Abstract

A procedure is developed to improve the quantitative evaluation of hydrogen transfer rates in polyatomic molecules and solids. The aim is to introduce a dynamical model that includes explicitly all vibrations participating in the transfer. This aim favors adoption of the golden-rule approach, since it treats all vibrational modes equally. To simplify the resulting multidimensional transfer integrals, two basic assumptions are introduced: (i) adiabatic separability of the hydrogenic modes directly involved in the tunneling from the other modes, and (ii) negligible anharmonicity for the latter. The number of effectively participating modes can then be reduced drastically by transformation to an appropriate local representation which allows analytical integration over most of these other modes. Those that remain involve vibrations of the atoms between which the hydrogen is transferred. Their frequency, reduced mass and displacement are expressed in terms of the harmonic force field of the system before and after transfer and can be unambiguously evaluated if these force fields are available. These modes replace the empirical effective modes used previously. The theory is applied successfully to single hydrogen transfer in dimethyl-glyoxime and double hydrogen transfer in porphine.

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