First-Principles Calculation of Jahn-Teller Rotational Distortion Parameters.

A theoretical and computational framework is presented for the parameters h1 and h2 that appear in the rotational Hamiltonian for molecules subject to the Jahn-Teller effect. Expressions that relate h1 and h2 to first and second moments of the degenerate normal coordinates as well as derivatives of the inertia tensor are presented in detail for both cylindrical and Cartesian coordinate systems. The method is demonstrated for three situations in which experimental information about h1 (and/or h2) is available: the ground 2E1″ and 2E states of the cyclopentadienyl (C5H5) and methoxy (CH3O) radicals, respectively, and the excited 2E″ state of the nitrate (NO3) radical. Results for h1 and h2 parametrized by ab initio calculations exhibit good agreement with measured values, and they are demonstrably superior to those obtained with an approach based on first-order perturbation theory. The computational technology developed for h1 and h2 can be used to benchmark quantum chemistry calculations for molecules with Jahn-Teller effects and facilitate the analysis of their spectra.