!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MEAM_Wagner_2007_SiC__SM_264944083668_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 = 2.916140556335449 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 5.215667307820323e+01 5.215667307725968e+01 9.43551e-10 1.84394e-09 2 -9.909374112704187e+01 -9.909374112737183e+01 3.29962e-10 1.33362e-09 3 -2.228028791653045e+02 -2.228028791652504e+02 5.41149e-11 4.32527e-09 ----------------------------------------------------------------------------------------------------- 2 C 1 -2.058412214936316e+02 -2.058412214937498e+02 1.18263e-10 1.39489e-08 2 1.026268843373742e+02 1.026268843372130e+02 1.61222e-10 2.34100e-09 3 -1.028771253305524e+02 -1.028771253305099e+02 4.25615e-11 1.75078e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.240284370911979e+03 -1.240284370907925e+03 4.05475e-09 2.36359e-08 2 -7.804241930708203e+02 -7.804241930710949e+02 2.74667e-10 1.62922e-08 3 1.293226522048458e+03 1.293226522050519e+03 2.06114e-09 1.62415e-08 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.336555080872768e+02 -1.336555080869372e+02 3.39583e-10 2.03636e-09 2 2.740139605141399e+02 2.740139605142112e+02 7.13385e-11 6.35316e-09 3 1.845031147547938e+02 1.845031147561294e+02 1.33562e-09 3.93862e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 1.899140602225603e+02 1.899140602237684e+02 1.20815e-09 7.00689e-09 2 -5.604023209666823e+01 -5.604023209651254e+01 1.55687e-10 5.24790e-09 3 3.912836955186327e+01 3.912836955184179e+01 2.14797e-11 5.95448e-09 ----------------------------------------------------------------------------------------------------- 6 C 1 -5.890904832460086e+01 -5.890904832588251e+01 1.28165e-09 1.69385e-08 2 3.124784040192749e+01 3.124784040198763e+01 6.01474e-11 7.45946e-09 3 1.234063146865315e+01 1.234063146850635e+01 1.46796e-10 1.36315e-09 ----------------------------------------------------------------------------------------------------- 7 C 1 5.731714303767858e+01 5.731714067471132e+01 2.36297e-06 5.82783e-05 * 2 -2.353318906597149e+02 -2.353318928703727e+02 2.21066e-06 7.09274e-06 * 3 -1.411382923223021e+02 -1.411382923007732e+02 2.15288e-08 1.31518e-05 * ----------------------------------------------------------------------------------------------------- 8 C 1 -6.284987815995074e+02 -6.284987815959117e+02 3.59569e-09 7.98798e-09 2 -9.411957527182826e+02 -9.411957527165713e+02 1.71133e-09 2.86424e-08 3 3.779464362366357e+02 3.779464362377694e+02 1.13369e-09 3.74638e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 9.112470051209208e+00 9.112470051157821e+00 5.13865e-11 1.10817e-09 2 -1.170173668514108e+02 -1.170173668521310e+02 7.20291e-10 4.86294e-09 3 -2.742958794578208e+01 -2.742958794515956e+01 6.22517e-10 1.01188e-08 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.580639144937749e+02 -1.580639144949044e+02 1.12948e-09 1.20096e-09 2 7.385227277581231e+01 7.385227277520764e+01 6.04672e-10 7.96547e-10 3 3.764548913141831e+00 3.764548913155520e+00 1.36890e-11 1.90305e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 8.288096036854661e+01 8.288096036781688e+01 7.29727e-10 2.35616e-09 2 -8.528337337603375e+01 -8.528337337708007e+01 1.04632e-09 1.49504e-09 3 8.823390127922448e+01 8.823390127903950e+01 1.84983e-10 5.02691e-09 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.799758141769129e+01 -1.799758141765631e+01 3.49765e-11 9.10987e-10 2 6.535174239800014e+01 6.535174239788765e+01 1.12493e-10 2.61566e-09 3 1.680685810256364e+01 1.680685810253058e+01 3.30616e-11 1.07910e-09 ----------------------------------------------------------------------------------------------------- 13 C 1 -2.601986697241025e+03 -2.601986697238041e+03 2.98314e-09 1.15784e-05 * 2 -1.186118401574671e+03 -1.186118401570813e+03 3.85830e-09 1.52334e-08 3 -1.125378600528894e+03 -1.125378600528782e+03 1.12095e-10 1.11389e-07 ----------------------------------------------------------------------------------------------------- 14 C 1 1.455567424460156e+03 1.455567424456920e+03 3.23666e-09 6.64165e-08 2 -5.525150759853013e+02 -5.525150759874847e+02 2.18336e-09 8.18670e-08 3 1.746192449851737e+03 1.746192449843096e+03 8.64088e-09 3.30051e-06 * ----------------------------------------------------------------------------------------------------- 15 C 1 1.953693810078460e+03 1.953693810078753e+03 2.92857e-10 1.52254e-08 2 2.768718749716197e+03 2.768718749709706e+03 6.49106e-09 1.14765e-07 3 -5.919870060551046e+02 -5.919870060533970e+02 1.70769e-09 1.78946e-07 * ----------------------------------------------------------------------------------------------------- 16 C 1 8.192342165744969e+01 8.192342165735784e+01 9.18590e-11 1.00648e-09 2 3.250567051432083e+02 3.250567051437513e+02 5.43025e-10 5.06287e-09 3 -1.798257148237993e+02 -1.798257148251787e+02 1.37942e-09 8.30278e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.348277785801343e+03 -1.348277785810240e+03 8.89713e-09 3.19951e-08 2 -3.505989470706239e+02 -3.505989470688991e+02 1.72480e-09 3.98211e-09 3 -1.991688489160277e+03 -1.991688489166644e+03 6.36783e-09 2.21445e-07 * ----------------------------------------------------------------------------------------------------- 18 C 1 1.206027529304704e+03 1.206027529303125e+03 1.57820e-09 1.55262e-08 2 1.519009175625590e+03 1.519009175627832e+03 2.24168e-09 3.55358e-07 * 3 3.367045711689663e+02 3.367045711682611e+02 7.05199e-10 1.23478e-08 ----------------------------------------------------------------------------------------------------- 19 C 1 2.132450331362355e+03 2.132450331367474e+03 5.11955e-09 7.61215e-08 2 -3.288695072030477e+02 -3.288695072036536e+02 6.05894e-10 5.49005e-09 3 8.761106725668398e+02 8.761106725671972e+02 3.57431e-10 1.85202e-08 ----------------------------------------------------------------------------------------------------- 20 C 1 -5.753160037725331e+02 -5.753160037731773e+02 6.44150e-10 7.58257e-09 2 -3.300820198168405e+01 -3.300820198114402e+01 5.40034e-10 5.06115e-09 3 -5.808642985248079e+02 -5.808642985258908e+02 1.08298e-09 3.09536e-08 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.530427279831318e+02 -3.530427278842130e+02 9.89188e-08 2.62860e-05 * 2 -2.419545027581264e+02 -2.419545048706879e+02 2.11256e-06 4.77697e-06 * 3 -6.834847583150820e+02 -6.834847660989124e+02 7.78383e-06 1.45780e-04 * ----------------------------------------------------------------------------------------------------- 22 C 1 -1.802844536367956e+02 -1.802844479755108e+02 5.66128e-06 1.05127e-05 * 2 1.855981594784092e+02 1.855981629078871e+02 3.42948e-06 1.95122e-04 * 3 -1.721032863305548e+01 -1.721032866296459e+01 2.99091e-08 1.34171e-06 * ----------------------------------------------------------------------------------------------------- 23 C 1 1.720751913985369e+01 1.720751913976552e+01 8.81712e-11 2.08608e-09 2 3.440609537412332e+02 3.440609537409583e+02 2.74895e-10 1.10782e-09 3 5.123217106331842e+02 5.123217106320820e+02 1.10219e-09 1.59190e-08 ----------------------------------------------------------------------------------------------------- 24 C 1 2.633429644978372e+02 2.633429644977712e+02 6.60521e-11 8.31250e-09 2 -1.192410808365005e+02 -1.192410808365571e+02 5.66018e-11 4.98225e-09 3 2.101766087423100e+02 2.101766087414734e+02 8.36678e-10 5.97225e-09 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.720775607415890e+02 -2.720775607417911e+02 2.02135e-10 1.31994e-08 2 6.183797397608358e+02 6.183797397601448e+02 6.90989e-10 5.25858e-09 3 1.003157660683560e+03 1.003157660684209e+03 6.48924e-10 5.90705e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -2.799035080805974e+02 -2.799035080803457e+02 2.51646e-10 1.13884e-08 2 2.300812613521170e+02 2.300812613524484e+02 3.31369e-10 5.97578e-09 3 2.093898467938801e+02 2.093898467940163e+02 1.36168e-10 9.23600e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 2.915119579239351e+03 2.915119579233205e+03 6.14637e-09 4.33452e-08 2 -2.044982514917199e+03 -2.044982514920816e+03 3.61774e-09 1.92726e-08 3 3.569681180455943e+02 3.569681180463302e+02 7.35895e-10 1.58556e-08 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.673831482920220e+03 -2.673831482916998e+03 3.22188e-09 1.43834e-07 * 2 1.321105329895255e+03 1.321105329887555e+03 7.70024e-09 7.69051e-08 3 -1.219078072932987e+03 -1.219078072930797e+03 2.18938e-09 1.00201e-08 ----------------------------------------------------------------------------------------------------- 29 C 1 2.324641212472665e+02 2.324641212497642e+02 2.49767e-09 6.53461e-08 2 -7.059710488950238e+02 -7.059710488931197e+02 1.90414e-09 6.49854e-08 3 -1.864447150404888e+02 -1.864447150392925e+02 1.19627e-09 7.44382e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 7.346535365431136e+01 7.346535365436773e+01 5.63745e-11 1.38168e-09 2 -4.669495832299075e+01 -4.669495832283248e+01 1.58266e-10 4.37600e-09 3 -1.352960955053380e+02 -1.352960955050949e+02 2.43148e-10 9.98767e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.836177929347112e+01 -2.836177929337900e+01 9.21112e-11 1.69253e-09 2 -1.444035528992909e+01 -1.444035529009522e+01 1.66130e-10 2.32007e-09 3 -1.986459660021407e+01 -1.986459660039040e+01 1.76328e-10 1.06211e-09 ----------------------------------------------------------------------------------------------------- 32 C 1 3.368906439922591e+01 3.368906439873967e+01 4.86239e-10 1.98568e-09 2 7.967836959496984e+01 7.967836959469481e+01 2.75023e-10 1.40160e-09 3 -4.160145995741809e+01 -4.160145995716337e+01 2.54715e-10 4.87386e-09 ----------------------------------------------------------------------------------------------------- * 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 = 9, direction = 3: |F_model - F_numer| error = ----------------------- = 2.26951e-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 = 4.199018478393555 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.643552321468394e+01 -1.643552321473141e+01 4.74749e-11 2.41425e-10 2 -2.674559015565464e+00 -2.674559015570498e+00 5.03420e-12 7.36372e-10 3 1.390237044834729e+01 1.390237044834660e+01 6.92779e-13 5.47221e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 2.475050569161132e+01 2.475050569151804e+01 9.32765e-11 4.07038e-09 * 2 1.937356254484659e+01 1.937356254489084e+01 4.42526e-11 2.51075e-09 3 -1.535872343805002e+01 -1.535872343794127e+01 1.08749e-10 3.89678e-09 * ----------------------------------------------------------------------------------------------------- 3 Si 1 5.218472205684750e+00 5.218472205677180e+00 7.56994e-12 5.34026e-11 2 -1.073759958383455e+01 -1.073759958379436e+01 4.01865e-11 4.25937e-10 3 3.067218390123019e+00 3.067218390138018e+00 1.49991e-11 8.95477e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.075818703895906e+01 -1.075818703898415e+01 2.50910e-11 1.76614e-10 2 -6.586045290561587e+00 -6.586045290506314e+00 5.52722e-11 2.37625e-10 3 -5.857896698529540e+00 -5.857896698458913e+00 7.06271e-11 1.96590e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.092480018889405e+01 -1.092480018893745e+01 4.34017e-11 1.05757e-10 2 -3.002115577301198e+00 -3.002115577311538e+00 1.03406e-11 2.49718e-10 3 -4.558441863494123e+00 -4.558441863484898e+00 9.22462e-12 2.09297e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.448709253857753e+00 2.448709253799263e+00 5.84892e-11 7.44631e-11 2 -1.350430897932766e+01 -1.350430897931256e+01 1.50973e-11 2.59366e-09 * 3 -5.883566955514872e+00 -5.883566955510858e+00 4.01368e-12 3.27605e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 6.872315878904239e+00 6.872315878905134e+00 8.95284e-13 1.51282e-09 2 5.943140392070272e+00 5.943140392149262e+00 7.89901e-11 4.40499e-10 3 1.412712199472543e+00 1.412712199473697e+00 1.15352e-12 3.58023e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.255408899175348e-01 3.255408898913634e-01 2.61713e-11 2.29034e-10 2 8.460185122312277e+00 8.460185122315208e+00 2.93099e-12 1.74362e-10 3 5.190188768225867e+00 5.190188768222971e+00 2.89635e-12 1.40754e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 1.396027977333057e+00 1.396027977342718e+00 9.66027e-12 1.47184e-10 2 -3.408562744208498e-01 -3.408562744184978e-01 2.35195e-12 1.24494e-10 3 5.827668270499555e-01 5.827668270539041e-01 3.94862e-12 2.93338e-09 * ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.646397438255298e+00 -1.646397438265202e+00 9.90363e-12 6.13429e-11 2 2.153477488480037e+00 2.153477488485856e+00 5.81935e-12 2.25533e-10 3 -4.009666561885855e+00 -4.009666561884099e+00 1.75682e-12 1.51569e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 2.692588944073866e+00 2.692588944089660e+00 1.57945e-11 1.70659e-10 2 -8.088110776588049e+00 -8.088110776622278e+00 3.42286e-11 5.76211e-10 3 4.749155718011507e+00 4.749155717998256e+00 1.32507e-11 4.58291e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.776595165490698e+00 -2.776595165485002e+00 5.69589e-12 7.09572e-10 2 3.221632911393201e+00 3.221632911339906e+00 5.32943e-11 2.34424e-10 3 -3.512263526859270e+00 -3.512263526805628e+00 5.36420e-11 1.78563e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.426381137427049e+01 -1.426381137452187e+01 2.51388e-10 4.50600e-10 2 -7.933271391973898e+00 -7.933271392021465e+00 4.75673e-11 7.09933e-10 3 -9.344351058105296e+00 -9.344351058116652e+00 1.13562e-11 4.34644e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.619569700064053e+00 7.619569700110571e+00 4.65175e-11 4.91724e-10 2 -2.099204387332514e-01 -2.099204387307407e-01 2.51071e-12 1.12173e-10 3 3.903431310963036e+00 3.903431310952261e+00 1.07754e-11 2.38813e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 7.479979748503167e+00 7.479979748606160e+00 1.02993e-10 2.05324e-09 2 1.681155916438526e+01 1.681155916435105e+01 3.42091e-11 9.95836e-10 3 1.509730641279838e+01 1.509730641283754e+01 3.91562e-11 1.58886e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -6.013451601475359e-01 -6.013451601480544e-01 5.18474e-13 4.39553e-10 2 4.797012837555267e+00 4.797012837584108e+00 2.88418e-11 1.39420e-10 3 5.816954444520952e+00 5.816954444470876e+00 5.00764e-11 1.98030e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.249805385551517e+00 1.249805385569831e+00 1.83145e-11 3.77085e-10 2 -3.183177860317186e+00 -3.183177860303799e+00 1.33871e-11 7.77747e-11 3 4.490115150982366e+00 4.490115151004987e+00 2.26201e-11 7.71951e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.031761088782835e+00 2.031761088816970e+00 3.41345e-11 6.07625e-11 2 1.204208062364311e+01 1.204208062363933e+01 3.78364e-12 2.77613e-10 3 -1.214923357073178e+00 -1.214923357129232e+00 5.60545e-11 1.72924e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.597755395857714e+00 -4.597755395879888e+00 2.21743e-11 2.57278e-10 2 -3.553560426882079e+00 -3.553560426854073e+00 2.80056e-11 7.20396e-10 3 1.094483049716282e+00 1.094483049725377e+00 9.09539e-12 2.16983e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -4.936290325157599e-01 -4.936290325100538e-01 5.70610e-12 1.90581e-10 2 4.593560777865612e-02 4.593560777684669e-02 1.80943e-12 7.73975e-10 3 -1.309224323632111e-01 -1.309224323663605e-01 3.14945e-12 1.05085e-09 ----------------------------------------------------------------------------------------------------- 21 Si 1 4.607723848108456e-01 4.607723848073741e-01 3.47145e-12 4.74804e-11 2 -1.110320932614087e+01 -1.110320932612543e+01 1.54348e-11 3.23878e-10 3 5.045701057389918e+00 5.045701057423434e+00 3.35163e-11 2.02236e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 8.622011941876707e+00 8.622011941917881e+00 4.11742e-11 9.51950e-10 2 9.372564098463140e+00 9.372564098418756e+00 4.43841e-11 2.49747e-10 3 -1.459443242854575e+01 -1.459443242865141e+01 1.05659e-10 9.29100e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.278298530437746e+00 -2.278298530426943e+00 1.08025e-11 6.08562e-11 2 -9.387273351560706e+00 -9.387273351542998e+00 1.77085e-11 1.64579e-10 3 6.090303175810653e-01 6.090303175927277e-01 1.16624e-11 5.19063e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -9.011890185934964e+00 -9.011890185954410e+00 1.94458e-11 1.22635e-09 2 2.784019255678813e+00 2.784019255673043e+00 5.77005e-12 1.60249e-10 3 8.309886037396529e+00 8.309886037516165e+00 1.19636e-10 3.97185e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -4.874296390620261e+00 -4.874296390611565e+00 8.69615e-12 2.08148e-10 2 -4.420384788625134e+00 -4.420384788616397e+00 8.73612e-12 1.52146e-09 3 1.889339641977877e+00 1.889339641845734e+00 1.32143e-10 4.54259e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 6.460239948338049e+00 6.460239948336190e+00 1.85896e-12 9.24310e-10 2 4.173907782404208e+00 4.173907782386748e+00 1.74598e-11 3.22300e-09 * 3 -3.833964275283818e+00 -3.833964275287041e+00 3.22320e-12 1.03605e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.446229768627068e-01 -1.446229768783128e-01 1.56061e-11 1.04440e-10 2 -7.268736657850082e+00 -7.268736657837864e+00 1.22187e-11 5.33724e-10 3 2.524723447855624e+00 2.524723447824578e+00 3.10454e-11 1.17108e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.804772868368574e+00 -2.804772868346033e+00 2.25415e-11 8.08515e-10 2 -3.115085008304774e-01 -3.115085008472687e-01 1.67912e-11 3.71636e-11 3 2.312680695695148e+00 2.312680695699608e+00 4.45954e-12 1.71886e-09 ----------------------------------------------------------------------------------------------------- 29 Si 1 -6.064147181450175e+00 -6.064147181439263e+00 1.09122e-11 1.57049e-09 2 -5.845632734687791e+00 -5.845632734538285e+00 1.49506e-10 4.88655e-09 * 3 -1.528343656382259e+01 -1.528343656384943e+01 2.68443e-11 7.00634e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 4.276960397062888e+00 4.276960397044578e+00 1.83098e-11 8.60103e-11 2 3.799930642248973e+00 3.799930642262072e+00 1.30993e-11 1.00524e-09 3 -3.107959781925866e+00 -3.107959781873934e+00 5.19313e-11 9.92855e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.462923983859840e+00 5.462923983903381e+00 4.35412e-11 2.64961e-09 * 2 -2.067007669754894e+00 -2.067007669772813e+00 1.79190e-11 6.88525e-11 3 3.174083853962786e+00 3.174083853936154e+00 2.66320e-11 3.95587e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.078867225165478e-01 3.078867225155610e-01 9.86822e-13 3.80069e-11 2 7.238270173695915e+00 7.238270173697516e+00 1.60050e-12 2.15514e-09 3 3.518401169383235e+00 3.518401169410676e+00 2.74412e-11 1.99992e-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 = 27, direction = 1: |F_model - F_numer| error = ----------------------- = 1.07909e-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 = 3.5952494672596913 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -8.414565335439553e+01 -8.414565335462068e+01 2.25143e-10 3.23152e-09 2 -5.972756357091231e+01 -5.972756357089679e+01 1.55183e-11 4.99845e-10 3 4.651022812566754e+01 4.651022812567605e+01 8.51230e-12 2.81624e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.486758637299783e+02 1.486758637297866e+02 1.91704e-10 5.48462e-09 2 3.531088670420201e+01 3.531088670428365e+01 8.16343e-11 5.65166e-11 3 -2.918512041122873e+01 -2.918512041132788e+01 9.91527e-11 8.30749e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.081966987372033e+01 -2.081966987369359e+01 2.67377e-11 6.51596e-10 2 1.798690157341815e+00 1.798690157352675e+00 1.08600e-11 1.80477e-10 3 2.241576992442867e+01 2.241576992453639e+01 1.07718e-10 2.35170e-09 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.416415792337934e+01 -1.416415792341337e+01 3.40350e-11 2.07837e-09 2 -2.660877977705102e+01 -2.660877977678893e+01 2.62091e-10 3.62551e-10 3 -2.396245820712478e+01 -2.396245820715332e+01 2.85461e-11 3.68381e-09 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.256451328048728e+01 -1.256451328046581e+01 2.14637e-11 5.04117e-09 2 1.340999671465379e+01 1.340999671473987e+01 8.60823e-11 4.82341e-10 3 -1.898466957821902e+01 -1.898466957815971e+01 5.93126e-11 1.76641e-09 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.736767283222690e+01 -2.736767283185939e+01 3.67507e-10 2.01972e-09 2 7.746376728729194e+01 7.746376728687444e+01 4.17501e-10 9.68461e-09 * 3 -6.145689590011462e+01 -6.145689589908290e+01 1.03172e-09 5.84431e-09 ----------------------------------------------------------------------------------------------------- 7 Si 1 1.900559168638817e+01 1.900559168627993e+01 1.08244e-10 8.68745e-10 2 -4.967521801171333e+01 -4.967521801155370e+01 1.59638e-10 4.55479e-10 3 7.329002634286336e+01 7.329002634279102e+01 7.23333e-11 1.23482e-09 ----------------------------------------------------------------------------------------------------- 8 C 1 5.672649307289628e+00 5.672649307407115e+00 1.17486e-10 2.73784e-10 2 -2.228174857746742e+00 -2.228174857718125e+00 2.86176e-11 1.40299e-10 3 4.396486513386921e-01 4.396486513464137e-01 7.72166e-12 2.00512e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 -3.009196906578590e+01 -3.009196906572476e+01 6.11315e-11 1.22156e-09 2 6.714086696042187e+01 6.714086696005842e+01 3.63457e-10 5.12024e-09 3 3.648941840890502e+01 3.648941840888489e+01 2.01297e-11 2.82718e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 3.058863606937214e+01 3.058863606942099e+01 4.88569e-11 3.46787e-10 2 -5.161845466422830e+00 -5.161845466275863e+00 1.46967e-10 2.47014e-10 3 -1.711807798649246e+01 -1.711807798649373e+01 1.27187e-12 1.57838e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -9.199873225453182e+00 -9.199873225356164e+00 9.70175e-11 8.50575e-10 2 1.750089676611972e+00 1.750089676581728e+00 3.02443e-11 5.80086e-09 3 2.097849170954932e-01 2.097849171392620e-01 4.37688e-11 2.11353e-09 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.383907936358795e+01 -2.383907936359904e+01 1.10916e-11 5.00496e-10 2 -2.624961802243341e+01 -2.624961802245129e+01 1.78844e-11 1.08997e-10 3 8.683018377506182e+00 8.683018377510935e+00 4.75353e-12 1.19227e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 2.076476526812529e+01 2.076476526787065e+01 2.54637e-10 3.58778e-09 2 -2.155963798694631e+01 -2.155963798719501e+01 2.48701e-10 2.95389e-09 3 1.741433801587442e+00 1.741433801678858e+00 9.14158e-11 9.62783e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -8.881349713746205e+00 -8.881349713779162e+00 3.29567e-11 7.91935e-11 2 4.746205494700020e+00 4.746205494732505e+00 3.24851e-11 9.77900e-10 3 -4.223525264853818e+00 -4.223525264848702e+00 5.11591e-12 9.76225e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 -5.501586514715534e+00 -5.501586514625041e+00 9.04929e-11 2.28029e-09 2 -1.029491406295608e+01 -1.029491406307785e+01 1.21773e-10 1.04045e-09 3 7.655238116136445e+00 7.655238116124171e+00 1.22737e-11 8.54720e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 4.077522503899962e-01 4.077522503998683e-01 9.87210e-12 1.84939e-10 2 7.378855656449217e-01 7.378855656606962e-01 1.57745e-11 4.80191e-11 3 -8.960883085704578e+00 -8.960883085712553e+00 7.97407e-12 4.15293e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.228031668426929e+01 -3.228031668425125e+01 1.80407e-11 1.48802e-10 2 -2.990522840167887e+01 -2.990522840159439e+01 8.44835e-11 1.25848e-08 * 3 -2.778920983701094e+01 -2.778920983710174e+01 9.07932e-11 8.43183e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 5.337998421128284e+01 5.337998421149506e+01 2.12218e-10 2.76903e-09 2 4.729366973285919e+01 4.729366973270591e+01 1.53278e-10 4.81307e-10 3 -4.257367751962593e+01 -4.257367751975517e+01 1.29234e-10 6.17872e-09 ----------------------------------------------------------------------------------------------------- 19 Si 1 3.236056578418587e+01 3.236056578434797e+01 1.62096e-10 1.70300e-08 * 2 -4.262182615519663e+01 -4.262182615524421e+01 4.75850e-11 4.12953e-09 3 1.387282332236310e+01 1.387282332222328e+01 1.39821e-10 9.95920e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -3.085928475347173e+01 -3.085928475340701e+01 6.47269e-11 1.79388e-09 2 4.691442404243180e+01 4.691442404245672e+01 2.49187e-11 1.46451e-09 3 2.823834534862046e+01 2.823834534860414e+01 1.63212e-11 1.26909e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.172024744432106e+01 -3.172024744454609e+01 2.25025e-10 4.30965e-09 2 -1.606386256253504e+01 -1.606386256254887e+01 1.38272e-11 2.16563e-09 3 -3.968899193840340e+01 -3.968899193849295e+01 8.95568e-11 1.61612e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.012450720472316e+01 -1.012450720473462e+01 1.14593e-11 5.05924e-10 2 -2.818252748094530e+01 -2.818252748098505e+01 3.97478e-11 3.19453e-10 3 -2.612645217414326e+01 -2.612645217390289e+01 2.40377e-10 7.45036e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 9.820818399473689e+00 9.820818399487788e+00 1.40989e-11 8.97327e-11 2 2.037957921159738e+01 2.037957921164279e+01 4.54108e-11 1.26146e-10 3 3.187101655255973e+01 3.187101655255417e+01 5.55644e-12 9.31575e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 2.638124143012694e+01 2.638124143018747e+01 6.05240e-11 8.36522e-11 2 -9.837509838505785e+00 -9.837509838530316e+00 2.45315e-11 1.10140e-08 * 3 3.470647591604066e+00 3.470647591586784e+00 1.72813e-11 2.53854e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.370809433856090e+00 -2.370809433850945e+00 5.14477e-12 8.70997e-11 2 -5.663169343486985e+00 -5.663169343497811e+00 1.08260e-11 1.59536e-09 3 -1.312621718976680e+01 -1.312621718969245e+01 7.43512e-11 1.80060e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.092198992682631e+00 1.092198992692486e+00 9.85545e-12 1.55420e-11 2 1.798508681274192e+00 1.798508681284168e+00 9.97646e-12 2.52549e-11 3 5.730368957405799e+00 5.730368957398459e+00 7.34079e-12 2.74001e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 7.254717584933556e+00 7.254717584984421e+00 5.08651e-11 1.07953e-10 2 -3.511658576209753e+01 -3.511658576221911e+01 1.21581e-10 9.06134e-10 3 -1.513204088509803e+00 -1.513204088526668e+00 1.68658e-11 1.38226e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -1.276535445890227e+01 -1.276535445895975e+01 5.74794e-11 4.15982e-09 2 2.126423433257868e+01 2.126423433254806e+01 3.06208e-11 9.74993e-10 3 4.080714556962294e+00 4.080714556958549e+00 3.74545e-12 2.36907e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 3.249562020851705e+00 3.249562020904437e+00 5.27316e-11 4.29941e-10 2 -9.431354765547093e+00 -9.431354765536534e+00 1.05587e-11 5.12530e-09 3 -5.732915902440962e+00 -5.732915902456022e+00 1.50600e-11 2.46931e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 -4.511250623972967e-01 -4.511250623899745e-01 7.32220e-12 2.83650e-11 2 6.787758965496583e+00 6.787758965507056e+00 1.04725e-11 4.74635e-09 3 8.949145537658211e+00 8.949145537646283e+00 1.19282e-11 2.77417e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.573085732547956e+00 -5.573085732544128e+00 3.82805e-12 2.76999e-10 2 3.151372422787762e+01 3.151372422774227e+01 1.35348e-10 9.86873e-10 3 3.037998235555560e+01 3.037998235558076e+01 2.51603e-11 1.25298e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.065909186906276e+00 4.065909186900308e+00 5.96767e-12 2.84759e-11 2 1.752831119146866e-02 1.752831119661770e-02 5.14904e-12 8.18042e-07 * 3 -3.585311804619041e+00 -3.585311804619035e+00 6.21725e-15 1.49501e-06 * ----------------------------------------------------------------------------------------------------- * 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 = 11, direction = 3: |F_model - F_numer| error = ----------------------- = 2.08637e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.08637e-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 2.08637e-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.