!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_GW_GaoWeber_2002_SiC__SM_606253546840_000 Supported species : C Si 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 = C | a0 = 3.226238250732422 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 9.299412383523121e+00 9.299412383527583e+00 4.46221e-12 2.40110e-11 2 4.834859096967312e+00 4.834859096965574e+00 1.73817e-12 1.35813e-10 3 5.571008703263275e+00 5.571008703264934e+00 1.65912e-12 2.16902e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.940828102744490e+00 -1.940828102746065e+00 1.57452e-12 4.26614e-12 2 4.145992721231952e-01 4.145992721278134e-01 4.61825e-12 1.15092e-10 3 3.171864543929629e+00 3.171864543930973e+00 1.34426e-12 2.69123e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.550595675125694e+00 -2.550595675128177e+00 2.48335e-12 6.08997e-11 2 3.829178355251571e+00 3.829178355252366e+00 7.95364e-13 7.38622e-11 3 -6.327788496191466e+00 -6.327788496196222e+00 4.75620e-12 3.19238e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 5.339214186698370e+00 5.339214186686917e+00 1.14531e-11 1.34922e-10 2 5.733358278951630e+00 5.733358278951323e+00 3.06422e-13 4.77272e-11 3 3.837467362923703e-01 3.837467362839496e-01 8.42076e-12 3.93227e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -9.532763207454987e-01 -9.532763207413830e-01 4.11571e-12 1.67023e-11 2 4.762238712595122e+00 4.762238712601727e+00 6.60538e-12 7.51443e-11 3 5.048110786496300e+00 5.048110786498590e+00 2.29061e-12 9.95133e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -4.151378161371333e+00 -4.151378161380254e+00 8.92175e-12 2.09930e-11 2 -5.116375899526514e+00 -5.116375899516362e+00 1.01519e-11 1.62652e-11 3 3.506035092537446e+00 3.506035092535458e+00 1.98774e-12 2.46647e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -2.624085551989388e+00 -2.624085551991187e+00 1.79945e-12 3.28941e-11 2 1.829358350985550e+00 1.829358350990375e+00 4.82481e-12 1.29574e-11 3 -4.359044216342048e+00 -4.359044216342516e+00 4.68070e-13 2.53824e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -6.820772983836211e-01 -6.820772983849266e-01 1.30551e-12 1.04469e-10 2 1.178562656490167e+00 1.178562656482024e+00 8.14282e-12 1.51230e-11 3 3.860120093096238e-01 3.860120093173904e-01 7.76662e-12 5.28729e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 1.254277395425893e+00 1.254277395429589e+00 3.69593e-12 5.21395e-05 * 2 -1.854386561669422e+00 -1.854386561667630e+00 1.79257e-12 2.77958e-11 3 4.151849617462945e+00 4.151849617462931e+00 1.42109e-14 1.05011e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -2.675249224562057e+00 -2.675249224571768e+00 9.71090e-12 6.05449e-11 2 -1.454953002273587e+00 -1.454953002274400e+00 8.12461e-13 2.27900e-11 3 1.117670404573611e+00 1.117670404577664e+00 4.05365e-12 3.57963e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -5.210737359813665e+00 -5.210737359802816e+00 1.08491e-11 6.93738e-11 2 -7.754422522849984e+00 -7.754422522850579e+00 5.95080e-13 1.89363e-10 3 -3.748318345419120e+00 -3.748318345423885e+00 4.76552e-12 2.65072e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 1.682183709074937e+00 1.682183709083866e+00 8.92952e-12 1.85436e-11 2 -1.800883961862396e+00 -1.800883961861106e+00 1.28941e-12 6.51714e-11 3 -1.344880754666957e+00 -1.344880754662506e+00 4.45066e-12 9.33142e-12 ----------------------------------------------------------------------------------------------------- 13 C 1 1.043949080760242e+00 1.043949080757903e+00 2.33902e-12 4.87992e-11 2 -2.092687165571137e+00 -2.092687165576870e+00 5.73319e-12 5.37943e-11 3 -1.912935985480751e+00 -1.912935985493665e+00 1.29130e-11 1.54690e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -3.090762164490752e+00 -3.090762164486966e+00 3.78586e-12 4.43685e-11 2 -4.037459573379905e+00 -4.037459573372490e+00 7.41540e-12 3.80380e-11 3 1.114397869346978e+00 1.114397869343511e+00 3.46789e-12 2.92877e-12 ----------------------------------------------------------------------------------------------------- 15 C 1 3.465418085748090e-01 3.465418085645033e-01 1.03057e-11 3.06042e-11 2 3.074990110977960e+00 3.074990110971107e+00 6.85318e-12 2.03035e-10 3 -2.950655962845337e-01 -2.950655962837468e-01 7.86815e-13 3.11922e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 9.680514088210553e-01 9.680514088203461e-01 7.09210e-13 1.88861e-10 2 3.274643476120550e+00 3.274643476121712e+00 1.16218e-12 3.01359e-11 3 2.200049974622932e+00 2.200049974626953e+00 4.02123e-12 3.72572e-10 * ----------------------------------------------------------------------------------------------------- 17 C 1 3.320692350935232e+00 3.320692350934602e+00 6.29718e-13 7.55898e-11 2 1.424372238041461e+00 1.424372238042927e+00 1.46660e-12 1.86704e-11 3 -7.856367504051475e-01 -7.856367504057206e-01 5.73097e-13 1.18783e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.373856194414025e+00 5.373856194426395e+00 1.23697e-11 1.59703e-11 2 -3.487354099928575e+00 -3.487354099913075e+00 1.55005e-11 2.87770e-11 3 3.006593418557243e+00 3.006593418565584e+00 8.34177e-12 6.22880e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 4.354208546183880e+00 4.354208546189278e+00 5.39746e-12 5.24292e-12 2 5.678327178404976e+00 5.678327178399506e+00 5.46940e-12 4.11973e-11 3 -1.344317948525029e+00 -1.344317948524432e+00 5.96634e-13 1.09015e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 3.486204144931623e+00 3.486204144936965e+00 5.34151e-12 1.67741e-11 2 8.205641606239187e-01 8.205641606206597e-01 3.25895e-12 1.08764e-10 3 -1.967130089003676e+00 -1.967130089010277e+00 6.60050e-12 5.57665e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -2.560029250905285e+00 -2.560029250911767e+00 6.48148e-12 1.05085e-11 2 4.130228476744199e+00 4.130228476754812e+00 1.06128e-11 5.87539e-11 3 4.930237106586294e+00 4.930237106601325e+00 1.50306e-11 9.03091e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 -1.524238360207661e+00 -1.524238360207097e+00 5.63993e-13 7.13607e-12 2 -2.506410883666603e+00 -2.506410883670924e+00 4.32099e-12 6.46172e-11 3 2.863443501641602e+00 2.863443501625080e+00 1.65219e-11 7.44875e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.564493071229061e+00 -2.564493071226533e+00 2.52864e-12 9.20481e-11 2 2.381498992194088e+00 2.381498992200164e+00 6.07647e-12 3.75078e-11 3 -4.564852518058358e+00 -4.564852518075057e+00 1.66986e-11 4.80016e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -3.372696241337290e+00 -3.372696241341211e+00 3.92086e-12 2.75767e-10 * 2 -5.274598271817791e+00 -5.274598271800128e+00 1.76623e-11 2.94191e-11 3 -6.654610148868059e+00 -6.654610148869992e+00 1.93268e-12 1.13276e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 1.645633786186172e-01 1.645633786203737e-01 1.75654e-12 2.26788e-12 2 -1.799119607074128e+00 -1.799119607070743e+00 3.38507e-12 5.81275e-11 3 -3.392968577716718e+00 -3.392968577712143e+00 4.57501e-12 5.77542e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 3.111562497478960e-01 3.111562497466039e-01 1.29208e-12 1.13118e-11 2 -6.170329800716170e-02 -6.170329801034526e-02 3.18356e-12 8.34919e-11 3 2.654530812961860e+00 2.654530812980731e+00 1.88707e-11 7.40856e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 -2.914450317177087e-01 -2.914450317080826e-01 9.62613e-12 5.84477e-10 * 2 -2.694767537016575e+00 -2.694767537017768e+00 1.19282e-12 7.64024e-11 3 -8.933611715472425e-01 -8.933611715435337e-01 3.70881e-12 1.80574e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -6.418164654343755e-01 -6.418164654342039e-01 1.71640e-13 1.12528e-11 2 2.383945505824576e-01 2.383945505764827e-01 5.97492e-12 2.20245e-11 3 -2.342669015943719e+00 -2.342669015940297e+00 3.42171e-12 6.31006e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 2.269469505864531e+00 2.269469505846950e+00 1.75815e-11 3.51892e-11 2 2.149975934341288e+00 2.149975934345704e+00 4.41602e-12 6.22271e-11 3 2.306031801582898e+00 2.306031801583782e+00 8.84626e-13 6.41172e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.578836839966561e+00 -1.578836839969727e+00 3.16636e-12 5.18030e-11 2 -5.663293225834378e+00 -5.663293225835855e+00 1.47704e-12 1.62025e-10 3 3.381908553633022e+00 3.381908553622727e+00 1.02944e-11 2.79261e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.596833644658540e+00 -5.596833644666974e+00 8.43414e-12 3.13340e-11 2 4.440658872752810e+00 4.440658872772965e+00 2.01554e-11 2.08891e-11 3 -4.476625029584048e+00 -4.476625029587471e+00 3.42215e-12 6.12577e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 2.795598421108755e+00 2.795598421089819e+00 1.89355e-11 2.01981e-10 2 -4.597393103670087e+00 -4.597393103665564e+00 4.52260e-12 2.76978e-11 3 -1.383286288761177e+00 -1.383286288751041e+00 1.01359e-11 4.40787e-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 = 26, direction = 2: |F_model - F_numer| error = ----------------------- = 5.15946e-11 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 = Si | a0 = 3.4026260375976562 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.489559160745980e+00 -1.489559160746659e+00 6.79012e-13 4.27940e-11 2 -1.437498409015729e+00 -1.437498409015620e+00 1.09912e-13 7.50264e-11 3 -1.701136149779690e+00 -1.701136149774418e+00 5.27245e-12 1.50773e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 -7.290760941199059e+00 -7.290760941212975e+00 1.39160e-11 1.09418e-10 2 5.598427351523311e+00 5.598427351527379e+00 4.06786e-12 8.76774e-11 3 -3.301267022951885e+01 -3.301267022951833e+01 5.18696e-13 1.19506e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.704712218285229e+00 1.704712218274761e+00 1.04674e-11 3.27756e-11 2 -2.580563422472932e+01 -2.580563422465689e+01 7.24292e-11 3.30107e-10 3 1.443547607195125e+01 1.443547607192351e+01 2.77378e-11 1.66978e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.393577547174066e+01 -2.393577547173853e+01 2.13163e-12 1.63439e-10 2 -3.008753747876696e+00 -3.008753747879560e+00 2.86393e-12 1.22039e-10 3 -1.333964615690397e+01 -1.333964615689118e+01 1.27862e-11 5.95826e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.071926132957719e+01 1.071926132955671e+01 2.04761e-11 1.04681e-11 2 -1.180727551441390e+00 -1.180727551441645e+00 2.54241e-13 5.42695e-11 3 -4.265618849611744e+00 -4.265618849608697e+00 3.04734e-12 4.51399e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -5.534092990186029e+00 -5.534092990193609e+00 7.58060e-12 2.36691e-11 2 -4.780658061106186e+00 -4.780658061098722e+00 7.46336e-12 6.42508e-12 3 -3.235754602386046e-01 -3.235754602380450e-01 5.59552e-13 8.68283e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 -3.971509656310978e-01 -3.971509656302732e-01 8.24618e-13 8.70048e-12 2 2.801172534239990e+00 2.801172534240049e+00 5.90639e-14 6.12741e-11 3 2.644424186959657e+00 2.644424186963488e+00 3.83160e-12 2.22666e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 1.858859425757282e+01 1.858859425762575e+01 5.29390e-11 7.66775e-09 * 2 9.660013770691966e-01 9.660013770852407e-01 1.60441e-11 1.75209e-11 3 7.814326039056780e+00 7.814326039026833e+00 2.99476e-11 3.40991e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.725962071765758e+00 4.725962071773683e+00 7.92522e-12 3.64642e-11 2 4.030738141936569e+00 4.030738141937319e+00 7.50511e-13 6.18678e-11 3 1.183632813868497e-01 1.183632813876494e-01 7.99666e-13 1.93781e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.796190084844058e+00 -9.796190084842918e+00 1.14042e-12 2.31495e-11 2 2.832374462238260e+00 2.832374462240494e+00 2.23332e-12 5.38702e-11 3 -1.527974548780100e+00 -1.527974548778632e+00 1.46838e-12 3.40730e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 9.407632975360510e+00 9.407632975375602e+00 1.50919e-11 3.64846e-11 2 1.461216166290173e+01 1.461216166285908e+01 4.26468e-11 5.08251e-11 3 -2.707118107190924e+00 -2.707118107193093e+00 2.16938e-12 1.70600e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.715986104728437e+01 -1.715986104726938e+01 1.49818e-11 5.30491e-11 2 1.761570978194188e+01 1.761570978195566e+01 1.37845e-11 3.06812e-11 3 -1.847007644326827e+01 -1.847007644329056e+01 2.22968e-11 1.70246e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 6.390338037209295e+00 6.390338037203135e+00 6.16041e-12 1.66802e-10 2 -7.859082707311874e+00 -7.859082707308055e+00 3.81917e-12 3.34772e-11 3 -5.080510028118151e+00 -5.080510028128054e+00 9.90319e-12 5.46994e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.020077015372104e+00 1.020077015371242e+00 8.61311e-13 3.15208e-11 2 -2.575895057754074e+00 -2.575895057760178e+00 6.10401e-12 4.09082e-11 3 1.457365818872015e+00 1.457365818868785e+00 3.23008e-12 4.70979e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 -3.552526296658344e+00 -3.552526296653344e+00 5.00000e-12 2.01696e-04 * 2 -3.206030174315802e+00 -3.206030174311970e+00 3.83205e-12 4.06297e-11 3 6.500407856271356e+00 6.500407856277935e+00 6.57874e-12 1.80407e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 7.482837808352397e-01 7.482837808360624e-01 8.22675e-13 2.95575e-10 2 2.108375824802572e+00 2.108375824804852e+00 2.27995e-12 1.98272e-10 3 4.127294954922228e+00 4.127294954927637e+00 5.40901e-12 1.52260e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -4.387291741409563e+00 -4.387291741408832e+00 7.30971e-13 3.94200e-11 2 -4.852535386494843e+00 -4.852535386504582e+00 9.73888e-12 4.85043e-11 3 -7.976276515394678e+00 -7.976276515398482e+00 3.80407e-12 4.58984e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.288796521406825e+01 1.288796521403926e+01 2.89937e-11 5.04832e-10 * 2 -2.363278789844014e+01 -2.363278789841463e+01 2.55049e-11 1.67613e-10 3 4.680836639251958e+00 4.680836639261400e+00 9.44134e-12 6.29408e-10 * ----------------------------------------------------------------------------------------------------- 19 Si 1 1.371997075862144e+01 1.371997075856734e+01 5.41043e-11 3.70282e-11 2 -4.156038603771310e+00 -4.156038603773064e+00 1.75415e-12 2.90292e-11 3 -2.814625086555971e+00 -2.814625086555098e+00 8.72635e-13 7.28786e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 -9.822609473223288e+00 -9.822609473231360e+00 8.07177e-12 3.81561e-11 2 4.046650359083242e+00 4.046650359090367e+00 7.12497e-12 6.03517e-11 3 1.024520228699376e+01 1.024520228698393e+01 9.82503e-12 3.03492e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 -7.144964176713351e+00 -7.144964176700095e+00 1.32561e-11 1.24056e-10 2 -2.335518831591950e-01 -2.335518831592898e-01 9.47575e-14 5.62417e-12 3 6.119869593809204e+00 6.119869593807405e+00 1.79945e-12 2.42730e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.737499447702393e+00 -1.737499447702324e+00 6.90559e-14 2.68561e-11 2 2.662900428745996e+00 2.662900428746048e+00 5.15143e-14 4.90021e-11 3 -5.834313943594449e+00 -5.834313943595751e+00 1.30207e-12 9.48486e-12 ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.144767297786012e-01 -1.144767297783976e-01 2.03615e-13 3.93721e-12 2 7.001594326916492e-01 7.001594326916828e-01 3.36398e-14 2.63423e-12 3 -6.497168280451284e-01 -6.497168280444853e-01 6.43152e-13 1.82933e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 3.507833452884134e+00 3.507833452886675e+00 2.54063e-12 4.93006e-11 2 -2.748691424501731e+00 -2.748691424503196e+00 1.46461e-12 3.51372e-11 3 -2.933650913778107e+00 -2.933650913777142e+00 9.64118e-13 6.86384e-12 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.881903513830488e+01 -1.881903513830104e+01 3.84759e-12 1.75646e-11 2 -2.725991389035386e+00 -2.725991389043619e+00 8.23341e-12 1.25047e-11 3 1.528929844633731e+01 1.528929844634041e+01 3.09441e-12 5.33547e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 1.505474027110302e+01 1.505474027107754e+01 2.54730e-11 8.01617e-11 2 1.188580786030678e+01 1.188580786031737e+01 1.05818e-11 9.78506e-11 3 6.706567053184408e+00 6.706567053180846e+00 3.56160e-12 5.76827e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -5.233536827496389e-02 -5.233536827529926e-02 3.35364e-13 6.33702e-11 2 8.712214414576085e+00 8.712214414578488e+00 2.40341e-12 8.02611e-11 3 1.124707444169314e+01 1.124707444170362e+01 1.04805e-11 1.45768e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -5.200181158259210e+00 -5.200181158259765e+00 5.55112e-13 6.73595e-12 2 2.547854139398677e+00 2.547854139398384e+00 2.92655e-13 4.51683e-12 3 8.315626936527867e+00 8.315626936528712e+00 8.45546e-13 9.48397e-12 ----------------------------------------------------------------------------------------------------- 29 Si 1 1.456133417404814e+01 1.456133417404221e+01 5.93303e-12 3.75008e-10 2 3.205393278121544e+00 3.205393278120888e+00 6.55476e-13 2.59988e-11 3 -4.426291204702570e-02 -4.426291204519561e-02 1.83010e-12 3.46406e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.002481151872325e+01 1.002481151874806e+01 2.48104e-11 1.98039e-10 2 2.926480114317370e+00 2.926480114308931e+00 8.43903e-12 1.38155e-10 3 -1.148769285564410e+01 -1.148769285564416e+01 5.86198e-14 1.26246e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.507905887326483e+00 5.507905887322017e+00 4.46665e-12 1.11264e-10 2 -6.278190742721946e+00 -6.278190742723294e+00 1.34825e-12 7.38423e-11 3 1.781190707696302e+00 1.781190707694526e+00 1.77569e-12 4.63178e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.213511277079696e+01 -1.213511277080810e+01 1.11395e-11 3.53024e-10 2 7.229646097780759e+00 7.229646097786361e+00 5.60174e-12 9.17044e-11 3 1.068554071355566e+01 1.068554071355810e+01 2.43361e-12 9.05480e-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 = 29, direction = 3: |F_model - F_numer| error = ----------------------- = 4.13461e-11 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 = C Si | a0 = 3.333461959152919 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -4.390577222134429e+00 -4.390577222130976e+00 3.45324e-12 2.38227e-11 2 -3.443080866007364e+00 -3.443080866008831e+00 1.46683e-12 2.25322e-11 3 1.735666653748277e+00 1.735666653747565e+00 7.12763e-13 6.54743e-12 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.103623811857311e+00 -4.103623811855991e+00 1.31983e-12 8.72404e-11 2 -1.054640336930211e+01 -1.054640336928410e+01 1.80087e-11 1.03784e-10 3 -9.067876184566577e+00 -9.067876184570149e+00 3.57225e-12 1.85665e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -6.950422111495813e+00 -6.950422111487277e+00 8.53628e-12 7.46851e-11 2 1.366729645130342e+00 1.366729645129788e+00 5.54223e-13 2.58162e-11 3 2.621487805532721e+00 2.621487805534400e+00 1.67910e-12 1.96430e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 2.096578968892033e+00 2.096578968892421e+00 3.87246e-13 3.86340e-11 2 -8.197286069900610e-01 -8.197286069875047e-01 2.55629e-12 1.18727e-12 3 -2.896159414597090e+00 -2.896159414599079e+00 1.98863e-12 3.12568e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 5.940323283583123e+00 5.940323283583918e+00 7.94920e-13 5.11715e-11 2 1.840926139495418e+00 1.840926139495849e+00 4.31655e-13 5.85518e-11 3 8.711523822929829e+00 8.711523822926356e+00 3.47278e-12 3.09299e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -3.333968199274371e+00 -3.333968199272599e+00 1.77192e-12 5.22142e-11 2 3.193961588028497e+00 3.193961588033876e+00 5.37836e-12 5.07092e-11 3 6.218425786266919e+00 6.218425786273301e+00 6.38156e-12 5.32330e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -1.182876828588704e+01 -1.182876828588029e+01 6.75016e-12 1.22027e-10 2 2.333358833881134e+00 2.333358833880193e+00 9.41469e-13 3.05844e-11 3 -1.435750794281199e+00 -1.435750794287364e+00 6.16462e-12 5.43861e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 9.224159766375154e+00 9.224159766387258e+00 1.21041e-11 1.53577e-10 2 -3.113987616213216e+00 -3.113987616207744e+00 5.47162e-12 8.78013e-11 3 2.135631608986798e+01 2.135631608988480e+01 1.68114e-11 2.14161e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 -6.846538287930050e+00 -6.846538287935204e+00 5.15410e-12 6.97229e-11 2 -6.225745090912945e+00 -6.225745090906964e+00 5.98011e-12 1.73177e-11 3 -7.563841836230445e+00 -7.563841836235452e+00 5.00666e-12 1.99805e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.018749776143489e+01 1.018749776143264e+01 2.24532e-12 1.25331e-10 2 -1.599900653444368e+00 -1.599900653442882e+00 1.48592e-12 5.74960e-11 3 4.135051916069476e+00 4.135051916067455e+00 2.02061e-12 1.17330e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 5.099423817123315e+00 5.099423817123034e+00 2.80664e-13 5.71854e-11 2 -4.721620459597204e+00 -4.721620459592121e+00 5.08305e-12 7.52189e-11 3 5.283212336015579e+00 5.283212336004611e+00 1.09672e-11 2.58158e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 -8.045793986949290e+00 -8.045793986939600e+00 9.69003e-12 1.24158e-10 2 9.691985651710031e+00 9.691985651660222e+00 4.98090e-11 1.18165e-10 3 8.198941919433219e+00 8.198941919343364e+00 8.98552e-11 1.59073e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 2.764480401646161e+00 2.764480401646871e+00 7.10543e-13 5.43485e-11 2 1.425912307017484e+01 1.425912307017884e+01 3.99503e-12 2.84635e-10 3 -7.235410700403322e+00 -7.235410700404244e+00 9.21929e-13 1.70379e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 2 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 3 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 ----------------------------------------------------------------------------------------------------- 15 C 1 -3.995192141768926e+00 -3.995192141775138e+00 6.21192e-12 2.00369e-11 2 -4.253592466920199e+00 -4.253592466922982e+00 2.78355e-12 1.13456e-11 3 -2.078060213399489e-03 -2.078060215865469e-03 2.46598e-12 1.62218e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -2.315896703445572e+00 -2.315896703444838e+00 7.33635e-13 8.68807e-11 2 -1.797982092727752e+00 -1.797982092728060e+00 3.07532e-13 5.60085e-12 3 4.200721060413201e-01 4.200721060420620e-01 7.41907e-13 2.03869e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 6.292879949285214e+00 6.292879949277398e+00 7.81597e-12 1.11787e-10 2 2.563776957076380e-01 2.563776957080077e-01 3.69704e-13 3.71832e-11 3 -5.987829938632218e+00 -5.987829938643070e+00 1.08527e-11 1.95630e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 9.183548222848525e+00 9.183548222853119e+00 4.59366e-12 1.86233e-11 2 6.857972478890001e+00 6.857972478892258e+00 2.25686e-12 1.54447e-10 3 -6.137661752846052e+00 -6.137661752865196e+00 1.91438e-11 5.42508e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 7.648796704437257e+00 7.648796704445605e+00 8.34799e-12 1.08873e-11 2 2.838335751888422e+00 2.838335751886557e+00 1.86517e-12 2.90048e-11 3 -3.936633532932020e+00 -3.936633532935142e+00 3.12150e-12 8.95151e-12 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.800256400140760e+00 3.800256400144035e+00 3.27516e-12 7.37499e-12 2 3.458175786789114e+00 3.458175786787391e+00 1.72262e-12 2.57372e-11 3 -6.662401837172938e-01 -6.662401837170296e-01 2.64122e-13 1.50918e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 4.925498976431422e+00 4.925498976433296e+00 1.87406e-12 4.05720e-11 2 5.757365306395990e+00 5.757365306404940e+00 8.94929e-12 3.49107e-11 3 7.917652394159947e-01 7.917652394183831e-01 2.38831e-12 1.40062e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 -4.750738862769840e+00 -4.750738862768457e+00 1.38289e-12 4.10765e-11 2 -2.647945277104470e-01 -2.647945277111131e-01 6.66134e-13 6.92064e-11 3 8.110718770269669e+00 8.110718770273079e+00 3.41061e-12 1.71095e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.180665943710977e+00 -2.180665943713541e+00 2.56417e-12 9.63629e-12 2 3.442095533896877e+00 3.442095533898583e+00 1.70619e-12 2.42770e-11 3 -4.543974207604644e+00 -4.543974207614462e+00 9.81792e-12 8.98659e-12 ----------------------------------------------------------------------------------------------------- 24 C 1 -8.132370167372240e+00 -8.132370167368126e+00 4.11404e-12 4.81357e-11 2 8.072934149042421e-01 8.072934149039400e-01 3.02092e-13 3.53851e-11 3 -4.954628563197057e+00 -4.954628563206183e+00 9.12603e-12 5.49827e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 4.086094177166437e+00 4.086094177166480e+00 4.26326e-14 6.01021e-11 2 2.904919162124894e+00 2.904919162113386e+00 1.15081e-11 9.66804e-11 3 1.242697514612525e+00 1.242697514669849e+00 5.73244e-11 3.61495e-10 * ----------------------------------------------------------------------------------------------------- 26 C 1 2.650081508459234e+00 2.650081508460736e+00 1.50191e-12 7.42006e-11 2 -8.197891361635175e+00 -8.197891361649960e+00 1.47846e-11 1.29656e-10 3 2.131695980761933e+00 2.131695980762366e+00 4.32987e-13 9.00431e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -4.805593163405173e+00 -4.805593163424541e+00 1.93685e-11 1.25169e-10 2 -3.481681169341512e+00 -3.481681169344298e+00 2.78533e-12 3.44880e-11 3 -1.280159279085568e+00 -1.280159279078512e+00 7.05591e-12 7.55238e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 1.316115119084870e+00 1.316115119085494e+00 6.23279e-13 1.83373e-11 2 -2.451364195072440e+00 -2.451364195074403e+00 1.96287e-12 1.03040e-10 3 -1.195904006884780e+00 -1.195904006885224e+00 4.44755e-13 1.66012e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 -8.990127961796400e+00 -8.990127961795936e+00 4.63629e-13 1.49591e-10 2 -3.596151652328503e+00 -3.596151652327988e+00 5.14699e-13 1.85426e-10 3 -8.075092656440919e+00 -8.075092656444253e+00 3.33422e-12 8.34550e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.913434469649035e+00 -1.913434469644175e+00 4.85989e-12 2.53120e-11 2 7.403038871216304e+00 7.403038871225354e+00 9.04965e-12 4.59650e-11 3 -2.330908294941922e+00 -2.330908294943173e+00 1.25100e-12 2.08833e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.406541534188279e-01 -5.406541534149266e-01 3.90132e-12 6.19297e-11 2 -5.962323552831275e+00 -5.962323552849045e+00 1.77707e-11 3.93259e-11 3 1.935554472359352e+00 1.935554472353204e+00 6.14842e-12 1.90168e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 7.908630415956879e+00 7.908630415952373e+00 4.50573e-12 3.61933e-11 2 -5.935411249199141e+00 -5.935411249193567e+00 5.57332e-12 4.34284e-11 3 -5.582981006750289e+00 -5.582981006751814e+00 1.52500e-12 1.67635e-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 = 15, direction = 3: |F_model - F_numer| error = ----------------------- = 1.18667e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.18667e-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: A Comment: The letter grade A was assigned because the normalized error in the computation was 1.18667e-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.