Ab initio CI calculation of the radiationless transition of the 1(nπ) state of formaldehyde

This paper reports an ab initio CI calculation of the radiationless decay of the formaldehyde 1A2 state. First we derive quantitative conditions, which a basis set must satisfy if it is to be used for describing radiationless decay. We checked these conditions for the formaldehyde molecule and found them to be satisfied for the adiabatic Born–Oppenheimer set used in the calculation. We then derive a general equation for the coupling elements resulting from this basis set. With the method used, rotational coupling could be treated completely equivalent with vibrational coupling; this rotational coupling turned out to be not important in formaldehyde however. The coupling elements for D2CO are a factor 10 smaller than the corresponding ones in H2CO. The results of the calculation show, that the internal conversion in formaldehyde is an example of the so-called resonance case. Therefore the decay cannot be described by the model proposed by Yeung and Moore, where S1¿S0 internal conversion is the rate determining step in the photodissociation. Finally, we discuss the applicability of the ’’golden rule’’ in describing radiationless decay.