# Singlet–Triplet Gap in Covalently and Weakly Bound Carbenes: Studying the Dependence on the Exchange–Correlation Functional

## TL;DR

This paper evaluates how different computational methods perform in predicting energy gaps in carbenes, finding that simpler methods sometimes work better than more complex ones.

## Contribution

The study reveals that lower-level functionals can outperform more advanced ones for carbene singlet–triplet gaps.

## Key findings

- Low-level functionals like BLYP and PBE show lower errors than hybrid or double-hybrid functionals for carbene energy gaps.
- Double-hybrid functionals like PBE-QIDH correct biases in triplet state energy predictions.
- Recommended double-hybrid functionals achieve ±1–2 kcal/mol accuracy for carbene studies.

## Abstract

We systematically analyze here the performance of density
functional
approximations for the calculation of the singlet–triplet gap
of covalently bound carbenes (i.e., substituted arylcarbenes of increasing
size and with different electroactive substituents) and weakly bound
carbenes (diphenylcarbene noncovalently interacting with H2O, CH3OH, ClCF3, BrCF3, and ICF3 molecules). The calculations revealed an unexpected functional
dependence, in the sense that low levels of the functional hierarchy
(e.g., BLYP or PBE) provide lower errors than more sophisticated functionals
(e.g., hybrid and double-hybrid expressions), thus evidencing a subtle
yet marked interplay between the ingredients of any modern exchange–correlation
functional. The decomposition of the results as a function of those
ingredients allowed us to isolate those functionals overestimating
(by default) the energy stability of the triplet state and how (nonempirical)
formulations of double-hybrid functional are able to cope with that
initial bias. We recommend double-hybrid functionals (e.g., PBE-QIDH)
to get robust and sufficiently accurate results (averaged deviation
of ±1–2 kcal/mol with respect to reference results) for
other applications and studies involving these challenging carbene
species.