A simple diagnostic is developed for the purpose of determining when a third state must be considered to calculate the electronic coupling element for a given pair of diabatic states within the context of the generalized Mulliken−Hush approach (Chem. Phys. Lett. 1996, 275, 15−19). The diagnostic is formulated on the basis of Löwdin partitioning theory. In addition, an effective 2-state GMH expression is derived for the coupling as it is modified by the presence of the third state. Results are presented for (i) a model system involving charge transfer from ethylene to methaniminium cation, (ii) a pair of donor−acceptor-substituted acridinium ions, and (iii) (dimethylamino)benzonitrile, and the diagnostic is shown to be a useful indicator of the importance of multistate effects. The effective 2-state GMH expression is also shown to yield excellent agreement with the exact 3-state GMH results in most cases. For cases involving more than three interacting states a similar diagnostic is presented and several approximations to the full n-state GMH result are explored.
© 2002 American Chemical Society
Rust, M.; Lappe, J.; Cave, R. J. “Multistate Effects in Calculations of the Electronic Coupling Element for Electron Transfer using the Generalized Mulliken-Hush Method,” J. Phys. Chem. A 2002, 106, 3930. DOI: 10.1021/jp0142886