Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The role of depth and flatness of a potential energy surface in chemical
  reaction dynamics   In this study, we analyze how changes in the geometry of a potential energy
surface in terms of depth and flatness can affect the reaction dynamics. We
formulate depth and flatness in the context of one and two degree-of-freedom
(DOF) Hamiltonian normal form for the saddle-node bifurcation and quantify
their influence on chemical reaction dynamics. In a recent work,
Garc\'ia-Garrido, Naik, and Wiggins illustrated how changing the well-depth of
a potential energy surface (PES) can lead to a saddle-node bifurcation. They
have shown how the geometry of cylindrical manifolds associated with the rank-1
saddle changes en route to the saddle-node bifurcation. Using the formulation
presented here, we show how changes in the parameters of the potential energy
control the depth and flatness and show their role in the quantitative measures
of a chemical reaction. We quantify this role of the depth and flatness by
calculating the ratio of the bottleneck-width and well-width, reaction
probability (also known as transition fraction or population fraction), gap
time (or first passage time) distribution, and directional flux through the
dividing surface (DS) for small to high values of total energy. The results
obtained for these quantitative measures are in agreement with the qualitative
understanding of the reaction dynamics.

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph