Effects of High Rotational Quantum Numbers on Rydberg–Klein–Rees Franck–Condon Factors: The Nitric Oxide (NO) Beta Band System

Abstract

Rydberg–Klein–Rees (RKR) Franck–Condon factors ${\mathrm{(q}}_{\mathrm{\upsilon \prime \upsilon ″}})$ have been calculated for the nitric oxide (NO) beta ${\mathrm{(B}}^2{\Pi }_r{\mathrm{-X}}^2{\Pi }_r)$ band system incorporating high vibrational and rotational quantum numbers and accounting for spin–orbit couplings and centrifugal distortions. Franck–Condon factors (FCF's) calculated using the rotationless potential indicate that some of these may differ appreciably (in some cases by more than a factor of 2) when compared with factors calculated with $\text{J\hspace{0.17em}=\hspace{0.17em}60}$ . Franck–Condon factors calculated for specific bands, but for separate fine structure components ${\mathrm{(B}}^2{\Pi }_{\text{1/2,3/2}}{\mathrm{-X}}^2{\Pi }_{\text{1/2,3/2}})$ were often found to be quite different. The results also indicate that adding the rotational contribution directly to the rotationless potential to form an effective potential as is usually done within the framework of the Born–Oppenheimer approximation may not be appropriate for some systems.