!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_HoytGarvinWebb_2003_PbCu__MO_119135752160_005 Supported species : Cu Pb 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 = 3.6150341033935547 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 5.073054851679210e-01 5.073054852087526e-01 4.08317e-11 5.48829e-10 2 9.010571978995122e-02 9.010571986348351e-02 7.35323e-11 5.45595e-10 3 -9.940822076616815e-02 -9.940822093784861e-02 1.71680e-10 4.09892e-09 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.441923447764998e-01 -4.441923448114543e-01 3.49545e-11 1.60007e-10 2 5.945747907365261e-01 5.945747907233495e-01 1.31766e-11 1.75075e-09 3 7.894730627693314e-01 7.894730628564307e-01 8.70993e-11 4.21966e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 2.290464740895988e-01 2.290464738445895e-01 2.45009e-10 2.06643e-09 2 6.178778758602571e-01 6.178778757592283e-01 1.01029e-10 2.81832e-10 3 4.592643810398079e-01 4.592643808652394e-01 1.74568e-10 1.81114e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 6.460742152749448e-01 6.460742153415386e-01 6.65938e-11 3.22374e-10 2 4.495015881009810e-01 4.495015880788324e-01 2.21486e-11 1.54998e-10 3 5.178506572728844e-01 5.178506573934295e-01 1.20545e-10 5.76598e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 2.783273415490399e-01 2.783273414865750e-01 6.24649e-11 5.85823e-10 2 3.406599279105088e-01 3.406599278834238e-01 2.70850e-11 2.75772e-09 3 1.109079173392405e-02 1.109079167301406e-02 6.09100e-11 1.77304e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -9.986871897267776e-01 -9.986871897129476e-01 1.38300e-11 1.89642e-10 2 3.755324566993173e-01 3.755324564753842e-01 2.23933e-10 1.61727e-09 3 9.266860695929521e-01 9.266860695515222e-01 4.14299e-11 2.60903e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.577413945172313e+00 1.577413945201035e+00 2.87217e-11 3.24568e-10 2 -2.615102772832040e+00 -2.615102772909115e+00 7.70752e-11 8.82308e-10 3 -3.216993557171236e+00 -3.216993556864321e+00 3.06915e-10 2.17020e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.280434827593915e+00 -2.280434827739692e+00 1.45777e-10 4.42543e-09 2 -5.230364152324283e-01 -5.230364150192428e-01 2.13185e-10 1.63328e-08 * 3 -8.482829935126367e-01 -8.482829941248764e-01 6.12240e-10 1.22676e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 8.388580364737204e-02 8.388580371384297e-02 6.64709e-11 4.72995e-09 2 -2.130172633184340e+00 -2.130172633093057e+00 9.12830e-11 2.55073e-10 3 -1.788036151236472e+00 -1.788036150904595e+00 3.31877e-10 1.41553e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.122029059482617e+00 -1.122029059597735e+00 1.15118e-10 6.87665e-09 2 1.201817157007016e+00 1.201817157366130e+00 3.59115e-10 5.82923e-09 3 -1.596260156212651e+00 -1.596260155290879e+00 9.21772e-10 2.08607e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -7.092924930775747e-01 -7.092924930692873e-01 8.28737e-12 1.76333e-09 2 -1.894043059256340e+00 -1.894043059335129e+00 7.87881e-11 1.36957e-09 3 1.506778456043007e+00 1.506778456197082e+00 1.54075e-10 1.04489e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 2.856094053351756e-01 2.856094058005982e-01 4.65423e-10 6.09355e-09 2 1.726923991054490e+00 1.726923990986540e+00 6.79499e-11 1.05030e-08 * 3 1.915119918868145e+00 1.915119919502173e+00 6.34028e-10 3.95587e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -9.608347486874091e-01 -9.608347482242485e-01 4.63161e-10 1.46835e-09 2 -2.235992765282552e+00 -2.235992765095783e+00 1.86769e-10 5.90644e-10 3 -3.300247391474105e+00 -3.300247392003623e+00 5.29518e-10 3.71731e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 1.406984787896131e-01 1.406984783572629e-01 4.32350e-10 3.44950e-10 2 6.703610803686650e-01 6.703610803724473e-01 3.78231e-12 2.09367e-10 3 -6.334119759573473e-02 -6.334119759535402e-02 3.80709e-13 1.56335e-11 ----------------------------------------------------------------------------------------------------- 15 Cu 1 2.998991423877037e+00 2.998991423617422e+00 2.59615e-10 4.19685e-09 2 -1.126069229376151e+00 -1.126069229415337e+00 3.91864e-11 1.01288e-09 3 9.609484252138886e-01 9.609484249888131e-01 2.25076e-10 1.57968e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.080682026350376e+00 1.080682026362075e+00 1.16986e-11 1.10937e-09 2 2.291713505464140e+00 2.291713505523658e+00 5.95173e-11 2.67827e-09 3 1.461493529438278e+00 1.461493529263634e+00 1.74644e-10 1.46222e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -1.183215724913389e+00 -1.183215724624563e+00 2.88826e-10 3.98399e-09 2 -6.626420465331291e-01 -6.626420464223718e-01 1.10757e-10 6.49150e-10 3 -7.255702705928252e-01 -7.255702707045425e-01 1.11717e-10 1.39962e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.720399295917258e+00 1.720399295567728e+00 3.49530e-10 2.35858e-09 2 1.464240153941655e+00 1.464240153682572e+00 2.59082e-10 3.86093e-09 3 -1.546510790181088e-02 -1.546510753231577e-02 3.69495e-10 2.25474e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 8.305936394187126e-01 8.305936397264694e-01 3.07757e-10 2.60826e-09 2 4.483311734393781e-01 4.483311734598799e-01 2.05018e-11 8.41400e-10 3 1.643349389027859e-01 1.643349389892756e-01 8.64897e-11 1.01750e-09 ----------------------------------------------------------------------------------------------------- 20 Cu 1 6.686149498914580e-01 6.686149498918170e-01 3.59046e-13 8.86158e-10 2 5.127220397949290e-01 5.127220398280257e-01 3.30966e-11 1.79122e-10 3 -5.306225791809390e-01 -5.306225792124707e-01 3.15317e-11 3.46647e-11 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -2.456368792441711e+00 -2.456368792095892e+00 3.45819e-10 1.32336e-09 2 -3.794661664704535e-01 -3.794661664945024e-01 2.40489e-11 2.23150e-09 3 1.939593415519667e+00 1.939593416099276e+00 5.79609e-10 9.97459e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.121110815592056e+00 1.121110815566436e+00 2.56204e-11 2.29977e-09 2 2.620174288091821e+00 2.620174288113716e+00 2.18949e-11 1.12495e-09 3 2.116129691236824e+00 2.116129691328803e+00 9.19784e-11 2.68473e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -6.878930319638309e-01 -6.878930320110785e-01 4.72477e-11 2.53412e-10 2 6.689379501019210e-01 6.689379501278211e-01 2.59001e-11 2.18838e-10 3 -5.273321072195493e-01 -5.273321071226226e-01 9.69267e-11 1.56640e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 9.317512546898338e-02 9.317512577223469e-02 3.03251e-10 2.77400e-09 2 3.558912723427568e-01 3.558912736979545e-01 1.35520e-09 4.78267e-09 3 -9.602076901357582e-01 -9.602076901210561e-01 1.47021e-11 2.13821e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -6.943820438362323e-01 -6.943820434871896e-01 3.49043e-10 2.59984e-09 2 -8.456417115494194e-01 -8.456417115205818e-01 2.88376e-11 1.31422e-09 3 -5.236364209247283e-01 -5.236364206764889e-01 2.48239e-10 1.65477e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.139458730230758e+00 -1.139458730144796e+00 8.59623e-11 2.92585e-09 2 1.220824219244073e+00 1.220824219088189e+00 1.55883e-10 1.63207e-09 3 -1.639248385479441e+00 -1.639248385664971e+00 1.85529e-10 3.14701e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 1.571320489955494e+00 1.571320490080500e+00 1.25006e-10 7.46671e-10 2 -3.593787242925904e+00 -3.593787242830550e+00 9.53539e-11 6.03781e-10 3 9.623161882702961e-01 9.623161884304819e-01 1.60186e-10 1.34495e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -1.335952728351348e+00 -1.335952728248917e+00 1.02431e-10 1.41551e-10 2 1.443659415151454e+00 1.443659415142855e+00 8.59912e-12 2.82636e-10 3 -1.381180794768463e-01 -1.381180794021572e-01 7.46891e-11 8.31753e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -5.765578483232286e-01 -5.765578482078184e-01 1.15410e-10 2.96055e-09 2 -1.415896277441431e+00 -1.415896277671746e+00 2.30315e-10 5.14137e-10 3 1.361700388254395e+00 1.361700388151505e+00 1.02890e-10 2.19859e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -1.303879678442462e-01 -1.303879678853554e-01 4.11091e-11 5.51170e-10 2 9.388064183306072e-01 9.388064184115293e-01 8.09222e-11 8.88497e-09 * 3 2.590691023005502e-01 2.590691022287347e-01 7.18155e-11 5.79935e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -6.304112698124656e-01 -6.304112698185006e-01 6.03495e-12 1.18295e-09 2 -9.375681423138623e-01 -9.375681422734025e-01 4.04599e-11 7.67880e-10 3 -1.783289950084966e-01 -1.783289949242880e-01 8.42085e-11 6.72843e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.516849885564649e+00 1.516849885575476e+00 1.08269e-11 2.06052e-09 2 3.267634389676057e-01 3.267634389496319e-01 1.79738e-11 4.56618e-10 3 7.992502874326616e-01 7.992502874372136e-01 4.55203e-12 1.96035e-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 = 18, direction = 3: |F_model - F_numer| error = ----------------------- = 2.38922e-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 = Pb | a0 = 4.910130500793462 | (Configuration in file "config-Pb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pb 1 2.660950600404259e-01 2.660950600410492e-01 6.23279e-13 1.21707e-09 2 2.097432597073169e-01 2.097432596962409e-01 1.10760e-11 9.63564e-10 3 2.453024103149407e-01 2.453024103148407e-01 9.99756e-14 4.28989e-10 ----------------------------------------------------------------------------------------------------- 2 Pb 1 1.914961602082783e-01 1.914961602762957e-01 6.80175e-11 1.26896e-10 2 2.815564608736568e-01 2.815564608159467e-01 5.77101e-11 2.07514e-10 3 4.364043359431603e-01 4.364043359471553e-01 3.99503e-12 4.43705e-11 ----------------------------------------------------------------------------------------------------- 3 Pb 1 2.324814710702990e-01 2.324814711204195e-01 5.01205e-11 3.36452e-10 2 4.989183780641396e-01 4.989183780721527e-01 8.01303e-12 2.80065e-10 3 1.515269727518992e-01 1.515269727337124e-01 1.81868e-11 5.04354e-10 ----------------------------------------------------------------------------------------------------- 4 Pb 1 4.373042910379479e-01 4.373042910345438e-01 3.40405e-12 4.37989e-10 2 2.125362232144948e-01 2.125362231902531e-01 2.42417e-11 9.30562e-11 3 2.776686915932923e-01 2.776686915615325e-01 3.17599e-11 6.35628e-10 ----------------------------------------------------------------------------------------------------- 5 Pb 1 -2.699865944730031e-01 -2.699865944753710e-01 2.36794e-12 4.74648e-10 2 3.129730609861606e-01 3.129730609921707e-01 6.01008e-12 4.44919e-11 3 4.624596340057593e-01 4.624596340200564e-01 1.42971e-11 1.60049e-10 ----------------------------------------------------------------------------------------------------- 6 Pb 1 -4.159702888510663e-01 -4.159702888561871e-01 5.12079e-12 4.07910e-11 2 1.869104265429129e-01 1.869104265441894e-01 1.27653e-12 1.74006e-09 * 3 3.532931666412138e-01 3.532931666518485e-01 1.06347e-11 1.15394e-10 ----------------------------------------------------------------------------------------------------- 7 Pb 1 -3.650321752677794e-01 -3.650321752699061e-01 2.12663e-12 3.51416e-11 2 3.438362156639041e-01 3.438362156543400e-01 9.56407e-12 1.96931e-10 3 1.553293419232256e-01 1.553293419319093e-01 8.68372e-12 5.37735e-11 ----------------------------------------------------------------------------------------------------- 8 Pb 1 -2.082231486497813e-01 -2.082231486571971e-01 7.41585e-12 1.21138e-10 2 4.553453868630879e-01 4.553453868504701e-01 1.26178e-11 2.28074e-07 * 3 -5.963506868015814e-01 -5.963506867603355e-01 4.12459e-11 2.11681e-08 * ----------------------------------------------------------------------------------------------------- 9 Pb 1 4.310535726696435e-01 4.310535726805382e-01 1.08947e-11 6.05616e-12 2 -2.716257244543934e-01 -2.716257243716325e-01 8.27609e-11 5.70068e-10 3 4.044623164197103e-01 4.044623164138871e-01 5.82323e-12 4.08593e-10 ----------------------------------------------------------------------------------------------------- 10 Pb 1 3.238384564091483e-01 3.238384563706631e-01 3.84852e-11 2.45681e-11 2 -3.925188445641669e-01 -3.925188445648324e-01 6.65523e-13 1.71911e-10 3 2.810754730534307e-01 2.810754730898101e-01 3.63794e-11 1.28214e-10 ----------------------------------------------------------------------------------------------------- 11 Pb 1 2.479681470770723e-01 2.479681466987497e-01 3.78323e-10 1.72982e-09 * 2 -1.187649650434820e-01 -1.187649649643798e-01 7.91021e-11 8.40806e-10 3 1.558883396981109e-01 1.558883397214733e-01 2.33625e-11 6.99937e-10 ----------------------------------------------------------------------------------------------------- 12 Pb 1 3.274552332436692e-01 3.274552332409513e-01 2.71788e-12 8.09005e-11 2 -4.037890298473710e-01 -4.037890298507861e-01 3.41516e-12 1.45431e-08 * 3 3.015213176049850e-01 3.015213175957097e-01 9.27530e-12 4.03546e-10 ----------------------------------------------------------------------------------------------------- 13 Pb 1 -3.408577619593386e-01 -3.408577619803125e-01 2.09738e-11 2.54338e-10 2 -1.014422967637579e-01 -1.014422967786226e-01 1.48647e-11 2.14084e-10 3 1.336907372247953e-01 1.336907372070908e-01 1.77044e-11 5.31956e-10 ----------------------------------------------------------------------------------------------------- 14 Pb 1 -3.000934913823748e-01 -3.000934913788391e-01 3.53573e-12 7.99899e-12 2 -3.538313020485663e-01 -3.538313020655481e-01 1.69817e-11 1.29462e-10 3 2.768502729002449e-01 2.768502728887806e-01 1.14643e-11 4.60026e-11 ----------------------------------------------------------------------------------------------------- 15 Pb 1 -6.025658811540806e-02 -6.025658811749695e-02 2.08888e-12 1.59134e-10 2 -1.141877411894238e-01 -1.141877411816262e-01 7.79762e-12 2.14419e-10 3 2.890696205852997e-01 2.890696205752528e-01 1.00469e-11 1.16878e-10 ----------------------------------------------------------------------------------------------------- 16 Pb 1 -3.809909250848114e-01 -3.809909248030681e-01 2.81743e-10 4.91173e-10 2 -2.878909473729596e-01 -2.878909471506201e-01 2.22339e-10 1.46598e-10 3 1.994873927863931e-01 1.994873928229926e-01 3.65995e-11 2.11694e-10 ----------------------------------------------------------------------------------------------------- 17 Pb 1 4.267672415756897e-01 4.267672415862244e-01 1.05347e-11 8.78283e-11 2 4.337553192575916e-01 4.337553192439647e-01 1.36269e-11 5.93918e-11 3 -1.997096643295878e-01 -1.997096643009123e-01 2.86755e-11 4.26056e-11 ----------------------------------------------------------------------------------------------------- 18 Pb 1 2.116845943137994e-01 2.116845942949631e-01 1.88362e-11 6.53830e-10 2 6.972845831666927e-02 6.972845834978185e-02 3.31126e-11 5.88631e-10 3 -1.965730296188445e-01 -1.965730296989325e-01 8.00880e-11 2.63455e-11 ----------------------------------------------------------------------------------------------------- 19 Pb 1 -3.656572655148640e-01 -3.656572655341516e-01 1.92875e-11 1.53477e-10 2 -2.880878495347877e-03 -2.880878510260839e-03 1.49130e-11 1.70191e-10 3 -3.700245292823344e-01 -3.700245292961425e-01 1.38081e-11 3.64317e-10 ----------------------------------------------------------------------------------------------------- 20 Pb 1 4.322707192455377e-01 4.322707192709820e-01 2.54443e-11 3.01108e-10 2 1.796436190293131e-01 1.796436190637761e-01 3.44630e-11 5.51169e-10 3 -3.720230950251227e-01 -3.720230950193238e-01 5.79886e-12 2.51466e-09 * ----------------------------------------------------------------------------------------------------- 21 Pb 1 -4.712801057105348e-01 -4.712801057930724e-01 8.25376e-11 3.95751e-10 2 -4.822779845251020e-01 -4.822779845436603e-01 1.85583e-11 6.44560e-11 3 3.057411304360602e-01 3.057411304464264e-01 1.03662e-11 5.72591e-10 ----------------------------------------------------------------------------------------------------- 22 Pb 1 1.001062742347186e-01 1.001062742413863e-01 6.66769e-12 7.12133e-11 2 2.888084712610901e-01 2.888084712847865e-01 2.36964e-11 2.13489e-10 3 -2.354110316537256e-01 -2.354110316710485e-01 1.73229e-11 3.33848e-10 ----------------------------------------------------------------------------------------------------- 23 Pb 1 -2.877621038709258e-01 -2.877621039402582e-01 6.93324e-11 1.69240e-10 2 3.900517684234363e-01 3.900517684448930e-01 2.14567e-11 4.64965e-10 3 -3.622761012940752e-01 -3.622761013317273e-01 3.76522e-11 2.63525e-10 ----------------------------------------------------------------------------------------------------- 24 Pb 1 2.074687274817101e-01 2.074687274585418e-01 2.31684e-11 1.38349e-10 2 6.612083303157128e-01 6.612083303325137e-01 1.68009e-11 2.27460e-10 3 -3.373569594437719e-01 -3.373569594302740e-01 1.34979e-11 9.45782e-10 ----------------------------------------------------------------------------------------------------- 25 Pb 1 4.436127172135819e-01 4.436127171887798e-01 2.48021e-11 4.05755e-10 2 -1.787987517432907e-01 -1.787987517622024e-01 1.89117e-11 1.29363e-10 3 -9.327616303487259e-02 -9.327616304325304e-02 8.38045e-12 8.11356e-11 ----------------------------------------------------------------------------------------------------- 26 Pb 1 -6.356137012596522e-02 -6.356137013586739e-02 9.90218e-12 1.05727e-10 2 -5.080159426118739e-01 -5.080159425617454e-01 5.01285e-11 4.04779e-10 3 -6.421146638607923e-01 -6.421146638761074e-01 1.53151e-11 9.65307e-10 ----------------------------------------------------------------------------------------------------- 27 Pb 1 -2.503208517564475e-01 -2.503208517806026e-01 2.41552e-11 1.96323e-11 2 -4.539614234783743e-01 -4.539614234912237e-01 1.28494e-11 2.22550e-11 3 -4.646409949336842e-01 -4.646409949328691e-01 8.15126e-13 1.45417e-08 * ----------------------------------------------------------------------------------------------------- 28 Pb 1 1.294298595859145e-01 1.294298595972108e-01 1.12963e-11 4.99774e-10 2 -3.711562001803009e-01 -3.711562001785913e-01 1.70958e-12 3.07879e-10 3 -2.244286349311455e-01 -2.244286349294695e-01 1.67605e-12 3.16850e-11 ----------------------------------------------------------------------------------------------------- 29 Pb 1 -3.212666236519084e-01 -3.212666236665563e-01 1.46479e-11 1.14520e-10 2 2.301210849483874e-01 2.301210850389658e-01 9.05784e-11 3.83437e-10 3 1.530014148080550e-01 1.530014148114367e-01 3.38163e-12 3.21080e-11 ----------------------------------------------------------------------------------------------------- 30 Pb 1 -4.801210321666505e-01 -4.801210321709553e-01 4.30483e-12 1.72288e-11 2 -3.975145749611397e-01 -3.975145749558275e-01 5.31225e-12 7.20006e-09 * 3 -1.590886544248096e-01 -1.590886544269552e-01 2.14553e-12 1.29886e-10 ----------------------------------------------------------------------------------------------------- 31 Pb 1 -3.915855646425101e-01 -3.915855646164495e-01 2.60606e-11 4.18749e-10 2 -2.060497898723267e-01 -2.060497897748217e-01 9.75049e-11 1.84842e-10 3 -2.484658839936045e-01 -2.484658839966573e-01 3.05281e-12 1.61441e-10 ----------------------------------------------------------------------------------------------------- 32 Pb 1 5.639333658159333e-01 5.639333657941599e-01 2.17735e-11 1.97825e-09 * 2 -1.104300663159972e-01 -1.104300663517933e-01 3.57961e-11 5.57977e-10 3 -8.103247606262431e-02 -8.103247609478835e-02 3.21640e-11 1.57588e-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 = 2: |F_model - F_numer| error = ----------------------- = 5.17653e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Cu Pb | a0 = 4.313832836261192 | (Configuration in file "config-CuPb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 5.675542982722648e-01 5.675542983025238e-01 3.02590e-11 2.50225e-10 2 6.213117312914775e-01 6.213117313072798e-01 1.58022e-11 6.39568e-11 3 7.758651386546090e-01 7.758651386726477e-01 1.80387e-11 5.66740e-11 ----------------------------------------------------------------------------------------------------- 2 Pb 1 -6.193435353117891e-01 -6.193435353194225e-01 7.63345e-12 9.70791e-10 2 -1.631906259112542e-01 -1.631906259654427e-01 5.41885e-11 2.00150e-09 3 7.196696224081081e-01 7.196696221205273e-01 2.87581e-10 1.03835e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 3.835387024928618e-02 3.835387019092010e-02 5.83661e-11 2.77129e-10 2 8.880415622624508e-01 8.880415622307180e-01 3.17328e-11 3.17984e-10 3 -3.528865702285273e-01 -3.528865702891752e-01 6.06479e-11 8.37175e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 1.131739581407406e+00 1.131739581435581e+00 2.81752e-11 7.34892e-10 2 3.635786497286816e-02 3.635786500246011e-02 2.95919e-11 1.27649e-10 3 2.436168655605929e-02 2.436168652752852e-02 2.85308e-11 4.39165e-11 ----------------------------------------------------------------------------------------------------- 5 Pb 1 -2.146881340901499e-01 -2.146881341947707e-01 1.04621e-10 2.85355e-10 2 2.414912595627569e-01 2.414912595799347e-01 1.71778e-11 1.33490e-09 3 4.135572538993776e-01 4.135572538931295e-01 6.24806e-12 3.49574e-10 ----------------------------------------------------------------------------------------------------- 6 Pb 1 2.836680503478614e-01 2.836680503474822e-01 3.79141e-13 1.39238e-10 2 -6.227275914199246e-01 -6.227275913622407e-01 5.76840e-11 6.35069e-11 3 1.930845539550107e-01 1.930845539096319e-01 4.53788e-11 3.06035e-10 ----------------------------------------------------------------------------------------------------- 7 Pb 1 -3.707263526454444e-01 -3.707263526104361e-01 3.50083e-11 1.25024e-10 2 7.310572133156060e-01 7.310572133106554e-01 4.95060e-12 1.09398e-09 3 2.131102904151924e-01 2.131102903967443e-01 1.84481e-11 4.21207e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 3.780566904591609e-02 3.780566904656685e-02 6.50764e-13 1.03814e-09 2 -3.433833187278355e-01 -3.433833186270996e-01 1.00736e-10 1.86517e-10 3 3.837771483276881e-02 3.837771484021273e-02 7.44393e-12 6.80268e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 7.195610144621347e-01 7.195610144069892e-01 5.51456e-11 9.73883e-10 2 -3.140559733831735e-02 -3.140559732607674e-02 1.22406e-11 1.08415e-09 3 8.412743536559164e-01 8.412743536678302e-01 1.19138e-11 1.29086e-10 ----------------------------------------------------------------------------------------------------- 10 Pb 1 -8.670555189064577e-02 -8.670555176272851e-02 1.27917e-10 2.41953e-09 2 -2.298476087546724e-01 -2.298476088029826e-01 4.83102e-11 4.49378e-10 3 3.207085726052142e-01 3.207085727019110e-01 9.66968e-11 1.84404e-10 ----------------------------------------------------------------------------------------------------- 11 Pb 1 -1.244001702755412e+00 -1.244001702689107e+00 6.63052e-11 5.58552e-10 2 -6.768787187221065e-02 -6.768787243500879e-02 5.62798e-10 1.17174e-09 3 2.502844311719218e-01 2.502844310204779e-01 1.51444e-10 1.64672e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 8.300955092181399e-01 8.300955092799671e-01 6.18272e-11 8.94851e-11 2 -7.343305193780291e-01 -7.343305193211894e-01 5.68396e-11 1.90091e-10 3 -1.768818119979360e-02 -1.768818124984596e-02 5.00524e-11 2.73098e-10 ----------------------------------------------------------------------------------------------------- 13 Pb 1 -4.008547156877084e-01 -4.008547157500577e-01 6.23493e-11 1.02875e-09 2 6.822553772786841e-01 6.822553772817785e-01 3.09441e-12 1.63280e-09 3 4.972610918260542e-01 4.972610918004572e-01 2.55970e-11 6.96101e-10 ----------------------------------------------------------------------------------------------------- 14 Pb 1 -5.167800558394813e-01 -5.167800559123190e-01 7.28377e-11 3.10896e-10 2 -1.682262170534662e-01 -1.682262170486325e-01 4.83372e-12 1.86807e-10 3 3.955097491050302e-01 3.955097489900654e-01 1.14965e-10 6.63892e-10 ----------------------------------------------------------------------------------------------------- 15 Pb 1 -3.982600305199954e-01 -3.982600305138273e-01 6.16812e-12 7.69117e-10 2 2.853295395798319e-01 2.853295397094783e-01 1.29646e-10 1.91916e-09 3 6.386668736258658e-01 6.386668735448406e-01 8.10252e-11 9.11108e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 8.021657482462238e-03 8.021657469918387e-03 1.25439e-11 3.65814e-10 2 -6.243607776827634e-01 -6.243607776829444e-01 1.80966e-13 1.31248e-10 3 2.669626489725690e-01 2.669626488975301e-01 7.50389e-11 6.69975e-10 ----------------------------------------------------------------------------------------------------- 17 Pb 1 -7.696301197444645e-01 -7.696301193075952e-01 4.36869e-10 6.19180e-09 * 2 7.385460002863472e-01 7.385460010987405e-01 8.12393e-10 7.16248e-09 * 3 -8.448467092721039e-01 -8.448467093022609e-01 3.01570e-11 2.31762e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 -1.462139821585263e-01 -1.462139817466534e-01 4.11873e-10 1.84863e-09 2 -1.266014401402018e-01 -1.266014382064471e-01 1.93375e-09 2.90525e-09 3 -2.927890217175285e-01 -2.927890217218188e-01 4.29029e-12 2.41909e-09 ----------------------------------------------------------------------------------------------------- 19 Pb 1 5.985068098271895e-01 5.985068098182420e-01 8.94751e-12 2.32966e-11 2 -7.613666458030677e-02 -7.613666464560358e-02 6.52968e-11 1.06697e-09 3 3.066634065743730e-01 3.066634065335751e-01 4.07979e-11 1.39321e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 9.442403720110266e-01 9.442403719964575e-01 1.45691e-11 3.50001e-10 2 2.325510178424922e-01 2.325510178524299e-01 9.93769e-12 2.30865e-11 3 -7.524706496048345e-01 -7.524706495994116e-01 5.42288e-12 9.92139e-11 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -2.459075182175999e-01 -2.459075180879083e-01 1.29692e-10 1.51002e-09 2 8.379515694897179e-01 8.379515695800129e-01 9.02950e-11 6.36314e-10 3 -1.380248734683280e-01 -1.380248732701825e-01 1.98146e-10 1.82024e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -8.944478645659401e-01 -8.944478645883439e-01 2.24039e-11 1.41002e-10 2 -1.174017855456529e-01 -1.174017854954494e-01 5.02036e-11 3.80897e-09 * 3 8.944600061869584e-02 8.944600050164835e-02 1.17047e-10 2.73034e-09 ----------------------------------------------------------------------------------------------------- 23 Pb 1 -1.684248812132958e-01 -1.684248812411951e-01 2.78994e-11 4.86392e-10 2 2.969371786487414e-01 2.969371786826757e-01 3.39343e-11 1.07335e-10 3 -4.343753961349507e-01 -4.343753961353324e-01 3.81639e-13 1.47433e-11 ----------------------------------------------------------------------------------------------------- 24 Pb 1 2.728395640069848e-01 2.728395641137521e-01 1.06767e-10 3.50603e-09 2 1.037614877933281e+00 1.037614877981606e+00 4.83251e-11 1.16192e-09 3 -5.829877267803923e-01 -5.829877267465852e-01 3.38072e-11 3.92976e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 1.017291921670857e+00 1.017291921638612e+00 3.22455e-11 4.24300e-10 2 -2.988400767019154e-01 -2.988400767141837e-01 1.22684e-11 7.72377e-10 3 -3.273778406509546e-01 -3.273778406378628e-01 1.30917e-11 2.45943e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -9.936678037373511e-02 -9.936678014020497e-02 2.33530e-10 2.03416e-09 2 -9.325017110135478e-01 -9.325017109507139e-01 6.28340e-11 1.92264e-10 3 -3.223994154547496e-01 -3.223994155899336e-01 1.35184e-10 6.24703e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -2.974357458708177e-01 -2.974357457036512e-01 1.67166e-10 2.04994e-10 2 -1.074942565209049e-01 -1.074942565233647e-01 2.45984e-12 2.38242e-10 3 -6.078768545411050e-01 -6.078768544607904e-01 8.03145e-11 2.27743e-10 ----------------------------------------------------------------------------------------------------- 28 Pb 1 7.535594618162393e-01 7.535594618091689e-01 7.07046e-12 8.32910e-10 2 -4.481961845230126e-01 -4.481961846139641e-01 9.09515e-11 5.01236e-10 3 -5.912818266894632e-01 -5.912818267480543e-01 5.85911e-11 9.28108e-11 ----------------------------------------------------------------------------------------------------- 29 Pb 1 5.188888142925880e-01 5.188888142708611e-01 2.17270e-11 2.26443e-10 2 -7.178692210358995e-02 -7.178692213411222e-02 3.05223e-11 8.86082e-10 3 8.907251533355776e-01 8.907251533309747e-01 4.60287e-12 1.13089e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -4.122651310983299e-01 -4.122651311122197e-01 1.38898e-11 1.39459e-10 2 -8.354098809096500e-01 -8.354098808981182e-01 1.15318e-11 7.32318e-11 3 -2.281033407423864e-01 -2.281033407467300e-01 4.34361e-12 2.71599e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -5.302044880572142e-01 -5.302044880611908e-01 3.97660e-12 1.02090e-10 2 4.479925302051754e-02 4.479925301862780e-02 1.88974e-12 3.71653e-10 3 -8.973850596871342e-01 -8.973850596637424e-01 2.33918e-11 1.21894e-10 ----------------------------------------------------------------------------------------------------- 32 Pb 1 -3.068700040698075e-01 -3.068700043032583e-01 2.33451e-10 1.95628e-09 2 -6.747153953075169e-01 -6.747153953744713e-01 6.69544e-11 2.16430e-10 3 -4.850350760400919e-01 -4.850350760542847e-01 1.41928e-11 2.38492e-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 = 18, direction = 2: |F_model - F_numer| error = ----------------------- = 1.52744e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.38922e-08 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 2.38922e-08 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.