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Dispersion formulas for hyperpolarizability averages

Christof Hättig

*Department of Chemistry, Århus University,
DK-8000 Århus C, Denmark
*

*Mol. Phys.*, **94** (1998) 455-460

(Received 12 December 1997; accepted 22 January 1998)

The frequency-dependence of experimentally-derived or point-wise ab
initio calculated hyperpolarizability averages is often expanded up
to fourth order in the frequencies using the dispersion formula
*X*_{||}^{(n)}(w_{1};...,w_{n})
= X_{||}^{(n)}(0)
(1 + A w_{L}^{2} + B w_{L}^{4}
+ O(w_{i}^{6}) )
with *w*_{L}^{2} = sum_{i} w_{i}^{2},
where the coefficient *A* is independent of the optical process.
We derive an extension of this dispersion formula which is open ended
in the powers of the frequencies, uses only process-independent
coefficients, and involves a minimal number of terms per order.
It is shown that the dispersion formula can be cast into a form where
dispersion coefficients drop out in a systematic manner
for optical processes involving static electric fields.
We discuss how the concept of these dispersion formulas can be
generalized to other hyperpolarizability components and exemplify this
approach at the experimentally important components *ß*_{_|_}
and *ß*_{K} of the first hyperpolarizability.

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