Vibration–Rotation Interaction Effects in Calculated Franck–Condon Factors. I. The Ionization of H2 and D2

Computed Franck–Condon factors for the ionization of H₂ and D₂ are reported which include previously neglected vibration–rotation interaction effects. Eigenfunctions were obtained by direct solution of the Schrödinger equation in which the exact centrifugal potential is explicitly included. Only $\text{υ″\hspace{0.17em}=\hspace{0.17em}0}$ and small $\mathrm{K″}$ states of the neutral molecule have been considered and attention is confined to those transitions for which $\text{|K″\hspace{0.17em}−\hspace{0.17em}K|\hspace{0.17em}=\hspace{0.17em}0, 2}$ . The results show a clear dependence of the computed Franck–Condon factor on rotational quantum number. For $\mathrm{K″\hspace{0.17em}=\hspace{0.17em}K}$ , this effect is small except for transitions to the uppermost vibrational states of the ion. For $\text{|K″\hspace{0.17em}−\hspace{0.17em}K|\hspace{0.17em}=\hspace{0.17em}2}$ , the effect is substantial even for transitions to low‐lying vibrational states of the ion. By using a sum rule, it is shown that the probability of dissociative ionization exhibits a similar dependence on rotational state. Comparison of the present results for the case $\text{K″\hspace{0.17em}=\hspace{0.17em}K\hspace{0.17em}=\hspace{0.17em}0}$ with previous computation shows that adiabatic corrections for nuclear motion, explicitly included in this work, have a wholly negligible influence on computed Franck–Condon factors.