Knowledge Bank

We have recently described a semi-empirical parameterization of Pople’s CNDO method, which we have called CNDO/S. In the present work the CNDO/S wavefunctions of formaldehyde and azulene have been used as a starting point for a perturbation treatment of spin-orbit coupling in these molecules. The assumed spin-orbit Hamiltonian is {H}{so}=\alpha^{2}\Sigma{\underline{{p}}}[{Z}{k}({r}{\underline{{p}}K})/{r}^{3}{\underline{{p}}K}]{1\sim}{\underline{{p}}}\cdot {S}{\sim}{\underline{{p}}} where the sum extends over all the electrons of the system. Utilizing CNDO/S wavefunctions and assuming that only one center integrals survive, the matrix elements of $Hao$ may be developed in a straightforward manner. In the case of formaldehyde, the calculations indicate that the transition from the ground state to the A, component of the lowest triplet is the most intense, having an oscillator strength of $1.7\times 10-7$. This result is in agreement with experiment. In the case of azulene, the singlet-triplet transition is predicted to be polarized perpendicular to the molecular plane and the calculated oscillator strength is $1.4\times 10-11$. This suggests that the transition should be very difficult to observe experimentally.