Quantum Monte Carlo studies of covalent and metallic clusters: Accuracy of density functional approximations

Abstract

To assess the accuracy of exchange-correlation approximations within density functional theory ͑DFT͒, diffusion quantum Monte Carlo ͑DMC͒ and DFT methods are used to calculate the energies of isomers of three covalently bonded carbon and boron clusters ͑C 20 , B 18 , and B 20 ͒, and three metallic aluminum and copper clusters ͑Al 13 , Al 55 , and Cu 13 ͒. We find that local and semilocal DFT methods predict the same energy ordering as DMC for the metallic clusters but not for the covalent clusters, implying that the DFT functionals are inadequate in such systems. In addition, we find that DFT fails to describe energy reductions arising from Jahn-Teller distortions.

Failure of Conventional Density Functionals for the Prediction of Molecular Crystal Polymorphism: A Quantum Monte Carlo Study

“…Even for some covalent clusters, such as C 20 or B 20 , several commonlyused functionals have been shown to be highly unreliable in predicting geometries and relative ground-state energies. 18 Nevertheless, in most cases, DFT is essentially the most accurate method available due to its favorable computational cost.…”

Quantum Monte Carlo vs. Density Functional Methods for the Prediction of Relative Energies of Small Si-C Clusters

“…To quantify to which extent the DFT approaches can predict the relative stability of the cluster isomers, we perform the correlation analysis introduced in Ref. [4]. The correlation (corr) between the DFT and DMC energies and the relative amplitude (L) is given by…”

“…The question arises how reliable are the widely used density functional theory (DFT) based approaches for the determination of these semi-empirical potentials, and how accurately they are able to predict, for example, the relative energies of small cluster isomers. In a recent study, Hsing and coworkers [4] have shown that the DFT methods are able to describe correctly the relative stability of monoatomic metallic aluminum and copper cluster isomers, but fail in predicting the relative stability of covalently bonded carbon and boron isomers. For benchmark calculations, the diffusion Monte Carlo (DMC) method was used, which is the most accurate method for system of interacting electrons known up to now.…”

Towards novel boron nanostructural materials

“…Monte Carlo confirmation: Different isomers of boron clusters B 18 were also investigated by Hsing et al 72 using diffusion quantum Monte Carlo methods (DMC) to calculate their relative energies. The aim of this work was first to examine the accuracy of various density functional theory (DFT) exchange-correlation (XC) functionals in predicting the relative energies of cluster isomers and to provide new benchmark data.…”

“…Monte Carlo confirmation: In order to examine the accuracy of various DFT exchange-correlation XC functionals in predicting the relative energies of cluster isomers and to provide new benchmark data, Hsing et al 72 16,18,20,24) using quantum chemical methods.…”