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

To assess the accuracy of exchange-correlation approximations within density functional theory (DFT), diffusion quantum Monte Carlo (DMC) and DFT methods are used to calculate the energies of isomers of three covalently bonded carbon and boron clusters (${\text{C}}_{20}$, ${\text{B}}_{18}$, and ${\text{B}}_{20}$), and three metallic aluminum and copper clusters (${\text{Al}}_{13}$, ${\text{Al}}_{55}$, and ${\text{Cu}}_{13}$). 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.

Figure 1

(Color online) Energy relative to the average for isomers of (a) ${\text{C}}_{20}$, (b) ${\text{B}}_{18}$, (c) ${\text{B}}_{20}$, (d) ${\text{Al}}_{13}$, (e) ${\text{Al}}_{55}$, and (f) ${\text{Cu}}_{13}$ obtained using the DFT-LDA, DFT-PBE, DFT-PW91, and DMC methods. The DMC error bars are about 50 meV for ${\text{C}}_{20}$, less than 27 meV for ${\text{B}}_{18}$ and ${\text{B}}_{20}$, less than 48 meV for the Al clusters, and less than 60 meV for ${\text{Cu}}_{13}$.