!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_ZopeMishin_2003_TiAl__MO_117656786760_005 Supported species : Al Ti 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 = Al | a0 = 4.049999237060547 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.044837010296998e-01 3.044837010944417e-01 6.47419e-11 1.61436e-10 2 -3.308126424895000e-02 -3.308126429478130e-02 4.58313e-11 2.56764e-10 3 1.215433178713964e-01 1.215433178737581e-01 2.36171e-12 1.47496e-09 ----------------------------------------------------------------------------------------------------- 2 Al 1 4.736378447399882e-01 4.736378446241274e-01 1.15861e-10 1.09952e-09 2 9.278059034184187e-01 9.278059033305130e-01 8.79057e-11 3.42739e-10 3 1.059527977870769e+00 1.059527977993598e+00 1.22829e-10 1.01371e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 5.558805987041098e-01 5.558805987412241e-01 3.71143e-11 2.47238e-10 2 8.334620840639200e-01 8.334620840269886e-01 3.69313e-11 3.24399e-10 3 3.026239161229606e-01 3.026239160781646e-01 4.47960e-11 1.01495e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 9.912524074600880e-01 9.912524074993928e-01 3.93048e-11 6.08694e-11 2 6.302228404650525e-01 6.302228403474345e-01 1.17618e-10 3.85969e-10 3 8.662426576648973e-01 8.662426575836937e-01 8.12036e-11 1.04611e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -1.065095417011479e-01 -1.065095416863605e-01 1.47874e-11 3.98639e-10 2 4.852280094880514e-01 4.852280095821461e-01 9.40947e-11 4.38779e-10 3 4.281620730273800e-01 4.281620730187981e-01 8.58186e-12 4.49896e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 -7.140785151890726e-01 -7.140785152014295e-01 1.23569e-11 7.01511e-11 2 6.450814367488362e-01 6.450814367425124e-01 6.32383e-12 1.01822e-09 3 7.287641609087291e-01 7.287641609515952e-01 4.28662e-11 2.89314e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.358682543426159e-01 2.358682543784270e-01 3.58111e-11 6.58359e-10 2 -5.285602019639634e-01 -5.285602017203134e-01 2.43650e-10 4.50336e-10 3 -8.952373073435812e-01 -8.952373072397376e-01 1.03844e-10 3.71810e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.550963714149838e+00 -1.550963713981440e+00 1.68398e-10 2.94611e-10 2 -1.143171520464151e-01 -1.143171520345231e-01 1.18920e-11 3.65172e-10 3 7.256197511838380e-01 7.256197513890240e-01 2.05186e-10 2.43163e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 5.455461901014250e-01 5.455461900675460e-01 3.38790e-11 2.54762e-10 2 -7.150668124018675e-01 -7.150668123528170e-01 4.90505e-11 8.02879e-10 3 1.378565833413217e-01 1.378565833184372e-01 2.28844e-11 2.00220e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.639107813576297e-01 -6.639107812198802e-01 1.37749e-10 7.97325e-10 2 -3.592919159080316e-01 -3.592919159796965e-01 7.16648e-11 2.27816e-10 3 2.998274669101535e-01 2.998274669106434e-01 4.89941e-13 2.31826e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 4.961101893049397e-01 4.961101892799306e-01 2.50091e-11 9.53757e-09 * 2 -9.471775859899196e-01 -9.471775860992813e-01 1.09362e-10 7.39507e-10 3 2.348256209226381e-01 2.348256211752597e-01 2.52622e-10 1.57203e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 8.615675513155220e-01 8.615675512427770e-01 7.27450e-11 7.37853e-10 2 -2.391729622686576e-02 -2.391729626867762e-02 4.18119e-11 7.55098e-10 3 6.574410129021317e-01 6.574410129326378e-01 3.05060e-11 1.16152e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -8.520662717182663e-01 -8.520662716673663e-01 5.09001e-11 4.33778e-10 2 -1.495289068808779e+00 -1.495289068835977e+00 2.71987e-11 5.04031e-10 3 -8.804939419346515e-01 -8.804939420138546e-01 7.92031e-11 7.08575e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 -2.509936085452379e-01 -2.509936085869123e-01 4.16743e-11 4.91847e-10 2 2.276777481786609e-01 2.276777482163471e-01 3.76862e-11 8.17221e-10 3 1.951321331452608e-01 1.951321330733685e-01 7.18923e-11 4.77913e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 8.417408954592481e-01 8.417408953687283e-01 9.05198e-11 2.98646e-10 2 -1.038420744269011e+00 -1.038420744286591e+00 1.75799e-11 3.58188e-10 3 7.464095981902922e-01 7.464095982868806e-01 9.65884e-11 3.99740e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 2.351644869083005e-01 2.351644869424611e-01 3.41606e-11 3.38904e-10 2 5.095387706969020e-01 5.095387707713128e-01 7.44108e-11 4.33552e-10 3 9.303272550378430e-01 9.303272550905313e-01 5.26883e-11 4.79130e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 2.452209586534770e-01 2.452209586843714e-01 3.08945e-11 1.44684e-09 2 4.950276930322803e-01 4.950276928197704e-01 2.12510e-10 2.09511e-08 * 3 -6.270925229656676e-01 -6.270925230383935e-01 7.27258e-11 2.79743e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 5.617239641634846e-01 5.617239639833548e-01 1.80130e-10 6.76970e-10 2 1.114039070052039e+00 1.114039070286974e+00 2.34935e-10 1.54479e-09 3 -5.755234901664629e-01 -5.755234901939271e-01 2.74643e-11 5.31460e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 6.392027865722183e-01 6.392027865478690e-01 2.43493e-11 5.78572e-10 2 2.983586023534412e-01 2.983586023198666e-01 3.35746e-11 5.53859e-10 3 -2.982865268247633e-01 -2.982865267125227e-01 1.12241e-10 3.23733e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 7.508150011605742e-01 7.508150010878128e-01 7.27614e-11 2.30402e-10 2 9.259478939762160e-01 9.259478939805693e-01 4.35330e-12 4.01740e-10 3 -7.017750918231422e-01 -7.017750918659769e-01 4.28346e-11 6.06081e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.418826631029816e+00 -1.418826630959537e+00 7.02791e-11 1.26667e-09 2 6.437979574626923e-01 6.437979574529529e-01 9.73943e-12 4.74516e-10 3 2.926262436952687e-01 2.926262438157335e-01 1.20465e-10 8.48948e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 -5.977866572762550e-01 -5.977866571634891e-01 1.12766e-10 1.80453e-10 2 1.620477496302722e+00 1.620477496250613e+00 5.21090e-11 4.30669e-10 3 4.498076484663015e-01 4.498076484210599e-01 4.52416e-11 4.54571e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -5.895089838385525e-01 -5.895089839816618e-01 1.43109e-10 6.88435e-10 2 4.527025374766219e-01 4.527025372723147e-01 2.04307e-10 4.88226e-10 3 -2.964738222791306e-01 -2.964738222507866e-01 2.83440e-11 2.92250e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.087983213299881e-03 7.087983144830412e-03 6.84695e-11 5.29921e-10 2 5.042873101429706e-01 5.042873101744106e-01 3.14401e-11 8.31031e-10 3 -1.242554367421452e+00 -1.242554367430122e+00 8.66995e-12 4.72916e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.057027755684031e-01 -2.057027755202583e-01 4.81448e-11 5.41627e-10 2 -1.419889739640623e+00 -1.419889739637529e+00 3.09419e-12 5.15999e-10 3 -5.515852852682532e-01 -5.515852852370549e-01 3.11984e-11 1.88889e-09 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.557399584189235e-01 -1.557399584029308e-01 1.59927e-11 7.16391e-10 2 6.848215515499911e-01 6.848215516077093e-01 5.77182e-11 1.80189e-10 3 -1.117438746430174e+00 -1.117438746383963e+00 4.62115e-11 4.76054e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.117807172254733e+00 1.117807172059052e+00 1.95681e-10 1.50757e-09 2 -2.099903755013962e+00 -2.099903755033534e+00 1.95719e-11 2.72565e-10 3 1.141939852548473e-01 1.141939852277704e-01 2.70770e-11 3.44473e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -2.406178723753473e-01 -2.406178724504372e-01 7.50899e-11 7.23206e-10 2 4.514502941312569e-01 4.514502939846780e-01 1.46579e-10 4.27527e-10 3 -2.757833192140531e-01 -2.757833191311699e-01 8.28832e-11 3.64259e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -5.098628640210581e-01 -5.098628640785127e-01 5.74546e-11 4.29241e-10 2 -1.368898648051526e+00 -1.368898648121494e+00 6.99680e-11 6.59882e-09 * 3 2.039848254045282e-01 2.039848256495800e-01 2.45052e-10 1.10444e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.730110539974908e-01 -7.730110541163385e-01 1.18848e-10 1.18329e-09 2 1.013122563886320e-01 1.013122563499059e-01 3.87261e-11 3.91601e-10 3 -3.318957391039403e-01 -3.318957391106520e-01 6.71169e-12 2.96464e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.219092869069655e-01 -4.219092868160556e-01 9.09099e-11 1.26977e-10 2 -1.001649956654351e+00 -1.001649956708538e+00 5.41875e-11 1.22427e-09 3 -1.760010166212009e-01 -1.760010165926938e-01 2.85071e-11 1.95371e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 1.883785307102793e-01 1.883785306385203e-01 7.17589e-11 5.09874e-10 2 -4.057753147044403e-01 -4.057753147306994e-01 2.62591e-11 1.75115e-10 3 -5.247750505240834e-01 -5.247750507597670e-01 2.35684e-10 3.38197e-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 = 24, direction = 1: |F_model - F_numer| error = ----------------------- = 9.65994e-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 = Ti | a0 = 4.148337364196777 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 3.677501440668687e-01 3.677501440452235e-01 2.16452e-11 4.23637e-10 2 4.294126869594903e-01 4.294126870642341e-01 1.04744e-10 3.10951e-10 3 8.538381287187135e-01 8.538381286141226e-01 1.04591e-10 8.66850e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 7.039666223611734e-01 7.039666225426778e-01 1.81504e-10 2.53028e-09 2 8.846232871439272e-01 8.846232869685672e-01 1.75360e-10 2.46197e-10 3 -7.480256879492353e-01 -7.480256880777936e-01 1.28558e-10 1.52491e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -8.580612308228108e-01 -8.580612305006275e-01 3.22183e-10 3.38621e-09 2 -7.461303493754743e-01 -7.461303484061491e-01 9.69325e-10 2.35384e-09 3 8.214295022063550e-01 8.214295020774971e-01 1.28858e-10 2.38037e-09 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.035010896402840e+00 -1.035010896486665e+00 8.38254e-11 2.24562e-08 * 2 -9.001563420143449e-01 -9.001563422364453e-01 2.22100e-10 1.26219e-09 3 7.234656248847025e-01 7.234656248123474e-01 7.23550e-11 5.32874e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.192200486250464e-01 -5.192200485230817e-01 1.01965e-10 2.32332e-09 2 -3.595236717371948e-02 -3.595236742580811e-02 2.52089e-10 1.55720e-09 3 -1.090504704418764e+00 -1.090504704373991e+00 4.47733e-11 1.09832e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.109395149949936e-01 -2.109395146370016e-01 3.57992e-10 1.21038e-09 2 6.967599917855469e-01 6.967599917388048e-01 4.67422e-11 4.53077e-10 3 4.446280998134766e-01 4.446280996312499e-01 1.82227e-10 2.68407e-09 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.213829930769835e-01 1.213829932745680e-01 1.97585e-10 1.15714e-09 2 7.400654230712873e-01 7.400654232884539e-01 2.17167e-10 2.10973e-09 3 1.368378644042406e+00 1.368378643904614e+00 1.37792e-10 3.04386e-09 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.960329081427816e-02 8.960329036205428e-02 4.52224e-10 2.02348e-09 2 7.002302945754092e-01 7.002302949843876e-01 4.08978e-10 8.63694e-10 3 1.505541429339000e+00 1.505541429176134e+00 1.62865e-10 6.45911e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.061933056584294e-01 3.061933052326236e-01 4.25806e-10 5.16405e-09 2 5.791164328114201e-01 5.791164330590794e-01 2.47659e-10 7.68704e-10 3 1.494368566915520e-01 1.494368567160211e-01 2.44691e-11 8.74895e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.191094079385182e-01 5.191094086861848e-01 7.47667e-10 2.56202e-10 2 -7.026376037118311e-01 -7.026376038333580e-01 1.21527e-10 2.81406e-09 3 1.216245918658354e+00 1.216245918803520e+00 1.45166e-10 3.33886e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 5.005334144680149e-01 5.005334148337135e-01 3.65699e-10 1.70024e-09 2 1.295912427997445e+00 1.295912427502875e+00 4.94569e-10 1.79714e-09 3 -2.600375690082243e-01 -2.600375692577620e-01 2.49538e-10 4.09458e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.236090268197137e+00 1.236090268299249e+00 1.02112e-10 1.48428e-09 2 -1.389731387042165e+00 -1.389731387107430e+00 6.52647e-11 4.10373e-10 3 4.363202827525539e-01 4.363202826145669e-01 1.37987e-10 7.39250e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 3.054689011095640e-01 3.054689010022640e-01 1.07300e-10 5.14601e-10 2 4.752515233592115e-01 4.752515248122351e-01 1.45302e-09 3.40511e-09 3 8.002055786098993e-01 8.002055778120563e-01 7.97843e-10 3.03137e-09 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -1.011375240192386e+00 -1.011375240338648e+00 1.46262e-10 1.17400e-09 2 6.790649125115934e-01 6.790649125259702e-01 1.43768e-11 1.31080e-09 3 -1.218208417714820e+00 -1.218208418949030e+00 1.23421e-09 1.92816e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -2.016123102358393e-01 -2.016123102948036e-01 5.89643e-11 2.41827e-09 2 -2.633963704189242e+00 -2.633963704497268e+00 3.08026e-10 1.34792e-09 3 1.808237805511239e+00 1.808237805684007e+00 1.72767e-10 1.91765e-09 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -7.805054328069695e-01 -7.805054337266614e-01 9.19692e-10 3.74116e-09 2 3.946551673137964e-01 3.946551681850881e-01 8.71292e-10 2.29886e-09 3 -4.394972005568527e-01 -4.394971998643034e-01 6.92549e-10 5.44848e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -1.047598790501222e+00 -1.047598790438445e+00 6.27769e-11 1.30467e-09 2 -1.284989612653453e+00 -1.284989613074835e+00 4.21382e-10 1.06451e-09 3 -1.418610637839459e-01 -1.418610633511586e-01 4.32787e-10 2.51320e-09 ----------------------------------------------------------------------------------------------------- 18 Ti 1 2.292023566510339e+00 2.292023566402054e+00 1.08285e-10 6.87946e-10 2 2.089091790707020e+00 2.089091790486373e+00 2.20648e-10 9.32803e-10 3 1.256376389121128e+00 1.256376388823604e+00 2.97524e-10 2.53584e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -3.461974135184934e-01 -3.461974148298754e-01 1.31138e-09 2.43763e-09 2 1.317419997901157e+00 1.317419997762670e+00 1.38487e-10 9.16744e-10 3 -7.719519409341264e-01 -7.719519398462971e-01 1.08783e-09 1.32831e-09 ----------------------------------------------------------------------------------------------------- 20 Ti 1 6.557561309586388e-01 6.557561310585279e-01 9.98891e-11 8.54191e-09 * 2 6.635524212435803e-02 6.635524232028306e-02 1.95925e-10 2.82759e-09 3 -7.510602048639866e-01 -7.510602053603922e-01 4.96406e-10 5.14573e-09 ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.078763998414128e+00 1.078763997948609e+00 4.65519e-10 2.61033e-09 2 5.602822891937297e-01 5.602822902285438e-01 1.03481e-09 2.32401e-09 3 -3.989830139531663e-01 -3.989830142164110e-01 2.63245e-10 2.43101e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -5.482111636114750e-01 -5.482111637038884e-01 9.24134e-11 6.70693e-10 2 -2.099512876110923e-02 -2.099512872718799e-02 3.39212e-11 3.54471e-09 3 -1.320652332021126e+00 -1.320652331938264e+00 8.28626e-11 2.32555e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.384011114113138e-01 -9.384011117648375e-01 3.53524e-10 3.58122e-09 2 6.669048159748325e-01 6.669048163417500e-01 3.66917e-10 1.19811e-09 3 -8.011772981277880e-01 -8.011772981949877e-01 6.71997e-11 1.52107e-09 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.252939830998261e+00 -1.252939831435929e+00 4.37668e-10 1.79551e-09 2 -1.178435283528740e+00 -1.178435283842431e+00 3.13691e-10 2.55578e-09 3 5.576183810733000e-01 5.576183810555342e-01 1.77658e-11 5.65560e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -7.384498992444351e-02 -7.384498893252761e-02 9.91916e-10 1.42680e-09 2 -1.119773901363439e+00 -1.119773900441621e+00 9.21818e-10 3.30040e-09 3 -1.667371518289868e+00 -1.667371518481847e+00 1.91979e-10 1.55877e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -5.265456521532582e-01 -5.265456523350069e-01 1.81749e-10 7.66380e-09 2 3.130195210877577e-01 3.130195224299167e-01 1.34216e-09 2.97445e-09 3 -9.796775946813975e-01 -9.796775946148941e-01 6.65034e-11 6.34961e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 9.033451463119777e-01 9.033451462995924e-01 1.23853e-11 5.28625e-09 2 -1.106894382972760e-01 -1.106894384022773e-01 1.05001e-10 4.38125e-09 3 4.855032759832636e-01 4.855032752868617e-01 6.96402e-10 1.35764e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 8.394866357118733e-01 8.394866357111077e-01 7.65610e-13 6.89252e-09 2 -1.880512980588179e-01 -1.880512982554841e-01 1.96666e-10 4.46832e-09 3 2.150232732190827e-02 2.150232746292751e-02 1.41019e-10 2.19840e-09 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.885208714180149e-01 -2.885208711160268e-01 3.01988e-10 1.94007e-09 2 -1.913828358530486e+00 -1.913828357731615e+00 7.98871e-10 1.65435e-09 3 -2.608191425746002e+00 -2.608191426733508e+00 9.87506e-10 2.24691e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -4.912836613521440e-01 -4.912836614880409e-01 1.35897e-10 1.39800e-09 2 -2.164407825729254e-01 -2.164407825459991e-01 2.69263e-11 5.47049e-10 3 -8.274482189561394e-01 -8.274482187889368e-01 1.67203e-10 2.56538e-09 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.070958008502255e+00 1.070958008881462e+00 3.79206e-10 3.83122e-09 2 -7.609228794482717e-01 -7.609228793411631e-01 1.07109e-10 2.54806e-09 3 4.868900748228305e-01 4.868900744844170e-01 3.38414e-10 6.36473e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -8.601636751306685e-01 -8.601636750837309e-01 4.69376e-11 2.45065e-09 2 1.314532632203312e+00 1.314532632196110e+00 7.20179e-12 7.29018e-09 3 1.089029871454761e+00 1.089029871675347e+00 2.20586e-10 2.53666e-09 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 25, direction = 1: |F_model - F_numer| error = ----------------------- = 1.34324e-08 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 = Al Ti | a0 = 4.052361028928043 | (Configuration in file "config-AlTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -2.647130310421165e+00 -2.647130310345839e+00 7.53260e-11 5.61854e-10 2 -1.543585458430142e+00 -1.543585458354154e+00 7.59874e-11 7.00350e-08 * 3 5.212209009380839e-01 5.212209009282079e-01 9.87599e-12 8.03733e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 3.121124623852675e+00 3.121124624178894e+00 3.26219e-10 2.30293e-09 2 3.478253979503124e+00 3.478253979521443e+00 1.83187e-11 1.00503e-09 3 7.723370471278456e-01 7.723370470526560e-01 7.51895e-11 5.45816e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 8.685221765017744e-01 8.685221764849921e-01 1.67824e-11 5.35576e-10 2 4.952751064059116e-01 4.952751062988556e-01 1.07056e-10 6.56846e-10 3 7.670392432106272e-01 7.670392432595901e-01 4.89628e-11 1.09797e-09 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -9.833305751222301e-01 -9.833305755819899e-01 4.59760e-10 1.53326e-09 2 -3.186817306411697e+00 -3.186817305728812e+00 6.82885e-10 1.32620e-09 3 -6.335077520137712e-01 -6.335077521304391e-01 1.16668e-10 3.60066e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -5.110575331219505e-01 -5.110575331618716e-01 3.99212e-11 1.30000e-09 2 -1.293562338248397e+00 -1.293562338289854e+00 4.14577e-11 4.19525e-10 3 -1.685985780275836e+00 -1.685985780213642e+00 6.21945e-11 1.75473e-09 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -6.832692210070664e-01 -6.832692213283684e-01 3.21302e-10 2.16706e-09 2 -4.590173510611918e-01 -4.590173510199105e-01 4.12813e-11 4.02092e-10 3 9.332372243678185e-01 9.332372242957832e-01 7.20354e-11 5.22243e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 -4.479087487429778e-02 -4.479087498858950e-02 1.14292e-10 8.32226e-10 2 1.499120047957548e+00 1.499120047985094e+00 2.75462e-11 3.95099e-10 3 5.333011218366486e-01 5.333011232927132e-01 1.45606e-09 6.23501e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 3.774458420896190e-01 3.774458419456108e-01 1.44008e-10 4.23399e-10 2 2.759896888686262e+00 2.759896888571386e+00 1.14877e-10 4.06716e-10 3 1.123326121714743e+00 1.123326122307677e+00 5.92934e-10 2.86758e-09 ----------------------------------------------------------------------------------------------------- 9 Al 1 7.732782207880318e-01 7.732782204308715e-01 3.57160e-10 3.50091e-10 2 -6.545133348058384e-01 -6.545133348402488e-01 3.44104e-11 2.52446e-08 * 3 8.598692250687169e-01 8.598692251253249e-01 5.66081e-11 1.13681e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.819871855045859e+00 -2.819871854585853e+00 4.60007e-10 7.74173e-10 2 2.174179121003512e+00 2.174179121177957e+00 1.74444e-10 1.60904e-09 3 -3.992143418197537e+00 -3.992143418996594e+00 7.99057e-10 1.31988e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 4.353589614380103e+00 4.353589613808197e+00 5.71906e-10 3.85635e-10 2 -3.238325574955536e+00 -3.238325576531635e+00 1.57610e-09 1.17813e-09 3 2.015774985829259e+00 2.015774985847617e+00 1.83578e-11 3.12348e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.533427981901490e+00 -1.533427981688343e+00 2.13147e-10 1.56118e-09 2 4.439340840676627e+00 4.439340840769113e+00 9.24860e-11 1.05067e-09 3 -2.347826327208550e+00 -2.347826326744805e+00 4.63745e-10 3.13655e-09 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.115188426766556e+00 1.115188427065894e+00 2.99338e-10 5.41769e-08 * 2 -2.473474274671313e+00 -2.473474275044766e+00 3.73453e-10 4.43614e-09 3 -1.023842168013544e+00 -1.023842166851980e+00 1.16156e-09 4.43497e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 -9.268826773052095e-01 -9.268826772895201e-01 1.56893e-11 5.51803e-10 2 -6.613655207123272e-01 -6.613655208434722e-01 1.31145e-10 1.69925e-08 * 3 5.162323613896032e-01 5.162323614709844e-01 8.13812e-11 2.66171e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 -9.996988070406063e-01 -9.996988074593891e-01 4.18783e-10 2.44096e-08 * 2 -2.847302699698526e-01 -2.847302699204247e-01 4.94279e-11 1.69452e-09 3 1.174306406244914e+00 1.174306406125079e+00 1.19835e-10 2.00457e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 2.311382715756535e+00 2.311382715510955e+00 2.45580e-10 1.41488e-10 2 1.031420427797257e+00 1.031420428289017e+00 4.91760e-10 1.00160e-08 3 4.112666208158411e+00 4.112666209831888e+00 1.67348e-09 3.28102e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -3.293632498678341e-01 -3.293632498114456e-01 5.63885e-11 2.47007e-09 2 1.027898871841012e+00 1.027898871788949e+00 5.20639e-11 1.32575e-09 3 -1.140145040349989e+00 -1.140145040369386e+00 1.93972e-11 2.47319e-09 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.117329510702972e+00 -2.117329510268322e+00 4.34650e-10 2.54574e-09 2 -1.688221524385944e+00 -1.688221522906445e+00 1.47950e-09 2.31804e-08 * 3 -2.205958450036454e+00 -2.205958448474151e+00 1.56230e-09 4.46759e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 1.450314139252788e+00 1.450314139695624e+00 4.42836e-10 8.56372e-10 2 8.367341044628879e-01 8.367341040411376e-01 4.21750e-10 1.45413e-09 3 2.485091958631213e-01 2.485091956075866e-01 2.55535e-10 4.51944e-09 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.298153469349836e+00 -1.298153469370592e+00 2.07561e-11 2.53676e-09 2 -1.973661318333528e+00 -1.973661318678954e+00 3.45426e-10 1.85890e-09 3 -7.349058452967231e-01 -7.349058452421052e-01 5.46179e-11 4.03138e-09 ----------------------------------------------------------------------------------------------------- 21 Al 1 1.773820858589857e-01 1.773820863184390e-01 4.59453e-10 3.46765e-09 2 4.738215722391620e-01 4.738215724558383e-01 2.16676e-10 2.47547e-09 3 7.705090523037739e-01 7.705090521941566e-01 1.09617e-10 2.74449e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -9.671897477776792e-01 -9.671897478320163e-01 5.43371e-11 7.20710e-10 2 -8.811889783431099e-01 -8.811889778376532e-01 5.05457e-10 1.37086e-09 3 -9.076975655760657e-01 -9.076975656047263e-01 2.86605e-11 3.14464e-08 * ----------------------------------------------------------------------------------------------------- 23 Ti 1 -1.018369814338019e+00 -1.018369814119940e+00 2.18078e-10 1.24608e-09 2 1.157331785383164e+00 1.157331785857974e+00 4.74811e-10 1.09970e-09 3 -1.065045423658734e+00 -1.065045423027655e+00 6.31078e-10 7.21172e-09 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.567047465170960e+00 -1.567047465423107e+00 2.52147e-10 3.23610e-09 2 -2.563953484883157e+00 -2.563953485119745e+00 2.36588e-10 2.56752e-09 3 1.603911478058707e-01 1.603911466098671e-01 1.19600e-09 1.53339e-09 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.540050599576335e-01 -1.540050597858650e-01 1.71769e-10 4.05851e-10 2 -2.070014180020229e+00 -2.070014179393885e+00 6.26344e-10 1.78714e-09 3 3.376668695802914e+00 3.376668695463817e+00 3.39097e-10 2.38922e-09 ----------------------------------------------------------------------------------------------------- 26 Al 1 -2.331827649526869e+00 -2.331827648128940e+00 1.39793e-09 3.43099e-09 2 -6.475988828363202e-01 -6.475988830496631e-01 2.13343e-10 7.54526e-10 3 -4.581630666889385e+00 -4.581630667088793e+00 1.99408e-10 1.99603e-08 * ----------------------------------------------------------------------------------------------------- 27 Al 1 2.394456332202867e+00 2.394456332730865e+00 5.27997e-10 1.75342e-09 2 3.001836018378612e+00 3.001836019361096e+00 9.82484e-10 1.99225e-08 * 3 1.260228082740662e+00 1.260228083564931e+00 8.24269e-10 8.54551e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.630366857483013e-01 -6.630366859838471e-01 2.35546e-10 6.42287e-10 2 -2.887056716809662e-01 -2.887056715162468e-01 1.64719e-10 2.15741e-09 3 5.118740839329201e-01 5.118740841112155e-01 1.78295e-10 2.11903e-09 ----------------------------------------------------------------------------------------------------- 29 Al 1 1.877582836710866e-01 1.877582833340849e-01 3.37002e-10 2.56001e-09 2 5.697612989158717e-01 5.697612987705006e-01 1.45371e-10 5.29029e-09 3 -8.861904344961969e-01 -8.861904342500161e-01 2.46181e-10 2.38619e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -4.419109199420601e-02 -4.419109197845543e-02 1.57506e-11 5.30990e-10 2 -1.036788423290663e+00 -1.036788423488113e+00 1.97449e-10 3.93617e-08 * 3 -8.725611751071087e-01 -8.725611751198292e-01 1.27205e-11 4.25374e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.641619105705497e+00 1.641619105738722e+00 3.32256e-11 1.94900e-09 2 2.543844418073680e+00 2.543844417739937e+00 3.33742e-10 1.47619e-09 3 -4.994331425001806e-01 -4.994331426244513e-01 1.24271e-10 2.11703e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 2.867912013447666e+00 2.867912012891606e+00 5.56060e-10 8.72042e-10 2 -5.431905882844195e-01 -5.431905882087903e-01 7.56292e-11 4.13257e-10 3 2.919382085284143e+00 2.919382083485945e+00 1.79820e-09 3.57570e-09 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 24, direction = 3: |F_model - F_numer| error = ----------------------- = 7.45679e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.34324e-08 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: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.34324e-08 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.