Knowledge Bank

“An approximate quantitative calculation is given for the effect of spin-orbit coupling in the $n\to \pi \ast$ singlet-triplet electronic transitions of polyatomic molecules. The method is similar to that of Mizushima and $Koide.1$ Spin-orbit coupling is treated as a perturbation which mixes singlet and triplet states of the spin-free Hamiltonian. The one-center terms in the atomic orbital expansion of the matrix elements of the perturbing operator are calculated explicitly, using approximate wave functions and potentials. Other quantities are evaluated semi-empirically. The calculations show that the $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}A2(n,\pi \ast )\leftarrow 1A1$ transition of formaldehyde, $H2CO$, should preferentially steal intensity from the $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A1\pi ,\pi \ast )\leftarrow 1A1$ transition, and that the long wavelength singlet-triplet absorption bands should be parallel bands (type A). The calculated oscillator strength for the $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}A2\leftarrow 1A1$ transition is $f=1.5\times 10-7$, and the corresponding calculated natural lifetime for the $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}A2\leftarrow 1A1$ transition is $\tau =1\times 10-2$ sec. The agreement between theory and experiment is excellent. In pyrazine (1,4-diaza-benzene), the calculated oscillator strength for the $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}B2o(n,\pi \ast )\leftarrow 1Ae$ transition is $f=6\times 10-8$, in excellent agreement with the value ($1\times 10-7$) recently $observed.2$ The perturbing singlet state in pyrazine is predicted to be $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}B1u(\pi ,\pi \ast )$ near 7 ev, rather than any of the lower singlet states. A possible experimental test of the calculations, based upon the polarization of the phosphorescence of pyrazine as a function of the wave-length of the exciting radiation, is also suggested.”