Study of vibronic, spin-orbit and vibronic-spin-orbit couplings of formaldehyde with applications to radiative and non-radiative processes

With the recent availability of large amounts of experimental data, theoretical models of radiative and nonradiative processes can be tested in detail. For this purpose, the absolute calculation of radiative and non-­radiative rate constants is required. The expression for the non-radiative rate constant consists of two parts, one from the electronic motion (the pro­moting part) and the other from the nuclear motion (the statistical part). All recent theoretical work has been focused on the calculation of the non-radiative rate constant of one single vibronic state relative to another so that the promoting part of the rate constant is cancelled and hence has been concerned mainly with the Franck–Condon factor calculation (the statistical part of the rate constant). That the calculation of the statistical part of the rate constant cannot provide a critical test for a theory of radiationless transitions is obvious. In the present investigation, the theory of radiationless transitions to be tested is that originally proposed by Robinson and Frosch and later developed by Lin & Bersohn, Siebrand & Henry, Freed, Nitzan & Jortner and Fischer. According to this theory, one way to calculate the promoting part of the non-radiative rate constant is to invoke the vibronic coupling for the internal conversion and to invoke the vibronic coupling plus the spin-orbit coupling and/or the vibronicspin-orbit coupling for the intersystem crossing. A numerical calculation is carried out for the internal conversion 1 A 2 → 1 A 1 and the intersystem crossing 1 A 2 → 3 A 2 of formaldehyde by using simple m. os. For radiative transitions, we calculate the lifetimes of the states, 3 A 2 ( n ↔ π * ), 1 A 2 ( n ↔ π * ), 1 B 1 ( n ↔σ*), and 1 A 1 ( π ↔ π * ). The corresponding transition moments are given. For symmetry forbidden transitions, we compared the Herzberg–Teller theory with the importance of the correc­tion to the breakdown of the adiabatic approximation. It is shown that for formaldehyde, the B.–O. correction is approximately one order of magnitude smaller than the first order vibronic coupling.