!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 3.22623825073 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 9.299412383523117e+00 9.299412383521847e+00 1.27010e-12 3.12070e-11 2 4.834859096967248e+00 4.834859096981283e+00 1.40350e-11 2.78888e-11 3 5.571008703263377e+00 5.571008703268875e+00 5.49782e-12 1.77751e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.940828102744231e+00 -1.940828102745159e+00 9.27480e-13 5.18254e-11 2 4.145992721229576e-01 4.145992721210541e-01 1.90342e-12 3.58275e-11 3 3.171864543929660e+00 3.171864543933399e+00 3.73968e-12 4.22720e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.550595675125696e+00 -2.550595675116683e+00 9.01323e-12 5.95684e-11 2 3.829178355251526e+00 3.829178355246360e+00 5.16609e-12 1.51669e-10 3 -6.327788496191594e+00 -6.327788496190493e+00 1.10134e-12 3.26343e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 5.339214186698517e+00 5.339214186681763e+00 1.67546e-11 2.51989e-10 * 2 5.733358278951688e+00 5.733358278946650e+00 5.03864e-12 1.20814e-10 3 3.837467362927579e-01 3.837467362918918e-01 8.66140e-13 3.67373e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -9.532763207449870e-01 -9.532763207422775e-01 2.70950e-12 1.08442e-10 2 4.762238712595361e+00 4.762238712593362e+00 1.99929e-12 3.78000e-11 3 5.048110786496557e+00 5.048110786492847e+00 3.70992e-12 1.44960e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -4.151378161371629e+00 -4.151378161372462e+00 8.33111e-13 2.43157e-11 2 -5.116375899526799e+00 -5.116375899527397e+00 5.97744e-13 7.47402e-12 3 3.506035092537644e+00 3.506035092514416e+00 2.32281e-11 5.49480e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -2.624085551989670e+00 -2.624085551988041e+00 1.62848e-12 7.18270e-12 2 1.829358350985582e+00 1.829358350988831e+00 3.24962e-12 7.45382e-12 3 -4.359044216342452e+00 -4.359044216329975e+00 1.24771e-11 2.52385e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -6.820772983836910e-01 -6.820772984056224e-01 2.19313e-11 1.89203e-11 2 1.178562656490263e+00 1.178562656484114e+00 6.14908e-12 2.12133e-11 3 3.860120093096643e-01 3.860120093016813e-01 7.98300e-12 2.91686e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 1.254277395425698e+00 1.254277395436836e+00 1.11375e-11 5.89422e-11 2 -1.854386561668931e+00 -1.854386561671161e+00 2.22999e-12 8.17364e-11 3 4.151849617462778e+00 4.151849617447026e+00 1.57518e-11 2.17967e-10 * ----------------------------------------------------------------------------------------------------- 10 C 1 -2.675249224562053e+00 -2.675249224534790e+00 2.72631e-11 2.80349e-11 2 -1.454953002273635e+00 -1.454953002273170e+00 4.65183e-13 1.14952e-11 3 1.117670404573636e+00 1.117670404571159e+00 2.47713e-12 1.47999e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -5.210737359813595e+00 -5.210737359782150e+00 3.14451e-11 3.49098e-10 * 2 -7.754422522849993e+00 -7.754422522853955e+00 3.96128e-12 4.71969e-11 3 -3.748318345419171e+00 -3.748318345438164e+00 1.89928e-11 1.52032e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 1.682183709074940e+00 1.682183709076361e+00 1.42153e-12 2.93641e-11 2 -1.800883961862373e+00 -1.800883961861718e+00 6.55254e-13 3.32034e-11 3 -1.344880754666970e+00 -1.344880754666759e+00 2.11609e-13 7.56639e-12 ----------------------------------------------------------------------------------------------------- 13 C 1 1.043949080760246e+00 1.043949080759511e+00 7.34524e-13 1.46070e-10 2 -2.092687165571117e+00 -2.092687165532670e+00 3.84466e-11 4.10599e-10 * 3 -1.912935985480657e+00 -1.912935985489770e+00 9.11227e-12 3.40836e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -3.090762164490744e+00 -3.090762164492051e+00 1.30695e-12 5.60214e-11 2 -4.037459573379906e+00 -4.037459573379392e+00 5.14255e-13 1.07037e-10 3 1.114397869346960e+00 1.114397869350474e+00 3.51430e-12 1.88374e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 3.465418085747221e-01 3.465418085842470e-01 9.52494e-12 3.63407e-11 2 3.074990110977993e+00 3.074990110978490e+00 4.96936e-13 5.60481e-11 3 -2.950655962844985e-01 -2.950655962901451e-01 5.64654e-12 3.11541e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 9.680514088209877e-01 9.680514088137121e-01 7.27562e-12 1.24535e-11 2 3.274643476120391e+00 3.274643476115505e+00 4.88587e-12 1.65907e-11 3 2.200049974622973e+00 2.200049974623456e+00 4.82281e-13 9.74865e-12 ----------------------------------------------------------------------------------------------------- 17 C 1 3.320692350935265e+00 3.320692350924147e+00 1.11182e-11 2.06630e-11 2 1.424372238041511e+00 1.424372238041970e+00 4.59188e-13 2.05376e-11 3 -7.856367504050834e-01 -7.856367504031017e-01 1.98175e-12 1.58656e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.373856194414191e+00 5.373856194429283e+00 1.50919e-11 6.54570e-11 2 -3.487354099928623e+00 -3.487354099931701e+00 3.07843e-12 2.38467e-11 3 3.006593418557128e+00 3.006593418561494e+00 4.36584e-12 1.57248e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 4.354208546184032e+00 4.354208546233131e+00 4.90985e-11 4.68061e-11 2 5.678327178405211e+00 5.678327178404234e+00 9.76996e-13 4.10063e-11 3 -1.344317948525070e+00 -1.344317948524897e+00 1.72973e-13 4.33751e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 3.486204144931503e+00 3.486204144928636e+00 2.86748e-12 4.43214e-11 2 8.205641606237963e-01 8.205641606263065e-01 2.51021e-12 8.27141e-11 3 -1.967130089003620e+00 -1.967130089009434e+00 5.81468e-12 5.24294e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -2.560029250905110e+00 -2.560029250912698e+00 7.58771e-12 1.75691e-11 2 4.130228476744359e+00 4.130228476743412e+00 9.47686e-13 1.10401e-11 3 4.930237106586612e+00 4.930237106589860e+00 3.24718e-12 2.32099e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 -1.524238360207677e+00 -1.524238360209378e+00 1.70131e-12 1.85958e-11 2 -2.506410883666789e+00 -2.506410883667137e+00 3.47722e-13 3.57256e-11 3 2.863443501641903e+00 2.863443501638264e+00 3.63976e-12 2.57998e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.564493071229464e+00 -2.564493071236880e+00 7.41540e-12 1.32836e-11 2 2.381498992194326e+00 2.381498992189405e+00 4.92140e-12 1.36149e-11 3 -4.564852518058855e+00 -4.564852518044964e+00 1.38902e-11 5.41682e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -3.372696241337362e+00 -3.372696241328632e+00 8.72946e-12 1.01823e-10 2 -5.274598271818178e+00 -5.274598271802883e+00 1.52944e-11 8.99831e-11 3 -6.654610148868260e+00 -6.654610148876347e+00 8.08686e-12 6.55929e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 1.645633786185868e-01 1.645633786153282e-01 3.25864e-12 2.76973e-11 2 -1.799119607074252e+00 -1.799119607075831e+00 1.57874e-12 1.10216e-10 3 -3.392968577716803e+00 -3.392968577722076e+00 5.27267e-12 3.66820e-10 * ----------------------------------------------------------------------------------------------------- 26 C 1 3.111562497478360e-01 3.111562497484208e-01 5.84810e-13 2.93079e-11 2 -6.170329800726583e-02 -6.170329801948580e-02 1.22200e-11 6.16373e-11 3 2.654530812961919e+00 2.654530812968489e+00 6.56986e-12 1.67844e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -2.914450317176635e-01 -2.914450317061142e-01 1.15493e-11 5.26242e-11 2 -2.694767537016435e+00 -2.694767536994860e+00 2.15756e-11 3.73381e-11 3 -8.933611715472796e-01 -8.933611715503277e-01 3.04812e-12 3.14976e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -6.418164654342514e-01 -6.418164654375205e-01 3.26905e-12 6.96290e-11 2 2.383945505824057e-01 2.383945505879640e-01 5.55825e-12 3.18686e-11 3 -2.342669015943830e+00 -2.342669015950716e+00 6.88605e-12 7.90923e-12 ----------------------------------------------------------------------------------------------------- 29 C 1 2.269469505864642e+00 2.269469505862579e+00 2.06324e-12 4.92411e-11 2 2.149975934341425e+00 2.149975934362714e+00 2.12892e-11 8.63318e-11 3 2.306031801582867e+00 2.306031801602438e+00 1.95715e-11 4.80855e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.578836839966664e+00 -1.578836839971760e+00 5.09681e-12 2.66842e-11 2 -5.663293225834590e+00 -5.663293225838902e+00 4.31211e-12 5.78506e-11 3 3.381908553633169e+00 3.381908553644878e+00 1.17089e-11 1.66648e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.596833644658628e+00 -5.596833644663011e+00 4.38316e-12 1.23528e-11 2 4.440658872753053e+00 4.440658872757444e+00 4.39115e-12 5.30864e-11 3 -4.476625029584259e+00 -4.476625029578318e+00 5.94103e-12 8.58531e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 2.795598421108815e+00 2.795598421122347e+00 1.35327e-11 4.70019e-10 * 2 -4.597393103670194e+00 -4.597393103671134e+00 9.39693e-13 4.72200e-11 3 -1.383286288761207e+00 -1.383286288761613e+00 4.05231e-13 5.68094e-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 dicontinuities. Maximum error obtained for particle = 26, direction = 2: |F_model - F_numer| error = ----------------------- = 1.98044e-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 = Si | a0 = 3.4026260376 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.489559160745803e+00 -1.489559160718309e+00 2.74940e-11 3.18627e-11 2 -1.437498409015630e+00 -1.437498409009209e+00 6.42064e-12 1.22824e-11 3 -1.701136149779469e+00 -1.701136149763186e+00 1.62836e-11 6.22760e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -7.290760941198980e+00 -7.290760941202581e+00 3.60156e-12 1.50777e-11 2 5.598427351523648e+00 5.598427351532676e+00 9.02833e-12 1.80442e-11 3 -3.301267022951865e+01 -3.301267022950364e+01 1.50067e-11 3.04681e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.704712218285251e+00 1.704712218292920e+00 7.66920e-12 8.60332e-11 2 -2.580563422472920e+01 -2.580563422472633e+01 2.87059e-12 2.50747e-10 * 3 1.443547607195122e+01 1.443547607194808e+01 3.13882e-12 7.67475e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.393577547174064e+01 -2.393577547173074e+01 9.90852e-12 2.71186e-10 * 2 -3.008753747876909e+00 -3.008753747887899e+00 1.09894e-11 2.34648e-10 * 3 -1.333964615690413e+01 -1.333964615690457e+01 4.40536e-13 2.97113e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.071926132957719e+01 1.071926132957499e+01 2.20446e-12 4.70912e-12 2 -1.180727551441356e+00 -1.180727551444577e+00 3.22098e-12 5.54203e-11 3 -4.265618849611785e+00 -4.265618849621988e+00 1.02025e-11 1.43004e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -5.534092990186060e+00 -5.534092990186831e+00 7.70051e-13 8.17186e-11 2 -4.780658061106195e+00 -4.780658061102222e+00 3.97282e-12 5.80513e-12 3 -3.235754602386103e-01 -3.235754602366616e-01 1.94872e-12 4.87899e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 -3.971509656311039e-01 -3.971509656335441e-01 2.44021e-12 1.33604e-11 2 2.801172534240030e+00 2.801172534234826e+00 5.20339e-12 9.48441e-12 3 2.644424186959699e+00 2.644424186956448e+00 3.25162e-12 7.15072e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 1.858859425757237e+01 1.858859425755772e+01 1.46443e-11 1.18792e-10 2 9.660013770687683e-01 9.660013770559688e-01 1.27995e-11 1.93476e-11 3 7.814326039056848e+00 7.814326039061340e+00 4.49241e-12 5.23544e-10 * ----------------------------------------------------------------------------------------------------- 9 Si 1 4.725962071765880e+00 4.725962071770983e+00 5.10259e-12 3.98268e-11 2 4.030738141936631e+00 4.030738141941863e+00 5.23226e-12 7.84288e-11 3 1.183632813868066e-01 1.183632813931032e-01 6.29659e-12 1.37245e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.796190084843861e+00 -9.796190084840562e+00 3.29869e-12 5.42855e-12 2 2.832374462237676e+00 2.832374462265139e+00 2.74629e-11 2.42641e-11 3 -1.527974548779692e+00 -1.527974548770332e+00 9.35985e-12 1.27325e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 9.407632975360261e+00 9.407632975355222e+00 5.03952e-12 1.98686e-11 2 1.461216166290249e+01 1.461216166290545e+01 2.96119e-12 7.47082e-11 3 -2.707118107191290e+00 -2.707118107184727e+00 6.56275e-12 1.28640e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.715986104728381e+01 -1.715986104728314e+01 6.75016e-13 2.73523e-11 2 1.761570978194162e+01 1.761570978192977e+01 1.18554e-11 2.50076e-11 3 -1.847007644326775e+01 -1.847007644326750e+01 2.45137e-13 1.37135e-12 ----------------------------------------------------------------------------------------------------- 13 Si 1 6.390338037209009e+00 6.390338037206440e+00 2.56950e-12 1.81961e-11 2 -7.859082707311542e+00 -7.859082707331657e+00 2.01155e-11 1.41309e-11 3 -5.080510028117808e+00 -5.080510028107955e+00 9.85256e-12 9.38583e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.020077015372073e+00 1.020077015372768e+00 6.94556e-13 6.00349e-11 2 -2.575895057754113e+00 -2.575895057751727e+00 2.38565e-12 3.04023e-12 3 1.457365818872056e+00 1.457365818870763e+00 1.29319e-12 1.84779e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 -3.552526296658361e+00 -3.552526296655749e+00 2.61169e-12 2.56355e-11 2 -3.206030174315585e+00 -3.206030174317561e+00 1.97620e-12 2.54730e-11 3 6.500407856271420e+00 6.500407856271781e+00 3.60600e-13 1.52483e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 7.482837808352080e-01 7.482837808349218e-01 2.86215e-13 1.40115e-11 2 2.108375824802302e+00 2.108375824811910e+00 9.60876e-12 2.81726e-11 3 4.127294954922020e+00 4.127294954923210e+00 1.19016e-12 1.35234e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -4.387291741409366e+00 -4.387291741408119e+00 1.24700e-12 6.54676e-12 2 -4.852535386494786e+00 -4.852535386494231e+00 5.55112e-13 3.62643e-12 3 -7.976276515394559e+00 -7.976276515394324e+00 2.35367e-13 2.50866e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.288796521406866e+01 1.288796521408906e+01 2.03944e-11 1.94657e-10 2 -2.363278789843982e+01 -2.363278789843775e+01 2.06768e-12 3.18725e-10 * 3 4.680836639251556e+00 4.680836639268044e+00 1.64881e-11 7.56772e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.371997075862142e+01 1.371997075862197e+01 5.50671e-13 1.03134e-10 2 -4.156038603771381e+00 -4.156038603779432e+00 8.05134e-12 4.23697e-11 3 -2.814625086556161e+00 -2.814625086557641e+00 1.48015e-12 5.58753e-12 ----------------------------------------------------------------------------------------------------- 20 Si 1 -9.822609473223595e+00 -9.822609473221434e+00 2.16183e-12 4.22951e-11 2 4.046650359083227e+00 4.046650359077891e+00 5.33618e-12 2.11662e-11 3 1.024520228699396e+01 1.024520228698963e+01 4.32365e-12 4.12133e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -7.144964176713387e+00 -7.144964176714006e+00 6.19060e-13 1.73523e-11 2 -2.335518831591943e-01 -2.335518831592373e-01 4.30489e-14 9.39038e-12 3 6.119869593809261e+00 6.119869593806120e+00 3.14060e-12 4.50484e-12 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.737499447702935e+00 -1.737499447710949e+00 8.01359e-12 2.27520e-11 2 2.662900428746421e+00 2.662900428747608e+00 1.18705e-12 1.00820e-10 3 -5.834313943593455e+00 -5.834313943596404e+00 2.94964e-12 5.56195e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.144767297786243e-01 -1.144767297786509e-01 2.66454e-14 2.84850e-12 2 7.001594326917977e-01 7.001594326744670e-01 1.73307e-11 6.11251e-11 3 -6.497168280452683e-01 -6.497168280473814e-01 2.11309e-12 1.38582e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 3.507833452884884e+00 3.507833452887944e+00 3.05933e-12 7.39764e-12 2 -2.748691424501428e+00 -2.748691424503135e+00 1.70708e-12 6.49392e-12 3 -2.933650913778579e+00 -2.933650913780664e+00 2.08455e-12 1.67604e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.881903513830483e+01 -1.881903513830444e+01 3.87246e-13 2.96829e-11 2 -2.725991389035205e+00 -2.725991389038114e+00 2.90878e-12 8.81077e-11 3 1.528929844633723e+01 1.528929844633375e+01 3.47455e-12 2.71605e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 1.505474027110296e+01 1.505474027110067e+01 2.29150e-12 2.23022e-11 2 1.188580786030624e+01 1.188580786029287e+01 1.33760e-11 3.03224e-11 3 6.706567053183790e+00 6.706567053185066e+00 1.27542e-12 5.73674e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -5.233536827461804e-02 -5.233536826776085e-02 6.85720e-12 3.67068e-11 2 8.712214414576213e+00 8.712214414576357e+00 1.43885e-13 1.73923e-11 3 1.124707444169273e+01 1.124707444168584e+01 6.88516e-12 9.15890e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 -5.200181158259188e+00 -5.200181158259521e+00 3.33067e-13 4.80149e-12 2 2.547854139398630e+00 2.547854139398273e+00 3.57048e-13 4.42757e-12 3 8.315626936527799e+00 8.315626936524311e+00 3.48876e-12 4.85478e-12 ----------------------------------------------------------------------------------------------------- 29 Si 1 1.456133417404836e+01 1.456133417405026e+01 1.90070e-12 4.52687e-11 2 3.205393278122020e+00 3.205393278125563e+00 3.54294e-12 1.58114e-11 3 -4.426291204613331e-02 -4.426291205013867e-02 4.00536e-12 2.23992e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.002481151872226e+01 1.002481151872105e+01 1.20615e-12 1.87779e-11 2 2.926480114316822e+00 2.926480114316256e+00 5.65770e-13 2.36313e-11 3 -1.148769285564352e+01 -1.148769285565073e+01 7.20668e-12 2.23093e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.507905887325821e+00 5.507905887326522e+00 7.00773e-13 2.84919e-11 2 -6.278190742722111e+00 -6.278190742722013e+00 9.76996e-14 6.60449e-12 3 1.781190707695594e+00 1.781190707695028e+00 5.65992e-13 4.94316e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.213511277079634e+01 -1.213511277081059e+01 1.42464e-11 1.51168e-11 2 7.229646097779917e+00 7.229646097773987e+00 5.93037e-12 3.77840e-11 3 1.068554071355484e+01 1.068554071356438e+01 9.53726e-12 1.78870e-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 dicontinuities. Maximum error obtained for particle = 27, direction = 1: |F_model - F_numer| error = ----------------------- = 1.31024e-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. MIXED STRUCTURE -- Species = C Si | a0 = 3.26072548241 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 3.734917702792200e+00 3.734917702793157e+00 9.57012e-13 1.63829e-10 2 3.172148748391051e+00 3.172148748391731e+00 6.79456e-13 1.39457e-10 3 1.748430991851305e+00 1.748430991853774e+00 2.46847e-12 4.17937e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 6.500309137400252e+00 6.500309137398295e+00 1.95666e-12 3.49605e-11 2 -1.548497546399283e+01 -1.548497546399181e+01 1.02318e-12 3.94174e-10 * 3 -8.609333380707310e+00 -8.609333380713760e+00 6.44995e-12 1.50120e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 3.177728698682140e+00 3.177728698689437e+00 7.29683e-12 6.66640e-11 2 -3.049652776042826e+00 -3.049652776039690e+00 3.13571e-12 4.06506e-11 3 -1.487758543162725e+00 -1.487758543162579e+00 1.46105e-13 1.51865e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -5.158868322750396e+00 -5.158868322748043e+00 2.35367e-12 3.13745e-10 * 2 6.160932109782519e-01 6.160932109742875e-01 3.96438e-12 4.85944e-11 3 -2.136668025940625e+00 -2.136668025933025e+00 7.59925e-12 4.25993e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -4.166297098378225e+00 -4.166297098379318e+00 1.09335e-12 2.67093e-11 2 8.568891294238217e+00 8.568891294224024e+00 1.41931e-11 2.85283e-11 3 3.589480171460952e+00 3.589480171458175e+00 2.77645e-12 3.50253e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -2.855265299380206e+00 -2.855265299382888e+00 2.68230e-12 3.37566e-11 2 -6.612382574892852e-01 -6.612382574862544e-01 3.03080e-12 1.69393e-11 3 2.095184518493831e+00 2.095184518474936e+00 1.88956e-11 1.81437e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 6.654821189959246e+00 6.654821189958035e+00 1.21059e-12 2.34168e-11 2 -6.584476424193022e+00 -6.584476424195633e+00 2.61036e-12 2.30669e-11 3 -1.260793236691466e+00 -1.260793236694823e+00 3.35776e-12 3.15423e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -6.725793609727543e+00 -6.725793609736815e+00 9.27169e-12 4.04669e-10 * 2 7.136998235508259e+00 7.136998235504291e+00 3.96838e-12 1.31193e-11 3 3.467549796372572e+00 3.467549796366183e+00 6.38956e-12 9.84581e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 -4.099675260443000e+00 -4.099675260435977e+00 7.02283e-12 4.90097e-12 2 6.202503594096056e+00 6.202503594099066e+00 3.01004e-12 6.04006e-11 3 1.295421055229286e+00 1.295421055236510e+00 7.22311e-12 4.73310e-12 ----------------------------------------------------------------------------------------------------- 10 C 1 -2.684429524716093e+00 -2.684429524718902e+00 2.80842e-12 1.75877e-11 2 -1.206809619270127e-01 -1.206809619256985e-01 1.31425e-12 1.30840e-11 3 5.558295455162065e+00 5.558295455160100e+00 1.96465e-12 4.45715e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 4.517053614807311e+00 4.517053614825383e+00 1.80727e-11 1.07121e-10 2 -5.978647592927688e+00 -5.978647592923237e+00 4.45066e-12 8.83258e-11 3 3.918690739087659e+00 3.918690739000263e+00 8.73968e-11 2.34096e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 3.727193985640403e+00 3.727193985643531e+00 3.12772e-12 5.33689e-11 2 -8.864265407031768e+00 -8.864265407016923e+00 1.48450e-11 3.99947e-11 3 -9.442012293852927e-01 -9.442012293914726e-01 6.17983e-12 1.64456e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 8.211316980347066e-01 8.211316980343901e-01 3.16525e-13 1.36506e-11 2 2.077315915570206e+00 2.077315915574710e+00 4.50351e-12 1.89448e-11 3 -1.232882088193617e+00 -1.232882088185615e+00 8.00182e-12 1.61868e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.072390800648072e+00 1.072390800647993e+00 7.94920e-14 3.22280e-11 2 -6.323297124240005e+00 -6.323297124236992e+00 3.01359e-12 1.36149e-11 3 5.246802870689481e+00 5.246802870695174e+00 5.69322e-12 2.78559e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 -2.763265704267047e+00 -2.763265704260802e+00 6.24523e-12 2.88205e-11 2 1.503590611416051e+00 1.503590611416849e+00 7.98250e-13 8.73777e-11 3 -6.221946857743238e+00 -6.221946857740075e+00 3.16280e-12 6.28244e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 2.075629596687688e+00 2.075629596680605e+00 7.08367e-12 3.12470e-11 2 6.720437907467397e+00 6.720437907454103e+00 1.32934e-11 1.10239e-10 3 -3.505930063598892e+00 -3.505930063599234e+00 3.41505e-13 4.42704e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 1.619425566686560e+00 1.619425566688121e+00 1.56142e-12 2.05351e-11 2 8.952936969817241e-01 8.952936969761334e-01 5.59075e-12 7.35767e-12 3 2.033055382564452e+00 2.033055382564468e+00 1.59872e-14 1.96305e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 4.904354439380433e+00 4.904354439381588e+00 1.15463e-12 3.09335e-11 2 1.409748024226670e+00 1.409748024208828e+00 1.78417e-11 1.62508e-11 3 5.321977906920236e-01 5.321977906812266e-01 1.07969e-11 8.48316e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 2.760284320588237e+00 2.760284320585930e+00 2.30704e-12 5.31593e-11 2 3.203277225711275e+00 3.203277225725983e+00 1.47073e-11 2.69349e-11 3 -1.967441811468531e+00 -1.967441811444181e+00 2.43501e-11 4.48743e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.950431389346434e+00 3.950431389346505e+00 7.10543e-14 5.77884e-11 2 -1.512003418936289e+00 -1.512003418942172e+00 5.88329e-12 5.26208e-11 3 2.557358488906469e+00 2.557358488901929e+00 4.54037e-12 3.71125e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -2.040599303949072e+00 -2.040599303956328e+00 7.25642e-12 2.63691e-10 2 1.088892415772309e+00 1.088892415775435e+00 3.12617e-12 5.11033e-11 3 1.299855746262218e-01 1.299855746378440e-01 1.16223e-11 9.51048e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 1.488427564240892e+00 1.488427564237308e+00 3.58358e-12 5.68783e-11 2 3.022107772660631e+00 3.022107772666918e+00 6.28653e-12 7.35092e-11 3 -2.155087173015342e+00 -2.155087172996789e+00 1.85527e-11 9.42988e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -4.564884206372562e+00 -4.564884206399150e+00 2.65885e-11 6.95044e-11 2 -2.400779478364907e+00 -2.400779478370792e+00 5.88507e-12 1.58540e-11 3 -5.666464397407396e-01 -5.666464397478972e-01 7.15761e-12 2.20932e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -3.660341820567125e+00 -3.660341820542607e+00 2.45177e-11 6.01402e-10 * 2 -4.172573033831035e+00 -4.172573033832506e+00 1.47082e-12 2.40893e-10 3 -2.761688463255189e-02 -2.761688461657254e-02 1.59793e-11 1.00057e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.218730861070411e+01 -1.218730861055323e+01 1.50875e-10 4.07558e-10 * 2 2.297752156987366e+00 2.297752156996477e+00 9.11138e-12 5.91660e-11 3 -2.164548536108564e+00 -2.164548536108516e+00 4.75175e-14 9.26714e-10 * ----------------------------------------------------------------------------------------------------- 26 Si 1 -2.103038158869298e+00 -2.103038158867847e+00 1.45173e-12 1.06083e-09 * 2 1.066038157106036e+01 1.066038157102618e+01 3.41771e-11 2.10377e-10 3 -2.277742999727132e+00 -2.277742999751772e+00 2.46407e-11 5.04952e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 -6.243242840909836e+00 -6.243242840928731e+00 1.88951e-11 1.29065e-10 2 1.061918687157707e+00 1.061918687165773e+00 8.06621e-12 1.14381e-10 3 -1.965228956573836e+00 -1.965228956560683e+00 1.31533e-11 3.42668e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 1.907680821569925e+00 1.907680821572961e+00 3.03579e-12 4.74154e-12 2 -2.729681348502785e+00 -2.729681348479517e+00 2.32681e-11 3.97526e-11 3 -3.551905275144857e-01 -3.551905275135259e-01 9.59732e-13 2.12179e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 -3.612203420496261e+00 -3.612203420497163e+00 9.01945e-13 4.69110e-10 * 2 -4.751780605538692e+00 -4.751780605566442e+00 2.77494e-11 3.15902e-10 * 3 -7.539065371340071e+00 -7.539065371383862e+00 4.37916e-11 7.18954e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 7.396159714216015e+00 7.396159714221858e+00 5.84244e-12 2.42739e-11 2 1.019735618399145e+01 1.019735618400523e+01 1.37810e-11 1.09818e-10 3 -9.233676347932999e+00 -9.233676347941712e+00 8.71303e-12 1.52767e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 1.314274973103786e+01 1.314274973098620e+01 5.16618e-11 6.26788e-11 2 -9.621477894406757e+00 -9.621477894417282e+00 1.05249e-11 8.73790e-11 3 8.864564831961443e+00 8.864564831960838e+00 6.05738e-13 7.68878e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -6.585476790187612e+00 -6.585476790197331e+00 9.71934e-12 3.39258e-11 2 2.420822535209944e+00 2.420822535220029e+00 1.00857e-11 4.65818e-11 3 1.261474080637967e+01 1.261474080637898e+01 6.87450e-13 8.66208e-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 dicontinuities. Maximum error obtained for particle = 24, direction = 3: |F_model - F_numer| error = ----------------------- = 5.78608e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.78608e-10 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 5.78608e-10 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.