 1.25728e-11 2.53680e-10 3 8.315593898040044e+00 8.315593898043803e+00 3.75877e-12 2.61879e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 9.315985932369406e-01 9.315985932424775e-01 5.53690e-12 3.91613e-11 2 1.220362889538978e+01 1.220362889541337e+01 2.35936e-11 1.43224e-10 3 2.460206238169973e+00 2.460206238164376e+00 5.59641e-12 3.04843e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 3.220332960128657e+00 3.220332960122469e+00 6.18794e-12 1.26750e-10 2 -7.205853100180604e+00 -7.205853100191393e+00 1.07896e-11 4.15943e-11 3 -5.090869481340915e+00 -5.090869481341188e+00 2.72671e-13 5.38467e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.976431657323893e+00 -3.976431657326854e+00 2.96119e-12 6.84484e-11 2 4.284040942634401e+00 4.284040942631641e+00 2.75957e-12 4.04677e-10 3 -7.351975463345739e+00 -7.351975463301949e+00 4.37899e-11 4.07097e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -4.578559422405029e+00 -4.578559422395998e+00 9.03100e-12 2.61942e-11 2 -1.066971218890088e+00 -1.066971218896554e+00 6.46549e-12 7.44136e-11 3 -1.217793151375802e+00 -1.217793151355254e+00 2.05482e-11 3.14168e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 3.361233890375622e+00 3.361233890382524e+00 6.90159e-12 3.52719e-10 2 2.729750183537815e+00 2.729750183550778e+00 1.29625e-11 2.14762e-11 3 6.287770925656551e+00 6.287770925654979e+00 1.57208e-12 3.39933e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -3.956439564244266e+00 -3.956439564246255e+00 1.98863e-12 5.46185e-11 2 -4.915292368232843e+00 -4.915292368236686e+00 3.84315e-12 4.16245e-11 3 -1.067005335308210e+01 -1.067005335309143e+01 9.33120e-12 2.13170e-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 = 12, direction = 2: |F_model - F_numer| error = ----------------------- = 2.03857e-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 = O Si | a0 = 3.1866844744664373 | (Configuration in file "config-OSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -7.516693848585922e+00 -7.516693848584987e+00 9.35252e-13 1.05596e-11 2 -7.306522240574169e+00 -7.306522240572670e+00 1.49925e-12 3.76170e-11 3 -4.158916315890677e+00 -4.158916315890941e+00 2.63789e-13 2.66525e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -8.286801910639291e-01 -8.286801910662258e-01 2.29672e-12 3.30402e-09 * 2 2.147834900857207e+01 2.147834900858201e+01 9.93694e-12 4.26006e-11 3 -7.732686300142081e+00 -7.732686300148205e+00 6.12399e-12 2.44693e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 6.829887669320319e+00 6.829887669305875e+00 1.44444e-11 6.06830e-11 2 -1.372388457238574e+01 -1.372388457238133e+01 4.40359e-12 1.79323e-11 3 -3.080666068765852e+00 -3.080666068781944e+00 1.60920e-11 1.71037e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.490629404708729e+01 -1.490629404707786e+01 9.43423e-12 1.40066e-10 2 4.992162405076802e+00 4.992162405090875e+00 1.40732e-11 6.37970e-11 3 -7.866990929999567e+00 -7.866990929988863e+00 1.07034e-11 2.43277e-09 * ----------------------------------------------------------------------------------------------------- 5 O 1 5.890700534200771e+00 5.890700534207248e+00 6.47660e-12 1.59046e-11 2 9.052190785802878e+00 9.052190785797793e+00 5.08571e-12 2.36183e-10 3 -7.997759447462476e-01 -7.997759447459249e-01 3.22631e-13 2.37416e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 7.593465644630552e+00 7.593465644603856e+00 2.66960e-11 7.94767e-10 * 2 -2.656742509437042e+01 -2.656742509432974e+01 4.06821e-11 5.08615e-09 * 3 -8.185883031164172e+00 -8.185883031115784e+00 4.83880e-11 1.28340e-10 ----------------------------------------------------------------------------------------------------- 7 O 1 5.883631960246410e-02 5.883631960956971e-02 7.10561e-12 1.88134e-10 2 3.075201455226172e+00 3.075201455195590e+00 3.05813e-11 1.02669e-09 * 3 2.639312692854121e+00 2.639312692850228e+00 3.89333e-12 1.08992e-09 * ----------------------------------------------------------------------------------------------------- 8 Si 1 2.170562448623211e+00 2.170562448630108e+00 6.89715e-12 3.29390e-11 2 -4.088247596029044e-01 -4.088247596453084e-01 4.24040e-11 5.37708e-10 3 -6.636323134546933e-01 -6.636323134050260e-01 4.96673e-11 1.78578e-10 ----------------------------------------------------------------------------------------------------- 9 O 1 5.279903136675689e+00 5.279903136688380e+00 1.26903e-11 5.67359e-11 2 -1.010508321379050e+01 -1.010508321379650e+01 6.00764e-12 2.50733e-11 3 -1.175067592380657e+00 -1.175067592343160e+00 3.74978e-11 1.08572e-10 ----------------------------------------------------------------------------------------------------- 10 O 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 O 1 -1.770570220720395e-01 -1.770570220661615e-01 5.87802e-12 7.16331e-10 * 2 4.182121261418142e+00 4.182121261412670e+00 5.47207e-12 3.52403e-11 3 -1.811402262614715e+00 -1.811402262632329e+00 1.76144e-11 3.68007e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 5.635786262343958e+00 5.635786262322447e+00 2.15108e-11 1.35700e-10 2 1.442259284589644e+00 1.442259284603648e+00 1.40035e-11 4.26821e-11 3 -5.003606818738924e+00 -5.003606818724262e+00 1.46620e-11 2.72278e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.754485985783035e+01 -1.754485985781567e+01 1.46763e-11 4.00817e-11 2 2.538938746136619e+01 2.538938746134722e+01 1.89679e-11 8.25544e-11 3 4.985265463665643e+00 4.985265463636049e+00 2.95941e-11 2.67793e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 3.842487585551518e+00 3.842487585533746e+00 1.77725e-11 2.22083e-10 2 3.709052338878850e+00 3.709052338862561e+00 1.62887e-11 5.42220e-11 3 1.792371637537511e-01 1.792371637629875e-01 9.23633e-12 1.89526e-10 ----------------------------------------------------------------------------------------------------- 15 O 1 1.308043220331711e+00 1.308043220337965e+00 6.25389e-12 3.52052e-11 2 5.992872067469800e+00 5.992872067467324e+00 2.47535e-12 3.04388e-10 3 4.395882144678009e+00 4.395882144667438e+00 1.05711e-11 5.32303e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 5.485555429311126e+00 5.485555429300671e+00 1.04547e-11 1.18013e-10 2 -3.087077069078641e+00 -3.087077069075009e+00 3.63221e-12 6.38778e-12 3 -3.224417806626804e+00 -3.224417806601697e+00 2.51070e-11 1.33341e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.143282035212299e+01 -1.143282035214246e+01 1.94689e-11 2.34895e-10 2 -1.406804948013195e+01 -1.406804948013018e+01 1.77458e-12 9.80140e-11 3 1.285060237736862e+01 1.285060237740562e+01 3.69944e-11 1.40460e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 7.858236301909015e+00 7.858236301921781e+00 1.27658e-11 1.55896e-10 2 1.606370922609020e+01 1.606370922608832e+01 1.88294e-12 1.44752e-10 3 1.861420426336491e+01 1.861420426335534e+01 9.56391e-12 3.29148e-10 ----------------------------------------------------------------------------------------------------- 19 O 1 2.696133383519986e+00 2.696133383558930e+00 3.89435e-11 7.09051e-11 2 -7.986099984010194e-01 -7.986099983990554e-01 1.96398e-12 4.39381e-11 3 -2.160884432151459e+00 -2.160884432137918e+00 1.35412e-11 1.43516e-10 ----------------------------------------------------------------------------------------------------- 20 O 1 3.543808447934807e-02 3.543808448906795e-02 9.71988e-12 4.69239e-12 2 4.075294419226696e+00 4.075294419229808e+00 3.11218e-12 1.05604e-11 3 -7.888626049537632e+00 -7.888626049524666e+00 1.29665e-11 8.46590e-10 * ----------------------------------------------------------------------------------------------------- 21 Si 1 -2.451979912211133e+01 -2.451979912211907e+01 7.73426e-12 6.46700e-11 2 -1.698617443817994e+01 -1.698617443816959e+01 1.03491e-11 4.70486e-11 3 -1.010350115694330e+00 -1.010350115722743e+00 2.84126e-11 1.44437e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.629758494940291e+01 1.629758494940197e+01 9.37916e-13 2.86661e-10 2 1.125769510340964e+01 1.125769510330271e+01 1.06931e-10 3.16856e-10 3 -1.354600303347884e+01 -1.354600303346941e+01 9.42890e-12 3.92090e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 1.488664129022232e+01 1.488664129023585e+01 1.35323e-11 6.98215e-11 2 -4.804301041617238e+00 -4.804301041610235e+00 7.00329e-12 5.31983e-11 3 2.186834029962949e+01 2.186834029962944e+01 4.61853e-14 6.57892e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 -1.005207831974295e+00 -1.005207831973145e+00 1.14997e-12 1.32742e-10 2 2.670112314470770e+00 2.670112314471124e+00 3.54383e-13 1.40350e-11 3 1.878354521226513e+00 1.878354521218152e+00 8.36131e-12 4.59803e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.032821139516442e+00 -2.032821139537895e+00 2.14535e-11 8.48548e-11 2 2.983040683924164e+00 2.983040683916085e+00 8.07931e-12 4.98352e-11 3 2.040552957742553e+01 2.040552957739459e+01 3.09370e-11 3.68050e-10 ----------------------------------------------------------------------------------------------------- 26 O 1 -2.074709837074732e+00 -2.074709837066270e+00 8.46212e-12 1.09206e-10 2 1.016969172206696e+00 1.016969172192255e+00 1.44407e-11 7.17510e-11 3 -1.576022831440753e+00 -1.576022831441757e+00 1.00431e-12 3.96709e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 5.110508578881181e+00 5.110508578883509e+00 2.32703e-12 2.07585e-11 2 -5.825470278157094e-01 -5.825470278164734e-01 7.63944e-13 1.00753e-12 3 -2.132329096100382e+00 -2.132329096077505e+00 2.28764e-11 8.44933e-11 ----------------------------------------------------------------------------------------------------- 28 O 1 -2.909174428610075e-01 -2.909174428599799e-01 1.02751e-12 2.74719e-12 2 -6.724348046236989e+00 -6.724348046237581e+00 5.91527e-13 7.65512e-11 3 -7.430180238164155e+00 -7.430180238155714e+00 8.44125e-12 1.49569e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 6.279003335972748e+00 6.279003335970316e+00 2.43183e-12 1.60901e-10 2 6.672559861469660e-01 6.672559861455416e-01 1.42442e-12 6.44935e-11 3 1.878484518971171e+00 1.878484518981489e+00 1.03177e-11 1.37536e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.221687456724798e+01 -1.221687456725619e+01 8.20677e-12 3.20455e-11 2 -1.162628343328657e+01 -1.162628343327580e+01 1.07772e-11 2.84555e-11 3 -6.942869445787704e+00 -6.942869445786816e+00 8.87290e-13 1.25222e-10 ----------------------------------------------------------------------------------------------------- 31 O 1 3.586294963283054e+00 3.586294963280721e+00 2.33324e-12 1.32293e-10 2 2.799007548137261e-01 2.799007548116627e-01 2.06335e-12 6.78990e-12 3 -2.625977161788064e+00 -2.625977161781867e+00 6.19726e-12 3.93916e-11 ----------------------------------------------------------------------------------------------------- 32 O 1 -6.298333878713560e+00 -6.298333878733235e+00 1.96749e-11 1.33069e-10 2 -1.538443313217641e+00 -1.538443313212800e+00 4.84102e-12 2.26417e-11 3 -6.789252342700375e-01 -6.789252342698301e-01 2.07390e-13 1.13828e-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 = ----------------------- = 2.74278e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.74278e-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 2.74278e-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.