!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_JeongLee_2020_PdC__MO_068985622065_000 Supported species : C 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 = C | a0 = 3.379122734069824 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 1.092309830761578e+00 1.092309830772645e+00 1.10665e-11 1.10298e-10 2 1.319831826400909e+00 1.319831826394857e+00 6.05271e-12 2.10776e-10 3 1.328900853730179e+00 1.328900853719570e+00 1.06093e-11 1.02235e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 1.492183345020174e-01 1.492183345100955e-01 8.07812e-12 1.67503e-10 2 1.026998445884790e-01 1.026998446215087e-01 3.30297e-11 8.04284e-11 3 -2.288644397149875e+00 -2.288644397166733e+00 1.68572e-11 1.57721e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.448196704790096e+00 -1.448196704773934e+00 1.61617e-11 9.36111e-11 2 -8.832314050943950e-01 -8.832314050510569e-01 4.33381e-11 2.80576e-10 3 1.658458342149162e-01 1.658458342282807e-01 1.33645e-11 1.64759e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.628311870237289e+00 -3.628311870186166e+00 5.11231e-11 1.41838e-10 2 -4.591922352379775e-01 -4.591922352594064e-01 2.14290e-11 3.03924e-10 3 -1.207589798044527e+00 -1.207589798060597e+00 1.60696e-11 3.75180e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 6.858700793924168e-01 6.858700794102293e-01 1.78124e-11 5.88968e-10 2 -5.153106640680629e-01 -5.153106641331031e-01 6.50402e-11 5.62349e-10 3 -2.258894168046437e+00 -2.258894168016274e+00 3.01630e-11 2.56423e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 2.110833937237838e-01 2.110833936347594e-01 8.90244e-11 4.30190e-10 2 -1.117054757952925e+00 -1.117054758023488e+00 7.05627e-11 2.96431e-10 3 -4.880986686415933e-01 -4.880986686293263e-01 1.22670e-11 3.30557e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 3.431911963438815e-01 3.431911963110956e-01 3.27859e-11 1.02238e-10 2 -2.569399848199392e+00 -2.569399848166439e+00 3.29528e-11 1.53027e-09 3 -7.952248793086802e-01 -7.952248792880602e-01 2.06201e-11 5.75071e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 5.473813321422672e-02 5.473813327558653e-02 6.13598e-11 7.50021e-09 * 2 1.563464211448300e+00 1.563464211549309e+00 1.01009e-10 3.08454e-10 3 7.934802631890240e-01 7.934802630930688e-01 9.59551e-11 4.30942e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -3.464296227710182e+00 -3.464296227698082e+00 1.21001e-11 2.41703e-10 2 -3.424179763805477e+00 -3.424179763811196e+00 5.71898e-12 1.19031e-10 3 5.112569275362000e-02 5.112569271763268e-02 3.59873e-11 3.66258e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.408664868571794e+00 -1.408664868549289e+00 2.25049e-11 7.12364e-11 2 7.681547630367758e+00 7.681547630379653e+00 1.18954e-11 1.52427e-10 3 -4.728738609288344e+00 -4.728738609310580e+00 2.22355e-11 1.50411e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.218321639478736e+00 -3.218321639504403e+00 2.56670e-11 2.67615e-10 2 -4.704251417317991e+00 -4.704251417299540e+00 1.84510e-11 4.89380e-10 3 -1.919712300068316e+00 -1.919712300006245e+00 6.20701e-11 5.26688e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -2.993055346980078e+00 -2.993055346976661e+00 3.41682e-12 3.56990e-11 2 1.325975401226325e+00 1.325975401249104e+00 2.27787e-11 6.88170e-11 3 9.093391701767757e-01 9.093391701663575e-01 1.04182e-11 4.49003e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 4.590136086008497e+00 4.590136085976851e+00 3.16467e-11 5.44442e-10 2 -1.663281241978062e+00 -1.663281242013248e+00 3.51856e-11 5.20265e-09 * 3 -7.883992620333652e+00 -7.883992620280928e+00 5.27240e-11 4.94028e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 1.546639148260378e+00 1.546639148284781e+00 2.44034e-11 6.16640e-11 2 1.382080238482530e-01 1.382080238557419e-01 7.48884e-12 1.17310e-10 3 -1.453227625699374e+00 -1.453227625704397e+00 5.02287e-12 2.83340e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 8.683784953615403e+00 8.683784953656177e+00 4.07745e-11 4.97240e-10 2 -5.423129967584334e+00 -5.423129967568956e+00 1.53779e-11 4.54246e-10 3 -3.414020365718696e-01 -3.414020366355230e-01 6.36534e-11 4.01655e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.498095065224441e+00 -5.498095065213999e+00 1.04423e-11 1.79694e-10 2 1.051576874221785e+01 1.051576874221358e+01 4.27391e-12 2.02681e-10 3 6.363586992346232e+00 6.363586992311068e+00 3.51639e-11 1.09051e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -2.888011844567568e+00 -2.888011844566788e+00 7.80265e-13 3.13358e-11 2 -3.584056113560441e+00 -3.584056113557610e+00 2.83107e-12 9.98178e-10 3 -1.094685389439817e+00 -1.094685389385391e+00 5.44265e-11 1.61106e-08 * ----------------------------------------------------------------------------------------------------- 18 C 1 1.281709217754617e+00 1.281709217688284e+00 6.63327e-11 3.76281e-10 2 2.089589244584773e+00 2.089589244501123e+00 8.36500e-11 4.74875e-10 3 -1.760938972461792e+00 -1.760938972509565e+00 4.77725e-11 3.39456e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 7.049561701727833e-01 7.049561700077317e-01 1.65052e-10 1.26717e-10 2 -2.849817364308621e+00 -2.849817364263386e+00 4.52349e-11 4.84581e-10 3 2.486429246392488e+00 2.486429246387599e+00 4.88898e-12 1.53015e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.087024485161280e+00 -2.087024485156933e+00 4.34630e-12 2.96096e-10 2 1.905507099197575e+00 1.905507099318833e+00 1.21257e-10 5.06043e-10 3 2.882481472440060e+00 2.882481472366220e+00 7.38400e-11 2.13776e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 8.950419265577767e-01 8.950419265744972e-01 1.67205e-11 1.80104e-10 2 -4.380691683427155e+00 -4.380691683407480e+00 1.96749e-11 5.17534e-10 3 2.298247779319476e+00 2.298247779363213e+00 4.37375e-11 2.31990e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 6.172679963637309e+00 6.172679963608408e+00 2.89013e-11 1.52663e-10 2 2.886466150278788e+00 2.886466150275023e+00 3.76499e-12 6.87410e-10 3 3.606962580263052e+00 3.606962580247945e+00 1.51070e-11 2.20432e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 -1.080359095471988e+00 -1.080359095529961e+00 5.79730e-11 3.85983e-10 2 4.007065522212708e-01 4.007065522097680e-01 1.15027e-11 1.07530e-10 3 -1.587128474382808e+00 -1.587128474291057e+00 9.17502e-11 5.32268e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 2.741909983231208e-01 2.741909982937534e-01 2.93674e-11 1.31371e-10 2 5.072927910943383e-01 5.072927911782831e-01 8.39447e-11 3.13842e-10 3 6.379951459816882e-01 6.379951459935245e-01 1.18363e-11 2.18723e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 1.450094253463424e-01 1.450094253456681e-01 6.74266e-13 6.60136e-11 2 -1.320626123330087e+00 -1.320626123329087e+00 9.99423e-13 2.09908e-10 3 -1.732980176939414e+00 -1.732980176938619e+00 7.94698e-13 5.46104e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.970944217322042e+00 1.970944217281859e+00 4.01839e-11 1.21971e-09 2 2.387488411099212e+00 2.387488411103012e+00 3.79963e-12 2.64198e-11 3 -2.776032599080335e+00 -2.776032599064031e+00 1.63043e-11 2.45415e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.445179751047403e+00 -4.445179751067003e+00 1.95994e-11 1.56406e-09 * 2 7.159566356237588e-01 7.159566356464276e-01 2.26689e-11 9.51292e-10 3 2.367241190755745e+00 2.367241190760275e+00 4.52927e-12 3.32429e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.436705572942337e+00 -2.436705573030498e+00 8.81610e-11 1.26395e-10 2 2.496988806146537e-01 2.496988806094665e-01 5.18724e-12 2.10273e-10 3 4.099964366343430e+00 4.099964366290184e+00 5.32463e-11 3.70690e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 9.263003963243019e-02 9.263003968184499e-02 4.94148e-11 1.17569e-09 2 -3.175489440176560e+00 -3.175489440171847e+00 4.71312e-12 2.00832e-09 * 3 3.241923769180135e-01 3.241923769098062e-01 8.20727e-12 3.45513e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 3.282266697808694e+00 3.282266697752145e+00 5.65494e-11 1.12901e-10 2 -5.810755344810068e-01 -5.810755344923730e-01 1.13662e-11 5.22740e-11 3 -2.973366236360493e-01 -2.973366236352754e-01 7.73881e-13 1.82284e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 2.882510236076805e-01 2.882510236022721e-01 5.40840e-12 6.55556e-10 2 9.345825319623818e-01 9.345825319613040e-01 1.07780e-12 4.48782e-09 * 3 -5.600674464499613e-01 -5.600674464603416e-01 1.03803e-11 3.90945e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 2.131571636198211e+00 2.131571636210843e+00 1.26321e-11 3.88594e-10 2 1.926003583747859e+00 1.926003583730775e+00 1.70846e-11 9.28631e-11 3 4.858901820718145e+00 4.858901820720077e+00 1.93179e-12 4.82888e-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 = 9, direction = 3: |F_model - F_numer| error = ----------------------- = 7.03899e-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. 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 1.020375888998226e+00 1.020375888991898e+00 6.32761e-12 1.08361e-10 2 7.112934708439705e-01 7.112934708455542e-01 1.58362e-12 5.37959e-11 3 9.536810698091642e-01 9.536810698181060e-01 8.94174e-12 7.83809e-11 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -5.967062843059638e-01 -5.967062842806409e-01 2.53230e-11 4.95274e-11 2 -3.488388354551437e-01 -3.488388354688119e-01 1.36683e-11 1.46655e-11 3 8.224918960537896e-01 8.224918960251324e-01 2.86572e-11 1.43127e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -1.205742646838988e-01 -1.205742646659827e-01 1.79161e-11 1.59709e-10 2 9.852512107081168e-01 9.852512106815833e-01 2.65336e-11 2.48266e-10 3 7.443142490103483e-02 7.443142490219208e-02 1.15725e-12 9.85952e-11 ----------------------------------------------------------------------------------------------------- 4 Pd 1 7.630213788353342e-01 7.630213788247679e-01 1.05662e-11 8.67810e-11 2 -7.249470567748914e-01 -7.249470568330799e-01 5.81886e-11 1.84286e-10 3 8.900213743050112e-03 8.900213786946963e-03 4.38969e-11 1.60317e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -4.986705323313650e+00 -4.986705323326197e+00 1.25464e-11 1.25295e-10 2 2.788432954946788e-01 2.788432955151214e-01 2.04426e-11 3.63155e-11 3 -3.968656465444207e+00 -3.968656465448225e+00 4.01768e-12 1.30793e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 2.085534726059986e+00 2.085534726081770e+00 2.17844e-11 3.38313e-10 2 -3.300088560581102e+00 -3.300088560624027e+00 4.29248e-11 2.05169e-10 3 2.351933619211747e-01 2.351933619181412e-01 3.03346e-12 1.32219e-09 * ----------------------------------------------------------------------------------------------------- 7 Pd 1 4.551985321063414e+00 4.551985321035840e+00 2.75744e-11 5.10453e-09 * 2 1.093070092615015e+00 1.093070092599572e+00 1.54425e-11 5.79281e-11 3 5.139192883320702e+00 5.139192883287100e+00 3.36025e-11 8.22303e-09 * ----------------------------------------------------------------------------------------------------- 8 Pd 1 1.576359332709979e+00 1.576359332709231e+00 7.48512e-13 4.67291e-11 2 -3.156533513842416e+00 -3.156533513833469e+00 8.94662e-12 7.01399e-10 3 -3.810153271313307e+00 -3.810153271337052e+00 2.37450e-11 1.27060e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 1.227891356680826e+00 1.227891356687319e+00 6.49236e-12 1.15127e-10 2 3.099199124091758e-01 3.099199124046008e-01 4.57501e-12 1.66449e-11 3 8.279607753745756e-01 8.279607753952231e-01 2.06475e-11 5.71369e-11 ----------------------------------------------------------------------------------------------------- 10 Pd 1 3.117320995277617e-03 3.117320996038512e-03 7.60895e-13 6.31709e-10 2 -1.601727605995171e+00 -1.601727606001272e+00 6.10045e-12 1.09206e-10 3 8.104665674079830e-01 8.104665674090378e-01 1.05482e-12 8.58491e-11 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -2.852101169312235e+00 -2.852101169233037e+00 7.91980e-11 4.55244e-10 2 3.719052197847839e-03 3.719052181860552e-03 1.59873e-11 5.31242e-11 3 -7.657681639836671e-01 -7.657681639604257e-01 2.32414e-11 8.63875e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 5.854186361200180e-01 5.854186361289261e-01 8.90810e-12 1.50657e-10 2 -7.765792660932744e-01 -7.765792660882817e-01 4.99278e-12 1.45698e-10 3 -2.693482580794651e-01 -2.693482580460264e-01 3.34386e-11 7.11573e-11 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -3.576517063605802e+00 -3.576517063646964e+00 4.11613e-11 9.78946e-11 2 2.968238693104468e+00 2.968238693144084e+00 3.96168e-11 2.43385e-10 3 -5.729614795120551e-01 -5.729614795215585e-01 9.50340e-12 1.47431e-08 * ----------------------------------------------------------------------------------------------------- 14 Pd 1 -1.292596914632912e+00 -1.292596914653399e+00 2.04874e-11 1.43556e-10 2 -3.653973171125953e-01 -3.653973170856091e-01 2.69861e-11 6.61067e-11 3 1.226524280207688e+00 1.226524280217861e+00 1.01730e-11 8.02245e-11 ----------------------------------------------------------------------------------------------------- 15 Pd 1 4.047688359958697e-01 4.047688360187319e-01 2.28622e-11 1.05545e-10 2 2.000624542206620e-01 2.000624542021235e-01 1.85385e-11 7.34318e-11 3 -1.137052142877192e+00 -1.137052142951905e+00 7.47138e-11 9.41089e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 2.020698149688234e+00 2.020698149725878e+00 3.76441e-11 1.77519e-10 2 1.340036918528615e+00 1.340036918522233e+00 6.38156e-12 1.36408e-10 3 8.906140858712348e-01 8.906140858816674e-01 1.04325e-11 2.29634e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 8.393182430972187e-01 8.393182430695346e-01 2.76841e-11 5.93728e-10 2 8.554380449356911e-01 8.554380449187128e-01 1.69783e-11 1.25900e-10 3 -1.297953729110115e-01 -1.297953729832955e-01 7.22841e-11 2.20367e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -3.036910649786084e+00 -3.036910649796322e+00 1.02380e-11 1.73954e-10 2 1.512388518414359e+00 1.512388518411280e+00 3.07931e-12 1.24887e-10 3 -1.271986798097760e+00 -1.271986798102942e+00 5.18163e-12 2.34914e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 -2.975109405225704e+00 -2.975109405252349e+00 2.66449e-11 1.93423e-10 2 -3.176007761117679e+00 -3.176007761124515e+00 6.83631e-12 9.08122e-11 3 7.230009060618823e-01 7.230009060490392e-01 1.28431e-11 8.33617e-11 ----------------------------------------------------------------------------------------------------- 20 Pd 1 8.044262372945704e-01 8.044262372770161e-01 1.75543e-11 7.84282e-11 2 1.227558673947698e-01 1.227558673744777e-01 2.02921e-11 1.89401e-09 * 3 -4.801710727102744e-01 -4.801710727290659e-01 1.87915e-11 3.09955e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -1.799067170031781e+00 -1.799067170054888e+00 2.31068e-11 1.23379e-10 2 -3.297478764886163e+00 -3.297478764866100e+00 2.00631e-11 1.41732e-10 3 -1.871451644672190e+00 -1.871451644669792e+00 2.39764e-12 4.82431e-09 * ----------------------------------------------------------------------------------------------------- 22 Pd 1 4.398199673796460e+00 4.398199673844704e+00 4.82441e-11 4.88229e-10 2 2.331330809156130e+00 2.331330809148560e+00 7.56950e-12 2.74635e-10 3 -4.079592746247881e+00 -4.079592746231830e+00 1.60512e-11 2.20616e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -5.924567314750206e-01 -5.924567314845750e-01 9.55436e-12 1.69238e-10 2 -5.886046814148593e-01 -5.886046814063931e-01 8.46623e-12 1.05941e-10 3 1.076394893212113e+00 1.076394893222762e+00 1.06484e-11 5.31774e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 1.580810885422407e+00 1.580810885425337e+00 2.93010e-12 1.99275e-10 2 4.607183160817904e+00 4.607183160815952e+00 1.95222e-12 2.49296e-10 3 5.116558059448624e+00 5.116558059462013e+00 1.33893e-11 3.16443e-09 * ----------------------------------------------------------------------------------------------------- 25 Pd 1 -2.671328477500001e-01 -2.671328477459796e-01 4.02056e-12 6.96151e-10 2 -6.389564301336171e-01 -6.389564300709665e-01 6.26507e-11 3.59532e-10 3 -1.536514020618650e+00 -1.536514020667336e+00 4.86857e-11 1.05011e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 1.960300761346650e-01 1.960300761298218e-01 4.84321e-12 4.60023e-10 2 -1.871133766474777e-02 -1.871133764386649e-02 2.08813e-11 4.96552e-09 * 3 -5.456546601067552e-01 -5.456546600601333e-01 4.66219e-11 2.10764e-09 * ----------------------------------------------------------------------------------------------------- 27 Pd 1 -8.859478118988120e-01 -8.859478118689214e-01 2.98906e-11 5.84116e-10 2 -2.300757489732926e+00 -2.300757489737485e+00 4.55858e-12 1.20435e-08 * 3 3.959044757276017e-01 3.959044757111647e-01 1.64370e-11 1.21102e-09 * ----------------------------------------------------------------------------------------------------- 28 Pd 1 2.600790808636931e-01 2.600790808704065e-01 6.71341e-12 1.65075e-10 2 2.107409862023993e-01 2.107409862074431e-01 5.04383e-12 1.20844e-10 3 2.153066520328286e-01 2.153066520174276e-01 1.54010e-11 3.77781e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 1.258936762733916e-01 1.258936762249189e-01 4.84727e-11 2.38286e-10 2 1.981434849532913e+00 1.981434849505327e+00 2.75853e-11 4.45626e-10 3 2.463135962604272e+00 2.463135962700906e+00 9.66338e-11 2.39424e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 -6.652132146670524e-01 -6.652132146712901e-01 4.23772e-12 4.64409e-11 2 -2.210643215027425e-01 -2.210643215094552e-01 6.71266e-12 1.94780e-10 3 4.084401445975934e-01 4.084401446124188e-01 1.48254e-11 2.30886e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 -7.828214404739937e-01 -7.828214404926942e-01 1.87005e-11 6.39877e-11 2 6.145848406469978e-03 6.145848399460727e-03 7.00925e-12 1.49870e-10 3 -4.062259965274502e-01 -4.062259965467355e-01 1.92852e-11 1.54127e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 1.985931471133340e+00 1.985931471136228e+00 2.88791e-12 9.44209e-11 2 9.978397573241471e-01 9.978397572855338e-01 3.86133e-11 1.19061e-10 3 -5.428655591934440e-01 -5.428655592065836e-01 1.31396e-11 6.61089e-11 ----------------------------------------------------------------------------------------------------- * 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 = 4, direction = 3: |F_model - F_numer| error = ----------------------- = 4.93211e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = C Pd | a0 = 3.669341514229472 | (Configuration in file "config-CPd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 9.373187428342671e-01 9.373187428487813e-01 1.45142e-11 1.37165e-11 2 7.678307499248533e-01 7.678307499246223e-01 2.31037e-13 2.64780e-10 3 8.785146910647738e-01 8.785146910594362e-01 5.33751e-12 4.24623e-11 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -6.375085343155209e-01 -6.375085343384470e-01 2.29261e-11 6.57790e-11 2 -2.895603105122999e+00 -2.895603105078490e+00 4.45088e-11 4.35079e-11 3 -2.896306280373283e-01 -2.896306280282460e-01 9.08223e-12 3.03438e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -3.580467719559798e+00 -3.580467719613283e+00 5.34852e-11 1.75620e-10 2 4.575463112956828e-01 4.575463112815153e-01 1.41675e-11 4.70481e-10 3 -6.224329093750716e-01 -6.224329093132764e-01 6.17951e-11 1.41589e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 1.749030410910865e-01 1.749030411098376e-01 1.87511e-11 8.86178e-11 2 5.391824545475310e-01 5.391824545430807e-01 4.45033e-12 1.51588e-10 3 -2.625806212491734e+00 -2.625806212471276e+00 2.04579e-11 6.19136e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -2.320648499034568e+00 -2.320648499021468e+00 1.30997e-11 9.99916e-11 2 8.734846393300478e-01 8.734846393521090e-01 2.20611e-11 4.70568e-11 3 -7.474205486023479e-01 -7.474205485992558e-01 3.09208e-12 4.73073e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -2.654748052279718e-01 -2.654748052464406e-01 1.84688e-11 8.03158e-11 2 9.880340205752943e-01 9.880340205789552e-01 3.66085e-12 1.56192e-10 3 -4.787733617944536e-01 -4.787733617899935e-01 4.46004e-12 4.21553e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.037225566505761e+00 -1.037225566508326e+00 2.56484e-12 5.89730e-10 2 -8.431848378685197e-02 -8.431848378497635e-02 1.87562e-12 1.44465e-10 3 2.534194055215570e+00 2.534194055183593e+00 3.19766e-11 1.20355e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -7.232883252383856e+00 -7.232883252438780e+00 5.49241e-11 1.04266e-10 2 -1.012073556716679e+00 -1.012073556753643e+00 3.69638e-11 7.61172e-10 3 -7.523259712574864e+00 -7.523259712506513e+00 6.83515e-11 8.66257e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -3.435926402559185e+00 -3.435926402570410e+00 1.12252e-11 1.00999e-10 2 -7.882671555930212e+00 -7.882671555973033e+00 4.28209e-11 1.89603e-10 3 -4.364972286672235e+00 -4.364972286687315e+00 1.50795e-11 3.73964e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 3.294353923618555e+00 3.294353923568951e+00 4.96039e-11 1.90163e-10 2 1.231116824492396e+00 1.231116824452367e+00 4.00289e-11 2.96168e-10 3 -6.681065486960731e-01 -6.681065486683527e-01 2.77204e-11 2.42302e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 1.639269495944487e+00 1.639269495980461e+00 3.59739e-11 1.87720e-09 * 2 -2.550394377028975e+00 -2.550394376906708e+00 1.22267e-10 1.47574e-09 * 3 7.384938029567458e-01 7.384938030399315e-01 8.31857e-11 9.55001e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -3.309088295114469e+00 -3.309088295152219e+00 3.77494e-11 2.89051e-10 2 5.020968803484729e+00 5.020968803404998e+00 7.97309e-11 4.10092e-10 3 2.569239178026231e+00 2.569239178063303e+00 3.70721e-11 3.24031e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 8.554311857465475e-01 8.554311857896533e-01 4.31057e-11 4.53860e-10 2 3.410764293914401e+00 3.410764293912545e+00 1.85585e-12 2.93698e-10 3 -2.173584662417472e+00 -2.173584662436207e+00 1.87352e-11 1.77240e-09 * ----------------------------------------------------------------------------------------------------- 14 Pd 1 -2.539564590955766e+00 -2.539564590860125e+00 9.56408e-11 1.44771e-10 2 -1.534723340914010e+00 -1.534723340847304e+00 6.67060e-11 3.13545e-10 3 -4.863336377365126e-01 -4.863336377070019e-01 2.95107e-11 6.32914e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 3.428163337839647e+00 3.428163337893611e+00 5.39639e-11 1.26051e-10 2 -1.611850490740814e+00 -1.611850490705286e+00 3.55278e-11 1.83361e-10 3 4.589269303054151e-01 4.589269302895586e-01 1.58565e-11 1.34081e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -9.629302413539728e-01 -9.629302413498726e-01 4.10016e-12 6.34709e-10 2 1.604833774905992e+00 1.604833774903241e+00 2.75069e-12 1.15639e-10 3 1.927772754270588e+00 1.927772754330093e+00 5.95053e-11 1.23213e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 1.608202329278602e+00 1.608202329310747e+00 3.21456e-11 1.99235e-10 2 -8.351622749978774e-01 -8.351622749638273e-01 3.40501e-11 8.36180e-11 3 1.525513476187226e+00 1.525513476155621e+00 3.16052e-11 3.16420e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.087555228112421e-01 5.087555226645279e-01 1.46714e-10 5.18606e-10 2 7.211434322425329e-01 7.211434322376542e-01 4.87865e-12 9.10222e-11 3 -2.670392337615584e+00 -2.670392337520654e+00 9.49298e-11 8.14353e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 -9.271080996701976e-01 -9.271080996619369e-01 8.26073e-12 1.21231e-10 2 1.688476800691088e-01 1.688476800226843e-01 4.64245e-11 3.47558e-10 3 -6.836061580708508e-01 -6.836061580380977e-01 3.27531e-11 9.44801e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 9.982213259693088e-01 9.982213259738715e-01 4.56268e-12 3.99821e-10 2 -3.283489336150041e-01 -3.283489336391336e-01 2.41295e-11 2.32257e-10 3 -7.617325606642976e-01 -7.617325606467380e-01 1.75596e-11 2.86018e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 3.859284303287591e+00 3.859284303237164e+00 5.04263e-11 4.01321e-10 2 3.758574149019930e-01 3.758574148903919e-01 1.16011e-11 1.26784e-10 3 9.604259518445475e-01 9.604259518288522e-01 1.56953e-11 2.49549e-09 * ----------------------------------------------------------------------------------------------------- 22 Pd 1 1.111277267125739e+01 1.111277267130868e+01 5.12888e-11 2.97461e-09 * 2 -3.379864704005255e+00 -3.379864704077491e+00 7.22364e-11 2.68351e-10 3 9.932666187314096e+00 9.932666187467452e+00 1.53356e-10 1.99916e-09 * ----------------------------------------------------------------------------------------------------- 23 C 1 -9.384786908139160e-01 -9.384786908073292e-01 6.58684e-12 6.65322e-11 2 3.669198591723847e-01 3.669198591729232e-01 5.38458e-13 3.03918e-10 3 -1.202003989106739e+00 -1.202003989105139e+00 1.60028e-12 2.65434e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 1.422201775815447e-01 1.422201776221791e-01 4.06344e-11 3.17750e-11 2 -1.149653602157974e+00 -1.149653602285112e+00 1.27138e-10 3.04416e-10 3 -5.539009762271248e-01 -5.539009764336336e-01 2.06509e-10 7.77520e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -1.393029328080309e-01 -1.393029327235245e-01 8.45064e-11 3.43628e-10 2 1.514243218384046e+00 1.514243218350978e+00 3.30687e-11 9.45326e-10 3 -3.594362718328666e-01 -3.594362718017057e-01 3.11609e-11 2.93463e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 -3.826309068205853e-01 -3.826309068046827e-01 1.59026e-11 5.68064e-11 2 1.689536617635533e+00 1.689536617712349e+00 7.68166e-11 7.48883e-11 3 4.670974431623135e+00 4.670974431781031e+00 1.57896e-10 1.28162e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 -1.450604129993883e+00 -1.450604130073617e+00 7.97338e-11 2.94970e-10 2 1.476281872121258e+00 1.476281871993484e+00 1.27774e-10 3.67908e-10 3 7.572911123584021e-01 7.572911124356489e-01 7.72469e-11 3.79009e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 2.047777649955543e+00 2.047777649970730e+00 1.51870e-11 2.16479e-10 2 -9.445638879952154e-01 -9.445638879971268e-01 1.91136e-12 1.74372e-10 3 -1.809877848267891e+00 -1.809877848266877e+00 1.01452e-12 1.30977e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -3.359001721596019e+00 -3.359001721619995e+00 2.39764e-11 1.67843e-09 * 2 -2.625101544800884e-01 -2.625101544860772e-01 5.98877e-12 2.14616e-10 3 -2.119597580845679e+00 -2.119597580913451e+00 6.77720e-11 1.12880e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 -7.548615059604187e-02 -7.548615059637609e-02 3.34219e-13 2.05204e-09 * 2 4.595759823121642e-01 4.595759823234590e-01 1.12949e-11 3.04628e-10 3 2.544696670606569e-01 2.544696670997308e-01 3.90739e-11 3.67956e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 3.896119327991126e+00 3.896119327965206e+00 2.59202e-11 6.27027e-11 2 -1.524023451171871e+00 -1.524023451143247e+00 2.86235e-11 5.22085e-11 3 2.741377942269195e-01 2.741377942273066e-01 3.87024e-13 5.56322e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 -1.908462495897393e+00 -1.908462495910645e+00 1.32516e-11 5.74363e-10 2 4.329593969353871e+00 4.329593969370730e+00 1.68594e-11 1.02634e-10 3 2.658248198574818e+00 2.658248198578327e+00 3.50875e-12 3.64780e-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 = 25, direction = 1: |F_model - F_numer| error = ----------------------- = 6.06637e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.93211e-09 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: A Comment: The letter grade A was assigned because the normalized error in the computation was 4.93211e-09 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.