Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple generalization of the energy gap law for nonradiative processes   For more than 50 years, an elegant energy gap (EG) law developed by Englman
and Jortner [Mol. Phys. {\bf 18}, 145 (1970)] has served as a key theory to
understand and model nearly exponential dependence of nonradiative transition
rates on the difference of energy between the initial and final states. This
work revisits the theory, clarifies key assumptions involved in the rate
expression, and provides a generalization for the cases where the effects of
temperature dependence and low frequency modes cannot be ignored. For a
specific example where the low frequency vibrational and/or solvation responses
can be modeled as an Ohmic spectral density, a simple generalization of the EG
law is provided. Test calculations demonstrate that this generalized EG law
brings significant improvement over the original EG law. Both the original and
generalized EG laws are also compared with stationary phase approximations
developed for electron transfer theory, which suggests the possibility of a
simple interpolation formula valid for any value of EG.

25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn