CoChat
Sign Up
Cited by 2,778Spectroscopy and Quantum Chemical StudiesPhotochemistry and Electron Transfer StudiesAdvanced Physical and Chemical Molecular Interactions

The DOI matches its Crossref record; 67 of the 67 references it cites were found in a registry or an index.

The energy gap law for radiationless transitions in large molecules

Englman, Robert, Jortner, Joshua·1970·Molecular Physics
DOI 10.1080/00268977000100171
Open this paper in CoChat — free account

Abstract

In this paper we present a unified treatment of non-radiative decay processes in large molecules which involve either electronic relaxation between two electronic states or unimolecular rearrangement reactions in excited electronic states. The present treatment is analogous to the formalism previously applied for the line shape problem in nuclear recoil and in the optical spectra of solids. We were able to derive theoretical expressions for the non-radiative decay probability so that an arbitrary number of different molecular vibrations can be incorporated in the vibrational overlap factors. The general expressions obtained herein can be reduced to analytical form for two limiting cases, which we call the strong coupling case (which corresponds to a substantial horizontal displacement of the potential energy surfaces of the two electronic states) and the weak coupling limit (whereupon the relative horizontal displacement of the two potential energy surfaces is small). Quantitative criteria for the applicability of these two coupling limits are provided. In the strong coupling limit the transition probability is determined by a gaussian function of the energy parameter (ΔE - EM ), where ΔE is the energy gap between the origins of the two electronic states and 2EM is the Stokes shift. This limit exhibits a generalized Arrhenius type temperature behaviour whereupon the transition probability depends exponentially on the energy barrier for the intersection of the two potential surfaces. At low temperatures the transition probability is determined by the mean vibrational frequency and is thus expected to reveal only a moderately weak deuterium isotope effect. The weak coupling limit reveals an exponential (or rather superexponential) dependence of the transition probability on the energy gap ΔE. In this limit the transition probability is dominated by the highest vibrational frequency (e.g. the C-H or C-D vibrations) and thus will reveal a marked isotope effect. When semi-empirical estimates of the pre-exponential factors are provided, the approximate theoretical expression for the weak coupling limit is found to be consistent with the available experimental data on electronic relaxation in large organic molecules.

Overview

Integrity signals

Registry

Crossref · 10.1080/00268977000100171

Cites

67 of 67 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Research works printed but not linked: 8

  1. Hunt G.R., 1961, Proc. chem. Soc., 11
  2. Robinson G.W., 1967, J. chem. Phys., 47
  3. Mulliken R.S., 1933, Phys. Rev., 43, 297
  4. Förster Th., 1952, Z. Elektrochem., 56, 716
  5. van der Lugt W.Th.A.M., 1968, Ph.D. Thesis
  6. Huang K., 1951, Proc. phys. Soc. A, 204, 413
  7. Hochstrasser R.M., private communication
  8. Englman R., to be published

Cited by

Sorted by citations

See all 2,778

Related

See all

Metadata

Authors
Englman, R., & Jortner, J.
Affiliations
  • Soreq Nuclear Research Center (IL)
  • Tel Aviv University (IL)
ORCID
Englman, Robert
Venue
Molecular Physics
Publisher
Informa UK Limited
Published
1970-02
Volume
18
Issue
2
Pages
145-164
ISSN
  • 0026-8976 (ISSN-L)
  • 1362-3028
DOI
10.1080/00268977000100171
OpenAlex
W1971274408
Cited by
2,778
References
67
Citations by year
2026: 147 · 2025: 186 · 2024: 173 · 2023: 154 · 2022: 160 · 2021: 155 · 2020: 120 · 2019: 105 · 2018: 91 · 2017: 88 · 2016: 84 · 2015: 66 · 2014: 59 · 2013: 57 · 2012: 44
FWCI
21.11
Type
journal article
Language
en
Open access
closed
Locations
Molecular Physics (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Spectroscopy and Quantum Chemical Studies
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Photochemistry and Electron Transfer Studies
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Keywords
nonradiative decay, radiationless transitions, electronic relaxation, unimolecular rearrangement, strong coupling limit, weak coupling limit, Stokes shift, deuterium isotope effect, energy gap law, large organic molecules, transition probabilities

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