!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : EAM_Dynamo_LandaWynblattSiegel_2000_AlPb__MO_699137396381_005 Supported species : Al Pb 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 = 4.03103637695 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.599866776178768e-01 1.599866776411946e-01 2.33178e-11 1.29831e-10 2 -8.876071716313903e-02 -8.876071721959690e-02 5.64579e-11 3.16803e-10 3 -3.888217056248213e-01 -3.888217056319256e-01 7.10426e-12 1.31572e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -3.988240747470976e-01 -3.988240748139469e-01 6.68493e-11 4.56101e-10 2 8.454171049675161e-01 8.454171050003547e-01 3.28386e-11 2.42164e-08 * 3 6.318095309131228e-01 6.318095309461444e-01 3.30217e-11 8.89803e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 4.677623094059001e-01 4.677623106604835e-01 1.25458e-09 1.69177e-09 2 6.128897738007444e-01 6.128897738779965e-01 7.72521e-11 1.74336e-09 3 9.447265438152339e-01 9.447265437979119e-01 1.73220e-11 9.55666e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 6.745119471409325e-01 6.745119467004282e-01 4.40504e-10 3.93131e-10 2 4.106489063686934e-01 4.106489063334616e-01 3.52318e-11 9.74174e-10 3 9.466520925216094e-01 9.466520924730856e-01 4.85239e-11 7.56852e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 3.084813391440985e-01 3.084813391337290e-01 1.03695e-11 3.09755e-10 2 4.187037687992391e-02 4.187037764742108e-02 7.67497e-10 1.78610e-09 3 1.879818460778614e-02 1.879818410182973e-02 5.05956e-10 1.94393e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 -7.254138915042546e-01 -7.254138915379209e-01 3.36663e-11 1.73380e-10 2 4.467129265191104e-01 4.467129264950612e-01 2.40493e-11 1.75476e-10 3 6.341390949695834e-01 6.341390949380152e-01 3.15682e-11 1.67415e-11 ----------------------------------------------------------------------------------------------------- 7 Al 1 1.222492549770055e+00 1.222492549828723e+00 5.86677e-11 5.81660e-10 2 -2.072748476830057e+00 -2.072748476806052e+00 2.40057e-11 8.21032e-11 3 -2.376642895083080e+00 -2.376642895143879e+00 6.07989e-11 3.74684e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.190170476696882e+00 -2.190170476614071e+00 8.28111e-11 2.17193e-10 2 -1.700767178504897e-01 -1.700767177518691e-01 9.86207e-11 4.03035e-10 3 -6.032300440929550e-01 -6.032300441014851e-01 8.53007e-12 3.99741e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.167434426970871e-01 -1.167434426325445e-01 6.45426e-11 2.83826e-09 2 -1.687672001889426e+00 -1.687672001828591e+00 6.08351e-11 3.11859e-10 3 -1.936323473382582e+00 -1.936323473562276e+00 1.79694e-10 8.77645e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.298938150866964e-01 -6.298938151377492e-01 5.10528e-11 2.56815e-08 * 2 1.465829629557817e-01 1.465829629932132e-01 3.74315e-11 1.98045e-10 3 -6.764358458437633e-01 -6.764358457300967e-01 1.13667e-10 2.74472e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.122017090110819e+00 1.122017090247826e+00 1.37007e-10 2.60205e-09 2 -1.127989071727046e+00 -1.127989071745973e+00 1.89275e-11 1.08450e-09 3 1.170516754088750e+00 1.170516754251356e+00 1.62605e-10 7.52402e-08 * ----------------------------------------------------------------------------------------------------- 12 Al 1 6.608743672933109e-02 6.608743673853605e-02 9.20496e-12 2.07607e-10 2 1.609118960466695e+00 1.609118960530461e+00 6.37657e-11 3.43337e-09 3 1.847641134169634e+00 1.847641134148386e+00 2.12481e-11 1.38389e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -1.422035350925690e+00 -1.422035350742707e+00 1.82983e-10 5.13379e-10 2 -1.616079113901065e+00 -1.616079113986519e+00 8.54541e-11 1.10594e-09 3 -2.109858103942639e+00 -2.109858103996043e+00 5.34039e-11 6.84867e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 6.606015802576262e-02 6.606015800877083e-02 1.69918e-11 9.13739e-10 2 6.131667532415067e-01 6.131667532340717e-01 7.43505e-12 6.48511e-10 3 -1.018841378091153e-01 -1.018841378114288e-01 2.31347e-12 2.04277e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 2.194244582953139e+00 2.194244582927332e+00 2.58065e-11 3.44394e-10 2 -6.041680197197719e-01 -6.041680196860104e-01 3.37614e-11 2.45652e-10 3 1.621752042705666e+00 1.621752042658655e+00 4.70108e-11 3.08759e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.798436718382565e-01 5.798436718475147e-01 9.25826e-12 5.26708e-11 2 1.286854471572007e+00 1.286854471529927e+00 4.20808e-11 1.89922e-10 3 1.149955849525619e+00 1.149955849580702e+00 5.50822e-11 1.95600e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -4.910772102142652e-01 -4.910772102031236e-01 1.11416e-11 6.68410e-10 2 2.333763523834749e-01 2.333763526356505e-01 2.52176e-10 2.15605e-10 3 -9.913079837394253e-01 -9.913079837405823e-01 1.15696e-12 6.32586e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 3.557184404797021e-01 3.557184404330471e-01 4.66550e-11 1.10662e-09 2 1.363269687895047e+00 1.363269687969146e+00 7.40992e-11 4.85864e-10 3 -1.468126963309244e+00 -1.468126963463276e+00 1.54031e-10 2.63070e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 9.321343647433175e-01 9.321343647253130e-01 1.80045e-11 7.12503e-10 2 -4.879810830509935e-01 -4.879810830469072e-01 4.08634e-12 2.17578e-10 3 7.169263909750423e-01 7.169263909209581e-01 5.40842e-11 6.38338e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 2.918257005257626e-01 2.918257005194826e-01 6.27998e-12 2.11713e-10 2 6.707595070976520e-01 6.707595070232960e-01 7.43560e-11 9.15953e-11 3 -2.344385969594158e-01 -2.344385970135889e-01 5.41732e-11 8.36886e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -2.354469605301637e+00 -2.354469605299641e+00 1.99529e-12 1.32888e-10 2 -2.998425680021884e-01 -2.998425679960674e-01 6.12105e-12 6.31768e-11 3 8.048262259495002e-01 8.048262260020324e-01 5.25322e-11 5.58566e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 8.045897693518921e-01 8.045897684898272e-01 8.62065e-10 2.65499e-09 2 2.724851593259795e+00 2.724851593345208e+00 8.54135e-11 6.62122e-09 * 3 1.281795009239075e+00 1.281795009208089e+00 3.09857e-11 1.81496e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 3.782249218766463e-02 3.782249220705415e-02 1.93895e-11 9.26301e-11 2 8.467998566638225e-02 8.467998563107849e-02 3.53038e-11 7.08721e-11 3 5.962623765945221e-01 5.962623767055993e-01 1.11077e-10 9.23851e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.750685949682092e-01 1.750685950650421e-01 9.68329e-11 7.70155e-10 2 4.030473785747953e-01 4.030473786141428e-01 3.93475e-11 3.27305e-11 3 -5.131389690383369e-01 -5.131389690711015e-01 3.27646e-11 6.23326e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.645697339169780e-01 -2.645697339141788e-01 2.79921e-12 6.14679e-10 2 -1.333470767046530e+00 -1.333470767032238e+00 1.42923e-11 2.65547e-10 3 -9.387667903936707e-01 -9.387667905101849e-01 1.16514e-10 5.10837e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.543784676493498e-01 -4.543784676131311e-01 3.62187e-11 7.74664e-10 2 4.112223751903507e-01 4.112223751676046e-01 2.27461e-11 5.24175e-10 3 -7.853805346866152e-01 -7.853805347308270e-01 4.42119e-11 3.26629e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.324819537894586e+00 1.324819537347848e+00 5.46737e-10 2.89539e-09 2 -2.615012870093155e+00 -2.615012870184717e+00 9.15628e-11 5.29777e-10 3 1.928312410064629e-01 1.928312410349532e-01 2.84903e-11 1.41801e-07 * ----------------------------------------------------------------------------------------------------- 28 Al 1 -1.180904947282336e+00 -1.180904947250641e+00 3.16949e-11 1.57954e-10 2 1.649598354804294e+00 1.649598354822574e+00 1.82798e-11 1.84905e-11 3 2.267350908298234e-01 2.267350908681678e-01 3.83444e-11 4.75195e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.076488646873558e+00 -1.076488646722918e+00 1.50640e-10 2.48038e-09 2 -7.003640271724294e-01 -7.003640269075893e-01 2.64840e-10 2.14031e-09 3 2.967636377174774e-01 2.967636381887249e-01 4.71247e-10 2.44044e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -6.094317713546069e-01 -6.094317712748326e-01 7.97743e-11 1.08872e-09 2 3.406115119222222e-01 3.406115119184753e-01 3.74684e-12 2.49766e-10 3 -8.179080599137477e-01 -8.179080599348060e-01 2.10583e-11 9.50927e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 6.134963118119781e-01 6.134963118164209e-01 4.44289e-12 3.30824e-09 2 -1.515725804072183e+00 -1.515725804071418e+00 7.65166e-13 1.29428e-10 3 8.235438967967478e-01 8.235438967823980e-01 1.43497e-11 5.91081e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.174384595511541e-01 5.174384595743035e-01 2.31494e-11 1.24533e-08 * 2 4.252122549524821e-01 4.252122540989077e-01 8.53574e-10 2.14027e-09 3 3.658900739375698e-02 3.658900737299740e-02 2.07596e-11 1.80620e-09 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 5, direction = 3: |F_model - F_numer| error = ----------------------- = 2.69152e-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 = Pb | a0 = 4.90912237167 | (Configuration in file "config-Pb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pb 1 3.565197336473957e-01 3.565197336530070e-01 5.61129e-12 9.98172e-11 2 3.553656944128213e-01 3.553656944116696e-01 1.15169e-12 7.10342e-11 3 3.193535740371683e-01 3.193535740428500e-01 5.68168e-12 2.47215e-11 ----------------------------------------------------------------------------------------------------- 2 Pb 1 3.066522099740658e-01 3.066522099796714e-01 5.60552e-12 3.13688e-10 2 1.173455927492410e-01 1.173455926977646e-01 5.14764e-11 2.05582e-11 3 4.419267680837328e-01 4.419267680871364e-01 3.40367e-12 8.52634e-11 ----------------------------------------------------------------------------------------------------- 3 Pb 1 2.401918503547143e-01 2.401918503271039e-01 2.76104e-11 5.67619e-10 2 5.260710620352806e-01 5.260710620310498e-01 4.23084e-12 1.29220e-10 3 1.446359667430388e-01 1.446359666164040e-01 1.26635e-10 1.87090e-09 * ----------------------------------------------------------------------------------------------------- 4 Pb 1 4.028110581311520e-01 4.028110581201718e-01 1.09802e-11 4.47217e-11 2 2.085317219876045e-01 2.085317219865604e-01 1.04411e-12 2.06338e-10 3 8.828596688733521e-02 8.828596690482825e-02 1.74930e-11 3.32405e-11 ----------------------------------------------------------------------------------------------------- 5 Pb 1 -1.764098317184508e-01 -1.764098317113196e-01 7.13121e-12 2.03072e-10 2 3.458845109112085e-01 3.458845109626709e-01 5.14624e-11 3.27463e-10 3 3.297759896203819e-01 3.297759895944543e-01 2.59276e-11 7.32454e-11 ----------------------------------------------------------------------------------------------------- 6 Pb 1 -3.092927198419038e-01 -3.092927198364261e-01 5.47773e-12 5.22062e-11 2 3.812800485583150e-01 3.812800485644803e-01 6.16523e-12 6.43245e-11 3 1.423618108193911e-01 1.423618108104366e-01 8.95450e-12 1.86153e-10 ----------------------------------------------------------------------------------------------------- 7 Pb 1 -1.582214769367928e-01 -1.582214769211400e-01 1.56528e-11 1.17477e-09 * 2 -7.218288778486738e-02 -7.218288777296102e-02 1.19064e-11 1.95126e-11 3 4.131998990959528e-01 4.131998991291921e-01 3.32393e-11 1.34395e-10 ----------------------------------------------------------------------------------------------------- 8 Pb 1 -5.793791316948053e-01 -5.793791316952995e-01 4.94271e-13 8.13971e-11 2 3.735125473585861e-01 3.735125473572783e-01 1.30779e-12 1.92007e-10 3 2.330140756897456e-01 2.330140756792535e-01 1.04921e-11 5.45024e-11 ----------------------------------------------------------------------------------------------------- 9 Pb 1 3.558850757972312e-01 3.558850757922102e-01 5.02104e-12 2.60214e-10 2 -8.616478077491788e-02 -8.616478077017671e-02 4.74117e-12 2.00782e-10 3 4.060452031882586e-01 4.060452032084587e-01 2.02001e-11 8.35068e-11 ----------------------------------------------------------------------------------------------------- 10 Pb 1 1.018756038642794e-01 1.018756039239390e-01 5.96597e-11 6.24313e-11 2 -4.053457586453126e-01 -4.053457586459455e-01 6.32938e-13 6.85256e-11 3 2.541668556489474e-01 2.541668556526534e-01 3.70604e-12 6.43949e-11 ----------------------------------------------------------------------------------------------------- 11 Pb 1 -9.680920415568650e-02 -9.680920414079994e-02 1.48866e-11 8.66038e-11 2 5.900150656896432e-02 5.900150659482199e-02 2.58577e-11 8.95116e-10 3 3.834744483182471e-02 3.834744479906168e-02 3.27630e-11 3.00385e-10 ----------------------------------------------------------------------------------------------------- 12 Pb 1 4.637812096088240e-01 4.637812096673096e-01 5.84856e-11 3.15932e-09 * 2 -3.915167782224862e-01 -3.915167781808788e-01 4.16073e-11 5.64030e-10 3 1.889339502507680e-01 1.889339502645130e-01 1.37450e-11 1.01485e-09 * ----------------------------------------------------------------------------------------------------- 13 Pb 1 -5.218159452888458e-01 -5.218159453009240e-01 1.20782e-11 8.20702e-11 2 -4.940834034560954e-01 -4.940834034887178e-01 3.26224e-11 1.45477e-09 * 3 3.438981447482765e-01 3.438981447483888e-01 1.12299e-13 2.71460e-11 ----------------------------------------------------------------------------------------------------- 14 Pb 1 6.075480024600061e-02 6.075480024947038e-02 3.46977e-12 6.93716e-11 2 -2.859657256241160e-02 -2.859657259234474e-02 2.99331e-11 6.38323e-11 3 1.550291859430682e-01 1.550291859413395e-01 1.72865e-12 1.23464e-10 ----------------------------------------------------------------------------------------------------- 15 Pb 1 -2.957849751338487e-01 -2.957849751251274e-01 8.72136e-12 1.16324e-10 2 -2.587352207623859e-01 -2.587352207338875e-01 2.84983e-11 1.67601e-10 3 5.835992360118095e-02 5.835992356444301e-02 3.67379e-11 1.16896e-10 ----------------------------------------------------------------------------------------------------- 16 Pb 1 -1.810106118307588e-01 -1.810106119213422e-01 9.05834e-11 8.92750e-10 2 -4.568826915108708e-01 -4.568826914932764e-01 1.75944e-11 4.91601e-10 3 3.772547805340146e-01 3.772547805492462e-01 1.52315e-11 1.67744e-10 ----------------------------------------------------------------------------------------------------- 17 Pb 1 3.492731513312479e-01 3.492731513223671e-01 8.88073e-12 2.04069e-10 2 -4.633643830807888e-03 -4.633643836337475e-03 5.52959e-12 1.87915e-11 3 -5.002514919950475e-01 -5.002514919953455e-01 2.97984e-13 1.33888e-10 ----------------------------------------------------------------------------------------------------- 18 Pb 1 2.528366460617991e-01 2.528366460874309e-01 2.56319e-11 2.04000e-11 2 -2.545792403637217e-01 -2.545792403395669e-01 2.41548e-11 1.07261e-10 3 -3.814219714486891e-01 -3.814219714518657e-01 3.17657e-12 9.14309e-10 ----------------------------------------------------------------------------------------------------- 19 Pb 1 2.801113040880903e-01 2.801113040820573e-01 6.03295e-12 5.76921e-11 2 1.944544086756530e-01 1.944544086795808e-01 3.92783e-12 4.47619e-11 3 -3.970085389333685e-01 -3.970085388120081e-01 1.21360e-10 7.87599e-10 ----------------------------------------------------------------------------------------------------- 20 Pb 1 8.694168315057753e-03 8.694168364149771e-03 4.90920e-11 3.04375e-10 2 6.774036384373709e-01 6.774036384935189e-01 5.61480e-11 1.26002e-10 3 2.670416736835524e-01 2.670416736905468e-01 6.99446e-12 2.18764e-10 ----------------------------------------------------------------------------------------------------- 21 Pb 1 -3.309089445057983e-01 -3.309089445073866e-01 1.58829e-12 2.72871e-10 2 3.077002821317762e-01 3.077002821415324e-01 9.75620e-12 4.33636e-11 3 -3.590283366395499e-01 -3.590283366500391e-01 1.04892e-11 4.03886e-09 * ----------------------------------------------------------------------------------------------------- 22 Pb 1 -2.095946308672511e-01 -2.095946309998749e-01 1.32624e-10 1.73173e-10 2 -1.719024916371352e-01 -1.719024915946680e-01 4.24673e-11 2.85701e-09 * 3 -7.027502575597334e-02 -7.027502576247886e-02 6.50552e-12 1.94675e-11 ----------------------------------------------------------------------------------------------------- 23 Pb 1 -9.357765636494654e-02 -9.357765636703741e-02 2.09087e-12 2.39692e-11 2 3.372866352577819e-01 3.372866352565140e-01 1.26793e-12 2.66158e-11 3 -1.747108171128211e-01 -1.747108171185598e-01 5.73866e-12 7.57552e-11 ----------------------------------------------------------------------------------------------------- 24 Pb 1 -2.252598519249940e-01 -2.252598519228432e-01 2.15081e-12 8.21315e-11 2 2.614062732707537e-01 2.614062732701850e-01 5.68656e-13 7.30213e-11 3 -3.971054056099862e-01 -3.971054056092166e-01 7.69607e-13 5.56794e-11 ----------------------------------------------------------------------------------------------------- 25 Pb 1 1.917879509411182e-01 1.917879509366922e-01 4.42593e-12 1.11197e-10 2 -4.137999634989318e-01 -4.137999635396073e-01 4.06755e-11 1.27576e-10 3 -1.857584003003163e-01 -1.857584002748954e-01 2.54209e-11 3.90055e-09 * ----------------------------------------------------------------------------------------------------- 26 Pb 1 3.041793202806095e-01 3.041793202757723e-01 4.83719e-12 3.89845e-10 2 -2.984061112252385e-01 -2.984061112147227e-01 1.05158e-11 7.77939e-12 3 -2.467755196937184e-01 -2.467755196794213e-01 1.42972e-11 1.08728e-10 ----------------------------------------------------------------------------------------------------- 27 Pb 1 1.024602307470472e-01 1.024602307444942e-01 2.55300e-12 5.81723e-10 2 -2.266304000989901e-02 -2.266304001448391e-02 4.58490e-12 1.54876e-10 3 -3.039195512385465e-01 -3.039195512388161e-01 2.69562e-13 1.56273e-10 ----------------------------------------------------------------------------------------------------- 28 Pb 1 4.198400337132780e-01 4.198400337190240e-01 5.74596e-12 9.48490e-11 2 -3.113977582910654e-01 -3.113977582969450e-01 5.87963e-12 4.43049e-11 3 -3.134265188297021e-01 -3.134265188455500e-01 1.58479e-11 1.27789e-10 ----------------------------------------------------------------------------------------------------- 29 Pb 1 -7.516023219097094e-02 -7.516023231634363e-02 1.25373e-10 1.68403e-09 * 2 2.260640954207162e-01 2.260640953483445e-01 7.23717e-11 7.08540e-10 3 -1.207944209216731e-01 -1.207944209396348e-01 1.79618e-11 1.85759e-11 ----------------------------------------------------------------------------------------------------- 30 Pb 1 -4.212535257089596e-01 -4.212535256987764e-01 1.01831e-11 6.21916e-09 * 2 -1.148535742227988e-01 -1.148535742209797e-01 1.81911e-12 1.37837e-10 3 6.351492950544227e-02 6.351492950474484e-02 6.97428e-13 2.58191e-10 ----------------------------------------------------------------------------------------------------- 31 Pb 1 -3.341276480892418e-01 -3.341276481098062e-01 2.05643e-11 1.63464e-10 2 -1.951808162774234e-01 -1.951808162649470e-01 1.24764e-11 2.52191e-10 3 -4.249845464409701e-01 -4.249845464545121e-01 1.35420e-11 4.37650e-11 ----------------------------------------------------------------------------------------------------- 32 Pb 1 -1.890479608486561e-01 -1.890479608365180e-01 1.21381e-11 2.51437e-10 2 -3.903832846997041e-01 -3.903832847046921e-01 4.98807e-12 1.38911e-10 3 -3.896855979917180e-01 -3.896855979898365e-01 1.88144e-12 1.60670e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 20, direction = 1: |F_model - F_numer| error = ----------------------- = 5.64655e-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 = Al Pb | a0 = 4.25874371249 | (Configuration in file "config-AlPb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 4.845195305192840e-01 4.845195305007852e-01 1.84988e-11 2.28237e-10 2 4.018749017266627e-01 4.018749016996199e-01 2.70428e-11 2.40136e-10 3 5.669274311057323e-01 5.669274311037100e-01 2.02227e-12 4.19241e-10 ----------------------------------------------------------------------------------------------------- 2 Pb 1 -9.902573291401445e-01 -9.902573299493670e-01 8.09222e-10 1.12757e-09 2 1.955104554707229e-01 1.955104554305916e-01 4.01313e-11 2.50182e-10 3 -4.023191072705627e-01 -4.023191073380080e-01 6.74453e-11 1.58402e-09 ----------------------------------------------------------------------------------------------------- 3 Al 1 -7.146037001447398e-01 -7.146037001016775e-01 4.30623e-11 1.35774e-09 2 1.615969112779923e-01 1.615969122862352e-01 1.00824e-09 9.52733e-09 * 3 -4.350517645051072e-01 -4.350517644662124e-01 3.88948e-11 4.19979e-10 ----------------------------------------------------------------------------------------------------- 4 Pb 1 -9.603598046930502e-01 -9.603598046922299e-01 8.20233e-13 4.61848e-09 * 2 -1.805768224107866e+00 -1.805768224152104e+00 4.42384e-11 3.12574e-10 3 -1.164580160168660e+00 -1.164580160152757e+00 1.59037e-11 6.92568e-11 ----------------------------------------------------------------------------------------------------- 5 Pb 1 1.177774883270666e+00 1.177774883263779e+00 6.88671e-12 7.80005e-11 2 -1.830563932447599e+00 -1.830563932418126e+00 2.94733e-11 1.44389e-10 3 -1.450636200593352e+00 -1.450636200518728e+00 7.46248e-11 1.45066e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -4.717597320158515e-01 -4.717597319880198e-01 2.78316e-11 4.77502e-10 2 -1.271302604874112e+00 -1.271302604852278e+00 2.18336e-11 2.07631e-09 3 -1.345279535413937e+00 -1.345279535422858e+00 8.92109e-12 6.02292e-11 ----------------------------------------------------------------------------------------------------- 7 Pb 1 4.164237887190588e-01 4.164237887178834e-01 1.17545e-12 4.04252e-09 * 2 -1.585876936230159e+00 -1.585876936201145e+00 2.90137e-11 1.59479e-10 3 -4.870311269728667e-01 -4.870311269642453e-01 8.62138e-12 1.00606e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 3.631908959687996e-01 3.631908960322660e-01 6.34663e-11 1.03328e-10 2 3.279868821722031e-01 3.279868821477460e-01 2.44571e-11 1.45893e-09 3 -8.785591414117354e-01 -8.785591414174753e-01 5.73985e-12 5.61130e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -4.593243561794190e-01 -4.593243561844992e-01 5.08016e-12 1.39261e-10 2 1.767769660058055e-01 1.767769660244053e-01 1.85998e-11 2.60762e-10 3 -8.021948381256588e-01 -8.021948381318801e-01 6.22125e-12 1.45902e-10 ----------------------------------------------------------------------------------------------------- 10 Pb 1 7.717266772354643e-02 7.717266771871964e-02 4.82679e-12 9.17748e-10 2 7.654159660476131e-01 7.654159660253389e-01 2.22742e-11 4.95483e-10 3 -1.585949557381510e+00 -1.585949557396604e+00 1.50939e-11 9.64029e-11 ----------------------------------------------------------------------------------------------------- 11 Pb 1 -3.173897884236045e+00 -3.173897884309973e+00 7.39280e-11 3.60953e-10 2 7.811097556046470e-01 7.811097563052285e-01 7.00581e-10 2.51237e-09 * 3 -3.686272695786494e+00 -3.686272695888848e+00 1.02355e-10 3.94653e-10 ----------------------------------------------------------------------------------------------------- 12 Pb 1 -1.633687389166258e+00 -1.633687389146708e+00 1.95508e-11 6.82636e-11 2 8.912634412147228e-01 8.912634412332853e-01 1.85625e-11 2.94869e-10 3 -2.227382488660008e-01 -2.227382488518015e-01 1.41993e-11 1.56165e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 1.018025343613365e+00 1.018025343481164e+00 1.32201e-10 1.17677e-09 2 -3.883745209294583e-01 -3.883745208600517e-01 6.94066e-11 5.32923e-10 3 -1.573485664499337e+00 -1.573485664508864e+00 9.52660e-12 2.55400e-10 ----------------------------------------------------------------------------------------------------- 14 Pb 1 1.076774909554569e+00 1.076774909553613e+00 9.56124e-13 8.68103e-11 2 9.066627862173259e-01 9.066627862112961e-01 6.02973e-12 1.12511e-10 3 -1.086420027102265e+00 -1.086420027060681e+00 4.15834e-11 2.87136e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 4.784824687219880e-01 4.784824687457871e-01 2.37991e-11 2.23802e-10 2 1.240049645026538e+00 1.240049645032429e+00 5.89040e-12 1.97833e-10 3 1.783823001832632e+00 1.783823001795273e+00 3.73590e-11 1.06489e-10 ----------------------------------------------------------------------------------------------------- 16 Pb 1 1.063437264039270e+00 1.063437264085220e+00 4.59501e-11 1.28819e-10 2 2.305132034797973e+00 2.305132034880262e+00 8.22893e-11 1.49413e-09 3 -5.637536566506152e-02 -5.637536569438166e-02 2.93201e-11 1.32285e-10 ----------------------------------------------------------------------------------------------------- 17 Pb 1 -1.736806005377431e+00 -1.736806005388984e+00 1.15532e-11 7.52939e-10 2 -1.026985782626740e+00 -1.026985783104829e+00 4.78089e-10 1.97564e-09 3 -2.608296656313895e-01 -2.608296656374984e-01 6.10889e-12 6.20767e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -1.423018417794822e+00 -1.423018417808071e+00 1.32490e-11 1.10078e-09 2 -5.060914135744410e-01 -5.060914135448257e-01 2.96153e-11 7.97304e-10 3 1.145203848524521e+00 1.145203848507528e+00 1.69926e-11 5.57122e-10 ----------------------------------------------------------------------------------------------------- 19 Pb 1 1.895310226715767e-01 1.895310226773198e-01 5.74304e-12 1.53883e-10 2 -3.260838186840399e-01 -3.260838186781875e-01 5.85237e-12 1.10858e-10 3 1.663690999058407e+00 1.663690999059837e+00 1.42997e-12 8.21032e-12 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.273092376704552e-01 4.273092376626054e-01 7.84983e-12 1.32230e-10 2 6.395550211025798e-01 6.395550210619276e-01 4.06521e-11 2.63094e-10 3 -6.277079094791103e-01 -6.277079094434728e-01 3.56375e-11 7.21595e-10 ----------------------------------------------------------------------------------------------------- 21 Pb 1 1.326063412498665e+00 1.326063412494043e+00 4.62230e-12 1.84421e-09 2 -2.740199728417841e+00 -2.740199728418561e+00 7.19425e-13 1.20524e-10 3 -7.240808889483831e-01 -7.240808888469226e-01 1.01461e-10 2.00131e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 7.581146263694153e-01 7.581146263665602e-01 2.85505e-12 1.12415e-09 2 5.847058973765947e-01 5.847058973501320e-01 2.64627e-11 7.81199e-10 3 1.174050093688937e+00 1.174050093708894e+00 1.99571e-11 2.91293e-09 * ----------------------------------------------------------------------------------------------------- 23 Pb 1 6.217953359598414e-01 6.217953359603517e-01 5.10370e-13 1.59450e-12 2 -2.922233582473875e-01 -2.922233585481314e-01 3.00744e-10 4.89239e-10 3 2.152877764201904e-01 2.152877764271178e-01 6.92738e-12 1.44526e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.290351109918759e-01 1.290351110213380e-01 2.94621e-11 2.00953e-10 2 1.214991021917571e+00 1.214991021933278e+00 1.57072e-11 5.58652e-10 3 1.601572281259313e+00 1.601572281264953e+00 5.64038e-12 1.78832e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -7.300301718958812e-01 -7.300301718803294e-01 1.55518e-11 6.83656e-10 2 2.272573331156372e-01 2.272573331058665e-01 9.77066e-12 2.10236e-10 3 1.986287788279746e+00 1.986287788328020e+00 4.82743e-11 1.65484e-10 ----------------------------------------------------------------------------------------------------- 26 Pb 1 1.242478055525395e+00 1.242478055515268e+00 1.01270e-11 2.80626e-10 2 1.074803957061749e+00 1.074803957088599e+00 2.68501e-11 2.17621e-10 3 -1.052800623441269e+00 -1.052800623435125e+00 6.14397e-12 2.73668e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 -4.849554943765049e-01 -4.849554943826229e-01 6.11805e-12 2.94268e-10 2 -9.155162454507304e-01 -9.155162454567674e-01 6.03695e-12 9.55265e-11 3 7.249022658633233e-01 7.249022658627274e-01 5.95857e-13 3.73420e-10 ----------------------------------------------------------------------------------------------------- 28 Pb 1 -2.379642553139047e+00 -2.379642553169383e+00 3.03357e-11 1.40015e-10 2 4.914226503016099e-01 4.914226502960358e-01 5.57410e-12 1.17696e-10 3 2.326829248776139e+00 2.326829248774001e+00 2.13740e-12 1.92204e-10 ----------------------------------------------------------------------------------------------------- 29 Pb 1 4.562234440877887e+00 4.562234440871131e+00 6.75637e-12 1.07739e-09 2 6.958400022132057e-01 6.958400021983137e-01 1.48921e-11 1.22621e-10 3 5.110407841602760e+00 5.110407841605338e+00 2.57749e-12 3.57150e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -2.238445675028731e-01 -2.238445675152683e-01 1.23952e-11 6.82927e-11 2 -2.774105787623267e-01 -2.774105788092593e-01 4.69326e-11 6.99163e-10 3 1.458987434939258e-01 1.458987434894636e-01 4.46221e-12 7.46216e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.052279396096291e-01 -4.052279395915329e-01 1.80962e-11 1.53168e-10 2 -1.418567513215616e-01 -1.418567513679953e-01 4.64337e-11 2.09805e-09 3 -5.310188558001648e-01 -5.310188558053668e-01 5.20195e-12 6.20890e-11 ----------------------------------------------------------------------------------------------------- 32 Al 1 3.750523505760380e-01 3.750523505728032e-01 3.23480e-12 5.18616e-11 2 2.629826702310820e-02 2.629826703385789e-02 1.07497e-11 1.30572e-10 3 -7.154994284276055e-02 -7.154994286560729e-02 2.28467e-11 2.76070e-09 * ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 23, direction = 2: |F_model - F_numer| error = ----------------------- = 1.02916e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.69152e-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 2.69152e-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.