Following gradient extremal paths

SummaryFor any point on a gradient extremal path, the gradient is an eigenvector of the hessian. Two new methods for following the gradient extremal path are presented. The first greatly reduces the number of second derivative calculations needed by using a modified updating scheme for the hessian. The second method follows the gradient extremal using only the gradient, avoiding the hessian evaluation entirely. The latter algorithm makes it possible to use gradient extremals to explore energy surfaces at higher levels of theory for which analytical hessians are not available.

[1]  H. Bernhard Schlegel,et al.  Reaction Path Following in Mass-Weighted Internal Coordinates , 1990 .

[2]  P. Barbara,et al.  Molecular vibrations in a gradient extremal path , 1989 .

[3]  J. Pancíř.  Calculation of the least energy path on the energy hypersurface , 1975 .

[4]  L. E. Scales,et al.  Introduction to Non-Linear Optimization , 1985 .

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

[6]  A. G. Shamov,et al.  The local definition of the Optimum ascent path on a multi-dimensional potential energy surface and its practical application for the location of saddle points , 1981 .

[7]  Kazuhiro Ishida,et al.  The intrinsic reaction coordinate. An ab initio calculation for HNC→HCN and H−+CH4→CH4+H− , 1977 .

[8]  P. Jørgensen,et al.  A gradient extremal walking algorithm , 1988 .

[9]  H. Bernhard Schlegel,et al.  An improved algorithm for reaction path following , 1989 .

[10]  Michael Page,et al.  Following steepest descent reaction paths. The use of higher energy derivatives with ab initio electronic structure methods , 1990 .

[11]  K. Fukui.  The path of chemical reactions - the IRC approach , 1981 .

[12]  Michael Page,et al.  On evaluating the reaction path Hamiltonian , 1988 .

[13]  Wolfgang Quapp,et al.  Gradient extremals and valley floor bifurcations on potential energy surfaces , 1989 .

[14]  H. Bernhard Schlegel,et al.  Improved algorithms for reaction path following: Higher‐order implicit algorithms , 1991 .

[15]  M. Gordon,et al.  Intrinsic reaction coordinate calculations for very flat potential energy surfaces: application to singlet disilenylidene isomerization , 1989 .

[16]  Mark S. Gordon,et al.  Algorithms and accuracy requirements for computing reaction paths by the method of steepest descent , 1988 .