The golden rule predicts that rate constants are proportional to the squares of mixing matrix elements divided by squared energy differences. As physical problems scale between different coupling limits, the calculated rate constant could first increase with mixing strength, reach a maximum, and then decrease as the mixing strength becomes larger. We demonstrate this general rate behavior as a function of Hamiltonian parameters, both for simple Huckel-type models and for a two-site Hubbard system. We demonstrate that the optical susceptibility in a two-site tunneling problem also shows such behavior. Such turnover phenomena appear to be quite general, as is suggested by scaling arguments.
ASJC Scopus subject areas
- Surfaces, Coatings and Films
- Physical and Theoretical Chemistry
- Materials Chemistry