!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Wagner_2007_SiC__MO_430846853065_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 5.215667307821342e+01 5.215667307829359e+01 8.01705e-11 2.61402e-09 2 -9.909374112704583e+01 -9.909374112759629e+01 5.50457e-10 2.73253e-09 3 -2.228028791653233e+02 -2.228028791652948e+02 2.84786e-11 1.54640e-09 ----------------------------------------------------------------------------------------------------- 2 C 1 -2.058412214936497e+02 -2.058412214928481e+02 8.01577e-10 8.25221e-09 2 1.026268843373722e+02 1.026268843375211e+02 1.48916e-10 1.40190e-09 3 -1.028771253305580e+02 -1.028771253302196e+02 3.38403e-10 2.33801e-09 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.240284370911841e+03 -1.240284370912577e+03 7.36009e-10 9.97852e-09 2 -7.804241930707470e+02 -7.804241930703964e+02 3.50610e-10 8.95591e-09 3 1.293226522048368e+03 1.293226522050465e+03 2.09639e-09 1.70753e-08 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.336555080872824e+02 -1.336555080871137e+02 1.68740e-10 4.68700e-09 2 2.740139605141607e+02 2.740139605138900e+02 2.70632e-10 3.78611e-09 3 1.845031147548012e+02 1.845031147551087e+02 3.07494e-10 1.86094e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 1.899140602225654e+02 1.899140602227185e+02 1.53079e-10 2.29911e-08 2 -5.604023209667504e+01 -5.604023209703963e+01 3.64594e-10 2.12843e-09 3 3.912836955186374e+01 3.912836955164412e+01 2.19622e-10 2.73430e-09 ----------------------------------------------------------------------------------------------------- 6 C 1 -5.890904832459915e+01 -5.890904832500151e+01 4.02352e-10 5.05013e-09 2 3.124784040193057e+01 3.124784040194028e+01 9.70957e-12 9.20945e-09 3 1.234063146864923e+01 1.234063146952164e+01 8.72413e-10 1.86684e-09 ----------------------------------------------------------------------------------------------------- 7 C 1 5.731714303766029e+01 5.731714127601576e+01 1.76164e-06 6.02185e-05 * 2 -2.353318906596991e+02 -2.353318907159103e+02 5.62112e-08 7.30769e-06 * 3 -1.411382923222839e+02 -1.411382923717659e+02 4.94820e-08 1.30838e-05 * ----------------------------------------------------------------------------------------------------- 8 C 1 -6.284987815994555e+02 -6.284987816024744e+02 3.01895e-09 2.89348e-08 2 -9.411957527182732e+02 -9.411957527133341e+02 4.93912e-09 1.71040e-08 3 3.779464362365583e+02 3.779464362352790e+02 1.27932e-09 1.19182e-08 ----------------------------------------------------------------------------------------------------- 9 C 1 9.112470051205676e+00 9.112470051265070e+00 5.93943e-11 1.52342e-09 2 -1.170173668514202e+02 -1.170173668517742e+02 3.54007e-10 4.23327e-10 3 -2.742958794577876e+01 -2.742958794557681e+01 2.01954e-10 7.95211e-09 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.580639144937766e+02 -1.580639144940781e+02 3.01469e-10 1.53219e-08 2 7.385227277581458e+01 7.385227277589870e+01 8.41140e-11 9.07548e-10 3 3.764548913143912e+00 3.764548913350237e+00 2.06325e-10 2.04050e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 8.288096036855111e+01 8.288096036741879e+01 1.13232e-09 4.10512e-09 2 -8.528337337602227e+01 -8.528337337676872e+01 7.46454e-10 3.22385e-09 3 8.823390127922511e+01 8.823390127896919e+01 2.55923e-10 1.66079e-09 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.799758141769101e+01 -1.799758141757729e+01 1.13722e-10 2.13110e-10 2 6.535174239799937e+01 6.535174239785216e+01 1.47210e-10 3.56204e-09 3 1.680685810256319e+01 1.680685810265892e+01 9.57350e-11 6.56095e-09 ----------------------------------------------------------------------------------------------------- 13 C 1 -2.601986697240701e+03 -2.601986697236963e+03 3.73848e-09 1.15788e-05 * 2 -1.186118401574529e+03 -1.186118401575700e+03 1.17052e-09 6.72958e-09 3 -1.125378600528776e+03 -1.125378600529140e+03 3.63798e-10 1.07720e-07 * ----------------------------------------------------------------------------------------------------- 14 C 1 1.455567424459981e+03 1.455567424460569e+03 5.88443e-10 3.25310e-08 2 -5.525150759852620e+02 -5.525150759836514e+02 1.61060e-09 6.24436e-09 3 1.746192449851546e+03 1.746192449856238e+03 4.69208e-09 3.28730e-06 * ----------------------------------------------------------------------------------------------------- 15 C 1 1.953693810078237e+03 1.953693810072077e+03 6.16023e-09 3.21634e-08 2 2.768718749715969e+03 2.768718749717208e+03 1.23873e-09 2.66096e-06 * 3 -5.919870060550068e+02 -5.919870060555369e+02 5.30122e-10 1.82021e-07 * ----------------------------------------------------------------------------------------------------- 16 C 1 8.192342165746737e+01 8.192342165752689e+01 5.95151e-11 6.30629e-09 2 3.250567051431736e+02 3.250567051449145e+02 1.74089e-09 2.73565e-09 3 -1.798257148237971e+02 -1.798257148240256e+02 2.28511e-10 9.87882e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.348277785801142e+03 -1.348277785801395e+03 2.52840e-10 1.39373e-08 2 -3.505989470707034e+02 -3.505989470708644e+02 1.60924e-10 1.93372e-08 3 -1.991688489160148e+03 -1.991688489164604e+03 4.45607e-09 2.20736e-07 * ----------------------------------------------------------------------------------------------------- 18 C 1 1.206027529304574e+03 1.206027529309549e+03 4.97585e-09 5.64364e-09 2 1.519009175625428e+03 1.519009175626927e+03 1.49885e-09 3.57005e-07 * 3 3.367045711689022e+02 3.367045711688835e+02 1.87015e-11 1.42581e-08 ----------------------------------------------------------------------------------------------------- 19 C 1 2.132450331362036e+03 2.132450331363002e+03 9.65883e-10 3.48277e-08 2 -3.288695072029667e+02 -3.288695072028336e+02 1.33070e-10 1.70244e-08 3 8.761106725667213e+02 8.761106725660928e+02 6.28461e-10 1.84938e-08 ----------------------------------------------------------------------------------------------------- 20 C 1 -5.753160037724191e+02 -5.753160037732960e+02 8.76867e-10 5.11477e-09 2 -3.300820198160403e+01 -3.300820198150803e+01 9.60014e-11 8.00000e-09 3 -5.808642985246603e+02 -5.808642985245120e+02 1.48248e-10 4.50962e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 -3.530427279831404e+02 -3.530427276634928e+02 3.19648e-07 2.54949e-05 * 2 -2.419545027581482e+02 -2.419545027394693e+02 1.86789e-08 1.60124e-06 * 3 -6.834847583151195e+02 -6.834847600906137e+02 1.77549e-06 1.62535e-04 * ----------------------------------------------------------------------------------------------------- 22 C 1 -1.802844536367680e+02 -1.802844481911358e+02 5.44563e-06 1.01794e-05 * 2 1.855981594783968e+02 1.855981628224752e+02 3.34408e-06 1.95567e-04 * 3 -1.721032863304091e+01 -1.721032859511442e+01 3.79265e-08 4.43611e-07 * ----------------------------------------------------------------------------------------------------- 23 C 1 1.720751913984131e+01 1.720751913966977e+01 1.71543e-10 1.49042e-09 2 3.440609537412570e+02 3.440609537418110e+02 5.53939e-10 6.97520e-09 3 5.123217106332035e+02 5.123217106332431e+02 3.96767e-11 3.12036e-09 ----------------------------------------------------------------------------------------------------- 24 C 1 2.633429644978586e+02 2.633429644971230e+02 7.35554e-10 1.85315e-09 2 -1.192410808365084e+02 -1.192410808360181e+02 4.90317e-10 8.58549e-10 3 2.101766087423277e+02 2.101766087426614e+02 3.33614e-10 1.87657e-09 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.720775607416031e+02 -2.720775607421469e+02 5.43764e-10 1.33463e-09 2 6.183797397608523e+02 6.183797397605268e+02 3.25485e-10 5.60317e-09 3 1.003157660683585e+03 1.003157660684534e+03 9.49171e-10 9.86563e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -2.799035080805894e+02 -2.799035080805697e+02 1.97247e-11 6.08077e-09 2 2.300812613521028e+02 2.300812613523974e+02 2.94619e-10 4.60037e-09 3 2.093898467938897e+02 2.093898467940636e+02 1.73884e-10 3.33907e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 2.915119579239422e+03 2.915119579237818e+03 1.60480e-09 1.08639e-07 * 2 -2.044982514917250e+03 -2.044982514916455e+03 7.94898e-10 1.15920e-08 3 3.569681180456014e+02 3.569681180421049e+02 3.49655e-09 2.00847e-08 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.673831482920285e+03 -2.673831482919418e+03 8.66294e-10 4.66434e-08 2 1.321105329895284e+03 1.321105329896509e+03 1.22486e-09 6.33815e-08 3 -1.219078072933019e+03 -1.219078072930596e+03 2.42312e-09 6.95968e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 2.324641212472599e+02 2.324641212488444e+02 1.58457e-09 7.02232e-09 2 -7.059710488949377e+02 -7.059710488942659e+02 6.71776e-10 1.98951e-08 3 -1.864447150404676e+02 -1.864447150405489e+02 8.12861e-11 2.92570e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 7.346535365431011e+01 7.346535365413152e+01 1.78588e-10 5.65925e-09 2 -4.669495832299501e+01 -4.669495832302061e+01 2.55937e-11 6.11614e-10 3 -1.352960955053360e+02 -1.352960955054963e+02 1.60270e-10 8.34063e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.836177929347280e+01 -2.836177929350799e+01 3.51861e-11 2.89173e-08 2 -1.444035528992494e+01 -1.444035529036660e+01 4.41657e-10 7.74092e-10 3 -1.986459660021652e+01 -1.986459660049808e+01 2.81563e-10 5.48248e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 3.368906439923268e+01 3.368906439943439e+01 2.01709e-10 1.28578e-09 2 7.967836959497166e+01 7.967836959495013e+01 2.15294e-11 3.52667e-09 3 -4.160145995741983e+01 -4.160145995714870e+01 2.71136e-10 5.07265e-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 = 6, direction = 3: |F_model - F_numer| error = ----------------------- = 7.06944e-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 -1.643552321468383e+01 -1.643552321476047e+01 7.66320e-11 3.68487e-10 2 -2.674559015565164e+00 -2.674559015560910e+00 4.25393e-12 1.07680e-10 3 1.390237044834518e+01 1.390237044832038e+01 2.47979e-11 1.23206e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 2.475050569160964e+01 2.475050569145921e+01 1.50429e-10 4.09663e-11 2 1.937356254484495e+01 1.937356254487153e+01 2.65707e-11 2.62323e-09 3 -1.535872343804890e+01 -1.535872343792669e+01 1.22213e-10 1.04436e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 5.218472205685926e+00 5.218472205662405e+00 2.35216e-11 2.53826e-09 2 -1.073759958383422e+01 -1.073759958379710e+01 3.71170e-11 1.19820e-09 3 3.067218390123376e+00 3.067218390098278e+00 2.50981e-11 1.30024e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.075818703895866e+01 -1.075818703890207e+01 5.65965e-11 4.04595e-10 2 -6.586045290560719e+00 -6.586045290565099e+00 4.38050e-12 2.01823e-10 3 -5.857896698529205e+00 -5.857896698525837e+00 3.36797e-12 1.17708e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.092480018889412e+01 -1.092480018893765e+01 4.35367e-11 3.77032e-11 2 -3.002115577301143e+00 -3.002115577298922e+00 2.22089e-12 7.19476e-10 3 -4.558441863494088e+00 -4.558441863495217e+00 1.12887e-12 3.20339e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.448709253857834e+00 2.448709253879858e+00 2.20242e-11 2.38575e-10 2 -1.350430897932780e+01 -1.350430897934331e+01 1.55147e-11 2.49394e-09 3 -5.883566955515202e+00 -5.883566955494432e+00 2.07701e-11 1.92954e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 6.872315878904274e+00 6.872315878929977e+00 2.57030e-11 1.50020e-09 2 5.943140392070005e+00 5.943140392084433e+00 1.44285e-11 8.70700e-10 3 1.412712199472533e+00 1.412712199473709e+00 1.17573e-12 2.06761e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 3.255408899173093e-01 3.255408899304144e-01 1.31051e-11 1.20025e-09 2 8.460185122312607e+00 8.460185122319288e+00 6.68088e-12 1.29625e-09 3 5.190188768226062e+00 5.190188768195495e+00 3.05675e-11 2.16977e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 1.396027977333077e+00 1.396027977338453e+00 5.37548e-12 3.30493e-11 2 -3.408562744209035e-01 -3.408562744259093e-01 5.00577e-12 2.65034e-11 3 5.827668270499297e-01 5.827668270539041e-01 3.97449e-12 2.93338e-09 * ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.646397438255119e+00 -1.646397438279465e+00 2.43465e-11 4.33265e-11 2 2.153477488480049e+00 2.153477488477280e+00 2.76845e-12 6.96514e-11 3 -4.009666561885898e+00 -4.009666561890642e+00 4.74376e-12 3.63504e-09 * ----------------------------------------------------------------------------------------------------- 11 Si 1 2.692588944073480e+00 2.692588944071617e+00 1.86251e-12 2.96519e-10 2 -8.088110776588870e+00 -8.088110776640207e+00 5.13367e-11 5.61856e-10 3 4.749155718011296e+00 4.749155718022036e+00 1.07399e-11 2.51385e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.776595165490654e+00 -2.776595165472628e+00 1.80260e-11 2.62103e-09 2 3.221632911393170e+00 3.221632911372955e+00 2.02149e-11 2.01666e-10 3 -3.512263526859083e+00 -3.512263526826501e+00 3.25828e-11 1.68263e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.426381137427050e+01 -1.426381137430965e+01 3.91545e-11 3.46800e-10 2 -7.933271391973833e+00 -7.933271391815998e+00 1.57836e-10 5.67795e-11 3 -9.344351058105197e+00 -9.344351058110155e+00 4.95781e-12 1.61069e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 7.619569700064313e+00 7.619569700067805e+00 3.49232e-12 2.65636e-10 2 -2.099204387337994e-01 -2.099204387347432e-01 9.43801e-13 1.77745e-09 3 3.903431310963278e+00 3.903431310975642e+00 1.23648e-11 2.08805e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 7.479979748502852e+00 7.479979748527139e+00 2.42872e-11 1.38330e-10 2 1.681155916438596e+01 1.681155916444345e+01 5.74900e-11 7.04969e-10 3 1.509730641279804e+01 1.509730641281663e+01 1.85931e-11 3.52588e-09 * ----------------------------------------------------------------------------------------------------- 16 Si 1 -6.013451601479658e-01 -6.013451600966010e-01 5.13648e-11 1.00028e-10 2 4.797012837555463e+00 4.797012837579667e+00 2.42046e-11 7.31127e-10 3 5.816954444521728e+00 5.816954444526477e+00 4.74909e-12 4.01670e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.249805385551536e+00 1.249805385549545e+00 1.99107e-12 1.38288e-10 2 -3.183177860317281e+00 -3.183177860300170e+00 1.71103e-11 1.77215e-10 3 4.490115150982501e+00 4.490115150960943e+00 2.15588e-11 1.03102e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.031761088782921e+00 2.031761088785055e+00 2.13340e-12 6.45382e-11 2 1.204208062364331e+01 1.204208062368202e+01 3.87050e-11 4.91085e-09 * 3 -1.214923357073565e+00 -1.214923357185520e+00 1.11954e-10 1.65221e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.597755395857797e+00 -4.597755395865658e+00 7.86038e-12 4.70726e-11 2 -3.553560426882240e+00 -3.553560426862555e+00 1.96851e-11 1.47920e-10 3 1.094483049716429e+00 1.094483049729793e+00 1.33635e-11 1.47146e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -4.936290325158439e-01 -4.936290325167089e-01 8.64975e-13 2.10398e-09 2 4.593560777868095e-02 4.593560777804562e-02 6.35332e-13 1.23306e-10 3 -1.309224323631654e-01 -1.309224323604992e-01 2.66615e-12 9.26294e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 4.607723848109206e-01 4.607723848077664e-01 3.15425e-12 9.44809e-11 2 -1.110320932614065e+01 -1.110320932615616e+01 1.55094e-11 3.76053e-10 3 5.045701057389729e+00 5.045701057441302e+00 5.15730e-11 2.96905e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 8.622011941876584e+00 8.622011941883105e+00 6.52101e-12 9.59480e-10 2 9.372564098462863e+00 9.372564098516108e+00 5.32445e-11 1.95579e-10 3 -1.459443242854555e+01 -1.459443242840049e+01 1.45059e-10 8.19721e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.278298530437536e+00 -2.278298530441651e+00 4.11449e-12 1.63869e-11 2 -9.387273351560484e+00 -9.387273351544950e+00 1.55342e-11 1.70571e-10 3 6.090303175811728e-01 6.090303175901889e-01 9.01612e-12 2.94998e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -9.011890185934755e+00 -9.011890185942780e+00 8.02558e-12 3.38662e-10 2 2.784019255678630e+00 2.784019255660476e+00 1.81535e-11 6.30371e-11 3 8.309886037396499e+00 8.309886037309610e+00 8.68887e-11 3.07564e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -4.874296390620053e+00 -4.874296390613335e+00 6.71818e-12 8.03583e-10 2 -4.420384788625249e+00 -4.420384788622393e+00 2.85549e-12 1.24629e-10 3 1.889339641978120e+00 1.889339641923563e+00 5.45577e-11 1.53742e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 6.460239948338775e+00 6.460239948338538e+00 2.37144e-13 4.38730e-10 2 4.173907782404680e+00 4.173907782428056e+00 2.33769e-11 1.12060e-10 3 -3.833964275284244e+00 -3.833964275359010e+00 7.47664e-11 1.06014e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.446229768630400e-01 -1.446229768459461e-01 1.70940e-11 1.59638e-10 2 -7.268736657849727e+00 -7.268736657876235e+00 2.65077e-11 4.04522e-10 3 2.524723447855510e+00 2.524723447866759e+00 1.12483e-11 2.47462e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.804772868368629e+00 -2.804772868354206e+00 1.44227e-11 5.21272e-11 2 -3.115085008304330e-01 -3.115085008698898e-01 3.94568e-11 9.55205e-11 3 2.312680695695289e+00 2.312680695683764e+00 1.15250e-11 1.72420e-09 ----------------------------------------------------------------------------------------------------- 29 Si 1 -6.064147181450024e+00 -6.064147181484666e+00 3.46416e-11 1.60230e-09 2 -5.845632734687503e+00 -5.845632734738667e+00 5.11635e-11 6.85561e-10 3 -1.528343656382272e+01 -1.528343656382874e+01 6.02007e-12 4.67434e-09 * ----------------------------------------------------------------------------------------------------- 30 Si 1 4.276960397063030e+00 4.276960397060623e+00 2.40696e-12 1.66475e-10 2 3.799930642249049e+00 3.799930642265450e+00 1.64015e-11 2.54167e-10 3 -3.107959781925892e+00 -3.107959781927637e+00 1.74438e-12 4.58091e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.462923983859818e+00 5.462923983844886e+00 1.49329e-11 4.08263e-10 2 -2.067007669754861e+00 -2.067007669762479e+00 7.61746e-12 1.10803e-09 3 3.174083853962799e+00 3.174083853963968e+00 1.16840e-12 1.81842e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.078867225162497e-01 3.078867225080389e-01 8.21082e-12 1.91401e-10 2 7.238270173695454e+00 7.238270173717931e+00 2.24762e-11 1.19079e-10 3 3.518401169383233e+00 3.518401169345161e+00 3.80718e-11 1.13130e-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 = 28, direction = 2: |F_model - F_numer| error = ----------------------- = 1.26664e-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 -8.414565335439575e+01 -8.414565335425438e+01 1.41370e-10 3.39426e-09 2 -5.972756357091230e+01 -5.972756357114365e+01 2.31353e-10 2.97531e-09 3 4.651022812566715e+01 4.651022812557589e+01 9.12621e-11 1.22107e-10 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.486758637299782e+02 1.486758637297691e+02 2.09070e-10 5.48263e-09 2 3.531088670420192e+01 3.531088670426534e+01 6.34230e-11 3.56977e-10 3 -2.918512041122838e+01 -2.918512041119329e+01 3.50937e-11 2.30557e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.081966987371946e+01 -2.081966987380645e+01 8.69953e-11 2.02053e-10 2 1.798690157341274e+00 1.798690157360626e+00 1.93519e-11 2.20819e-09 3 2.241576992442848e+01 2.241576992449539e+01 6.69047e-11 2.79790e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.416415792337904e+01 -1.416415792335379e+01 2.52509e-11 1.01597e-10 2 -2.660877977705108e+01 -2.660877977679261e+01 2.58471e-10 1.89015e-10 3 -2.396245820712501e+01 -2.396245820722370e+01 9.86873e-11 3.74165e-09 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.256451328049001e+01 -1.256451328051532e+01 2.53060e-11 5.06174e-09 2 1.340999671465358e+01 1.340999671467073e+01 1.71543e-11 1.19609e-10 3 -1.898466957821876e+01 -1.898466957824985e+01 3.10898e-11 1.40382e-09 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.736767283222677e+01 -2.736767283247625e+01 2.49479e-10 1.41814e-09 2 7.746376728729199e+01 7.746376728650510e+01 7.86883e-10 1.28126e-09 3 -6.145689590011566e+01 -6.145689590022941e+01 1.13751e-10 5.12885e-04 * ----------------------------------------------------------------------------------------------------- 7 Si 1 1.900559168638854e+01 1.900559168637274e+01 1.58060e-11 4.91720e-10 2 -4.967521801171225e+01 -4.967521801175997e+01 4.77201e-11 2.26173e-10 3 7.329002634286387e+01 7.329002634312016e+01 2.56293e-10 5.92379e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 5.672649307289639e+00 5.672649307368895e+00 7.92557e-11 2.14174e-09 2 -2.228174857747311e+00 -2.228174857798979e+00 5.16676e-11 5.21363e-10 3 4.396486513385376e-01 4.396486513259968e-01 1.25407e-11 1.99428e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 -3.009196906578623e+01 -3.009196906577984e+01 6.39133e-12 1.18418e-09 2 6.714086696042169e+01 6.714086696046260e+01 4.09131e-11 5.33595e-09 3 3.648941840890526e+01 3.648941840897531e+01 7.00524e-11 7.16788e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 3.058863606937285e+01 3.058863606940151e+01 2.86597e-11 2.38729e-09 2 -5.161845466422199e+00 -5.161845466463813e+00 4.16138e-11 2.60203e-10 3 -1.711807798649271e+01 -1.711807798649324e+01 5.29354e-13 2.16424e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -9.199873225452986e+00 -9.199873225438996e+00 1.39906e-11 2.13724e-10 2 1.750089676612075e+00 1.750089676581577e+00 3.04976e-11 3.62692e-10 3 2.097849170954421e-01 2.097849170571529e-01 3.82892e-11 2.17119e-09 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.383907936358770e+01 -2.383907936352488e+01 6.28155e-11 2.77712e-10 2 -2.624961802243383e+01 -2.624961802241849e+01 1.53406e-11 1.39476e-10 3 8.683018377505890e+00 8.683018377473628e+00 3.22622e-11 1.17524e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 2.076476526812656e+01 2.076476526768061e+01 4.45947e-10 1.32582e-09 2 -2.155963798694734e+01 -2.155963798729207e+01 3.44734e-10 1.21288e-09 3 1.741433801588166e+00 1.741433801635251e+00 4.70848e-11 1.34474e-09 ----------------------------------------------------------------------------------------------------- 14 Si 1 -8.881349713745989e+00 -8.881349713772613e+00 2.66240e-11 5.89363e-10 2 4.746205494699587e+00 4.746205494709017e+00 9.42979e-12 9.53277e-10 3 -4.223525264853266e+00 -4.223525264856641e+00 3.37508e-12 9.59732e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 -5.501586514716097e+00 -5.501586514670485e+00 4.56115e-11 1.05105e-10 2 -1.029491406295364e+01 -1.029491406305834e+01 1.04700e-10 5.30960e-10 3 7.655238116136843e+00 7.655238116040674e+00 9.61693e-11 8.74913e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 4.077522503899229e-01 4.077522503839125e-01 6.01041e-12 5.01321e-10 2 7.378855656449930e-01 7.378855656555632e-01 1.05702e-11 6.04289e-11 3 -8.960883085704550e+00 -8.960883085689758e+00 1.47917e-11 1.62599e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.228031668426986e+01 -3.228031668429099e+01 2.11315e-11 4.47166e-10 2 -2.990522840167929e+01 -2.990522840159500e+01 8.42917e-11 1.28837e-08 * 3 -2.778920983701104e+01 -2.778920983703207e+01 2.10321e-11 1.18712e-09 ----------------------------------------------------------------------------------------------------- 18 Si 1 5.337998421128373e+01 5.337998421149791e+01 2.14186e-10 8.55600e-10 2 4.729366973285983e+01 4.729366973283195e+01 2.78817e-11 6.52435e-10 3 -4.257367751962549e+01 -4.257367751962396e+01 1.53477e-12 8.97749e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 3.236056578418619e+01 3.236056578420333e+01 1.71454e-11 9.49626e-10 2 -4.262182615519691e+01 -4.262182615537201e+01 1.75099e-10 3.80413e-09 3 1.387282332236292e+01 1.387282332229296e+01 6.99636e-11 1.22980e-09 ----------------------------------------------------------------------------------------------------- 20 Si 1 -3.085928475347219e+01 -3.085928475336592e+01 1.06272e-10 2.67629e-10 2 4.691442404243202e+01 4.691442404250283e+01 7.08056e-11 2.50978e-08 * 3 2.823834534862066e+01 2.823834534855030e+01 7.03579e-11 1.50229e-08 * ----------------------------------------------------------------------------------------------------- 21 C 1 -3.172024744431958e+01 -3.172024744443395e+01 1.14369e-10 6.05574e-10 2 -1.606386256253395e+01 -1.606386256259441e+01 6.04601e-11 2.39157e-09 3 -3.968899193840086e+01 -3.968899193834856e+01 5.22959e-11 8.14779e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.012450720472266e+01 -1.012450720473106e+01 8.39862e-12 1.14824e-10 2 -2.818252748094472e+01 -2.818252748093927e+01 5.44986e-12 4.43130e-10 3 -2.612645217414259e+01 -2.612645217427620e+01 1.33610e-10 3.79448e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 9.820818399473671e+00 9.820818399461320e+00 1.23510e-11 1.05576e-10 2 2.037957921159569e+01 2.037957921163733e+01 4.16414e-11 9.55708e-10 3 3.187101655255806e+01 3.187101655255841e+01 3.51719e-13 6.27072e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 2.638124143012486e+01 2.638124143008640e+01 3.84617e-11 1.55154e-10 2 -9.837509838505117e+00 -9.837509838523321e+00 1.82041e-11 3.70422e-10 3 3.470647591603366e+00 3.470647591607835e+00 4.46887e-12 1.55965e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.370809433856260e+00 -2.370809433851174e+00 5.08615e-12 8.20863e-11 2 -5.663169343486070e+00 -5.663169343486800e+00 7.30083e-13 1.33229e-10 3 -1.312621718976524e+01 -1.312621718964192e+01 1.23324e-10 2.79670e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.092198992681916e+00 1.092198992694271e+00 1.23554e-11 1.10054e-10 2 1.798508681274156e+00 1.798508681298260e+00 2.41038e-11 6.59157e-11 3 5.730368957405390e+00 5.730368957437686e+00 3.22959e-11 8.81206e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 7.254717584934132e+00 7.254717584990488e+00 5.63567e-11 1.18135e-08 * 2 -3.511658576209810e+01 -3.511658576216579e+01 6.76863e-11 4.05849e-09 3 -1.513204088509401e+00 -1.513204088567877e+00 5.84757e-11 1.21548e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -1.276535445890259e+01 -1.276535445891619e+01 1.35998e-11 4.30663e-09 2 2.126423433257806e+01 2.126423433258256e+01 4.50129e-12 3.50372e-10 3 4.080714556960897e+00 4.080714556930810e+00 3.00870e-11 3.74598e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 3.249562020851680e+00 3.249562020933208e+00 8.15281e-11 2.60847e-10 2 -9.431354765546450e+00 -9.431354765639352e+00 9.29017e-11 5.09308e-09 3 -5.732915902441024e+00 -5.732915902433205e+00 7.81952e-12 2.28010e-08 * ----------------------------------------------------------------------------------------------------- 30 C 1 -4.511250623969029e-01 -4.511250623811178e-01 1.57851e-11 7.90610e-11 2 6.787758965495907e+00 6.787758965513438e+00 1.75318e-11 6.06963e-11 3 8.949145537657220e+00 8.949145537659014e+00 1.79412e-12 1.56076e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.573085732547425e+00 -5.573085732521913e+00 2.55120e-11 9.98801e-11 2 3.151372422787625e+01 3.151372422793928e+01 6.30287e-11 1.21748e-09 3 3.037998235555442e+01 3.037998235563530e+01 8.08846e-11 2.69843e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.065909186905628e+00 4.065909186891188e+00 1.44400e-11 4.66916e-08 * 2 1.752831119151825e-02 1.752831119972170e-02 8.20344e-12 8.18035e-07 * 3 -3.585311804618613e+00 -3.585311804617450e+00 1.16307e-12 4.90301e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 11, direction = 3: |F_model - F_numer| error = ----------------------- = 1.82516e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.82516e-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 1.82516e-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.