Abstract
The phenyl-shift reaction in $\beta$-phenethyl phenyl ether ($\beta - \rm PhCH_2CH_2OPh$, $\beta$-PPE) is an integral step in the pyrolysis of PPE, which is a model compound for the $\beta$-O-4 linkage in lignin. We investigated the influence of natural occurring substituents (hydroxy, methoxy) on the reaction rate by calculating relative rate constant using density functional theory in combination with transition state theory, including anharmonic correction for low-frequency modes. The phenyl-shift reaction proceeds through an intermediate and the overall rate constants were computed invoking the steady-state approximation (its validity was confirmed). Substituents on the phenethyl group have only little influence on the rate constants. If a methoxy substituent is located in para position of the phenyl ring adjacent to the ether oxygen, the energies of the intermediate and second transition state are lowered, but the overall rate constant is not significantly altered. This is a consequence of the dominating first transition from pre-complex to intermediate in the overall rate constant. {\it O}- and di-{\it o}-methoxy substituents accelerate the phenyl-migration rate compared to $\beta$-PPE.