!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MishinMehlPapaconstantopoulos_2002_NiAl__MO_109933561507_005 Supported species : Al Ni 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 = 4.05152664185 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 5.344203440740556e-02 5.344203435351810e-02 5.38875e-11 1.20833e-10 2 -1.841151957609723e-01 -1.841151957127955e-01 4.81769e-11 1.82709e-10 3 -5.187490858726265e-01 -5.187490858626738e-01 9.95271e-12 8.97664e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.311416289221889e+00 -1.311416289168747e+00 5.31417e-11 9.94675e-11 2 2.437587281248421e+00 2.437587281189909e+00 5.85123e-11 1.41538e-10 3 1.254095243268197e-01 1.254095242946271e-01 3.21926e-11 8.96904e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 3.349247020685360e-01 3.349247021139711e-01 4.54351e-11 7.66279e-10 2 -5.708355018572994e-01 -5.708355018727661e-01 1.54667e-11 2.78822e-10 3 7.483768682017953e-01 7.483768681379400e-01 6.38553e-11 2.74093e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 2.049191648416241e-01 2.049191648765288e-01 3.49047e-11 1.17526e-09 2 5.327586939533467e-01 5.327586939194368e-01 3.39100e-11 1.97866e-10 3 6.735427529908795e-01 6.735427530252002e-01 3.43207e-11 4.22813e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 1.747391575935610e+00 1.747391576143370e+00 2.07760e-10 3.33601e-10 2 -1.206946116690341e+00 -1.206946116744495e+00 5.41540e-11 5.98817e-10 3 2.599214130824401e-01 2.599214130277763e-01 5.46638e-11 4.57246e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -6.274188327138240e-01 -6.274188327316221e-01 1.77981e-11 2.82550e-10 2 6.211281368154077e-01 6.211281368308780e-01 1.54703e-11 2.35134e-10 3 5.150760459751934e-01 5.150760459110053e-01 6.41881e-11 2.34275e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 4.137743232537002e-01 4.137743232631871e-01 9.48686e-12 4.43767e-10 2 -3.374672879418014e+00 -3.374672879373033e+00 4.49809e-11 3.63475e-10 3 -3.791115903311939e+00 -3.791115903504826e+00 1.92887e-10 3.32488e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.082067886582775e+00 -2.082067886525994e+00 5.67808e-11 6.22164e-10 2 -1.006690834458817e+00 -1.006690834471783e+00 1.29659e-11 6.77579e-10 3 -7.400879949267607e-01 -7.400879947655191e-01 1.61242e-10 6.60236e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -4.771210260270035e-01 -4.771210260737827e-01 4.67791e-11 1.43335e-10 2 -1.488336336975163e+00 -1.488336336913687e+00 6.14762e-11 1.71928e-09 3 -1.957019264971726e+00 -1.957019265022296e+00 5.05695e-11 1.12554e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -9.080397694522589e-01 -9.080397693267804e-01 1.25479e-10 3.92596e-10 2 3.772461749830244e-01 3.772461749233998e-01 5.96246e-11 1.14851e-09 3 -1.238192647171847e+00 -1.238192647177726e+00 5.87952e-12 2.66698e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 4.206052861035862e+00 4.206052861028643e+00 7.21911e-12 9.97235e-10 2 -1.480863291351106e+00 -1.480863291422901e+00 7.17948e-11 1.14719e-10 3 -8.811498414997831e-01 -8.811498415924336e-01 9.26504e-11 3.76701e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.614740837002548e-01 -1.614740836958494e-01 4.40542e-12 5.59667e-10 2 2.400057041453755e+00 2.400057041499721e+00 4.59659e-11 2.28525e-10 3 6.080178490789342e-01 6.080178490787241e-01 2.10054e-13 1.25319e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 -2.356793734103928e+00 -2.356793734164229e+00 6.03002e-11 2.80487e-10 2 -2.305322067798892e+00 -2.305322067832420e+00 3.35278e-11 2.27497e-10 3 -3.666801245813500e+00 -3.666801245763629e+00 4.98712e-11 1.97402e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 -2.570950603150136e-02 -2.570950608159218e-02 5.00908e-11 1.92049e-11 2 2.022719418716379e-01 2.022719419918382e-01 1.20200e-10 1.94955e-10 3 3.550397305606442e-01 3.550397305384901e-01 2.21541e-11 4.77713e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 3.756131957148285e+00 3.756131957105989e+00 4.22964e-11 1.63630e-10 2 -6.376346574354891e-01 -6.376346574278859e-01 7.60314e-12 2.82457e-09 * 3 1.383109423124298e+00 1.383109423085263e+00 3.90343e-11 3.33020e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 6.949699060253812e-01 6.949699060002436e-01 2.51377e-11 6.78520e-10 2 2.074436885343573e+00 2.074436885335452e+00 8.12062e-12 2.02176e-10 3 1.890331863477884e+00 1.890331863426441e+00 5.14424e-11 2.96001e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.509035047725029e-02 4.509035047840129e-02 1.15100e-12 3.56446e-10 2 -7.837211342685095e-01 -7.837211343609145e-01 9.24050e-11 4.79256e-11 3 -1.469808248161468e+00 -1.469808248217551e+00 5.60829e-11 6.55231e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.282419106905501e-01 2.282419107534240e-01 6.28739e-11 6.02850e-10 2 1.377500938877435e+00 1.377500938942303e+00 6.48677e-11 1.68401e-10 3 8.332368481162391e-01 8.332368481707744e-01 5.45353e-11 1.52528e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 1.031346136844441e+00 1.031346136880627e+00 3.61864e-11 2.50660e-10 2 -1.108427066267096e-01 -1.108427066277639e-01 1.05431e-12 8.21144e-10 3 -4.342963965320537e-01 -4.342963966807457e-01 1.48692e-10 1.20096e-09 ----------------------------------------------------------------------------------------------------- 20 Al 1 1.707728970851626e-01 1.707728970887647e-01 3.60206e-12 2.35712e-10 2 2.010623673131616e+00 2.010623673139462e+00 7.84572e-12 5.36169e-10 3 5.361704314874475e-01 5.361704314231822e-01 6.42653e-11 7.47624e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -3.190595981972602e+00 -3.190595981957487e+00 1.51150e-11 6.43191e-10 2 6.075616845684061e-02 6.075616854193923e-02 8.50986e-11 3.01985e-10 3 -8.171495217263018e-01 -8.171495217066530e-01 1.96488e-11 3.08172e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 6.498885499031108e-01 6.498885499597408e-01 5.66299e-11 6.20414e-10 2 4.125630233499901e+00 4.125630233469203e+00 3.06981e-11 8.18502e-10 3 2.972617656509533e+00 2.972617656325967e+00 1.83566e-10 5.96112e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 1.368514164921441e+00 1.368514164914599e+00 6.84208e-12 1.63961e-09 2 1.168429265104898e-02 1.168429265726794e-02 6.21896e-12 1.76003e-10 3 1.740213508893252e+00 1.740213508878130e+00 1.51217e-11 1.58260e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 -5.884722357518034e-01 -5.884722356116427e-01 1.40161e-10 3.22606e-10 2 4.466592869432218e-01 4.466592871606381e-01 2.17416e-10 5.40604e-10 3 -8.466574983250615e-01 -8.466574981749267e-01 1.50135e-10 7.60410e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.185105635033410e+00 -2.185105635028360e+00 5.05063e-12 1.07747e-10 2 -1.320226838462243e+00 -1.320226838419357e+00 4.28859e-11 1.67766e-10 3 3.713915419776875e+00 3.713915419837891e+00 6.10156e-11 5.84457e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -8.269294374546465e-01 -8.269294374646806e-01 1.00341e-11 3.86991e-10 2 1.654164869579216e+00 1.654164869546251e+00 3.29645e-11 1.93520e-10 3 -2.033034426870015e+00 -2.033034426883443e+00 1.34279e-11 2.09991e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.986568317940143e+00 1.986568317766864e+00 1.73279e-10 1.02816e-09 2 -5.300369171746878e+00 -5.300369171843809e+00 9.69314e-11 4.81096e-10 3 6.180006551565347e-01 6.180006550506565e-01 1.05878e-10 6.96193e-11 ----------------------------------------------------------------------------------------------------- 28 Al 1 -2.376053897069202e+00 -2.376053896999493e+00 6.97091e-11 1.42374e-09 2 2.204860806564096e+00 2.204860806553613e+00 1.04836e-11 4.83489e-10 3 -2.231379342893333e-01 -2.231379343718790e-01 8.25457e-11 3.47412e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.113538392904574e+00 -1.113538392880187e+00 2.43876e-11 5.66825e-10 2 -1.073522425357546e+00 -1.073522425535580e+00 1.78034e-10 4.77842e-10 3 6.019731643088202e-01 6.019731643029007e-01 5.91949e-12 1.12261e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -4.771116344225454e-01 -4.771116344082221e-01 1.43234e-11 3.58872e-10 2 4.948393159207820e-01 4.948393160159570e-01 9.51750e-11 2.43369e-10 3 1.917199832869736e-01 1.917199832395669e-01 4.74067e-11 1.22545e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 9.908655653960052e-01 9.908655654094141e-01 1.34088e-11 4.70989e-10 2 -1.134565426620018e+00 -1.134565426635534e+00 1.55158e-11 9.54206e-10 3 2.979628934330593e-01 2.979628934229741e-01 1.00852e-11 1.70917e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 8.249539244677100e-01 8.249539243695688e-01 9.81412e-11 1.77843e-10 2 9.464588435346744e-01 9.464588434875868e-01 4.70876e-11 2.46904e-10 3 5.525639776847939e-01 5.525639777629975e-01 7.82036e-11 1.75364e-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 = 14, direction = 1: |F_model - F_numer| error = ----------------------- = 1.94834e-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. MONOATOMIC STRUCTURE -- Species = Ni | a0 = 3.4524641037 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 1.407304288928020e+00 1.407304288963156e+00 3.51359e-11 6.43727e-10 2 1.035545812769842e+00 1.035545812652562e+00 1.17280e-10 6.94661e-10 3 1.400598491963057e+00 1.400598492166406e+00 2.03349e-10 1.02870e-09 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -4.119659934235404e+00 -4.119659934196791e+00 3.86127e-11 7.20063e-10 2 2.571851976826636e+00 2.571851976860566e+00 3.39297e-11 5.72090e-10 3 -8.591653858351209e-01 -8.591653860121344e-01 1.77014e-10 7.87802e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 1.388405455980444e+00 1.388405455983437e+00 2.99294e-12 7.02782e-10 2 9.147631719445433e-01 9.147631719393217e-01 5.22160e-12 2.47483e-10 3 -9.962511689064825e-01 -9.962511689318327e-01 2.53503e-11 6.88814e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.548775965696487e+00 1.548775965671993e+00 2.44940e-11 6.57409e-10 2 1.094204415370863e+00 1.094204415329003e+00 4.18596e-11 5.89232e-10 3 -8.784552307725937e-01 -8.784552305443958e-01 2.28198e-10 1.87102e-09 ----------------------------------------------------------------------------------------------------- 5 Ni 1 1.801819270026628e+00 1.801819270053300e+00 2.66718e-11 3.70542e-10 2 -6.426176830491971e+00 -6.426176830580417e+00 8.84457e-11 8.70518e-10 3 -3.745884563317644e+00 -3.745884563132339e+00 1.85306e-10 7.04542e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 1.860293894791036e+00 1.860293894931952e+00 1.40917e-10 3.81749e-09 2 -2.711012446650590e+00 -2.711012446607154e+00 4.34359e-11 6.62485e-09 * 3 1.965364941064666e-01 1.965364938645486e-01 2.41918e-10 1.44124e-09 ----------------------------------------------------------------------------------------------------- 7 Ni 1 -1.859753428862982e+00 -1.859753428895113e+00 3.21307e-11 3.93077e-10 2 1.698131943336181e+00 1.698131943362910e+00 2.67286e-11 3.80577e-10 3 2.227705424951023e-02 2.227705430804615e-02 5.85359e-11 1.15306e-09 ----------------------------------------------------------------------------------------------------- 8 Ni 1 9.778046471103945e-01 9.778046470594949e-01 5.08996e-11 3.54039e-09 2 4.254740488722562e+00 4.254740488366283e+00 3.56279e-10 9.65228e-09 * 3 8.113718430164795e+00 8.113718430192050e+00 2.72546e-11 2.66208e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 1.746032929288364e+00 1.746032929109216e+00 1.79148e-10 9.88890e-10 2 -5.396343887406974e-02 -5.396343894857803e-02 7.45083e-11 6.05467e-10 3 1.978733420130232e+00 1.978733420016006e+00 1.14226e-10 2.41613e-09 ----------------------------------------------------------------------------------------------------- 10 Ni 1 3.227753411897205e-02 3.227753408739942e-02 3.15726e-11 5.50194e-10 2 -1.491700372515238e+00 -1.491700372162210e+00 3.53027e-10 6.99329e-10 3 1.942018751682218e+00 1.942018751824337e+00 1.42119e-10 1.43622e-09 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -8.280930814558829e-02 -8.280930802977352e-02 1.15815e-10 1.24312e-10 2 1.662351812489565e-01 1.662351810605235e-01 1.88433e-10 1.32810e-09 3 -5.439621445861801e-01 -5.439621446674286e-01 8.12486e-11 1.11509e-09 ----------------------------------------------------------------------------------------------------- 12 Ni 1 1.417905592941127e+00 1.417905592927829e+00 1.32983e-11 9.10384e-10 2 -1.832615649565052e+00 -1.832615649534956e+00 3.00959e-11 2.30171e-09 3 -2.171463766707971e-01 -2.171463766222262e-01 4.85709e-11 3.76123e-09 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -4.715647798521758e+00 -4.715647798503660e+00 1.80975e-11 8.67537e-09 * 2 3.061021899992929e+00 3.061021899834342e+00 1.58587e-10 2.42671e-10 3 -1.362662289015586e+00 -1.362662289191931e+00 1.76345e-10 3.84576e-09 ----------------------------------------------------------------------------------------------------- 14 Ni 1 3.400542395396303e+00 3.400542395393534e+00 2.76845e-12 9.99173e-10 2 -8.749106264624079e-01 -8.749106264938987e-01 3.14908e-11 6.33588e-10 3 -2.696870767886125e+00 -2.696870768071565e+00 1.85440e-10 7.23215e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.082281515964989e+00 1.082281515973700e+00 8.71014e-12 7.65115e-11 2 2.192937639736753e+00 2.192937639743256e+00 6.50280e-12 1.54162e-10 3 -1.120016096161869e+00 -1.120016096130433e+00 3.14360e-11 3.31345e-09 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -5.890788845909974e+00 -5.890788845925728e+00 1.57545e-11 7.13010e-10 2 -1.052525539183763e+00 -1.052525539109047e+00 7.47156e-11 5.65388e-10 3 4.387766507551104e+00 4.387766507641746e+00 9.06413e-11 8.63544e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.427586366402435e+00 -1.427586366444765e+00 4.23301e-11 3.42010e-10 2 -6.859697772089337e-01 -6.859697771442084e-01 6.47253e-11 3.61849e-10 3 2.156466089743872e+00 2.156466089952484e+00 2.08611e-10 3.75400e-09 ----------------------------------------------------------------------------------------------------- 18 Ni 1 2.638110996121001e+00 2.638110996071014e+00 4.99871e-11 9.00147e-10 2 2.296532974017756e+00 2.296532974162351e+00 1.44595e-10 2.07136e-10 3 -2.335443344959517e+00 -2.335443344985831e+00 2.63136e-11 1.39161e-09 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.192941368057714e+00 1.192941368169508e+00 1.11795e-10 3.33327e-10 2 -9.881993976616097e-01 -9.881993976838559e-01 2.22462e-11 8.27914e-10 3 -5.061831275840986e-01 -5.061831276067145e-01 2.26159e-11 4.42452e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 -4.665907039641677e-01 -4.665907039787074e-01 1.45398e-11 5.32584e-09 * 2 8.235337601267431e-01 8.235337601152729e-01 1.14702e-11 1.17006e-10 3 4.508475561545619e-01 4.508475560594972e-01 9.50647e-11 7.93477e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -8.357671476817409e-01 -8.357671477473652e-01 6.56243e-11 4.67179e-10 2 1.001957618642785e+00 1.001957618655310e+00 1.25244e-11 4.25646e-10 3 -7.408814363078785e-01 -7.408814361220327e-01 1.85846e-10 1.48202e-09 ----------------------------------------------------------------------------------------------------- 22 Ni 1 -5.543988972824166e-01 -5.543988973859030e-01 1.03486e-10 2.95040e-10 2 -2.554782463586383e+00 -2.554782463526964e+00 5.94182e-11 3.72055e-09 3 3.131238265688133e+00 3.131238265475006e+00 2.13127e-10 3.26565e-09 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -9.755081845942623e-01 -9.755081845906447e-01 3.61755e-12 9.97965e-09 * 2 1.461357040873594e+00 1.461357040946944e+00 7.33502e-11 4.06253e-10 3 -1.172445561352936e+00 -1.172445561339927e+00 1.30091e-11 4.25956e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 1.472764883954916e+00 1.472764883990866e+00 3.59497e-11 1.77037e-10 2 -1.512447607539204e+00 -1.512447607619198e+00 7.99947e-11 1.76927e-09 3 -2.268640271033823e-01 -2.268640271685302e-01 6.51479e-11 6.57540e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 1.457982277668440e+00 1.457982277611404e+00 5.70359e-11 4.41439e-10 2 1.182719133704406e+00 1.182719133453407e+00 2.50999e-10 2.68172e-10 3 -7.099512624870982e-01 -7.099512624194115e-01 6.76866e-11 1.10010e-09 ----------------------------------------------------------------------------------------------------- 26 Ni 1 3.758968389213230e-01 3.758968390373777e-01 1.16055e-10 5.73564e-10 2 -1.653997312434863e+00 -1.653997312421729e+00 1.31337e-11 3.58087e-10 3 -1.257870811985996e+00 -1.257870812104910e+00 1.18914e-10 5.14625e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 -5.758527647116867e+00 -5.758527646980447e+00 1.36420e-10 7.69100e-10 2 -9.107849072449954e-01 -9.107849071202710e-01 1.24724e-10 4.00625e-09 3 1.276915840901993e+00 1.276915841042580e+00 1.40587e-10 5.12605e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 9.543545443698596e-01 9.543545444708508e-01 1.00991e-10 3.78479e-10 2 -1.282976224302852e+00 -1.282976224075635e+00 2.27218e-10 4.37655e-10 3 -7.650798173580253e-01 -7.650798173778184e-01 1.97931e-11 7.38155e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 2.817095820832121e+00 2.817095820805459e+00 2.66618e-11 4.78992e-10 2 1.246946366783407e-01 1.246946366386956e-01 3.96451e-11 3.63759e-10 3 -3.919884316639894e+00 -3.919884316653198e+00 1.33049e-11 6.33797e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 -1.061148246149314e+00 -1.061148246148498e+00 8.16458e-13 3.33912e-10 2 -7.837273689219623e-01 -7.837273689854342e-01 6.34719e-11 1.11000e-08 * 3 8.952343163894259e-01 8.952343163278043e-01 6.16216e-11 3.99775e-09 ----------------------------------------------------------------------------------------------------- 31 Ni 1 -1.809413537660687e+00 -1.809413537515036e+00 1.45652e-10 5.94062e-10 2 -2.844718168323886e-01 -2.844718168832408e-01 5.08522e-11 5.67763e-10 3 -1.829294064693307e+00 -1.829294064676437e+00 1.68696e-11 1.65870e-09 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.985009826359456e+00 1.985009826284166e+00 7.52896e-11 9.20118e-10 2 1.220034085483387e+00 1.220034085563276e+00 7.98890e-11 4.63456e-10 3 -6.803942510083716e-02 -6.803942487590864e-02 2.24929e-10 7.30677e-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 = 32, direction = 3: |F_model - F_numer| error = ----------------------- = 3.30586e-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 Ni | a0 = 3.50791257595 | (Configuration in file "config-AlNi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 -2.844548149617617e-01 -2.844548148781271e-01 8.36346e-11 4.77349e-10 2 -2.666520428940843e+00 -2.666520428972531e+00 3.16880e-11 7.31726e-11 3 -2.192303331896769e+00 -2.192303331877823e+00 1.89457e-11 3.53562e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 1.427726645019447e+00 1.427726645192160e+00 1.72713e-10 2.22041e-09 2 -2.098645506912235e-01 -2.098645507186139e-01 2.73903e-11 9.65434e-10 3 -8.776064722985256e+00 -8.776064722785909e+00 1.99346e-10 1.01120e-09 ----------------------------------------------------------------------------------------------------- 3 Ni 1 -9.784498148794328e-01 -9.784498147995542e-01 7.98787e-11 5.80521e-10 2 -5.158414296951749e-01 -5.158414297347736e-01 3.95988e-11 4.98556e-10 3 1.514645419451667e+00 1.514645419499090e+00 4.74227e-11 9.43655e-09 * ----------------------------------------------------------------------------------------------------- 4 Ni 1 9.564518215913369e-01 9.564518216231565e-01 3.18195e-11 2.26983e-10 2 5.082163219077823e-02 5.082163214939992e-02 4.13783e-11 1.28212e-09 3 4.066804381539711e+00 4.066804381672382e+00 1.32671e-10 9.94354e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -8.372258840459361e+00 -8.372258840681951e+00 2.22590e-10 3.10025e-09 2 -1.402232973786383e+01 -1.402232973783898e+01 2.48495e-11 3.55529e-10 3 -1.554010434544374e+01 -1.554010434562981e+01 1.86072e-10 7.06933e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.683552716284586e+00 1.683552716373777e+00 8.91913e-11 6.49751e-10 2 3.611711929535985e+00 3.611711929542384e+00 6.39888e-12 1.63120e-10 3 -3.743547498443625e+00 -3.743547498496616e+00 5.29909e-11 3.46182e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 1.467010139405527e+01 1.467010139372401e+01 3.31264e-10 2.58309e-09 2 -8.014216155845221e+00 -8.014216156071312e+00 2.26091e-10 8.77844e-10 3 5.185781332356563e+00 5.185781332296582e+00 5.99814e-11 3.27783e-09 ----------------------------------------------------------------------------------------------------- 8 Al 1 2.109690318091173e+00 2.109690318091728e+00 5.55556e-13 8.82410e-10 2 1.413615703035865e+01 1.413615703032497e+01 3.36851e-11 1.35457e-09 3 1.557370338968363e+01 1.557370338974083e+01 5.72005e-11 1.00513e-09 ----------------------------------------------------------------------------------------------------- 9 Al 1 -9.336081468903629e+00 -9.336081468880826e+00 2.28031e-11 1.45534e-09 2 6.063719731479609e+00 6.063719731450656e+00 2.89528e-11 3.77175e-10 3 -4.892917632907740e-01 -4.892917632502948e-01 4.04791e-11 3.73953e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 1.382278508547085e+00 1.382278508475031e+00 7.20539e-11 6.61925e-10 2 -5.104103755768710e-01 -5.104103753026907e-01 2.74180e-10 3.17396e-10 3 1.371876206245724e+00 1.371876206144023e+00 1.01700e-10 9.29562e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 5.096172129741332e+00 5.096172129775989e+00 3.46567e-11 5.79209e-10 2 -9.377151256489333e-01 -9.377151254018148e-01 2.47119e-10 2.25616e-10 3 -6.821824065259854e+00 -6.821824065125366e+00 1.34488e-10 7.40002e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 5.877063100626588e-01 5.877063100069720e-01 5.56868e-11 3.07220e-10 2 7.941923971305678e-01 7.941923971989746e-01 6.84068e-11 1.50770e-10 3 -7.129044113615022e-01 -7.129044111735412e-01 1.87961e-10 2.77196e-10 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -3.644049964916522e+00 -3.644049964753915e+00 1.62606e-10 8.83966e-10 2 -4.099718015387858e+00 -4.099718015212897e+00 1.74961e-10 4.38064e-09 * 3 -8.691685632838375e-01 -8.691685633760561e-01 9.22186e-11 5.37937e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 5.227403511351434e+00 5.227403511321902e+00 2.95319e-11 1.77345e-09 2 3.916696267957395e+00 3.916696267801206e+00 1.56188e-10 1.78133e-09 3 -2.962005470943648e+00 -2.962005471001142e+00 5.74945e-11 3.91013e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 -4.190341400431328e-01 -4.190341400277169e-01 1.54159e-11 8.19049e-10 2 -2.088264621195501e+00 -2.088264620943920e+00 2.51581e-10 1.03853e-09 3 1.408013745530681e+00 1.408013746117423e+00 5.86742e-10 5.70357e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -4.354453955436989e+00 -4.354453955495790e+00 5.88019e-11 2.34533e-09 2 3.192891208317311e-01 3.192891208872340e-01 5.55029e-11 2.41100e-10 3 4.762316561406476e+00 4.762316561346226e+00 6.02505e-11 6.47470e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 1.749503012442128e+00 1.749503012454877e+00 1.27489e-11 5.99594e-10 2 1.783950753308307e+00 1.783950753258005e+00 5.03022e-11 3.04272e-09 3 -5.128993270556073e-01 -5.128993269326154e-01 1.22992e-10 5.20508e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.333406618707120e-01 2.333406617807957e-01 8.99162e-11 1.14551e-09 2 -4.318188015793695e+00 -4.318188015870406e+00 7.67102e-11 8.95030e-10 3 2.578546527440158e+00 2.578546527399295e+00 4.08638e-11 2.54184e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 2.882770155009445e-01 2.882770156398131e-01 1.38869e-10 9.39658e-10 2 1.862905790319467e+00 1.862905790418732e+00 9.92648e-11 2.89723e-10 3 -1.772950888253864e+00 -1.772950888280373e+00 2.65088e-11 4.56942e-09 * ----------------------------------------------------------------------------------------------------- 20 Al 1 -3.861670310587586e-01 -3.861670306929267e-01 3.65832e-10 3.11629e-10 2 -1.053541380153721e+00 -1.053541380175806e+00 2.20843e-11 1.80766e-10 3 -5.733040967882627e-02 -5.733040969746031e-02 1.86340e-11 1.45837e-09 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -4.132684846391580e+00 -4.132684846346596e+00 4.49845e-11 7.90116e-10 2 -3.394952454259568e+00 -3.394952454216163e+00 4.34048e-11 8.99039e-09 * 3 7.617957070933472e-01 7.617957070346341e-01 5.87131e-11 1.08936e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 5.326490534735971e+00 5.326490534642288e+00 9.36824e-11 7.75318e-11 2 9.974532181677409e+00 9.974532181597816e+00 7.95932e-11 2.83156e-09 3 1.294815715058374e+00 1.294815715009545e+00 4.88287e-11 1.08653e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 -6.412713329509236e-01 -6.412713325620623e-01 3.88861e-10 9.54813e-10 2 -1.950571528376378e+00 -1.950571528415674e+00 3.92963e-11 5.64161e-10 3 2.440606831462956e+00 2.440606831438842e+00 2.41145e-11 1.54329e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -1.389254444006054e+00 -1.389254442898574e+00 1.10748e-09 1.35472e-09 2 1.382354632766730e-03 1.382354643958514e-03 1.11918e-11 7.74692e-10 3 1.140314734031981e+00 1.140314734150306e+00 1.18325e-10 3.90613e-09 ----------------------------------------------------------------------------------------------------- 25 Al 1 -7.068270154043841e+00 -7.068270154042772e+00 1.06848e-12 6.27634e-09 * 2 1.347283883130367e+00 1.347283883259256e+00 1.28889e-10 8.43305e-10 3 3.998663615274502e+00 3.998663615216257e+00 5.82450e-11 1.24725e-09 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -5.779893280814892e-01 -5.779893280627418e-01 1.87473e-11 1.93879e-10 2 1.612539372964188e+00 1.612539373129946e+00 1.65757e-10 4.20221e-10 3 1.865022639796848e+00 1.865022639681177e+00 1.15671e-10 6.96234e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.683949235535495e+00 1.683949235467962e+00 6.75331e-11 1.30049e-09 2 -1.288804469237480e+00 -1.288804469299806e+00 6.23259e-11 1.01730e-09 3 3.148245176485363e-01 3.148245175790423e-01 6.94940e-11 1.77635e-09 ----------------------------------------------------------------------------------------------------- 28 Ni 1 -7.162706128632352e-01 -7.162706128715522e-01 8.31701e-12 1.12516e-09 2 2.131942159012243e-01 2.131942159727924e-01 7.15681e-11 1.03427e-09 3 -1.582130971024174e+00 -1.582130970932159e+00 9.20151e-11 3.43021e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 1.503896132518969e+00 1.503896132603648e+00 8.46789e-11 4.56380e-10 2 8.064051958099241e-01 8.064051960463331e-01 2.36409e-10 8.08917e-10 3 2.355076991017325e-01 2.355076990894042e-01 1.23283e-11 6.09700e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -1.466390661123938e+00 -1.466390661080830e+00 4.31077e-11 2.02139e-10 2 1.821297954304884e+00 1.821297954224549e+00 8.03344e-11 5.61498e-10 3 -2.390772762963242e+00 -2.390772762923537e+00 3.97051e-11 3.63640e-09 ----------------------------------------------------------------------------------------------------- 31 Ni 1 -1.588501583944664e+00 -1.588501583998906e+00 5.42419e-11 3.81360e-09 2 -2.987351134970891e+00 -2.987351134978049e+00 7.15783e-12 1.03833e-10 3 1.412063186627760e+00 1.412063186384503e+00 2.43256e-10 1.01075e-09 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.429043046716775e+00 1.429043046708796e+00 7.97917e-12 2.08889e-10 2 -2.577903878960693e-01 -2.577903878696518e-01 2.64175e-11 2.25570e-10 3 -1.502003677865924e+00 -1.502003678034054e+00 1.68130e-10 1.84115e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 8.09617e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 8.09617e-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: B Comment: The letter grade B was assigned because the normalized error in the computation was 8.09617e-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.