Virtual transitions in nonadiabatic condensed-phase reactions

Julian S. Joseph, William Bialek

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We calculate the rate of a reaction proceeding through a virtual intermediate for arbitrary vibrational potentials in three electronic states, expressing it in a form amenable to saddle-point approximations. Treating the mode-specific case, in which a small number of vibrational modes are coupled to the electronic transitions, dissipation is included by vibrational coupling to a large collection of harmonic oscillators. A semiclassical saddle-point expansion at large energy denominator allows us to identify the criteria for the validity of the two-state approximation, in which the intermediate state is ignored, aside from generating an effective coupling between the initial and final states. We discuss the physical meaning of these criteria, which define a high-energy intermediate. In this case, virtual transfer may dominate over the two-step process. In the limit of a small energy denominator, we find that the virtual transfer rate is not necessarily negligible compared to the first step of a two-step transfer. In this case, the rate is found to depend on the damping of the vibrationally coupled modes over a certain range.

Original languageEnglish (US)
Pages (from-to)3245-3256
Number of pages12
JournalJournal of physical chemistry
Issue number13
StatePublished - 1993

All Science Journal Classification (ASJC) codes

  • General Engineering
  • Physical and Theoretical Chemistry


Dive into the research topics of 'Virtual transitions in nonadiabatic condensed-phase reactions'. Together they form a unique fingerprint.

Cite this