Locating transition states by quadratic image gradient descent on potential energy surfaces
- Ames Laboratory, USDOE, and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)
An analysis is given of the so-called image function'' approach to finding transition states. It is demonstrated that, in fact, [ital such] [ital functions] [ital do] [ital not] [ital exist] [ital for] [ital general] [ital potential] [ital energy] [ital surfaces] so that a plain minimum search is inappropriate. Nonconservative image gradient fields do exist, however, and their field lines, defined by Euler's equation, can lead to transition states as exemplified by quantitative integrations of these equations for the Mueller--Brown surface. As do gradient fields, image gradient fields contain streambeds and ridges, but their global structure is considerably more complex than that of gradient fields. In particular, they contain certain singular points where the image gradients change sign without passing through zero. They are the points where the two lowest eigenvalues of the Hessian are degenerate. Some of them can act as [ital singular] [ital attractors] for the image gradient descent and any algorithm must contain safeguards for avoiding them. (Such regions are equally troublesome for quasi-Newton-type transition-state searches.) Image gradient fields appear to have considerably larger [ital catchment] [ital basins] around transition states than do quasi-Newton-type or gradient-norm-type transition-state searches. A quantitative quadratic image-gradient-following algorithm is formulated and, through applications to the Mueller--Brown surface, shown to be effective in finding transition states.
- DOE Contract Number:
- W-7405-ENG-82
- OSTI ID:
- 7185176
- Journal Information:
- Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 101:3; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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74 ATOMIC AND MOLECULAR PHYSICS
ACTIVATION ENERGY
ALGORITHMS
ATTRACTORS
CHEMICAL REACTIONS
COORDINATES
ENERGY
MATHEMATICAL LOGIC
MATHEMATICS
POTENTIAL ENERGY
SINGULARITY