Double-hybrid density-functional theory made rigorous

TL;DR

This paper rigorously derives a class of double-hybrid density functionals that combine Hartree-Fock exchange, second-order Moller-Plesset correlation, and semilocal functionals, with minimal empirical parameters, and evaluates their performance.

Contribution

It provides a theoretical foundation for double-hybrid functionals with only one empirical parameter, connecting them to standard methods and assessing their accuracy.

Findings

The 1DH-BLYP approximation performs well on test sets.

Neglecting density scaling simplifies the double-hybrid scheme.

Theoretical support for standard double-hybrid methods is established.

Abstract

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Moller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.