Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-the renormalized ALDA and electron gas kernels

TL;DR

This paper evaluates various exchange-correlation kernels within adiabatic-connection fluctuation-dissipation DFT for predicting the structural properties of solids, showing that model kernels improve correlation energy estimates while preserving accuracy.

Contribution

It introduces and tests a set of model kernels, including the renormalized ALDA, for better correlation energy calculations in solids within the ACFD-DFT framework.

Findings

Model kernels correct RPA overestimation of correlation energy.

Kernels maintain high accuracy for lattice constants and bulk moduli.

Improved description of atomization energy of H₂ molecule.

Abstract

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently-introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence or (c) display a 1/$k^2$ divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally-bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF) and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H$_2$ molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA's tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.