Metal surface energy: Persistent cancellation of short-range correlation effects beyond the random phase approximation

J M Pitarke,J P Perdew

doi:10.1103/physrevb.67.045101

Abstract

The role that nonlocal short-range correlation plays at metal surfaces is investigated by analyzing the correlation surface-energy into contributions from dynamical density fluctuations of various two-dimensional wave vectors. Although short-range correlation is known to yield considerable correction to the ground-state energy of both uniform and nonuniform systems, short-range correlation effects on intermediate and short-wavelength contributions to the surface formation energy are found to compensate one another. As a result, our calculated surface energies, which are based on a nonlocal exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation, and support the conclusion that the error introduced by the local-density approximation is small.

Highlights

The widely used Kohn-Sham formulation of the densityfunctional theory1 ͑DFTrequires approximations to the exchange-correlationXCenergy Excn(r)͔
Our calculated surface energies, which are based on a nonlocal exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation, and support the conclusion that the error introduced by the local-density approximation is small
We have investigated the role that short-range correlation plays at metal surfaces, on the basis of a wave-vector analysis of the correlation surface energy

Summary

INTRODUCTION

The widely used Kohn-Sham formulation of the densityfunctional theory1 ͑DFTrequires approximations to the exchange-correlationXCenergy Excn(r)͔. The simplest approximation to this functional is the so-called local-density approximationLDA, where Excn(r)͔ is given at each point by the XC energy of a uniform electron gas at the local density This approximation was found to be remarkably accurate in some rather inhomogeneous situations,[2] and its widespread use in condensed-matter physics led to the early success of DFT. While RPA is known to be a poor approximation for the total correlation energy, our calculations show that it is a surprisingly good approximation for those changes in the correlation energy that arise in surface formation This is in contrast with FHNC and DMC slab calculations,[8,9] which predict surface energies that are significantly higher than those obtained either in the LDARef. 3͒ or in a fully nonlocal RPA.[14]. We show that surface formation energies obtained from slab calculations, either by a linear fit in the slab thickness[8] or as differences between slab energies and an independently determined bulk energy,[9] may result in substantial imprecision, and conclude that wave-function-based estimates need to be reconsidered

THEORETICAL FRAMEWORK

RESULTS AND DISCUSSION

SUMMARY AND CONCLUSIONS