Dispersion coefficients for second hyperpolarizabilities using coupled cluster cubic response theory

Christof Hättig and Poul Jørgensen
Department of Chemistry, Århus University, DK-8000 Århus C, Denmark

Advances in Quantum Chemistry, 35 (1999) 111-148

The frequency-dependence of polarizabilities and hyperpolarizabilities can in the normal dispersion region be expressed by means of a Taylor series in the frequency arguments. The dispersion coefficients obtained in this way are transferable between different non-linear optical processes and provide a compact way to express the dispersion of frequency-dependent properties. We derive analytic expressions for the dispersion coefficients for general fourth-order properties based on coupled cluster cubic response theory and present an implementation for the three coupled cluster models CCS, CC2 and CCSD. Calculations are reported for the second hyperpolarizability of methane, for which we investigate the sensitivity of the dispersion coefficients on the dynamic correlation treatment and on the choice of the one-electron basis set. We examine the convergence of Taylor expansions and Padé approximants with the order of the dispersion coefficients. Good convergence of the Taylor expansions is found for the dc-Kerr effect, degenerated four wave mixing and electric field induced second harmonic generation. Padé approximants improve the convergence rate dramatically and extend the application range of the dispersion expansion to higher frequencies and to other optical processes including third harmonic generation.

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