The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Theory of activated rate processes: A new derivation of Kramers’ expression
Abstract
The generalized Langevin equation of motion for a particle trapped in a one-dimensional well with a barrier height V0 and coupled to a dissipative medium is modeled by a harmonic bath. Using the properties of the bath and a normal mode analysis we prove that the reactive frequency defined by Grote and Hynes for averaged motion across the barrier is actually a renormalized effective barrier frequency. We then show that the Kramers–Grote–Hynes expression for the rate of escape over the barrier is just the continuum limit of the usual gas phase harmonic transition state theory expression.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Brownian motion in a field of force and the diffusion model of chemical reactions
Kramers, H. A. (1940) · Physica · doi:10.1016/s0031-8914(40)90098-2 · Cited by 8,625
Quantum tunnelling in a dissipative system
Caldeira, A. O., & Leggett, A. J. (1983) · Annals of Physics · doi:10.1016/0003-4916(83)90202-6 · Cited by 3,647
Reaction path Hamiltonian for polyatomic molecules
Miller, W. H., Handy, N. C., & Adams, J. E. (1980) · The Journal of Chemical Physics · doi:10.1063/1.438959 · Cited by 1,430
Grote, R. F., & Hynes, J. T. (1980) · The Journal of Chemical Physics · doi:10.1063/1.440485 · Cited by 1,338
Dynamics of Molecular Collisions: Part A
(1976) · Springer eBooks · doi:10.1007/978-1-4615-8867-2 · Cited by 1,134
Nonequilibrium solvation dynamics in solution reactions
van der Zwan, G., & Hynes, J. T. (1983) · The Journal of Chemical Physics · doi:10.1063/1.445094 · Cited by 250
On the generalized Langevin equation: Classical and quantum mechanicala)
Cortés, E., West, B. J., & Lindenberg, K. (1985) · The Journal of Chemical Physics · doi:10.1063/1.448268 · Cited by 215
van der Zwan, G., & Hynes, J. T. (1984) · Chemical Physics · doi:10.1016/0301-0104(84)85078-8 · Cited by 114
Transition-state theory for tunneling in dissipative media
Pollak, E. (1986) · Physical Review A · doi:10.1103/physreva.33.4244 · Cited by 86
Self-citation
Cited by
Reaction-rate theory: fifty years after Kramers
Hänggi, P., Talkner, P., & Borkovec, M. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.251 · Cited by 6,154
Current Status of Transition-State Theory
Truhlar, D. G., Garrett, B. C., & Klippenstein, S. J. (1996) · The Journal of Physical Chemistry · doi:10.1021/jp953748q · Cited by 2,279
Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics
Mandal, A., Taylor, M. A. D., Weight, B. M., Koessler, E. R., Li, X., & Huo, P. (2023) · Chemical Reviews · doi:10.1021/acs.chemrev.2c00855 · Cited by 270
Diffusion of inert gases in silica sodalite: Importance of lattice flexibility
Kopelevich, D. I., & Chang, H.-C. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1414373 · Cited by 55
Liu, Y., Yan, Y., Xing, T., & Shi, Q. (2021) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.1c02851 · Cited by 23
Metadata
- Authors
- Pollak, E.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1986-07-15
- Volume
- 85
- Issue
- 2
- Pages
- 865-867
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2059980347
- Cited by
- 406
- References
- 9
- FWCI
- 9.81
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Theory of activated rate processes: A new derivation of Kramers’ expression. https://app.cochat.ai/papers/10.1063/1.451294
- The paper
- Pollak, E. (1986). Theory of activated rate processes: A new derivation of Kramers’ expression. The Journal of Chemical Physics. https://doi.org/10.1063/1.451294
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
