Quantum-chemical basis for second-order polarizabilities

3 Quantum-chemical basis for second-order polarizabilities 

The molecular polarizabilities can be interpreted quantum mechanically by using the methods of time-dependent perturbation theory. Under the influence of the electric field, the molecular ground state ( g)) is changed by admixture of excited states ( /), m). ..). Collections of such expressions are available in the literature (Ward, 1965 Orr and Ward, 1971 Bishop, 1994b). A comprehensive treatment has also been given by Flytzanis (1975). Here, we only quote the results for the linear optical polarizability o (-w w) and the second-order polarizability /3(-2w w,w). The linear optical polarizability may be represented by the sum of two-level contributions (45). 

They arise from ground state g) and excited state /) and are given by (46). 

/rj = l [1 1 g) is the Cartesian component r of the electric transition dipole moment between states g) and Z) and is a dispersion function 

The second-order polarizability can be written as a sum of two-level contributions and a double sum of three-level contributions in the form (48) (Wolff et al 1997), 

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Non-linear optics non-Unear susceptibilities Molecular polarizabilities 133 Quantum-chemical basis for second-order polarizabilities Perturbation theoretical expressions 136 Molecular design and two- and three-level contributions Molecular orbital calculations for second-order polarizabilities of rr systems 141... 

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