Rationale for a new class of double-hybrid approximations in density-functional theory

TL;DR

This paper rationalizes a new class of double-hybrid density functional approximations that interpolate between MP2 and density-functional theory, supported by numerical results with the PBE functional.

Contribution

It provides a theoretical understanding of a double-hybrid model combining MP2 and DFT, linking it to the density-scaled correlation functional approach.

Findings

The double-hybrid model interpolates between MP2 and DFT.

Numerical results with PBE support the model's relevance.

The model is understood as a linear approximation of the density-scaled correlation functional.

Abstract

We provide a rationale for a new class of double-hybrid approximations introduced by Br\'emond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by $\l$ and second-order M{\o}ller-Plesset (MP2) correlation weighted by $\l^3$. We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional $E_c[n_{1/\l}]$ by a linear function of $\l$, interpolating between MP2 at $\l=0$ and a density-functional approximation at $\l=1$. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.