APPROXIMATE SUM RULE FOR DIATOMIC VIBRONIC STATES AS A TOOL FOR THE EVALUATION OF MOLECULAR PROPERTIES
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Date
1995
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
The simple expression $<\nu^{\prime\prime} |f\Delta U^{\prime} g|\nu>$ is offered to approximate sums of the form $\Sigma^{\infty}_{\nu^{\prime\prime} = 0}<\nu^{\prime} |f|\nu^{\prime\prime}>< \nu^{\prime\prime} |g|\nu ^{\prime}> (E_{\nu} - E_{\nu})^{n}$ where f and g are some operators which couple the vibrational levels $\nu^{\prime}$ and $\nu^{\prime\prime}$ of two interacting electronic states and $\Delta U = U^{\prime} U^{\prime\prime}$ is the difference of the corresponding internuclear $potentials^{1}$. The rigorous quantum proofs as well as semiclassical justification of this formula are presented. The approximate sum rule is numerically tested for radiative lifetimes, electronic polarizabilities, fine-structure constants and Lande factors for the vibronic states of the NaK $molecule^{2}$ and its absolute accuracy is estimated in a closed functional forms:- $<\nu^{\prime} |n\Delta U^{n-1} g^{\prime}f^{\prime} + n(n-1) \Delta U^{n-2} \Delta U^{\prime}(fg)^{\prime}/2 + n(n-1)(n-2) \Delta U^{n-3} (\Delta U^{\prime})^{n}/g/6| \nu > /2m$. The approximation is demonstrated to have high accuracy and efficiency for non-diagonal systems, especially for those with significant continuum contributions.
Description
1. A.V. Stolyarov and V.I. Pupyshev, Phys. Rev. A 49, 1693 (1994) 2. E.A.Pazyuk, A.V.Stolyarov, and V.I. Pupyshev, Chem. Phys. Lett. 228, 219 (1994)
Author Institution: Moscow State University, Moscow, Russia 119899
Author Institution: Moscow State University, Moscow, Russia 119899