Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy

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

Intern. J. Quant. Chem.68, 1-52 (1998).
(Received 24 September 1997; revised 3 December 1997; accepted 4 December 1997)

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann-Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2n+1 and 2n+2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self-consistent field, and second-order Møller-Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state properties.

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