Theoretical Chemistry Accounts

ISSN: 1432-881X (printed version)
ISSN: 1432-2234 (electronic version)
Volume 105 Issue 2 (2000) pp 145-155
DOI 10.1007/s002140000192

Following the streambed reaction on potential-energy surfaces:
a new robust method

Wolfgang Quapp (1), Michael Hirsch (1), Dietmar Heidrich (2)

(1) Mathematisches Institut, Universität Leipzig, Augustus-Platz, 04109
    Leipzig, Germany
(2) Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie,
    Universität Leipzig, Linne´str.2, 04103 Leipzig, Germany

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 H_2O, 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.

Key words:
Potential-energy surface · Reaction-path following ·
Saddle point · Reduced gradient · Gradient extremal