!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MendelevKramerOtt_2009_CuZr__MO_600021860456_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 = 3.639084815979004 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 2.848745361916776e-01 2.848745365982986e-01 4.06621e-10 1.96707e-09 2 7.842283921249031e-02 7.842283862918782e-02 5.83302e-10 7.62280e-09 3 -1.531972247360455e-01 -1.531972249745678e-01 2.38522e-10 7.05401e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.433498255058165e-01 -4.433498250719749e-01 4.33842e-10 1.55453e-10 2 8.955482108257424e-01 8.955482113747969e-01 5.49054e-10 9.74082e-09 3 9.857095694666030e-01 9.857095689575204e-01 5.09083e-10 3.36762e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 4.172910048554433e-01 4.172910046153966e-01 2.40047e-10 5.77429e-08 * 2 6.608133954134032e-01 6.608133970239337e-01 1.61053e-09 2.13577e-09 3 4.421526829325170e-01 4.421526836086020e-01 6.76085e-10 7.04555e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 9.519930267457553e-01 9.519930267759908e-01 3.02356e-11 8.45016e-10 2 5.306500416692670e-01 5.306500414881693e-01 1.81098e-10 5.58963e-09 3 2.566651404429125e-01 2.566651417176090e-01 1.27470e-09 2.06087e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 4.035071369503998e-01 4.035071352605406e-01 1.68986e-09 6.33579e-10 2 2.344493707858232e-01 2.344493703737433e-01 4.12080e-10 1.36729e-09 3 3.565792670884487e-01 3.565792668517948e-01 2.36654e-10 3.50851e-08 * ----------------------------------------------------------------------------------------------------- 6 Cu 1 -9.132161375276565e-01 -9.132161373863298e-01 1.41327e-10 5.30186e-09 2 6.576376885433768e-01 6.576376881873499e-01 3.56027e-10 1.14773e-09 3 9.100294184951592e-01 9.100294189442272e-01 4.49068e-10 1.59729e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 3.184858809102191e-01 3.184858801976498e-01 7.12569e-10 7.66248e-09 2 -8.166624967186061e-01 -8.166624959630806e-01 7.55526e-10 1.32328e-09 3 -1.019650476970333e+00 -1.019650476167987e+00 8.02346e-10 1.45953e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.261850766775334e+00 -1.261850767001548e+00 2.26214e-10 1.25804e-08 2 -1.308937096433504e+00 -1.308937095616284e+00 8.17220e-10 4.05993e-10 3 -6.423586859537803e-01 -6.423586856676410e-01 2.86139e-10 2.93603e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 2.188891012115702e-01 2.188891008662758e-01 3.45294e-10 5.31855e-10 2 -1.096450425859335e+00 -1.096450426618582e+00 7.59247e-10 3.58928e-09 3 -9.787755547678466e-02 -9.787755511785315e-02 3.58932e-10 1.77064e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -3.418700149813353e-01 -3.418700160819997e-01 1.10066e-09 4.05545e-09 2 3.854417258565472e-01 3.854417255545220e-01 3.02025e-10 1.44599e-09 3 -4.942718500611394e-01 -4.942718511142766e-01 1.05314e-09 1.24937e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -2.057938140701852e-01 -2.057938143179259e-01 2.47741e-10 9.01246e-09 2 -9.841197907011416e-01 -9.841197899309717e-01 7.70170e-10 2.53048e-09 3 2.128850638681519e-01 2.128850645841940e-01 7.16042e-10 5.07395e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.093642446054584e-01 3.093642447036746e-01 9.82163e-11 2.00294e-09 2 4.385729507714325e-01 4.385729508313005e-01 5.98679e-11 4.86155e-09 3 3.881203861486313e-01 3.881203862796956e-01 1.31064e-10 8.21208e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -6.608469727091280e-01 -6.608469724766479e-01 2.32480e-10 3.81048e-09 2 -1.429108979879757e+00 -1.429108981409192e+00 1.52944e-09 4.36471e-09 3 -1.298649277124017e+00 -1.298649276401288e+00 7.22728e-10 5.33074e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -3.457382897363799e-02 -3.457382891433257e-02 5.93054e-11 5.80161e-09 2 4.879581190662975e-01 4.879581194283574e-01 3.62060e-10 1.94494e-09 3 6.209729970958958e-02 6.209729992005152e-02 2.10462e-10 4.93974e-09 ----------------------------------------------------------------------------------------------------- 15 Cu 1 1.356123548195333e+00 1.356123548212761e+00 1.74276e-11 2.27374e-09 2 -1.169948403194824e+00 -1.169948403321256e+00 1.26432e-10 2.10682e-09 3 3.520693482147345e-01 3.520693485922137e-01 3.77479e-10 3.82240e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 8.265253543168825e-01 8.265253545498368e-01 2.32954e-10 1.26328e-09 2 1.001181017164481e+00 1.001181015982112e+00 1.18237e-09 4.27678e-09 3 6.680838035941917e-01 6.680838037090746e-01 1.14883e-10 3.74227e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -7.660330597229783e-01 -7.660330592032413e-01 5.19737e-10 4.16249e-09 2 -1.592087790901848e-01 -1.592087777142160e-01 1.37597e-09 4.46598e-09 3 -7.424961994350757e-01 -7.424961997432878e-01 3.08212e-10 3.12719e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.333307620593523e+00 1.333307619031965e+00 1.56156e-09 4.16870e-09 2 1.088537783905817e+00 1.088537788459371e+00 4.55355e-09 9.67490e-09 3 2.339028748209695e-01 2.339028762948797e-01 1.47391e-09 4.72598e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 6.637701918448601e-01 6.637701921375301e-01 2.92670e-10 7.96865e-09 2 1.742684039218297e-01 1.742684040351452e-01 1.13316e-10 2.51026e-09 3 5.474941255431949e-02 5.474941346477646e-02 9.10457e-10 8.85144e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.302413774334685e-01 7.302413775928749e-01 1.59406e-10 2.34409e-08 * 2 7.040873030180530e-01 7.040873031443339e-01 1.26281e-10 1.52888e-08 3 -4.892147935777739e-01 -4.892147936596660e-01 8.18920e-11 4.03438e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.248000101937484e+00 -1.248000101844543e+00 9.29414e-11 5.54120e-09 2 5.901521358697026e-01 5.901521355438778e-01 3.25825e-10 7.39771e-10 3 2.666704927811379e-01 2.666704924160023e-01 3.65136e-10 4.92383e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -2.252221989342705e-01 -2.252221978532036e-01 1.08107e-09 1.54671e-09 2 1.571457705132098e+00 1.571457706143261e+00 1.01116e-09 5.53151e-09 3 1.037304284001721e+00 1.037304284396843e+00 3.95122e-10 1.58351e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -5.712311611500973e-01 -5.712311612497754e-01 9.96780e-11 1.35267e-09 2 5.084821726106855e-01 5.084821727148219e-01 1.04136e-10 2.59491e-09 3 -3.925181201988902e-01 -3.925181195331730e-01 6.65717e-10 3.20340e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 3.242574807266262e-01 3.242574805712073e-01 1.55419e-10 3.60437e-09 2 3.393589402170465e-01 3.393589411878044e-01 9.70758e-10 2.32459e-09 3 -1.212908348751273e+00 -1.212908347334490e+00 1.41678e-09 3.30027e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -3.332868505109732e-01 -3.332868509099216e-01 3.98948e-10 3.14067e-09 2 -8.884741673612122e-01 -8.884741687917657e-01 1.43055e-09 1.94557e-08 * 3 5.090201442442174e-01 5.090201451915676e-01 9.47350e-10 6.65661e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.061114045108460e+00 -1.061114044669728e+00 4.38732e-10 3.59822e-09 2 4.354193996058774e-01 4.354193999047904e-01 2.98913e-10 3.73688e-09 3 -1.073466011099627e+00 -1.073466012016604e+00 9.16977e-10 8.02226e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 5.601275310042297e-01 5.601275263840911e-01 4.62014e-09 5.17748e-09 2 -1.995215711734750e+00 -1.995215706631114e+00 5.10364e-09 4.30816e-09 3 -1.809770714040375e-01 -1.809770714442850e-01 4.02474e-11 4.05338e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -2.658630121144154e-01 -2.658630086617874e-01 3.45263e-09 6.08659e-09 2 4.329842215431419e-01 4.329842169746362e-01 4.56851e-09 5.09794e-09 3 -2.695499343715521e-01 -2.695499344133179e-01 4.17658e-11 5.93874e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.838210366601043e-01 -9.838210372616092e-01 6.01505e-10 1.70503e-08 * 2 -1.402196550237281e+00 -1.402196548971585e+00 1.26570e-09 4.53847e-09 3 4.576457061621607e-01 4.576457049364700e-01 1.22569e-09 1.87844e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.743245988189262e-01 -2.743245988735639e-01 5.46376e-11 1.07412e-08 2 8.304389090596540e-01 8.304389098067971e-01 7.47143e-10 2.36250e-09 3 -1.992593178898906e-01 -1.992593176935521e-01 1.96338e-10 2.62492e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 2.681892701109975e-01 2.681892704527726e-01 3.41775e-10 2.51912e-09 2 -1.332215402092796e+00 -1.332215402078772e+00 1.40241e-11 1.38635e-09 3 4.890325663115886e-01 4.890325660910366e-01 2.20552e-10 3.10504e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 6.234501198043600e-01 6.234501200713526e-01 2.66993e-10 5.56179e-09 2 5.366754691106228e-01 5.366754688786988e-01 2.31924e-10 5.03423e-09 3 5.836774062131640e-01 5.836774064118059e-01 1.98642e-10 7.62667e-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 discontinuities. Maximum error obtained for particle = 19, direction = 3: |F_model - F_numer| error = ----------------------- = 1.66295e-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 = 4.5445245742797855 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 5.644315776294463e-01 5.644315762000295e-01 1.42942e-09 4.44836e-09 2 6.216762701266894e-01 6.216762706553082e-01 5.28619e-10 3.63475e-09 3 4.282878022061007e-01 4.282878017604377e-01 4.45663e-10 2.01560e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -2.876111707351187e-01 -2.876111704415327e-01 2.93586e-10 4.24193e-09 2 -1.814149293274034e-01 -1.814149289652028e-01 3.62201e-10 2.11855e-09 3 -9.243993653414122e-01 -9.243993646646242e-01 6.76788e-10 2.43961e-09 ----------------------------------------------------------------------------------------------------- 3 Zr 1 4.741179223630179e-01 4.741179218463756e-01 5.16642e-10 2.34453e-09 2 7.228549144328397e-01 7.228549142434026e-01 1.89437e-10 2.23019e-09 3 3.428058263809832e-01 3.428058263635612e-01 1.74220e-11 2.17090e-09 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -9.746757383393462e-01 -9.746757383379375e-01 1.40865e-12 1.21162e-09 2 -8.651485589159775e-01 -8.651485593927802e-01 4.76803e-10 3.65986e-09 3 5.679194120526672e-01 5.679194120029349e-01 4.97322e-11 2.54629e-09 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -3.473971767463488e-01 -3.473971768116083e-01 6.52595e-11 4.08964e-09 2 -4.284769872944474e-01 -4.284769871617489e-01 1.32699e-10 2.64079e-09 3 2.191188395025183e-01 2.191188399248655e-01 4.22347e-10 3.72312e-10 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -7.632488950466605e-01 -7.632488951368929e-01 9.02324e-11 1.73205e-09 2 7.545008188239084e-01 7.545008192310360e-01 4.07128e-10 6.12505e-09 3 9.897343712313190e-01 9.897343714382072e-01 2.06888e-10 3.84865e-09 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -8.903941735508957e-01 -8.903941737196736e-01 1.68778e-10 3.42194e-09 2 1.229101161437046e+00 1.229101161268414e+00 1.68632e-10 7.55084e-09 3 3.718267747099659e-01 3.718267747474197e-01 3.74538e-11 5.15654e-09 ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.291508654335907e+00 1.291508654264620e+00 7.12876e-11 1.88718e-09 2 -2.516679794945634e-01 -2.516679798658874e-01 3.71324e-10 1.40820e-09 3 1.400941957422824e+00 1.400941957707020e+00 2.84196e-10 2.26638e-09 ----------------------------------------------------------------------------------------------------- 9 Zr 1 5.180984377436691e-01 5.180984370316498e-01 7.12019e-10 1.54098e-09 2 3.315253176405670e-01 3.315253173816791e-01 2.58888e-10 1.30014e-08 3 9.078964741558119e-01 9.078964726037979e-01 1.55201e-09 7.66446e-09 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -7.052352653548979e-01 -7.052352651666719e-01 1.88226e-10 8.41667e-09 2 1.061449807928016e-01 1.061449805306323e-01 2.62169e-10 2.71432e-09 3 6.433716939291074e-01 6.433716932030634e-01 7.26044e-10 4.82118e-09 ----------------------------------------------------------------------------------------------------- 11 Zr 1 8.161191586209841e-01 8.161191584056398e-01 2.15344e-10 4.40819e-09 2 1.420492980395956e+00 1.420492979371878e+00 1.02408e-09 3.44259e-09 3 -1.896597597890189e+00 -1.896597597988392e+00 9.82030e-11 2.71214e-09 ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.545597893790786e-01 3.545597899758325e-01 5.96754e-10 8.62557e-10 2 2.152575578975557e-01 2.152575592610453e-01 1.36349e-09 2.18732e-09 3 -1.188513663060499e+00 -1.188513662830848e+00 2.29651e-10 3.30120e-09 ----------------------------------------------------------------------------------------------------- 13 Zr 1 9.942314422700563e-01 9.942314429167021e-01 6.46646e-10 5.87257e-09 2 -1.048259550212369e+00 -1.048259549628205e+00 5.84164e-10 3.65639e-09 3 4.336378851455874e-01 4.336378864429609e-01 1.29737e-09 2.88550e-09 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -7.187846073378320e-01 -7.187846074537155e-01 1.15884e-10 2.59980e-09 2 -8.889386100998334e-01 -8.889386104735643e-01 3.73731e-10 8.72368e-11 3 6.947308885918180e-01 6.947308884196343e-01 1.72184e-10 1.99692e-09 ----------------------------------------------------------------------------------------------------- 15 Zr 1 3.195703454489370e-01 3.195703463461675e-01 8.97231e-10 2.23310e-09 2 4.479877890723779e-01 4.479877891994155e-01 1.27038e-10 2.32977e-09 3 -7.168462761102661e-01 -7.168462754889398e-01 6.21326e-10 5.48439e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -3.110329851426267e-01 -3.110329852833059e-01 1.40679e-10 2.38343e-09 2 -6.512363211400668e-01 -6.512363206206653e-01 5.19402e-10 3.76905e-09 3 8.393776978307554e-01 8.393776982627165e-01 4.31961e-10 2.78102e-08 * ----------------------------------------------------------------------------------------------------- 17 Zr 1 3.958592740121654e-01 3.958592735029181e-01 5.09247e-10 5.51969e-09 2 8.585947478692022e-01 8.585947476875538e-01 1.81648e-10 6.26845e-09 3 -9.249688574269849e-01 -9.249688569412003e-01 4.85785e-10 5.48002e-09 ----------------------------------------------------------------------------------------------------- 18 Zr 1 1.201317683896797e-01 1.201317669209327e-01 1.46875e-09 2.63228e-09 2 -1.898615293532274e+00 -1.898615293936241e+00 4.03966e-10 5.47486e-09 3 6.781404898741973e-01 6.781404911373383e-01 1.26314e-09 1.65797e-08 * ----------------------------------------------------------------------------------------------------- 19 Zr 1 4.640931818706944e-01 4.640931814389620e-01 4.31732e-10 3.87965e-09 2 9.638062807901234e-01 9.638062801921715e-01 5.97952e-10 1.01333e-08 3 -3.183043522923492e-01 -3.183043528889884e-01 5.96639e-10 5.81396e-09 ----------------------------------------------------------------------------------------------------- 20 Zr 1 7.322677819038539e-01 7.322677819112244e-01 7.37055e-12 4.14901e-09 2 4.525400644354404e-01 4.525400631370297e-01 1.29841e-09 1.97586e-09 3 -7.325511557513791e-01 -7.325511557492240e-01 2.15505e-12 8.66880e-09 ----------------------------------------------------------------------------------------------------- 21 Zr 1 2.682479677925264e-01 2.682479673093400e-01 4.83186e-10 2.69551e-08 * 2 7.413121954041544e-01 7.413121943557662e-01 1.04839e-09 1.38215e-09 3 -2.007484124499238e-01 -2.007484138635366e-01 1.41361e-09 1.60810e-09 ----------------------------------------------------------------------------------------------------- 22 Zr 1 -5.576135082304400e-01 -5.576135080188716e-01 2.11568e-10 4.54225e-10 2 -6.788378033448296e-01 -6.788378011005076e-01 2.24432e-09 9.42236e-09 3 8.026411084581329e-02 8.026410979171779e-02 1.05410e-09 9.50996e-09 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.415709357730682e+00 -1.415709357952143e+00 2.21461e-10 7.43619e-10 2 1.291720314103089e+00 1.291720314311507e+00 2.08418e-10 4.68675e-09 3 -1.280906439297558e+00 -1.280906439261685e+00 3.58731e-11 2.55539e-09 ----------------------------------------------------------------------------------------------------- 24 Zr 1 9.948201577813618e-01 9.948201581704644e-01 3.89103e-10 4.46139e-09 2 -3.233385874904908e-01 -3.233385874461201e-01 4.43707e-11 3.18509e-09 3 -3.891971418730057e-01 -3.891971420543186e-01 1.81313e-10 6.54016e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -1.255771478856856e+00 -1.255771479404498e+00 5.47642e-10 7.45240e-10 2 -1.839673119883670e+00 -1.839673119759943e+00 1.23727e-10 9.42571e-09 3 1.098655091117481e+00 1.098655091805205e+00 6.87724e-10 4.73369e-09 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.773977143413047e+00 1.773977143862734e+00 4.49687e-10 5.78170e-09 2 5.694357853088317e-01 5.694357854504053e-01 1.41574e-10 5.99704e-09 3 -6.621132637322242e-01 -6.621132633406377e-01 3.91587e-10 7.52947e-09 ----------------------------------------------------------------------------------------------------- 27 Zr 1 3.260248598232153e-01 3.260248613145275e-01 1.49131e-09 2.79116e-09 2 3.614629226892744e-01 3.614629228411259e-01 1.51851e-10 9.27359e-09 3 -6.369199092530617e-01 -6.369199096735265e-01 4.20465e-10 2.40896e-09 ----------------------------------------------------------------------------------------------------- 28 Zr 1 -4.715300025782713e-01 -4.715300018856948e-01 6.92576e-10 2.91182e-09 2 1.143409057559606e-01 1.143409056073215e-01 1.48639e-10 7.86336e-09 3 7.392627526779818e-01 7.392627528512298e-01 1.73248e-10 1.59148e-09 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.092495881250579e+00 1.092495881593153e+00 3.42574e-10 2.83083e-09 2 3.657060237519994e-01 3.657060232328834e-01 5.19116e-10 4.82687e-09 3 1.579380144158921e+00 1.579380141947998e+00 2.21092e-09 1.68273e-08 * ----------------------------------------------------------------------------------------------------- 30 Zr 1 -8.794801399056457e-01 -8.794801400541855e-01 1.48540e-10 2.26312e-09 2 -1.181458504144100e+00 -1.181458503773227e+00 3.70873e-10 3.15570e-09 3 -7.942800457899014e-01 -7.942800460124677e-01 2.22566e-10 1.14190e-09 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -1.252828420293209e+00 -1.252828420442064e+00 1.48855e-10 3.96986e-09 2 -3.922846386678976e-01 -3.922846383157673e-01 3.52130e-10 1.97500e-09 3 -1.017168612298256e+00 -1.017168612087308e+00 2.10949e-10 3.69764e-09 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -6.692424241793907e-01 -6.692424263445080e-01 2.16512e-09 2.89967e-09 2 -9.391101471798928e-01 -9.391101464149728e-01 7.64920e-10 1.74157e-09 3 -3.318371192668421e-01 -3.318371204366972e-01 1.16986e-09 5.96372e-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 discontinuities. Maximum error obtained for particle = 22, direction = 3: |F_model - F_numer| error = ----------------------- = 1.31328e-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. MIXED STRUCTURE -- Species = Cu Zr | a0 = 4.110881229813203 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 1.167568263346124e+00 1.167568263508577e+00 1.62453e-10 4.07656e-09 2 8.996111540320226e-01 8.996111540698806e-01 3.78579e-11 3.96877e-09 3 1.366166921292758e+00 1.366166921351514e+00 5.87559e-11 5.12902e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -5.995051256016969e-01 -5.995051256706545e-01 6.89576e-11 2.80704e-09 2 -7.712603410566818e-01 -7.712603425620833e-01 1.50540e-09 4.71203e-09 3 3.523879537834912e-01 3.523879533042746e-01 4.79217e-10 3.32509e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 5.554183011928941e-01 5.554183017100242e-01 5.17130e-10 7.68924e-09 2 1.031647598575113e+00 1.031647598405899e+00 1.69214e-10 4.92778e-09 3 -4.847810899117746e-01 -4.847810902608016e-01 3.49027e-10 3.29480e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 5.105091019700259e-01 5.105091011764096e-01 7.93616e-10 7.13519e-10 2 -4.933770509034244e-01 -4.933770510427428e-01 1.39318e-10 3.58246e-09 3 -3.856476365753801e-01 -3.856476359392191e-01 6.36161e-10 6.97129e-09 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -6.800480793889987e-01 -6.800480799305274e-01 5.41529e-10 3.49234e-08 * 2 9.262141473463142e-01 9.262141472786100e-01 6.77043e-11 6.56733e-09 3 4.956970188399839e-01 4.956970207886323e-01 1.94865e-09 4.57497e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -9.376262579854170e-01 -9.376262582677265e-01 2.82310e-10 1.88980e-09 2 1.269915818657701e-01 1.269915812592512e-01 6.06519e-10 2.29431e-09 3 1.086910735461094e+00 1.086910736019334e+00 5.58240e-10 2.54738e-10 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -4.096500996067021e-01 -4.096500988998756e-01 7.06826e-10 1.99853e-09 2 9.410816368753623e-01 9.410816362652764e-01 6.10086e-10 6.82213e-09 3 8.090311634689890e-01 8.090311651168298e-01 1.64784e-09 3.79003e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.213653785389243e+00 -1.213653786484828e+00 1.09558e-09 1.09708e-08 2 -1.219102055437500e+00 -1.219102056956331e+00 1.51883e-09 9.65371e-10 3 -8.015660888809660e-01 -8.015660890294195e-01 1.48453e-10 2.47977e-08 * ----------------------------------------------------------------------------------------------------- 9 Cu 1 7.117867469967117e-01 7.117867471024911e-01 1.05779e-10 1.42321e-08 2 -2.920914000245440e-01 -2.920914012235002e-01 1.19896e-09 8.78628e-09 3 7.934524592552796e-01 7.934524580208766e-01 1.23440e-09 6.22411e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -2.256637099970590e+00 -2.256637097610105e+00 2.36048e-09 7.00397e-09 2 -9.701495200207104e-01 -9.701495189792411e-01 1.04147e-09 1.61041e-09 3 -2.405026075101780e+00 -2.405026073625777e+00 1.47600e-09 2.04897e-09 ----------------------------------------------------------------------------------------------------- 11 Zr 1 3.646858292939735e-01 3.646858294599121e-01 1.65939e-10 2.39339e-09 2 7.877562289713205e-02 7.877562016533460e-02 2.73180e-09 2.57967e-08 * 3 7.686223043795392e-01 7.686223050555966e-01 6.76057e-10 1.05973e-08 ----------------------------------------------------------------------------------------------------- 12 Cu 1 8.472762973218523e-01 8.472762969680719e-01 3.53780e-10 2.62953e-09 2 -6.461523739365816e-01 -6.461523716152099e-01 2.32137e-09 8.15353e-09 3 4.316545396532241e-02 4.316544934400095e-02 4.62132e-09 8.73156e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 6.310882389918048e-01 6.310882388997490e-01 9.20558e-11 9.46899e-09 2 3.973071813348011e-01 3.973071804062550e-01 9.28546e-10 1.77579e-09 3 8.706164573080541e-01 8.706164570776689e-01 2.30385e-10 1.43498e-09 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -7.240535254014421e-01 -7.240535261281127e-01 7.26671e-10 4.11264e-09 2 -8.678458896504362e-01 -8.678458892283353e-01 4.22101e-10 5.92691e-09 3 7.802939695514104e-01 7.802939717868581e-01 2.23545e-09 4.91762e-09 ----------------------------------------------------------------------------------------------------- 15 Zr 1 6.394594454073753e-01 6.394594482211859e-01 2.81381e-09 1.03678e-08 2 1.006745589325981e+00 1.006745589580316e+00 2.54336e-10 3.59390e-09 3 -2.684941753998819e+00 -2.684941753382367e+00 6.16451e-10 2.00352e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 2.184168796756953e+00 2.184168795720673e+00 1.03628e-09 1.17207e-09 2 2.418437003751544e-01 2.418437001090155e-01 2.66139e-10 1.25202e-09 3 2.835529001758029e+00 2.835529000664236e+00 1.09379e-09 4.59297e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 6.483979847251117e-01 6.483979851277089e-01 4.02597e-10 1.15688e-08 2 1.041880761783710e+00 1.041880762020296e+00 2.36585e-10 2.45378e-09 3 2.817735267081883e-01 2.817735284985067e-01 1.79032e-09 8.79441e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 -4.650912808161694e-01 -4.650912774986807e-01 3.31749e-09 7.28750e-09 2 -7.820608725904994e-01 -7.820608722393312e-01 3.51168e-10 1.32445e-08 3 -3.290226683341359e-01 -3.290226722073394e-01 3.87320e-09 1.97547e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 8.018907357990952e-02 8.018907361096522e-02 3.10557e-11 2.37944e-09 2 1.026001434160336e+00 1.026001434336701e+00 1.76364e-10 2.36281e-09 3 -7.916303051853976e-01 -7.916303066359643e-01 1.45057e-09 3.59096e-09 ----------------------------------------------------------------------------------------------------- 20 Zr 1 8.855168430621051e-01 8.855168433563870e-01 2.94282e-10 2.17002e-09 2 -4.916474633590209e-01 -4.916474631166330e-01 2.42388e-10 4.49650e-09 3 -7.571118444393181e-01 -7.571118437266443e-01 7.12674e-10 3.18408e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 4.797514648097340e-01 4.797514618913759e-01 2.91836e-09 7.61152e-10 2 1.183776190710688e+00 1.183776190747673e+00 3.69846e-11 5.77351e-09 3 -2.288199662554622e-01 -2.288199660693390e-01 1.86123e-10 1.07702e-09 ----------------------------------------------------------------------------------------------------- 22 Zr 1 3.461009656674387e-01 3.461009658145121e-01 1.47073e-10 1.37648e-09 2 -3.053781963010630e+00 -3.053781963343457e+00 3.32828e-10 4.09916e-10 3 1.234490555380310e+00 1.234490555178313e+00 2.01997e-10 4.45858e-09 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.211803022906454e+00 -1.211803022927679e+00 2.12250e-11 4.94554e-09 2 1.498679313903062e+00 1.498679313859043e+00 4.40190e-11 3.59021e-09 3 -1.492959760165140e+00 -1.492959759487957e+00 6.77183e-10 2.21454e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 2.471263305344889e-01 2.471263312770652e-01 7.42576e-10 5.49520e-09 2 -3.296854562968317e-01 -3.296854575161863e-01 1.21935e-09 2.71611e-09 3 -1.043040650733717e+00 -1.043040652799597e+00 2.06588e-09 3.08347e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 6.305437530623592e-01 6.305437543167731e-01 1.25441e-09 3.62990e-09 2 8.755346145751892e-01 8.755346148332372e-01 2.58048e-10 4.33094e-09 3 5.421033450824770e-01 5.421033463298335e-01 1.24736e-09 4.48372e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 4.425718188530323e-02 4.425718335901929e-02 1.47372e-09 2.00885e-08 * 2 -1.272875411221260e+00 -1.272875411784072e+00 5.62812e-10 3.75042e-09 3 -1.098416853256217e-01 -1.098416860557795e-01 7.30158e-10 1.65180e-09 ----------------------------------------------------------------------------------------------------- 27 Zr 1 -6.969252474545522e-01 -6.969252476436388e-01 1.89087e-10 2.64456e-09 2 3.579275633394877e-01 3.579275632044628e-01 1.35025e-10 3.81996e-09 3 -3.922845729589430e-01 -3.922845729705876e-01 1.16446e-11 6.83136e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 9.789647245234911e-01 9.789647252093532e-01 6.85862e-10 2.20788e-09 2 -1.028910083018339e+00 -1.028910083142507e+00 1.24168e-10 3.87775e-09 3 -8.687091607280930e-01 -8.687091609928083e-01 2.64715e-10 3.64870e-09 ----------------------------------------------------------------------------------------------------- 29 Zr 1 -3.216379075109038e+00 -3.216379076470125e+00 1.36109e-09 1.16938e-08 2 4.095147466316573e-01 4.095147488788501e-01 2.24719e-09 5.81006e-09 3 1.088957872787563e-01 1.088957872214963e-01 5.72600e-11 4.33484e-09 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -1.410312127089902e-02 -1.410312133769572e-02 6.67967e-11 1.99194e-09 2 8.694777853693423e-01 8.694777848466622e-01 5.22680e-10 1.74364e-09 3 -5.495595406536986e-01 -5.495595406368291e-01 1.68695e-11 2.32901e-09 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -1.838484975428767e-03 -1.838485049619025e-03 7.41903e-11 1.13283e-09 2 -2.740562241309303e-01 -2.740562235039634e-01 6.26967e-10 9.04409e-10 3 1.743260894407859e+00 1.743260894943573e+00 5.35713e-10 3.22381e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 4.745048627489753e-01 4.745048619221460e-01 8.26829e-10 5.80711e-09 2 -4.200145184437329e-01 -4.200145182480622e-01 1.95671e-10 3.75787e-09 3 -7.874547486732939e-01 -7.874547486611115e-01 1.21824e-11 1.80391e-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 discontinuities. Maximum error obtained for particle = 12, direction = 3: |F_model - F_numer| error = ----------------------- = 1.07061e-07 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.07061e-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 1.07061e-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.