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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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