!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 4.049994468688965 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.393930048962313e-01 1.393930049661631e-01 6.99318e-11 8.81343e-10 2 -1.750690676975158e-01 -1.750690677786466e-01 8.11308e-11 9.66616e-10 3 -2.750491136829051e-01 -2.750491135280414e-01 1.54864e-10 5.87534e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.229460125073901e+00 -1.229460125054560e+00 1.93412e-11 6.73257e-10 2 1.594994074204953e+00 1.594994074201110e+00 3.84359e-12 1.92257e-10 3 5.395732468827052e-01 5.395732469612868e-01 7.85816e-11 6.37522e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 4.668849393906641e-01 4.668849392142542e-01 1.76410e-10 3.83021e-10 2 5.939913493812293e-01 5.939913494713925e-01 9.01632e-11 3.29294e-10 3 3.597383870094737e-01 3.597383869032397e-01 1.06234e-10 1.37383e-09 ----------------------------------------------------------------------------------------------------- 4 Al 1 5.481448313271567e-01 5.481448315127544e-01 1.85598e-10 2.44065e-10 2 2.556464611720473e-01 2.556464612067165e-01 3.46692e-11 4.84376e-10 3 6.051008140221780e-01 6.051008140092118e-01 1.29662e-11 8.22041e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 6.586252647432767e-01 6.586252647500938e-01 6.81710e-12 9.29793e-10 2 -1.208311135315300e+00 -1.208311135304251e+00 1.10487e-11 7.71028e-10 3 2.082378550365633e-01 2.082378548401663e-01 1.96397e-10 1.00584e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 -1.110193605579303e-01 -1.110193604253984e-01 1.32532e-10 9.91689e-10 2 7.740148432192433e-01 7.740148432040976e-01 1.51457e-11 4.75245e-10 3 3.437865833266259e-01 3.437865832130399e-01 1.13586e-10 3.86789e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 5.967858286338102e-01 5.967858285529154e-01 8.08948e-11 9.00444e-10 2 -1.662459608011103e+00 -1.662459607989934e+00 2.11688e-11 1.26884e-09 3 -1.761890180781359e+00 -1.761890180755835e+00 2.55242e-11 1.94326e-09 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.813444902634423e+00 -1.813444902999029e+00 3.64606e-10 1.18981e-09 2 -4.835925544739896e-01 -4.835925542812546e-01 1.92735e-10 1.04142e-09 3 -2.858299138786450e-01 -2.858299137905875e-01 8.80576e-11 1.25414e-09 ----------------------------------------------------------------------------------------------------- 9 Al 1 1.740367780009347e-01 1.740367778410566e-01 1.59878e-10 6.18487e-10 2 -7.958747102242090e-01 -7.958747101537033e-01 7.05057e-11 1.23698e-10 3 -5.133690906462873e-01 -5.133690904627823e-01 1.83505e-10 7.77380e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.922408304755473e-01 -5.922408304154634e-01 6.00839e-11 1.20681e-09 2 2.116292359951245e-01 2.116292359801310e-01 1.49935e-11 7.67666e-10 3 -7.168699187450351e-01 -7.168699187624227e-01 1.73875e-11 8.06784e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.417618404209460e+00 1.417618404124103e+00 8.53573e-11 1.21294e-09 2 -8.897530493750867e-01 -8.897530494528371e-01 7.77504e-11 1.25089e-09 3 -2.423630944933962e-01 -2.423630944029846e-01 9.04117e-11 7.63487e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 4.574047168028002e-02 4.574047159516573e-02 8.51143e-11 5.97851e-10 2 8.451269754488385e-01 8.451269755154239e-01 6.65854e-11 4.22950e-10 3 4.550640792460456e-01 4.550640793110027e-01 6.49572e-11 4.26166e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -1.674428899617433e+00 -1.674428899691918e+00 7.44851e-11 1.50806e-09 2 -1.911739045953851e+00 -1.911739045900071e+00 5.37799e-11 3.41766e-10 3 -1.808641995613835e+00 -1.808641995751267e+00 1.37433e-10 2.26830e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 5.708265169136317e-01 5.708265169395805e-01 2.59488e-11 1.39619e-09 2 1.016091319973807e+00 1.016091319921466e+00 5.23412e-11 4.62208e-10 3 -1.969265830872602e-01 -1.969265832092775e-01 1.22017e-10 6.61912e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.896895971031293e+00 1.896895971083948e+00 5.26550e-11 7.41423e-10 2 -1.324632774447540e+00 -1.324632774594243e+00 1.46703e-10 4.26195e-10 3 6.402246715382874e-01 6.402246716195359e-01 8.12485e-11 7.04352e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 4.132485561183289e-01 4.132485560246663e-01 9.36626e-11 1.34765e-09 2 1.212152829572092e+00 1.212152829515625e+00 5.64671e-11 1.06761e-09 3 8.719331491059229e-01 8.719331493185457e-01 2.12623e-10 2.10423e-09 ----------------------------------------------------------------------------------------------------- 17 Al 1 -2.293538345344808e-01 -2.293538345296651e-01 4.81573e-12 8.59342e-10 2 1.884258219216140e-01 1.884258219371268e-01 1.55128e-11 1.32057e-10 3 -5.032387566224623e-01 -5.032387567609740e-01 1.38512e-10 4.46361e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.372637695263493e-01 1.372637694771578e-01 4.91915e-11 6.94020e-10 2 1.207252532879274e+00 1.207252533157784e+00 2.78511e-10 1.60241e-09 3 -1.608904800880824e+00 -1.608904800964145e+00 8.33207e-11 7.85757e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 5.048085652027144e-01 5.048085652362648e-01 3.35504e-11 8.47468e-10 2 -7.139018204356413e-01 -7.139018205272524e-01 9.16111e-11 7.33097e-10 3 4.928833384098760e-01 4.928833383322241e-01 7.76519e-11 1.03398e-09 ----------------------------------------------------------------------------------------------------- 20 Al 1 1.987219940864743e-01 1.987219941884416e-01 1.01967e-10 1.60071e-09 2 6.834581500751615e-01 6.834581500389389e-01 3.62226e-11 3.45456e-10 3 -2.460761385283783e-01 -2.460761383689715e-01 1.59407e-10 1.39141e-09 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.683166678356642e+00 -1.683166678463586e+00 1.06944e-10 8.85429e-10 2 -1.034343293308474e-01 -1.034343296224146e-01 2.91567e-10 7.23289e-11 3 1.461746867901086e-01 1.461746868330832e-01 4.29746e-11 5.82673e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 5.011171927457551e-01 5.011171926618870e-01 8.38680e-11 3.49747e-10 2 2.373500909680180e+00 2.373500909485371e+00 1.94810e-10 1.78165e-09 3 1.620210972795828e+00 1.620210973042104e+00 2.46276e-10 6.86792e-08 * ----------------------------------------------------------------------------------------------------- 23 Al 1 5.796444921332976e-02 5.796444918458631e-02 2.87435e-11 3.75509e-10 2 1.187621857075287e-01 1.187621856126705e-01 9.48582e-11 3.14639e-10 3 4.478820493862216e-01 4.478820492505574e-01 1.35664e-10 6.82599e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 5.850851509634482e-01 5.850851511547174e-01 1.91269e-10 4.26904e-10 2 4.391923596453476e-01 4.391923597139393e-01 6.85917e-11 6.60765e-10 3 -2.887833737377350e-01 -2.887833739024439e-01 1.64709e-10 1.04574e-09 ----------------------------------------------------------------------------------------------------- 25 Al 1 -9.484135432675016e-01 -9.484135432758961e-01 8.39451e-12 1.71252e-10 2 -9.511350471698211e-01 -9.511350472097198e-01 3.98986e-11 5.47233e-10 3 1.074588328682648e+00 1.074588328370621e+00 3.12028e-10 6.70420e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.891694644625497e-01 -6.891694644431053e-01 1.94443e-11 9.62891e-10 2 1.002589270079702e+00 1.002589270103378e+00 2.36764e-11 2.83577e-10 3 -1.389736337893538e+00 -1.389736338028928e+00 1.35390e-10 5.83233e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 8.255039791084626e-01 8.255039791833242e-01 7.48616e-11 5.90018e-10 2 -2.856408117539859e+00 -2.856408117558967e+00 1.91078e-11 9.08402e-10 3 5.851153506658097e-01 5.851153505431114e-01 1.22698e-10 4.04873e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -1.110128697703703e+00 -1.110128697714766e+00 1.10627e-11 6.36237e-10 2 1.067585487625703e+00 1.067585487768430e+00 1.42727e-10 4.08469e-10 3 -3.472146896557694e-02 -3.472146920687156e-02 2.41295e-10 2.24609e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -7.376213522881739e-01 -7.376213525325380e-01 2.44364e-10 2.57084e-10 2 -9.605542385022161e-01 -9.605542385018111e-01 4.05009e-13 8.20922e-10 3 3.387234743315981e-01 3.387234744084775e-01 7.68794e-11 3.73722e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -1.783882885678056e-01 -1.783882885660652e-01 1.74041e-12 1.11164e-10 2 6.146202916893231e-01 6.146202917412176e-01 5.18945e-11 6.76391e-11 3 6.562961907416581e-01 6.562961906841782e-01 5.74799e-11 3.98343e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 5.571103205473841e-01 5.571103204208505e-01 1.26534e-10 6.08213e-10 2 -8.727440322264273e-01 -8.727440323080194e-01 8.15922e-11 7.75386e-10 3 8.217964554971739e-02 8.217964556253429e-02 1.28169e-11 1.15775e-09 ----------------------------------------------------------------------------------------------------- 32 Al 1 7.010599892011070e-01 7.010599892307515e-01 2.96445e-11 8.98122e-10 2 7.105754324322385e-01 7.105754325115331e-01 7.92946e-11 1.47554e-09 3 4.046879440359706e-01 4.046879440098633e-01 2.61073e-11 5.69756e-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 discontinuities. Maximum error obtained for particle = 28, direction = 3: |F_model - F_numer| error = ----------------------- = 6.94944e-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 = 3.6149988174438477 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 5.891565669128532e-01 5.891565667911423e-01 1.21711e-10 8.99854e-11 2 3.551691687369628e-01 3.551691687583137e-01 2.13509e-11 4.54451e-10 3 3.380628508368259e-01 3.380628507843617e-01 5.24641e-11 1.48082e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 7.204569354961025e-01 7.204569356038376e-01 1.07735e-10 7.93114e-10 2 -8.549494131074435e-01 -8.549494133807090e-01 2.73265e-10 8.74610e-11 3 -6.915129411821833e-01 -6.915129411036521e-01 7.85312e-11 1.00325e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 7.483818598326066e-01 7.483818598619401e-01 2.93334e-11 4.55483e-10 2 1.767065511671683e-02 1.767065514930453e-02 3.25877e-11 4.20517e-10 3 -3.277635597622582e-01 -3.277635596041091e-01 1.58149e-10 2.28754e-08 * ----------------------------------------------------------------------------------------------------- 4 Cu 1 -9.120442925647400e-01 -9.120442923957672e-01 1.68973e-10 1.11608e-09 2 5.583922871107869e-01 5.583922870759209e-01 3.48660e-11 4.85009e-10 3 8.186224348882097e-01 8.186224350328122e-01 1.44602e-10 3.59320e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -3.501184351519570e+00 -3.501184351460738e+00 5.88325e-11 4.38883e-10 2 -8.198527479931419e-01 -8.198527480706275e-01 7.74856e-11 8.06219e-10 3 -1.306927415865980e+00 -1.306927415947613e+00 8.16329e-11 2.03866e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 7.411913521459641e-01 7.411913520713012e-01 7.46629e-11 8.63416e-10 2 1.986619608892638e+00 1.986619608918601e+00 2.59626e-11 5.36671e-10 3 3.993542601939032e-01 3.993542601351913e-01 5.87119e-11 3.10080e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.207320194727441e+00 1.207320194787107e+00 5.96656e-11 6.10349e-10 2 6.544712788184416e-01 6.544712787764619e-01 4.19796e-11 6.31034e-11 3 2.634364341670225e+00 2.634364341575635e+00 9.45892e-11 4.07411e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 3.857470314537294e-01 3.857470314906588e-01 3.69294e-11 1.33456e-09 2 -1.663528131138170e+00 -1.663528131133609e+00 4.56124e-12 1.33307e-09 3 -7.505121848330215e-01 -7.505121847242948e-01 1.08727e-10 7.08883e-11 ----------------------------------------------------------------------------------------------------- 9 Cu 1 7.646416646600062e-01 7.646416646791645e-01 1.91583e-11 1.55722e-09 2 -8.526869779887716e-05 -8.526861315259892e-05 8.46463e-11 2.88356e-10 3 9.715498337545138e-01 9.715498336851764e-01 6.93373e-11 6.38525e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -7.482594366151181e-01 -7.482594364912257e-01 1.23892e-10 1.87698e-10 2 1.753374391656081e+00 1.753374391737601e+00 8.15203e-11 2.99651e-10 3 -1.157683689487549e+00 -1.157683689349329e+00 1.38220e-10 3.23702e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -1.519966391235452e+00 -1.519966391245317e+00 9.86455e-12 4.59146e-10 2 -1.706753122047703e-01 -1.706753120848497e-01 1.19921e-10 8.31905e-10 3 2.861489743791541e+00 2.861489743937240e+00 1.45699e-10 1.09662e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 6.300465778902592e-01 6.300465779594643e-01 6.92051e-11 3.54358e-10 2 -9.280806478030897e-01 -9.280806476563384e-01 1.46751e-10 3.07027e-10 3 3.477138494700904e-01 3.477138495030330e-01 3.29426e-11 3.73739e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 1.187009476134908e+00 1.187009475991007e+00 1.43901e-10 4.29601e-10 2 -4.636964553310702e-01 -4.636964552680231e-01 6.30472e-11 2.66360e-09 3 -4.339847361288622e-01 -4.339847361266760e-01 2.18620e-12 5.40923e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -4.109261639267929e-01 -4.109261639721838e-01 4.53910e-11 7.71965e-10 2 9.966037474912313e-01 9.966037473587043e-01 1.32527e-10 1.31850e-09 3 -1.299042006409582e+00 -1.299042006589552e+00 1.79971e-10 2.05849e-09 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -2.378928075371044e-01 -2.378928075401898e-01 3.08537e-12 3.10110e-10 2 -2.317925498079879e+00 -2.317925498187213e+00 1.07335e-10 6.51780e-10 3 1.600550040967245e+00 1.600550041036404e+00 6.91589e-11 2.62944e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -2.074471914502971e-01 -2.074471916046271e-01 1.54330e-10 1.57556e-09 2 9.191561383237544e-01 9.191561382873314e-01 3.64230e-11 7.75619e-10 3 -7.608827938306524e-01 -7.608827939188916e-01 8.82392e-11 5.79833e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -1.980467314603358e+00 -1.980467314367334e+00 2.36023e-10 7.84525e-10 2 -3.802709584284703e+00 -3.802709584274893e+00 9.81037e-12 1.36708e-10 3 -2.508025777747427e+00 -2.508025777717459e+00 2.99685e-11 1.53920e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 4.068130990190740e+00 4.068130990254989e+00 6.42491e-11 1.44329e-09 2 3.118937103484654e+00 3.118937103436043e+00 4.86109e-11 5.36650e-10 3 -3.002091642281612e+00 -3.002091642155769e+00 1.25843e-10 7.15755e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -8.672158916231463e-01 -8.672158915133662e-01 1.09780e-10 5.50286e-10 2 -7.670328807965926e-01 -7.670328808975719e-01 1.00979e-10 1.96747e-10 3 2.162809886113216e+00 2.162809886195354e+00 8.21379e-11 1.23962e-09 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -2.078051721875989e+00 -2.078051721822290e+00 5.36984e-11 3.12169e-10 2 2.867088307661969e+00 2.867088307695174e+00 3.32050e-11 9.12253e-10 3 4.046058341281925e+00 4.046058341269047e+00 1.28777e-11 2.06723e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 1.798161447711304e+00 1.798161447696904e+00 1.44005e-11 4.08156e-10 2 4.296635212937725e-01 4.296635213203441e-01 2.65716e-11 2.04984e-09 3 -1.869285407211202e+00 -1.869285407328086e+00 1.16883e-10 1.53005e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.380696091221061e+00 1.380696091437051e+00 2.15990e-10 5.31306e-10 2 -6.467878765488352e-01 -6.467878765331480e-01 1.56872e-11 3.61240e-10 3 -1.264640328661534e+00 -1.264640328719143e+00 5.76086e-11 8.91514e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -1.021169818151798e+00 -1.021169818102913e+00 4.88847e-11 4.05293e-08 * 2 7.351272370491013e-01 7.351272370632929e-01 1.41915e-11 3.44233e-10 3 -7.844614893264102e-01 -7.844614895608297e-01 2.34419e-10 1.75305e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 -8.162684345971748e-01 -8.162684346288430e-01 3.16682e-11 2.25147e-09 2 5.067931455362283e-01 5.067931454761977e-01 6.00306e-11 3.89151e-10 3 6.116874570101581e-01 6.116874568986098e-01 1.11548e-10 3.41569e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 8.033320598663747e-01 8.033320599470450e-01 8.06704e-11 4.34546e-10 2 -2.775866282384877e-01 -2.775866283587029e-01 1.20215e-10 4.74078e-10 3 -4.307532514740725e-01 -4.307532514046347e-01 6.94378e-11 7.74561e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -7.476011422425369e-01 -7.476011424351540e-01 1.92617e-10 3.08977e-10 2 -6.604460631316190e-01 -6.604460629748046e-01 1.56814e-10 8.61456e-10 3 3.565772302559700e-02 3.565772288104168e-02 1.44555e-10 3.15858e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 7.790092835028573e-01 7.790092834363403e-01 6.65169e-11 2.11973e-10 2 -1.314587974209863e-01 -1.314587974752851e-01 5.42988e-11 9.52665e-10 3 -6.998880202162773e-01 -6.998880201884768e-01 2.78004e-11 4.46263e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 5.703269774053399e-01 5.703269774100997e-01 4.75986e-12 1.63142e-09 2 -5.674526121756381e-02 -5.674526121374721e-02 3.81661e-12 6.82495e-10 3 -5.273332746089887e-01 -5.273332743823793e-01 2.26609e-10 1.22319e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.907312264238242e-01 -1.907312264504304e-01 2.66062e-11 4.41902e-10 2 -5.593918237059936e-01 -5.593918236155309e-01 9.04627e-11 1.14684e-09 3 1.806133307701638e+00 1.806133307710826e+00 9.18843e-12 1.77096e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -4.531541177363682e-01 -4.531541177617136e-01 2.53454e-11 9.88389e-11 2 -5.965207753860420e-01 -5.965207754568073e-01 7.07653e-11 6.72014e-10 3 6.245280014005453e-01 6.245280015855762e-01 1.85031e-10 4.91143e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -9.717309684858644e-01 -9.717309684550200e-01 3.08443e-11 3.30499e-08 * 2 4.241495570841955e-01 4.241495570199877e-01 6.42078e-11 7.06999e-10 3 -4.687012339753575e-01 -4.687012341254422e-01 1.50085e-10 3.50402e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 2.905027614375855e-01 2.905027614515614e-01 1.39759e-11 4.96133e-10 2 -6.057429831703460e-01 -6.057429831919349e-01 2.15888e-11 3.30507e-10 3 -9.750923191026641e-01 -9.750923191307083e-01 2.80441e-11 4.95194e-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 discontinuities. Maximum error obtained for particle = 9, direction = 2: |F_model - F_numer| error = ----------------------- = 9.92701e-07 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 = 3.774603639767156 | (Configuration in file "config-AlCu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 8.393072970447989e-01 8.393072973929938e-01 3.48195e-10 7.57864e-10 2 3.638818888573201e-01 3.638818889457057e-01 8.83856e-11 1.33801e-10 3 6.677126743777277e-01 6.677126745139352e-01 1.36207e-10 3.25297e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 1.461554954700814e+00 1.461554954572123e+00 1.28691e-10 1.85868e-10 2 -2.141233067847951e+00 -2.141233067824330e+00 2.36211e-11 5.95405e-10 3 -1.377566164540483e+00 -1.377566164576130e+00 3.56473e-11 1.74499e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.810900634176321e+00 1.810900633976330e+00 1.99991e-10 4.46220e-10 2 1.066655606795068e+00 1.066655606570687e+00 2.24381e-10 8.86913e-10 3 -2.120279448653726e-01 -2.120279450526520e-01 1.87279e-10 1.34270e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -1.062525318618567e+00 -1.062525318614006e+00 4.56146e-12 3.49735e-10 2 -3.295968693303192e-01 -3.295968693160417e-01 1.42775e-11 3.48816e-10 3 -9.579252147875876e-01 -9.579252147994204e-01 1.18328e-11 6.65824e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -9.334717838403305e-01 -9.334717838037223e-01 3.66082e-11 8.70776e-10 2 7.682039642607903e-01 7.682039641070781e-01 1.53712e-10 2.06996e-10 3 5.140838804203857e-01 5.140838806149816e-01 1.94596e-10 3.64666e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 2.219299242025996e-01 2.219299240345479e-01 1.68052e-10 4.33082e-10 2 -1.885007289822789e+00 -1.885007289812719e+00 1.00693e-11 9.54091e-10 3 -7.806685916527034e-01 -7.806685916421362e-01 1.05672e-11 1.52964e-09 ----------------------------------------------------------------------------------------------------- 7 Al 1 -1.122991483742128e+00 -1.122991483820561e+00 7.84337e-11 7.88545e-11 2 1.221072571453268e+00 1.221072571571583e+00 1.18314e-10 6.52137e-10 3 6.994609675987590e-01 6.994609676332048e-01 3.44458e-11 6.09612e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 4.173714296983267e-01 4.173714296515108e-01 4.68160e-11 4.92378e-10 2 -3.822644162491073e+00 -3.822644162835079e+00 3.44006e-10 6.64081e-10 3 -1.262843365789091e+00 -1.262843365809950e+00 2.08595e-11 1.79612e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -7.410365809494512e-01 -7.410365810026122e-01 5.31609e-11 1.53366e-09 2 7.537751568234615e-01 7.537751569138856e-01 9.04241e-11 1.10878e-09 3 1.460361451717423e+00 1.460361451775859e+00 5.84359e-11 8.18256e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 5.368924240018788e-02 5.368924235780292e-02 4.23850e-11 3.37540e-10 2 -6.907510375157397e-01 -6.907510377594790e-01 2.43739e-10 5.61373e-10 3 5.244005640838268e-01 5.244005641580780e-01 7.42512e-11 1.37692e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 2.305174446868687e+00 2.305174446587141e+00 2.81546e-10 2.14134e-10 2 4.387228105265893e+00 4.387228104957060e+00 3.08833e-10 2.67312e-09 3 2.456754164597806e+00 2.456754164699899e+00 1.02093e-10 1.28922e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 6.458090554629763e-01 6.458090556017023e-01 1.38726e-10 3.45213e-10 2 -1.462976363692752e+00 -1.462976363799360e+00 1.06607e-10 3.18384e-10 3 -3.716016022841194e-01 -3.716016025757618e-01 2.91642e-10 2.91683e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -7.211754669459493e-01 -7.211754670035004e-01 5.75512e-11 6.36534e-10 2 9.898664122499666e-01 9.898664123603962e-01 1.10430e-10 1.05795e-09 3 -8.608533675318126e-03 -8.608533819189371e-03 1.43871e-10 5.16120e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -1.551694100434066e+00 -1.551694100405659e+00 2.84073e-11 1.82851e-10 2 -7.173575388732968e-01 -7.173575388684350e-01 4.86178e-12 3.52060e-10 3 1.834669355081412e+00 1.834669355070714e+00 1.06981e-11 1.55476e-08 * ----------------------------------------------------------------------------------------------------- 15 Al 1 1.410421749484750e+00 1.410421749506725e+00 2.19749e-11 1.10837e-09 2 3.261468077290895e+00 3.261468077357093e+00 6.61977e-11 3.15008e-10 3 1.250449174946683e+00 1.250449174602345e+00 3.44339e-10 5.48278e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 7.431273219119935e-01 7.431273219387960e-01 2.68026e-11 1.01341e-09 2 1.794685921871211e-01 1.794685918205531e-01 3.66568e-10 5.48092e-10 3 -8.874156652577128e-01 -8.874156653859600e-01 1.28247e-10 7.03740e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 1.764521409464762e-01 1.764521409480332e-01 1.55692e-12 2.19597e-10 2 -7.647235393362591e-01 -7.647235392851989e-01 5.10603e-11 3.90720e-10 3 5.376908864571346e-01 5.376908864172831e-01 3.98515e-11 6.35683e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.379034255070058e+00 1.379034255119068e+00 4.90104e-11 1.74842e-09 2 -3.372327206492067e+00 -3.372327206491879e+00 1.88294e-13 6.51921e-10 3 -2.430396946348621e-01 -2.430396946202233e-01 1.46388e-11 3.88994e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -1.579647081459552e+00 -1.579647081391042e+00 6.85094e-11 1.32808e-09 2 3.383345523805280e-01 3.383345523125942e-01 6.79338e-11 2.33084e-09 3 -1.559998728132828e+00 -1.559998728129279e+00 3.54872e-12 1.51378e-09 ----------------------------------------------------------------------------------------------------- 20 Al 1 -4.158471394723658e-01 -4.158471395532751e-01 8.09092e-11 1.68191e-09 2 2.197160467639530e-02 2.197160451240212e-02 1.63993e-10 2.25067e-10 3 2.393448527402187e+00 2.393448527432640e+00 3.04525e-11 6.83694e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.064529010086782e+00 -1.064529010076539e+00 1.02425e-11 5.70493e-10 2 7.824777886586498e-01 7.824777885054764e-01 1.53173e-10 7.24234e-10 3 -1.074590015402032e+00 -1.074590015044256e+00 3.57776e-10 1.48147e-09 ----------------------------------------------------------------------------------------------------- 22 Al 1 -8.504971900390583e-01 -8.504971901941464e-01 1.55088e-10 1.32941e-09 2 1.476744181284976e+00 1.476744181292214e+00 7.23710e-12 8.06311e-10 3 -1.572931235471347e+00 -1.572931235800761e+00 3.29413e-10 2.75437e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 9.156447542039245e-02 9.156447550358687e-02 8.31944e-11 5.31214e-10 2 -1.364033347217261e+00 -1.364033347167315e+00 4.99463e-11 9.12955e-10 3 6.341465762452332e-01 6.341465761516112e-01 9.36220e-11 2.19048e-09 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.030310951857130e+00 1.030310951839357e+00 1.77729e-11 2.63644e-09 2 2.131769119355384e+00 2.131769119395435e+00 4.00506e-11 8.21744e-10 3 6.360042568861359e-01 6.360042567247994e-01 1.61336e-10 5.86881e-08 * ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.628360123975016e+00 -1.628360124194740e+00 2.19724e-10 1.91180e-09 2 1.520938379985588e+00 1.520938379954772e+00 3.08156e-11 6.27728e-10 3 -6.132032388987850e-01 -6.132032392854763e-01 3.86691e-10 3.64968e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 1.031377336924851e+00 1.031377336900395e+00 2.44558e-11 6.70571e-10 2 -6.502135208188293e-01 -6.502135208467140e-01 2.78847e-11 4.67266e-10 3 -8.013758961572018e-02 -8.013758943461566e-02 1.81105e-10 5.42939e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -8.749142038484364e-01 -8.749142037665738e-01 8.18626e-11 4.09563e-10 2 -2.227072798464711e+00 -2.227072798253301e+00 2.11410e-10 4.35025e-10 3 -5.998794674792254e-01 -5.998794676720750e-01 1.92850e-10 5.41889e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 1.512977161613411e-01 1.512977161589749e-01 2.36622e-12 7.70163e-11 2 -2.583888289203941e-01 -2.583888290142990e-01 9.39050e-11 7.04701e-10 3 -5.699195935427830e-01 -5.699195933785730e-01 1.64210e-10 7.07416e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 2.349928661875533e+00 2.349928661777717e+00 9.78160e-11 1.66706e-09 2 2.854909839021389e+00 2.854909839008589e+00 1.28009e-11 1.66455e-09 3 3.128093901586812e+00 3.128093901540395e+00 4.64166e-11 9.82120e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.203283498504839e+00 -2.203283498337757e+00 1.67082e-10 3.72530e-10 2 -2.369860105940059e+00 -2.369860105796930e+00 1.43129e-10 1.21801e-09 3 -1.567260826794568e+00 -1.567260826784978e+00 9.59011e-12 1.25826e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -2.165044923962228e+00 -2.165044923876947e+00 8.52816e-11 6.68335e-10 2 -8.394213782562907e-01 -8.394213783036372e-01 4.73465e-11 1.70154e-09 3 -1.025931838398149e+00 -1.025931838367187e+00 3.09619e-11 3.38469e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 7.957663116715329e-01 7.957663116304962e-01 4.10367e-11 1.04631e-09 2 7.768412144730967e-01 7.768412146811806e-01 2.08084e-10 5.96547e-10 3 -1.971727070178836e+00 -1.971727070479467e+00 3.00631e-10 1.98502e-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 = 13, direction = 3: |F_model - F_numer| error = ----------------------- = 1.67126e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 9.92701e-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 9.92701e-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.