Gradient extremals and steepest descent lines on potential energy surfaces

Journal Article · Tue Jun 15 00:00:00 EDT 1993 · Journal of Chemical Physics; (United States)

DOI:https://doi.org/10.1063/1.464349· OSTI ID:6606197

Sun, J; Ruedenberg, K ^[1]

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

Relationships between steepest descent lines and gradient extremals on potential surfaces are elucidated. It is shown that gradient extremals are the curves which connect those points where the steepest descent lines have zero curvature. This condition gives rise to a direct method for the global determination of gradient extremals which is illustrated on the Mueller--Brown surface. Furthermore, explicit expressions are obtained for the derivatives of the steepest-descent-line curvatures and, from them, for the gradient extremal tangents. With the help of these formulas, a new gradient extremal following algorithm is formulated.

• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 6606197
• Journal Information: Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 98:12; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
661100 -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CHEMICAL REACTIONS
COORDINATES
ENERGY
EQUATIONS
MATHEMATICAL LOGIC
POTENTIAL ENERGY