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A microscopic theory for solution chemical reactions: Introduction of reactant and medium structures into generalized langevin equation formalism
Author(s) -
Nagaoka Masataka,
Okuno Yoshishige,
Yoshida Naoto,
Yamabe Tokio
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560510617
Subject(s) - chemistry , hamiltonian (control theory) , reaction rate constant , reaction coordinate , thermodynamics , non equilibrium thermodynamics , ab initio , equilibrium constant , langevin equation , computational chemistry , physics , quantum mechanics , kinetics , mathematical optimization , mathematics , organic chemistry
A microscopic formulation of solution chemical reactions, taking reactants and medium structures into consideration, is presented on the basis of microscopic understandings obtained by recent quantum chemical methods (i.e., ab initio molecular orbital theory, etc.). Assuming thermal equilibrium of the medium bath, an effective internal Hamiltonian is derived, and, further, its derivative with respect to internal normal coordinates is proved explicitly to give the same force field as is provided by the free‐energy surface or potential of mean force. The free‐energy surface can be expressed in the composite normal coordinate system ( CNCS ) consisting of some normal coordinate systems of isolated reactants and surrounding solvent molecules (i.e., medium solvent molecules). In CNCS , in use of diagonal elements obtained in the Hessian matrix of the free‐energy surface, effective normal‐mode frequencies, which reflect the equilibrium solvent effect, are estimated. Furthermore, on the generalized Langevin equation ( GLE ) treatment, a closed expression of the time‐dependent frictional coefficient is derived on a microscopic basis, reflecting the reactant and solvent structures. The nonequilibrium effect is estimated by an analytical expression similar to that in the Grote–Hynes theory. The rate constant is evaluated for a typical model system and it is shown that the equilibrium rate constants should be reduced by a factor 0.997. Finally, it is concluded that the present microscopic theory is reasonably applicable to the estimation of chemical reaction rate constants in solution. © 1994 John Wiley & Sons, Inc.