!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_DongKimKo_2012_CoAl__MO_099716416216_002 Supported species : Al Co 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 = 4.044651031494141 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.436525887322459e-01 3.436525887151528e-01 1.70932e-11 8.21658e-11 2 -2.618078013059398e-02 -2.618078012420912e-02 6.38486e-12 7.94072e-10 3 3.437088702147270e-02 3.437088701976310e-02 1.70960e-12 4.72355e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099684402225e-01 -8.101099684343036e-01 5.91893e-12 1.28447e-10 2 8.600116124285215e-01 8.600116124253129e-01 3.20866e-12 7.51363e-11 3 3.127577256335160e-01 3.127577256239265e-01 9.58955e-12 6.44420e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242118367687234e-02 -8.242118366816785e-02 8.70450e-12 6.57937e-10 2 -4.844095559540117e-02 -4.844095559115920e-02 4.24197e-12 5.93260e-11 3 -2.547490082104492e-01 -2.547490082114773e-01 1.02812e-12 4.15210e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906826524607e-01 4.983906826273157e-01 2.51449e-11 1.25149e-10 2 2.408671394307411e-01 2.408671394320609e-01 1.31981e-12 1.35487e-10 3 3.779437321759949e-01 3.779437321787494e-01 2.75452e-12 9.36169e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111419208698e-01 7.931111419080926e-01 1.27772e-11 4.72781e-11 2 -3.817072234508387e-01 -3.817072234497845e-01 1.05421e-12 3.43682e-11 3 2.806999060513611e-01 2.806999060559845e-01 4.62347e-12 8.61993e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254973231868e-01 -3.438254973232057e-01 1.88738e-14 3.06321e-10 2 2.501152956639251e-01 2.501152956884190e-01 2.44939e-11 9.79931e-11 3 3.380287544197739e-01 3.380287544364503e-01 1.66764e-11 2.23980e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574681105392247e-01 2.574681105381419e-01 1.08286e-12 3.41880e-11 2 -1.219046653943463e+00 -1.219046653960040e+00 1.65770e-11 2.43145e-10 3 -1.651118793526997e+00 -1.651118793481574e+00 4.54226e-11 1.38817e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221784176451463e-01 -7.221784176759782e-01 3.08319e-11 4.52208e-10 2 -4.748263058675943e-01 -4.748263059090433e-01 4.14490e-11 5.73096e-10 3 -7.562197538222701e-01 -7.562197538119400e-01 1.03302e-11 5.27075e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288844025746376e-02 4.288844025185330e-02 5.61046e-12 4.83549e-11 2 -1.188167805006370e+00 -1.188167805005353e+00 1.01785e-12 1.06454e-10 3 -1.184618212225004e+00 -1.184618212237056e+00 1.20517e-11 2.02754e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641769484507e-01 -5.398641769350081e-01 1.34426e-11 2.32374e-10 2 4.980765860330944e-01 4.980765861040878e-01 7.09934e-11 8.58721e-11 3 -7.222686200180112e-01 -7.222686200175749e-01 4.36318e-13 1.70723e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753130726002e-01 -3.572753129828758e-01 8.97244e-11 3.19087e-10 2 -8.581020012537173e-01 -8.581020013078891e-01 5.41718e-11 4.99608e-10 3 7.845981082358283e-01 7.845981082371533e-01 1.32494e-12 1.11923e-09 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596031319910259e-02 2.596031318005226e-02 1.90503e-11 2.15522e-10 2 1.245097671222573e+00 1.245097671215061e+00 7.51132e-12 3.88029e-09 * 3 7.763446127940955e-01 7.763446127933223e-01 7.73159e-13 1.10537e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365342007914724e-01 -5.365342008095371e-01 1.80647e-11 3.10724e-10 2 -1.200162165117639e+00 -1.200162165113093e+00 4.54614e-12 2.29838e-10 3 -1.957550096924832e+00 -1.957550096932229e+00 7.39742e-12 1.91000e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988770936043128e-02 8.988770936888626e-02 8.45499e-12 2.40738e-10 2 4.855436345119641e-01 4.855436344980700e-01 1.38941e-11 4.97438e-11 3 -1.387144626393406e-01 -1.387144626296564e-01 9.68414e-12 7.65990e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761451035216512e+00 1.761451035178273e+00 3.82387e-11 4.74390e-09 * 2 -6.436068979754913e-01 -6.436068979650884e-01 1.04029e-11 5.64628e-11 3 7.520277720007028e-01 7.520277719892031e-01 1.14997e-11 1.56457e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494756306548e-01 5.978494756655720e-01 3.49172e-11 9.25225e-10 2 1.336599637619232e+00 1.336599637609188e+00 1.00440e-11 1.46826e-10 3 8.753613030427162e-01 8.753613030560545e-01 1.33383e-11 2.51997e-11 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232218181632726e-01 4.232218181324402e-01 3.08324e-11 8.09244e-11 2 3.604704536977737e-01 3.604704536936757e-01 4.09800e-12 2.66424e-10 3 -9.557914869742344e-02 -9.557914867230467e-02 2.51188e-11 5.93779e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049824049588291e-01 -5.049824049386326e-01 2.01965e-11 1.71181e-10 2 4.028584613917059e-01 4.028584613928127e-01 1.10684e-12 1.09237e-10 3 1.019475218100237e+00 1.019475218107122e+00 6.88560e-12 1.52266e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575296475746754e-01 2.575296475697338e-01 4.94155e-12 8.83118e-10 2 3.782444212810283e-01 3.782444212748871e-01 6.14120e-12 1.95372e-10 3 -4.712358500882987e-01 -4.712358501009360e-01 1.26373e-11 2.10477e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062635578236175e-01 4.062635577428702e-01 8.07473e-11 1.01935e-10 2 3.112967180681481e-01 3.112967180913646e-01 2.32164e-11 1.53006e-10 3 -4.574995162202993e-01 -4.574995162126553e-01 7.64400e-12 5.20453e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.519579255165166e-01 -9.519579254457428e-01 7.07738e-11 2.00151e-10 2 4.430056383664394e-02 4.430056386062867e-02 2.39847e-11 2.24187e-09 * 3 8.201330421005264e-01 8.201330421057982e-01 5.27178e-12 1.16702e-09 * ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278253472054e-01 2.873278253343325e-01 1.28729e-11 4.64982e-10 2 1.511178771492702e+00 1.511178771495694e+00 2.99250e-12 1.69540e-10 3 1.447152281236705e+00 1.447152281198431e+00 3.82743e-11 9.94266e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449441207763351e-01 -3.449441207817149e-01 5.37981e-12 5.51223e-11 2 3.006117549940310e-01 3.006117549947688e-01 7.37799e-13 4.39617e-11 3 -3.734060034584073e-01 -3.734060034573934e-01 1.01386e-12 6.60967e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.548683812487404e-02 7.548683812770983e-02 2.83579e-12 7.42058e-11 2 -5.942093508757897e-04 -5.942093458390922e-04 5.03670e-12 1.25966e-10 3 -6.192826982805564e-01 -6.192826982761435e-01 4.41291e-12 1.12764e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619447309022211e-01 -3.619447308693010e-01 3.29201e-11 2.22766e-10 2 -8.543631740988503e-01 -8.543631740960690e-01 2.78133e-12 2.14567e-09 * 3 2.198728306724407e-01 2.198728307916065e-01 1.19166e-10 4.11949e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995054625264395e-01 -4.995054625325245e-01 6.08502e-12 1.33643e-10 2 1.019970120957396e+00 1.019970120977796e+00 2.04001e-11 5.04417e-11 3 -7.917982408277793e-01 -7.917982408458423e-01 1.80630e-11 1.70651e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695233004712437e-01 5.695233004516854e-01 1.95582e-11 3.02255e-10 2 -2.393202179116337e+00 -2.393202179097494e+00 1.88431e-11 5.01057e-10 3 7.839007904311678e-01 7.839007904286450e-01 2.52276e-12 4.43997e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446252994106219e-01 -5.446252994141357e-01 3.51386e-12 4.05318e-11 2 6.944324440643135e-01 6.944324440863654e-01 2.20519e-11 1.83952e-10 3 -2.318274124545710e-01 -2.318274124572524e-01 2.68136e-12 1.05167e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440921556166240e-01 -2.440921556285044e-01 1.18804e-11 2.57179e-10 2 -7.057626656573426e-01 -7.057626656620811e-01 4.73854e-12 1.94174e-09 * 3 6.755894761654935e-01 6.755894761960467e-01 3.05532e-11 5.31206e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998223838726057e-02 -7.998223841274080e-02 2.54802e-11 5.72761e-11 2 6.365060356456019e-01 6.365060356372706e-01 8.33134e-12 1.30700e-11 3 -3.994794256969324e-01 -3.994794256722345e-01 2.46979e-11 7.06430e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -7.196131332866144e-02 -7.196131328768827e-02 4.09732e-11 1.28487e-10 2 -9.584853832076661e-01 -9.584853831698562e-01 3.78099e-11 2.18746e-10 3 4.908346291899299e-01 4.908346292675876e-01 7.76577e-11 1.10053e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661919243076066e-01 5.661919242706817e-01 3.69249e-11 1.18754e-10 2 3.764670774327869e-01 3.764670774030850e-01 2.97019e-11 2.05633e-10 3 1.162561738192104e-01 1.162561737893117e-01 2.98987e-11 1.70070e-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 = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 8.47630e-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 = Co | a0 = 3.5365657806396484 | (Configuration in file "config-Co.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Co 1 6.485088426759660e-01 6.485088426669197e-01 9.04632e-12 2.37704e-10 2 6.990251602096700e-01 6.990251602001508e-01 9.51916e-12 6.83287e-11 3 7.051165624608332e-01 7.051165624576882e-01 3.14504e-12 2.71863e-10 ----------------------------------------------------------------------------------------------------- 2 Co 1 4.952782839404976e-01 4.952782839415600e-01 1.06243e-12 2.11255e-09 * 2 -8.374551606477045e-01 -8.374551606347148e-01 1.29897e-11 1.81497e-11 3 1.780509367685435e+00 1.780509367675525e+00 9.90985e-12 1.43441e-09 ----------------------------------------------------------------------------------------------------- 3 Co 1 -1.049858775176962e+00 -1.049858775198686e+00 2.17240e-11 1.26445e-10 2 1.430819593492611e+00 1.430819593511792e+00 1.91804e-11 2.47683e-09 * 3 -5.930745099318449e-01 -5.930745099610194e-01 2.91746e-11 9.65782e-11 ----------------------------------------------------------------------------------------------------- 4 Co 1 9.251347323942665e-01 9.251347323174367e-01 7.68298e-11 4.65161e-10 2 1.847185605282825e-01 1.847185604870986e-01 4.11839e-11 2.41519e-10 3 -9.942491783363725e-01 -9.942491783365165e-01 1.43996e-13 2.05025e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 -4.926497571928059e-01 -4.926497571531893e-01 3.96166e-11 4.10273e-09 * 2 4.702630732414036e-01 4.702630732376851e-01 3.71847e-12 1.96353e-10 3 -4.095238032240969e-02 -4.095238030671332e-02 1.56964e-11 8.23715e-11 ----------------------------------------------------------------------------------------------------- 6 Co 1 -1.507597136687161e-01 -1.507597136612830e-01 7.43311e-12 8.80195e-10 2 4.913844275807172e-01 4.913844276596591e-01 7.89420e-11 8.28439e-10 3 -4.885669056314605e-01 -4.885669056442752e-01 1.28146e-11 1.68866e-10 ----------------------------------------------------------------------------------------------------- 7 Co 1 1.455214618196758e+00 1.455214618184590e+00 1.21687e-11 1.14491e-10 2 -1.770106899804605e+00 -1.770106899779426e+00 2.51792e-11 9.06478e-10 3 1.069588904736801e+00 1.069588904749863e+00 1.30618e-11 4.02808e-10 ----------------------------------------------------------------------------------------------------- 8 Co 1 -2.881525051229560e+00 -2.881525051235400e+00 5.83933e-12 5.91993e-11 2 1.318718242298574e+00 1.318718242365776e+00 6.72016e-11 2.99150e-10 3 1.568541213092912e-01 1.568541212332503e-01 7.60409e-11 1.80873e-10 ----------------------------------------------------------------------------------------------------- 9 Co 1 6.766301757076492e-01 6.766301757122595e-01 4.61031e-12 5.64937e-10 2 3.991670773813838e-01 3.991670773878128e-01 6.42902e-12 1.84401e-11 3 9.558468821906971e-01 9.558468821874414e-01 3.25573e-12 8.08963e-11 ----------------------------------------------------------------------------------------------------- 10 Co 1 -3.396504802393738e-02 -3.396504794459496e-02 7.93424e-11 4.87565e-10 2 -1.004662187945575e+00 -1.004662187882760e+00 6.28151e-11 7.59486e-11 3 7.091305992487695e-01 7.091305992697348e-01 2.09652e-11 2.31280e-10 ----------------------------------------------------------------------------------------------------- 11 Co 1 -1.122986154601710e+00 -1.122986154511232e+00 9.04778e-11 1.77196e-10 2 1.823109755205160e+00 1.823109755179953e+00 2.52072e-11 2.34967e-10 3 -1.975499215945307e+00 -1.975499215918777e+00 2.65297e-11 1.14654e-09 ----------------------------------------------------------------------------------------------------- 12 Co 1 9.978811148984036e-01 9.978811148395137e-01 5.88899e-11 2.86895e-10 2 -7.117088929205188e-01 -7.117088929125946e-01 7.92411e-12 4.23830e-09 * 3 -2.635324537683921e-01 -2.635324538002967e-01 3.19046e-11 7.74826e-11 ----------------------------------------------------------------------------------------------------- 13 Co 1 -1.290388725282605e+00 -1.290388725279601e+00 3.00404e-12 1.44178e-10 2 -7.961106042312269e-01 -7.961106042233023e-01 7.92466e-12 1.15613e-09 3 8.213586489585802e-01 8.213586489648861e-01 6.30584e-12 3.94630e-11 ----------------------------------------------------------------------------------------------------- 14 Co 1 1.097729496476169e+00 1.097729496525067e+00 4.88980e-11 1.03758e-09 2 5.693640257200955e-01 5.693640257216670e-01 1.57152e-12 3.38089e-10 3 8.570083673939491e-02 8.570083671768738e-02 2.17075e-11 8.46478e-11 ----------------------------------------------------------------------------------------------------- 15 Co 1 -1.615199295731476e-01 -1.615199295255794e-01 4.75682e-11 1.60280e-10 2 1.337392105849038e+00 1.337392105826029e+00 2.30089e-11 1.04682e-09 3 -6.342648095661321e-01 -6.342648095669053e-01 7.73270e-13 2.22947e-10 ----------------------------------------------------------------------------------------------------- 16 Co 1 -5.318937050053080e-01 -5.318937051169197e-01 1.11612e-10 1.16117e-10 2 -1.412708359134518e+00 -1.412708358989992e+00 1.44526e-10 4.77443e-10 3 8.786146764805511e-01 8.786146765379348e-01 5.73837e-11 2.63087e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 6.915074903847552e-01 6.915074903951521e-01 1.03969e-11 2.21663e-10 2 -9.829117400192525e-01 -9.829117400335431e-01 1.42906e-11 8.33097e-11 3 -1.598673031164938e+00 -1.598673031180564e+00 1.56264e-11 2.70080e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 7.015826978995222e-01 7.015826978361624e-01 6.33598e-11 5.45616e-10 2 -2.814145369451363e+00 -2.814145369495157e+00 4.37939e-11 5.02866e-10 3 7.844780597289456e-01 7.844780597129533e-01 1.59923e-11 6.18493e-10 ----------------------------------------------------------------------------------------------------- 19 Co 1 -6.225568893765392e-02 -6.225568898461359e-02 4.69597e-11 3.18894e-10 2 1.200440395603355e-01 1.200440395587049e-01 1.63064e-12 1.02424e-09 3 -1.087469966454387e+00 -1.087469966505393e+00 5.10061e-11 2.14419e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 -2.360803393251594e-02 -2.360803392776587e-02 4.75007e-12 6.62466e-11 2 1.992728330742332e+00 1.992728330741598e+00 7.34524e-13 7.56042e-11 3 1.400068895790143e+00 1.400068895757231e+00 3.29117e-11 8.39382e-09 * ----------------------------------------------------------------------------------------------------- 21 Co 1 -1.037668287918647e-01 -1.037668289004394e-01 1.08575e-10 2.34973e-10 2 9.110391141555166e-01 9.110391141338924e-01 2.16243e-11 1.13065e-09 3 -1.811942783956130e-01 -1.811942783626251e-01 3.29878e-11 2.19671e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 9.038292111061944e-02 9.038292109640092e-02 1.42185e-11 6.25108e-09 * 2 -1.874450693036562e+00 -1.874450693053806e+00 1.72435e-11 2.11130e-10 3 1.506262358501468e+00 1.506262358494584e+00 6.88427e-12 1.15889e-09 ----------------------------------------------------------------------------------------------------- 23 Co 1 1.328829993393943e-01 1.328829993389972e-01 3.97127e-13 2.53720e-10 2 4.821304112639568e-01 4.821304112709844e-01 7.02755e-12 1.46655e-09 3 2.387805762364358e-01 2.387805762230599e-01 1.33759e-11 1.65428e-09 ----------------------------------------------------------------------------------------------------- 24 Co 1 1.064343156205479e+00 1.064343156110021e+00 9.54583e-11 5.34047e-10 2 6.380254895963353e-01 6.380254897343055e-01 1.37970e-10 3.76735e-10 3 -1.062587685930443e+00 -1.062587685891896e+00 3.85467e-11 5.35370e-10 ----------------------------------------------------------------------------------------------------- 25 Co 1 -1.237699499311616e+00 -1.237699499296001e+00 1.56151e-11 1.06316e-10 2 -1.204150315791169e+00 -1.204150315775554e+00 1.56148e-11 1.50372e-10 3 5.953470153364712e-01 5.953470153497761e-01 1.33049e-11 2.52243e-10 ----------------------------------------------------------------------------------------------------- 26 Co 1 1.126237376081141e+00 1.126237376029429e+00 5.17120e-11 2.39476e-10 2 -1.119149513025585e-01 -1.119149512845242e-01 1.80343e-11 4.92409e-10 3 2.194061626637771e-01 2.194061626676184e-01 3.84129e-12 3.88346e-09 * ----------------------------------------------------------------------------------------------------- 27 Co 1 -6.834631605512517e-01 -6.834631605305725e-01 2.06791e-11 1.54890e-09 2 7.413006792165826e-01 7.413006792345943e-01 1.80117e-11 7.56237e-10 3 -8.744615251486350e-01 -8.744615251809233e-01 3.22884e-11 2.45205e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 9.841179806382486e-01 9.841179806759086e-01 3.76600e-11 2.44578e-10 2 -5.025721290957174e-01 -5.025721291142524e-01 1.85351e-11 1.64128e-10 3 -7.298429980283443e-01 -7.298429980538015e-01 2.54572e-11 7.34923e-11 ----------------------------------------------------------------------------------------------------- 29 Co 1 1.520982940618281e-01 1.520982940653633e-01 3.53514e-12 1.92291e-10 2 1.756805650646875e+00 1.756805650639037e+00 7.83773e-12 1.63394e-10 3 1.933580998783204e-01 1.933580998566937e-01 2.16266e-11 7.50913e-11 ----------------------------------------------------------------------------------------------------- 30 Co 1 -7.232508651645634e-01 -7.232508651627541e-01 1.80933e-12 6.06947e-10 2 -5.431922558304427e-01 -5.431922558174768e-01 1.29660e-11 9.56702e-11 3 2.045010151127515e-01 2.045010151727465e-01 5.99949e-11 2.52798e-10 ----------------------------------------------------------------------------------------------------- 31 Co 1 -8.244630581004162e-01 -8.244630580940799e-01 6.33626e-12 6.48742e-11 2 1.913997385514300e-01 1.913997385363735e-01 1.50565e-11 1.35504e-10 3 -9.247281876738941e-01 -9.247281876747006e-01 8.06466e-13 6.65115e-10 ----------------------------------------------------------------------------------------------------- 32 Co 1 1.345238145339354e-01 1.345238145668799e-01 3.29445e-11 7.90651e-11 2 -9.913459160290876e-01 -9.913459160441512e-01 1.50636e-11 7.67663e-11 3 -8.558256567604919e-01 -8.558256567520641e-01 8.42781e-12 4.91715e-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 = 10, direction = 1: |F_model - F_numer| error = ----------------------- = 2.33600e-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 = Al Co | a0 = 3.710617724948497 | (Configuration in file "config-AlCo.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Co 1 -3.364719424212027e-01 -3.364719424258671e-01 4.66438e-12 2.59363e-09 * 2 -6.707514569274412e-01 -6.707514568796120e-01 4.78292e-11 1.83633e-10 3 -1.333699828757648e+00 -1.333699828762650e+00 5.00155e-12 1.52493e-09 ----------------------------------------------------------------------------------------------------- 2 Co 1 -4.702422918911192e-01 -4.702422919078974e-01 1.67782e-11 5.25858e-10 2 -3.157352706777057e+00 -3.157352706734704e+00 4.23532e-11 2.70478e-10 3 -5.088441693591297e+00 -5.088441693635371e+00 4.40741e-11 6.30136e-11 ----------------------------------------------------------------------------------------------------- 3 Co 1 2.180068732294752e+00 2.180068732302921e+00 8.16902e-12 2.27037e-10 2 -2.237568390724854e+00 -2.237568390669601e+00 5.52527e-11 4.70261e-10 3 1.707044259957988e+00 1.707044259908833e+00 4.91556e-11 2.70781e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -1.228974399733247e+00 -1.228974399732680e+00 5.66880e-13 1.27170e-10 2 3.607372996720728e+00 3.607372996717693e+00 3.03491e-12 2.61156e-09 * 3 6.452209190473694e-01 6.452209190441616e-01 3.20788e-12 1.81351e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 5.879539366057693e-01 5.879539365686909e-01 3.70785e-11 6.22723e-10 2 8.961142960665780e-01 8.961142960482625e-01 1.83155e-11 6.74929e-11 3 -6.932087768970746e-01 -6.932087769165678e-01 1.94932e-11 8.99107e-11 ----------------------------------------------------------------------------------------------------- 6 Co 1 -6.003884310581331e-01 -6.003884310472345e-01 1.08986e-11 3.87518e-11 2 -1.746931105867320e-01 -1.746931105719726e-01 1.47594e-11 2.67029e-09 * 3 9.092410588156028e-01 9.092410588059676e-01 9.63518e-12 2.35855e-11 ----------------------------------------------------------------------------------------------------- 7 Al 1 -7.310544615264056e-01 -7.310544615385577e-01 1.21521e-11 6.39037e-11 2 5.679954461342421e-01 5.679954461298002e-01 4.44189e-12 9.57125e-11 3 -7.151583706644117e-02 -7.151583708516146e-02 1.87203e-11 1.42253e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 2.828004210940170e+00 2.828004211078661e+00 1.38491e-10 5.52190e-10 2 -1.365317214278379e+00 -1.365317214277111e+00 1.26832e-12 1.90421e-10 3 4.497931883794736e+00 4.497931883717995e+00 7.67404e-11 7.37364e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.682032604651235e+00 -1.682032604655729e+00 4.49463e-12 5.36702e-11 2 3.579738430873127e+00 3.579738430870823e+00 2.30438e-12 2.32131e-10 3 -2.057199430527850e+00 -2.057199430511078e+00 1.67724e-11 3.20735e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 5.998324113238669e-01 5.998324113271630e-01 3.29614e-12 2.54369e-10 2 -2.577319355674388e-01 -2.577319355685721e-01 1.13326e-12 1.11186e-10 3 -2.130853972002265e+00 -2.130853971984625e+00 1.76401e-11 1.33515e-10 ----------------------------------------------------------------------------------------------------- 11 Co 1 -9.687885315783614e-01 -9.687885315954115e-01 1.70500e-11 4.41390e-10 2 1.601386981442008e+00 1.601386981455370e+00 1.33620e-11 6.11786e-10 3 2.100493474526508e+00 2.100493474501967e+00 2.45408e-11 1.77992e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -8.608674689934156e-01 -8.608674690084145e-01 1.49989e-11 1.00458e-10 2 4.049035651887998e-01 4.049035652198751e-01 3.10753e-11 4.90473e-11 3 6.185653845649152e-01 6.185653845327526e-01 3.21626e-11 1.28897e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 4.621920216487909e-01 4.621920216926643e-01 4.38735e-11 2.51109e-10 2 8.174506913630841e-01 8.174506913754040e-01 1.23199e-11 6.24818e-11 3 -6.506423190313138e-01 -6.506423190347161e-01 3.40239e-12 2.91359e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 -8.023605573782989e-01 -8.023605573720136e-01 6.28531e-12 3.28374e-11 2 -6.432463488758250e-01 -6.432463488866401e-01 1.08151e-11 6.48233e-11 3 6.162360939593566e-01 6.162360939950219e-01 3.56652e-11 9.46706e-11 ----------------------------------------------------------------------------------------------------- 15 Co 1 -1.315063094618599e+00 -1.315063094637487e+00 1.88882e-11 7.94314e-11 2 1.617584708658941e+00 1.617584708811948e+00 1.53007e-10 2.01447e-10 3 -1.987121906447036e+00 -1.987121906472201e+00 2.51643e-11 8.18780e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 3.326421586311568e+00 3.326421586316846e+00 5.27844e-12 1.31690e-10 2 4.343115068374870e-01 4.343115068528562e-01 1.53692e-11 4.42855e-10 3 -7.711629078742933e-01 -7.711629077518316e-01 1.22462e-10 1.50756e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -3.975538844683201e-01 -3.975538844498400e-01 1.84801e-11 2.95584e-11 2 -3.526554973155223e+00 -3.526554973139223e+00 1.59996e-11 6.72114e-10 3 2.387158213749097e+00 2.387158213714779e+00 3.43174e-11 7.55793e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 -6.815868163584994e-01 -6.815868163663590e-01 7.85960e-12 1.85129e-10 2 2.043058250860725e+00 2.043058250847002e+00 1.37232e-11 2.87533e-10 3 -1.258306445404200e+00 -1.258306445420376e+00 1.61764e-11 5.32423e-11 ----------------------------------------------------------------------------------------------------- 19 Co 1 -3.270553719144742e+00 -3.270553719062354e+00 8.23879e-11 9.80992e-10 2 -3.181306007772657e+00 -3.181306007763959e+00 8.69749e-12 6.14548e-11 3 3.260044302658791e-01 3.260044301463648e-01 1.19514e-10 3.38599e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 9.590562557706153e-01 9.590562557679141e-01 2.70117e-12 9.25793e-12 2 1.883721661013895e-01 1.883721661327318e-01 3.13423e-11 5.44016e-09 * 3 2.344899011749223e-01 2.344899011822374e-01 7.31512e-12 3.80083e-10 ----------------------------------------------------------------------------------------------------- 21 Co 1 1.355729633349661e+00 1.355729633212384e+00 1.37276e-10 4.88281e-10 2 -2.466928645305829e+00 -2.466928645317080e+00 1.12514e-11 3.65844e-10 3 -3.027432205240033e+00 -3.027432205117073e+00 1.22960e-10 2.04504e-09 * ----------------------------------------------------------------------------------------------------- 22 Al 1 4.972821642629059e-01 4.972821643086653e-01 4.57595e-11 5.92280e-10 2 -3.729211305246812e+00 -3.729211305192841e+00 5.39706e-11 7.75054e-10 3 1.292195239541051e+00 1.292195239496199e+00 4.48519e-11 4.22135e-10 ----------------------------------------------------------------------------------------------------- 23 Co 1 -6.269613128790433e-01 -6.269613128847487e-01 5.70533e-12 2.41764e-10 2 8.014878227712682e-01 8.014878227706077e-01 6.60472e-13 3.91242e-10 3 -9.628785547266907e-01 -9.628785547333881e-01 6.69742e-12 1.19699e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 3.419940097599340e+00 3.419940097604746e+00 5.40545e-12 2.03282e-10 2 4.626912821817108e+00 4.626912821823785e+00 6.67733e-12 3.19955e-10 3 4.824139022960524e+00 4.824139022938081e+00 2.24434e-11 1.82258e-10 ----------------------------------------------------------------------------------------------------- 25 Co 1 1.295187906741528e+00 1.295187906719334e+00 2.21934e-11 4.34485e-09 * 2 -8.345778772983723e-01 -8.345778772972775e-01 1.09479e-12 3.54810e-10 3 9.086999099962303e-01 9.086999100245507e-01 2.83205e-11 5.41344e-10 ----------------------------------------------------------------------------------------------------- 26 Co 1 -1.704282248395000e+00 -1.704282248394110e+00 8.90177e-13 1.06487e-09 2 -1.236804276993935e+00 -1.236804276992509e+00 1.42553e-12 1.60226e-10 3 2.113319098748126e+00 2.113319098679993e+00 6.81331e-11 2.63676e-10 ----------------------------------------------------------------------------------------------------- 27 Co 1 -1.438708467315667e+00 -1.438708467307443e+00 8.22453e-12 2.77965e-10 2 9.581785836097804e-01 9.581785836154213e-01 5.64093e-12 3.23265e-10 3 -7.698342354347288e-01 -7.698342354364092e-01 1.68032e-12 5.83544e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 6.964153453738855e-01 6.964153453451464e-01 2.87391e-11 1.34730e-10 2 -8.504673752696089e-01 -8.504673752195070e-01 5.01019e-11 1.57568e-10 3 -8.684405961603399e-01 -8.684405961629752e-01 2.63534e-12 4.57959e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.742369447605645e+00 -1.742369447598630e+00 7.01417e-12 1.15359e-09 2 1.336025322906467e+00 1.336025322878244e+00 2.82230e-11 1.11094e-10 3 -1.868165529592823e+00 -1.868165529529961e+00 6.28619e-11 4.64940e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 4.307607729112413e-01 4.307607729683995e-01 5.71582e-11 3.49451e-10 2 4.126885157677218e-01 4.126885157486189e-01 1.91029e-11 1.01463e-10 3 -9.183928294344095e-01 -9.183928294138342e-01 2.05753e-11 4.30554e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.365427051088649e+00 1.365427051080983e+00 7.66587e-12 2.37754e-11 2 -1.011016028702685e+00 -1.011016028674865e+00 2.78202e-11 2.00384e-10 3 9.669734376134026e-01 9.669734375523387e-01 6.10639e-11 3.41021e-11 ----------------------------------------------------------------------------------------------------- 32 Al 1 -1.146012446205811e+00 -1.146012446244467e+00 3.86557e-11 6.22291e-11 2 1.449945546363394e+00 1.449945546334217e+00 2.91769e-11 3.43838e-11 3 3.095847394727357e-01 3.095847393969525e-01 7.57832e-11 1.30020e-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 = 19, direction = 3: |F_model - F_numer| error = ----------------------- = 3.66603e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 8.47630e-09 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 8.47630e-09 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.