Excited states, single discussion

Cole JM, Raithby PR, Wulff M, Schotte F, Plech A, Teat SJ, Bushnell-Wye G (2002) Nanosecond time-resolved crystallography of photo-induced species case smdy and instrument development for high-resolution excited-state single-crystal structure determination. Faraday Discuss 122 119-129... 

All the previous discussion in this chapter has been concerned with absorption or emission of a single photon. However, it is possible for an atom or molecule to absorb two or more photons simultaneously from a light beam to produce an excited state whose energy is the sum of the energies of the photons absorbed. This can happen even when there is no intemrediate stationary state of the system at the energy of one of the photons. The possibility was first demonstrated theoretically by Maria Goppert-Mayer in 1931 [29], but experimental observations had to await the development of the laser. Multiphoton spectroscopy is now a iisefiil technique [30, 31]. 

The discussion in the previous sections assumed that the electron dynamics is adiabatic, i.e. the electronic wavefiinction follows the nuclear dynamics and at every nuclear configuration only the lowest energy (or more generally, for excited states, a single) electronic wavefiinction is relevant. This is the Bom-Oppenlieimer approxunation which allows the separation of nuclear and electronic coordinates in the Schrodinger equation. 

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. 

Its irreducibility the prime means that the only transitions allowed in Eq. (429) are such that one starts with a single excited particle wave number (k 0) and arrives at the final state kf without any such intermediate state. As discussed previously in other contexts (see Section II-C), this condition implies that describes a dynamical process that is localized both in space and time ... 

In the present work the Cl procedure ( ) employed includes single, double, and higher excited configurations, and can treat in a natural way, using the localized monomer basis orbitals, intra- as well as inter-molecular excitations. States which arise from such monomer-based excitations can then be interpreted in terms of their locally-excited, excitonic, CT, or "mixed" character. Details as to the nature of the dimer states have been discussed in our earlier works (7, 8). 

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