Theory for a single excited state

Q Time-Independent Theories for a Single Excited State... 

Two theories for a single excited state [37—401 are the focus of this chapter. A nonvariational theory [37,38] based on Kato s theorem is reviewed in Section 9.2. Sections 9.3 and 9.4 summarize the variational density functional theory of a single excited state [39,40], Section 9.5 presents some application to atoms and molecules. Section 9.6 is devoted to discussion. 

THEORY FOR A SINGLE EXCITED STATE DIFFERENTIAL VIRIAL THEOREM... 

A recently proposed theory for a single excited state based on Kato s theorem is reviewed. This theory is valid for Coulomb systems. The concept of adiabatic connection leads to Kohn-Sham equations. Differenticil virial theorem is derived. Excitation energies and inner-shell transition energies are presented. 

Abstract The theory for a single excited state based on Kato s theorem is revisited. Density scaling proposed by Chan and Handy is used to construct a Kohn-Sham scheme with a scaled density. It is shown that there exists a value of the scaling factor for which the correlation energy disappears. Generalized OPM and KLI methods incorporating correlation are proposed. A KLI method as simple as the original KLI method is presented for excited states. 

Theory of exact exchange relations for a single excited state 13... 

In order to perform calculations one needs explicit expressions for the functionals. In the ground-state theory, exchange can be treated exactly (or very accurately) via the optimized potential method [60] (or KLI method [61]). Now, these methods are combined with density scaling for a single excited state. 

The simplest description of an excited state is the orbital picture where one electron has been moved from an occupied to an unoccupied orbital, i.e. an S-type determinant as illustrated in Figure 4.1. The lowest level of theory for a qualitative description of excited states is therefore a Cl including only the singly excited determinants, denoted CIS. CIS gives wave functions of roughly HF quality for excited states, since no orbital optimization is involved. For valence excited states, for example those arising from excitations between rr-orbitals in an unsaturated system, this may be a reasonable description. There are, however, normally also quite low-lying states which essentially correspond to a double excitation, and those require at least inclusion of the doubles as well, i.e. CISD. 

Variational Theory for a Nondegenerate Single Excited State. 125... 

Variational Theory for a Degenerate Single Excited State. 127... 

There are other noteworthy single excited-state theories. Gorling developed a stationary principle for excited states in density functional theory [41]. A formalism based on the integral and differential virial theorems of quantum mechanics was proposed by Sahni and coworkers for excited state densities [42], The local scaling approach of Ludena and Kryachko has also been generalized to excited states [43]. 

VARIATIONAL THEORY FOR A NONDEGENERATE SINGLE EXCITED STATE... 

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