Beyond transition-state theory: A rigorous quantum theory of chemical reaction rates

Journal Article · Thu Apr 01 04:00:00 EST 1993 · Accounts of Chemical Research; (United States)

DOI:https://doi.org/10.1021/ar00028a007· OSTI ID:6028193

Miller, W H ^[1]

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1. Lawrence Berkeley Laboratory, CA (United States)

Transition-state theory (TST) provides a simple and useful way to understand and estimate the rates of chemical reactions. The fundamental assumption of transition-state theory, however, is based inherently on classical mechanics, so the theory must be quantized if it is to provide a quantitative description of chemical reaction rates. Unlike classical mechanics, though, there seems to be no way to construct a rigorous quantum mechanical theory that contains as its only approximation the transition-state assumption of [open quotes]direct dynamics[close quotes]. Pechukas has discussed this quite clearly: as soon as one tries to rid a quantum mechanical version of transition-state theory of all approximations (e.g., separability of a one-dimensional reaction coordinate) beyond the basic transition-state assumption itself, one is faced with having to solve the full (multidimensional) quantum reaction dynamics problem. But a correct treatment of the full quantum dynamics must yield the exact rate constant and is no longer a transition-state [open quotes]theory[close quotes]. Though there is no rigorous quantum prescription for determining the rate constant of a chemical reaction that avoids, the necessity of solving the Schroedinger equation, there is nevertheless a rigorous theoretical approach that avoids having to solve the complete state-to-state reactive scattering problem; one does not avoid solving the Schroedinger equation, but needs to solve it only locally, in the vicinity of the transition state, with no explicit information about reactant and product states being required. After reviewing some of the notions alluded to above, the purpose of the Account is to describe this [open quotes]direct[close quotes] theoretical approach for calculating chemical reaction rates, the logical conclusion in the quest for a [open quotes]rigorous[close quotes] quantum mechanical version of transition-state theory. 20 refs., 3 figs.

• OSTI ID: 6028193
• Journal Information: Accounts of Chemical Research; (United States), Journal Name: Accounts of Chemical Research; (United States) Vol. 26:4; ISSN 0001-4842; ISSN ACHRE4
• 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
CHEMICAL REACTION KINETICS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
DYNAMICS
ELEMENTS
EQUATIONS
HYDROGEN
KINETICS
MATHEMATICAL MODELS
MECHANICS
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
REACTION KINETICS
SCHROEDINGER EQUATION
WAVE EQUATIONS