Correlation energies of inhomogeneous many-electron systems

We generalize the uniform-gas correlation energy formalism of Singwi, Tosi, Land and Sjolander to the case of an arbitrary inhomogeneous many-particle system. For jellium slabs of finite thickness with a self-consistent LDA groundstate Kohn-Sham potential as input, our numerical results for the correlation energy agree well with diffusion Monte Carlo results. For a helium atom we also obtain a good correlation energy.Comment: 4 pages,1 figur

Metal Surface Energy: Persistent Cancellation of Short-Range Correlation Effects beyond the Random-Phase Approximation

The role that non-local 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 non-uniform 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 non-local 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.Comment: 5 pages, 1 figure, to appear in Phys. Rev.

Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

We calculate the correlation energy of a two-dimensional homogeneous electron gas using several available approximations for the exchange-correlation kernel $f_{\rm xc}(q,\omega)$ entering the linear dielectric response of the system. As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431 (2000)] on the three-dimensional electron gas, we give attention to the relative roles of the wave number and frequency dependence of the kernel and analyze the correlation energy in terms of contributions from the $(q, i\omega)$ plane. We find that consistency of the kernel with the electron-pair distribution function is important and in this case the nonlocality of the kernel in time is of minor importance, as far as the correlation energy is concerned. We also show that, and explain why, the popular Adiabatic Local Density Approximation performs much better in the two-dimensional case than in the three-dimensional one.Comment: 9 Pages, 4 Figure

Evolution of electronic and ionic structure of Mg-clusters with the growth cluster size

The optimized structure and electronic properties of neutral and singly charged magnesium clusters have been investigated using ab initio theoretical methods based on density-functional theory and systematic post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system. We have systematically calculated the optimized geometries of neutral and singly charged magnesium clusters consisting of up to 21 atoms, electronic shell closures, binding energies per atom, ionization potentials and the gap between the highest occupied and the lowest unoccupied molecular orbitals. We have investigated the transition to the hcp structure and metallic evolution of the magnesium clusters, as well as the stability of linear chains and rings of magnesium atoms. The results obtained are compared with the available experimental data and the results of other theoretical works.Comment: 30 pages, 10 figures, 3 table

Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a {\it fundamental limitation} of the local density approximation (LDA), and its semi-local extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semi-local (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation (ADA) is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi-)local density functional method.Comment: 21 pages including 9 figures, to be published in Phys. Rev.

Density-functional versus wave-function methods: Toward a benchmark for the jellium surface energy

For the surface energy of jellium at alkali-metal densities, the local-density approximation (LDA) and more advanced density-functional methods disagree strongly with the wave-function-based Fermi hypernetted-chain and diffusion Monte Carlo methods. We present a wave-vector interpolation correction to the generalized gradient approximation which gives jellium surface energies consistent with two other estimates based on advanced density functionals. LDA makes compensating errors at intermediate and small wave vectors. Studies of small jellium clusters also support the density-functional estimate for the jellium surface energ