Intensity of the Symmetry-Forbidden Electronic Absorption Band of Formaldehyde

The weak bands of formaldehyde extending from λ3500 A to λ2300 A are normally assigned to a 1A2←1A1, n→π transition (C2ν symmetry) which is forbidden by electronic selection rules. The present paper gives a quantitative theoretical discussion of the total intensity of these bands in each of the three directions of polarization. Using approximate wave functions for the various electronic states involved, the theory shows that the intensity of the perpendicular bands can be accounted for by vibrationally-induced mixing of excited electronic states. The calculated total intensity due to this mechanism is f=3×10—4. It is predicted that most of this intensity is produced by the out-of-plane bending vibration and is consequently polarized perpendicular to the C–O axis and in the molecular plane (B1 polarized). The contribution due to in-plane vibrations (CH2 wagging and antisymmetric C–H stretch), which would be polarized perpendicular to the molecular plane (B2 polarized), is predicted to be much weaker. This is in agreement with experiment. The weak parallel bands that have been observed cannot be interpreted in terms of vibrational-electronic interaction. It is suggested that these derive their intensity by borrowing, induced by rotation around the C–O axis, from the strong 1A1←1A1, π→π transition. A quantitative theory of this effect gives f∼10—6 for the total oscillator strength of the parallel bands. Several predictions which might be tested experimentally are made on the basis of this hypothesis.