Accurate prediction of heats of formation by a combined method of B3LYP and neural network correction

Abstract

Recently, we proposed the X1 method which combines the B3LYP/6-311+G(3df,2p)//B3LYP/6-311+G(d,p) method with a neural network correction for an accurate yet efficient prediction of heats of formation (Wu and Xu, J Chem Phys 2007, 127, 214105). In this contribution, we discuss in detail how to set up the X1 neural network. We give examples, showing how to apply the X1 method and how the applicability of X1 can be extended. The overall mean absolute deviation of the X1 method from experiment for the 488 heats of formation is 1.52 kcal/mol compared with 9.44 kcal/mol for the original B3LYP results.

Gas‐Phase Thermodynamics as a Validation of Computational Catalysis on Surfaces: A Case Study of Fischer–Tropsch Synthesis

“…Indeed, as the chain length grows, a small error would eventually grow into a large error. Note that it would also be possible to adjust some of the PBE or B3LYP values [44,69,[73][74][75] to achieve the correct ther-modynamics of the net reaction. Table 7 lists the heats of reaction for Equation (1) to produce alkanes (C n H 2 n + 1 ) as n increases from 1 to 8.…”

The X1s Method for Accurate Bond Dissociation Energies

“…[10,36] {Wx ij } and {Wy j } are sets of the connection weights, where {Wx ij } connects the input neurons and the hidden neurons, and {Wy j } connects the hidden neurons and the output neuron. Since we use the numbers of each constituent element as descriptors, the number of weights may seem large.…”

“…Previously, we have put forward the X1 method, which combines B3LYP with a neural network (NN) correction, for an accurate yet efficient prediction of HOFs. [10,36] Without paying additional computational cost, X1 significantly eliminates the notorious size-dependent errors of B3LYP and reduces its MAD from 5.6 to 1.4 kcal mol À1 for HOFs of the G3/99 set. Furthermore, X1 reduces the B3LYP MAD for a set of 92 BDEs from 5.5 to 2.4 kcal mol À1 .…”

Can B3LYP be improved by optimization of the proportions of exchange and correlation functionals?

“…The performance in prediction of enthalpies of formation is often used to evaluate some new quantum chemical approaches, [11][12][13][14][15][16][17][18][19][20][21][22][23]41] here the performance of OpB3LYP is also evaluated against enthalpies of formation subset. Due to small molecules having up to three heavy atoms in G2-1 test set, MADs of B3LYP and OpB3LYP are both less than 3.0 kcal/mol.…”

“…Owing to its excellent cost-to-performance ratio, B3LYP functional was not abandoned, and great efforts have been made to improve it. [11][12][13][14][15][16][17][18][19][20][21][22][23] All improvements were obtained through complicated corrections, to a certain extent the ill-favored defects of B3LYP have been overcome. But the inconvenient postcorrections inevitably lead to accessorial computation cost.…”