Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

Abstract

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.

A Trip to the Density Functional Theory Zoo: Warnings and Recommendations for the User

“…39 contains an in-depth review of DHDFs and Ref. 40 provides the most recent overview of DHDF names and performance. Note that Fig.…”

“…In mid 2018, we increased the number of assessed DFAs in two subsequent studies to a total of 325 dispersion-corrected and uncorrected methods, with 115 dispersion-corrected ones being analysed thoroughly. [40,74] We focussed on the four highest rungs on Jacob's Ladder, as it had already been established that LDA functionals were not viable for molecular chemistry applications. [33] The three papers combined can be regarded as the largest published DFT benchmark study.…”

ACCDB: A collection of chemistry databases for broad computational purposes

“…Very recently, Goerigk and his group also used GMTKN55 to assess the performance of 29 double‐hybrid functionals. In a similar fashion to what was done by Bun Chan for MGCDB84, a “diet” version of the GMTKN55 database was recently proposed by Gould…”

“…Very recently, Goerigk and his group also used GMTKN55 to assess the performance of 29 doublehybrid functionals. [49] In a similar fashion to what was done by Bun Chan for MGCDB84, a "diet" version of the GMTKN55 database was recently proposed by Gould. [50] [a] For further details of all subsets of each database-and clarifications on the corresponding reference-see the Supporting Information.…”

Clam‐like Cyclotricatechylene‐based Capsules: Identifying the Roles of Protonation State and Guests as well as the Drivers for Stability and (Anti‐)Cooperativity

“…Herein, we analyse interaction energies without taking geometry-relaxation effects into account, as is common in such studies. [62,[66][67][68][69][70] In other words, when calculating interaction energies, the monomers assume the same internal coordinates as in the bound trimer. As such, the total interaction energy ΔE can be calculated as:…”