Spin-Orbit Coupling in the 3A2—1A1 Transition of Formaldehyde

Abstract

An approximate quantitative calculation is given for the effect of spin‐orbit coupling in perturbing the ³A₂ state of H₂CO. The spin‐orbit coupling mixes the ³A₂ state with some higher singlet state, and allows the ³A₂←¹A₁ transition to have nonvanishing probability. The calculations show that the ³A₂←¹A₁, n_p→π₂ transition of H₂CO should be perturbed principally by the ¹A₁←¹A₁, π₁→π₂ transition. The bands of the ³A₂←¹A₁ transition should therefore have the structure of a transition which is allowed by orbital symmetry with an oscillating electronic transition moment along the C–O axis (parallel bands). The oscillator strength, f, is calculated to be $f_{{}^3{A}_2{\to }^1{A}_1}{\text{≅1.5×10}}^{\text{−7}}$ . The natural radiative lifetime τ for the ³A₂→¹A₁ phosphorescence transition is calculated to be ${\text{τ≅1×10}}^{\text{−2}}\sec$ . The calculated value for τ is in agreement with the experimental values for the related molecules (CH₃)₂CO, (C₆H₅)₂CO, and C₆H₅COCH₃, insofar as a comparison can be made. It is further shown that the spin‐orbit perturbation in the π→π^* transitions of aromatic hydrocarbons should be about one thousand times less effective than the spin‐orbit perturbation in the n→π^* transitions of carbonyl compounds. This is in agreement with the few pieces of experimental data which have been reported thus far.