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We have earlier shown that the formation of $O2$($\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma g+$) can be sensitized by the electronically excited triplet molecule $SO2(3B1)$ [Davidson and Abrahamson, Photochem, Photobiol, 15, 403 (1972)], and that this $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma g+$ species can be quenched, presumably to the lower excited electronic species, $02(1\Delta g)$, by collision with a large variety of simple polyatomic molecules [Davidson, Kear and Abrahamson, Journ. Photochem. 1, 307 (1973)]. In our recent studies we have demonstrated Chat the quenching efficiency, q, for this process can be quite satisfactorily represented by the empirical equation $$ \log q=K\frac{\Delta{E}}{\nu_{\max}}+C $$ where K and C are constants characteristic of the molecular size, i.e., diatomic, triatomic, tetratomic, etc., $\Delta E$ is the energy difference between the $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma g+$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Delta g$ vibronic states, and $\nu max$ is the frequency of the highest energy normal mode vibration in the quenching molecule. The above study prompted us to attempt the development of a theoretical quantum mechanical treatment of the physical quenching of $O2(1\Sigma g+)$ by diatomic molecules. Following an earlier lead of Dickens, Linnett and Sovers [Discussions Faraday Soc. 33, 52 (1962)], who treated the quenching of excited atoms, the model, at its present stage of development, yields calculated quenching constants in essential agreement with experiment for those cases where the electronic energy cart be converted almost entirely into vibrational energy of the quencher. Where this energy discrepancy is greater than kT, the model indicates that it is partitioned into rotation and translation modes.