!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MendelevSordeletKramer_2007_CuZr__MO_120596890176_005 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 2.848745944818801e-01 2.848745944613525e-01 2.05276e-11 9.69167e-09 2 7.842285479292213e-02 7.842285485132754e-02 5.84054e-11 3.72413e-09 3 -1.531972495950493e-01 -1.531972494124479e-01 1.82601e-10 1.21337e-07 * ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.433497760922098e-01 -4.433497765351525e-01 4.42943e-10 2.51564e-08 * 2 8.955482182178753e-01 8.955482173899267e-01 8.27949e-10 3.16170e-09 3 9.857095875452272e-01 9.857095883585677e-01 8.13341e-10 3.67640e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 4.172909792820134e-01 4.172909795798407e-01 2.97827e-10 6.79789e-09 2 6.608134010458266e-01 6.608134018646760e-01 8.18849e-10 7.44180e-09 3 4.421526682570592e-01 4.421526672268709e-01 1.03019e-09 1.65236e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 9.519929838823711e-01 9.519929837381094e-01 1.44262e-10 2.91622e-09 2 5.306500783779365e-01 5.306500779732370e-01 4.04699e-10 3.55210e-09 3 2.566651454910979e-01 2.566651462792799e-01 7.88182e-10 2.70155e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 4.035070695316980e-01 4.035070703165873e-01 7.84889e-10 2.70958e-09 2 2.344494092597026e-01 2.344494092649056e-01 5.20295e-12 4.66696e-09 3 3.565793205378680e-01 3.565793224097609e-01 1.87189e-09 7.34436e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -9.132161761840761e-01 -9.132161763396448e-01 1.55569e-10 9.26848e-10 2 6.576377029434423e-01 6.576377034886066e-01 5.45164e-10 9.41422e-09 3 9.100294530934374e-01 9.100294531631370e-01 6.96996e-11 6.56646e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 3.184859018986503e-01 3.184859022794576e-01 3.80807e-10 4.80988e-10 2 -8.166624938479528e-01 -8.166624941682841e-01 3.20331e-10 2.55108e-09 3 -1.019650470802876e+00 -1.019650471887756e+00 1.08488e-09 1.95493e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.261850789436067e+00 -1.261850791142055e+00 1.70599e-09 2.19971e-09 2 -1.308937067190820e+00 -1.308937066748799e+00 4.42020e-10 6.27492e-09 3 -6.423587425479874e-01 -6.423587416453505e-01 9.02637e-10 1.21586e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 2.188890862662029e-01 2.188890860498894e-01 2.16313e-10 2.56343e-09 2 -1.096450435679767e+00 -1.096450435189636e+00 4.90130e-10 4.43728e-09 3 -9.787755777285907e-02 -9.787755808086880e-02 3.08010e-10 2.32254e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -3.418700130439279e-01 -3.418700118443008e-01 1.19963e-09 1.70701e-09 2 3.854416343623771e-01 3.854416343741504e-01 1.17734e-11 1.60721e-08 3 -4.942718464168518e-01 -4.942718465714598e-01 1.54608e-10 2.74472e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -2.057937881841378e-01 -2.057937894001435e-01 1.21601e-09 4.40098e-09 2 -9.841197822981056e-01 -9.841197823293762e-01 3.12707e-11 1.14073e-10 3 2.128851007019518e-01 2.128851004353814e-01 2.66570e-10 1.26457e-08 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.093642845862970e-01 3.093642851026133e-01 5.16316e-10 1.58525e-09 2 4.385729570644362e-01 4.385729575516208e-01 4.87185e-10 3.37692e-09 3 3.881203548110517e-01 3.881203545603686e-01 2.50683e-10 2.89354e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -6.608469723102215e-01 -6.608469753902935e-01 3.08007e-09 3.97987e-08 * 2 -1.429108980278005e+00 -1.429108980957225e+00 6.79221e-10 4.35128e-09 3 -1.298649251771415e+00 -1.298649252070374e+00 2.98958e-10 2.00539e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -3.457388253497170e-02 -3.457388217792975e-02 3.57042e-10 4.91709e-09 2 4.879580653437874e-01 4.879580658337724e-01 4.89985e-10 3.86287e-09 3 6.209737770507438e-02 6.209737778555713e-02 8.04828e-11 9.62879e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 1.356123565174655e+00 1.356123565742318e+00 5.67663e-10 2.37812e-09 2 -1.169948402136520e+00 -1.169948402414659e+00 2.78139e-10 2.69405e-09 3 3.520693605511622e-01 3.520693601091119e-01 4.42050e-10 7.20794e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 8.265252922020665e-01 8.265252925029291e-01 3.00863e-10 6.97118e-09 2 1.001181015645155e+00 1.001181015829160e+00 1.84005e-10 1.86713e-09 3 6.680837705577930e-01 6.680837704363091e-01 1.21484e-10 3.92956e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -7.660329799366006e-01 -7.660329804396241e-01 5.03024e-10 6.38702e-09 2 -1.592087182657209e-01 -1.592087185534726e-01 2.87752e-10 4.82352e-09 3 -7.424961902560546e-01 -7.424961911971449e-01 9.41090e-10 2.25863e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.333307616401351e+00 1.333307616339874e+00 6.14770e-11 3.28745e-08 * 2 1.088537781531278e+00 1.088537781947925e+00 4.16647e-10 1.88120e-08 3 2.339028808446073e-01 2.339028805641249e-01 2.80482e-10 1.01506e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 6.637701481390834e-01 6.637701480491400e-01 8.99434e-11 1.17083e-09 2 1.742683977287504e-01 1.742683977279320e-01 8.18429e-13 3.67260e-09 3 5.474943343588615e-02 5.474943357370488e-02 1.37819e-10 5.08405e-09 ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.302413871966467e-01 7.302413868654688e-01 3.31178e-10 7.10131e-09 2 7.040872433829413e-01 7.040872438161059e-01 4.33165e-10 2.23603e-09 3 -4.892147934086219e-01 -4.892147928799301e-01 5.28692e-10 1.15212e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.248000099931603e+00 -1.248000100038749e+00 1.07146e-10 2.64857e-09 2 5.901521318369241e-01 5.901521323755639e-01 5.38640e-10 2.06825e-09 3 2.666704866072462e-01 2.666704862672113e-01 3.40035e-10 6.30264e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -2.252222085547310e-01 -2.252222081608781e-01 3.93853e-10 6.87923e-09 2 1.571457749453158e+00 1.571457750747219e+00 1.29406e-09 2.09361e-09 3 1.037304258593725e+00 1.037304258533424e+00 6.03013e-11 3.03060e-08 * ----------------------------------------------------------------------------------------------------- 23 Cu 1 -5.712311934504146e-01 -5.712311939824918e-01 5.32077e-10 9.38286e-10 2 5.084821724594664e-01 5.084821727694677e-01 3.10001e-10 1.22688e-09 3 -3.925181661122308e-01 -3.925181666000064e-01 4.87776e-10 4.19398e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 3.242575256062609e-01 3.242575255308031e-01 7.54578e-11 8.86414e-10 2 3.393588542179207e-01 3.393588542089606e-01 8.96005e-12 1.53990e-07 * 3 -1.212908282117223e+00 -1.212908279961156e+00 2.15607e-09 2.22772e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -3.332868807449226e-01 -3.332868797421661e-01 1.00276e-09 3.29955e-08 * 2 -8.884741278165172e-01 -8.884741277920722e-01 2.44450e-11 3.29541e-09 3 5.090201289277978e-01 5.090201287545489e-01 1.73249e-10 8.36800e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.061114006320631e+00 -1.061114005749439e+00 5.71192e-10 8.31077e-09 2 4.354192614868289e-01 4.354192621063697e-01 6.19541e-10 2.68385e-09 3 -1.073466034229630e+00 -1.073466033245679e+00 9.83952e-10 5.57237e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 5.601275212146251e-01 5.601275197381332e-01 1.47649e-09 1.09429e-08 2 -1.995215724999478e+00 -1.995215725156753e+00 1.57276e-10 4.62942e-09 3 -1.809770932785802e-01 -1.809770953443590e-01 2.06578e-09 7.26075e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -2.658630369547145e-01 -2.658630336126782e-01 3.34204e-09 1.76599e-09 2 4.329842416100781e-01 4.329842380809874e-01 3.52909e-09 5.96893e-09 3 -2.695499494955947e-01 -2.695499500781339e-01 5.82539e-10 2.30469e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.838210270778049e-01 -9.838210265043987e-01 5.73406e-10 1.04499e-08 2 -1.402196461093351e+00 -1.402196460757030e+00 3.36321e-10 1.24533e-08 3 4.576456599531096e-01 4.576456567548964e-01 3.19821e-09 1.13170e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.743245343589026e-01 -2.743245346093637e-01 2.50461e-10 8.34323e-09 2 8.304389312564919e-01 8.304389309762801e-01 2.80212e-10 2.13209e-09 3 -1.992593296693834e-01 -1.992593296793151e-01 9.93167e-12 1.85263e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 2.681892568465127e-01 2.681892568184235e-01 2.80891e-11 8.17700e-10 2 -1.332215386626291e+00 -1.332215386913839e+00 2.87547e-10 1.55848e-09 3 4.890325567462089e-01 4.890325572724647e-01 5.26256e-10 1.67346e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 6.234501524056222e-01 6.234501527235301e-01 3.17908e-10 1.98982e-09 2 5.366754782152278e-01 5.366754785941058e-01 3.78878e-10 6.18092e-09 3 5.836774131140536e-01 5.836774129605203e-01 1.53533e-10 4.73962e-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 = 28, direction = 1: |F_model - F_numer| error = ----------------------- = 1.25705e-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 = Zr | a0 = 4.54452457428 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 5.644315454689667e-01 5.644315462837265e-01 8.14760e-10 7.99994e-09 2 6.216762518010092e-01 6.216762512636597e-01 5.37349e-10 2.66621e-08 * 3 4.282877151277624e-01 4.282877154921228e-01 3.64360e-10 3.37297e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -2.876111599119370e-01 -2.876111600052281e-01 9.32912e-11 1.00027e-09 2 -1.814149383600165e-01 -1.814149374856883e-01 8.74328e-10 7.42352e-10 3 -9.243993733687677e-01 -9.243993732691009e-01 9.96667e-11 9.10474e-09 ----------------------------------------------------------------------------------------------------- 3 Zr 1 4.741179517699213e-01 4.741179515798203e-01 1.90101e-10 4.50632e-09 2 7.228548047689487e-01 7.228548052757829e-01 5.06834e-10 4.79986e-09 3 3.428058158106687e-01 3.428058157075077e-01 1.03161e-10 4.43659e-09 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -9.746757732524608e-01 -9.746757719696425e-01 1.28282e-09 5.25601e-09 2 -8.651484638173715e-01 -8.651484623461517e-01 1.47122e-09 8.71609e-09 3 5.679194427040386e-01 5.679194426789469e-01 2.50917e-11 1.89654e-09 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -3.473972010057264e-01 -3.473972009209174e-01 8.48089e-11 3.11645e-09 2 -4.284769027100294e-01 -4.284769021567020e-01 5.53327e-10 3.41656e-09 3 2.191188746755378e-01 2.191188743499064e-01 3.25631e-10 1.72305e-09 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -7.632489201553792e-01 -7.632489200304213e-01 1.24958e-10 2.78198e-09 2 7.545007767995873e-01 7.545007766120094e-01 1.87578e-10 7.54353e-09 3 9.897343544520802e-01 9.897343532427677e-01 1.20931e-09 5.40945e-09 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -8.903941543353147e-01 -8.903941537404692e-01 5.94846e-10 8.20837e-10 2 1.229101107989218e+00 1.229101106468092e+00 1.52113e-09 4.39055e-09 3 3.718266963208859e-01 3.718266968154754e-01 4.94589e-10 4.67092e-09 ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.291508630952132e+00 1.291508630676992e+00 2.75140e-10 1.14154e-08 2 -2.516680190481410e-01 -2.516680200174444e-01 9.69303e-10 3.45987e-09 3 1.400941899307304e+00 1.400941899529202e+00 2.21898e-10 2.87960e-07 * ----------------------------------------------------------------------------------------------------- 9 Zr 1 5.180984954708079e-01 5.180984964744987e-01 1.00369e-09 1.19243e-09 2 3.315253104038514e-01 3.315253081849039e-01 2.21895e-09 4.27883e-09 3 9.078964846809044e-01 9.078964848565897e-01 1.75685e-10 3.44878e-09 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -7.052353291952769e-01 -7.052353290461784e-01 1.49099e-10 3.74619e-09 2 1.061449736520598e-01 1.061449739760843e-01 3.24025e-10 7.17952e-09 3 6.433716858910062e-01 6.433716856811742e-01 2.09832e-10 3.87435e-09 ----------------------------------------------------------------------------------------------------- 11 Zr 1 8.161191284871374e-01 8.161191285078796e-01 2.07422e-11 5.17531e-09 2 1.420492950568352e+00 1.420492948073148e+00 2.49520e-09 9.26763e-09 3 -1.896597630771746e+00 -1.896597631244309e+00 4.72563e-10 9.96778e-09 ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.545597478214981e-01 3.545597480241706e-01 2.02672e-10 1.80372e-09 2 2.152575675692551e-01 2.152575677226289e-01 1.53374e-10 9.28381e-09 3 -1.188513713739919e+00 -1.188513714054523e+00 3.14604e-10 3.73616e-09 ----------------------------------------------------------------------------------------------------- 13 Zr 1 9.942314167793755e-01 9.942314167656403e-01 1.37352e-11 8.71860e-09 2 -1.048259573713085e+00 -1.048259573833983e+00 1.20898e-10 4.08140e-09 3 4.336378247527311e-01 4.336378247949799e-01 4.22488e-11 2.62240e-09 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -7.187845407863704e-01 -7.187845410429679e-01 2.56597e-10 6.21682e-09 2 -8.889385591305498e-01 -8.889385592541530e-01 1.23603e-10 9.40555e-10 3 6.947308193708037e-01 6.947308192658626e-01 1.04941e-10 1.48484e-09 ----------------------------------------------------------------------------------------------------- 15 Zr 1 3.195704503686245e-01 3.195704512760985e-01 9.07474e-10 8.21929e-10 2 4.479878016639143e-01 4.479878018518212e-01 1.87907e-10 3.26268e-09 3 -7.168462926839497e-01 -7.168462930724516e-01 3.88502e-10 1.46924e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -3.110330293768840e-01 -3.110330288764749e-01 5.00409e-10 1.12829e-08 2 -6.512362493498349e-01 -6.512362489998087e-01 3.50026e-10 6.29307e-09 3 8.393777088811480e-01 8.393777089213547e-01 4.02066e-11 2.03034e-09 ----------------------------------------------------------------------------------------------------- 17 Zr 1 3.958592519529337e-01 3.958592527530025e-01 8.00069e-10 1.42093e-09 2 8.585947411003726e-01 8.585947413853972e-01 2.85025e-10 7.09187e-10 3 -9.249688049672095e-01 -9.249688050223317e-01 5.51222e-11 7.39795e-09 ----------------------------------------------------------------------------------------------------- 18 Zr 1 1.201317248998314e-01 1.201317249951384e-01 9.53070e-11 2.79434e-09 2 -1.898615266214189e+00 -1.898615265248275e+00 9.65914e-10 8.35471e-09 3 6.781405728377640e-01 6.781405706828978e-01 2.15487e-09 7.07959e-09 ----------------------------------------------------------------------------------------------------- 19 Zr 1 4.640932193626506e-01 4.640932189552828e-01 4.07368e-10 4.74955e-09 2 9.638063521559005e-01 9.638063520717621e-01 8.41384e-11 1.59409e-09 3 -3.183043863466463e-01 -3.183043853580806e-01 9.88566e-10 7.59488e-09 ----------------------------------------------------------------------------------------------------- 20 Zr 1 7.322678454087536e-01 7.322678456379609e-01 2.29207e-10 2.50474e-09 2 4.525400940579219e-01 4.525400937937485e-01 2.64173e-10 5.99224e-09 3 -7.325511956738440e-01 -7.325511954850968e-01 1.88747e-10 2.48869e-09 ----------------------------------------------------------------------------------------------------- 21 Zr 1 2.682479347591646e-01 2.682479347955660e-01 3.64014e-11 3.73646e-09 2 7.413122034148748e-01 7.413122032683890e-01 1.46486e-10 1.40721e-08 3 -2.007483281642458e-01 -2.007483296381675e-01 1.47392e-09 3.58883e-07 * ----------------------------------------------------------------------------------------------------- 22 Zr 1 -5.576133980044568e-01 -5.576133990834893e-01 1.07903e-09 4.78431e-09 2 -6.788378853619256e-01 -6.788378862593021e-01 8.97377e-10 4.62163e-09 3 8.026415507578942e-02 8.026415527260823e-02 1.96819e-10 3.90640e-09 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.415709389156662e+00 -1.415709389147374e+00 9.28857e-12 1.99173e-09 2 1.291720279485126e+00 1.291720274946669e+00 4.53846e-09 1.01373e-08 3 -1.280906407661103e+00 -1.280906406920858e+00 7.40245e-10 6.22529e-09 ----------------------------------------------------------------------------------------------------- 24 Zr 1 9.948200972004729e-01 9.948200961384829e-01 1.06199e-09 5.04373e-09 2 -3.233385976911640e-01 -3.233385976883587e-01 2.80526e-12 1.94878e-09 3 -3.891971873199471e-01 -3.891971859326082e-01 1.38734e-09 5.67179e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -1.255771407329006e+00 -1.255771407595500e+00 2.66494e-10 6.87383e-09 2 -1.839673226993556e+00 -1.839673227363809e+00 3.70253e-10 2.90898e-09 3 1.098655116788209e+00 1.098655116163359e+00 6.24851e-10 3.85357e-09 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.773977194900209e+00 1.773977194888233e+00 1.19755e-11 5.05275e-09 2 5.694358082958046e-01 5.694358081022475e-01 1.93557e-10 4.38755e-09 3 -6.621132761193210e-01 -6.621132767124717e-01 5.93151e-10 4.69034e-09 ----------------------------------------------------------------------------------------------------- 27 Zr 1 3.260248452101869e-01 3.260248453096823e-01 9.94954e-11 3.31086e-09 2 3.614628487874434e-01 3.614628484253429e-01 3.62101e-10 1.08612e-08 3 -6.369199649762702e-01 -6.369199642076563e-01 7.68614e-10 7.23876e-09 ----------------------------------------------------------------------------------------------------- 28 Zr 1 -4.715300696796324e-01 -4.715300702162095e-01 5.36577e-10 3.37681e-09 2 1.143409314457609e-01 1.143409316623530e-01 2.16592e-10 1.18133e-08 3 7.392628319736492e-01 7.392628322157816e-01 2.42132e-10 1.08920e-08 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.092495802018196e+00 1.092495803001034e+00 9.82838e-10 9.91034e-09 2 3.657060412737206e-01 3.657060417907858e-01 5.17065e-10 4.52449e-09 3 1.579380230422316e+00 1.579380229742583e+00 6.79733e-10 1.07013e-09 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -8.794801005163758e-01 -8.794801000509388e-01 4.65437e-10 9.78643e-09 2 -1.181458429702362e+00 -1.181458430759455e+00 1.05709e-09 3.81053e-09 3 -7.942800482856829e-01 -7.942800481642607e-01 1.21422e-10 4.57175e-09 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -1.252828373963349e+00 -1.252828373095960e+00 8.67389e-10 3.80125e-09 2 -3.922846136828488e-01 -3.922846135264395e-01 1.56409e-10 5.48145e-09 3 -1.017168521138718e+00 -1.017168520951454e+00 1.87263e-10 1.19729e-09 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -6.692424361620306e-01 -6.692424359911785e-01 1.70852e-10 1.25943e-08 2 -9.391101194580496e-01 -9.391101184916310e-01 9.66419e-10 6.52552e-10 3 -3.318370978552301e-01 -3.318370976789192e-01 1.76311e-10 8.87595e-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 = 9, direction = 2: |F_model - F_numer| error = ----------------------- = 6.69315e-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 = Cu Zr | a0 = 4.03094990171 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 9.224251432182569e-01 9.224251437286820e-01 5.10425e-10 7.08517e-09 2 8.030675649921353e-01 8.030675664175694e-01 1.42543e-09 9.57374e-09 3 7.542475112969736e-01 7.542475099735494e-01 1.32342e-09 3.83955e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -1.245781703235957e+00 -1.245781705828677e+00 2.59272e-09 9.99703e-09 2 -1.413324143340408e+00 -1.413324144462311e+00 1.12190e-09 1.17065e-09 3 -4.803537310528346e-01 -4.803537316118021e-01 5.58967e-10 5.40432e-09 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -3.535772757163122e-01 -3.535772757276031e-01 1.12909e-11 4.79021e-09 2 -3.592089185420499e-01 -3.592089188361392e-01 2.94089e-10 4.86175e-09 3 3.992548361780326e-01 3.992548355145398e-01 6.63493e-10 3.94898e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 3.053924122940469e-01 3.053924127717436e-01 4.77697e-10 1.86837e-09 2 6.710931992580470e-01 6.710932011402811e-01 1.88223e-09 5.98981e-09 3 -6.711787350838976e-01 -6.711787354344600e-01 3.50562e-10 1.14878e-08 ----------------------------------------------------------------------------------------------------- 5 Zr 1 7.554303911079405e-01 7.554303916408668e-01 5.32926e-10 3.50899e-09 2 5.293469899194080e-01 5.293469916485386e-01 1.72913e-09 7.68236e-09 3 4.805558450911201e-01 4.805558456274764e-01 5.36356e-10 7.53426e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -1.140885145993429e-01 -1.140885148908522e-01 2.91509e-10 6.17622e-09 2 -6.125447348768921e-01 -6.125447344115096e-01 4.65383e-10 5.38848e-09 3 5.289538603617900e-01 5.289538604528942e-01 9.11041e-11 4.39747e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -1.019371286260433e+00 -1.019371285623630e+00 6.36803e-10 7.17537e-09 2 4.339624755541615e-01 4.339624755094337e-01 4.47278e-11 1.81186e-09 3 -4.339390902061311e-01 -4.339390895235249e-01 6.82606e-10 5.00931e-09 ----------------------------------------------------------------------------------------------------- 8 Zr 1 -1.057972903609303e+00 -1.057972904096681e+00 4.87378e-10 3.38070e-09 2 -1.390369446711059e+00 -1.390369447532930e+00 8.21871e-10 5.12176e-09 3 -6.379508591544889e-01 -6.379508593990911e-01 2.44602e-10 6.61138e-09 ----------------------------------------------------------------------------------------------------- 9 Zr 1 -1.104796595595625e+00 -1.104796595840848e+00 2.45223e-10 8.82711e-09 2 -4.178783399613094e-01 -4.178783410438964e-01 1.08259e-09 3.53786e-09 3 1.787966838268242e-01 1.787966834626232e-01 3.64201e-10 1.03590e-08 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -2.803613393666406e-01 -2.803613393651663e-01 1.47432e-12 2.46860e-09 2 5.896928712699107e-01 5.896928704677261e-01 8.02185e-10 4.13255e-09 3 -1.739497818520311e-01 -1.739497811235074e-01 7.28524e-10 1.79938e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 1.807472117997056e+00 1.807472118602886e+00 6.05830e-10 1.27256e-09 2 -8.071432937327230e-01 -8.071432939613142e-01 2.28591e-10 1.50473e-08 3 -1.108039080329009e+00 -1.108039081436243e+00 1.10723e-09 2.54713e-09 ----------------------------------------------------------------------------------------------------- 12 Zr 1 -5.235942720570975e-01 -5.235942711557079e-01 9.01390e-10 4.30309e-09 2 7.805337122535424e-01 7.805337118804785e-01 3.73064e-10 4.66691e-09 3 -6.128503241095544e-01 -6.128503246319140e-01 5.22360e-10 3.36096e-09 ----------------------------------------------------------------------------------------------------- 13 Zr 1 1.391039051445325e+00 1.391039051631039e+00 1.85714e-10 4.14220e-09 2 1.320771538255900e+00 1.320771540908070e+00 2.65217e-09 1.47508e-08 3 -1.008407558591372e+00 -1.008407559928965e+00 1.33759e-09 1.29083e-08 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -7.624389799226196e-01 -7.624389805437948e-01 6.21175e-10 4.32576e-09 2 -5.912724844515677e-01 -5.912724844955928e-01 4.40251e-11 5.59834e-09 3 5.554485691578576e-01 5.554485686962813e-01 4.61576e-10 3.64513e-09 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -3.635550669991905e-01 -3.635550649746844e-01 2.02451e-09 8.66131e-09 2 6.694757491419999e-01 6.694757502255193e-01 1.08352e-09 6.97073e-09 3 1.090422044660039e-01 1.090422039152403e-01 5.50764e-10 3.28244e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 1.166398265782377e+00 1.166398265624397e+00 1.57979e-10 5.91359e-09 2 -1.856660238120755e-01 -1.856660219444485e-01 1.86763e-09 1.07213e-09 3 8.563197360502418e-01 8.563197341069586e-01 1.94328e-09 6.32857e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -1.141846824604387e+00 -1.141846823904071e+00 7.00316e-10 3.55064e-09 2 -1.216860131279703e+00 -1.216860131791006e+00 5.11303e-10 2.96774e-09 3 -7.736646544420045e-01 -7.736646553924879e-01 9.50483e-10 1.12036e-08 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.881274174357460e+00 1.881274174988523e+00 6.31062e-10 6.92422e-09 2 7.940370499885696e-01 7.940370491842161e-01 8.04353e-10 5.46234e-09 3 -1.124571073331988e+00 -1.124571072733864e+00 5.98125e-10 2.63986e-09 ----------------------------------------------------------------------------------------------------- 19 Zr 1 1.157768087349961e+00 1.157768087709232e+00 3.59272e-10 3.68258e-09 2 -1.010386493911287e+00 -1.010386493491661e+00 4.19627e-10 2.93825e-09 3 -4.223607734583733e-02 -4.223607852351948e-02 1.17768e-09 4.25772e-09 ----------------------------------------------------------------------------------------------------- 20 Zr 1 -2.272149315642981e+00 -2.272149315278355e+00 3.64626e-10 7.67161e-10 2 8.130246333682152e-02 8.130246296359937e-02 3.73222e-10 3.82811e-09 3 1.806964591148929e+00 1.806964590645061e+00 5.03868e-10 4.10547e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -5.926842623071574e-01 -5.926842629532126e-01 6.46055e-10 2.41548e-09 2 -4.418799217805344e-01 -4.418799209720681e-01 8.08466e-10 5.12819e-09 3 -1.203870168848155e-01 -1.203870188166455e-01 1.93183e-09 4.28108e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.767399857706489e+00 1.767399856533744e+00 1.17275e-09 7.92687e-09 2 6.799888380096371e-01 6.799888378184704e-01 1.91167e-10 9.65410e-09 3 8.759729612310100e-01 8.759729650625461e-01 3.83154e-09 1.70420e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 6.717143137254246e-01 6.717143131433370e-01 5.82088e-10 1.73342e-09 2 -8.271621043143614e-01 -8.271621041133234e-01 2.01038e-10 4.97241e-09 3 -4.934792603232718e-02 -4.934792090130096e-02 5.13103e-09 6.98866e-09 ----------------------------------------------------------------------------------------------------- 24 Zr 1 -8.203106614748541e-01 -8.203106616455904e-01 1.70736e-10 3.01443e-09 2 3.768409673520001e-01 3.768409672648082e-01 8.71919e-11 1.81090e-08 3 7.092008547462899e-01 7.092008534338897e-01 1.31240e-09 6.69728e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -2.783116386259927e+00 -2.783116385819942e+00 4.39984e-10 7.50168e-09 2 -1.833301326741504e+00 -1.833301326325499e+00 4.16005e-10 3.42126e-09 3 -6.813308629081681e-01 -6.813308630484214e-01 1.40253e-10 1.08487e-09 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.538793903773744e+00 1.538793902949272e+00 8.24472e-10 6.87187e-09 2 3.069418735622595e+00 3.069418734475567e+00 1.14703e-09 5.11771e-09 3 5.938534147782818e-01 5.938534145517576e-01 2.26524e-10 1.34658e-08 ----------------------------------------------------------------------------------------------------- 27 Zr 1 1.631942145599858e+00 1.631942145172461e+00 4.27396e-10 8.86955e-10 2 8.518700697206520e-01 8.518700700660123e-01 3.45360e-10 9.37192e-09 3 2.572538511402818e+00 2.572538511487152e+00 8.43334e-11 6.51422e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -4.341729980958290e-01 -4.341729988789662e-01 7.83137e-10 7.33768e-09 2 -2.761142998736194e-01 -2.761143003693180e-01 4.95699e-10 6.42416e-09 3 -1.440110976897264e-01 -1.440110971247852e-01 5.64941e-10 7.83217e-09 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.457478685238560e+00 1.457478682052377e+00 3.18618e-09 5.96786e-09 2 1.203559876374818e+00 1.203559876366525e+00 8.29314e-12 1.65016e-09 3 -7.656387437531679e-01 -7.656387440455720e-01 2.92404e-10 7.31469e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -9.967131979896269e-01 -9.967131977723420e-01 2.17285e-10 6.20632e-09 2 -9.487523725676090e-01 -9.487523699851715e-01 2.58244e-09 1.50199e-08 3 -2.249279096618604e-01 -2.249279107913511e-01 1.12949e-09 3.00023e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -3.848263027971922e-01 -3.848263009732252e-01 1.82397e-09 3.16016e-09 2 2.389132929039653e-01 2.389132945552363e-01 1.65127e-09 4.45336e-09 3 -5.701773525915793e-01 -5.701773525754549e-01 1.61244e-11 6.24872e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 -2.031706630620230e-01 -2.031706626859961e-01 3.76027e-10 3.96115e-09 2 -7.620113580574613e-01 -7.620113570482149e-01 1.00925e-09 4.12075e-09 3 -7.981877047153788e-01 -7.981877044099205e-01 3.05458e-10 2.66246e-09 ----------------------------------------------------------------------------------------------------- Maximum error obtained for particle = 23, direction = 3: |F_model - F_numer| error = ----------------------- = 1.03977e-07 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.03977e-07 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 1.03977e-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.