!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 3.436525887494077e-01 2.18894e-11 2.21447e-09 * 2 -2.618078064062982e-02 -2.618078064718857e-02 6.55875e-12 2.54339e-11 3 3.437088645165465e-02 3.437088650864478e-02 5.69901e-11 6.40840e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099697114952e-01 -8.101099697036193e-01 7.87592e-12 3.09517e-09 * 2 8.600116138441266e-01 8.600116138634697e-01 1.93431e-11 2.45459e-10 3 3.127577258458623e-01 3.127577258445591e-01 1.30312e-12 1.82789e-09 * ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242118384311885e-02 -8.242118384957012e-02 6.45127e-12 1.99902e-11 2 -4.844095591639676e-02 -4.844095594124094e-02 2.48442e-11 1.29901e-09 3 -2.547490086906117e-01 -2.547490086883437e-01 2.26807e-12 4.05870e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906831351019e-01 4.983906831279910e-01 7.11092e-12 2.22188e-09 * 2 2.408671397121293e-01 2.408671396895504e-01 2.25788e-11 5.96162e-10 3 3.779437328642208e-01 3.779437328723519e-01 8.13111e-12 1.57507e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111435108739e-01 7.931111435222129e-01 1.13390e-11 7.48104e-11 2 -3.817072244476382e-01 -3.817072244321287e-01 1.55094e-11 2.93079e-11 3 2.806999061862538e-01 2.806999061870058e-01 7.52010e-13 7.76801e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254976473408e-01 -3.438254976506622e-01 3.32145e-12 3.66433e-10 2 2.501152958385667e-01 2.501152958560526e-01 1.74858e-11 3.91562e-11 3 3.380287546419144e-01 3.380287547173200e-01 7.54056e-11 5.66954e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574681113901152e-01 2.574681113725212e-01 1.75939e-11 3.29382e-10 2 -1.219046656479634e+00 -1.219046656549852e+00 7.02187e-11 1.42063e-10 3 -1.651118796526784e+00 -1.651118796513706e+00 1.30784e-11 1.61694e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221784187581320e-01 -7.221784187798053e-01 2.16732e-11 4.29489e-10 2 -4.748263066644509e-01 -4.748263067016598e-01 3.72088e-11 4.35121e-10 3 -7.562197548477109e-01 -7.562197548501238e-01 2.41296e-12 6.16172e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288844001276352e-02 4.288844001655536e-02 3.79184e-12 4.68910e-11 2 -1.188167806753753e+00 -1.188167806735966e+00 1.77873e-11 8.78742e-11 3 -1.184618214624649e+00 -1.184618214622674e+00 1.97509e-12 1.95028e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641779155383e-01 -5.398641779195825e-01 4.04421e-12 2.27676e-10 2 4.980765867686628e-01 4.980765867713333e-01 2.67047e-12 1.15987e-10 3 -7.222686212488535e-01 -7.222686213007670e-01 5.19135e-11 4.87336e-09 * ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753133414842e-01 -3.572753130165028e-01 3.24981e-10 2.55008e-10 2 -8.581020023213164e-01 -8.581020024106462e-01 8.93298e-11 8.22864e-11 3 7.845981095706080e-01 7.845981095495811e-01 2.10270e-11 1.04944e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596031305529761e-02 2.596031306772045e-02 1.24228e-11 2.02519e-11 2 1.245097673566508e+00 1.245097673549043e+00 1.74645e-11 1.00880e-10 3 7.763446140592514e-01 7.763446140999050e-01 4.06536e-11 2.38848e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365342020510563e-01 -5.365342020301805e-01 2.08757e-11 1.25132e-10 2 -1.200162166887454e+00 -1.200162166835848e+00 5.16061e-11 1.10613e-10 3 -1.957550100011358e+00 -1.957550099980839e+00 3.05194e-11 1.87986e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988771002555355e-02 8.988771001566959e-02 9.88397e-12 1.67241e-10 2 4.855436357312822e-01 4.855436357048850e-01 2.63972e-11 1.50808e-10 3 -1.387144633123531e-01 -1.387144633240446e-01 1.16914e-11 6.57631e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761451037876223e+00 1.761451037864170e+00 1.20530e-11 4.16096e-11 2 -6.436068985548461e-01 -6.436068985386120e-01 1.62341e-11 1.74736e-10 3 7.520277736138696e-01 7.520277736267007e-01 1.28311e-11 4.76678e-09 * ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494766277741e-01 5.978494766364105e-01 8.63642e-12 1.22583e-10 2 1.336599639554143e+00 1.336599639558277e+00 4.13447e-12 1.79345e-09 * 3 8.753613043449752e-01 8.753613043248554e-01 2.01198e-11 1.77708e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232218182708506e-01 4.232218182639046e-01 6.94600e-12 7.03598e-11 2 3.604704538566768e-01 3.604704538413654e-01 1.53113e-11 9.39150e-11 3 -9.557914876491863e-02 -9.557914875357526e-02 1.13434e-11 2.66716e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049824056000369e-01 -5.049824056252855e-01 2.52486e-11 8.61831e-10 2 4.028584621819862e-01 4.028584621759789e-01 6.00731e-12 3.65525e-10 3 1.019475219395497e+00 1.019475219388671e+00 6.82610e-12 7.07407e-11 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575296478882422e-01 2.575296478859965e-01 2.24576e-12 1.22286e-10 2 3.782444214493004e-01 3.782444214481884e-01 1.11194e-12 2.63970e-10 3 -4.712358503399028e-01 -4.712358503434113e-01 3.50842e-12 2.13726e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062635579241795e-01 4.062635579487807e-01 2.46012e-11 7.49773e-11 2 3.112967184921566e-01 3.112967184990758e-01 6.91919e-12 1.54963e-10 3 -4.574995164050278e-01 -4.574995164035131e-01 1.51468e-12 3.36096e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.519579269344997e-01 -9.519579267439875e-01 1.90512e-10 2.32051e-10 2 4.430056377461727e-02 4.430056376854855e-02 6.06872e-12 4.89014e-10 3 8.201330431559853e-01 8.201330431623642e-01 6.37890e-12 1.94367e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278260487808e-01 2.873278260350689e-01 1.37119e-11 3.79391e-10 2 1.511178773901759e+00 1.511178773986585e+00 8.48261e-11 1.67820e-09 * 3 1.447152283428595e+00 1.447152283397814e+00 3.07812e-11 1.51944e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449441208158874e-01 -3.449441208065199e-01 9.36756e-12 1.38390e-10 2 3.006117549858595e-01 3.006117549816515e-01 4.20797e-12 5.16777e-11 3 -3.734060033068488e-01 -3.734060033025022e-01 4.34658e-12 5.29793e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.548683834255006e-02 7.548683834206932e-02 4.80740e-13 1.00726e-09 2 -5.942094354385377e-04 -5.942094495228996e-04 1.40844e-11 4.67164e-11 3 -6.192826988180952e-01 -6.192826988024281e-01 1.56670e-11 1.70609e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619447313837871e-01 -3.619447313400200e-01 4.37670e-11 3.69797e-10 2 -8.543631750219945e-01 -8.543631750461587e-01 2.41641e-11 2.44883e-09 * 3 2.198728311538212e-01 2.198728312665998e-01 1.12779e-10 4.12541e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995054630761463e-01 -4.995054628989141e-01 1.77232e-10 6.41724e-10 2 1.019970122531736e+00 1.019970122404879e+00 1.26857e-10 3.86204e-10 3 -7.917982423073944e-01 -7.917982423096777e-01 2.28328e-12 3.27688e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695233018296072e-01 5.695233018141920e-01 1.54152e-11 2.66382e-10 2 -2.393202182937114e+00 -2.393202182915301e+00 2.18123e-11 3.29705e-11 3 7.839007915966316e-01 7.839007915678592e-01 2.87724e-11 1.30255e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446253011926659e-01 -5.446253012270474e-01 3.43815e-11 6.70416e-11 2 6.944324457877642e-01 6.944324457842886e-01 3.47555e-12 7.58481e-11 3 -2.318274122770182e-01 -2.318274122936031e-01 1.65849e-11 2.14340e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440921562913293e-01 -2.440921564178901e-01 1.26561e-10 6.56430e-10 2 -7.057626663444554e-01 -7.057626663780919e-01 3.36365e-11 1.97603e-09 * 3 6.755894770101792e-01 6.755894770113360e-01 1.15674e-12 4.03850e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998223837645208e-02 -7.998223838202244e-02 5.57036e-12 4.62360e-10 2 6.365060367959603e-01 6.365060368541261e-01 5.81658e-11 2.67474e-10 3 -3.994794263457406e-01 -3.994794263114670e-01 3.42736e-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 8.59990e-11 3 4.908346303115275e-01 4.908346303388320e-01 2.73044e-11 9.39046e-11 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661919252989692e-01 5.661919252932421e-01 5.72709e-12 3.94993e-10 2 3.764670780212212e-01 3.764670779902465e-01 3.09747e-11 4.36227e-09 * 3 1.162561741964186e-01 1.162561742055457e-01 9.12705e-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 9.441064889960266e-01 1.83393e-11 3.09526e-11 2 1.020074408241868e+00 1.020074408237608e+00 4.26015e-12 3.77265e-09 * 3 1.008782580009200e+00 1.008782580008782e+00 4.17888e-13 1.17174e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 1.376979813703016e+00 1.376979813664510e+00 3.85056e-11 1.74624e-10 2 -1.645185690582662e+00 -1.645185690585003e+00 2.34146e-12 5.83817e-11 3 6.404130703000894e-01 6.404130702734826e-01 2.66068e-11 4.35446e-11 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -8.798725614481723e-01 -8.798725614687892e-01 2.06170e-11 9.22082e-11 2 1.027269420024547e+00 1.027269420036024e+00 1.14768e-11 8.95255e-11 3 5.034985868673149e-01 5.034985868929409e-01 2.56261e-11 4.21937e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 6.658369015037627e-01 6.658369014584126e-01 4.53502e-11 1.17973e-10 2 1.022506121798648e+00 1.022506121807640e+00 8.99125e-12 4.86797e-10 3 -8.883457893177515e-01 -8.883457893096873e-01 8.06422e-12 3.52431e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -1.016901515283267e+00 -1.016901515288557e+00 5.28977e-12 6.94584e-11 2 -1.022241969760618e+00 -1.022241969808895e+00 4.82776e-11 7.36295e-10 3 -1.983735492641745e+00 -1.983735492640390e+00 1.35447e-12 1.88997e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 8.032764231745069e-01 8.032764231726638e-01 1.84308e-12 3.44398e-11 2 1.555823570810387e+00 1.555823570810538e+00 1.51212e-13 8.99867e-11 3 -1.211123035663784e+00 -1.211123035675399e+00 1.16145e-11 1.61082e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 3.708224896824219e+00 3.708224896845989e+00 2.17693e-11 2.38558e-10 2 -3.296108937351056e+00 -3.296108937323517e+00 2.75389e-11 1.96785e-11 3 2.194308496525284e+00 2.194308496577781e+00 5.24971e-11 2.27852e-08 * ----------------------------------------------------------------------------------------------------- 8 Pd 1 -6.093811753545425e+00 -6.093811753554826e+00 9.40137e-12 1.30929e-10 2 2.097194508633037e+00 2.097194508682457e+00 4.94205e-11 1.95211e-10 3 1.253276392253734e+00 1.253276392202338e+00 5.13964e-11 1.31962e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -7.480616013700015e-01 -7.480616013385668e-01 3.14347e-11 6.64108e-11 2 1.268267965856569e+00 1.268267965861764e+00 5.19473e-12 5.01947e-10 3 1.311059281056142e+00 1.311059281053696e+00 2.44627e-12 8.10205e-11 ----------------------------------------------------------------------------------------------------- 10 Pd 1 5.200989425875183e-01 5.200989425625647e-01 2.49536e-11 6.79660e-11 2 -8.170076905566198e-01 -8.170076905275155e-01 2.91043e-11 1.43740e-10 3 2.845686933634616e-01 2.845686933386408e-01 2.48208e-11 3.36153e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -1.622689113193994e+00 -1.622689113243746e+00 4.97518e-11 2.95517e-10 2 2.357032959216786e+00 2.357032959320555e+00 1.03769e-10 3.71486e-10 3 -1.568614114701329e+00 -1.568614114629027e+00 7.23028e-11 1.65121e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 6.738419780279001e-01 6.738419780222890e-01 5.61118e-12 6.88274e-11 2 -8.620589776357261e-01 -8.620589776210269e-01 1.46992e-11 1.11057e-10 3 1.935087931340687e-01 1.935087932266648e-01 9.25961e-11 2.17998e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -2.294893447561845e+00 -2.294893447495752e+00 6.60925e-11 1.14401e-09 2 -1.883336849201879e+00 -1.883336849190670e+00 1.12088e-11 1.12468e-10 3 -9.639915787989675e-01 -9.639915787769279e-01 2.20396e-11 2.06827e-10 ----------------------------------------------------------------------------------------------------- 14 Pd 1 2.019397565274193e+00 2.019397565284306e+00 1.01128e-11 1.33205e-11 2 1.556109911921926e+00 1.556109911928083e+00 6.15707e-12 3.91618e-11 3 -1.003976299483485e+00 -1.003976299495169e+00 1.16838e-11 5.15384e-09 * ----------------------------------------------------------------------------------------------------- 15 Pd 1 5.320899128412946e+00 5.320899128455841e+00 4.28955e-11 1.43835e-09 2 7.521681258082396e-01 7.521681257253291e-01 8.29105e-11 7.16864e-10 3 -6.821036070738720e+00 -6.821036070801382e+00 6.26619e-11 3.34474e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 -1.808858066164008e+00 -1.808858066132124e+00 3.18836e-11 1.90138e-10 2 1.152028319253190e+00 1.152028319238169e+00 1.50213e-11 2.14700e-10 3 1.367445420177775e+00 1.367445420173000e+00 4.77485e-12 2.16678e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 1.078376491174329e+00 1.078376491171168e+00 3.16014e-12 1.18713e-10 2 -2.446578744155157e+00 -2.446578744173362e+00 1.82050e-11 3.36537e-10 3 -2.190446337861007e+00 -2.190446337774629e+00 8.63780e-11 3.57330e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 2.413035324131912e+00 2.413035324160705e+00 2.87925e-11 1.20816e-09 2 -3.280996613310664e+00 -3.280996613317581e+00 6.91713e-12 1.50186e-10 3 1.323945436225807e+00 1.323945436250597e+00 2.47902e-11 9.41615e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 7.093301652325023e-01 7.093301653185108e-01 8.60085e-11 1.87522e-10 2 -8.800632105221644e-01 -8.800632105417967e-01 1.96323e-11 6.07836e-09 * 3 -1.471292320141924e+00 -1.471292320120136e+00 2.17879e-11 1.11320e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -1.363276405567539e+00 -1.363276405580951e+00 1.34117e-11 2.27759e-10 2 4.408347633417660e+00 4.408347633431282e+00 1.36220e-11 7.75446e-10 3 2.923482813670875e+00 2.923482813671213e+00 3.38396e-13 2.81958e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -6.566739595290421e-01 -6.566739595160818e-01 1.29603e-11 4.07901e-10 2 9.304128738890446e-02 9.304128737188563e-02 1.70188e-11 7.81657e-09 * 3 -5.650383426287147e-02 -5.650383427850504e-02 1.56336e-11 2.33803e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 3.651760867884323e+00 3.651760867867932e+00 1.63909e-11 7.10256e-10 2 -4.775452856416858e+00 -4.775452856515963e+00 9.91047e-11 2.64156e-10 3 1.937657227618895e+00 1.937657227674965e+00 5.60696e-11 5.40965e-11 ----------------------------------------------------------------------------------------------------- 23 Pd 1 1.937056022719184e-01 1.937056023006466e-01 2.87282e-11 6.77780e-11 2 5.781932581552870e-01 5.781932581606845e-01 5.39746e-12 2.51673e-09 * 3 -4.556787413757997e-01 -4.556787413921434e-01 1.63437e-11 3.02803e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -1.700339582303424e+00 -1.700339582183910e+00 1.19514e-10 5.27081e-10 2 -7.811461433191694e-01 -7.811461433818624e-01 6.26930e-11 2.66421e-09 * 3 2.011896410125007e-01 2.011896410715294e-01 5.90287e-11 9.20125e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -4.167666758072082e-01 -4.167666757430271e-01 6.41810e-11 2.07553e-10 2 -4.449214282518885e-01 -4.449214282013687e-01 5.05198e-11 3.11577e-10 3 -9.641562169896610e-01 -9.641562168756607e-01 1.14000e-10 2.24042e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 9.560062008343891e-02 9.560062003672171e-02 4.67172e-11 1.39132e-10 2 -3.571829612645409e-01 -3.571829613115357e-01 4.69948e-11 2.89644e-10 3 -4.900070529559604e-01 -4.900070529433434e-01 1.26170e-11 4.32340e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 -4.426628985502938e-01 -4.426628985685899e-01 1.82961e-11 8.66604e-10 2 6.637630064188258e-01 6.637630064059805e-01 1.28453e-11 2.96209e-10 3 -5.209947354115595e-01 -5.209947354553430e-01 4.37835e-11 4.95398e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 1.166279204347801e+00 1.166279204330959e+00 1.68423e-11 2.23454e-10 2 -1.025403954177941e+00 -1.025403954128114e+00 4.98266e-11 8.24793e-10 3 -4.714344298798856e-01 -4.714344298811624e-01 1.27676e-12 3.01543e-11 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -7.381575588088736e+00 -7.381575588138126e+00 4.93898e-11 2.22573e-10 2 2.090160249120190e+00 2.090160249089566e+00 3.06239e-11 1.99680e-09 * 3 5.898753670592678e+00 5.898753670577032e+00 1.56453e-11 1.19435e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 5.168133711810197e-01 5.168133711846974e-01 3.67772e-12 4.91135e-11 2 1.524537674900518e+00 1.524537674926242e+00 2.57248e-11 6.63196e-11 3 9.551138333513762e-01 9.551138333634271e-01 1.20509e-11 4.21131e-11 ----------------------------------------------------------------------------------------------------- 31 Pd 1 7.399764516965610e-01 7.399764516552534e-01 4.13076e-11 5.84992e-10 2 1.296797120153849e+00 1.296797120209451e+00 5.56020e-11 1.07293e-10 3 -2.362794425753303e-01 -2.362794425815170e-01 6.18672e-12 1.37296e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 -1.711570681132780e-01 -1.711570681265642e-01 1.32862e-11 2.18409e-10 2 -9.456295146134870e-01 -9.456295146208935e-01 7.40652e-12 3.44048e-11 3 -6.993884433594181e-01 -6.993884433614137e-01 1.99563e-12 8.42043e-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 3.00115e-12 2.75949e-10 2 8.325717649395118e-01 8.325717649567200e-01 1.72082e-11 2.47131e-10 3 8.092342570056063e-01 8.092342569737014e-01 3.19048e-11 7.99778e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -5.952315838775868e-01 -5.952315838804704e-01 2.88358e-12 1.22671e-10 2 -6.965300863738171e-01 -6.965300863492078e-01 2.46093e-11 2.22519e-10 3 6.952268853950730e-01 6.952268854128631e-01 1.77901e-11 1.97245e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 5.012520896189163e-01 5.012520896620970e-01 4.31807e-11 2.42533e-11 2 2.845586638039335e-01 2.845586637828830e-01 2.10505e-11 6.26172e-10 3 -1.507213785576907e+00 -1.507213785600480e+00 2.35729e-11 1.83250e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 6.467192826652153e-01 6.467192826948943e-01 2.96790e-11 1.27129e-10 2 -2.862302274298633e+00 -2.862302274298233e+00 4.00124e-13 1.05154e-10 3 -3.697458185073711e-01 -3.697458184732949e-01 3.40762e-11 4.21982e-11 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -6.047194789170041e-01 -6.047194789227041e-01 5.70000e-12 1.08993e-10 2 6.091389041047505e-01 6.091389041105073e-01 5.75684e-12 9.13568e-11 3 2.918281123289371e-01 2.918281123210102e-01 7.92694e-12 7.39488e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 -4.753488203000636e-01 -4.753488202980446e-01 2.01905e-12 1.06194e-10 2 -2.787437318370926e-01 -2.787437318423543e-01 5.26174e-12 1.27325e-10 3 -3.740481177131446e-01 -3.740481177371124e-01 2.39678e-11 8.83928e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 -3.241624092684258e-01 -3.241624092585215e-01 9.90430e-12 9.69141e-11 2 5.314478541799923e-01 5.314478541732229e-01 6.76936e-12 1.33168e-10 3 3.816268341521197e-01 3.816268341672378e-01 1.51181e-11 1.25590e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -1.034569595799142e+00 -1.034569595780896e+00 1.82454e-11 2.72220e-10 2 -9.108730689165146e-01 -9.108730689444906e-01 2.79760e-11 6.19022e-11 3 1.038464005549449e+00 1.038464005604929e+00 5.54803e-11 8.12663e-11 ----------------------------------------------------------------------------------------------------- 9 Pd 1 1.594363403415051e-01 1.594363403464727e-01 4.96761e-12 1.35135e-10 2 6.363106368705757e-01 6.363106369143577e-01 4.37821e-11 8.71969e-11 3 -5.821371387842217e-01 -5.821371386999054e-01 8.43163e-11 1.59042e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -7.992520916141888e-02 -7.992520915191241e-02 9.50647e-12 4.50018e-10 2 4.163716197870392e-01 4.163716197554975e-01 3.15417e-11 1.13903e-10 3 -1.850266215720350e+00 -1.850266215705519e+00 1.48308e-11 3.90648e-09 * ----------------------------------------------------------------------------------------------------- 11 Al 1 8.049313331972768e-01 8.049313331905142e-01 6.76259e-12 4.94587e-09 * 2 -4.907742121927028e-01 -4.907742121887956e-01 3.90715e-12 1.40609e-10 3 -6.286903709771939e-01 -6.286903709653039e-01 1.18900e-11 9.09355e-11 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.050092022958230e+00 -1.050092022939527e+00 1.87026e-11 4.88905e-10 2 4.709396717560127e-02 4.709396719030811e-02 1.47068e-11 4.55710e-11 3 1.179373371283245e+00 1.179373371331527e+00 4.82820e-11 1.11592e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 9.916863093193421e-01 9.916863093190337e-01 3.08420e-13 3.13221e-10 2 1.053384733174670e-01 1.053384732404775e-01 7.69895e-11 1.93818e-10 3 -5.635690995117817e-01 -5.635690994914953e-01 2.02864e-11 2.11732e-10 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -9.703871366760319e-01 -9.703871366664275e-01 9.60443e-12 2.65538e-11 2 -1.203143254348001e+00 -1.203143254357589e+00 9.58833e-12 2.15981e-11 3 3.972584211907785e-01 3.972584211862871e-01 4.49135e-12 4.57487e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.391707817094043e+00 1.391707817095788e+00 1.74483e-12 1.51906e-10 2 1.136861951713730e+00 1.136861951725431e+00 1.17004e-11 1.86389e-10 3 -2.001531810649982e+00 -2.001531810654540e+00 4.55858e-12 2.40122e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 1.554958640059555e+00 1.554958640085258e+00 2.57032e-11 2.79153e-10 2 3.674984558104253e-01 3.674984558120304e-01 1.60510e-12 1.26326e-08 * 3 2.671939461200124e+00 2.671939461206994e+00 6.86917e-12 1.37161e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -1.182315174167498e+00 -1.182315174158040e+00 9.45843e-12 1.60328e-10 2 -2.584423313118455e-01 -2.584423313240946e-01 1.22491e-11 6.05426e-11 3 -3.230053956257187e-01 -3.230053956138263e-01 1.18924e-11 1.65037e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.790276236831856e+00 1.790276236787311e+00 4.45455e-11 2.45076e-10 2 1.369810962996020e+00 1.369810962999914e+00 3.89400e-12 4.77687e-09 * 3 -1.451281545366010e+00 -1.451281545365579e+00 4.30544e-13 3.35219e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 8.214939367214004e-01 8.214939367049133e-01 1.64870e-11 1.01824e-10 2 -5.426758423580661e-01 -5.426758423586373e-01 5.71210e-13 3.79846e-11 3 8.798502408420025e-01 8.798502409065819e-01 6.45795e-11 5.67695e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 -1.477056097262959e+00 -1.477056097270834e+00 7.87526e-12 2.40615e-09 * 2 1.342836158103829e+00 1.342836158103149e+00 6.79679e-13 8.29070e-10 3 1.035705197435190e+00 1.035705197431525e+00 3.66462e-12 5.76607e-09 * ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.221871015006705e+00 -1.221871014959968e+00 4.67373e-11 4.05122e-09 * 2 -2.024965656084103e+00 -2.024965656098530e+00 1.44267e-11 2.74388e-10 3 -3.192320709210422e-02 -3.192320709603953e-02 3.93531e-12 1.77586e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.410645522960738e+00 2.410645522974225e+00 1.34879e-11 2.17409e-10 2 5.113392057424501e-01 5.113392057127336e-01 2.97165e-11 1.79613e-09 * 3 2.031348841726940e-01 2.031348841139558e-01 5.87383e-11 8.20038e-11 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -4.951713879733114e-01 -4.951713879687804e-01 4.53104e-12 1.30311e-10 2 5.332544659423230e-01 5.332544659086145e-01 3.37085e-11 2.36680e-09 * 3 -7.267649473696733e-01 -7.267649473790703e-01 9.39693e-12 3.73793e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -2.311198667906501e-01 -2.311198667967666e-01 6.11655e-12 4.03620e-10 2 -7.990673631013714e-01 -7.990673631159416e-01 1.45702e-11 1.23842e-09 3 -2.715032226522468e-01 -2.715032226528327e-01 5.85920e-13 8.83710e-11 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -6.347812210508846e-01 -6.347812210536428e-01 2.75813e-12 1.11898e-09 2 1.223532180144299e+00 1.223532180112953e+00 3.13465e-11 1.88573e-10 3 1.402957958429063e+00 1.402957958347876e+00 8.11877e-11 2.20264e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 4.943993363886238e-01 4.943993363928033e-01 4.17949e-12 3.20299e-10 2 1.599734990930782e+00 1.599734991056851e+00 1.26069e-10 8.36595e-11 3 -1.319038726753217e+00 -1.319038726789176e+00 3.59586e-11 3.68079e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 2.356585615295329e+00 2.356585615290097e+00 5.23181e-12 1.03003e-08 * 2 -3.358218315637955e+00 -3.358218315747254e+00 1.09299e-10 3.36755e-10 3 2.248208138077571e+00 2.248208138080058e+00 2.48734e-12 6.33231e-11 ----------------------------------------------------------------------------------------------------- 28 Pd 1 -1.220549057214940e+00 -1.220549057218579e+00 3.63953e-12 7.56506e-11 2 7.959374362985073e-01 7.959374363097524e-01 1.12451e-11 5.99792e-11 3 -1.259706817936050e+00 -1.259706817903630e+00 3.24196e-11 5.54077e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.428301983628354e+00 -2.428301983652670e+00 2.43161e-11 4.28922e-09 * 2 5.385297554540872e-01 5.385297554876729e-01 3.35857e-11 2.44044e-10 3 7.322520558479326e-01 7.322520557774769e-01 7.04558e-11 1.09659e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 4.725812922906495e-01 4.725812922677988e-01 2.28507e-11 2.47579e-09 * 2 6.580570052668666e-01 6.580570052754949e-01 8.62832e-12 2.38821e-09 * 3 -5.275036943267293e-02 -5.275036941475834e-02 1.79146e-11 3.94652e-09 * ----------------------------------------------------------------------------------------------------- 31 Pd 1 -5.504072819347777e-01 -5.504072819409855e-01 6.20781e-12 3.15936e-10 2 2.984530411340841e-01 2.984530411303914e-01 3.69271e-12 2.24595e-09 * 3 -5.594090984800308e-01 -5.594090985566365e-01 7.66056e-11 1.22311e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 -8.261963541829959e-01 -8.261963541788826e-01 4.11327e-12 5.17394e-09 * 2 -4.129413572561732e-01 -4.129413572632019e-01 7.02866e-12 3.35281e-10 3 -9.447413476111148e-02 -9.447413476264679e-02 1.53531e-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 = ----------------------- = 7.30877e-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.