Quadratic steepest descent on potential energy surfaces. IV. Adaptation to singular Hessians

Journal Article · Fri Apr 15 00:00:00 EDT 1994 · Journal of Chemical Physics; (United States)

DOI:https://doi.org/10.1063/1.467123· OSTI ID:5003453

Ruedenberg, K; Sun, J ^[1]

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1. Ames Laboratory, United States Department of Energy, and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)

It is shown that the quadratic steepest descent procedure developed in three previous papers goes smoothly and naturally into a limiting form, presenting no computational problems, when the Hessian becomes singular. This is in contrast to quasi-Newton algorithms which, in the case of singular or near-singular Hessians, yield unrealistic search directions and are kept from breaking down only by introducing arbitrary additional assumptions. The reason is that quasi-Newton algorithms give inadequate weight to the first order variation of the energy, i.e., its gradient.

• OSTI ID: 5003453
• Journal Information: Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 100:8; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
CALCULATION METHODS
COORDINATES
EIGENVALUES
ENERGY
INVARIANCE PRINCIPLES
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATRICES
POTENTIAL ENERGY
SINGULARITY
VARIATIONS