Formaldehyde spin-orbit coupling

Ellis, Squire, and Jaffe have carried out a detailed study of the spin-orbit coupling in formaldehyde and azulene. The wave functions were calculated using the CNDO/S method, which is more general than the PPP method discussed earlier and also allows ff-orbitals to be included. Let us review their findings on formaldehyde ... 

Lin (145) has carried out an extensive theoretical investigation of the radiative and nonradiative mechanisms involving vibronic, spin-orbit, and vibronic-spin-orbit coupling in formaldehyde. Earlier, Yeung (254) calculated the SVL values of Tg, and Yeung and Moore (255) calculated the SVL values of x g. Lin used the left-hand Cartesian coordinate system in which planar formaldehyde lies in the x-z plane rather than in the y-z planes for the right-hand coordinate, which is accepted as the standard spectroscopic convention. Here, we adhere to the latter... 

In the molecular orbital description of the states of formaldehyde the active nonbonding orbital is mainly a pi(0) orbital. The inr states involve p (0) and Py C) orbitals. To have a significant value, the spin-orbit coupling matrix elements must include orbitals that have significant overlap. The effective matrix element for this particular interaction is of the type (py(0), (Rp (0)). The operator (R, rotates the p, orbital on the o.xygen into strong overlap with the Py orbital on oxygen and this is the portion of (R that can effectively mix the As and Mi states. The other components of (R are not so effective. 

The lowest excited triplet state ( A2) in formaldehyde lies some 3500 cm below the Si origin. Assuming that the vibrational frequencies in are the same as in Si (Problem 7.1), evaluate the semiclassical density of states in Tj at the energy of the vibrationless Si state. If the relevant spin-orbit coupling... 

Fig. 8 Simplified model for a one-center spin-flip process coupled to a change of angular momentum py -> in formaldehyde. The picture of this spin-orbit allowed -> n,n transition is inspired by reference 103. (Reproduced with permission from J. Chem. Phys., 2008, 129, 064117. Copyright 2008 American Institute of Physics).

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