!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 4.04999923706 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.044837010297036e-01 3.044837011118360e-01 8.21324e-11 9.12589e-10 2 -3.308126424894674e-02 -3.308126432832881e-02 7.93821e-11 4.81437e-10 3 1.215433178714005e-01 1.215433178207817e-01 5.06187e-11 2.29142e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 4.736378447399816e-01 4.736378447727301e-01 3.27485e-11 1.46154e-10 2 9.278059034184237e-01 9.278059034622895e-01 4.38658e-11 2.99978e-10 3 1.059527977870768e+00 1.059527977873906e+00 3.13838e-12 4.02059e-09 * ----------------------------------------------------------------------------------------------------- 3 Al 1 5.558805987041127e-01 5.558805987805725e-01 7.64598e-11 4.39293e-10 2 8.334620840639174e-01 8.334620840182866e-01 4.56308e-11 2.05702e-10 3 3.026239161229576e-01 3.026239161223789e-01 5.78704e-13 9.89950e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 9.912524074600874e-01 9.912524074082421e-01 5.18453e-11 8.22229e-10 2 6.302228404650531e-01 6.302228403743123e-01 9.07407e-11 3.85609e-09 * 3 8.662426576648951e-01 8.662426576086144e-01 5.62806e-11 3.57597e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -1.065095417011504e-01 -1.065095416416669e-01 5.94835e-11 5.05823e-11 2 4.852280094880512e-01 4.852280095426721e-01 5.46210e-11 1.38988e-10 3 4.281620730273802e-01 4.281620730664102e-01 3.90300e-11 1.13851e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -7.140785151890763e-01 -7.140785150822508e-01 1.06825e-10 1.92445e-10 2 6.450814367488351e-01 6.450814365280584e-01 2.20777e-10 6.31017e-11 3 7.287641609087345e-01 7.287641609120291e-01 3.29459e-12 3.04560e-09 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.358682543426157e-01 2.358682542411743e-01 1.01441e-10 3.13555e-10 2 -5.285602019639624e-01 -5.285602018677963e-01 9.61661e-11 2.95822e-09 3 -8.952373073435855e-01 -8.952373072922337e-01 5.13518e-11 2.65376e-09 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.550963714149823e+00 -1.550963714111714e+00 3.81091e-11 8.75571e-11 2 -1.143171520464167e-01 -1.143171520444973e-01 1.91941e-12 3.84704e-10 3 7.256197511838357e-01 7.256197511499078e-01 3.39279e-11 6.47783e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 5.455461901014284e-01 5.455461904840838e-01 3.82655e-10 3.66615e-09 * 2 -7.150668124018837e-01 -7.150668123942859e-01 7.59781e-12 5.05163e-10 3 1.378565833413104e-01 1.378565833951474e-01 5.38370e-11 3.34947e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.639107813576288e-01 -6.639107811258612e-01 2.31768e-10 1.99799e-10 2 -3.592919159080331e-01 -3.592919159028308e-01 5.20223e-12 2.81096e-10 3 2.998274669101476e-01 2.998274670034006e-01 9.32531e-11 6.97418e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 4.961101893049397e-01 4.961101893029380e-01 2.00162e-12 5.29045e-10 2 -9.471775859899272e-01 -9.471775859204739e-01 6.94533e-11 3.98314e-09 * 3 2.348256209226245e-01 2.348256209355905e-01 1.29661e-11 2.45684e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 8.615675513155153e-01 8.615675512481594e-01 6.73559e-11 6.71614e-10 2 -2.391729622685021e-02 -2.391729619052448e-02 3.63257e-11 5.58908e-10 3 6.574410129021432e-01 6.574410129019469e-01 1.96287e-13 3.08046e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -8.520662717182781e-01 -8.520662717210803e-01 2.80220e-12 4.24457e-10 2 -1.495289068808781e+00 -1.495289068883921e+00 7.51397e-11 4.07321e-11 3 -8.804939419346602e-01 -8.804939419136479e-01 2.10123e-11 1.09384e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 -2.509936085452317e-01 -2.509936085736668e-01 2.84350e-11 3.92610e-10 2 2.276777481786734e-01 2.276777481319554e-01 4.67180e-11 2.83782e-10 3 1.951321331452511e-01 1.951321331481305e-01 2.87939e-12 7.96210e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 8.417408954592481e-01 8.417408954604201e-01 1.17195e-12 3.75113e-09 * 2 -1.038420744269033e+00 -1.038420744289059e+00 2.00266e-11 3.51313e-09 * 3 7.464095981903051e-01 7.464095982313674e-01 4.10624e-11 4.34680e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 2.351644869083092e-01 2.351644868873494e-01 2.09598e-11 2.88493e-09 2 5.095387706969071e-01 5.095387707753638e-01 7.84567e-11 2.21417e-10 3 9.303272550378530e-01 9.303272550461840e-01 8.33100e-12 2.58725e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 2.452209586534845e-01 2.452209586023148e-01 5.11698e-11 6.52047e-10 2 4.950276930322855e-01 4.950276930108957e-01 2.13898e-11 1.02397e-09 3 -6.270925229656639e-01 -6.270925229486467e-01 1.70172e-11 7.33498e-09 * ----------------------------------------------------------------------------------------------------- 18 Al 1 5.617239641634713e-01 5.617239641915922e-01 2.81210e-11 2.50255e-09 2 1.114039070052036e+00 1.114039070435197e+00 3.83161e-10 5.30255e-10 3 -5.755234901664634e-01 -5.755234900927358e-01 7.37276e-11 7.52080e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 6.392027865722104e-01 6.392027865969849e-01 2.47745e-11 2.08698e-09 2 2.983586023534455e-01 2.983586023567201e-01 3.27455e-12 4.06221e-10 3 -2.982865268247669e-01 -2.982865268050285e-01 1.97384e-11 4.18693e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 7.508150011605789e-01 7.508150013207708e-01 1.60192e-10 1.06904e-09 2 9.259478939762102e-01 9.259478939241720e-01 5.20383e-11 6.28781e-11 3 -7.017750918231462e-01 -7.017750917249116e-01 9.82346e-11 8.37270e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.418826631029816e+00 -1.418826630959537e+00 7.02784e-11 7.66966e-10 2 6.437979574626882e-01 6.437979574396324e-01 2.30558e-11 1.14440e-10 3 2.926262436952680e-01 2.926262438483923e-01 1.53124e-10 7.89838e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 -5.977866572762548e-01 -5.977866573285664e-01 5.23116e-11 2.23107e-10 2 1.620477496302728e+00 1.620477496404471e+00 1.01743e-10 1.57517e-09 3 4.498076484662955e-01 4.498076484910895e-01 2.47940e-11 5.32220e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -5.895089838385541e-01 -5.895089838572152e-01 1.86611e-11 6.57909e-10 2 4.527025374766206e-01 4.527025373160417e-01 1.60579e-10 3.14739e-10 3 -2.964738222791243e-01 -2.964738222996761e-01 2.05517e-11 8.09229e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.087983213306620e-03 7.087983283697097e-03 7.03905e-11 2.17899e-10 2 5.042873101429717e-01 5.042873101573248e-01 1.43531e-11 2.11214e-10 3 -1.242554367421444e+00 -1.242554367361591e+00 5.98530e-11 7.95500e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.057027755684132e-01 -2.057027752555652e-01 3.12848e-10 7.45515e-10 2 -1.419889739640622e+00 -1.419889739767453e+00 1.26831e-10 8.68492e-10 3 -5.515852852682468e-01 -5.515852853135318e-01 4.52850e-11 5.30986e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.557399584189230e-01 -1.557399583746613e-01 4.42617e-11 3.36693e-10 2 6.848215515499982e-01 6.848215514842957e-01 6.57026e-11 7.08310e-10 3 -1.117438746430150e+00 -1.117438746331507e+00 9.86422e-11 4.47303e-09 * ----------------------------------------------------------------------------------------------------- 27 Al 1 1.117807172254737e+00 1.117807172282657e+00 2.79194e-11 3.77285e-10 2 -2.099903755013951e+00 -2.099903755038919e+00 2.49680e-11 1.08634e-09 3 1.141939852548478e-01 1.141939853498751e-01 9.50273e-11 1.98543e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -2.406178723753387e-01 -2.406178722629571e-01 1.12382e-10 4.24872e-10 2 4.514502941312499e-01 4.514502941060592e-01 2.51907e-11 4.08491e-10 3 -2.757833192140611e-01 -2.757833191713271e-01 4.27339e-11 1.06339e-09 ----------------------------------------------------------------------------------------------------- 29 Al 1 -5.098628640210459e-01 -5.098628640721177e-01 5.10718e-11 8.28288e-09 * 2 -1.368898648051519e+00 -1.368898647867192e+00 1.84327e-10 1.92340e-10 3 2.039848254045275e-01 2.039848254634554e-01 5.89279e-11 7.64322e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.730110539974963e-01 -7.730110540683396e-01 7.08433e-11 3.27267e-10 2 1.013122563886365e-01 1.013122563472833e-01 4.13532e-11 1.08610e-10 3 -3.318957391039420e-01 -3.318957390737656e-01 3.01764e-11 1.27564e-09 ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.219092869069607e-01 -4.219092869777165e-01 7.07558e-11 2.00005e-10 2 -1.001649956654362e+00 -1.001649956619335e+00 3.50278e-11 1.01336e-09 3 -1.760010166211986e-01 -1.760010165408613e-01 8.03373e-11 1.59247e-09 ----------------------------------------------------------------------------------------------------- 32 Al 1 1.883785307102612e-01 1.883785306461596e-01 6.41016e-11 4.28949e-10 2 -4.057753147044421e-01 -4.057753146678029e-01 3.66391e-11 3.56269e-10 3 -5.247750505240926e-01 -5.247750506718322e-01 1.47740e-10 4.86714e-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 dicontinuities. Maximum error obtained for particle = 24, direction = 1: |F_model - F_numer| error = ----------------------- = 9.93096e-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 = 4.1483373642 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 3.677501440668760e-01 3.677501440673382e-01 4.62297e-13 6.41058e-11 2 4.294126869594953e-01 4.294126869551709e-01 4.32443e-12 1.72587e-10 3 8.538381287187127e-01 8.538381287075247e-01 1.11879e-11 4.02233e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 7.039666223611662e-01 7.039666223589838e-01 2.18248e-12 1.12857e-09 2 8.846232871439188e-01 8.846232869908965e-01 1.53022e-10 2.99002e-09 3 -7.480256879492275e-01 -7.480256877289282e-01 2.20299e-10 2.68645e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -8.580612308228210e-01 -8.580612308057992e-01 1.70218e-11 7.07378e-10 2 -7.461303493754812e-01 -7.461303494472933e-01 7.18121e-11 2.98464e-09 3 8.214295022063309e-01 8.214295022448557e-01 3.85247e-11 6.07863e-08 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.035010896402829e+00 -1.035010896343224e+00 5.96054e-11 2.89982e-10 2 -9.001563420143355e-01 -9.001563422158197e-01 2.01484e-10 9.44611e-10 3 7.234656248847005e-01 7.234656252059478e-01 3.21247e-10 1.58647e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.192200486250461e-01 -5.192200485287568e-01 9.62893e-11 2.26283e-10 2 -3.595236717372238e-02 -3.595236736530354e-02 1.91581e-10 3.57819e-10 3 -1.090504704418766e+00 -1.090504704283245e+00 1.35520e-10 1.73630e-09 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.109395149950024e-01 -2.109395150452754e-01 5.02730e-11 2.67586e-10 2 6.967599917855434e-01 6.967599918390165e-01 5.34731e-11 6.79940e-10 3 4.446280998134921e-01 4.446280998631845e-01 4.96925e-11 4.96397e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.213829930769855e-01 1.213829926637434e-01 4.13242e-10 2.50937e-09 2 7.400654230712873e-01 7.400654231914185e-01 1.20131e-10 2.11754e-09 3 1.368378644042401e+00 1.368378644032235e+00 1.01654e-11 8.93751e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.960329081429048e-02 8.960328929267136e-02 1.52162e-09 4.56222e-09 2 7.002302945754207e-01 7.002302930159555e-01 1.55947e-09 2.96046e-09 3 1.505541429338992e+00 1.505541429459571e+00 1.20579e-10 3.97908e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.061933056584244e-01 3.061933055711440e-01 8.72804e-11 8.40777e-10 2 5.791164328114152e-01 5.791164326045551e-01 2.06860e-10 1.10677e-09 3 1.494368566915539e-01 1.494368565885396e-01 1.03014e-10 1.82767e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.191094079385257e-01 5.191094094681226e-01 1.52960e-09 3.06395e-09 2 -7.026376037118256e-01 -7.026376042328740e-01 5.21048e-10 2.15971e-09 3 1.216245918658353e+00 1.216245918784864e+00 1.26511e-10 1.44120e-09 ----------------------------------------------------------------------------------------------------- 11 Ti 1 5.005334144679958e-01 5.005334145711319e-01 1.03136e-10 1.25012e-09 2 1.295912427997428e+00 1.295912427587887e+00 4.09542e-10 1.28781e-09 3 -2.600375690082267e-01 -2.600375693730435e-01 3.64817e-10 1.77015e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.236090268197136e+00 1.236090268244676e+00 4.75393e-11 3.48671e-10 2 -1.389731387042165e+00 -1.389731387162909e+00 1.20744e-10 1.07162e-09 3 4.363202827525549e-01 4.363202826995910e-01 5.29639e-11 1.15302e-09 ----------------------------------------------------------------------------------------------------- 13 Ti 1 3.054689011095583e-01 3.054689010020933e-01 1.07465e-10 1.81916e-09 2 4.752515233592076e-01 4.752515227968767e-01 5.62331e-10 1.42975e-09 3 8.002055786098985e-01 8.002055790092198e-01 3.99321e-10 5.11194e-09 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -1.011375240192382e+00 -1.011375239406411e+00 7.85970e-10 3.17027e-09 2 6.790649125115991e-01 6.790649125099700e-01 1.62903e-12 3.40577e-09 3 -1.218208417714824e+00 -1.218208417784147e+00 6.93234e-11 9.68788e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -2.016123102358321e-01 -2.016123102629357e-01 2.71036e-11 2.60603e-10 2 -2.633963704189244e+00 -2.633963704835041e+00 6.45798e-10 1.43625e-09 3 1.808237805511243e+00 1.808237805512122e+00 8.78853e-13 2.49729e-09 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -7.805054328069646e-01 -7.805054326578226e-01 1.49142e-10 2.67597e-10 2 3.946551673138111e-01 3.946551677584087e-01 4.44598e-10 2.31728e-09 3 -4.394972005568528e-01 -4.394972001293271e-01 4.27526e-10 7.78600e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -1.047598790501237e+00 -1.047598790166318e+00 3.34920e-10 2.92122e-09 2 -1.284989612653468e+00 -1.284989612652744e+00 7.23865e-13 2.24939e-09 3 -1.418610637839440e-01 -1.418610650598592e-01 1.27592e-09 4.69020e-09 ----------------------------------------------------------------------------------------------------- 18 Ti 1 2.292023566510340e+00 2.292023566552484e+00 4.21432e-11 5.51985e-09 2 2.089091790707046e+00 2.089091790097128e+00 6.09918e-10 4.82021e-09 3 1.256376389121128e+00 1.256376389115495e+00 5.63305e-12 2.65194e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -3.461974135184894e-01 -3.461974143066625e-01 7.88173e-10 1.71682e-09 2 1.317419997901154e+00 1.317419997886789e+00 1.43654e-11 5.41985e-10 3 -7.719519409341242e-01 -7.719519409266919e-01 7.43228e-12 6.45484e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 6.557561309586362e-01 6.557561311336016e-01 1.74965e-10 4.00429e-09 2 6.635524212435917e-02 6.635524220519277e-02 8.08336e-11 4.88911e-09 3 -7.510602048639846e-01 -7.510602048854558e-01 2.14712e-11 6.72160e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.078763998414142e+00 1.078763998582016e+00 1.67873e-10 1.08974e-09 2 5.602822891937224e-01 5.602822891287037e-01 6.50187e-11 1.42898e-09 3 -3.989830139531496e-01 -3.989830143889223e-01 4.35773e-10 2.16217e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -5.482111636114865e-01 -5.482111632984453e-01 3.13041e-10 1.21718e-08 * 2 -2.099512876111260e-02 -2.099512850996508e-02 2.51148e-10 1.38913e-09 3 -1.320652332021113e+00 -1.320652331544442e+00 4.76671e-10 1.53829e-09 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.384011114113130e-01 -9.384011124196937e-01 1.00838e-09 3.38923e-09 2 6.669048159748368e-01 6.669048155950279e-01 3.79809e-10 6.35127e-10 3 -8.011772981277968e-01 -8.011772981805596e-01 5.27628e-11 9.63718e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.252939830998243e+00 -1.252939830922280e+00 7.59630e-11 1.43200e-09 2 -1.178435283528734e+00 -1.178435283530253e+00 1.51901e-12 8.82070e-09 3 5.576183810732974e-01 5.576183810996046e-01 2.63072e-11 1.86090e-09 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -7.384498992443321e-02 -7.384498971771046e-02 2.06723e-10 1.04847e-09 2 -1.119773901363444e+00 -1.119773901425966e+00 6.25211e-11 3.48649e-09 3 -1.667371518289866e+00 -1.667371518333549e+00 4.36837e-11 4.20950e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -5.265456521532406e-01 -5.265456523988991e-01 2.45658e-10 4.44376e-10 2 3.130195210877164e-01 3.130195211788630e-01 9.11466e-11 7.32090e-09 3 -9.796775946813743e-01 -9.796775945839030e-01 9.74713e-11 1.59812e-09 ----------------------------------------------------------------------------------------------------- 27 Ti 1 9.033451463119799e-01 9.033451463475323e-01 3.55523e-11 3.57952e-09 2 -1.106894382972472e-01 -1.106894383835735e-01 8.63263e-11 1.27190e-09 3 4.855032759832346e-01 4.855032758454684e-01 1.37766e-10 5.55402e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 8.394866357118718e-01 8.394866358505422e-01 1.38670e-10 7.74141e-10 2 -1.880512980588105e-01 -1.880512982042077e-01 1.45397e-10 1.99534e-09 3 2.150232732191564e-02 2.150232738449431e-02 6.25787e-11 2.19256e-09 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.885208714180358e-01 -2.885208714657966e-01 4.77608e-11 1.06095e-09 2 -1.913828358530465e+00 -1.913828358696303e+00 1.65837e-10 4.15316e-09 3 -2.608191425745988e+00 -2.608191424306746e+00 1.43924e-09 1.04585e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -4.912836613521368e-01 -4.912836617096935e-01 3.57557e-10 1.04687e-09 2 -2.164407825729109e-01 -2.164407826374980e-01 6.45872e-11 2.56745e-09 3 -8.274482189561593e-01 -8.274482190951028e-01 1.38944e-10 1.39680e-09 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.070958008502249e+00 1.070958008232609e+00 2.69640e-10 2.70090e-09 2 -7.609228794482981e-01 -7.609228795363496e-01 8.80516e-11 2.27711e-09 3 4.868900748228405e-01 4.868900744176663e-01 4.05174e-10 7.26244e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -8.601636751306867e-01 -8.601636752794342e-01 1.48747e-10 1.29524e-09 2 1.314532632203302e+00 1.314532631842043e+00 3.61259e-10 1.42135e-09 3 1.089029871454749e+00 1.089029871576741e+00 1.21993e-10 2.19055e-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 dicontinuities. Maximum error obtained for particle = 8, direction = 1: |F_model - F_numer| error = ----------------------- = 1.69817e-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 = 3.92048331768 | (Configuration in file "config-AlTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 9.580872584672038e-01 9.580872585354037e-01 6.81999e-11 3.28782e-09 2 8.501261875084263e-01 8.501261874654789e-01 4.29474e-11 1.41704e-09 3 1.134889044756705e+00 1.134889044572017e+00 1.84688e-10 3.70133e-09 ----------------------------------------------------------------------------------------------------- 2 Ti 1 2.103419944630242e+00 2.103419944948783e+00 3.18541e-10 8.21282e-10 2 -1.226474364744864e+00 -1.226474364755528e+00 1.06641e-11 1.24779e-09 3 -1.969903603695769e+00 -1.969903604038024e+00 3.42255e-10 2.01965e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -5.869319986119332e+00 -5.869319986559194e+00 4.39862e-10 2.07414e-09 2 -2.238284247685917e+00 -2.238284247550853e+00 1.35064e-10 4.13431e-09 3 -9.422669623526430e+00 -9.422669622441454e+00 1.08498e-09 8.34058e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -2.333637539359532e+00 -2.333637539883666e+00 5.24134e-10 1.72139e-09 2 1.558685537127031e+00 1.558685538138778e+00 1.01175e-09 4.63563e-09 3 -6.599580027606831e-01 -6.599580025758912e-01 1.84792e-10 4.64245e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -4.072302726982521e+00 -4.072302727008524e+00 2.60032e-11 2.87613e-08 * 2 -8.784792402343857e-01 -8.784792400412145e-01 1.93171e-10 1.76275e-09 3 -3.080470798122430e+00 -3.080470798434141e+00 3.11712e-10 3.57704e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 4.120118221616977e-01 4.120118218662179e-01 2.95480e-10 2.37627e-09 2 1.884662866564883e+00 1.884662866454240e+00 1.10642e-10 9.37493e-10 3 -6.987021410319382e-01 -6.987021415331849e-01 5.01247e-10 1.62841e-09 ----------------------------------------------------------------------------------------------------- 7 Ti 1 3.358745272146757e+00 3.358745271609038e+00 5.37719e-10 4.46532e-09 2 -1.751213323980627e+00 -1.751213323800392e+00 1.80235e-10 5.34241e-09 3 4.083686026914044e+00 4.083686026999292e+00 8.52483e-11 1.62918e-09 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -2.078859446183992e+00 -2.078859446450011e+00 2.66019e-10 1.42868e-09 2 1.725826222813348e+00 1.725826223336161e+00 5.22813e-10 1.91203e-09 3 2.758019480773609e-01 2.758019482135274e-01 1.36167e-10 2.07490e-09 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -1.577169354429414e+00 -1.577169354652922e+00 2.23508e-10 8.94442e-11 2 -1.621847002919093e+00 -1.621847003116313e+00 1.97220e-10 6.29936e-09 3 -1.306546856700204e+00 -1.306546856745785e+00 4.55811e-11 6.65012e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.537253628104694e+00 1.537253627820741e+00 2.83953e-10 7.42314e-09 2 1.567673567791424e+00 1.567673567551949e+00 2.39475e-10 1.39497e-09 3 -3.749993481789837e+00 -3.749993481535471e+00 2.54366e-10 1.66571e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 5.308734297840093e-01 5.308734311068187e-01 1.32281e-09 3.77330e-09 2 -2.074373177780226e+00 -2.074373177171525e+00 6.08701e-10 1.06518e-09 3 1.117997011158351e+00 1.117997011208355e+00 5.00040e-11 3.56790e-09 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.343282927802789e+00 -1.343282927294390e+00 5.08399e-10 4.00324e-09 2 9.887516901972484e-01 9.887516900206470e-01 1.76601e-10 4.13206e-10 3 2.894239208452797e+00 2.894239208187730e+00 2.65067e-10 4.00679e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 -2.523014585480693e+00 -2.523014585223465e+00 2.57228e-10 1.86221e-09 2 -5.801918354950052e-01 -5.801918352907454e-01 2.04260e-10 3.18350e-09 3 -8.884147261022269e-01 -8.884147261860502e-01 8.38233e-11 1.05945e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 -2.027665590606207e-02 -2.027665599884166e-02 9.27796e-11 1.45284e-09 2 2.554366055742258e-01 2.554366055914488e-01 1.72230e-11 9.80546e-10 3 8.129787240902873e-01 8.129787240706098e-01 1.96775e-11 1.60805e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.094998969985614e+00 1.094998970491422e+00 5.05808e-10 3.81209e-09 2 -1.005450716700564e+00 -1.005450716644010e+00 5.65539e-11 3.31670e-09 3 -1.681479318430539e+00 -1.681479318460048e+00 2.95093e-11 2.72165e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 2.536610500191215e+00 2.536610500411334e+00 2.20119e-10 3.00857e-10 2 1.388464339600437e+00 1.388464339242025e+00 3.58412e-10 1.69749e-09 3 -6.638040349225788e-02 -6.638040179479729e-02 1.69746e-09 5.55410e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -9.746166753033356e-01 -9.746166751535569e-01 1.49779e-10 3.93206e-09 2 -1.695699746703825e+00 -1.695699746662164e+00 4.16609e-11 5.34996e-09 3 1.893940366013753e+00 1.893940364714213e+00 1.29954e-09 4.79753e-09 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.571601688495322e+00 2.571601688400428e+00 9.48943e-11 5.16511e-09 2 2.636102237834230e+00 2.636102238025869e+00 1.91639e-10 3.97052e-09 3 2.385367662033758e+00 2.385367662157512e+00 1.23753e-10 1.62967e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 -8.184346995465681e-01 -8.184346994429958e-01 1.03572e-10 1.76491e-09 2 7.530689901469181e-01 7.530689902596095e-01 1.12691e-10 1.34100e-09 3 -1.077142143322423e+00 -1.077142142888827e+00 4.33596e-10 2.48064e-09 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -4.374815366289744e+00 -4.374815365729638e+00 5.60106e-10 1.99428e-09 2 -4.764601472369474e+00 -4.764601473826122e+00 1.45665e-09 3.68166e-09 3 -4.418514595208334e-01 -4.418514590648265e-01 4.56007e-10 1.96179e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 7.221165772361480e+00 7.221165772108677e+00 2.52802e-10 1.32557e-09 2 -3.762187433420496e-01 -3.762187432311595e-01 1.10890e-10 2.85745e-09 3 7.133123829371021e+00 7.133123830055142e+00 6.84121e-10 1.51973e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 6.595091527680985e-01 6.595091510330305e-01 1.73507e-09 3.36012e-09 2 -5.293307910937526e-01 -5.293307916733861e-01 5.79634e-10 3.37385e-09 3 2.349204148226307e+00 2.349204148623577e+00 3.97270e-10 9.81870e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 -6.606553988129733e-01 -6.606553987614521e-01 5.15212e-11 5.04750e-10 2 7.385356724252098e-01 7.385356697247958e-01 2.70041e-09 3.36651e-09 3 -8.602576321269538e-01 -8.602576321070124e-01 1.99414e-11 1.07599e-09 ----------------------------------------------------------------------------------------------------- 24 Al 1 2.659367634473214e-01 2.659367635184751e-01 7.11537e-11 2.03978e-09 2 6.971058863199066e-01 6.971058868483910e-01 5.28484e-10 5.86896e-09 3 -9.025848205388645e-01 -9.025848208956521e-01 3.56788e-10 9.37920e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.316045734990889e+00 -2.316045735244123e+00 2.53235e-10 4.42225e-09 2 3.328080281812881e-01 3.328080273062672e-01 8.75021e-10 1.55921e-09 3 -1.933864212324174e+00 -1.933864211609513e+00 7.14660e-10 1.61518e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -2.498601807512262e+00 -2.498601808467703e+00 9.55442e-10 6.99555e-09 2 1.042677819357622e+00 1.042677818535070e+00 8.22552e-10 3.57892e-09 3 -8.789948433650392e-01 -8.789948431519937e-01 2.13045e-10 3.38481e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 6.993633462171394e+00 6.993633462555114e+00 3.83720e-10 3.01567e-09 2 4.846352833754611e+00 4.846352833802736e+00 4.81251e-11 9.28779e-10 3 1.048474672487359e+00 1.048474671742202e+00 7.45157e-10 3.57226e-08 * ----------------------------------------------------------------------------------------------------- 28 Al 1 2.577469910047913e-01 2.577469911703068e-01 1.65516e-10 1.37386e-09 2 -5.521390119410299e-02 -5.521390255120242e-02 1.35710e-09 4.12212e-09 3 5.496690336208320e-01 5.496690337373312e-01 1.16499e-10 1.26202e-08 * ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.082651045776440e+00 1.082651046057122e+00 2.80682e-10 2.24433e-09 2 -2.982683048024260e+00 -2.982683047750724e+00 2.73535e-10 2.18319e-09 3 2.062024333055067e+00 2.062024332216682e+00 8.38385e-10 3.53650e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -9.864752715184530e-02 -9.864752691821660e-02 2.33629e-10 4.61882e-10 2 1.296932646824420e+00 1.296932646656030e+00 1.68389e-10 3.62299e-09 3 1.404377714433643e+00 1.404377714120699e+00 3.12943e-10 9.91342e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -1.141349680104719e+00 -1.141349680042774e+00 6.19451e-11 6.22322e-09 2 -2.648730253953624e-01 -2.648730232758678e-01 2.11949e-09 5.53032e-09 3 -1.186759529828592e+00 -1.186759530223125e+00 3.94534e-10 2.97794e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.116784410480390e+00 1.116784409582668e+00 8.97722e-10 2.61762e-09 2 -5.182764943577230e-01 -5.182764956647103e-01 1.30699e-09 6.01670e-09 3 1.660199873987907e+00 1.660199874412832e+00 4.24925e-10 3.34240e-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 dicontinuities. Maximum error obtained for particle = 16, direction = 3: |F_model - F_numer| error = ----------------------- = 2.55717e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.55717e-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 2.55717e-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.