Density functional theory/single excitation

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. 

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]. 

The fluorescence properties of free 2AP are simple. AJablonski diagram of 2AP (Fig. 13.IB) computed with time-dependent density functional theory (TDDFT) finds a dominant singlet excited state transition from S() to at 292 nm (Jean and Hall, 2001). In solution, the free nucleobase has a fluorescence excitation maximum of 305 nm and an emission maximum of 360 nm at pH 7. Its quantum yield is not high 0.68 at pH 7.0 in 100 mM NaCl, 25 °C. Its fluorescence lifetime in aqueous solution is 10 ns at 22 °C and is described by a single exponential decay. 

By contrast, the alternative PCM-LR approach [15-17] determines in a single step calculation the excitation energies for a whole manifold of excited states. This general theory may be combined with the Time-Dependent Density Functional Theory (TDDFT) as QM level for the solute. Within the PCM-TDDFT formalism, the excitation energies are obtained by proper diagonalization of the free energy functional Hessian. 

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