!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LeeLee_2014_ZrH__MO_946208788356_000 Supported species : H Zr 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 = H | a0 = 8.375 | (Configuration in file "config-H.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 H 1 3.095929774133086e+00 3.095929774128481e+00 4.60565e-12 2.69074e-11 2 2.300879476116960e+00 2.300879476140592e+00 2.36322e-11 2.18798e-10 3 2.056768586774592e+00 2.056768586745591e+00 2.90017e-11 1.39004e-10 ----------------------------------------------------------------------------------------------------- 2 H 1 2.874509081010485e+00 2.874509080998692e+00 1.17928e-11 6.87317e-11 2 -5.582742744713975e+00 -5.582742744720948e+00 6.97309e-12 8.85851e-11 3 -9.491978240856525e-02 -9.491978241477721e-02 6.21196e-12 4.55869e-10 ----------------------------------------------------------------------------------------------------- 3 H 1 -7.575511580303435e+00 -7.575511580310629e+00 7.19425e-12 2.56222e-11 2 1.565598523292491e+00 1.565598523310969e+00 1.84783e-11 2.80751e-11 3 7.694394705103318e-01 7.694394705706953e-01 6.03635e-11 2.05815e-10 ----------------------------------------------------------------------------------------------------- 4 H 1 -3.468698846925681e+00 -3.468698846922663e+00 3.01759e-12 4.75691e-11 2 -1.328982111340264e+00 -1.328982111337061e+00 3.20233e-12 3.51923e-10 3 -5.677739544199428e+00 -5.677739544182816e+00 1.66116e-11 8.02833e-11 ----------------------------------------------------------------------------------------------------- 5 H 1 1.988283054688715e+00 1.988283054699888e+00 1.11731e-11 2.77484e-10 2 -2.910782620243091e+00 -2.910782620243064e+00 2.66454e-14 5.32130e-11 3 -6.212661292658197e+00 -6.212661292659464e+00 1.26654e-12 1.33973e-11 ----------------------------------------------------------------------------------------------------- 6 H 1 1.488731282394981e+00 1.488731282396070e+00 1.08891e-12 2.00401e-10 2 -4.672484740392174e+00 -4.672484740399499e+00 7.32481e-12 1.18662e-10 3 -2.547981180602993e+00 -2.547981180618393e+00 1.54001e-11 2.38228e-10 ----------------------------------------------------------------------------------------------------- 7 H 1 -5.839178400340861e+00 -5.839178400342709e+00 1.84741e-12 6.24896e-11 2 5.629575520457869e+00 5.629575520475213e+00 1.73443e-11 9.37372e-10 * 3 2.044452125396171e+00 2.044452125356502e+00 3.96696e-11 1.61801e-10 ----------------------------------------------------------------------------------------------------- 8 H 1 6.293139994199134e+00 6.293139994188771e+00 1.03624e-11 4.92664e-11 2 2.457531690694142e+00 2.457531690701287e+00 7.14451e-12 6.49369e-11 3 3.274500035024932e+00 3.274500035007849e+00 1.70837e-11 4.83280e-11 ----------------------------------------------------------------------------------------------------- 9 H 1 -9.441055805818779e-01 -9.441055805899243e-01 8.04645e-12 2.72381e-08 * 2 4.673890104814260e+00 4.673890104823532e+00 9.27169e-12 3.65817e-10 3 1.016195448033403e+00 1.016195448026335e+00 7.06857e-12 1.09179e-11 ----------------------------------------------------------------------------------------------------- 10 H 1 -1.037008557120120e+00 -1.037008557121665e+00 1.54543e-12 8.80383e-10 * 2 5.462104927260953e+00 5.462104927261887e+00 9.34364e-13 1.49963e-10 3 -1.062878418176868e+00 -1.062878418157328e+00 1.95404e-11 1.55275e-10 ----------------------------------------------------------------------------------------------------- 11 H 1 -7.129510871099650e+00 -7.129510871099167e+00 4.83169e-13 7.23865e-11 2 -6.568744863038158e+00 -6.568744863048993e+00 1.08349e-11 4.37200e-10 3 -6.597775345570091e+00 -6.597775345564340e+00 5.75096e-12 2.74363e-10 ----------------------------------------------------------------------------------------------------- 12 H 1 -4.407044180664009e+00 -4.407044180656284e+00 7.72538e-12 1.02522e-10 2 2.684244467754452e+00 2.684244467754820e+00 3.68150e-13 1.06640e-10 3 1.347484008895547e-01 1.347484008863772e-01 3.17754e-12 8.36825e-12 ----------------------------------------------------------------------------------------------------- 13 H 1 8.843768112324963e+00 8.843768112277417e+00 4.75460e-11 3.00156e-10 2 4.210140746681097e+00 4.210140746658480e+00 2.26166e-11 1.80767e-10 3 2.370672362601759e+00 2.370672362599054e+00 2.70539e-12 1.56055e-10 ----------------------------------------------------------------------------------------------------- 14 H 1 9.457559637851830e-01 9.457559637866862e-01 1.50324e-12 1.21111e-10 2 1.520231321813158e+00 1.520231321808044e+00 5.11391e-12 4.00164e-11 3 -8.470088391904121e-01 -8.470088391938366e-01 3.42448e-12 1.03811e-10 ----------------------------------------------------------------------------------------------------- 15 H 1 -1.980615158917079e+00 -1.980615158922798e+00 5.71898e-12 2.66724e-11 2 -9.686309446461683e-01 -9.686309446804982e-01 3.43299e-11 1.52701e-10 3 -3.627271136427757e+00 -3.627271136424494e+00 3.26272e-12 1.59746e-09 * ----------------------------------------------------------------------------------------------------- 16 H 1 -8.346573280917573e+00 -8.346573280889908e+00 2.76650e-11 2.06692e-10 2 -9.144947730210138e-01 -9.144947730065706e-01 1.44432e-11 2.27338e-10 3 -7.327244880197390e+00 -7.327244880190467e+00 6.92335e-12 5.25260e-11 ----------------------------------------------------------------------------------------------------- 17 H 1 -1.176749835984968e+00 -1.176749836004761e+00 1.97933e-11 2.22993e-11 2 -3.672183217957094e+00 -3.672183217961735e+00 4.64073e-12 1.19311e-10 3 8.022900446889281e-01 8.022900447246005e-01 3.56725e-11 2.00604e-10 ----------------------------------------------------------------------------------------------------- 18 H 1 -2.845067225289982e-01 -2.845067225219765e-01 7.02177e-12 3.02303e-11 2 -7.666259125707620e+00 -7.666259125710986e+00 3.36620e-12 4.41238e-11 3 -3.440415993974022e+00 -3.440415994033656e+00 5.96341e-11 5.70553e-09 * ----------------------------------------------------------------------------------------------------- 19 H 1 -3.329827207915384e-01 -3.329827207485566e-01 4.29818e-11 1.10488e-10 2 -2.070417006918444e+00 -2.070417006923848e+00 5.40457e-12 5.56843e-11 3 1.760682196949225e+00 1.760682196938091e+00 1.11342e-11 1.09174e-10 ----------------------------------------------------------------------------------------------------- 20 H 1 -4.480065533370596e-01 -4.480065533000649e-01 3.69947e-11 7.48193e-11 2 -2.642526123198281e-01 -2.642526123294842e-01 9.65605e-12 6.66023e-10 3 2.730797525481937e+00 2.730797525465015e+00 1.69225e-11 3.45199e-11 ----------------------------------------------------------------------------------------------------- 21 H 1 2.845175902946999e+00 2.845175902937731e+00 9.26725e-12 1.09837e-10 2 -4.711768549207907e+00 -4.711768549197855e+00 1.00515e-11 7.63061e-11 3 1.340071298827740e+00 1.340071298824346e+00 3.39440e-12 2.52858e-11 ----------------------------------------------------------------------------------------------------- 22 H 1 1.052802420650364e+00 1.052802420647350e+00 3.01426e-12 5.39446e-11 2 -5.340074228187950e+00 -5.340074228187026e+00 9.23706e-13 1.36016e-11 3 7.756199002532296e-01 7.756199002535543e-01 3.24740e-13 3.60532e-11 ----------------------------------------------------------------------------------------------------- 23 H 1 2.462623147902088e+00 2.462623147893741e+00 8.34710e-12 4.56311e-11 2 -4.286755040961236e-01 -4.286755040933150e-01 2.80870e-12 4.81196e-11 3 1.884399475934367e+00 1.884399475935536e+00 1.16862e-12 4.18685e-11 ----------------------------------------------------------------------------------------------------- 24 H 1 4.766777109408447e-01 4.766777109545190e-01 1.36743e-11 2.96092e-10 2 -1.455018126089704e-01 -1.455018126199218e-01 1.09514e-11 4.39356e-11 3 2.547468883318976e+00 2.547468883310452e+00 8.52340e-12 4.24221e-09 * ----------------------------------------------------------------------------------------------------- 25 H 1 6.452213240172317e+00 6.452213240181820e+00 9.50262e-12 3.58918e-09 * 2 5.267385820374741e-01 5.267385820350783e-01 2.39586e-12 7.21913e-10 3 2.035829436254541e-01 2.035829436208665e-01 4.58769e-12 4.60042e-11 ----------------------------------------------------------------------------------------------------- 26 H 1 4.736647306337574e+00 4.736647306329273e+00 8.30180e-12 4.07381e-11 2 1.315487269407777e+00 1.315487269415665e+00 7.88858e-12 1.74548e-10 3 2.696606038624285e+00 2.696606038608736e+00 1.55489e-11 4.24918e-11 ----------------------------------------------------------------------------------------------------- 27 H 1 -5.320965601287351e+00 -5.320965601222627e+00 6.47242e-11 3.01013e-11 2 6.790855701196435e+00 6.790855701201224e+00 4.78906e-12 3.93097e-10 3 -1.357209332339179e+00 -1.357209332339125e+00 5.44009e-14 1.13347e-10 ----------------------------------------------------------------------------------------------------- 28 H 1 -2.561989411219983e+00 -2.561989411219831e+00 1.52323e-13 1.69454e-10 2 4.405449209328055e-01 4.405449209277362e-01 5.06933e-12 1.64339e-08 * 3 7.387641885221479e+00 7.387641885217206e+00 4.27303e-12 9.16103e-11 ----------------------------------------------------------------------------------------------------- 29 H 1 4.711372769177346e+00 4.711372769174842e+00 2.50377e-12 7.84707e-10 2 9.557649151920058e-01 9.557649151866076e-01 5.39824e-12 1.11653e-10 3 -3.431387607255910e+00 -3.431387607268995e+00 1.30855e-11 2.04239e-10 ----------------------------------------------------------------------------------------------------- 30 H 1 1.465294369322153e+00 1.465294369322174e+00 2.10942e-14 6.47795e-11 2 2.320851923938713e-01 2.320851923891582e-01 4.71306e-12 1.05551e-10 3 1.754831301355427e+00 1.754831301352703e+00 2.72338e-12 2.57129e-10 ----------------------------------------------------------------------------------------------------- 31 H 1 1.720553183146301e+00 1.720553183121027e+00 2.52742e-11 5.40601e-09 * 2 2.046427634889477e+00 2.046427634885405e+00 4.07274e-12 6.28826e-11 3 3.172568495084693e+00 3.172568495102535e+00 1.78413e-11 8.65970e-11 ----------------------------------------------------------------------------------------------------- 32 H 1 -6.000300111123491e-01 -6.000300111080128e-01 4.33631e-12 3.44732e-10 2 4.433893859463546e+00 4.433893859470071e+00 6.52456e-12 9.80869e-11 3 3.501156934404326e+00 3.501156934398578e+00 5.74740e-12 2.53415e-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 = 1: |F_model - F_numer| error = ----------------------- = 1.29081e-10 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 = Zr | a0 = 4.532810211181641 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 -1.089680766663144e-01 -1.089680766634308e-01 2.88354e-12 4.24081e-11 2 -2.166459951001059e-01 -2.166459951166848e-01 1.65788e-11 8.09232e-11 3 -1.126024194302370e-01 -1.126024194353180e-01 5.08102e-12 2.40624e-11 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -8.411734333825324e-01 -8.411734334008000e-01 1.82676e-11 3.89550e-09 * 2 1.293481297008596e-02 1.293481294259654e-02 2.74894e-11 1.14529e-10 3 8.268425490491538e-01 8.268425490462908e-01 2.86293e-12 3.69569e-11 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -8.679222409729411e-01 -8.679222409569933e-01 1.59478e-11 2.89965e-11 2 6.945479289102866e-01 6.945479289276482e-01 1.73616e-11 1.93940e-09 * 3 -1.764569889244592e-01 -1.764569889356031e-01 1.11439e-11 1.38671e-10 ----------------------------------------------------------------------------------------------------- 4 Zr 1 1.085745420112428e+00 1.085745420092732e+00 1.96965e-11 8.36780e-11 2 -1.515497971883229e-01 -1.515497971900968e-01 1.77391e-12 1.12315e-06 * 3 5.101587230984224e-01 5.101587231269658e-01 2.85434e-11 3.19646e-09 * ----------------------------------------------------------------------------------------------------- 5 Zr 1 4.135431350142936e-01 4.135431350757773e-01 6.14837e-11 1.75898e-10 2 2.495217225047287e-02 2.495217224286373e-02 7.60914e-12 5.19426e-11 3 3.587299167974199e-01 3.587299168727334e-01 7.53135e-11 1.41328e-10 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -3.385426375066380e-01 -3.385426374894462e-01 1.71919e-11 8.06143e-11 2 -7.480453415856458e-01 -7.480453415850317e-01 6.14175e-13 2.03617e-11 3 -6.965221932165971e-02 -6.965221931900394e-02 2.65578e-12 4.13316e-11 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -1.763134422371465e-02 -1.763134420537624e-02 1.83384e-11 4.78999e-11 2 4.088511708993385e-01 4.088511709186091e-01 1.92706e-11 7.16440e-11 3 -1.973884748599780e-01 -1.973884748421656e-01 1.78124e-11 1.21690e-09 ----------------------------------------------------------------------------------------------------- 8 Zr 1 9.959346271945775e-01 9.959346271876169e-01 6.96054e-12 9.09005e-11 2 3.005812684225924e-01 3.005812684350057e-01 1.24133e-11 9.08012e-07 * 3 -2.081327840668207e+00 -2.081327840657683e+00 1.05240e-11 9.80336e-11 ----------------------------------------------------------------------------------------------------- 9 Zr 1 4.953513180807369e-01 4.953513180687507e-01 1.19862e-11 8.60990e-10 2 1.316118842311801e-01 1.316118842344718e-01 3.29173e-12 3.63154e-10 3 -1.364682580077315e-01 -1.364682579843013e-01 2.34302e-11 1.95689e-09 * ----------------------------------------------------------------------------------------------------- 10 Zr 1 5.996266490027211e-01 5.996266489125465e-01 9.01746e-11 5.42125e-10 2 -1.525433971216257e-01 -1.525433971188089e-01 2.81680e-12 1.70398e-10 3 5.637554269657093e-01 5.637554269642079e-01 1.50147e-12 3.67306e-11 ----------------------------------------------------------------------------------------------------- 11 Zr 1 -5.800736290179256e-01 -5.800736290208833e-01 2.95775e-12 2.07806e-10 2 7.849262540739139e-01 7.849262540289890e-01 4.49250e-11 2.88433e-10 3 -5.435756675579650e-01 -5.435756675947169e-01 3.67518e-11 3.79147e-10 ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.685826605959038e-01 3.685826605744595e-01 2.14443e-11 9.19852e-11 2 -5.364056703576561e-01 -5.364056703941485e-01 3.64925e-11 2.48811e-09 * 3 1.241896491020135e-01 1.241896491045059e-01 2.49234e-12 2.12009e-09 * ----------------------------------------------------------------------------------------------------- 13 Zr 1 -6.663328385560693e-01 -6.663328386244890e-01 6.84197e-11 2.48968e-10 2 6.665092765020458e-01 6.665092764878442e-01 1.42016e-11 1.68655e-10 3 -3.145033339522941e-01 -3.145033339809133e-01 2.86192e-11 4.55890e-10 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -6.155579820173931e-01 -6.155579819995853e-01 1.78078e-11 1.22611e-10 2 -4.089481393121961e-01 -4.089481392720457e-01 4.01504e-11 2.02551e-10 3 2.741957146398808e-01 2.741957146720408e-01 3.21601e-11 8.18350e-11 ----------------------------------------------------------------------------------------------------- 15 Zr 1 5.902190316733082e-01 5.902190316341577e-01 3.91506e-11 6.84796e-11 2 7.175251775909954e-01 7.175251775991740e-01 8.17857e-12 5.06913e-11 3 8.034534398410738e-01 8.034534398292585e-01 1.18152e-11 1.29360e-10 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -7.613580047624381e-01 -7.613580047614313e-01 1.00675e-12 3.49060e-09 * 2 -5.342278925777109e-02 -5.342278927481776e-02 1.70467e-11 2.69267e-10 3 -7.776646558170135e-01 -7.776646558314777e-01 1.44642e-11 2.84469e-09 * ----------------------------------------------------------------------------------------------------- 17 Zr 1 4.821975044358635e-01 4.821975044482490e-01 1.23856e-11 1.04749e-09 2 3.931363041537840e-01 3.931363041548837e-01 1.09962e-12 5.01709e-11 3 -1.978129105170745e-01 -1.978129105193402e-01 2.26569e-12 1.08806e-10 ----------------------------------------------------------------------------------------------------- 18 Zr 1 -9.702111801850427e-01 -9.702111801522241e-01 3.28186e-11 1.42752e-10 2 -1.025096733136324e+00 -1.025096733100178e+00 3.61458e-11 3.04533e-10 3 -9.844790176267794e-02 -9.844790185144491e-02 8.87670e-11 1.03452e-10 ----------------------------------------------------------------------------------------------------- 19 Zr 1 -9.991913175633389e-01 -9.991913175502294e-01 1.31095e-11 1.45817e-10 2 -4.196712151288307e-01 -4.196712151275513e-01 1.27942e-12 1.66974e-10 3 -3.502454312072293e-01 -3.502454312387905e-01 3.15611e-11 1.37084e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 1.998534658248183e-01 1.998534658266873e-01 1.86900e-12 1.67764e-10 2 2.543489287196907e-01 2.543489286947365e-01 2.49542e-11 1.93294e-10 3 -1.927680821729140e-01 -1.927680821747214e-01 1.80742e-12 4.63238e-10 ----------------------------------------------------------------------------------------------------- 21 Zr 1 -2.697122918258751e-01 -2.697122918932500e-01 6.73749e-11 8.99558e-10 2 -1.480626927647316e+00 -1.480626927616880e+00 3.04357e-11 5.05294e-10 3 1.276326522930090e+00 1.276326522878031e+00 5.20595e-11 8.29480e-10 ----------------------------------------------------------------------------------------------------- 22 Zr 1 1.205165856836663e+00 1.205165856880123e+00 4.34603e-11 1.97809e-10 2 -1.242064485942941e+00 -1.242064485979383e+00 3.64422e-11 1.36793e-11 3 -7.094034903600919e-01 -7.094034903417924e-01 1.82995e-11 8.66305e-11 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -4.531683156996489e-01 -4.531683157012670e-01 1.61804e-12 8.49419e-10 2 4.795437732895300e-01 4.795437732862184e-01 3.31157e-12 3.93696e-11 3 -5.778909748888807e-01 -5.778909748812108e-01 7.66998e-12 1.53741e-09 ----------------------------------------------------------------------------------------------------- 24 Zr 1 7.734568785610895e-01 7.734568785723736e-01 1.12841e-11 1.49584e-10 2 5.697284961078726e-01 5.697284960848014e-01 2.30712e-11 1.48917e-10 3 8.932512506715673e-01 8.932512507148406e-01 4.32733e-11 5.32099e-11 ----------------------------------------------------------------------------------------------------- 25 Zr 1 1.312313110145606e+00 1.312313110131216e+00 1.43900e-11 5.29792e-11 2 -1.598896600216503e-01 -1.598896599752095e-01 4.64408e-11 3.77167e-11 3 6.508221922408808e-01 6.508221922453161e-01 4.43534e-12 2.63700e-09 * ----------------------------------------------------------------------------------------------------- 26 Zr 1 4.538314957263472e-01 4.538314957081470e-01 1.82002e-11 6.61918e-11 2 -8.843046260787052e-01 -8.843046260702212e-01 8.48399e-12 1.53642e-10 3 -2.620163191391459e+00 -2.620163191328794e+00 6.26654e-11 6.06928e-11 ----------------------------------------------------------------------------------------------------- 27 Zr 1 -7.307897448121943e-01 -7.307897448296885e-01 1.74942e-11 1.74902e-09 2 2.157247156316667e-01 2.157247156533703e-01 2.17036e-11 1.33003e-10 3 -6.887607806459234e-01 -6.887607806442767e-01 1.64668e-12 2.10551e-10 ----------------------------------------------------------------------------------------------------- 28 Zr 1 -1.429353659949700e+00 -1.429353659953033e+00 3.33267e-12 2.15812e-09 * 2 -1.269375295547312e-01 -1.269375295389338e-01 1.57974e-11 9.68742e-10 3 1.083887720130353e+00 1.083887720141953e+00 1.15998e-11 9.35407e-11 ----------------------------------------------------------------------------------------------------- 29 Zr 1 -5.506670978589296e-01 -5.506670978603231e-01 1.39344e-12 7.21616e-11 2 1.541794803271164e+00 1.541794803279282e+00 8.11795e-12 4.78242e-11 3 9.773599833319240e-01 9.773599834120767e-01 8.01528e-11 5.10147e-09 * ----------------------------------------------------------------------------------------------------- 30 Zr 1 -3.421065754023968e-01 -3.421065753891166e-01 1.32802e-11 3.31820e-10 2 1.588497098888375e-01 1.588497098788842e-01 9.95329e-12 2.46501e-11 3 -1.975471766717933e-01 -1.975471766631743e-01 8.61894e-12 1.59457e-09 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -4.225374705321605e-02 -4.225374702796461e-02 2.52514e-11 3.60420e-11 2 4.742645095826594e-01 4.742645095881956e-01 5.53624e-12 3.37079e-11 3 7.974491094518810e-01 7.974491094498898e-01 1.99118e-12 1.28613e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 1.609192964251953e+00 1.609192964258018e+00 6.06581e-12 5.12961e-11 2 -2.236788790622941e-01 -2.236788790483147e-01 1.39794e-11 7.25727e-11 3 9.022575999072190e-01 9.022575999021282e-01 5.09082e-12 1.13812e-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 = 2, direction = 2: |F_model - F_numer| error = ----------------------- = 2.12523e-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 = H Zr | a0 = 4.603255005513347 | (Configuration in file "config-HZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 H 1 9.349675682955703e-01 9.349675682865153e-01 9.05498e-12 8.27581e-11 2 -6.110699500368926e-01 -6.110699500255846e-01 1.13080e-11 5.19055e-10 3 -3.280097407446080e-01 -3.280097407400984e-01 4.50961e-12 5.17158e-11 ----------------------------------------------------------------------------------------------------- 2 Zr 1 5.052152924163000e-02 5.052152923126919e-02 1.03608e-11 3.92594e-11 2 -1.882172387768848e-02 -1.882172388356584e-02 5.87737e-12 9.64703e-10 * 3 1.469451828762858e+00 1.469451828746414e+00 1.64444e-11 1.37120e-10 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -4.745994334483851e-01 -4.745994334421256e-01 6.25955e-12 2.59741e-10 2 1.777715905904782e+00 1.777715905903323e+00 1.45994e-12 5.11591e-11 3 -6.075327301132405e-02 -6.075327301477429e-02 3.45024e-12 1.78567e-11 ----------------------------------------------------------------------------------------------------- 4 H 1 -1.549813396375443e+00 -1.549813396376444e+00 1.00053e-12 3.16416e-11 2 -1.635676749822286e+00 -1.635676749851603e+00 2.93174e-11 3.18610e-11 3 1.481669592923510e-01 1.481669593009390e-01 8.58799e-12 1.15732e-10 ----------------------------------------------------------------------------------------------------- 5 Zr 1 5.279835054485127e-02 5.279835054764341e-02 2.79214e-12 3.48613e-11 2 2.362620672021901e-01 2.362620671922592e-01 9.93092e-12 3.27554e-11 3 6.194515740108202e-01 6.194515739963701e-01 1.44501e-11 2.59156e-11 ----------------------------------------------------------------------------------------------------- 6 H 1 -7.035907947844672e-01 -7.035907947841622e-01 3.04978e-13 4.58669e-11 2 -8.909102478062596e-02 -8.909102479143213e-02 1.08062e-11 2.24574e-10 3 7.785656446769094e-01 7.785656446709258e-01 5.98355e-12 2.22571e-11 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -1.207926191009962e-01 -1.207926190723175e-01 2.86787e-11 1.59963e-10 2 3.992184338205164e-01 3.992184338216390e-01 1.12260e-12 7.31475e-11 3 1.703697031235348e-01 1.703697031202311e-01 3.30375e-12 8.96812e-11 ----------------------------------------------------------------------------------------------------- 8 Zr 1 -7.059899914466020e-02 -7.059899922867915e-02 8.40190e-11 6.34211e-11 2 1.553857575017396e-01 1.553857575342683e-01 3.25287e-11 5.38224e-10 3 -1.150181356125730e+00 -1.150181356085653e+00 4.00775e-11 1.36871e-10 ----------------------------------------------------------------------------------------------------- 9 H 1 -5.649842689909600e-01 -5.649842689941887e-01 3.22875e-12 3.09701e-11 2 1.530724029472482e+00 1.530724029475285e+00 2.80309e-12 5.39235e-12 3 -9.588773863652593e-01 -9.588773863691150e-01 3.85569e-12 6.70431e-11 ----------------------------------------------------------------------------------------------------- 10 Zr 1 8.640475190097358e-02 8.640475189627546e-02 4.69812e-12 1.83845e-10 2 -5.076055621812822e-01 -5.076055621843427e-01 3.06055e-12 1.47781e-11 3 2.064556231990187e-01 2.064556231718672e-01 2.71514e-11 1.03916e-10 ----------------------------------------------------------------------------------------------------- 11 H 1 1.593492067258813e+00 1.593492067304454e+00 4.56404e-11 2.36997e-10 2 1.792101933192047e+00 1.792101933184840e+00 7.20735e-12 1.58090e-10 3 5.216370595734469e-01 5.216370595721934e-01 1.25344e-12 1.25224e-10 ----------------------------------------------------------------------------------------------------- 12 Zr 1 2.426431213327694e+00 2.426431213338494e+00 1.08002e-11 8.27973e-11 2 -5.913970967932698e-01 -5.913970967817227e-01 1.15471e-11 7.28504e-11 3 5.425151177166202e-01 5.425151177285367e-01 1.19165e-11 2.58902e-09 * ----------------------------------------------------------------------------------------------------- 13 Zr 1 -4.257773605770759e-01 -4.257773605450898e-01 3.19861e-11 8.33116e-10 * 2 5.217387022221548e-02 5.217387020758112e-02 1.46344e-11 1.08065e-10 3 1.426619372421336e+00 1.426619372466156e+00 4.48206e-11 8.83135e-10 * ----------------------------------------------------------------------------------------------------- 14 H 1 -6.354627823194361e-01 -6.354627823191673e-01 2.68785e-13 2.43312e-11 2 -5.191683034275871e-01 -5.191683034337482e-01 6.16107e-12 2.40364e-11 3 6.873484575802473e-01 6.873484575810804e-01 8.33111e-13 3.04340e-11 ----------------------------------------------------------------------------------------------------- 15 Zr 1 -1.985823154741375e+00 -1.985823154718718e+00 2.26570e-11 1.05470e-09 * 2 1.663528000947838e+00 1.663528000928866e+00 1.89728e-11 2.34914e-10 3 -3.547735550923876e-01 -3.547735550757401e-01 1.66475e-11 3.40560e-10 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -1.880216982438528e-01 -1.880216981527822e-01 9.10707e-11 7.41785e-11 2 -9.341072973599786e-01 -9.341072973671000e-01 7.12141e-12 2.58210e-09 * 3 -3.640011222076823e-01 -3.640011221968719e-01 1.08105e-11 9.91189e-11 ----------------------------------------------------------------------------------------------------- 17 H 1 -3.610386309217190e-01 -3.610386309097701e-01 1.19489e-11 2.46427e-11 2 -8.840001877245538e-01 -8.840001877764051e-01 5.18513e-11 3.94421e-10 3 -1.631761755354987e-01 -1.631761755457667e-01 1.02680e-11 2.14734e-10 ----------------------------------------------------------------------------------------------------- 18 H 1 1.045934232003630e+00 1.045934232014736e+00 1.11064e-11 5.18172e-11 2 -2.959267691789178e+00 -2.959267691794197e+00 5.01910e-12 5.67635e-11 3 -5.869517000147639e+00 -5.869517000151372e+00 3.73301e-12 9.71792e-11 ----------------------------------------------------------------------------------------------------- 19 H 1 7.778297361531287e-01 7.778297361608313e-01 7.70262e-12 1.84600e-10 2 -2.818117393192460e+00 -2.818117393193205e+00 7.44294e-13 1.50449e-10 3 2.102009357354452e-01 2.102009357342775e-01 1.16770e-12 1.15971e-10 ----------------------------------------------------------------------------------------------------- 20 H 1 -1.862841636731765e+00 -1.862841636730710e+00 1.05427e-12 1.14131e-11 2 8.800305049878575e-01 8.800305049251530e-01 6.27045e-11 6.10398e-11 3 1.179329210598405e+00 1.179329210545850e+00 5.25548e-11 8.04712e-11 ----------------------------------------------------------------------------------------------------- 21 Zr 1 -7.990996580824544e-01 -7.990996580884655e-01 6.01108e-12 1.37730e-09 * 2 3.650729446279434e+00 3.650729446290653e+00 1.12190e-11 1.20832e-09 * 3 3.599423113341404e+00 3.599423113373971e+00 3.25677e-11 1.05634e-09 * ----------------------------------------------------------------------------------------------------- 22 Zr 1 -1.588241083392584e+00 -1.588241083383046e+00 9.53815e-12 1.67904e-10 2 -7.385182170715641e-01 -7.385182169988306e-01 7.27335e-11 3.08566e-10 3 8.120139899909813e-01 8.120139900021114e-01 1.11301e-11 1.15517e-10 ----------------------------------------------------------------------------------------------------- 23 H 1 5.002422886469111e-01 5.002422886465695e-01 3.41616e-13 1.16669e-10 2 -1.248422552289784e+00 -1.248422552292872e+00 3.08886e-12 1.02282e-10 3 -1.562281329008340e+00 -1.562281329007452e+00 8.87290e-13 7.87059e-12 ----------------------------------------------------------------------------------------------------- 24 H 1 -4.668547631612611e-01 -4.668547631616455e-01 3.84415e-13 1.11434e-10 2 2.032512064359013e+00 2.032512064363074e+00 4.06075e-12 1.33475e-10 3 -2.082424997678335e+00 -2.082424997686170e+00 7.83462e-12 4.49156e-11 ----------------------------------------------------------------------------------------------------- 25 Zr 1 1.406564992382026e+00 1.406564992381264e+00 7.61613e-13 8.96958e-11 2 -1.688338521706222e+00 -1.688338521730951e+00 2.47298e-11 8.20577e-11 3 5.453198326711236e-01 5.453198326687216e-01 2.40197e-12 8.99798e-11 ----------------------------------------------------------------------------------------------------- 26 H 1 -1.633507922188602e+00 -1.633507922183020e+00 5.58220e-12 9.34079e-11 2 3.699856023730301e+00 3.699856023750860e+00 2.05591e-11 6.79830e-11 3 1.542762759959327e+00 1.542762759966158e+00 6.83054e-12 2.64989e-10 ----------------------------------------------------------------------------------------------------- 27 H 1 -2.326211394609666e+00 -2.326211394616992e+00 7.32614e-12 1.45372e-10 2 1.546925571643010e+00 1.546925571644542e+00 1.53255e-12 5.88591e-11 3 4.655583077099749e+00 4.655583077093705e+00 6.04405e-12 4.50182e-11 ----------------------------------------------------------------------------------------------------- 28 Zr 1 1.098432771055455e+00 1.098432771067960e+00 1.25049e-11 2.53968e-11 2 -2.680256273488199e-01 -2.680256273404431e-01 8.37674e-12 4.71043e-11 3 -2.046206198885868e+00 -2.046206198914284e+00 2.84155e-11 9.73972e-11 ----------------------------------------------------------------------------------------------------- 29 H 1 7.530859023506613e+00 7.530859023478294e+00 2.83196e-11 3.16192e-10 2 -7.249531831033770e-01 -7.249531830860428e-01 1.73341e-11 1.16024e-10 3 -9.739109638398757e-02 -9.739109636621551e-02 1.77721e-11 2.53434e-10 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -9.211436375331452e-01 -9.211436375545201e-01 2.13749e-11 5.92418e-11 2 -1.143822828802939e+00 -1.143822828806903e+00 3.96416e-12 6.45211e-11 3 -4.332050969700078e-01 -4.332050969639456e-01 6.06215e-12 1.99263e-10 ----------------------------------------------------------------------------------------------------- 31 H 1 4.597471836527052e-01 4.597471836515618e-01 1.14342e-12 3.05525e-11 2 7.737701931325821e-01 7.737701931209690e-01 1.16132e-11 5.66014e-11 3 1.852428186194172e-01 1.852428186403106e-01 2.08934e-11 7.54119e-11 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -1.285822473622155e+00 -1.285822473644140e+00 2.19855e-11 8.60267e-11 2 -2.810529891087503e+00 -2.810529891089951e+00 2.44826e-12 1.70927e-10 3 -3.829658750216327e+00 -3.829658750169965e+00 4.63625e-11 3.04643e-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 = 8, direction = 1: |F_model - F_numer| error = ----------------------- = 1.19009e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.12523e-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 2.12523e-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.