!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Zope_Mishin_TiAl__MO_117656786760_004 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 3.044837010297034e-01 3.044837010295632e-01 1.40221e-13 6.10498e-11 2 -3.308126424894669e-02 -3.308126426489168e-02 1.59450e-11 5.12815e-09 * 3 1.215433178714005e-01 1.215433178432645e-01 2.81360e-11 1.18311e-09 ----------------------------------------------------------------------------------------------------- 2 Al 1 4.736378447399816e-01 4.736378447186399e-01 2.13417e-11 1.32549e-09 2 9.278059034184233e-01 9.278059033945079e-01 2.39154e-11 8.62195e-10 3 1.059527977870768e+00 1.059527977676202e+00 1.94566e-10 4.24334e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 5.558805987041127e-01 5.558805987268516e-01 2.27389e-11 4.18050e-10 2 8.334620840639175e-01 8.334620839797142e-01 8.42033e-11 4.91308e-10 3 3.026239161229575e-01 3.026239161472095e-01 2.42520e-11 1.76177e-09 ----------------------------------------------------------------------------------------------------- 4 Al 1 9.912524074600870e-01 9.912524073332958e-01 1.26791e-10 2.47842e-09 2 6.302228404650532e-01 6.302228405549781e-01 8.99250e-11 1.17589e-09 3 8.662426576648951e-01 8.662426576098982e-01 5.49969e-11 7.26448e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -1.065095417011505e-01 -1.065095417709707e-01 6.98202e-11 4.29403e-10 2 4.852280094880509e-01 4.852280095560847e-01 6.80338e-11 2.72940e-10 3 4.281620730273804e-01 4.281620729674113e-01 5.99691e-11 5.39980e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -7.140785151890762e-01 -7.140785151598181e-01 2.92580e-11 2.05433e-10 2 6.450814367488348e-01 6.450814363829582e-01 3.65877e-10 6.29356e-10 3 7.287641609087345e-01 7.287641608934191e-01 1.53154e-11 1.24131e-09 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.358682543426158e-01 2.358682543513612e-01 8.74539e-12 3.66541e-10 2 -5.285602019639623e-01 -5.285602017907097e-01 1.73253e-10 9.49148e-10 3 -8.952373073435852e-01 -8.952373072058540e-01 1.37731e-10 3.72678e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.550963714149823e+00 -1.550963714143258e+00 6.56541e-12 7.95815e-10 2 -1.143171520464167e-01 -1.143171520275682e-01 1.88485e-11 5.85819e-09 * 3 7.256197511838357e-01 7.256197511209029e-01 6.29328e-11 1.56942e-09 ----------------------------------------------------------------------------------------------------- 9 Al 1 5.455461901014281e-01 5.455461899702276e-01 1.31200e-10 5.96928e-10 2 -7.150668124018837e-01 -7.150668125334314e-01 1.31548e-10 3.62845e-09 3 1.378565833413105e-01 1.378565833636773e-01 2.23668e-11 2.75245e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.639107813576288e-01 -6.639107812364414e-01 1.21187e-10 3.18806e-09 2 -3.592919159080329e-01 -3.592919158676249e-01 4.04081e-11 3.72315e-10 3 2.998274669101474e-01 2.998274669426585e-01 3.25112e-11 8.65707e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 4.961101893049395e-01 4.961101893527389e-01 4.77994e-11 7.82358e-10 2 -9.471775859899275e-01 -9.471775859400752e-01 4.98523e-11 3.46884e-09 3 2.348256209226245e-01 2.348256209333187e-01 1.06942e-11 1.77145e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 8.615675513155155e-01 8.615675513789620e-01 6.34465e-11 1.82855e-09 2 -2.391729622685029e-02 -2.391729619098047e-02 3.58698e-11 6.52775e-10 3 6.574410129021433e-01 6.574410130389655e-01 1.36822e-10 7.80379e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 -8.520662717182782e-01 -8.520662717097480e-01 8.53018e-12 4.19730e-10 2 -1.495289068808781e+00 -1.495289068832770e+00 2.39890e-11 5.16802e-10 3 -8.804939419346605e-01 -8.804939419272501e-01 7.41041e-12 1.15024e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 -2.509936085452316e-01 -2.509936088245478e-01 2.79316e-10 8.31128e-10 2 2.276777481786735e-01 2.276777483814764e-01 2.02803e-10 7.12274e-10 3 1.951321331452510e-01 1.951321331176938e-01 2.75573e-11 6.81197e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 8.417408954592484e-01 8.417408954407085e-01 1.85398e-11 9.25871e-10 2 -1.038420744269033e+00 -1.038420744279632e+00 1.05997e-11 6.00559e-10 3 7.464095981903049e-01 7.464095980553451e-01 1.34960e-10 1.10755e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 2.351644869083092e-01 2.351644869271886e-01 1.88794e-11 2.28485e-09 2 5.095387706969072e-01 5.095387707211417e-01 2.42345e-11 1.07240e-10 3 9.303272550378534e-01 9.303272550059311e-01 3.19224e-11 1.97121e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 2.452209586534845e-01 2.452209585099873e-01 1.43497e-10 1.18276e-09 2 4.950276930322853e-01 4.950276929932161e-01 3.90692e-11 1.00899e-09 3 -6.270925229656635e-01 -6.270925229233805e-01 4.22831e-11 1.72328e-09 ----------------------------------------------------------------------------------------------------- 18 Al 1 5.617239641634713e-01 5.617239639125816e-01 2.50890e-10 3.73918e-10 2 1.114039070052036e+00 1.114039070165512e+00 1.13476e-10 4.32567e-09 3 -5.755234901664636e-01 -5.755234901866954e-01 2.02317e-11 2.45304e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 6.392027865722103e-01 6.392027866024438e-01 3.02335e-11 1.44421e-09 2 2.983586023534456e-01 2.983586024247858e-01 7.13402e-11 5.62852e-10 3 -2.982865268247669e-01 -2.982865268996415e-01 7.48746e-11 2.88649e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 7.508150011605790e-01 7.508150011571046e-01 3.47433e-12 2.90048e-10 2 9.259478939762104e-01 9.259478939634849e-01 1.27255e-11 2.26980e-10 3 -7.017750918231462e-01 -7.017750917627330e-01 6.04132e-11 2.89902e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.418826631029816e+00 -1.418826631053849e+00 2.40330e-11 4.97245e-10 2 6.437979574626884e-01 6.437979576439490e-01 1.81261e-10 4.58748e-10 3 2.926262436952679e-01 2.926262435580057e-01 1.37262e-10 4.46369e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 -5.977866572762547e-01 -5.977866572597189e-01 1.65358e-11 2.24493e-10 2 1.620477496302728e+00 1.620477496184697e+00 1.18031e-10 2.33631e-09 3 4.498076484662956e-01 4.498076484867343e-01 2.04387e-11 1.48163e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 -5.895089838385540e-01 -5.895089838092882e-01 2.92658e-11 5.73787e-09 * 2 4.527025374766206e-01 4.527025377569597e-01 2.80339e-10 2.30746e-09 3 -2.964738222791243e-01 -2.964738222524116e-01 2.67127e-11 4.61224e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.087983213306587e-03 7.087983398650495e-03 1.85344e-10 1.37452e-09 2 5.042873101429719e-01 5.042873102713510e-01 1.28379e-10 1.73115e-09 3 -1.242554367421445e+00 -1.242554367480728e+00 5.92830e-11 8.68145e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.057027755684133e-01 -2.057027756566464e-01 8.82330e-11 3.57581e-10 2 -1.419889739640623e+00 -1.419889739613618e+00 2.70044e-11 8.68957e-09 * 3 -5.515852852682468e-01 -5.515852854249532e-01 1.56706e-10 6.94389e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.557399584189231e-01 -1.557399587212067e-01 3.02284e-10 1.31636e-09 2 6.848215515499982e-01 6.848215518032277e-01 2.53229e-10 9.34143e-10 3 -1.117438746430149e+00 -1.117438746489139e+00 5.89895e-11 5.51974e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.117807172254737e+00 1.117807172552566e+00 2.97828e-10 8.68801e-10 2 -2.099903755013951e+00 -2.099903754955407e+00 5.85443e-11 3.79042e-10 3 1.141939852548477e-01 1.141939854684927e-01 2.13645e-10 1.60640e-09 ----------------------------------------------------------------------------------------------------- 28 Al 1 -2.406178723753384e-01 -2.406178719697758e-01 4.05563e-10 2.64674e-10 2 4.514502941312501e-01 4.514502941930407e-01 6.17906e-11 1.15573e-10 3 -2.757833192140611e-01 -2.757833192075832e-01 6.47787e-12 3.70283e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -5.098628640210459e-01 -5.098628639151891e-01 1.05857e-10 4.48971e-10 2 -1.368898648051519e+00 -1.368898648015073e+00 3.64460e-11 6.34132e-10 3 2.039848254045275e-01 2.039848255100742e-01 1.05547e-10 1.70484e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.730110539974961e-01 -7.730110539534847e-01 4.40115e-11 1.61158e-09 2 1.013122563886365e-01 1.013122561934116e-01 1.95225e-10 1.03622e-09 3 -3.318957391039419e-01 -3.318957389595344e-01 1.44408e-10 8.90997e-09 * ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.219092869069606e-01 -4.219092867037885e-01 2.03172e-10 1.02524e-08 * 2 -1.001649956654362e+00 -1.001649956550934e+00 1.03428e-10 1.15232e-09 3 -1.760010166211987e-01 -1.760010167470048e-01 1.25806e-10 7.00970e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 1.883785307102611e-01 1.883785305769539e-01 1.33307e-10 5.24475e-10 2 -4.057753147044420e-01 -4.057753146808692e-01 2.35728e-11 7.23053e-11 3 -5.247750505240926e-01 -5.247750504044085e-01 1.19684e-10 6.00283e-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 = --------------------------------- = 2.61490e-08 max{(|F_model|+|F_numer|)/2, 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 3.677501440839441e-01 1.70682e-11 2.68437e-10 2 4.294126869594954e-01 4.294126868012267e-01 1.58269e-10 1.07151e-09 3 8.538381287187127e-01 8.538381288073091e-01 8.85965e-11 2.52303e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 7.039666223611664e-01 7.039666225474196e-01 1.86253e-10 1.24010e-09 2 8.846232871439189e-01 8.846232870744408e-01 6.94781e-11 3.35399e-10 3 -7.480256879492277e-01 -7.480256880444350e-01 9.52073e-11 1.15754e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -8.580612308228212e-01 -8.580612306303148e-01 1.92506e-10 1.25862e-09 2 -7.461303493754812e-01 -7.461303474416062e-01 1.93387e-09 3.55771e-09 3 8.214295022063306e-01 8.214295022627193e-01 5.63887e-11 6.04471e-08 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.035010896402829e+00 -1.035010896390204e+00 1.26246e-11 1.10715e-09 2 -9.001563420143355e-01 -9.001563422178975e-01 2.03562e-10 8.66416e-10 3 7.234656248847005e-01 7.234656257567933e-01 8.72093e-10 1.60527e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.192200486250460e-01 -5.192200484356106e-01 1.89435e-10 8.76763e-10 2 -3.595236717372236e-02 -3.595236741054900e-02 2.36827e-10 4.10496e-10 3 -1.090504704418766e+00 -1.090504704589382e+00 1.70616e-10 4.60458e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.109395149950025e-01 -2.109395153125492e-01 3.17547e-10 1.21130e-10 2 6.967599917855433e-01 6.967599917430930e-01 4.24503e-11 7.44551e-10 3 4.446280998134919e-01 4.446281000435437e-01 2.30052e-10 9.51880e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.213829930769855e-01 1.213829931343147e-01 5.73292e-11 8.48638e-10 2 7.400654230712875e-01 7.400654230024489e-01 6.88386e-11 2.26362e-09 3 1.368378644042400e+00 1.368378643970027e+00 7.23732e-11 1.61581e-09 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.960329081429050e-02 8.960329139383195e-02 5.79541e-10 2.37803e-09 2 7.002302945754210e-01 7.002302945127656e-01 6.26553e-11 1.67605e-09 3 1.505541429338991e+00 1.505541429326833e+00 1.21589e-11 2.64254e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.061933056584245e-01 3.061933053690117e-01 2.89413e-10 2.45557e-09 2 5.791164328114152e-01 5.791164326400757e-01 1.71339e-10 1.87794e-09 3 1.494368566915539e-01 1.494368566467060e-01 4.48479e-11 1.01933e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.191094079385256e-01 5.191094070114770e-01 9.27049e-10 6.77598e-10 2 -7.026376037118257e-01 -7.026376044096955e-01 6.97870e-10 9.23251e-10 3 1.216245918658353e+00 1.216245918013324e+00 6.45030e-10 1.45823e-09 ----------------------------------------------------------------------------------------------------- 11 Ti 1 5.005334144679958e-01 5.005334142590856e-01 2.08910e-10 2.49957e-09 2 1.295912427997428e+00 1.295912429160838e+00 1.16341e-09 4.24029e-09 3 -2.600375690082266e-01 -2.600375690128706e-01 4.64395e-12 2.25690e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.236090268197136e+00 1.236090268142246e+00 5.48903e-11 9.83561e-10 2 -1.389731387042165e+00 -1.389731387289686e+00 2.47521e-10 7.17669e-10 3 4.363202827525551e-01 4.363202829845070e-01 2.31952e-10 2.09878e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 3.054689011095582e-01 3.054689012145926e-01 1.05034e-10 5.82759e-09 2 4.752515233592076e-01 4.752515234190272e-01 5.98196e-11 1.93029e-09 3 8.002055786098985e-01 8.002055772581895e-01 1.35171e-09 1.51448e-09 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -1.011375240192382e+00 -1.011375239841340e+00 3.51041e-10 4.73594e-09 2 6.790649125115997e-01 6.790649130849445e-01 5.73345e-10 9.85353e-10 3 -1.218208417714824e+00 -1.218208418042453e+00 3.27629e-10 2.70478e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -2.016123102358323e-01 -2.016123101051351e-01 1.30697e-10 4.87382e-10 2 -2.633963704189244e+00 -2.633963704540121e+00 3.50877e-10 7.98365e-10 3 1.808237805511243e+00 1.808237805431045e+00 8.01978e-11 3.36397e-09 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -7.805054328069642e-01 -7.805054323012188e-01 5.05745e-10 7.25281e-09 2 3.946551673138108e-01 3.946551683808326e-01 1.06702e-09 1.82498e-09 3 -4.394972005568530e-01 -4.394971999452209e-01 6.11632e-10 7.10230e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -1.047598790501237e+00 -1.047598790444867e+00 5.63698e-11 7.34671e-10 2 -1.284989612653468e+00 -1.284989612590297e+00 6.31708e-11 2.16627e-09 3 -1.418610637839440e-01 -1.418610638908351e-01 1.06891e-10 2.68278e-09 ----------------------------------------------------------------------------------------------------- 18 Ti 1 2.292023566510340e+00 2.292023566377799e+00 1.32541e-10 1.67431e-09 2 2.089091790707045e+00 2.089091789336020e+00 1.37103e-09 1.09647e-09 3 1.256376389121128e+00 1.256376389399618e+00 2.78490e-10 3.18429e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -3.461974135184894e-01 -3.461974136495726e-01 1.31083e-10 4.27579e-09 2 1.317419997901154e+00 1.317419997925618e+00 2.44644e-11 1.59947e-09 3 -7.719519409341242e-01 -7.719519396520863e-01 1.28204e-09 6.49858e-09 ----------------------------------------------------------------------------------------------------- 20 Ti 1 6.557561309586358e-01 6.557561313193073e-01 3.60671e-10 1.82392e-09 2 6.635524212435931e-02 6.635524190783863e-02 2.16521e-10 5.33813e-09 3 -7.510602048639845e-01 -7.510602053198809e-01 4.55896e-10 2.82172e-09 ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.078763998414142e+00 1.078763998682652e+00 2.68509e-10 4.09936e-09 2 5.602822891937225e-01 5.602822895883893e-01 3.94667e-10 1.46465e-09 3 -3.989830139531497e-01 -3.989830136792217e-01 2.73928e-10 2.66497e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -5.482111636114865e-01 -5.482111636890369e-01 7.75504e-11 9.24063e-09 2 -2.099512876111254e-02 -2.099512830168724e-02 4.59425e-10 5.10947e-09 3 -1.320652332021113e+00 -1.320652331812605e+00 2.08509e-10 2.76398e-09 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.384011114113130e-01 -9.384011121837891e-01 7.72476e-10 2.53377e-08 * 2 6.669048159748370e-01 6.669048162017757e-01 2.26939e-10 6.61615e-10 3 -8.011772981277970e-01 -8.011772980540519e-01 7.37451e-11 1.91807e-09 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.252939830998243e+00 -1.252939830485381e+00 5.12862e-10 3.44584e-09 2 -1.178435283528733e+00 -1.178435283115444e+00 4.13289e-10 7.91211e-10 3 5.576183810732973e-01 5.576183810613726e-01 1.19247e-11 4.28619e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -7.384498992443318e-02 -7.384498964826602e-02 2.76167e-10 5.75106e-09 2 -1.119773901363444e+00 -1.119773901752146e+00 3.88702e-10 2.64556e-10 3 -1.667371518289866e+00 -1.667371517073329e+00 1.21654e-09 3.21019e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -5.265456521532405e-01 -5.265456520203593e-01 1.32881e-10 1.46785e-09 2 3.130195210877162e-01 3.130195217371178e-01 6.49402e-10 6.90402e-09 3 -9.796775946813743e-01 -9.796775940326753e-01 6.48699e-10 9.36842e-08 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 9.033451463119796e-01 9.033451466386452e-01 3.26666e-10 8.26838e-09 2 -1.106894382972474e-01 -1.106894382323891e-01 6.48583e-11 4.38832e-09 3 4.855032759832346e-01 4.855032760491337e-01 6.58991e-11 8.68494e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 8.394866357118718e-01 8.394866353090824e-01 4.02789e-10 4.75233e-09 2 -1.880512980588107e-01 -1.880512982041677e-01 1.45357e-10 4.37848e-09 3 2.150232732191569e-02 2.150232710420712e-02 2.17709e-10 1.99634e-09 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.885208714180357e-01 -2.885208714698820e-01 5.18463e-11 3.22760e-09 2 -1.913828358530465e+00 -1.913828359186114e+00 6.55649e-10 1.58048e-09 3 -2.608191425745987e+00 -2.608191424523364e+00 1.22262e-09 1.15302e-08 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -4.912836613521369e-01 -4.912836609446349e-01 4.07502e-10 1.07630e-09 2 -2.164407825729110e-01 -2.164407819950869e-01 5.77824e-10 2.58744e-09 3 -8.274482189561591e-01 -8.274482199380536e-01 9.81895e-10 7.05378e-09 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.070958008502249e+00 1.070958008838256e+00 3.36007e-10 4.43276e-09 2 -7.609228794482981e-01 -7.609228801226329e-01 6.74335e-10 5.10145e-09 3 4.868900748228404e-01 4.868900746313253e-01 1.91515e-10 1.62260e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -8.601636751306867e-01 -8.601636752001797e-01 6.94930e-11 3.46461e-09 2 1.314532632203302e+00 1.314532633288603e+00 1.08530e-09 6.53478e-09 3 1.089029871454748e+00 1.089029866398722e+00 5.05603e-09 5.10699e-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 = 22, direction = 2: |F_model - F_numer| error = --------------------------------- = 2.18825e-08 max{(|F_model|+|F_numer|)/2, 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 4.900315246242826e-01 9.974221761952405e-01 5.07391e-01 1.59165e-07 2 5.239146091554245e-01 7.716898622854612e-01 2.47775e-01 8.99159e-10 3 9.081962158696389e-01 1.186050029266148e+00 2.77854e-01 1.99003e-07 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -3.844986255214085e+00 -4.188067548760948e+00 3.43081e-01 8.03497e-09 2 3.705726583079374e+00 3.734545081454877e+00 2.88185e-02 3.87863e-09 3 -9.876829986658813e-01 -7.430720948878284e-01 2.44611e-01 1.72579e-07 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -5.283671947639306e+00 -5.617756695656348e+00 3.34085e-01 5.98854e-09 2 -3.253409096653262e+00 -3.042603586350650e+00 2.10806e-01 2.02380e-09 3 -9.496730654986479e+00 -1.005203965105465e+01 5.55309e-01 7.82178e-06 * ----------------------------------------------------------------------------------------------------- 4 Al 1 -1.206270914825982e+00 -7.801749522691116e-01 4.26096e-01 1.02371e-08 2 1.371795892750714e+00 1.188803054153142e+00 1.82993e-01 4.43810e-09 3 -1.101907886328460e+00 -1.112739578239330e+00 1.08317e-02 5.59783e-07 ----------------------------------------------------------------------------------------------------- 5 Al 1 1.532389005261548e+00 1.394425996440223e+00 1.37963e-01 3.35593e-09 2 -3.988961901373180e+00 -3.779702219813018e+00 2.09260e-01 2.26236e-07 3 -1.833113502650526e+00 -1.196240932145717e+00 6.36873e-01 6.68890e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 2.035588094133167e-01 -1.306409871311772e-01 3.34200e-01 1.89967e-06 2 1.177958103523008e+00 1.082888491632041e+00 9.50696e-02 8.25218e-10 3 3.925806222664561e-02 8.044824770142180e-01 7.65224e-01 2.73489e-07 ----------------------------------------------------------------------------------------------------- 7 Ti 1 5.067450209882913e-01 3.249088874852712e-01 1.81836e-01 3.34516e-06 * 2 2.672251115300409e-01 4.842512295982150e-01 2.17026e-01 2.45457e-07 3 1.921157370949329e+00 1.653638051267491e+00 2.67519e-01 6.93878e-07 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -8.801546338345009e-01 -8.305185222767210e-01 4.96361e-02 2.32203e-09 2 8.992019075645007e-01 7.555405058506928e-01 1.43661e-01 2.39959e-09 3 4.971551754273579e-01 -2.377771345074067e-01 7.34932e-01 1.37984e-06 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -5.521114568159371e-01 -5.397873094415010e-01 1.23241e-02 1.26375e-08 2 -1.633005746283620e+00 -1.590393644385128e+00 4.26121e-02 5.36252e-09 3 -1.642788177835559e+00 -1.407824427869971e+00 2.34964e-01 4.87126e-07 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.243362296729041e+00 -1.115092276319680e+00 1.28270e-01 3.23463e-09 2 2.673901340914637e+00 2.590417709142242e+00 8.34836e-02 1.13952e-07 3 -3.706900934446157e+00 -3.458015592692286e+00 2.48885e-01 5.37765e-08 ----------------------------------------------------------------------------------------------------- 11 Al 1 8.703432723038097e-01 1.076958349475852e+00 2.06615e-01 1.07254e-08 2 -3.207328863982013e+00 -3.388716500508599e+00 1.81388e-01 2.88729e-06 * 3 2.841797478798765e+00 3.153518423029612e+00 3.11721e-01 1.90187e-06 ----------------------------------------------------------------------------------------------------- 12 Al 1 -7.693170240385995e-01 -4.054499333464407e-01 3.63867e-01 2.12405e-08 2 1.765907346291147e+00 1.547523775693822e+00 2.18384e-01 5.13629e-09 3 5.444659298121441e-01 7.679292681095863e-01 2.23463e-01 5.73587e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 -2.334253930338183e-01 -2.693997031944692e-01 3.59743e-02 1.69101e-09 2 -1.953812750260043e+00 -2.350010904203209e+00 3.96198e-01 1.14891e-09 3 -7.723628570584123e-01 -3.009492162351087e-01 4.71414e-01 5.72193e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 7.128181366932359e-01 7.188684029383262e-01 6.05027e-03 1.40688e-06 2 1.285156453203090e+00 1.083639012422285e+00 2.01517e-01 4.73255e-07 3 -7.607880702032255e-01 -3.736612585152927e-01 3.87127e-01 3.48290e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 8.143991012510748e-01 3.701579150018071e-01 4.44241e-01 1.40894e-06 2 -2.426389851537473e+00 -1.953007914386814e+00 4.73382e-01 3.05044e-06 * 3 -9.205511981398089e-01 -1.797561466772994e+00 8.77010e-01 4.36415e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 4.199003275901884e-01 5.387756176453834e-01 1.18875e-01 5.52182e-07 2 1.739825791491127e+00 1.383218383258746e+00 3.56607e-01 1.25270e-06 3 5.945736261203158e-01 1.135731215309147e+00 5.41158e-01 1.19813e-06 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -1.738349982962860e+00 -1.530133571428886e+00 2.08216e-01 4.00719e-09 2 -1.408623990276038e+00 -1.234892389802218e+00 1.73732e-01 7.67721e-07 3 1.391780717231620e+00 1.488305709840420e+00 9.65250e-02 4.81812e-07 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.893398961769381e+00 2.056381132242177e+00 1.62982e-01 1.56076e-07 2 4.811304051795112e+00 5.065800037972252e+00 2.54496e-01 3.52097e-09 3 3.113002948076150e+00 2.971297442761113e+00 1.41706e-01 2.88655e-08 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.072043474441160e-01 -1.813675772940633e-01 4.88572e-01 4.92539e-09 2 -2.578345872563763e-01 -2.232372567604684e-01 3.45973e-02 2.11318e-07 3 -8.457208149340141e-01 -9.421934159632845e-01 9.64726e-02 1.30177e-09 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -2.579702669174100e+00 -2.283967416472809e+00 2.95735e-01 1.99052e-06 2 -1.952080776347248e+00 -2.138249873251687e+00 1.86169e-01 5.04242e-07 3 -7.906970319241354e-01 -8.200386063384356e-01 2.93416e-02 1.92316e-06 ----------------------------------------------------------------------------------------------------- 21 Al 1 6.897743977740885e+00 7.311872965254020e+00 4.14129e-01 3.09711e-06 * 2 -9.250244398572771e-01 -4.572400733830085e-01 4.67784e-01 2.47815e-07 3 7.466432137969044e+00 7.229769471709750e+00 2.36663e-01 3.04996e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.558321869648830e+00 1.113092634982103e+00 4.45229e-01 1.13568e-06 2 2.950207792292244e-02 -5.802643269892894e-01 6.09766e-01 2.61613e-07 3 1.550004094514000e+00 2.183839499546117e+00 6.33835e-01 1.79238e-06 ----------------------------------------------------------------------------------------------------- 23 Al 1 -4.739978043855875e-01 -3.917168312062875e-01 8.22810e-02 9.99145e-10 2 3.346986234990766e-01 5.183072744799806e-01 1.83609e-01 1.07764e-08 3 -6.834678817777667e-01 -8.779988123752398e-01 1.94531e-01 1.02643e-08 ----------------------------------------------------------------------------------------------------- 24 Al 1 -2.716171719357028e-01 7.747798279308940e-02 3.49095e-01 3.97006e-07 2 9.252969662287607e-01 1.242240264732047e+00 3.16943e-01 5.55113e-07 3 -4.880031894328571e-01 -9.356832684220798e-01 4.47680e-01 1.50974e-06 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.184744548206694e+00 -1.978828066101918e+00 2.05916e-01 2.96937e-07 2 -2.776452669488285e+00 -2.697760332284194e+00 7.86923e-02 9.71316e-09 3 -2.988448661285425e+00 -3.376075207020422e+00 3.87627e-01 4.83486e-06 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 -8.447673352920141e-01 -1.368966114289486e+00 5.24199e-01 4.39068e-08 2 1.438602615504718e+00 1.160457489486823e+00 2.78145e-01 2.27817e-06 3 -1.585909567778814e+00 -1.670606750518921e+00 8.46972e-02 3.41121e-07 ----------------------------------------------------------------------------------------------------- 27 Al 1 4.639440123248466e+00 4.881649054378350e+00 2.42209e-01 3.10654e-09 2 1.652762929439248e+00 2.057929791365998e+00 4.05167e-01 2.89246e-09 3 1.874687833291608e+00 1.472349579984977e+00 4.02338e-01 1.41254e-06 ----------------------------------------------------------------------------------------------------- 28 Al 1 -3.971741514373986e-01 5.541540695747098e-02 4.52590e-01 5.91022e-09 2 1.352460278390187e+00 1.231763181795003e+00 1.20697e-01 5.75076e-09 3 2.372548105607049e+00 1.856366351228246e+00 5.16182e-01 5.42227e-08 ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.006300339852370e+00 3.986025175698145e-01 6.07698e-01 1.58908e-06 2 -2.867265383543058e+00 -2.993127196448328e+00 1.25862e-01 8.87450e-09 3 8.651861474424980e-01 9.442887555690396e-01 7.91026e-02 3.09743e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.904259211871659e-01 3.947537471574386e-01 9.56722e-02 1.27294e-08 2 1.264243513344064e+00 1.344935445180527e+00 8.06919e-02 2.74869e-10 3 1.943118399236467e+00 1.703405609460308e+00 2.39713e-01 2.16637e-06 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -9.843638713012276e-01 -1.080049681687118e+00 9.56858e-02 3.89512e-09 2 -4.245729772652811e-01 -5.548417743092324e-01 1.30269e-01 4.69399e-07 3 -1.165648050082649e+00 -1.143641890486127e+00 2.20062e-02 6.65178e-08 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.144996717809892e+00 9.811496015964004e-01 1.63847e-01 8.26532e-09 2 -1.447211615039974e-01 -2.599200388928793e-01 1.15199e-01 2.11719e-08 3 1.847357234957535e+00 1.895190904761107e+00 4.78337e-02 1.93376e-08 ----------------------------------------------------------------------------------------------------- * 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 = 6, direction = 1: |F_model - F_numer| error = --------------------------------- = 2.00000e+00 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.00000e+00 Machine precision = 2.22045e-16 Grade: F Comment: The letter grade F was assigned because the normalized error in the computation was 2.00000e+00 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. 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.