!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_ADP_ApostolMishin_2011_AlCu__SM_667696763561_000 Supported species : Al Cu random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Al | a0 = 4.04999446869 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.393930048962259e-01 1.393930052078527e-01 3.11627e-10 6.41078e-10 2 -1.750690676975055e-01 -1.750690677296046e-01 3.20991e-11 5.46096e-10 3 -2.750491136829110e-01 -2.750491136967095e-01 1.37985e-11 1.00728e-08 * ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.229460125073900e+00 -1.229460124988536e+00 8.53642e-11 4.56765e-10 2 1.594994074204954e+00 1.594994074243945e+00 3.89910e-11 2.73782e-09 3 5.395732468827024e-01 5.395732470703483e-01 1.87646e-10 7.01514e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 4.668849393906774e-01 4.668849392283489e-01 1.62328e-10 1.05312e-08 * 2 5.939913493812240e-01 5.939913494628720e-01 8.16480e-11 3.53835e-10 3 3.597383870094972e-01 3.597383872100720e-01 2.00575e-10 8.99163e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 5.481448313271490e-01 5.481448314595061e-01 1.32357e-10 6.15570e-10 2 2.556464611720443e-01 2.556464612101300e-01 3.80857e-11 1.49480e-10 3 6.051008140221795e-01 6.051008139880729e-01 3.41066e-11 5.64376e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 6.586252647432880e-01 6.586252647663869e-01 2.30990e-11 2.26476e-09 2 -1.208311135315288e+00 -1.208311135253226e+00 6.20619e-11 8.41806e-10 3 2.082378550365715e-01 2.082378548795541e-01 1.57017e-10 4.04218e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -1.110193605579347e-01 -1.110193604321054e-01 1.25829e-10 3.31345e-10 2 7.740148432192392e-01 7.740148432005015e-01 1.87377e-11 4.43526e-10 3 3.437865833266266e-01 3.437865833537199e-01 2.70932e-11 4.98288e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 5.967858286338237e-01 5.967858284528007e-01 1.81023e-10 8.62318e-10 2 -1.662459608011126e+00 -1.662459608093995e+00 8.28686e-11 5.67121e-10 3 -1.761890180781384e+00 -1.761890180714269e+00 6.71152e-11 3.19732e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.813444902634457e+00 -1.813444902613838e+00 2.06193e-11 6.46784e-10 2 -4.835925544740000e-01 -4.835925545724846e-01 9.84847e-11 2.49471e-10 3 -2.858299138786798e-01 -2.858299139143231e-01 3.56433e-11 3.41760e-09 ----------------------------------------------------------------------------------------------------- 9 Al 1 1.740367780009201e-01 1.740367781811842e-01 1.80264e-10 6.80096e-10 2 -7.958747102242297e-01 -7.958747102096076e-01 1.46221e-11 4.10256e-10 3 -5.133690906463158e-01 -5.133690905785034e-01 6.78123e-11 2.12776e-09 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.922408304755631e-01 -5.922408305538035e-01 7.82404e-11 1.01433e-09 2 2.116292359951480e-01 2.116292359982002e-01 3.05220e-12 9.37384e-10 3 -7.168699187450563e-01 -7.168699187497310e-01 4.67471e-12 2.90930e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.417618404209471e+00 1.417618404266748e+00 5.72775e-11 1.77115e-09 2 -8.897530493751102e-01 -8.897530494659647e-01 9.08544e-11 1.41539e-09 3 -2.423630944933778e-01 -2.423630944333096e-01 6.00682e-11 6.35894e-09 * ----------------------------------------------------------------------------------------------------- 12 Al 1 4.574047168027043e-02 4.574047165315048e-02 2.71199e-11 1.39828e-10 2 8.451269754488792e-01 8.451269753470221e-01 1.01857e-10 4.86711e-10 3 4.550640792460414e-01 4.550640792685428e-01 2.25014e-11 7.93649e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -1.674428899617491e+00 -1.674428899622297e+00 4.80593e-12 1.50600e-09 2 -1.911739045953913e+00 -1.911739045993357e+00 3.94436e-11 7.53186e-10 3 -1.808641995613897e+00 -1.808641995687732e+00 7.38349e-11 4.07167e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 5.708265169136796e-01 5.708265169327901e-01 1.91105e-11 1.00200e-08 * 2 1.016091319973867e+00 1.016091319994930e+00 2.10627e-11 1.17084e-09 3 -1.969265830872984e-01 -1.969265831071214e-01 1.98230e-11 5.89531e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.896895971031347e+00 1.896895971041344e+00 9.99645e-12 2.93607e-09 2 -1.324632774447609e+00 -1.324632774396107e+00 5.15026e-11 8.22100e-10 3 6.402246715383245e-01 6.402246716731184e-01 1.34794e-10 3.45181e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 4.132485561183092e-01 4.132485561078310e-01 1.04783e-11 2.68511e-09 2 1.212152829572139e+00 1.212152829502099e+00 7.00398e-11 5.69527e-10 3 8.719331491059741e-01 8.719331490939026e-01 1.20715e-11 1.08262e-09 ----------------------------------------------------------------------------------------------------- 17 Al 1 -2.293538345344869e-01 -2.293538345321035e-01 2.38334e-12 2.96642e-10 2 1.884258219216146e-01 1.884258219976696e-01 7.60550e-11 4.00043e-10 3 -5.032387566224773e-01 -5.032387568477467e-01 2.25269e-10 7.11734e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.372637695263307e-01 1.372637696089341e-01 8.26034e-11 1.39736e-10 2 1.207252532879283e+00 1.207252532695941e+00 1.83342e-10 1.16690e-09 3 -1.608904800880884e+00 -1.608904800867460e+00 1.34237e-11 5.12615e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 5.048085652027083e-01 5.048085652531519e-01 5.04435e-11 1.60374e-10 2 -7.139018204356715e-01 -7.139018203061342e-01 1.29537e-10 2.22080e-09 3 4.928833384099009e-01 4.928833383798894e-01 3.00115e-11 4.09508e-09 * ----------------------------------------------------------------------------------------------------- 20 Al 1 1.987219940864690e-01 1.987219941850772e-01 9.86083e-11 4.54277e-10 2 6.834581500751621e-01 6.834581501561255e-01 8.09635e-11 1.52517e-09 3 -2.460761385283679e-01 -2.460761386520853e-01 1.23717e-10 3.30944e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.683166678356667e+00 -1.683166678431140e+00 7.44724e-11 2.95637e-09 2 -1.034343293308692e-01 -1.034343297390444e-01 4.08175e-10 2.87206e-10 3 1.461746867900996e-01 1.461746869810556e-01 1.90956e-10 8.08500e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 5.011171927457831e-01 5.011171927298448e-01 1.59384e-11 8.44436e-10 2 2.373500909680197e+00 2.373500909990496e+00 3.10299e-10 8.49798e-10 3 1.620210972795844e+00 1.620210973509367e+00 7.13523e-10 9.10013e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 5.796444921334727e-02 5.796444929115449e-02 7.78072e-11 1.23804e-09 2 1.187621857075243e-01 1.187621856596276e-01 4.78967e-11 1.53246e-10 3 4.478820493862370e-01 4.478820494643558e-01 7.81188e-11 1.32938e-09 ----------------------------------------------------------------------------------------------------- 24 Al 1 5.850851509634722e-01 5.850851510500862e-01 8.66139e-11 5.36637e-10 2 4.391923596453707e-01 4.391923596046146e-01 4.07561e-11 8.39083e-10 3 -2.887833737376982e-01 -2.887833740641995e-01 3.26501e-10 4.29192e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -9.484135432675237e-01 -9.484135431843147e-01 8.32090e-11 2.11026e-09 2 -9.511350471698601e-01 -9.511350472829464e-01 1.13086e-10 5.42004e-10 3 1.074588328682624e+00 1.074588328505985e+00 1.76640e-10 7.86571e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.891694644625304e-01 -6.891694645922449e-01 1.29715e-10 9.20226e-10 2 1.002589270079749e+00 1.002589269749910e+00 3.29839e-10 6.57834e-09 * 3 -1.389736337893567e+00 -1.389736337864710e+00 2.88565e-11 3.62353e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 8.255039791084954e-01 8.255039791543255e-01 4.58301e-11 7.27433e-10 2 -2.856408117539890e+00 -2.856408117568293e+00 2.84026e-11 2.75699e-09 3 5.851153506658648e-01 5.851153507478074e-01 8.19426e-11 5.75643e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -1.110128697703729e+00 -1.110128697572216e+00 1.31513e-10 4.06608e-10 2 1.067585487625732e+00 1.067585487571975e+00 5.37566e-11 9.80795e-10 3 -3.472146896555307e-02 -3.472146889772065e-02 6.78324e-11 3.98806e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -7.376213522882000e-01 -7.376213523967695e-01 1.08569e-10 3.67835e-10 2 -9.605542385022243e-01 -9.605542384434393e-01 5.87850e-11 2.42158e-10 3 3.387234743315719e-01 3.387234743220481e-01 9.52377e-12 1.46294e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -1.783882885677912e-01 -1.783882885568055e-01 1.09857e-11 8.06090e-10 2 6.146202916893639e-01 6.146202916931796e-01 3.81561e-12 1.34333e-10 3 6.562961907416660e-01 6.562961906608686e-01 8.07974e-11 2.21725e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 5.571103205474455e-01 5.571103206006750e-01 5.32295e-11 9.31789e-10 2 -8.727440322264697e-01 -8.727440322037427e-01 2.27269e-11 5.95711e-10 3 8.217964554974999e-02 8.217964554509417e-02 4.65582e-12 1.12498e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 7.010599892010625e-01 7.010599891165858e-01 8.44766e-11 6.92590e-10 2 7.105754324322755e-01 7.105754322849647e-01 1.47311e-10 7.44356e-10 3 4.046879440359912e-01 4.046879440876835e-01 5.16924e-11 1.28919e-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 = 21, direction = 2: |F_model - F_numer| error = ----------------------- = 3.94623e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Cu | a0 = 3.61499881744 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 5.891565669128286e-01 5.891565669462079e-01 3.33793e-11 1.14620e-09 2 3.551691687369390e-01 3.551691687715592e-01 3.46201e-11 3.17733e-10 3 3.380628508367948e-01 3.380628508456497e-01 8.85492e-12 1.17557e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 7.204569354961228e-01 7.204569356039879e-01 1.07865e-10 4.78269e-09 2 -8.549494131075062e-01 -8.549494130839395e-01 2.35667e-11 4.78213e-10 3 -6.915129411822450e-01 -6.915129411291788e-01 5.30662e-11 3.17397e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 7.483818598326420e-01 7.483818595768196e-01 2.55822e-10 2.05432e-09 2 1.767065511670945e-02 1.767065522018394e-02 1.03474e-10 2.12275e-09 3 -3.277635597622210e-01 -3.277635595842304e-01 1.77991e-10 3.81766e-11 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -9.120442925647672e-01 -9.120442928342333e-01 2.69466e-10 1.11954e-09 2 5.583922871108036e-01 5.583922871265635e-01 1.57599e-11 4.88452e-10 3 8.186224348882265e-01 8.186224346694906e-01 2.18736e-10 7.05763e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -3.501184351519534e+00 -3.501184351490917e+00 2.86171e-11 1.04197e-09 2 -8.198527479931459e-01 -8.198527479875133e-01 5.63261e-12 1.54801e-10 3 -1.306927415865915e+00 -1.306927415966421e+00 1.00506e-10 8.04422e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 7.411913521459824e-01 7.411913521488142e-01 2.83173e-12 4.66519e-10 2 1.986619608892651e+00 1.986619608943394e+00 5.07432e-11 4.92872e-10 3 3.993542601938908e-01 3.993542601753297e-01 1.85611e-11 1.94514e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.207320194727394e+00 1.207320194906785e+00 1.79391e-10 7.53504e-10 2 6.544712788184338e-01 6.544712788228909e-01 4.45710e-12 1.02203e-09 3 2.634364341670167e+00 2.634364341802518e+00 1.32351e-10 9.14320e-09 * ----------------------------------------------------------------------------------------------------- 8 Cu 1 3.857470314537004e-01 3.857470313233778e-01 1.30323e-10 6.58392e-10 2 -1.663528131138206e+00 -1.663528131198119e+00 5.99136e-11 5.39227e-10 3 -7.505121848330480e-01 -7.505121848780285e-01 4.49805e-11 1.31525e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 7.646416646599700e-01 7.646416646953680e-01 3.53980e-11 1.53495e-10 2 -8.526869777366708e-05 -8.526881000505798e-05 1.12231e-10 5.03668e-10 3 9.715498337544904e-01 9.715498337339595e-01 2.05309e-11 4.33317e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -7.482594366151075e-01 -7.482594366532513e-01 3.81438e-11 3.14287e-09 2 1.753374391656109e+00 1.753374391583274e+00 7.28351e-11 1.46347e-09 3 -1.157683689487590e+00 -1.157683689577939e+00 9.03484e-11 3.61791e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -1.519966391235429e+00 -1.519966391212992e+00 2.24367e-11 1.58313e-09 2 -1.706753122047513e-01 -1.706753123026541e-01 9.79029e-11 8.44589e-10 3 2.861489743791613e+00 2.861489743482906e+00 3.08707e-10 4.44439e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 6.300465778902249e-01 6.300465779264036e-01 3.61787e-11 2.01704e-09 2 -9.280806478030859e-01 -9.280806478075846e-01 4.49873e-12 2.73035e-10 3 3.477138494701173e-01 3.477138494590131e-01 1.11042e-11 3.68978e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 1.187009476134953e+00 1.187009476563181e+00 4.28229e-10 3.92282e-11 2 -4.636964553310460e-01 -4.636964550590444e-01 2.72002e-10 3.85799e-09 3 -4.339847361288764e-01 -4.339847362525484e-01 1.23672e-10 7.30220e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -4.109261639268085e-01 -4.109261638333025e-01 9.35059e-11 3.51267e-09 2 9.966037474911796e-01 9.966037475964857e-01 1.05306e-10 1.29576e-09 3 -1.299042006409512e+00 -1.299042006432610e+00 2.30986e-11 2.47874e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -2.378928075371192e-01 -2.378928074881424e-01 4.89767e-11 2.09491e-09 2 -2.317925498079843e+00 -2.317925497959923e+00 1.19921e-10 3.73299e-09 3 1.600550040967168e+00 1.600550041260863e+00 2.93694e-10 5.77163e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -2.074471914502717e-01 -2.074471914785846e-01 2.83129e-11 7.69759e-10 2 9.191561383237088e-01 9.191561382922375e-01 3.14713e-11 1.93913e-09 3 -7.608827938305865e-01 -7.608827938660330e-01 3.54464e-11 1.39507e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -1.980467314603436e+00 -1.980467314849772e+00 2.46336e-10 3.77598e-10 2 -3.802709584284792e+00 -3.802709584165652e+00 1.19141e-10 5.21528e-10 3 -2.508025777747434e+00 -2.508025778010297e+00 2.62863e-10 7.96032e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 4.068130990190832e+00 4.068130990316594e+00 1.25762e-10 2.81180e-10 2 3.118937103484710e+00 3.118937103483687e+00 1.02318e-12 4.66176e-10 3 -3.002091642281641e+00 -3.002091642376366e+00 9.47251e-11 1.11908e-08 * ----------------------------------------------------------------------------------------------------- 19 Cu 1 -8.672158916232197e-01 -8.672158915348352e-01 8.83844e-11 9.41918e-10 2 -7.670328807965975e-01 -7.670328808881556e-01 9.15581e-11 1.30469e-10 3 2.162809886113266e+00 2.162809886149630e+00 3.63642e-11 3.28860e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -2.078051721876015e+00 -2.078051721852348e+00 2.36677e-11 6.01372e-10 2 2.867088307661926e+00 2.867088307544442e+00 1.17484e-10 1.56114e-08 * 3 4.046058341281958e+00 4.046058341341471e+00 5.95133e-11 1.20397e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 1.798161447711335e+00 1.798161447795968e+00 8.46330e-11 2.03438e-10 2 4.296635212937474e-01 4.296635213193972e-01 2.56498e-11 4.63584e-10 3 -1.869285407211275e+00 -1.869285407110541e+00 1.00734e-10 6.59544e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.380696091221147e+00 1.380696091183386e+00 3.77602e-11 5.84188e-10 2 -6.467878765488279e-01 -6.467878765323999e-01 1.64280e-11 2.73289e-09 3 -1.264640328661572e+00 -1.264640328558168e+00 1.03404e-10 1.95676e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -1.021169818151785e+00 -1.021169817979069e+00 1.72716e-10 5.44724e-10 2 7.351272370490884e-01 7.351272369918121e-01 5.72763e-11 1.92425e-10 3 -7.844614893264078e-01 -7.844614894582017e-01 1.31794e-10 3.42462e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 -8.162684345972081e-01 -8.162684348399200e-01 2.42712e-10 4.88230e-10 2 5.067931455362599e-01 5.067931455562169e-01 1.99570e-11 4.35460e-10 3 6.116874570102374e-01 6.116874569631622e-01 4.70752e-11 1.59281e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 8.033320598663534e-01 8.033320596822271e-01 1.84126e-10 9.05358e-10 2 -2.775866282384798e-01 -2.775866282758360e-01 3.73562e-11 5.21814e-10 3 -4.307532514740960e-01 -4.307532515242524e-01 5.01564e-11 3.59268e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -7.476011422424889e-01 -7.476011423158083e-01 7.33195e-11 2.88807e-10 2 -6.604460631316587e-01 -6.604460632264220e-01 9.47633e-11 2.17783e-09 3 3.565772302560785e-02 3.565772318457558e-02 1.58968e-10 7.63310e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 7.790092835029000e-01 7.790092833925112e-01 1.10389e-10 8.41792e-10 2 -1.314587974209222e-01 -1.314587974690435e-01 4.81213e-11 1.89375e-09 3 -6.998880202162632e-01 -6.998880200431352e-01 1.73128e-10 2.40994e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 5.703269774053463e-01 5.703269774073051e-01 1.95877e-12 1.78064e-10 2 -5.674526121756422e-02 -5.674526130760792e-02 9.00437e-11 3.81145e-10 3 -5.273332746089795e-01 -5.273332746156585e-01 6.67899e-12 2.08540e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.907312264238679e-01 -1.907312264958169e-01 7.19490e-11 1.22823e-09 2 -5.593918237058594e-01 -5.593918237003339e-01 5.52547e-12 7.84700e-10 3 1.806133307701620e+00 1.806133307674070e+00 2.75504e-11 5.84450e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -4.531541177363712e-01 -4.531541178498673e-01 1.13496e-10 4.41544e-09 2 -5.965207753860320e-01 -5.965207754408866e-01 5.48546e-11 1.48742e-10 3 6.245280014005510e-01 6.245280014365830e-01 3.60321e-11 8.99396e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -9.717309684858652e-01 -9.717309684516858e-01 3.41793e-11 4.45915e-10 2 4.241495570841906e-01 4.241495571145986e-01 3.04080e-11 2.05554e-09 3 -4.687012339753663e-01 -4.687012336274385e-01 3.47928e-10 3.36738e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 2.905027614375610e-01 2.905027613750832e-01 6.24778e-11 2.27210e-09 2 -6.057429831703653e-01 -6.057429832561433e-01 8.57779e-11 2.09126e-10 3 -9.750923191026785e-01 -9.750923188970118e-01 2.05667e-10 1.14860e-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 = ----------------------- = 1.31621e-06 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Al Cu | a0 = 3.66132566234 | (Configuration in file "config-AlCu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 -1.362588743097485e+00 -1.362588742850739e+00 2.46746e-10 6.80942e-09 * 2 -1.531892749270846e+00 -1.531892749408920e+00 1.38074e-10 9.33982e-10 3 3.366400981755851e-01 3.366400979613369e-01 2.14248e-10 6.48798e-09 * ----------------------------------------------------------------------------------------------------- 2 Al 1 -3.350099448259091e+00 -3.350099448145032e+00 1.14059e-10 4.93444e-10 2 3.162466237727397e+00 3.162466237684562e+00 4.28342e-11 1.18578e-09 3 -2.247613210536853e+00 -2.247613209382928e+00 1.15392e-09 1.33368e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 -1.734179873117297e+00 -1.734179872773019e+00 3.44279e-10 1.48687e-09 2 -1.119163611769722e+00 -1.119163611036553e+00 7.33168e-10 2.04487e-09 3 1.786274399877137e+00 1.786274400580484e+00 7.03347e-10 7.93450e-09 * ----------------------------------------------------------------------------------------------------- 4 Cu 1 3.997079369862753e-01 3.997079368820601e-01 1.04215e-10 4.27544e-09 2 -2.156121692127158e+00 -2.156121692061448e+00 6.57092e-11 3.86079e-09 3 5.735440108703068e-01 5.735440109376966e-01 6.73898e-11 6.39653e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 8.840973711649064e-01 8.840973712642004e-01 9.92940e-11 2.06358e-09 2 -5.098050134723847e+00 -5.098050134819928e+00 9.60814e-11 1.04498e-09 3 -2.022226019692264e+00 -2.022226019568150e+00 1.24114e-10 4.75730e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.420363062649339e+00 1.420363062755747e+00 1.06408e-10 1.34454e-10 2 1.264863219533011e+00 1.264863219542638e+00 9.62741e-12 2.46218e-10 3 -7.961027845436167e-01 -7.961027844402048e-01 1.03412e-10 9.78203e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -1.735054705986434e+00 -1.735054706011913e+00 2.54783e-11 6.23215e-10 2 1.259954191239080e+00 1.259954191426615e+00 1.87536e-10 7.09062e-10 3 1.445477154760001e+00 1.445477154646499e+00 1.13502e-10 1.32612e-09 ----------------------------------------------------------------------------------------------------- 8 Al 1 2.527980415143723e+00 2.527980415012177e+00 1.31545e-10 1.30269e-10 2 2.246939435219303e+00 2.246939435612417e+00 3.93114e-10 2.70351e-10 3 6.055715297568372e+00 6.055715297462852e+00 1.05520e-10 3.99547e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -1.587842394357878e+00 -1.587842394381710e+00 2.38323e-11 7.02853e-10 2 -1.480651316163503e+00 -1.480651316240219e+00 7.67155e-11 2.22436e-10 3 -2.597213550251188e+00 -2.597213549968207e+00 2.82981e-10 3.07489e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 1.959883138755163e+00 1.959883138739286e+00 1.58769e-11 2.70484e-10 2 1.657459240418455e+00 1.657459240424063e+00 5.60729e-12 2.49610e-10 3 -9.198365033723856e-01 -9.198365032916933e-01 8.06923e-11 4.19484e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 3.500343426762825e+00 3.500343427055942e+00 2.93117e-10 2.14329e-09 2 -7.658235950175707e-01 -7.658235950354736e-01 1.79029e-11 1.40186e-09 3 4.747310068439627e+00 4.747310068737192e+00 2.97565e-10 8.56311e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.227864040333797e+00 -1.227864040117527e+00 2.16269e-10 1.02381e-09 2 1.192259663709752e+00 1.192259663686696e+00 2.30556e-11 8.31500e-10 3 1.270348925250591e+00 1.270348925250953e+00 3.62155e-13 1.25839e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 1.140754011838268e+00 1.140754011871809e+00 3.35412e-11 5.43151e-10 2 2.307350550689592e+00 2.307350550586126e+00 1.03466e-10 1.57928e-09 3 1.466457243496891e+00 1.466457243457733e+00 3.91576e-11 1.85387e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -1.221640598610512e-01 -1.221640598197869e-01 4.12642e-11 9.25511e-10 2 -3.603567310071926e-01 -3.603567312174773e-01 2.10285e-10 2.67328e-09 3 9.703046758409342e-02 9.703046762620142e-02 4.21080e-11 1.66813e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 -1.152591220283883e+00 -1.152591219982430e+00 3.01454e-10 1.83419e-10 2 -3.832328313803118e-01 -3.832328312873879e-01 9.29239e-11 2.41733e-10 3 -9.952558895933280e-01 -9.952558895599432e-01 3.33849e-11 9.85571e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 -1.242213207960536e+00 -1.242213207922652e+00 3.78841e-11 3.89172e-10 2 -6.307387165227322e-01 -6.307387165439562e-01 2.12240e-11 9.43466e-10 3 -2.134046875818476e+00 -2.134046875942174e+00 1.23698e-10 5.68496e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 1.498882478227007e+00 1.498882478176315e+00 5.06928e-11 1.04721e-09 2 1.333386732944234e+00 1.333386732906890e+00 3.73441e-11 1.12791e-09 3 -2.587725987984264e+00 -2.587725987818340e+00 1.65924e-10 4.45620e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 7.925138112572053e-01 7.925138113502924e-01 9.30871e-11 1.48902e-09 2 -4.554112844474144e-01 -4.554112843966030e-01 5.08114e-11 3.73585e-10 3 -3.049025180252793e+00 -3.049025180593883e+00 3.41090e-10 2.23332e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 -2.533582919623174e-01 -2.533582919864569e-01 2.41396e-11 7.35945e-10 2 -1.028040926100287e+00 -1.028040925929170e+00 1.71117e-10 8.35170e-10 3 1.757006791937369e+00 1.757006792017040e+00 7.96709e-11 4.18569e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -1.470509029505561e+00 -1.470509029429916e+00 7.56450e-11 1.78366e-09 2 6.057941898916989e-01 6.057941898159395e-01 7.57594e-11 4.65469e-10 3 1.056587909507815e+00 1.056587909503796e+00 4.01856e-12 1.44451e-09 ----------------------------------------------------------------------------------------------------- 21 Al 1 1.264235029974988e+00 1.264235029715442e+00 2.59546e-10 1.18081e-09 2 -1.017913767970883e+00 -1.017913767507192e+00 4.63692e-10 1.23186e-09 3 -3.278309953333574e+00 -3.278309953330525e+00 3.04912e-12 4.94206e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -6.028801623998120e-01 -6.028801624295680e-01 2.97560e-11 2.92672e-10 2 -7.444844809042330e-01 -7.444844808150879e-01 8.91451e-11 1.11700e-09 3 9.911278733289425e-01 9.911278734238770e-01 9.49345e-11 6.19894e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 8.535769314193078e-02 8.535769307164710e-02 7.02837e-11 1.41806e-09 2 1.476880172851663e-01 1.476880173714863e-01 8.63200e-11 4.52007e-10 3 -2.992797038936389e-01 -2.992797038863689e-01 7.26996e-12 1.90328e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 -1.535874521636906e+00 -1.535874521585100e+00 5.18063e-11 8.73080e-10 2 1.929159439642437e+00 1.929159439209302e+00 4.33134e-10 1.70882e-09 3 2.611728973980527e-01 2.611728973726619e-01 2.53908e-11 2.96733e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 5.698616701624964e-01 5.698616701125370e-01 4.99595e-11 1.03934e-09 2 1.182156392805559e+00 1.182156392774588e+00 3.09717e-11 3.74141e-10 3 -3.182804708124790e-01 -3.182804706619533e-01 1.50526e-10 2.08679e-09 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.176510225518464e+00 -1.176510225793818e+00 2.75354e-10 1.90438e-09 2 5.731976813073688e-01 5.731976814082659e-01 1.00897e-10 6.81762e-09 * 3 -6.134218452621635e-01 -6.134218453860377e-01 1.23874e-10 5.84717e-09 * ----------------------------------------------------------------------------------------------------- 27 Cu 1 -6.303019028186065e-01 -6.303019029894934e-01 1.70887e-10 1.64192e-09 2 -1.519873702801997e+00 -1.519873702937544e+00 1.35548e-10 1.08899e-09 3 6.030050389275502e-01 6.030050391555604e-01 2.28010e-10 1.77266e-09 ----------------------------------------------------------------------------------------------------- 28 Al 1 -3.160512474680530e-01 -3.160512474872719e-01 1.92188e-11 2.93314e-10 2 -5.221928051401304e-01 -5.221928050776526e-01 6.24778e-11 3.45615e-10 3 -1.680928374331194e-01 -1.680928374522029e-01 1.90835e-11 4.85083e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 3.715867422662349e-01 3.715867423886671e-01 1.22432e-10 1.60804e-09 2 -2.554464373439939e+00 -2.554464373489894e+00 4.99552e-11 1.03109e-09 3 -1.419649816931771e+00 -1.419649816781601e+00 1.50170e-10 9.56850e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 1.012861317461158e+00 1.012861317467546e+00 6.38845e-12 1.19905e-09 2 3.762349107591083e-01 3.762349107624077e-01 3.29942e-12 9.49900e-10 3 7.207916936518209e-01 7.207916935509945e-01 1.00826e-10 4.23178e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 2.073996655979716e-01 2.073996655770614e-01 2.09102e-11 2.24309e-10 2 1.436446837453788e+00 1.436446837341266e+00 1.12522e-10 6.72888e-10 3 -8.104436841577851e-01 -8.104436844900640e-01 3.32279e-10 1.10086e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.864255303177678e+00 1.864255303200715e+00 2.30362e-11 9.97423e-09 * 2 6.930559781618166e-01 6.930559780400939e-01 1.21723e-10 6.82681e-10 3 1.088034443095546e+00 1.088034443180314e+00 8.47680e-11 4.37933e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 23, direction = 1: |F_model - F_numer| error = ----------------------- = 8.23402e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.31621e-06 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 1.31621e-06 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.