Time-dependent local density

Casida, M. E., Jamorski, C., Casida, K. C., Salahub, D. R., 1998, Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory Characterization and Correction of the Time-Dependent Local Density Approximation Ionization Threshold , J. Chem. Phys., 108, 4439. 

The effective Time Dependent Kohn-Sham (TDKS) potential vks p (r>0 is decomposed into several pieces. The external source field vext(r,0 characterizes the excitation mechanism, namely the electromagentic pulse as delivered by a by passing ion or a laser pulse. The term vlon(r,/) accounts for the effect of ions on electrons (the time dependence reflects here the fact that ions are allowed to move). Finally, appear the Coulomb (direct part) potential of the total electron density p, and the exchange correlation potential vxc[p](r,/). The latter xc potential is expressed as a functional of the electronic density, which is at the heart of the DFT description. In practice, the functional form of the potential has to be approximated. The simplest choice consists in the Time Dependent Local Density Approximation (TDLDA). This latter approximation approximation to express vxc[p(r, /)]... 

For multi-electron systems, it is not feasible, except possibly in the case of helium, to solve the exact atom-laser problem in 3 -dimensional space, where n is the number of electrons. One might consider using time-dependent Hartree Fock (TDHF) or the time-dependent local density approximation to represent the state of the system. These approaches lead to at least njl coupled equations in 3-dimensional space which is much more attractive computationally. For example, in TDHF the wave function for a closed shell system can be approximated by a single Slater determinant of time dependent orbitals,... 

In the following we describe the optical properties of metal clusters within the jellium model. We begin by introducing the TDLDA (time-dependent local density approximation)... 

The theoretical framework for all regimes is the (time-dependent) local-density approximation (TDLDA) which is much discussed also in Chapter 1 of this book. We thus will present here only a short discussion of the essential ingredients and compare it with the analog mean-field models in nuclear physics. This is done as a starter in the next section. 

Fig. 1 Size dependence of optical gaps of silicon nanocrystals calculated using quantum Monte Carlo (QMC), time-dependent local-density approximation (TD-LDA), Hartree-Fock configuration interactions (HF-CI), and semiempirical tight binding (TB). The inset shows schematically the bandgap enlargement due to reducing die nanocrystal size...

Casida ME, Jamorski C, Casida KC, Salahub DR (1998) Molecular excitation energies to high-l5ting bound states from timedependent density-functional response theory characterization and correction of the time-dependent local density approximation ionization threshold. J Chem Phys 108 4439 1449... 

Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory Characterization and Correction of the Time-Dependent Local Density Approximation Ionization Threshold. 

Phys., 113, 7062 (2000). Charge-Transfer Correction for Improved Time-Dependent Local Density Approximation Excited-State Potential Energy Curves Analysis within the Two-Level Model with Illustration for H2 and LiH. 

Figure 5.2 Absorption cross section of SissHse calculated using (1) tight-binding approach with local field effects (solid thick line), (2) the tight-binding energy levels with a classical model for the surface polarization contribution (dashed line) and (3) a time-dependent local density approximation (TDLDA) within density functional theory (solid thin line). TDLDA results from ref. 39.

A TIME-DEPENDENT LOCAL DENSITY APPROXIMATION OF ATOMIC PHOTOIONIZATION... 

Concurrent with these developments, the density functional formalism has emerged as an alternative to a Hartree Fock based description of the electronic structure of atoms, molecules and solids. In its most common form as a local density approximation (LDA) the question of atomic photoionization can again be addressed. Here too, one finds that the simplest approach falls to adequately charr-. acterize the experimental results in many cases. However, a recent straightforward generalization of density functional theory to time-dependent phenomena has been applied successfully to the problem of the optical response of atoms. In particular, highly accurate photoionization cross sections can be readily obtained. The purpose of the present article is to review this time-dependent local density approximation (TDLDA), illustrate its scope and limitations and compare it to the more familiar Hartree-Fock based methods. 

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