!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_001 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 = 4.044651031494144 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.436525887322554e-01 3.436525887149216e-01 1.73338e-11 2.21627e-09 * 2 -2.618078013057730e-02 -2.618078015046139e-02 1.98841e-11 8.31583e-10 3 3.437088702148990e-02 3.437088700998506e-02 1.15048e-11 1.08178e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099684402183e-01 -8.101099684596536e-01 1.94352e-11 5.24101e-11 2 8.600116124285074e-01 8.600116124102927e-01 1.82148e-11 1.25009e-10 3 3.127577256335263e-01 3.127577256605851e-01 2.70587e-11 1.79623e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242118367687803e-02 -8.242118367840301e-02 1.52497e-12 5.73929e-11 2 -4.844095559538655e-02 -4.844095559177430e-02 3.61225e-12 2.18848e-10 3 -2.547490082104512e-01 -2.547490082079679e-01 2.48329e-12 4.74674e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906826524701e-01 4.983906825930616e-01 5.94084e-11 8.93847e-11 2 2.408671394307264e-01 2.408671393872364e-01 4.34901e-11 3.33824e-10 3 3.779437321759817e-01 3.779437321771869e-01 1.20515e-12 1.15970e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111419208594e-01 7.931111419218952e-01 1.03584e-12 1.51726e-10 2 -3.817072234508247e-01 -3.817072234594807e-01 8.65602e-12 4.38002e-11 3 2.806999060513650e-01 2.806999060599010e-01 8.53601e-12 8.69422e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254973231907e-01 -3.438254973227398e-01 4.50917e-13 2.86639e-10 2 2.501152956639220e-01 2.501152956903286e-01 2.64066e-11 1.41284e-10 3 3.380287544197822e-01 3.380287545101162e-01 9.03340e-11 6.14792e-11 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574681105392224e-01 2.574681105723346e-01 3.31122e-11 8.32141e-10 2 -1.219046653943438e+00 -1.219046653947405e+00 3.96660e-12 3.41483e-10 3 -1.651118793526987e+00 -1.651118793588865e+00 6.18781e-11 1.48545e-09 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221784176451395e-01 -7.221784176233668e-01 2.17727e-11 3.60824e-10 2 -4.748263058676039e-01 -4.748263058352823e-01 3.23215e-11 1.88696e-10 3 -7.562197538222759e-01 -7.562197538122164e-01 1.00595e-11 5.37221e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288844025747830e-02 4.288844026365585e-02 6.17754e-12 1.70352e-09 * 2 -1.188167805006356e+00 -1.188167805007006e+00 6.49703e-13 2.32256e-10 3 -1.184618212224978e+00 -1.184618212193563e+00 3.14151e-11 6.11646e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641769484498e-01 -5.398641769713896e-01 2.29398e-11 1.49638e-10 2 4.980765860330841e-01 4.980765860607396e-01 2.76555e-11 2.32572e-10 3 -7.222686200179957e-01 -7.222686199959928e-01 2.20030e-11 9.62898e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753130726158e-01 -3.572753129864010e-01 8.62148e-11 2.48866e-10 2 -8.581020012537109e-01 -8.581020012056584e-01 4.80526e-11 1.42574e-10 3 7.845981082358104e-01 7.845981083542691e-01 1.18459e-10 2.26229e-09 * ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596031319911202e-02 2.596031318002901e-02 1.90830e-11 1.79608e-10 2 1.245097671222554e+00 1.245097671228180e+00 5.62550e-12 2.72200e-10 3 7.763446127940796e-01 7.763446128374676e-01 4.33880e-11 7.68732e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365342007914679e-01 -5.365342008163090e-01 2.48411e-11 1.03990e-11 2 -1.200162165117635e+00 -1.200162165115409e+00 2.22555e-12 9.36673e-11 3 -1.957550096924806e+00 -1.957550096926957e+00 2.15117e-12 1.89156e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988770936042807e-02 8.988770936688886e-02 6.46079e-12 3.78110e-11 2 4.855436345119571e-01 4.855436344929248e-01 1.90323e-11 9.41056e-11 3 -1.387144626393326e-01 -1.387144626201578e-01 1.91748e-11 6.40189e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761451035216499e+00 1.761451035195688e+00 2.08111e-11 1.06999e-10 2 -6.436068979754836e-01 -6.436068979725695e-01 2.91411e-12 7.64602e-11 3 7.520277720006838e-01 7.520277719796794e-01 2.10044e-11 1.29460e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494756306516e-01 5.978494756375644e-01 6.91280e-12 3.02768e-10 2 1.336599637619225e+00 1.336599637616534e+00 2.69096e-12 2.56716e-10 3 8.753613030426992e-01 8.753613030237551e-01 1.89441e-11 1.25719e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232218181632803e-01 4.232218181361097e-01 2.71706e-11 5.08436e-10 2 3.604704536977812e-01 3.604704536899877e-01 7.79349e-12 1.80758e-10 3 -9.557914869742137e-02 -9.557914868863228e-02 8.78909e-12 2.04205e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049824049588346e-01 -5.049824049655939e-01 6.75926e-12 4.06815e-10 2 4.028584613916945e-01 4.028584613866855e-01 5.00894e-12 1.08525e-10 3 1.019475218100231e+00 1.019475218100988e+00 7.57616e-13 7.43507e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575296475746688e-01 2.575296475707571e-01 3.91176e-12 2.23077e-09 * 2 3.782444212810367e-01 3.782444212830892e-01 2.05241e-12 1.10553e-10 3 -4.712358500883023e-01 -4.712358501078623e-01 1.95600e-11 2.46694e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062635578236253e-01 4.062635578066208e-01 1.70046e-11 6.58390e-11 2 3.112967180681401e-01 3.112967180808662e-01 1.27261e-11 1.59561e-10 3 -4.574995162203039e-01 -4.574995162280346e-01 7.73065e-12 3.57909e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.519579255165155e-01 -9.519579255073184e-01 9.19709e-12 2.87750e-10 2 4.430056383665106e-02 4.430056384021056e-02 3.55951e-12 1.88416e-10 3 8.201330421005257e-01 8.201330420300377e-01 7.04881e-11 1.22283e-09 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278253471955e-01 2.873278253570418e-01 9.84635e-12 1.57249e-10 2 1.511178771492685e+00 1.511178771528474e+00 3.57889e-11 1.73633e-09 * 3 1.447152281236693e+00 1.447152281244043e+00 7.34990e-12 1.04599e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449441207763360e-01 -3.449441207776809e-01 1.34492e-12 1.29801e-10 2 3.006117549940326e-01 3.006117549855803e-01 8.45224e-12 9.38337e-11 3 -3.734060034584101e-01 -3.734060034302955e-01 2.81146e-11 3.06560e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.548683812487494e-02 7.548683808329372e-02 4.15812e-11 1.66153e-10 2 -5.942093508792465e-04 -5.942093671161976e-04 1.62370e-11 1.73028e-10 3 -6.192826982805582e-01 -6.192826982695736e-01 1.09845e-11 1.25508e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619447309022095e-01 -3.619447308808021e-01 2.14074e-11 5.51921e-10 2 -8.543631740988483e-01 -8.543631740707854e-01 2.80629e-11 1.00031e-10 3 2.198728306724434e-01 2.198728307084147e-01 3.59713e-11 2.62199e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995054625264457e-01 -4.995054625288018e-01 2.35617e-12 1.15118e-09 2 1.019970120957392e+00 1.019970120986049e+00 2.86577e-11 2.15460e-10 3 -7.917982408277775e-01 -7.917982408370778e-01 9.30034e-12 1.53537e-09 * ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695233004712275e-01 5.695233004155006e-01 5.57269e-11 4.67463e-10 2 -2.393202179116325e+00 -2.393202179073250e+00 4.30749e-11 5.02913e-11 3 7.839007904311630e-01 7.839007902468166e-01 1.84346e-10 3.51334e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446252994106073e-01 -5.446252994057967e-01 4.81060e-12 1.54747e-10 2 6.944324440643000e-01 6.944324440684594e-01 4.15934e-12 3.17211e-11 3 -2.318274124545759e-01 -2.318274124577573e-01 3.18146e-12 2.24390e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440921556166249e-01 -2.440921556382259e-01 2.16010e-11 3.43239e-10 2 -7.057626656573426e-01 -7.057626656552638e-01 2.07878e-12 2.76199e-10 3 6.755894761654937e-01 6.755894762694460e-01 1.03952e-10 5.82736e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998223838726028e-02 -7.998223841054722e-02 2.32869e-11 4.28072e-11 2 6.365060356456024e-01 6.365060356403007e-01 5.30165e-12 2.41406e-10 3 -3.994794256969323e-01 -3.994794256899253e-01 7.00701e-12 7.33769e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -7.196131332866167e-02 -7.196131333954901e-02 1.08873e-11 3.41107e-09 * 2 -9.584853832076650e-01 -9.584853832485714e-01 4.09064e-11 4.75636e-10 3 4.908346291899297e-01 4.908346292288723e-01 3.89426e-11 1.23092e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661919243076067e-01 5.661919242800675e-01 2.75392e-11 2.69271e-10 2 3.764670774327864e-01 3.764670774180595e-01 1.47269e-11 1.93167e-10 3 1.162561738192102e-01 1.162561737866365e-01 3.25737e-11 7.94511e-11 ----------------------------------------------------------------------------------------------------- * 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 = ----------------------- = 2.73253e-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 = 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 6.485088426669195e-01 9.04643e-12 2.37705e-10 2 6.990251602096700e-01 6.990251602001507e-01 9.51927e-12 6.83281e-11 3 7.051165624608332e-01 7.051165624576881e-01 3.14515e-12 2.71863e-10 ----------------------------------------------------------------------------------------------------- 2 Co 1 4.952782839404976e-01 4.952782839415600e-01 1.06243e-12 2.11255e-09 * 2 -8.374551606477045e-01 -8.374551606347146e-01 1.29899e-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 2.17237e-11 1.26446e-10 2 1.430819593492611e+00 1.430819593511792e+00 1.91804e-11 2.47683e-09 * 3 -5.930745099318449e-01 -5.930745099610192e-01 2.91743e-11 9.65786e-11 ----------------------------------------------------------------------------------------------------- 4 Co 1 9.251347323942665e-01 9.251347323174366e-01 7.68299e-11 4.65160e-10 2 1.847185605282825e-01 1.847185604870986e-01 4.11839e-11 2.41519e-10 3 -9.942491783363725e-01 -9.942491783365165e-01 1.43996e-13 2.05026e-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 -4.095238030671331e-02 1.56964e-11 8.23715e-11 ----------------------------------------------------------------------------------------------------- 6 Co 1 -1.507597136687161e-01 -1.507597136612830e-01 7.43314e-12 8.80195e-10 2 4.913844275807172e-01 4.913844276596590e-01 7.89419e-11 8.28438e-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 -1.770106899779425e+00 2.51794e-11 9.06477e-10 3 1.069588904736801e+00 1.069588904749862e+00 1.30616e-11 4.02808e-10 ----------------------------------------------------------------------------------------------------- 8 Co 1 -2.881525051229560e+00 -2.881525051235399e+00 5.83888e-12 5.91998e-11 2 1.318718242298574e+00 1.318718242365776e+00 6.72011e-11 2.99150e-10 3 1.568541213092912e-01 1.568541212332505e-01 7.60407e-11 1.80873e-10 ----------------------------------------------------------------------------------------------------- 9 Co 1 6.766301757076492e-01 6.766301757122595e-01 4.61031e-12 5.64937e-10 2 3.991670773813838e-01 3.991670773878124e-01 6.42858e-12 1.84397e-11 3 9.558468821906971e-01 9.558468821874414e-01 3.25573e-12 8.08963e-11 ----------------------------------------------------------------------------------------------------- 10 Co 1 -3.396504802393738e-02 -3.396504794459497e-02 7.93424e-11 4.87565e-10 2 -1.004662187945575e+00 -1.004662187882760e+00 6.28153e-11 7.59479e-11 3 7.091305992487695e-01 7.091305992697344e-01 2.09649e-11 2.31280e-10 ----------------------------------------------------------------------------------------------------- 11 Co 1 -1.122986154601710e+00 -1.122986154511232e+00 9.04781e-11 1.77197e-10 2 1.823109755205160e+00 1.823109755179953e+00 2.52074e-11 2.34967e-10 3 -1.975499215945307e+00 -1.975499215918777e+00 2.65297e-11 1.14654e-09 ----------------------------------------------------------------------------------------------------- 12 Co 1 9.978811148984036e-01 9.978811148395130e-01 5.88906e-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 3.00449e-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 3.94632e-11 ----------------------------------------------------------------------------------------------------- 14 Co 1 1.097729496476169e+00 1.097729496525067e+00 4.88973e-11 1.03758e-09 2 5.693640257200955e-01 5.693640257216670e-01 1.57152e-12 3.38089e-10 3 8.570083673939491e-02 8.570083671768737e-02 2.17075e-11 8.46477e-11 ----------------------------------------------------------------------------------------------------- 15 Co 1 -1.615199295731476e-01 -1.615199295255794e-01 4.75683e-11 1.60280e-10 2 1.337392105849038e+00 1.337392105826029e+00 2.30094e-11 1.04682e-09 3 -6.342648095661321e-01 -6.342648095669052e-01 7.73159e-13 2.22947e-10 ----------------------------------------------------------------------------------------------------- 16 Co 1 -5.318937050053080e-01 -5.318937051169191e-01 1.11611e-10 1.16117e-10 2 -1.412708359134518e+00 -1.412708358989992e+00 1.44526e-10 4.77442e-10 3 8.786146764805511e-01 8.786146765379347e-01 5.73835e-11 2.63088e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 6.915074903847552e-01 6.915074903951518e-01 1.03966e-11 2.21663e-10 2 -9.829117400192525e-01 -9.829117400335431e-01 1.42906e-11 8.33097e-11 3 -1.598673031164938e+00 -1.598673031180564e+00 1.56262e-11 2.70081e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 7.015826978995222e-01 7.015826978361626e-01 6.33597e-11 5.45615e-10 2 -2.814145369451363e+00 -2.814145369495156e+00 4.37930e-11 5.02866e-10 3 7.844780597289456e-01 7.844780597129533e-01 1.59923e-11 6.18494e-10 ----------------------------------------------------------------------------------------------------- 19 Co 1 -6.225568893765392e-02 -6.225568898461360e-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 2.14418e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 -2.360803393251594e-02 -2.360803392776586e-02 4.75008e-12 6.62466e-11 2 1.992728330742332e+00 1.992728330741598e+00 7.34746e-13 7.56035e-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 3.29879e-11 2.19671e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 9.038292111061944e-02 9.038292109640092e-02 1.42185e-11 6.25108e-09 * 2 -1.874450693036562e+00 -1.874450693053805e+00 1.72431e-11 2.11131e-10 3 1.506262358501468e+00 1.506262358494583e+00 6.88449e-12 1.15889e-09 ----------------------------------------------------------------------------------------------------- 23 Co 1 1.328829993393943e-01 1.328829993389971e-01 3.97155e-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 9.54585e-11 5.34049e-10 2 6.380254895963353e-01 6.380254897343053e-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 -1.237699499296000e+00 1.56153e-11 1.06317e-10 2 -1.204150315791169e+00 -1.204150315775554e+00 1.56151e-11 1.50371e-10 3 5.953470153364712e-01 5.953470153497759e-01 1.33047e-11 2.52244e-10 ----------------------------------------------------------------------------------------------------- 26 Co 1 1.126237376081141e+00 1.126237376029428e+00 5.17122e-11 2.39477e-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 -8.744615251809232e-01 3.22883e-11 2.45206e-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 1.64129e-10 3 -7.298429980283443e-01 -7.298429980538016e-01 2.54573e-11 7.34915e-11 ----------------------------------------------------------------------------------------------------- 29 Co 1 1.520982940618281e-01 1.520982940653633e-01 3.53517e-12 1.92291e-10 2 1.756805650646875e+00 1.756805650639037e+00 7.83795e-12 1.63395e-10 3 1.933580998783204e-01 1.933580998566937e-01 2.16266e-11 7.50913e-11 ----------------------------------------------------------------------------------------------------- 30 Co 1 -7.232508651645634e-01 -7.232508651627539e-01 1.80944e-12 6.06948e-10 2 -5.431922558304427e-01 -5.431922558174765e-01 1.29662e-11 9.56707e-11 3 2.045010151127515e-01 2.045010151727464e-01 5.99949e-11 2.52798e-10 ----------------------------------------------------------------------------------------------------- 31 Co 1 -8.244630581004162e-01 -8.244630580940797e-01 6.33649e-12 6.48742e-11 2 1.913997385514300e-01 1.913997385363735e-01 1.50565e-11 1.35504e-10 3 -9.247281876738941e-01 -9.247281876747003e-01 8.06244e-13 6.65115e-10 ----------------------------------------------------------------------------------------------------- 32 Co 1 1.345238145339354e-01 1.345238145668798e-01 3.29445e-11 7.90652e-11 2 -9.913459160290876e-01 -9.913459160441510e-01 1.50634e-11 7.67660e-11 3 -8.558256567604919e-01 -8.558256567520648e-01 8.42715e-12 4.91716e-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 = 3.7106177249484986 | (Configuration in file "config-AlCo.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Co 1 -3.364719424212320e-01 -3.364719424258671e-01 4.63518e-12 2.59363e-09 * 2 -6.707514569274838e-01 -6.707514569349109e-01 7.42706e-12 8.52390e-11 3 -1.333699828757709e+00 -1.333699828761835e+00 4.12625e-12 6.17197e-11 ----------------------------------------------------------------------------------------------------- 2 Co 1 -4.702422918910878e-01 -4.702422918711814e-01 1.99064e-11 2.08887e-10 2 -3.157352706777077e+00 -3.157352706647604e+00 1.29473e-10 2.59310e-10 3 -5.088441693591385e+00 -5.088441693605393e+00 1.40084e-11 2.11331e-10 ----------------------------------------------------------------------------------------------------- 3 Co 1 2.180068732294811e+00 2.180068732302784e+00 7.97273e-12 1.30093e-10 2 -2.237568390724941e+00 -2.237568390796274e+00 7.13332e-11 4.91173e-09 * 3 1.707044259958029e+00 1.707044260029375e+00 7.13460e-11 1.86742e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -1.228974399733318e+00 -1.228974399737911e+00 4.59366e-12 2.56561e-11 2 3.607372996720804e+00 3.607372996717692e+00 3.11262e-12 2.61159e-09 * 3 6.452209190474185e-01 6.452209190436013e-01 3.81717e-12 2.96218e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 5.879539366057751e-01 5.879539366142632e-01 8.48810e-12 1.10630e-10 2 8.961142960665603e-01 8.961142960670125e-01 4.52194e-13 2.53488e-10 3 -6.932087768971035e-01 -6.932087769153584e-01 1.82550e-11 1.01971e-10 ----------------------------------------------------------------------------------------------------- 6 Co 1 -6.003884310581230e-01 -6.003884310565361e-01 1.58695e-12 1.39081e-10 2 -1.746931105867269e-01 -1.746931105719622e-01 1.47647e-11 2.66009e-09 * 3 9.092410588155889e-01 9.092410588137824e-01 1.80655e-12 1.73755e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 -7.310544615263925e-01 -7.310544615569045e-01 3.05119e-11 8.12388e-11 2 5.679954461342275e-01 5.679954461298000e-01 4.42746e-12 9.57130e-11 3 -7.151583706643039e-02 -7.151583703083175e-02 3.55986e-11 1.32638e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 2.828004210940183e+00 2.828004211007873e+00 6.76903e-11 9.83001e-10 2 -1.365317214278358e+00 -1.365317214393700e+00 1.15342e-10 1.24622e-10 3 4.497931883794789e+00 4.497931883810941e+00 1.61524e-11 2.68879e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.682032604651296e+00 -1.682032604645672e+00 5.62439e-12 1.16419e-10 2 3.579738430873181e+00 3.579738430875288e+00 2.10720e-12 1.04139e-10 3 -2.057199430527902e+00 -2.057199430522906e+00 4.99512e-12 4.22777e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 5.998324113238853e-01 5.998324112857325e-01 3.81528e-11 2.54424e-10 2 -2.577319355674210e-01 -2.577319355563820e-01 1.10390e-11 1.29693e-10 3 -2.130853972002317e+00 -2.130853971993854e+00 8.46301e-12 3.15228e-09 * ----------------------------------------------------------------------------------------------------- 11 Co 1 -9.687885315783457e-01 -9.687885315332364e-01 4.51092e-11 1.11096e-09 2 1.601386981442003e+00 1.601386981428555e+00 1.34481e-11 2.31648e-10 3 2.100493474526550e+00 2.100493474553469e+00 2.69189e-11 3.69753e-11 ----------------------------------------------------------------------------------------------------- 12 Al 1 -8.608674689934538e-01 -8.608674689709001e-01 2.25537e-11 3.29026e-09 * 2 4.049035651888201e-01 4.049035651902347e-01 1.41459e-12 1.26254e-10 3 6.185653845649227e-01 6.185653845752566e-01 1.03338e-11 2.72451e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 4.621920216487837e-01 4.621920216461207e-01 2.66298e-12 6.01932e-11 2 8.174506913630809e-01 8.174506913765522e-01 1.34713e-11 4.41861e-11 3 -6.506423190313325e-01 -6.506423190140226e-01 1.73099e-11 1.33649e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 -8.023605573782887e-01 -8.023605573704061e-01 7.88258e-12 1.15206e-10 2 -6.432463488758208e-01 -6.432463488766010e-01 7.80265e-13 5.11057e-11 3 6.162360939593481e-01 6.162360939682090e-01 8.86091e-12 1.15187e-10 ----------------------------------------------------------------------------------------------------- 15 Co 1 -1.315063094618592e+00 -1.315063094608149e+00 1.04428e-11 5.70937e-11 2 1.617584708658928e+00 1.617584708613614e+00 4.53135e-11 3.08848e-10 3 -1.987121906447045e+00 -1.987121906436374e+00 1.06712e-11 3.86738e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 3.326421586311575e+00 3.326421586192888e+00 1.18687e-10 4.42277e-10 2 4.343115068375156e-01 4.343115067811751e-01 5.63405e-11 2.67263e-10 3 -7.711629078742623e-01 -7.711629079408341e-01 6.65717e-11 1.10843e-09 ----------------------------------------------------------------------------------------------------- 17 Al 1 -3.975538844683563e-01 -3.975538844570514e-01 1.13049e-11 5.88729e-11 2 -3.526554973155302e+00 -3.526554973156255e+00 9.52571e-13 1.37732e-10 3 2.387158213749118e+00 2.387158213714883e+00 3.42348e-11 8.12173e-11 ----------------------------------------------------------------------------------------------------- 18 Co 1 -6.815868163584865e-01 -6.815868163674549e-01 8.96838e-12 7.03936e-11 2 2.043058250860781e+00 2.043058250841384e+00 1.93974e-11 9.67043e-10 3 -1.258306445404237e+00 -1.258306445411780e+00 7.54352e-12 8.89076e-09 * ----------------------------------------------------------------------------------------------------- 19 Co 1 -3.270553719144768e+00 -3.270553719091607e+00 5.31610e-11 6.49409e-11 2 -3.181306007772680e+00 -3.181306007801050e+00 2.83693e-11 4.40326e-10 3 3.260044302658893e-01 3.260044301233047e-01 1.42585e-10 1.11783e-08 * ----------------------------------------------------------------------------------------------------- 20 Al 1 9.590562557706082e-01 9.590562557477351e-01 2.28730e-11 1.14190e-10 2 1.883721661013847e-01 1.883721661358503e-01 3.44655e-11 5.16757e-11 3 2.344899011749490e-01 2.344899011721404e-01 2.80867e-12 6.13174e-10 ----------------------------------------------------------------------------------------------------- 21 Co 1 1.355729633349677e+00 1.355729633360109e+00 1.04321e-11 1.90494e-10 2 -2.466928645305915e+00 -2.466928645301721e+00 4.19442e-12 4.11906e-11 3 -3.027432205240102e+00 -3.027432205224036e+00 1.60667e-11 3.78014e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 4.972821642629326e-01 4.972821642912514e-01 2.83188e-11 1.11852e-10 2 -3.729211305246830e+00 -3.729211305267579e+00 2.07487e-11 8.98833e-10 3 1.292195239541034e+00 1.292195239556536e+00 1.55020e-11 3.17620e-10 ----------------------------------------------------------------------------------------------------- 23 Co 1 -6.269613128790347e-01 -6.269613128854874e-01 6.45273e-12 7.67777e-11 2 8.014878227712656e-01 8.014878227752124e-01 3.94673e-12 1.64496e-10 3 -9.628785547266897e-01 -9.628785547330648e-01 6.37512e-12 6.28825e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 3.419940097599345e+00 3.419940097604528e+00 5.18297e-12 1.19262e-10 2 4.626912821817188e+00 4.626912821874187e+00 5.69997e-11 2.81855e-10 3 4.824139022960643e+00 4.824139022973629e+00 1.29861e-11 8.06284e-09 * ----------------------------------------------------------------------------------------------------- 25 Co 1 1.295187906741518e+00 1.295187906755758e+00 1.42404e-11 3.50617e-10 2 -8.345778772983836e-01 -8.345778774123216e-01 1.13938e-10 2.24243e-10 3 9.086999099962348e-01 9.086999099117887e-01 8.44461e-11 8.36750e-10 ----------------------------------------------------------------------------------------------------- 26 Co 1 -1.704282248394990e+00 -1.704282248408375e+00 1.33857e-11 1.56740e-10 2 -1.236804276993921e+00 -1.236804276974456e+00 1.94644e-11 3.00793e-10 3 2.113319098748122e+00 2.113319098735903e+00 1.22191e-11 9.10969e-11 ----------------------------------------------------------------------------------------------------- 27 Co 1 -1.438708467315677e+00 -1.438708467318042e+00 2.36522e-12 2.86132e-10 2 9.581785836097690e-01 9.581785836082760e-01 1.49303e-12 2.65526e-10 3 -7.698342354347160e-01 -7.698342354374339e-01 2.71794e-12 5.23085e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 6.964153453738833e-01 6.964153453182399e-01 5.56434e-11 1.51144e-10 2 -8.504673752696010e-01 -8.504673752985692e-01 2.89682e-11 6.63306e-11 3 -8.684405961603346e-01 -8.684405961577492e-01 2.58549e-12 6.64979e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.742369447605670e+00 -1.742369447624165e+00 1.84954e-11 2.13160e-10 2 1.336025322906457e+00 1.336025322916644e+00 1.01865e-11 6.91887e-11 3 -1.868165529592860e+00 -1.868165529621999e+00 2.91389e-11 1.80710e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 4.307607729112685e-01 4.307607729155812e-01 4.31272e-12 4.87341e-10 2 4.126885157677554e-01 4.126885157289228e-01 3.88326e-11 1.97255e-10 3 -9.183928294344236e-01 -9.183928294635174e-01 2.90938e-11 1.01001e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.365427051088689e+00 1.365427051084449e+00 4.24039e-12 6.77891e-11 2 -1.011016028702709e+00 -1.011016028705997e+00 3.28848e-12 8.80416e-10 3 9.669734376134410e-01 9.669734374897715e-01 1.23670e-10 2.09094e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 -1.146012446205824e+00 -1.146012446257340e+00 5.15163e-11 1.89592e-10 2 1.449945546363450e+00 1.449945546367085e+00 3.63487e-12 3.57292e-11 3 3.095847394727682e-01 3.095847394948004e-01 2.20322e-11 7.12003e-11 ----------------------------------------------------------------------------------------------------- * 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 = 7, direction = 3: |F_model - F_numer| error = ----------------------- = 4.97773e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.73253e-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 2.73253e-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.