Electronic excitations: densityfunctional versus manybody Green'sfunction approaches
Abstract
Electronic excitations lie at the origin of most of the commonly measured spectra. However, the firstprinciples computation of excited states requires a larger effort than groundstate calculations, which can be very efficiently carried out within densityfunctional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, manybody perturbation theory, is based on a set of Green'sfunction equations, starting with a oneelectron propagator and considering the electronhole Green's function for the response. Key ingredients are the electron's selfenergy Σ and the electronhole interaction. A good approximation for Σ is obtained with Hedin's GW approach, using densityfunctional theory as a zeroorder solution. Firstprinciples GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electronhole interaction is well described by the BetheSalpeter equation, via a functional derivative of Σ. An alternative approach to calculating electronic excitations is the timedependent densityfunctional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the BetheSalpeter one, but with a twopoint, rather than a fourpoint, interaction kernel. At present, the simple adiabatic localdensity approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of manybody perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.
 Publication:

Reviews of Modern Physics
 Pub Date:
 April 2002
 DOI:
 10.1103/RevModPhys.74.601
 Bibcode:
 2002RvMP...74..601O
 Keywords:

 71.15.Mb;
 02.30.f;
 01.30.Rr;
 Density functional theory local density approximation gradient and other corrections;
 Function theory analysis;
 Surveys and tutorial papers;
 resource letters