J. Phys. Chem. 1990, 94, 8664-8670
8664
A Model for Adiabatk S,P-Substttution Reactions in Polar Solvents Alexander M. Kuznetsovt School of Science and Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: June 5, 1989; In Final Form: November 20, 1989)
A model of nonseparable potentials is suggested for adiabatic SN2-substitutionreactions in polar solvents, taking into account the interaction of the reactants with the medium polarization. The dynamics of the motion along reactive modes of the reaction complex and along effective coordinates describing solvent polarization is discussed. The expressions for transition probability per unit time are obtained for various limiting cases involving both slow and fast solvent relaxation regimes. It is shown that in general solvent polarization may create a Franck-Condon barrier for the transition and solvent dynamics may determine the kinetics of the reaction.
I. Introduction Ligand substitution reactions in liquid solutions were the object of experimental and theoretical investigation during many years and a number of theoretical models were suggested.’-31 The reactions of this type represent rather complicated reaction systems. The reaction complex itself involves several degrees of freedom participating in the transition. In addition the interaction of the reactants with polar solvent must be taken into account for reactions in water and in other polar liquids. It makes general theoretical consideration of this problem very difficult. A model of linear reaction complex Y-R...X(1) is usually used.1~2-8,29.30 It is assumed that the ligands X and Y (which usually are F, CI, Br, I) and the group R are located in a straight line and only motion along this line is considered. Theoretical models for adiabatic reactions operate usually with one effective reaction ~ o o r d i n a t e . ~ ’ *A* ~two , ~ reactive coordinates system was considered in refs 10 and 1 1. Many vibrational coordinates of the reacting system were taken into account in the quantum mechanical model for nonadiabatic reaction.8 In the present paper we will combine this latter model with the model of nonseparable potentials suggested in ref 32 to describe the mechanism of the elementary act of the reaction in the adiabatic regime (a limit of strong coupling). In section I1 we will outline briefly the model of nonseparable potentials for linear reaction complex of eq 1. The model for the description of the interaction of the reactants with the solvent will be presented in section 111. Then in section IV the adiabatic free energy surface will be constructed. In section V we will describe the dynamics of the transition for various limiting cases and will present general expressions for kinetics parameters for symmetrical systems (identity substitution). A brief discussion of the results in section VI concludes the paper. A consideration of nonsymmetrical reactions and discussion of some experimental systems will be given in a separate paper. For definiteness we discuss SN2ligand substitution in methyl halides (R = CH3),although the model and general approach that will be discussed are applicable to a more wide class of substitution reactions. 11. Model of Nonseparable Potentials for the Reaction Complex A set of three coordinates will be used for the description of linear reaction complex of eq 1 : the dimensionless distances between the atoms X and C (x) and between the atoms Y and C (y) and dimensionless coordinate qH describing the symmetric deformation vibrations of the protons in the CH, group (Figure 1). ‘Permanent address and address for correspondence: The A. N. Frumkin Institute of Electrochemistry of the Academy of Sciences of the USSR, Leninskii Prospect 31, Moscow 117071, USSR.
0022-3654/90/2094-8664$02.50/0
Aiming to construct the adiabatic potential energy surface Uad, we introduce first the diabatic potential energy surfaces Ui and 0; for the initial and final states
ui = us + U;H3Yb,qH)
+ vi(xd’,qH) + vrs + J i
uf = us + u;H,X(x,qH)
+
‘f/TcyIx,qH)
+
