!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Mendelev_Kramer_CuZr__MO_600021860456_004 Supported species : Cu Zr 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 = Cu | a0 = 3.63908481598 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 2.848745361916832e-01 2.848745354596616e-01 7.32022e-10 6.95825e-09 2 7.842283921249459e-02 7.842283957570131e-02 3.63207e-10 3.85038e-09 3 -1.531972247360387e-01 -1.531972248635134e-01 1.27475e-10 1.24248e-07 * ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.433498255058185e-01 -4.433498267026209e-01 1.19680e-09 3.03317e-09 2 8.955482108257441e-01 8.955482117481331e-01 9.22389e-10 3.66536e-09 3 9.857095694666042e-01 9.857095691454300e-01 3.21174e-10 6.10896e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 4.172910048554448e-01 4.172910045072543e-01 3.48191e-10 1.20821e-09 2 6.608133954133943e-01 6.608133961337650e-01 7.20371e-10 5.83304e-09 3 4.421526829325064e-01 4.421526826773765e-01 2.55130e-10 2.52158e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 9.519930267457488e-01 9.519930266784329e-01 6.73159e-11 4.84168e-09 2 5.306500416692672e-01 5.306500435705037e-01 1.90124e-09 6.39755e-09 3 2.566651404429074e-01 2.566651412703732e-01 8.27466e-10 2.68033e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 4.035071369504029e-01 4.035071356725215e-01 1.27788e-09 7.04692e-09 2 2.344493707858247e-01 2.344493705568478e-01 2.28977e-10 1.80854e-09 3 3.565792670884563e-01 3.565792667967014e-01 2.91755e-10 9.31616e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -9.132161375276581e-01 -9.132161389723886e-01 1.44473e-09 4.01513e-09 2 6.576376885433769e-01 6.576376884468961e-01 9.64808e-11 1.61978e-08 3 9.100294184951595e-01 9.100294190459746e-01 5.50815e-10 9.51341e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 3.184858809102163e-01 3.184858818872734e-01 9.77057e-10 6.46997e-09 2 -8.166624967186035e-01 -8.166624970078737e-01 2.89270e-10 5.13320e-09 3 -1.019650476970336e+00 -1.019650477779812e+00 8.09476e-10 5.46286e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.261850766775329e+00 -1.261850767680236e+00 9.04907e-10 7.92727e-09 2 -1.308937096433503e+00 -1.308937096848376e+00 4.14873e-10 1.01797e-08 3 -6.423586859537890e-01 -6.423586859904354e-01 3.66465e-11 1.82600e-08 ----------------------------------------------------------------------------------------------------- 9 Cu 1 2.188891012115722e-01 2.188891022873249e-01 1.07575e-09 5.01806e-09 2 -1.096450425859340e+00 -1.096450427001678e+00 1.14234e-09 7.01789e-09 3 -9.787755547679172e-02 -9.787755564028749e-02 1.63496e-10 4.38748e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -3.418700149813366e-01 -3.418700138436938e-01 1.13764e-09 1.30012e-08 2 3.854417258565470e-01 3.854417230564330e-01 2.80011e-09 8.95437e-09 3 -4.942718500611437e-01 -4.942718503389472e-01 2.77803e-10 3.93687e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -2.057938140701762e-01 -2.057938267027489e-01 1.26326e-08 1.55090e-08 2 -9.841197907011350e-01 -9.841197901078771e-01 5.93258e-10 3.91081e-09 3 2.128850638681465e-01 2.128850642643755e-01 3.96229e-10 1.08231e-08 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.093642446054515e-01 3.093642419722706e-01 2.63318e-09 2.70288e-09 2 4.385729507714355e-01 4.385729523223323e-01 1.55090e-09 1.03738e-08 3 3.881203861486445e-01 3.881203857858082e-01 3.62836e-10 1.57930e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -6.608469727091364e-01 -6.608469715664623e-01 1.14267e-09 6.59784e-09 2 -1.429108979879773e+00 -1.429108978821887e+00 1.05789e-09 8.78962e-09 3 -1.298649277124021e+00 -1.298649275863230e+00 1.26079e-09 8.33746e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -3.457382897362377e-02 -3.457382980857516e-02 8.34951e-10 2.16036e-09 2 4.879581190663139e-01 4.879581186471398e-01 4.19174e-10 1.08766e-08 3 6.209729970957489e-02 6.209729937111897e-02 3.38456e-10 3.34210e-09 ----------------------------------------------------------------------------------------------------- 15 Cu 1 1.356123548195343e+00 1.356123547522256e+00 6.73087e-10 4.60712e-09 2 -1.169948403194843e+00 -1.169948403414192e+00 2.19349e-10 2.20275e-09 3 3.520693482147499e-01 3.520693479855506e-01 2.29199e-10 2.43519e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 8.265253543168649e-01 8.265253546474575e-01 3.30593e-10 1.13075e-09 2 1.001181017164487e+00 1.001181016801018e+00 3.63469e-10 6.04628e-09 3 6.680838035942038e-01 6.680838043300761e-01 7.35872e-10 8.07238e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -7.660330597229721e-01 -7.660330565923936e-01 3.13058e-09 7.20641e-09 2 -1.592087790901758e-01 -1.592087808310726e-01 1.74090e-09 4.76296e-09 3 -7.424961994350646e-01 -7.424961993371414e-01 9.79232e-11 1.68732e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.333307620593510e+00 1.333307619726354e+00 8.67156e-10 1.47514e-08 2 1.088537783905811e+00 1.088537783735365e+00 1.70446e-10 7.38825e-09 3 2.339028748209933e-01 2.339028740436585e-01 7.77335e-10 5.64465e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 6.637701918448539e-01 6.637701917172377e-01 1.27616e-10 1.38632e-09 2 1.742684039218362e-01 1.742684035623698e-01 3.59466e-10 3.03883e-09 3 5.474941255431441e-02 5.474941048331801e-02 2.07100e-09 6.29876e-09 ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.302413774334758e-01 7.302413769286539e-01 5.04822e-10 1.45564e-08 2 7.040873030180471e-01 7.040873033082319e-01 2.90185e-10 3.34538e-09 3 -4.892147935777870e-01 -4.892147932810054e-01 2.96782e-10 5.73010e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.248000101937482e+00 -1.248000102490561e+00 5.53078e-10 4.44931e-09 2 5.901521358697005e-01 5.901521353607695e-01 5.08931e-10 5.58100e-09 3 2.666704927811386e-01 2.666704930348454e-01 2.53707e-10 7.50552e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -2.252221989342730e-01 -2.252221966205292e-01 2.31374e-09 1.25670e-09 2 1.571457705132101e+00 1.571457703517254e+00 1.61485e-09 4.35176e-09 3 1.037304284001716e+00 1.037304284658800e+00 6.57084e-10 8.36060e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -5.712311611500974e-01 -5.712311611008196e-01 4.92778e-11 4.54514e-09 2 5.084821726106830e-01 5.084821721513966e-01 4.59286e-10 2.01265e-09 3 -3.925181201988900e-01 -3.925181198693456e-01 3.29544e-10 6.84765e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 3.242574807266224e-01 3.242574807171226e-01 9.49973e-12 1.55639e-09 2 3.393589402170500e-01 3.393589401514390e-01 6.56110e-11 4.64750e-09 3 -1.212908348751274e+00 -1.212908348761961e+00 1.06872e-11 1.63936e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -3.332868505109794e-01 -3.332868504558312e-01 5.51482e-11 3.38602e-08 * 2 -8.884741673612140e-01 -8.884741715981900e-01 4.23698e-09 5.84092e-09 3 5.090201442442055e-01 5.090201439482277e-01 2.95978e-10 6.40941e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.061114045108449e+00 -1.061114043939498e+00 1.16895e-09 1.02810e-08 2 4.354193996058812e-01 4.354194012278023e-01 1.62192e-09 5.40255e-09 3 -1.073466011099633e+00 -1.073466010246928e+00 8.52705e-10 5.24278e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 5.601275310042497e-01 5.601275282915291e-01 2.71272e-09 1.16436e-08 2 -1.995215711734763e+00 -1.995215709483097e+00 2.25167e-09 6.57805e-08 * 3 -1.809770714040287e-01 -1.809770721589144e-01 7.54886e-10 3.15176e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -2.658630121144284e-01 -2.658630083966446e-01 3.71778e-09 9.80848e-09 2 4.329842215431535e-01 4.329842201234828e-01 1.41967e-09 7.41777e-09 3 -2.695499343715466e-01 -2.695499353739284e-01 1.00238e-09 5.33164e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.838210366601116e-01 -9.838210374591471e-01 7.99036e-10 7.16995e-09 2 -1.402196550237276e+00 -1.402196549458814e+00 7.78462e-10 4.53421e-09 3 4.576457061621607e-01 4.576457046050820e-01 1.55708e-09 4.05322e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.743245988189243e-01 -2.743245948859010e-01 3.93302e-09 1.46543e-08 2 8.304389090596553e-01 8.304389090247336e-01 3.49217e-11 5.60212e-09 3 -1.992593178898870e-01 -1.992593179280983e-01 3.82114e-11 8.08150e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 2.681892701110001e-01 2.681892701675591e-01 5.65590e-11 3.71759e-09 2 -1.332215402092793e+00 -1.332215401978419e+00 1.14373e-10 6.98489e-10 3 4.890325663115903e-01 4.890325668901522e-01 5.78562e-10 9.92343e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 6.234501198043575e-01 6.234501191562387e-01 6.48119e-10 6.53271e-09 2 5.366754691106135e-01 5.366754691835985e-01 7.29851e-11 3.91946e-09 3 5.836774062131578e-01 5.836774062026286e-01 1.05291e-11 3.29294e-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 = 11, direction = 1: |F_model - F_numer| error = --------------------------------- = 6.13846e-08 max{(|F_model|+|F_numer|)/2, 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 = Zr | a0 = 4.54452457428 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 5.644315776294258e-01 5.644315777748040e-01 1.45378e-10 1.06518e-08 2 6.216762701266779e-01 6.216762701610256e-01 3.43476e-11 2.61484e-08 3 4.282878022060850e-01 4.282878009624513e-01 1.24363e-09 1.23990e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -2.876111707350785e-01 -2.876111708069808e-01 7.19023e-11 3.65286e-09 2 -1.814149293274021e-01 -1.814149288051459e-01 5.22256e-10 5.40729e-09 3 -9.243993653414367e-01 -9.243993649719561e-01 3.69481e-10 7.01889e-09 ----------------------------------------------------------------------------------------------------- 3 Zr 1 4.741179223630392e-01 4.741179231401241e-01 7.77085e-10 8.21136e-09 2 7.228549144328238e-01 7.228549140545577e-01 3.78266e-10 8.76283e-09 3 3.428058263810025e-01 3.428058270920744e-01 7.11072e-10 2.98824e-09 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -9.746757383393706e-01 -9.746757396637225e-01 1.32435e-09 1.58330e-08 2 -8.651485589159739e-01 -8.651485573516775e-01 1.56430e-09 1.01146e-08 3 5.679194120526994e-01 5.679194117533497e-01 2.99350e-10 9.56236e-09 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -3.473971767463753e-01 -3.473971766200014e-01 1.26374e-10 3.25062e-09 2 -4.284769872944588e-01 -4.284769865549399e-01 7.39519e-10 1.41588e-09 3 2.191188395024978e-01 2.191188406901001e-01 1.18760e-09 1.38594e-09 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -7.632488950466448e-01 -7.632488944396967e-01 6.06948e-10 9.74164e-09 2 7.545008188239185e-01 7.545008191391126e-01 3.15194e-10 1.30436e-09 3 9.897343712313083e-01 9.897343708861617e-01 3.45147e-10 4.58397e-09 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -8.903941735508825e-01 -8.903941731028788e-01 4.48004e-10 6.82804e-09 2 1.229101161437033e+00 1.229101163074456e+00 1.63742e-09 1.11045e-08 3 3.718267747099787e-01 3.718267732180751e-01 1.49190e-09 1.09466e-08 ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.291508654335890e+00 1.291508651940520e+00 2.39537e-09 6.22069e-09 2 -2.516679794945251e-01 -2.516679767906556e-01 2.70387e-09 2.89903e-07 * 3 1.400941957422854e+00 1.400941957702814e+00 2.79960e-10 2.91086e-07 * ----------------------------------------------------------------------------------------------------- 9 Zr 1 5.180984377436594e-01 5.180984384780056e-01 7.34346e-10 2.16083e-09 2 3.315253176405770e-01 3.315253157613396e-01 1.87924e-09 1.01153e-08 3 9.078964741557988e-01 9.078964729535554e-01 1.20224e-09 2.40339e-07 * ----------------------------------------------------------------------------------------------------- 10 Zr 1 -7.052352653549017e-01 -7.052352655341031e-01 1.79201e-10 1.12731e-08 2 1.061449807928088e-01 1.061449758418938e-01 4.95092e-09 4.92792e-09 3 6.433716939291032e-01 6.433716936896112e-01 2.39492e-10 1.20851e-08 ----------------------------------------------------------------------------------------------------- 11 Zr 1 8.161191586210158e-01 8.161191579235689e-01 6.97447e-10 2.16221e-08 2 1.420492980395937e+00 1.420492979963297e+00 4.32640e-10 2.15053e-08 3 -1.896597597890161e+00 -1.896597599319509e+00 1.42935e-09 1.58991e-08 ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.545597893790680e-01 3.545597897568721e-01 3.77804e-10 2.76926e-09 2 2.152575578975614e-01 2.152575580120139e-01 1.14452e-10 1.89015e-09 3 -1.188513663060504e+00 -1.188513663331846e+00 2.71342e-10 3.34774e-09 ----------------------------------------------------------------------------------------------------- 13 Zr 1 9.942314422700517e-01 9.942314449107343e-01 2.64068e-09 1.60564e-08 2 -1.048259550212389e+00 -1.048259550442785e+00 2.30395e-10 4.01588e-09 3 4.336378851455810e-01 4.336378853681238e-01 2.22543e-10 3.53613e-09 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -7.187846073378255e-01 -7.187846078484785e-01 5.10653e-10 5.71548e-09 2 -8.889386100998273e-01 -8.889386095598623e-01 5.39965e-10 7.27773e-09 3 6.947308885918085e-01 6.947308880362609e-01 5.55548e-10 3.10497e-09 ----------------------------------------------------------------------------------------------------- 15 Zr 1 3.195703454489456e-01 3.195703449110902e-01 5.37855e-10 6.23170e-09 2 4.479877890723650e-01 4.479877898660026e-01 7.93638e-10 1.81088e-09 3 -7.168462761102529e-01 -7.168462755660852e-01 5.44168e-10 3.72914e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -3.110329851426302e-01 -3.110329857607850e-01 6.18155e-10 8.48994e-09 2 -6.512363211400518e-01 -6.512363212290952e-01 8.90434e-11 5.03130e-09 3 8.393776978307609e-01 8.393776976957534e-01 1.35007e-10 1.97093e-08 ----------------------------------------------------------------------------------------------------- 17 Zr 1 3.958592740121513e-01 3.958592728095874e-01 1.20256e-09 2.10635e-09 2 8.585947478691938e-01 8.585947476349277e-01 2.34266e-10 7.43230e-09 3 -9.249688574269984e-01 -9.249688570277715e-01 3.99227e-10 8.17546e-09 ----------------------------------------------------------------------------------------------------- 18 Zr 1 1.201317683896943e-01 1.201317695461997e-01 1.15651e-09 9.85425e-09 2 -1.898615293532238e+00 -1.898615292209430e+00 1.32281e-09 2.73422e-09 3 6.781404898741844e-01 6.781404899831501e-01 1.08966e-10 1.80359e-08 ----------------------------------------------------------------------------------------------------- 19 Zr 1 4.640931818707080e-01 4.640931821488006e-01 2.78093e-10 7.18681e-10 2 9.638062807901175e-01 9.638062796049356e-01 1.18518e-09 6.08614e-09 3 -3.183043522923341e-01 -3.183043504802810e-01 1.81205e-09 9.33032e-09 ----------------------------------------------------------------------------------------------------- 20 Zr 1 7.322677819038547e-01 7.322677823702334e-01 4.66379e-10 5.79920e-09 2 4.525400644354495e-01 4.525400648065617e-01 3.71112e-10 1.22903e-08 3 -7.325511557513715e-01 -7.325511563509106e-01 5.99539e-10 1.92910e-08 ----------------------------------------------------------------------------------------------------- 21 Zr 1 2.682479677925184e-01 2.682479684110674e-01 6.18549e-10 2.65163e-08 2 7.413121954041521e-01 7.413121950223048e-01 3.81847e-10 6.23526e-09 3 -2.007484124499431e-01 -2.007484133976193e-01 9.47676e-10 3.95523e-09 ----------------------------------------------------------------------------------------------------- 22 Zr 1 -5.576135082304371e-01 -5.576135079580385e-01 2.72399e-10 1.18980e-08 2 -6.788378033448160e-01 -6.788378000927023e-01 3.25211e-09 5.14898e-09 3 8.026411084580518e-02 8.026411211270715e-02 1.26690e-09 2.85479e-09 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.415709357730677e+00 -1.415709357577841e+00 1.52836e-10 3.79971e-09 2 1.291720314103085e+00 1.291720313936012e+00 1.67073e-10 4.26793e-09 3 -1.280906439297549e+00 -1.280906441178773e+00 1.88122e-09 7.47143e-09 ----------------------------------------------------------------------------------------------------- 24 Zr 1 9.948201577813414e-01 9.948201567384125e-01 1.04293e-09 5.12423e-09 2 -3.233385874904772e-01 -3.233385878994331e-01 4.08956e-10 5.20126e-09 3 -3.891971418730090e-01 -3.891971422263197e-01 3.53311e-10 3.30024e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -1.255771478856860e+00 -1.255771478055854e+00 8.01006e-10 4.02944e-09 2 -1.839673119883691e+00 -1.839673119622689e+00 2.61002e-10 1.26985e-08 3 1.098655091117474e+00 1.098655090658698e+00 4.58776e-10 1.69544e-08 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.773977143413059e+00 1.773977143276203e+00 1.36856e-10 6.74588e-09 2 5.694357853088493e-01 5.694357876664423e-01 2.35759e-09 6.46006e-09 3 -6.621132637322249e-01 -6.621132633832642e-01 3.48961e-10 1.23499e-08 ----------------------------------------------------------------------------------------------------- 27 Zr 1 3.260248598232262e-01 3.260248583223596e-01 1.50087e-09 1.38470e-09 2 3.614629226892441e-01 3.614629224867972e-01 2.02447e-10 7.27889e-09 3 -6.369199092530570e-01 -6.369199086161411e-01 6.36916e-10 1.38064e-08 ----------------------------------------------------------------------------------------------------- 28 Zr 1 -4.715300025782813e-01 -4.715300018334102e-01 7.44871e-10 3.17302e-09 2 1.143409057559721e-01 1.143409066363678e-01 8.80396e-10 3.77200e-09 3 7.392627526779899e-01 7.392627517861075e-01 8.91882e-10 4.20625e-09 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.092495881250559e+00 1.092495881596199e+00 3.45640e-10 7.33161e-09 2 3.657060237519744e-01 3.657060232945666e-01 4.57408e-10 1.48414e-08 3 1.579380144158913e+00 1.579380144265953e+00 1.07040e-10 1.48176e-08 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -8.794801399056345e-01 -8.794801404892800e-01 5.83646e-10 2.22488e-09 2 -1.181458504144095e+00 -1.181458502574188e+00 1.56991e-09 1.36696e-09 3 -7.942800457899158e-01 -7.942800458222166e-01 3.23007e-11 5.74303e-09 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -1.252828420293204e+00 -1.252828418848625e+00 1.44458e-09 2.26600e-09 2 -3.922846386679097e-01 -3.922846381218086e-01 5.46101e-10 4.89124e-09 3 -1.017168612298256e+00 -1.017168613042604e+00 7.44348e-10 4.72968e-09 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -6.692424241794056e-01 -6.692424265790937e-01 2.39969e-09 3.33888e-09 2 -9.391101471798849e-01 -9.391101461256623e-01 1.05422e-09 5.40280e-09 3 -3.318371192668305e-01 -3.318371181311636e-01 1.13567e-09 1.15552e-08 ----------------------------------------------------------------------------------------------------- * 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 = 10, direction = 2: |F_model - F_numer| error = --------------------------------- = 4.66430e-08 max{(|F_model|+|F_numer|)/2, 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 = Cu Zr | a0 = 3.99479868611 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 8.740212510608160e-01 8.740212508771735e-01 1.83642e-10 3.35672e-09 2 8.756431900908227e-01 8.756431899794451e-01 1.11378e-10 4.96420e-09 3 6.483925594998149e-01 6.483925600934020e-01 5.93587e-10 6.62947e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -1.182086182464231e+00 -1.182086182177514e+00 2.86717e-10 1.02896e-08 2 -1.237484058758448e+00 -1.237484059212921e+00 4.54473e-10 1.19444e-08 3 -6.795236602977009e-01 -6.795236614862852e-01 1.18858e-09 6.15419e-09 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -4.663145503256138e-01 -4.663145500297781e-01 2.95836e-10 3.76007e-09 2 -3.043696505842048e-01 -3.043696513488339e-01 7.64629e-10 5.77538e-09 3 7.549891162073948e-01 7.549891159883048e-01 2.19090e-10 2.37130e-08 ----------------------------------------------------------------------------------------------------- 4 Cu 1 4.501969681512483e-01 4.501969675004629e-01 6.50785e-10 7.35891e-09 2 3.571301023139040e-01 3.571301026187262e-01 3.04822e-10 2.82062e-09 3 -2.111798697124913e-01 -2.111798706129582e-01 9.00467e-10 4.40621e-09 ----------------------------------------------------------------------------------------------------- 5 Zr 1 8.021074039263136e-01 8.021074028390994e-01 1.08721e-09 4.86940e-09 2 3.750740253357613e-01 3.750740252916666e-01 4.40947e-11 4.12007e-09 3 3.987253958036895e-01 3.987253963759602e-01 5.72271e-10 3.69248e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -7.530780594147003e-02 -7.530780621322569e-02 2.71756e-10 1.19596e-09 2 -5.718069091978419e-01 -5.718069086868144e-01 5.11028e-10 5.98445e-09 3 5.116481630719987e-01 5.116481630734139e-01 1.41520e-12 5.30382e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -9.770869007756188e-01 -9.770869018111907e-01 1.03557e-09 5.54222e-09 2 3.897001178351344e-01 3.897001188925725e-01 1.05744e-09 3.66312e-09 3 -5.438788210745398e-01 -5.438788218725205e-01 7.97981e-10 5.67387e-09 ----------------------------------------------------------------------------------------------------- 8 Zr 1 -6.161731539326627e-01 -6.161731536688984e-01 2.63764e-10 2.94850e-08 2 -1.514372929291957e+00 -1.514372929322979e+00 3.10225e-11 2.57338e-08 3 4.481216425609088e-01 4.481216414486695e-01 1.11224e-09 2.59540e-08 ----------------------------------------------------------------------------------------------------- 9 Zr 1 -1.171671279700556e+00 -1.171671279886183e+00 1.85627e-10 4.01687e-09 2 -5.790165941679456e-01 -5.790165954079268e-01 1.23998e-09 3.71409e-09 3 1.960158740632376e-01 1.960158749051709e-01 8.41933e-10 2.25860e-07 * ----------------------------------------------------------------------------------------------------- 10 Zr 1 -2.309660305886889e-01 -2.309660308440398e-01 2.55351e-10 4.54452e-09 2 6.338230783886534e-01 6.338230749923311e-01 3.39632e-09 5.17648e-09 3 -1.803373549661501e-01 -1.803373539589739e-01 1.00718e-09 8.60347e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 5.548723496994510e+00 5.548723495843410e+00 1.15110e-09 4.48767e-09 2 -1.125398811033562e-01 -1.125398821893121e-01 1.08596e-09 6.79519e-09 3 -5.204975369942121e+00 -5.204975369977393e+00 3.52722e-11 2.34838e-09 ----------------------------------------------------------------------------------------------------- 12 Zr 1 -6.865776860436367e-01 -6.865776861504554e-01 1.06819e-10 2.37722e-08 2 1.054142368560510e+00 1.054142368822884e+00 2.62374e-10 9.70618e-10 3 -6.997426014762778e-01 -6.997426024988078e-01 1.02253e-09 1.37707e-09 ----------------------------------------------------------------------------------------------------- 13 Zr 1 1.453474828619856e+00 1.453474828506092e+00 1.13764e-10 4.02396e-10 2 1.207782594460325e+00 1.207782593747905e+00 7.12419e-10 5.09790e-07 * 3 -1.072861316114362e+00 -1.072861315079698e+00 1.03466e-09 4.34140e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -7.532296756742345e-01 -7.532296751238535e-01 5.50381e-10 7.97981e-09 2 -5.929092775322070e-01 -5.929092783424516e-01 8.10245e-10 5.18190e-10 3 5.106815514650570e-01 5.106815521905369e-01 7.25480e-10 2.03837e-09 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -1.597510844838278e-01 -1.597510852995253e-01 8.15698e-10 3.23067e-09 2 6.156762708254627e-01 6.156762713570932e-01 5.31631e-10 1.04507e-08 3 5.170386749488491e-03 5.170384779470734e-03 1.97002e-09 4.28222e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 1.104176297851995e+00 1.104176297470437e+00 3.81558e-10 6.53242e-09 2 6.405353329192408e-01 6.405353318964091e-01 1.02283e-09 3.56658e-10 3 3.864421798244030e-01 3.864421802130590e-01 3.88656e-10 2.98712e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -9.555561513830105e-01 -9.555561521524727e-01 7.69462e-10 8.57644e-09 2 -1.368001190873609e+00 -1.368001190730373e+00 1.43236e-10 2.18191e-09 3 -1.293119435986622e+00 -1.293119434842263e+00 1.14436e-09 1.24645e-08 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.763512869407430e+00 1.763512868628716e+00 7.78714e-10 2.87818e-09 2 9.702068391533852e-01 9.702068365324344e-01 2.62095e-09 4.88364e-09 3 -1.085516760223025e+00 -1.085516758346469e+00 1.87656e-09 1.14087e-08 ----------------------------------------------------------------------------------------------------- 19 Zr 1 1.122085858630906e+00 1.122085861833640e+00 3.20273e-09 1.07505e-08 2 -1.290703143111909e+00 -1.290703142898831e+00 2.13078e-10 1.06382e-08 3 -1.386521103289743e-01 -1.386521109791199e-01 6.50146e-10 1.94063e-09 ----------------------------------------------------------------------------------------------------- 20 Zr 1 -2.627739513660885e+00 -2.627739513221794e+00 4.39091e-10 2.04529e-07 * 2 5.780460182732188e-01 5.780460196742325e-01 1.40101e-09 1.30889e-08 3 1.771864818633804e+00 1.771864817767148e+00 8.66656e-10 4.75019e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -4.175443714489391e-01 -4.175443710972556e-01 3.51684e-10 6.96147e-09 2 6.897911597926440e-02 6.897911609401942e-02 1.14755e-10 6.73022e-09 3 2.073680598787249e-01 2.073680614687200e-01 1.59000e-09 3.93108e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.204243573394781e+00 1.204243572766058e+00 6.28723e-10 1.16667e-09 2 1.113525130225107e+00 1.113525130650896e+00 4.25789e-10 2.42791e-09 3 3.124058277012797e-01 3.124058271236676e-01 5.77612e-10 7.82547e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 1.064061171621484e+00 1.064061169059259e+00 2.56223e-09 1.46245e-09 2 -1.592836864979411e+00 -1.592836866254297e+00 1.27489e-09 1.83998e-09 3 -1.109460993160624e-01 -1.109460992486610e-01 6.74014e-11 9.68088e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 -1.490825765554904e+00 -1.490825759149292e+00 6.40561e-09 9.90461e-09 2 1.688585409318308e+00 1.688585407588314e+00 1.72999e-09 1.98378e-08 3 -1.262347138293439e-01 -1.262347157724803e-01 1.94314e-09 4.29265e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -6.376418120079764e+00 -6.376418119938026e+00 1.41738e-10 3.47183e-09 2 -2.929840530830368e+00 -2.929840536863920e+00 6.03355e-09 1.38142e-08 3 3.747032646352963e+00 3.747032647342357e+00 9.89394e-10 1.48354e-08 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.273680720879759e+00 1.273680720746132e+00 1.33628e-10 3.81753e-08 * 2 3.082623415151083e+00 3.082623415419366e+00 2.68283e-10 2.03111e-08 3 3.370185991086116e-01 3.370186000935510e-01 9.84939e-10 7.10875e-09 ----------------------------------------------------------------------------------------------------- 27 Zr 1 1.888180681590530e+00 1.888180677963936e+00 3.62659e-09 8.19267e-09 2 7.074496134206638e-01 7.074496137849519e-01 3.64288e-10 7.01380e-09 3 2.048205414095248e+00 2.048205414118345e+00 2.30971e-11 5.78582e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -5.982674886855158e-01 -5.982674884714019e-01 2.14114e-10 1.36303e-09 2 -2.811158617414078e-01 -2.811158604814818e-01 1.25993e-09 1.21207e-09 3 8.665635699051180e-02 8.665635707298411e-02 8.24723e-11 1.03236e-09 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.766481924420493e+00 1.766481923884895e+00 5.35598e-10 1.04010e-08 2 -6.304188814264284e-01 -6.304188815628134e-01 1.36385e-10 3.36042e-09 3 6.000493700246807e-01 6.000493702351222e-01 2.10441e-10 1.45669e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -8.962967711885429e-01 -8.962967712604336e-01 7.18907e-11 6.30229e-09 2 -8.175681953828713e-01 -8.175681940262173e-01 1.35665e-09 4.33556e-09 3 -5.657098439605823e-02 -5.657098436395463e-02 3.21036e-11 1.57250e-08 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -7.639321461143989e-01 -7.639321456461071e-01 4.68292e-10 1.91700e-09 2 6.430154931752945e-02 6.430154903746468e-02 2.80065e-10 4.32205e-09 3 -8.768800627656865e-01 -8.768800627744151e-01 8.72857e-12 1.33178e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.307976314963809e-01 1.307976302098974e-01 1.28648e-09 1.02033e-08 2 -6.002402025864082e-01 -6.002402023081167e-01 2.78292e-10 1.46407e-09 3 -6.903688016024028e-01 -6.903688023154151e-01 7.13012e-10 1.56991e-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 = 15, direction = 3: |F_model - F_numer| error = --------------------------------- = 3.81019e-07 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.81019e-07 Machine precision = 2.22045e-16 Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 3.81019e-07 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. 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.