!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_JeongParkDo_2018_PdAl__MO_616482358807_001 Supported species : Al Pd 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 = 4.044651031494141 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.436525887712972e-01 3.436525887494076e-01 2.18895e-11 2.21447e-09 * 2 -2.618078064062982e-02 -2.618078064718859e-02 6.55877e-12 2.54340e-11 3 3.437088645165465e-02 3.437088650864481e-02 5.69902e-11 6.40841e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099697114952e-01 -8.101099697036188e-01 7.87637e-12 3.09517e-09 * 2 8.600116138441266e-01 8.600116138634704e-01 1.93437e-11 2.45458e-10 3 3.127577258458623e-01 3.127577258445590e-01 1.30329e-12 1.82789e-09 * ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242118384311885e-02 -8.242118384957017e-02 6.45133e-12 1.99901e-11 2 -4.844095591639676e-02 -4.844095594124097e-02 2.48442e-11 1.29901e-09 3 -2.547490086906117e-01 -2.547490086883435e-01 2.26819e-12 4.05870e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906831351019e-01 4.983906831279908e-01 7.11109e-12 2.22188e-09 * 2 2.408671397121293e-01 2.408671396895505e-01 2.25787e-11 5.96162e-10 3 3.779437328642208e-01 3.779437328723522e-01 8.13133e-12 1.57506e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111435108739e-01 7.931111435222135e-01 1.13396e-11 7.48104e-11 2 -3.817072244476382e-01 -3.817072244321290e-01 1.55092e-11 2.93078e-11 3 2.806999061862538e-01 2.806999061870061e-01 7.52287e-13 7.76798e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254976473408e-01 -3.438254976506620e-01 3.32123e-12 3.66433e-10 2 2.501152958385667e-01 2.501152958560527e-01 1.74860e-11 3.91562e-11 3 3.380287546419144e-01 3.380287547173203e-01 7.54059e-11 5.66954e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574681113901152e-01 2.574681113725214e-01 1.75938e-11 3.29382e-10 2 -1.219046656479634e+00 -1.219046656549854e+00 7.02205e-11 1.42063e-10 3 -1.651118796526784e+00 -1.651118796513707e+00 1.30773e-11 1.61694e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221784187581320e-01 -7.221784187798057e-01 2.16737e-11 4.29490e-10 2 -4.748263066644509e-01 -4.748263067016602e-01 3.72092e-11 4.35121e-10 3 -7.562197548477109e-01 -7.562197548501235e-01 2.41263e-12 6.16172e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288844001276352e-02 4.288844001655536e-02 3.79184e-12 4.68910e-11 2 -1.188167806753753e+00 -1.188167806735967e+00 1.77864e-11 8.78742e-11 3 -1.184618214624649e+00 -1.184618214622675e+00 1.97420e-12 1.95029e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641779155383e-01 -5.398641779195829e-01 4.04454e-12 2.27676e-10 2 4.980765867686628e-01 4.980765867713337e-01 2.67081e-12 1.15987e-10 3 -7.222686212488535e-01 -7.222686213007667e-01 5.19133e-11 4.87336e-09 * ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753133414842e-01 -3.572753130165030e-01 3.24981e-10 2.55008e-10 2 -8.581020023213164e-01 -8.581020024106467e-01 8.93303e-11 8.22866e-11 3 7.845981095706080e-01 7.845981095495814e-01 2.10266e-11 1.04944e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596031305529761e-02 2.596031306772047e-02 1.24229e-11 2.02519e-11 2 1.245097673566508e+00 1.245097673549045e+00 1.74631e-11 1.00879e-10 3 7.763446140592514e-01 7.763446140999055e-01 4.06541e-11 2.38848e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365342020510563e-01 -5.365342020301809e-01 2.08754e-11 1.25132e-10 2 -1.200162166887454e+00 -1.200162166835849e+00 5.16047e-11 1.10613e-10 3 -1.957550100011358e+00 -1.957550099980838e+00 3.05203e-11 1.87986e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988771002555355e-02 8.988771001566964e-02 9.88391e-12 1.67241e-10 2 4.855436357312822e-01 4.855436357048853e-01 2.63969e-11 1.50808e-10 3 -1.387144633123531e-01 -1.387144633240445e-01 1.16914e-11 6.57631e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761451037876223e+00 1.761451037864172e+00 1.20517e-11 4.16100e-11 2 -6.436068985548461e-01 -6.436068985386120e-01 1.62341e-11 1.74735e-10 3 7.520277736138696e-01 7.520277736267004e-01 1.28307e-11 4.76678e-09 * ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494766277741e-01 5.978494766364133e-01 8.63920e-12 1.22580e-10 2 1.336599639554143e+00 1.336599639558277e+00 4.13380e-12 1.79345e-09 * 3 8.753613043449752e-01 8.753613043248559e-01 2.01192e-11 1.77708e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232218182708506e-01 4.232218182639049e-01 6.94567e-12 7.03599e-11 2 3.604704538566768e-01 3.604704538413657e-01 1.53111e-11 9.39150e-11 3 -9.557914876491863e-02 -9.557914875357532e-02 1.13433e-11 2.66716e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049824056000369e-01 -5.049824056252860e-01 2.52490e-11 8.61831e-10 2 4.028584621819862e-01 4.028584621759792e-01 6.00697e-12 3.65525e-10 3 1.019475219395497e+00 1.019475219388672e+00 6.82543e-12 7.07407e-11 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575296478882422e-01 2.575296478859966e-01 2.24559e-12 1.22286e-10 2 3.782444214493004e-01 3.782444214481888e-01 1.11161e-12 2.63970e-10 3 -4.712358503399028e-01 -4.712358503434115e-01 3.50869e-12 2.13726e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062635579241795e-01 4.062635579487810e-01 2.46015e-11 7.49777e-11 2 3.112967184921566e-01 3.112967184990758e-01 6.91924e-12 1.54962e-10 3 -4.574995164050278e-01 -4.574995164035129e-01 1.51490e-12 3.36096e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.519579269344997e-01 -9.519579267439882e-01 1.90511e-10 2.32051e-10 2 4.430056377461727e-02 4.430056376854858e-02 6.06869e-12 4.89014e-10 3 8.201330431559853e-01 8.201330431623649e-01 6.37956e-12 1.94367e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278260487808e-01 2.873278260350691e-01 1.37117e-11 3.79392e-10 2 1.511178773901759e+00 1.511178773986584e+00 8.48253e-11 1.67820e-09 * 3 1.447152283428595e+00 1.447152283397814e+00 3.07818e-11 1.51945e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449441208158874e-01 -3.449441208065201e-01 9.36734e-12 1.38390e-10 2 3.006117549858595e-01 3.006117549816514e-01 4.20808e-12 5.16779e-11 3 -3.734060033068488e-01 -3.734060033025024e-01 4.34636e-12 5.29795e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.548683834255006e-02 7.548683834206928e-02 4.80782e-13 1.00726e-09 2 -5.942094354385377e-04 -5.942094495229000e-04 1.40844e-11 4.67164e-11 3 -6.192826988180952e-01 -6.192826988024279e-01 1.56672e-11 1.70610e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619447313837871e-01 -3.619447313400203e-01 4.37668e-11 3.69797e-10 2 -8.543631750219945e-01 -8.543631750461592e-01 2.41647e-11 2.44883e-09 * 3 2.198728311538212e-01 2.198728312666000e-01 1.12779e-10 4.12541e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995054630761463e-01 -4.995054628989144e-01 1.77232e-10 6.41724e-10 2 1.019970122531736e+00 1.019970122404880e+00 1.26856e-10 3.86204e-10 3 -7.917982423073944e-01 -7.917982423096782e-01 2.28384e-12 3.27689e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695233018296072e-01 5.695233018141924e-01 1.54148e-11 2.66382e-10 2 -2.393202182937114e+00 -2.393202182915303e+00 2.18101e-11 3.29701e-11 3 7.839007915966316e-01 7.839007915678597e-01 2.87719e-11 1.30255e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446253011926659e-01 -5.446253012270480e-01 3.43821e-11 6.70410e-11 2 6.944324457877642e-01 6.944324457842891e-01 3.47511e-12 7.58482e-11 3 -2.318274122770182e-01 -2.318274122936030e-01 1.65848e-11 2.14340e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440921562913293e-01 -2.440921564178903e-01 1.26561e-10 6.56430e-10 2 -7.057626663444554e-01 -7.057626663780915e-01 3.36361e-11 1.97603e-09 * 3 6.755894770101792e-01 6.755894770113364e-01 1.15719e-12 4.03851e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998223837645208e-02 -7.998223838202238e-02 5.57031e-12 4.62360e-10 2 6.365060367959603e-01 6.365060368541267e-01 5.81664e-11 2.67474e-10 3 -3.994794263457406e-01 -3.994794263114674e-01 3.42733e-11 2.41164e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 -7.196131306920950e-02 -7.196131304765027e-02 2.15592e-11 3.73983e-10 2 -9.584853843893342e-01 -9.584853844134837e-01 2.41496e-11 8.59983e-11 3 4.908346303115275e-01 4.908346303388323e-01 2.73048e-11 9.39048e-11 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661919252989692e-01 5.661919252932424e-01 5.72686e-12 3.94993e-10 2 3.764670780212212e-01 3.764670779902464e-01 3.09748e-11 4.36227e-09 * 3 1.162561741964186e-01 1.162561742055458e-01 9.12713e-12 2.06691e-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 = 2: |F_model - F_numer| error = ----------------------- = 2.37027e-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. MONOATOMIC STRUCTURE -- Species = Pd | a0 = 3.889087677001953 | (Configuration in file "config-Pd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 9.441064890143659e-01 9.441064889960274e-01 1.83384e-11 3.09528e-11 2 1.020074408241868e+00 1.020074408237607e+00 4.26059e-12 3.77265e-09 * 3 1.008782580009200e+00 1.008782580008783e+00 4.17222e-13 1.17174e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 1.376979813703016e+00 1.376979813682916e+00 2.01001e-11 2.09346e-10 2 -1.645185690582662e+00 -1.645185690585004e+00 2.34257e-12 5.83817e-11 3 6.404130703000894e-01 6.404130702734876e-01 2.66018e-11 4.35492e-11 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -8.798725614481723e-01 -8.798725614687898e-01 2.06175e-11 9.22080e-11 2 1.027269420024547e+00 1.027269420036025e+00 1.14775e-11 8.95255e-11 3 5.034985868673149e-01 5.034985868929412e-01 2.56264e-11 4.21937e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 6.658369015037627e-01 6.658369014584130e-01 4.53497e-11 1.17974e-10 2 1.022506121798648e+00 1.022506121807640e+00 8.99192e-12 4.86797e-10 3 -8.883457893177515e-01 -8.883457893096880e-01 8.06355e-12 3.52431e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -1.016901515283267e+00 -1.016901515288558e+00 5.29043e-12 6.94584e-11 2 -1.022241969760618e+00 -1.022241969808896e+00 4.82783e-11 7.36295e-10 3 -1.983735492641745e+00 -1.983735492640392e+00 1.35292e-12 1.88996e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 8.032764231745066e-01 8.032764231726643e-01 1.84230e-12 3.44398e-11 2 1.555823570810387e+00 1.555823570810540e+00 1.52545e-13 8.99858e-11 3 -1.211123035663784e+00 -1.211123035675399e+00 1.16147e-11 1.61080e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 3.708224896824219e+00 3.708224896845991e+00 2.17715e-11 2.38557e-10 2 -3.296108937351056e+00 -3.296108937323519e+00 2.75366e-11 1.96785e-11 3 2.194308496525284e+00 2.194308496577780e+00 5.24962e-11 2.27852e-08 * ----------------------------------------------------------------------------------------------------- 8 Pd 1 -6.093811753545425e+00 -6.093811753554830e+00 9.40492e-12 1.30927e-10 2 2.097194508633037e+00 2.097194508682459e+00 4.94222e-11 1.95213e-10 3 1.253276392253734e+00 1.253276392202339e+00 5.13956e-11 1.31962e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -7.480616013700015e-01 -7.480616013385673e-01 3.14343e-11 6.64110e-11 2 1.268267965856569e+00 1.268267965861765e+00 5.19562e-12 5.01947e-10 3 1.311059281056142e+00 1.311059281053696e+00 2.44604e-12 8.10199e-11 ----------------------------------------------------------------------------------------------------- 10 Pd 1 5.200989425875183e-01 5.200989425625625e-01 2.49558e-11 6.79631e-11 2 -8.170076905566198e-01 -8.170076905275160e-01 2.91038e-11 1.43739e-10 3 2.845686933634617e-01 2.845686933386410e-01 2.48207e-11 3.36153e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -1.622689113193994e+00 -1.622689113243747e+00 4.97529e-11 2.95515e-10 2 2.357032959216786e+00 2.357032959320557e+00 1.03771e-10 3.71486e-10 3 -1.568614114701329e+00 -1.568614114629028e+00 7.23017e-11 1.65121e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 6.738419780279001e-01 6.738419780222896e-01 5.61051e-12 6.88274e-11 2 -8.620589776357261e-01 -8.620589776210275e-01 1.46987e-11 1.11056e-10 3 1.935087931340687e-01 1.935087932266649e-01 9.25962e-11 2.17998e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -2.294893447561844e+00 -2.294893447495753e+00 6.60911e-11 1.14401e-09 2 -1.883336849201879e+00 -1.883336849190672e+00 1.12068e-11 1.12467e-10 3 -9.639915787989677e-01 -9.639915787769285e-01 2.20391e-11 2.06827e-10 ----------------------------------------------------------------------------------------------------- 14 Pd 1 2.019397565274193e+00 2.019397565284307e+00 1.01141e-11 1.33205e-11 2 1.556109911921926e+00 1.556109911928084e+00 6.15841e-12 3.91642e-11 3 -1.003976299483485e+00 -1.003976299495168e+00 1.16831e-11 5.15384e-09 * ----------------------------------------------------------------------------------------------------- 15 Pd 1 5.320899128412946e+00 5.320899128455845e+00 4.28990e-11 1.43835e-09 2 7.521681258082398e-01 7.521681257253295e-01 8.29102e-11 7.16864e-10 3 -6.821036070738720e+00 -6.821036070801386e+00 6.26663e-11 3.34474e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 -1.808858066164008e+00 -1.808858066132125e+00 3.18827e-11 1.90138e-10 2 1.152028319253191e+00 1.152028319238170e+00 1.50209e-11 2.14700e-10 3 1.367445420177775e+00 1.367445420173001e+00 4.77463e-12 2.16678e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 1.078376491174329e+00 1.078376491171170e+00 3.15903e-12 1.18712e-10 2 -2.446578744155157e+00 -2.446578744173364e+00 1.82072e-11 3.36541e-10 3 -2.190446337861007e+00 -2.190446337774630e+00 8.63767e-11 3.57325e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 2.413035324131912e+00 2.413035324160706e+00 2.87934e-11 1.20816e-09 2 -3.280996613310664e+00 -3.280996613317583e+00 6.91891e-12 1.50185e-10 3 1.323945436225807e+00 1.323945436250598e+00 2.47911e-11 9.41617e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 7.093301652325023e-01 7.093301653185117e-01 8.60094e-11 1.87522e-10 2 -8.800632105221644e-01 -8.800632105417963e-01 1.96319e-11 6.07836e-09 * 3 -1.471292320141924e+00 -1.471292320120137e+00 2.17872e-11 1.11320e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -1.363276405567539e+00 -1.363276405580952e+00 1.34130e-11 2.27758e-10 2 4.408347633417660e+00 4.408347633431285e+00 1.36255e-11 7.75449e-10 3 2.923482813670875e+00 2.923482813671214e+00 3.39728e-13 2.81959e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -6.566739595290421e-01 -6.566739595160822e-01 1.29599e-11 4.07901e-10 2 9.304128738890446e-02 9.304128737188558e-02 1.70189e-11 7.81657e-09 * 3 -5.650383426287147e-02 -5.650383427850507e-02 1.56336e-11 2.33803e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 3.651760867884323e+00 3.651760867867935e+00 1.63882e-11 7.10258e-10 2 -4.775452856416858e+00 -4.775452856515965e+00 9.91074e-11 2.64153e-10 3 1.937657227618895e+00 1.937657227674966e+00 5.60709e-11 5.40965e-11 ----------------------------------------------------------------------------------------------------- 23 Pd 1 1.937056022719184e-01 1.937056023006467e-01 2.87283e-11 6.77782e-11 2 5.781932581552870e-01 5.781932581606841e-01 5.39713e-12 2.51673e-09 * 3 -4.556787413757997e-01 -4.556787413921438e-01 1.63441e-11 3.02803e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -1.700339582303424e+00 -1.700339582183911e+00 1.19513e-10 5.27081e-10 2 -7.811461433191694e-01 -7.811461433818631e-01 6.26936e-11 2.66421e-09 * 3 2.011896410125007e-01 2.011896410715296e-01 5.90289e-11 9.20125e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -4.167666758072082e-01 -4.167666757430274e-01 6.41808e-11 2.07553e-10 2 -4.449214282518885e-01 -4.449214282013690e-01 5.05195e-11 3.11577e-10 3 -9.641562169896610e-01 -9.641562168756616e-01 1.13999e-10 2.24042e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 9.560062008343891e-02 9.560062003672172e-02 4.67172e-11 1.39132e-10 2 -3.571829612645409e-01 -3.571829613115360e-01 4.69951e-11 2.89644e-10 3 -4.900070529559604e-01 -4.900070529433437e-01 1.26167e-11 4.32340e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 -4.426628985502938e-01 -4.426628985685903e-01 1.82964e-11 8.66604e-10 2 6.637630064188258e-01 6.637630064059810e-01 1.28448e-11 2.96209e-10 3 -5.209947354115595e-01 -5.209947354553432e-01 4.37838e-11 4.95398e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 1.166279204347801e+00 1.166279204330960e+00 1.68412e-11 2.23455e-10 2 -1.025403954177941e+00 -1.025403954128115e+00 4.98259e-11 8.24793e-10 3 -4.714344298798856e-01 -4.714344298811627e-01 1.27709e-12 3.01543e-11 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -7.381575588088736e+00 -7.381575588138132e+00 4.93960e-11 2.22572e-10 2 2.090160249120190e+00 2.090160249089567e+00 3.06226e-11 1.99680e-09 * 3 5.898753670592678e+00 5.898753670577030e+00 1.56470e-11 1.20391e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 5.168133711810197e-01 5.168133711846978e-01 3.67817e-12 4.91140e-11 2 1.524537674900518e+00 1.524537674926243e+00 2.57256e-11 6.63196e-11 3 9.551138333513762e-01 9.551138333634278e-01 1.20516e-11 4.21133e-11 ----------------------------------------------------------------------------------------------------- 31 Pd 1 7.399764516965610e-01 7.399764516552541e-01 4.13070e-11 5.84992e-10 2 1.296797120153849e+00 1.296797120209452e+00 5.56031e-11 1.07293e-10 3 -2.362794425753303e-01 -2.362794425815171e-01 6.18686e-12 1.37296e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 -1.711570681132780e-01 -1.711570681265644e-01 1.32863e-11 2.18409e-10 2 -9.456295146134870e-01 -9.456295146208942e-01 7.40719e-12 3.44049e-11 3 -6.993884433594181e-01 -6.993884433614135e-01 1.99540e-12 8.42042e-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 = 26, direction = 1: |F_model - F_numer| error = ----------------------- = 4.88670e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Al Pd | a0 = 3.809023230613092 | (Configuration in file "config-AlPd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 1.005531943386529e+00 1.005531943389530e+00 3.00071e-12 2.75949e-10 2 8.325717649395118e-01 8.325717649567206e-01 1.72088e-11 2.47131e-10 3 8.092342570056063e-01 8.092342569737020e-01 3.19043e-11 7.99776e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -5.952315838775868e-01 -5.952315838804710e-01 2.88425e-12 1.22671e-10 2 -6.965300863738171e-01 -6.965300863492080e-01 2.46091e-11 2.22519e-10 3 6.952268853950730e-01 6.952268854128640e-01 1.77910e-11 1.97246e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 5.012520896189163e-01 5.012520896620973e-01 4.31810e-11 2.42533e-11 2 2.845586638039335e-01 2.845586637828831e-01 2.10503e-11 6.26172e-10 3 -1.507213785576907e+00 -1.507213785600482e+00 2.35743e-11 1.83251e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 6.467192826652153e-01 6.467192826948945e-01 2.96793e-11 1.27129e-10 2 -2.862302274298633e+00 -2.862302274298237e+00 3.96572e-13 1.05149e-10 3 -3.697458185073711e-01 -3.697458184732952e-01 3.40759e-11 4.21986e-11 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -6.047194789170041e-01 -6.047194789227044e-01 5.70033e-12 1.08994e-10 2 6.091389041047505e-01 6.091389041105076e-01 5.75717e-12 9.13569e-11 3 2.918281123289371e-01 2.918281123210105e-01 7.92666e-12 7.39487e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 -4.753488203000636e-01 -4.753488202980449e-01 2.01872e-12 1.06194e-10 2 -2.787437318370926e-01 -2.787437318423545e-01 5.26190e-12 1.27325e-10 3 -3.740481177131446e-01 -3.740481177371121e-01 2.39675e-11 8.83928e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 -3.241624092684258e-01 -3.241624092585217e-01 9.90408e-12 9.69139e-11 2 5.314478541799923e-01 5.314478541732233e-01 6.76903e-12 1.33167e-10 3 3.816268341521197e-01 3.816268341672382e-01 1.51185e-11 1.25589e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -1.034569595799142e+00 -1.034569595780897e+00 1.82447e-11 2.72220e-10 2 -9.108730689165146e-01 -9.108730689444904e-01 2.79757e-11 6.19014e-11 3 1.038464005549449e+00 1.038464005604930e+00 5.54805e-11 8.12654e-11 ----------------------------------------------------------------------------------------------------- 9 Pd 1 1.594363403415051e-01 1.594363403464728e-01 4.96769e-12 1.35135e-10 2 6.363106368705757e-01 6.363106369143582e-01 4.37825e-11 8.71969e-11 3 -5.821371387842217e-01 -5.821371386999057e-01 8.43160e-11 1.59041e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -7.992520916141888e-02 -7.992520915191245e-02 9.50642e-12 4.50018e-10 2 4.163716197870392e-01 4.163716197554978e-01 3.15414e-11 1.13903e-10 3 -1.850266215720350e+00 -1.850266215705518e+00 1.48317e-11 3.90648e-09 * ----------------------------------------------------------------------------------------------------- 11 Al 1 8.049313331972768e-01 8.049313331905138e-01 6.76303e-12 4.94587e-09 * 2 -4.907742121927028e-01 -4.907742121887960e-01 3.90682e-12 1.40609e-10 3 -6.286903709771939e-01 -6.286903709653083e-01 1.18856e-11 9.09313e-11 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.050092022958230e+00 -1.050092022939528e+00 1.87015e-11 4.88904e-10 2 4.709396717560127e-02 4.709396719030814e-02 1.47069e-11 4.55710e-11 3 1.179373371283245e+00 1.179373371331528e+00 4.82832e-11 1.11593e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 9.916863093193421e-01 9.916863093190343e-01 3.07754e-13 3.13221e-10 2 1.053384733174670e-01 1.053384732404777e-01 7.69893e-11 1.93817e-10 3 -5.635690995117817e-01 -5.635690994914957e-01 2.02860e-11 2.11732e-10 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -9.703871366760319e-01 -9.703871366664281e-01 9.60387e-12 2.65534e-11 2 -1.203143254348001e+00 -1.203143254357589e+00 9.58766e-12 2.15976e-11 3 3.972584211907785e-01 3.972584211862874e-01 4.49107e-12 4.57487e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.391707817094043e+00 1.391707817095788e+00 1.74571e-12 1.51908e-10 2 1.136861951713730e+00 1.136861951725431e+00 1.17011e-11 1.86389e-10 3 -2.001531810649982e+00 -2.001531810654542e+00 4.55991e-12 2.40122e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 1.554958640059555e+00 1.554958640085259e+00 2.57041e-11 2.79153e-10 2 3.674984558104253e-01 3.674984558120302e-01 1.60488e-12 1.26326e-08 * 3 2.671939461200124e+00 2.671939461206994e+00 6.87006e-12 1.37160e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -1.182315174167498e+00 -1.182315174158040e+00 9.45777e-12 1.60328e-10 2 -2.584423313118455e-01 -2.584423313240948e-01 1.22493e-11 6.05423e-11 3 -3.230053956257187e-01 -3.230053956138265e-01 1.18922e-11 1.65037e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.790276236831856e+00 1.790276236787310e+00 4.45466e-11 2.45079e-10 2 1.369810962996020e+00 1.369810962999913e+00 3.89355e-12 4.77687e-09 * 3 -1.451281545366010e+00 -1.451281545365580e+00 4.29656e-13 3.35217e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 8.214939367214004e-01 8.214939367049139e-01 1.64865e-11 1.01824e-10 2 -5.426758423580661e-01 -5.426758423586377e-01 5.71654e-13 3.79847e-11 3 8.798502408420025e-01 8.798502409065826e-01 6.45801e-11 5.67696e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 -1.477056097262959e+00 -1.477056097270833e+00 7.87437e-12 2.40614e-09 * 2 1.342836158103829e+00 1.342836158103148e+00 6.80567e-13 8.29070e-10 3 1.035705197435190e+00 1.035705197431525e+00 3.66507e-12 5.76607e-09 * ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.221871015006705e+00 -1.221871014959968e+00 4.67368e-11 4.05123e-09 * 2 -2.024965656084103e+00 -2.024965656098531e+00 1.44280e-11 2.74388e-10 3 -3.192320709210422e-02 -3.192320709603956e-02 3.93534e-12 1.77586e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.410645522960738e+00 2.410645522974226e+00 1.34888e-11 2.17410e-10 2 5.113392057424501e-01 5.113392057127339e-01 2.97161e-11 1.79613e-09 * 3 2.031348841726940e-01 2.031348841139559e-01 5.87381e-11 8.20037e-11 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -4.951713879733114e-01 -4.951713879687807e-01 4.53071e-12 1.30311e-10 2 5.332544659423230e-01 5.332544659086141e-01 3.37088e-11 2.36680e-09 * 3 -7.267649473696733e-01 -7.267649473790698e-01 9.39648e-12 3.73793e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -2.311198667906501e-01 -2.311198667967667e-01 6.11669e-12 4.03620e-10 2 -7.990673631013714e-01 -7.990673631159413e-01 1.45699e-11 1.23842e-09 3 -2.715032226522468e-01 -2.715032226528330e-01 5.86198e-13 8.83710e-11 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -6.347812210508846e-01 -6.347812210536425e-01 2.75791e-12 1.11898e-09 2 1.223532180144299e+00 1.223532180112953e+00 3.13458e-11 1.88571e-10 3 1.402957958429063e+00 1.402957958347876e+00 8.11871e-11 2.20264e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 4.943993363886238e-01 4.943993363928036e-01 4.17982e-12 3.20299e-10 2 1.599734990930782e+00 1.599734991056852e+00 1.26070e-10 8.36595e-11 3 -1.319038726753217e+00 -1.319038726789177e+00 3.59597e-11 3.68079e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 2.356585615295329e+00 2.356585615290096e+00 5.23315e-12 1.03003e-08 * 2 -3.358218315637955e+00 -3.358218315747256e+00 1.09301e-10 3.36752e-10 3 2.248208138077571e+00 2.248208138080061e+00 2.48956e-12 6.33218e-11 ----------------------------------------------------------------------------------------------------- 28 Pd 1 -1.220549057214940e+00 -1.220549057218580e+00 3.64042e-12 7.56499e-11 2 7.959374362985073e-01 7.959374363097529e-01 1.12456e-11 5.99789e-11 3 -1.259706817936050e+00 -1.259706817903631e+00 3.24185e-11 5.54075e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.428301983628354e+00 -2.428301983652669e+00 2.43148e-11 4.28922e-09 * 2 5.385297554540872e-01 5.385297554876735e-01 3.35862e-11 2.44043e-10 3 7.322520558479326e-01 7.322520557774771e-01 7.04555e-11 1.09659e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 4.725812922906495e-01 4.725812922677986e-01 2.28509e-11 2.47579e-09 * 2 6.580570052668666e-01 6.580570052754945e-01 8.62788e-12 2.38821e-09 * 3 -5.275036943267293e-02 -5.275036941475832e-02 1.79146e-11 3.94652e-09 * ----------------------------------------------------------------------------------------------------- 31 Pd 1 -5.504072819347777e-01 -5.504072819409859e-01 6.20815e-12 3.15937e-10 2 2.984530411340841e-01 2.984530411303912e-01 3.69288e-12 2.24595e-09 * 3 -5.594090984800308e-01 -5.594090985566366e-01 7.66057e-11 1.22311e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 -8.261963541829959e-01 -8.261963541788822e-01 4.11371e-12 5.17394e-09 * 2 -4.129413572561732e-01 -4.129413572632022e-01 7.02899e-12 3.35281e-10 3 -9.447413476111148e-02 -9.447413476264674e-02 1.53526e-12 1.09587e-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 = 13, direction = 2: |F_model - F_numer| error = ----------------------- = 7.30876e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.37027e-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 2.37027e-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.