Improving B3LYP heats of formation with three‐dimensional molecular descriptors

Abstract

In the present work, we propose the X3D method that extends the B3LYP method by correcting its errors on heats of formation of hydrocarbons (HCs) with three-dimensional (3D) molecular descriptors. Inspired by the widely used Wiener index, these 3D descriptors are developed to improve over the original B3LYP method for a better description of atom-atom, atom-bond and bond-bond interactions. On top of a training set of only 45 species, the X3D method is validated against various sets of different chemistry, displaying an overall near chemical accuracy. In particular, X3D improves over B3LYP, reducing its mean absolute errors from 28.4 to 0.3 kcal/mol for (Set 1) 21 n-alkanes up to n-C32 H66 , from 19.3 to 0.6 kcal/mol for (Set 2) n-C7 H16 and its branched isomers, from 29.5 to 1.6 kcal/mol for (Set 3) 36 polycyclic saturated HCs, from 8.6 to 1.1 kcal/mol for (Set 4) 41 C6 H8 isomers of rings, alkenes, alkynes, and cumulenes, from 20.3 to 0.6 kcal/mol for (Set 5) 41 benzene-based compounds, and 8.1 to 1.3 kcal/mol for (Set 6) 66 radicals, etc. Comparisons with the G4 results are also presented. © 2016 Wiley Periodicals, Inc.

Accurate heats of formation of polycyclic saturated hydrocarbons predicted by using the XYG3 type of doubly hybrid functionals

“…As shown in Table , this observation applies to other similar compounds. Hence, B3LYP leads to similar errors for HOFs of compounds 1, 6, 13, 14, and 33 to those of the respective n‐alkanes from the atomization procedure, which are smaller than those for the other PSHs of the same size.…”

“…For example, the X1 and X1s methods applied some neural‐network corrections to the B3LYP HOFs, where MADs of 6.7 and 5.9 kcal/mol, respectively, have been achieved for this PSH set. Notably, the recently developed X 3D scheme, where corrections in terms of some three‐dimensional descriptors were applied to the B3LYP HOFs, performs satisfactorily, giving an MAD of only 1.6 kcal/mol, which is comparable to that of the G4 theory of 1.4 kcal/mol …”

“…For compounds 20, and 23–30, there are no experimental HOFs available. Hence, the high level G4 calculation results are used as the reference data instead. Recently, Karton and coworkers have calculated HOFs for a set platonic hydrocarbon cages, (CH) n ( n = 4, 6, 8, 10, 12, 20), by means of high‐level thermochemical procedures .…”

“…distributions for the calculated HOFs of 36 polycyclic saturated hydrocarbons with B2PLYP and B2PLYP‐D3BJ. The experimental or G4 values are used as the reference. See Figure for the structure corresponding to the compound number.…”

“…). For HOF of n‐C 10 H 22 , B3LYP yields an error of −24.0 kcal/mol via the atomization procedure. Hence, fused ring structures increase B3LYP errors by another 7–17 kcal/mol.…”