Following the streambed reaction on potential-energy surfaces: a new robust method |
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Authors: | Wolfgang Quapp Michael Hirsch Dietmar Heidrich |
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Institution: | Mathematisches Institut, Universit?t Leipzig, Augustus-Platz, 04109 Leipzig, Germany, DE Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universit?t Leipzig, Linne′str.2, 04103 Leipzig, Germany, DE
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Abstract: | A simple procedure with low computational efforts is proposed to follow the reaction path of the potential-energy hypersurface
(PES) starting from minima or saddle points. The method uses a modification of the so-called “following the reduced gradient”
Quapp W, Hirsch M, Imig O, Heidrich D (1998) J Comput Chem 19:1087]. The original method connects points where the gradient has a constant direction. In the present article the procedure
is replaced by taking iterative varying directions of the gradient controlled by the last tangent of the searched curve. The
resulting minimum energy path is that valley floor gradient extremal (GE) which belongs to the smallest (absolute) eigenvalue
of the Hessian and, hence, that GE which usually leads along the streambed of a chemical reaction. The new method avoids third
derivatives of the PES and obtains the GE of least ascent by second-order calculations only. Nevertheless, we are able to
follow the streambed GE uphill or downhill. We can connect a minimum with its saddles if the streambed leads up to a saddle,
or we find a turning point or a bifurcation point. The effectiveness and the characteristic properties of the new algorithm
are demonstrated by using polynomial test surfaces, an ab initio PES of H2O, and the analytic potentials of Lennard-Jones (LJ) clusters. By tracing the streambeds we located previously identified
saddle points for LJ
N
with N=3, 7, 8, and 55. Saddles for LJ
N
with N=15, 20, and 30 as presented here are new results.
Received: 8 March 2000 / Accepted: 17 July 2000 / Published online: 24 October 2000 |
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Keywords: | : Potential-energy surface Reaction-path following Saddle point Reduced gradient Gradient extremal |
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