SPIN-ORBIT COUPLING IN THE ${n}\rightarrow \pi^{*}$ TRANSITIONS OF FORMALDEHYDE AND PYRAZINE
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Date
1958
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Ohio State University
Abstract
“An approximate quantitative calculation is given for the effect of spin-orbit coupling in the ${n}\rightarrow \pi^{*}$ 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 $^{2}{A}_{2}({n}, \pi^{*})\leftarrow ^{1}{A}^{1}$ transition of formaldehyde, $H_{2}CO$, should preferentially steal intensity from the $^{1}{A}_{1}{\pi, \pi^{*}})\leftarrow ^{1}{A}_{1}$ transition, and that the long wavelength singlet-triplet absorption bands should be parallel bands (type A). The calculated oscillator strength for the $^{3}{A}_{2}\leftarrow ^{1}{A}_{1}$ transition is ${f}=1.5\times 10^{-7}$, and the corresponding calculated natural lifetime for the $^{3}{A}_{2}\leftarrow ^{1}{A}_{1}$ 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 $^{2}{B}_{2{o}}({n}, \pi^{*})\leftarrow ^{1}{A}_{e}$ 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 $^{1}{B}_{1{u}}(\pi, \pi^{*})$ 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.”
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$^{\dagger}$After September 15, 1958, at School of Chemistry, University of Minnesota, Minneapolis 14, Minnesota $^{1}$M. Mizushima and S. Koide, J. Chem. Phys. 20, 765 (1952). $^{2}$L. Goodman and M. Kasha, J. Mol. Spectroscopy 2, 58 (1958).d
Author Institution: Department of Chemistry, Cornell University
Author Institution: Department of Chemistry, Cornell University