Dispersion coefficients for first hyperpolarizabilities using coupled cluster quadratic response theory

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

Theor. Chem. Acc. 110, 230-240 (1998).
Received: 26 March 1998 / Accepted: 21 July 1998 / Published online: 19 October 1998

The frequency-dependence of third-order properties can in the normal dispersion region be expanded in a Taylor series in the frequency arguments. The dispersion coefficients obtained in this way provide an efficient way of expressing the dispersion of frequency-dependent properties and are transferable between different optical processes. We derive analytic expressions for the dispersion coefficients of third-order properties in coupled cluster quadratic response theory and report an implementation for the three coupled cluster models CCS, CC2 and CCSD. Calculations are performed for the first hyperpolarizability of the NH3 molecule. The convergence of the dispersion expansion with the order of the coefficients is examined and we find good convergence up to about half the frequency at which the first pole in the hyperpolarizability occurs. Padé approximants improve the convergence dramatically and extend the application range of the dispersion expansion to frequencies close to the first pole. The sensitivity of the dispersion coefficients on the dynamic correlation treatment and on the choice of the one-electron basis set is investigated. The results demonstrate that contrary to presumptions in the literature the dispersion coefficients are similar sensitive to basis set effects and correlation treatment as the static hyperpolarizabilities.

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