Is explicitly correlated double hybrid DFT advantageous for vibrational frequencies?

TL;DR

This study evaluates the benefits of explicitly correlated F12 methods in double hybrid density functional theory for vibrational frequency calculations, showing accelerated basis set convergence and practical accuracy with smaller basis sets.

Contribution

It demonstrates that F12 geminals significantly improve basis set convergence for vibrational frequencies in double hybrid DFT, making calculations more efficient and accurate.

Findings

F12 accelerates basis set convergence by two zeta steps

Conventional triple-zeta basis sets are sufficiently accurate for frequencies

Implementation of analytical derivatives could further enhance F12 applicability

Abstract

We have investigated the effect of F12 geminals on the basis set convergence of harmonic frequencies calculated using two representative double-hybrid density functionals, namely B2GP-PLYP and revDSD-PBEP86-D4. Like previously found for energetics [N. Mehta and J. M. L. Martin, \textit{J. Chem. Theor. Comput.} \textbf{18}, 5978--5991 (2022)] one sees an acceleration by two zeta steps, such that even the cc-pVDZ-F12 basis set is quite close to the complete basis set (CBS) limit. However, the basis set convergence problem is not as acute as for energetics, and compared to experimental harmonic frequencies, conventional orbital calculations with augmented triple zeta quality basis set are acceptably close to the CBS limit, and can be carried out using analytical second derivatives. An efficient implementation of double hybrid-F12 analytical derivatives would make the F12 approach attractive in the sense that even an $spd$ orbital basis set would be adequate. For the accurate revDSD-PBEP86-D4 functional, the role of differing local correlation terms (Perdew-Zunger 1981 vs. VWN5) in different electronic structure programs has been investigated: while optimal double hybrid parameters and performance statistics for energetics as well as frequencies differ slightly between the two implementations, these differences are insignificant for practical purposes.