Multistate effects in calculations of the electronic coupling element for electron transfer using the generalized Mulliken-Hush method

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, 2 75, 15 - 19). The diagnostic is formulated on the basis of Lowdin 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.