Effect of two-electron spin-orbit interactions on singlet-triplet transition probabilities

Previously reported calculations concerned with spin-orbit enhancement of molecular S-T transitions have utilized an approximate one-electron spin-orbit Hamiltonian. The approximations are carried over from atomic spin-orbit theory and are justified on the basis of physical reasoning strictly applicable only to diagonal matrix elements. In order to test critically these assumptions, a treatment of spin-orbit enhancement of the formaldehyde 3 A 2 ↔ 1 A 1 transition is given using the complete spin-orbit Hamiltonian. A one-electron approximation to the spin-orbit Hamiltonian is found to be conceptually valid. The one-electron approximation which most closely approximates the complete spin-orbit Hamiltonian is the bare nuclear field Hamiltonian. Calculations on the lowest triplet state of the azines yield similar results. The polarization of the formaldehyde 3 A 2 ← 1 A 1 absorption is predicted to be almost solely along the C-O axis in agreement with the rotational experiments of Raynes. The predicted oscillator strength is 9 × 10-8). To investigate consequences of relaxation to the triplet equilibrium configuration before phosphorescence from the triplet state a spin-orbit calculation on formaldehyde in the 3 A 2 equilibrium configuration is carried out. It is not possible to predict whether the 3 A 2 → 1 A 1 transition moment should be almost solely along the C-O axis or whether it should have an appreciable component perpendicular to the C-O axis (y in the figure) in addition to the C-O component. The probability of T 1 → S 0 is predicted to be ∼ 3 times T 1 ← S 0.