Hedin and Lundqvist

Analytic or semi-analytic many-body methods provide an independent estimate of ec( .>0- Before the Diffusion Monte Carlo work, the best calculation was probably that of Singwi, Sjblander, Tosi and Land (SSTL) [38] which was parametrized by Hedin and Lundqvist (HL) [39] and chosen as the = 0 limit of Moruzzi, Janak and Williams (MJW) [40]. Table I shows that HL agrees within 4 millihartrees with PW92. A more recent calculation along the same lines, but with a more sophisticated exchange-correlation kernel [42], agrees with PW92 to better than 1 millihartree. 

Hedin- Lundqvist, HL, exchange-correlation potential [37], which is equivalent to our earlier use [130] of the von Barth-Hedin potential, vBH, [38] with parameter values as used by Hedin and Lundqvist. Calculations were also performed using the Xa form, with a = 0.7 [4] and the Vosko-Wilk-Nusair form of Vxc [41]. A somewhat lower total energy was obtained by inclusion of the 3d, and in particular the 3p and 3d, basis functions, compared with the results obtained using the minimal basis set. 

For high density system, the enhancement factor becomes unity, and exchange effects dominate over the correlation effects. When the density becomes lower, the enhancement factor kicks in and includes correlation effects into the exchange energies. The enhancement factor is not unique, but can be derived differently in different approximations. The most reliable ones are parameterizations of molecular Monte-Carlo data. Some well known, and regularly used, parameterizations have been made by Hedin and Lundqvist [29], von Barth and Hedin [22], Gun-narsson and Lundqvist [30], Ceperly and Adler [31], Vosko, Wilk, and Nusair [32], and Perdew and Zunger [27]. 

Several useful approximations to > or have been proposed (see Jones and Gunnarson [38], for review). The fact that most of them give very similar total energies suggests that the essence of is reasonably well known. We adopted the Hedin and Lundqvist [39] form for the potential ... 

The photoabsorption spectrum a(co) of a cluster measures the cross-section for electronic excitations induced by an external electromagnetic field oscillating at frequency co. Experimental measurements of a(co) of free clusters in a beam have been reported, most notably for size-selected alkali-metal clusters [4]. Data for size-selected silver aggregates are also available, both for free clusters and for clusters in a frozen argon matrix [94]. The experimental results for the very small species (dimers and trimers) display the variety of excitations that are characteristic of molecular spectra. Beyond these sizes, the spectra are dominated by collective modes, precursors of plasma excitations in the metal. This distinction provides a clear indication of which theoretical method is best suited to analyze the experimental data for the very small systems, standard chemical approaches are required (Cl, coupled clusters), whereas for larger aggregates the many-body perturbation methods developed by the solid-state community provide a computationally more appealing alternative. We briefly sketch two of these approaches, which can be adapted to a DFT framework (1) the random phase approximation (RPA) of Bohm and Pines [95] and the closely related time-dependent density functional theory (TD-DFT) [96], and (2) the GW method of Hedin and Lundqvist [97]. 

Within this approximation for pxc Hedin and Lundqvist [18] derived the current expression for Vxc ... 

As an example we consider photoemission and we essentially follow Hedin and Lundqvist (1969). The system is assumed to be described by a Hamiltonian H in the absence of any external fields. We introduce an operator t, which describes... 

In this section, the ground state properties of the lanthanides are studied with a first principles all-electron total energy band structure method. The LMTO method is employed within the local density (LDA) and local spin density (LSD) functional approximations (Hohenberg and Kohn 1964, Kohn and Sham 1965, Gunnarsson and Lundqvist 1976). The von Barth-Hedin (1972) interpolation formula is used for the exchange and correlation potential with the parameters of Hedin and Lundqvist (1971) and RPA scaling (Janak 1978). 

Thus, the many-body problem is reduced to a set of effective one-electron equations of the form of eq. (4), with an orbital-independent potential if the exchange-correlation potential is known. Approximate expressions for and have been derived by many authors (see e.g. Kohn and Sham 1965, Gunnarsson and Lundqvist 1976, Moruzzi et al. 1978, Mackintosh and Andersen 1979, Koelling 1981, Kohn and Vashista 1983, Hedin and Lundqvist 1971, von Barth and Hedin 1972). In particular, the local density approximation (LDA) uses for [n] the exchange and correlation energy of a uniform electron gas at the same local density. The exchange and correlation potential is then local. 

Hedin, L. and Lundqvist, S. (1969) Effects of electron-electron and electron-phononinteraction on the one-electron states of solids, In Solid state Physics, Eherenreich, H., Seitz, F. and Turnbull, D. (Eds.), Academic, New York,Vol. 23, pp. 1-181. 

Lars Hedin and Stig Lundqvist, Solid State Physics, (Academic Press, New York, 1969), Supplement 23. 

Hedin, L. and Lundqvist, B.I. (1971) Explicit local exchange-correlation potentials, J. Phys. C 4, 2064-2083. 

L. Hedin and S. Lundqvist, in Solid State Physics. Advances in Research and Applications, Vol. 23, ed. F. Seitz, H. Ehrenreich and D. Turnbull (Academic Press, New York, London, 1969), pp. 2-181. 

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