!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 3.436525887151524e-01 1.70935e-11 8.21661e-11 2 -2.618078013059398e-02 -2.618078012420913e-02 6.38484e-12 7.94072e-10 3 3.437088702147270e-02 3.437088701976312e-02 1.70958e-12 4.72355e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099684402225e-01 -8.101099684343029e-01 5.91960e-12 1.28447e-10 2 8.600116124285215e-01 8.600116124253121e-01 3.20943e-12 7.51370e-11 3 3.127577256335160e-01 3.127577256239262e-01 9.58983e-12 6.44418e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242118367687234e-02 -8.242118366816790e-02 8.70444e-12 6.57937e-10 2 -4.844095559540117e-02 -4.844095559115918e-02 4.24198e-12 5.93259e-11 3 -2.547490082104492e-01 -2.547490082114771e-01 1.02796e-12 4.15211e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906826524607e-01 4.983906826273152e-01 2.51454e-11 1.25149e-10 2 2.408671394307411e-01 2.408671394320607e-01 1.31958e-12 1.35487e-10 3 3.779437321759949e-01 3.779437321787491e-01 2.75419e-12 9.36172e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111419208698e-01 7.931111419080920e-01 1.27779e-11 4.72775e-11 2 -3.817072234508387e-01 -3.817072234497844e-01 1.05438e-12 3.43678e-11 3 2.806999060513611e-01 2.806999060559847e-01 4.62358e-12 8.61993e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254973231868e-01 -3.438254973232059e-01 1.90403e-14 3.06321e-10 2 2.501152956639251e-01 2.501152956884188e-01 2.44937e-11 9.79931e-11 3 3.380287544197739e-01 3.380287544364496e-01 1.66757e-11 2.23980e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574681105392247e-01 2.574681105381417e-01 1.08302e-12 3.41880e-11 2 -1.219046653943463e+00 -1.219046653960039e+00 1.65759e-11 2.43146e-10 3 -1.651118793526997e+00 -1.651118793481573e+00 4.54241e-11 1.38817e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221784176451463e-01 -7.221784176759777e-01 3.08313e-11 4.52207e-10 2 -4.748263058675943e-01 -4.748263059090429e-01 4.14486e-11 5.73096e-10 3 -7.562197538222701e-01 -7.562197538119403e-01 1.03298e-11 5.27075e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288844025746376e-02 4.288844025185326e-02 5.61050e-12 4.83550e-11 2 -1.188167805006370e+00 -1.188167805005352e+00 1.01852e-12 1.06454e-10 3 -1.184618212225004e+00 -1.184618212237055e+00 1.20508e-11 2.02754e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641769484507e-01 -5.398641769350078e-01 1.34429e-11 2.32374e-10 2 4.980765860330944e-01 4.980765861040875e-01 7.09931e-11 8.58721e-11 3 -7.222686200180112e-01 -7.222686200175742e-01 4.36984e-13 1.70723e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753130726002e-01 -3.572753129828755e-01 8.97248e-11 3.19087e-10 2 -8.581020012537173e-01 -8.581020013078884e-01 5.41711e-11 4.99608e-10 3 7.845981082358283e-01 7.845981082371527e-01 1.32439e-12 1.11923e-09 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596031319910259e-02 2.596031318005223e-02 1.90504e-11 2.15522e-10 2 1.245097671222573e+00 1.245097671215063e+00 7.51021e-12 3.88029e-09 * 3 7.763446127940955e-01 7.763446127933216e-01 7.73936e-13 1.10537e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365342007914724e-01 -5.365342008095366e-01 1.80642e-11 3.10724e-10 2 -1.200162165117639e+00 -1.200162165113092e+00 4.54703e-12 2.29837e-10 3 -1.957550096924832e+00 -1.957550096932230e+00 7.39853e-12 1.91000e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988770936043128e-02 8.988770936888618e-02 8.45490e-12 2.40738e-10 2 4.855436345119641e-01 4.855436344980696e-01 1.38946e-11 4.97438e-11 3 -1.387144626393406e-01 -1.387144626296563e-01 9.68428e-12 7.65989e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761451035216512e+00 1.761451035178274e+00 3.82381e-11 4.74390e-09 * 2 -6.436068979754913e-01 -6.436068979650890e-01 1.04023e-11 5.64625e-11 3 7.520277720007028e-01 7.520277719892025e-01 1.15004e-11 1.56457e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494756306548e-01 5.978494756655716e-01 3.49167e-11 9.25225e-10 2 1.336599637619232e+00 1.336599637609188e+00 1.00449e-11 1.46825e-10 3 8.753613030427162e-01 8.753613030560539e-01 1.33377e-11 2.52004e-11 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232218181632726e-01 4.232218181324398e-01 3.08328e-11 8.09245e-11 2 3.604704536977737e-01 3.604704536936759e-01 4.09778e-12 2.66424e-10 3 -9.557914869742344e-02 -9.557914867230459e-02 2.51189e-11 5.93779e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049824049588291e-01 -5.049824049386320e-01 2.01971e-11 1.71181e-10 2 4.028584613917059e-01 4.028584613928124e-01 1.10650e-12 1.09237e-10 3 1.019475218100237e+00 1.019475218107122e+00 6.88472e-12 1.52266e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575296475746754e-01 2.575296475697336e-01 4.94177e-12 8.83117e-10 2 3.782444212810283e-01 3.782444212748867e-01 6.14153e-12 1.95372e-10 3 -4.712358500882987e-01 -4.712358501009356e-01 1.26369e-11 2.10477e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062635578236175e-01 4.062635577428694e-01 8.07481e-11 1.01935e-10 2 3.112967180681483e-01 3.112967180913643e-01 2.32160e-11 1.53005e-10 3 -4.574995162202995e-01 -4.574995162126549e-01 7.64455e-12 5.20453e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.519579255165166e-01 -9.519579254457422e-01 7.07744e-11 2.00151e-10 2 4.430056383664394e-02 4.430056386062868e-02 2.39847e-11 2.24187e-09 * 3 8.201330421005264e-01 8.201330421057985e-01 5.27212e-12 1.16702e-09 * ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278253472054e-01 2.873278253343323e-01 1.28731e-11 4.64981e-10 2 1.511178771492702e+00 1.511178771495694e+00 2.99272e-12 1.69538e-10 3 1.447152281236705e+00 1.447152281198429e+00 3.82758e-11 9.94267e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449441207763351e-01 -3.449441207817146e-01 5.37953e-12 5.51220e-11 2 3.006117549940310e-01 3.006117549947689e-01 7.37910e-13 4.39617e-11 3 -3.734060034584073e-01 -3.734060034573931e-01 1.01419e-12 6.60971e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.548683812487404e-02 7.548683812770976e-02 2.83572e-12 7.42058e-11 2 -5.942093508757897e-04 -5.942093458390913e-04 5.03670e-12 1.25966e-10 3 -6.192826982805564e-01 -6.192826982761428e-01 4.41358e-12 1.12763e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619447309022211e-01 -3.619447308693007e-01 3.29204e-11 2.22766e-10 2 -8.543631740988505e-01 -8.543631740960694e-01 2.78111e-12 2.14567e-09 * 3 2.198728306724409e-01 2.198728307916062e-01 1.19165e-10 4.11949e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995054625264395e-01 -4.995054625325241e-01 6.08469e-12 1.33643e-10 2 1.019970120957396e+00 1.019970120977795e+00 2.03995e-11 5.04417e-11 3 -7.917982408277793e-01 -7.917982408458415e-01 1.80622e-11 1.70651e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695233004712437e-01 5.695233004516851e-01 1.95586e-11 3.02254e-10 2 -2.393202179116337e+00 -2.393202179097492e+00 1.88454e-11 5.01053e-10 3 7.839007904311678e-01 7.839007904286446e-01 2.52320e-12 4.43997e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446252994106219e-01 -5.446252994141354e-01 3.51352e-12 4.05316e-11 2 6.944324440643135e-01 6.944324440863648e-01 2.20514e-11 1.83953e-10 3 -2.318274124545710e-01 -2.318274124572522e-01 2.68122e-12 1.05167e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440921556166240e-01 -2.440921556285041e-01 1.18801e-11 2.57179e-10 2 -7.057626656573426e-01 -7.057626656620815e-01 4.73888e-12 1.94174e-09 * 3 6.755894761654935e-01 6.755894761960455e-01 3.05520e-11 5.31205e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998223838726057e-02 -7.998223841274071e-02 2.54801e-11 5.72761e-11 2 6.365060356456019e-01 6.365060356372699e-01 8.33200e-12 1.30700e-11 3 -3.994794256969324e-01 -3.994794256722343e-01 2.46981e-11 7.06429e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -7.196131332866144e-02 -7.196131328768822e-02 4.09732e-11 1.28487e-10 2 -9.584853832076661e-01 -9.584853831698553e-01 3.78108e-11 2.18746e-10 3 4.908346291899299e-01 4.908346292675876e-01 7.76577e-11 1.10052e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661919243076066e-01 5.661919242706808e-01 3.69258e-11 1.18753e-10 2 3.764670774327869e-01 3.764670774030847e-01 2.97022e-11 2.05633e-10 3 1.162561738192104e-01 1.162561737893116e-01 2.98988e-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 6.485088426669192e-01 9.04676e-12 2.37704e-10 2 6.990251602096700e-01 6.990251602001504e-01 9.51961e-12 6.83285e-11 3 7.051165624608332e-01 7.051165624576876e-01 3.14559e-12 2.71864e-10 ----------------------------------------------------------------------------------------------------- 2 Co 1 4.952782839404976e-01 4.952782839415601e-01 1.06254e-12 2.11255e-09 2 -8.374551606477045e-01 -8.374551606347140e-01 1.29905e-11 1.81497e-11 3 1.780509367685435e+00 1.780509367675526e+00 9.90896e-12 1.43441e-09 ----------------------------------------------------------------------------------------------------- 3 Co 1 -1.049858775176962e+00 -1.049858775198685e+00 2.17226e-11 1.26446e-10 2 1.430819593492611e+00 1.430819593511792e+00 1.91811e-11 2.47683e-09 * 3 -5.930745099318449e-01 -5.930745099610190e-01 2.91741e-11 9.65774e-11 ----------------------------------------------------------------------------------------------------- 4 Co 1 9.251347323942665e-01 9.251347323174360e-01 7.68304e-11 4.65160e-10 2 1.847185605282825e-01 1.847185604870985e-01 4.11840e-11 2.41520e-10 3 -9.942491783363725e-01 -9.942491783365158e-01 1.43330e-13 2.05026e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 -4.926497571928059e-01 -4.926497571531932e-01 3.96127e-11 4.10488e-09 * 2 4.702630732414036e-01 4.702630732603295e-01 1.89259e-11 3.25552e-09 * 3 -4.095238032240969e-02 -4.095238032811761e-02 5.70792e-12 4.37332e-09 * ----------------------------------------------------------------------------------------------------- 6 Co 1 -1.507597136687161e-01 -1.507597136302374e-01 3.84787e-11 2.55793e-10 2 4.913844275807172e-01 4.913844276589645e-01 7.82474e-11 8.35670e-10 3 -4.885669056314605e-01 -4.885669056441970e-01 1.27365e-11 1.44502e-10 ----------------------------------------------------------------------------------------------------- 7 Co 1 1.455214618196758e+00 1.455214618184588e+00 1.21698e-11 1.14491e-10 2 -1.770106899804605e+00 -1.770106899831711e+00 2.71065e-11 9.53582e-11 3 1.069588904736801e+00 1.069588904749861e+00 1.30607e-11 4.02809e-10 ----------------------------------------------------------------------------------------------------- 8 Co 1 -2.881525051229560e+00 -2.881525051237251e+00 7.69029e-12 4.61520e-11 2 1.318718242298574e+00 1.318718242263646e+00 3.49281e-11 3.04135e-10 3 1.568541213092912e-01 1.568541212417487e-01 6.75424e-11 5.74667e-10 ----------------------------------------------------------------------------------------------------- 9 Co 1 6.766301757076492e-01 6.766301757122597e-01 4.61053e-12 5.64937e-10 2 3.991670773813838e-01 3.991670773878123e-01 6.42847e-12 1.84399e-11 3 9.558468821906971e-01 9.558468821874417e-01 3.25540e-12 8.08968e-11 ----------------------------------------------------------------------------------------------------- 10 Co 1 -3.396504802393738e-02 -3.396504794424423e-02 7.96931e-11 4.85786e-10 2 -1.004662187945575e+00 -1.004662187969391e+00 2.38161e-11 1.25709e-10 3 7.091305992487695e-01 7.091305992697332e-01 2.09637e-11 2.31281e-10 ----------------------------------------------------------------------------------------------------- 11 Co 1 -1.122986154601710e+00 -1.122986154511232e+00 9.04781e-11 1.77196e-10 2 1.823109755205160e+00 1.823109755190243e+00 1.49178e-11 4.57998e-09 * 3 -1.975499215945307e+00 -1.975499215929102e+00 1.62053e-11 1.03120e-10 ----------------------------------------------------------------------------------------------------- 12 Co 1 9.978811148984036e-01 9.978811148395124e-01 5.88912e-11 2.86895e-10 2 -7.117088929205188e-01 -7.117088929125912e-01 7.92755e-12 4.24037e-09 * 3 -2.635324537683921e-01 -2.635324537484738e-01 1.99183e-11 1.19369e-09 ----------------------------------------------------------------------------------------------------- 13 Co 1 -1.290388725282605e+00 -1.290388725279600e+00 3.00560e-12 1.44179e-10 2 -7.961106042312269e-01 -7.961106043316233e-01 1.00396e-10 1.50426e-09 3 8.213586489585802e-01 8.213586489648855e-01 6.30529e-12 3.94634e-11 ----------------------------------------------------------------------------------------------------- 14 Co 1 1.097729496476169e+00 1.097729496491241e+00 1.50711e-11 1.62006e-10 2 5.693640257200955e-01 5.693640257216666e-01 1.57108e-12 3.38089e-10 3 8.570083673939491e-02 8.570083668855569e-02 5.08392e-11 8.17340e-11 ----------------------------------------------------------------------------------------------------- 15 Co 1 -1.615199295731476e-01 -1.615199295255792e-01 4.75684e-11 1.60280e-10 2 1.337392105849038e+00 1.337392105826027e+00 2.30105e-11 1.04682e-09 3 -6.342648095661321e-01 -6.342648095669048e-01 7.72715e-13 2.22947e-10 ----------------------------------------------------------------------------------------------------- 16 Co 1 -5.318937050053080e-01 -5.318937051614531e-01 1.56145e-10 7.41623e-11 2 -1.412708359134518e+00 -1.412708358974869e+00 1.59649e-10 1.68147e-10 3 8.786146764805511e-01 8.786146764627923e-01 1.77588e-11 3.67463e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 6.915074903847552e-01 6.915074903951517e-01 1.03965e-11 2.21664e-10 2 -9.829117400192525e-01 -9.829117400335424e-01 1.42899e-11 8.33101e-11 3 -1.598673031164938e+00 -1.598673031180563e+00 1.56251e-11 2.70080e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 7.015826978995222e-01 7.015826978361618e-01 6.33604e-11 5.45616e-10 2 -2.814145369451363e+00 -2.814145369495154e+00 4.37907e-11 5.02866e-10 3 7.844780597289456e-01 7.844780597129526e-01 1.59930e-11 6.18493e-10 ----------------------------------------------------------------------------------------------------- 19 Co 1 -6.225568893765392e-02 -6.225568898461355e-02 4.69596e-11 3.18894e-10 2 1.200440395603355e-01 1.200440395587050e-01 1.63058e-12 1.02424e-09 3 -1.087469966454387e+00 -1.087469966505392e+00 5.10052e-11 2.14419e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 -2.360803393251594e-02 -2.360803392776585e-02 4.75009e-12 6.62466e-11 2 1.992728330742332e+00 1.992728330741596e+00 7.36078e-13 7.56035e-11 3 1.400068895790143e+00 1.400068895757232e+00 3.29108e-11 8.39382e-09 * ----------------------------------------------------------------------------------------------------- 21 Co 1 -1.037668287918647e-01 -1.037668289004393e-01 1.08575e-10 2.34973e-10 2 9.110391141555166e-01 9.110391141338918e-01 2.16248e-11 1.13065e-09 3 -1.811942783956130e-01 -1.811942783626250e-01 3.29880e-11 2.19671e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 9.038292111061944e-02 9.038292109640099e-02 1.42184e-11 6.25108e-09 * 2 -1.874450693036562e+00 -1.874450693053804e+00 1.72420e-11 2.11131e-10 3 1.506262358501468e+00 1.506262358494582e+00 6.88583e-12 1.15889e-09 ----------------------------------------------------------------------------------------------------- 23 Co 1 1.328829993393943e-01 1.328829993279449e-01 1.14494e-11 2.77393e-10 2 4.821304112639568e-01 4.821304112729848e-01 9.02795e-12 1.40152e-09 3 2.387805762364358e-01 2.387805762360175e-01 4.18304e-13 8.68655e-10 ----------------------------------------------------------------------------------------------------- 24 Co 1 1.064343156205479e+00 1.064343156239642e+00 3.41627e-11 5.63493e-10 2 6.380254895963353e-01 6.380254895577887e-01 3.85466e-11 2.74101e-10 3 -1.062587685930443e+00 -1.062587685891897e+00 3.85463e-11 5.35369e-10 ----------------------------------------------------------------------------------------------------- 25 Co 1 -1.237699499311616e+00 -1.237699499296000e+00 1.56160e-11 1.06315e-10 2 -1.204150315791169e+00 -1.204150315775553e+00 1.56157e-11 1.50370e-10 3 5.953470153364712e-01 5.953470153497757e-01 1.33046e-11 2.52243e-10 ----------------------------------------------------------------------------------------------------- 26 Co 1 1.126237376081141e+00 1.126237376029428e+00 5.17131e-11 2.39476e-10 2 -1.119149513025585e-01 -1.119149512845241e-01 1.80344e-11 4.92409e-10 3 2.194061626637771e-01 2.194061626676185e-01 3.84140e-12 3.88346e-09 * ----------------------------------------------------------------------------------------------------- 27 Co 1 -6.834631605512517e-01 -6.834631605305720e-01 2.06797e-11 1.54890e-09 2 7.413006792165826e-01 7.413006792345938e-01 1.80111e-11 7.56237e-10 3 -8.744615251486350e-01 -8.744615252576563e-01 1.09021e-10 2.30445e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 9.841179806382486e-01 9.841179806759079e-01 3.76593e-11 2.44578e-10 2 -5.025721290957174e-01 -5.025721291142521e-01 1.85347e-11 1.64129e-10 3 -7.298429980283443e-01 -7.298429980538038e-01 2.54595e-11 8.76985e-11 ----------------------------------------------------------------------------------------------------- 29 Co 1 1.520982940618281e-01 1.520982940647988e-01 2.97062e-12 1.80972e-10 2 1.756805650646875e+00 1.756805650638795e+00 8.07976e-12 1.63933e-10 3 1.933580998783204e-01 1.933580998566935e-01 2.16269e-11 7.50914e-11 ----------------------------------------------------------------------------------------------------- 30 Co 1 -7.232508651645634e-01 -7.232508651627536e-01 1.80977e-12 6.06947e-10 2 -5.431922558304427e-01 -5.431922558174760e-01 1.29667e-11 9.56711e-11 3 2.045010151127515e-01 2.045010151604516e-01 4.77001e-11 8.94414e-10 ----------------------------------------------------------------------------------------------------- 31 Co 1 -8.244630581004162e-01 -8.244630581048356e-01 4.41935e-12 2.65501e-10 2 1.913997385514300e-01 1.913997384905068e-01 6.09232e-11 4.16523e-09 * 3 -9.247281876738941e-01 -9.247281876299878e-01 4.39063e-11 3.64676e-11 ----------------------------------------------------------------------------------------------------- 32 Co 1 1.345238145339354e-01 1.345238145668798e-01 3.29444e-11 7.90651e-11 2 -9.913459160290876e-01 -9.913459160469372e-01 1.78496e-11 7.11667e-11 3 -8.558256567604919e-01 -8.558256567680524e-01 7.56051e-12 5.12470e-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 = ----------------------- = 2.34633e-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 -3.364719424258674e-01 4.66466e-12 2.59363e-09 * 2 -6.707514569274412e-01 -6.707514568796114e-01 4.78299e-11 1.83633e-10 3 -1.333699828757648e+00 -1.333699828762651e+00 5.00222e-12 1.52493e-09 ----------------------------------------------------------------------------------------------------- 2 Co 1 -4.702422918911192e-01 -4.702422919078970e-01 1.67779e-11 5.25858e-10 2 -3.157352706777057e+00 -3.157352706734701e+00 4.23559e-11 2.70476e-10 3 -5.088441693591297e+00 -5.088441693635367e+00 4.40705e-11 6.30171e-11 ----------------------------------------------------------------------------------------------------- 3 Co 1 2.180068732294752e+00 2.180068732302920e+00 8.16769e-12 2.27037e-10 2 -2.237568390724854e+00 -2.237568390669598e+00 5.52558e-11 4.70262e-10 3 1.707044259957988e+00 1.707044259908831e+00 4.91571e-11 2.70781e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -1.228974399733247e+00 -1.228974399732680e+00 5.67546e-13 1.27171e-10 2 3.607372996720728e+00 3.607372996717694e+00 3.03402e-12 2.61156e-09 * 3 6.452209190473694e-01 6.452209190441611e-01 3.20832e-12 1.81351e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 5.879539366057693e-01 5.879539365686903e-01 3.70790e-11 6.22723e-10 2 8.961142960665780e-01 8.961142960482618e-01 1.83162e-11 6.74922e-11 3 -6.932087768970746e-01 -6.932087769165655e-01 1.94909e-11 8.99089e-11 ----------------------------------------------------------------------------------------------------- 6 Co 1 -6.003884310581331e-01 -6.003884310472339e-01 1.08992e-11 3.87521e-11 2 -1.746931105867320e-01 -1.746931105719727e-01 1.47593e-11 2.67029e-09 * 3 9.092410588156028e-01 9.092410588059667e-01 9.63607e-12 2.35855e-11 ----------------------------------------------------------------------------------------------------- 7 Al 1 -7.310544615264056e-01 -7.310544615385570e-01 1.21514e-11 6.39032e-11 2 5.679954461342421e-01 5.679954461297996e-01 4.44256e-12 9.57125e-11 3 -7.151583706644117e-02 -7.151583708516142e-02 1.87202e-11 1.42253e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 2.828004210940170e+00 2.828004211078659e+00 1.38489e-10 5.52190e-10 2 -1.365317214278379e+00 -1.365317214277110e+00 1.26965e-12 1.90421e-10 3 4.497931883794736e+00 4.497931883717992e+00 7.67439e-11 7.37364e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.682032604651235e+00 -1.682032604655728e+00 4.49329e-12 5.36695e-11 2 3.579738430873127e+00 3.579738430870820e+00 2.30749e-12 2.32131e-10 3 -2.057199430527850e+00 -2.057199430511226e+00 1.66240e-11 3.18088e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 5.998324113238669e-01 5.998324113271625e-01 3.29559e-12 2.54369e-10 2 -2.577319355674388e-01 -2.577319355685719e-01 1.13304e-12 1.11186e-10 3 -2.130853972002265e+00 -2.130853971984623e+00 1.76423e-11 1.33512e-10 ----------------------------------------------------------------------------------------------------- 11 Co 1 -9.687885315783614e-01 -9.687885315954106e-01 1.70491e-11 4.41390e-10 2 1.601386981442008e+00 1.601386981455369e+00 1.33609e-11 6.11785e-10 3 2.100493474526508e+00 2.100493474501966e+00 2.45417e-11 1.77991e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -8.608674689934156e-01 -8.608674690084138e-01 1.49982e-11 1.00459e-10 2 4.049035651887998e-01 4.049035652198749e-01 3.10751e-11 4.90477e-11 3 6.185653845649152e-01 6.185653845327520e-01 3.21632e-11 1.28897e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 4.621920216487909e-01 4.621920216926640e-01 4.38731e-11 2.51109e-10 2 8.174506913630841e-01 8.174506913754033e-01 1.23191e-11 6.24816e-11 3 -6.506423190313138e-01 -6.506423190347156e-01 3.40183e-12 2.91359e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 -8.023605573782989e-01 -8.023605573720130e-01 6.28597e-12 3.28365e-11 2 -6.432463488758250e-01 -6.432463488866397e-01 1.08147e-11 6.48230e-11 3 6.162360939593566e-01 6.162360939950227e-01 3.56660e-11 9.46702e-11 ----------------------------------------------------------------------------------------------------- 15 Co 1 -1.315063094618599e+00 -1.315063094637486e+00 1.88871e-11 7.94320e-11 2 1.617584708658941e+00 1.617584708811946e+00 1.53006e-10 2.01448e-10 3 -1.987121906447036e+00 -1.987121906472199e+00 2.51630e-11 8.18780e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 3.326421586311568e+00 3.326421586316843e+00 5.27534e-12 1.31690e-10 2 4.343115068374870e-01 4.343115068528559e-01 1.53689e-11 4.42855e-10 3 -7.711629078742933e-01 -7.711629077518311e-01 1.22462e-10 1.50755e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -3.975538844683201e-01 -3.975538844498396e-01 1.84805e-11 2.95584e-11 2 -3.526554973155223e+00 -3.526554973139220e+00 1.60032e-11 6.72113e-10 3 2.387158213749097e+00 2.387158213714776e+00 3.43201e-11 7.55792e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 -6.815868163584994e-01 -6.815868163663583e-01 7.85894e-12 1.85129e-10 2 2.043058250860725e+00 2.043058250847000e+00 1.37250e-11 2.87531e-10 3 -1.258306445404200e+00 -1.258306445420375e+00 1.61755e-11 5.32423e-11 ----------------------------------------------------------------------------------------------------- 19 Co 1 -3.270553719144742e+00 -3.270553719062351e+00 8.23910e-11 9.80990e-10 2 -3.181306007772657e+00 -3.181306007763958e+00 8.69882e-12 6.14535e-11 3 3.260044302658791e-01 3.260044301463645e-01 1.19515e-10 3.38599e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 9.590562557706153e-01 9.590562557679132e-01 2.70206e-12 9.25793e-12 2 1.883721661013895e-01 1.883721661327319e-01 3.13424e-11 5.44016e-09 * 3 2.344899011749223e-01 2.344899011822372e-01 7.31493e-12 3.80083e-10 ----------------------------------------------------------------------------------------------------- 21 Co 1 1.355729633349661e+00 1.355729633212383e+00 1.37278e-10 4.88283e-10 2 -2.466928645305829e+00 -2.466928645317078e+00 1.12492e-11 3.65846e-10 3 -3.027432205240033e+00 -3.027432205117070e+00 1.22963e-10 2.04504e-09 * ----------------------------------------------------------------------------------------------------- 22 Al 1 4.972821642629059e-01 4.972821643086651e-01 4.57592e-11 5.92281e-10 2 -3.729211305246812e+00 -3.729211305192838e+00 5.39737e-11 7.75055e-10 3 1.292195239541051e+00 1.292195239496198e+00 4.48532e-11 4.22135e-10 ----------------------------------------------------------------------------------------------------- 23 Co 1 -6.269613128790433e-01 -6.269613128847482e-01 5.70488e-12 2.41764e-10 2 8.014878227712682e-01 8.014878227706080e-01 6.60139e-13 3.91242e-10 3 -9.628785547266907e-01 -9.628785547333873e-01 6.69664e-12 1.19699e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 3.419940097599340e+00 3.419940097604743e+00 5.40279e-12 2.03284e-10 2 4.626912821817108e+00 4.626912821823782e+00 6.67466e-12 3.19955e-10 3 4.824139022960524e+00 4.824139022938076e+00 2.24478e-11 1.82254e-10 ----------------------------------------------------------------------------------------------------- 25 Co 1 1.295187906741528e+00 1.295187906719335e+00 2.21927e-11 4.34485e-09 * 2 -8.345778772983723e-01 -8.345778772972772e-01 1.09512e-12 3.54811e-10 3 9.086999099962303e-01 9.086999100245503e-01 2.83200e-11 5.41345e-10 ----------------------------------------------------------------------------------------------------- 26 Co 1 -1.704282248395000e+00 -1.704282248394108e+00 8.91731e-13 1.06487e-09 2 -1.236804276993935e+00 -1.236804276992508e+00 1.42641e-12 1.60226e-10 3 2.113319098748126e+00 2.113319098679991e+00 6.81348e-11 2.63678e-10 ----------------------------------------------------------------------------------------------------- 27 Co 1 -1.438708467315667e+00 -1.438708467307442e+00 8.22520e-12 2.77967e-10 2 9.581785836097804e-01 9.581785836154204e-01 5.64004e-12 3.23265e-10 3 -7.698342354347288e-01 -7.698342354364094e-01 1.68054e-12 5.83544e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 6.964153453738855e-01 6.964153453451458e-01 2.87397e-11 1.34729e-10 2 -8.504673752696089e-01 -8.504673752195063e-01 5.01026e-11 1.57568e-10 3 -8.684405961603399e-01 -8.684405961629743e-01 2.63445e-12 4.57957e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.742369447605645e+00 -1.742369447598629e+00 7.01572e-12 1.15359e-09 2 1.336025322906467e+00 1.336025322878243e+00 2.82239e-11 1.11094e-10 3 -1.868165529592823e+00 -1.868165529529959e+00 6.28635e-11 4.64941e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 4.307607729112413e-01 4.307607729683991e-01 5.71578e-11 3.49451e-10 2 4.126885157677218e-01 4.126885157486185e-01 1.91033e-11 1.01463e-10 3 -9.183928294344095e-01 -9.183928294138335e-01 2.05760e-11 4.30551e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.365427051088649e+00 1.365427051080982e+00 7.66720e-12 2.37754e-11 2 -1.011016028702685e+00 -1.011016028674864e+00 2.78211e-11 2.00384e-10 3 9.669734376134026e-01 9.669734375523378e-01 6.10648e-11 3.41021e-11 ----------------------------------------------------------------------------------------------------- 32 Al 1 -1.146012446205811e+00 -1.146012446244466e+00 3.86546e-11 6.22291e-11 2 1.449945546363394e+00 1.449945546334217e+00 2.91767e-11 3.43827e-11 3 3.095847394727357e-01 3.095847393969521e-01 7.57836e-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 = ----------------------- = 3.66604e-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.