On a quantum mechanical theory of absolute reaction rates

Iwao Yasumori, Kenji Fueki

Charles Alfred Coulson, Raphael David Levine

The methods of multichannel collision theory are used to introduce a yield operator Y which is an observable that determines the rate and yield of a reaction. When the reactants are characterized by a statistical operator U0, the reaction rate can be written as Tr(U0Y)/Tr(U0). By using Heisenberg's equation of motion it is possible to extend the formalism by introducing a yield operator YA that determines the rate of change of any measurable operator A in a system undergoing reactions. It is suggested to base semiempirical theories on approximations to the yield operator. Towards this aim the Arrhenius parameterization of the rate of thermal bimolecular reactions is discussed, and alternative forms for the yield operator are exhibited.

Jiřı́ Pokorný, Tsu-Ming Wu

Keisho Umesaki, Kei Odai

The reaction rate constant is defined as the rate at which a reactant annihilates or a product creates in a chemical reaction. The Hamiltonian of the reaction system describing elementary reactions has already been formulated by Miller et al（J. Chem. Phys. 1980, 72, 99-112） In addition, the reaction coordinates representing the progress of the reaction are also formulated by Fukui.（J. Phys. Chem. 1970, 74, 4161-4163） In the present paper, on the basis of these two theories, we first formulated the reaction rate constants of elementary reactions using classical statistical mechanics. Then we rewrited the rate constans quantum-mechanically according to the method of Wigner representations. By this rewriting, a correction term representing the quantum effect of the reaction rate constant was naturally derived.

James F. E. Croft, Constantinos Makrides, Ming Li +4 more

Abstract A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2 Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.

Kaitlin McCardle