On the computation of stationary points on potential energy hypersurfaces

In this article, a modification of a procedure proposed by Zirrilli et al. for solving nonlinear equations is presented. The method permits the computation of minima and saddle points of energy functionals. The Müller‐Brown test potential and the quantum chemical description of some proton transfer reactions are given as examples.

[1]  James S. Crighton,et al.  Locating transition states , 1984 .

[2]  Ajit Banerjee,et al.  Search for stationary points on surfaces , 1985 .

[3]  K. Müller,et al.  Location of saddle points and minimum energy paths by a constrained simplex optimization procedure , 1979 .

[4]  D. Heidrich,et al.  Quantenchemische modellierung der potentialhyperfläche des äthylkations im bereich der klassischen und nichtklassischen strukturen , 1976 .

[5]  J. Baker.  An algorithm for the location of transition states , 1986 .

[6]  P. Mezey.  Optimization and Analysis of Energy Hypersurfaces , 1981 .

[7]  Keith J. Laidler,et al.  Theories Of Chemical Reaction Rates , 1969 .

[8]  R. Zurmuhl,et al.  Matrizen und ihre technischen Anwendungen , 1962 .

[9]  J. Lambert,et al.  Multistep Methods with Variable Matrix Coefficients , 1972 .

[10]  P. Jørgensen,et al.  Walking on potential energy surfaces , 1983 .

[11]  James W. McIver,et al.  Structure of transition states in organic reactions. General theory and an application to the cyclobutene-butadiene isomerization using a semiempirical molecular orbital method , 1972 .

[12]  K. Fukui.  Formulation of the reaction coordinate , 1970 .

[13]  J. Pople,et al.  Molecular orbital theory of the electronic structure of organic molecules. 40. Structures and energies of C1-C3 carbocations including effects of electron correlation , 1981 .

[14]  V. Parisi,et al.  A New Method for Solving Nonlinear Simultaneous Equations , 1979 .

[15]  W. Rheinboldt.  Schwetlick H., Numerische Lösung nichtlinearer Gleichungen. Berlin VEB Deutscher Verlag der Wissenschaften 1979. 346 S., 21 Abb., M 68,— , 1980 .

[16]  F. Brauer,et al.  The Qualitative Theory of Ordinary Differential Equations: An Introduction , 1989 .

[17]  K. Müller,et al.  Reaction Paths on Multidimensional Energy Hypersurfaces , 1980 .

[18]  T. M. Williams,et al.  Practical Methods of Optimization. Vol. 1: Unconstrained Optimization , 1980 .

[19]  H. Fischer,et al.  A reparametrization of the CNDO method I. Hydrocarbons , 1969 .