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The methoxy, $CH3O$, and hydroxymethylene, $CH2OH$, radicals are postulated to appear as intermediate in atmospheric and combustion chemistry models. These species are related to one another via a 1,2-hydrogen shift, \begin{equation} CH_{3}O\stackrel{\rightarrow}{\leftarrow} CH_{2}OH. \end{equation} We report the calculation of transition state structures and relative energies for a series of unimolecular reactions that involve these two radicals. In addition to the 1,2-shift reaction, we consider two elimination reactions of the methoxy radical, \begin{eqnarray} CH_{3}O &\rightarrow& H + CH_{2}O \ CH_{3}O &\rightarrow& H_{2} + CHO, \end{eqnarray} as well as two elimination reactions of the $CH2OH$ radical, \begin{eqnarray} CH_{2}OH &\rightarrow& H + CH_{2}O \ CH_{2}OH &\rightarrow& H + HCOH \end{eqnarray} Transition state the equilibrium structures, and the matrix of second derivatives for each of the extrema, were obtained using analytic gradient based SCF methods. The classical barrier and classical dissociation energy for each reaction were computed using fourth-order many-body perturbation theory.