Solvation free energy and Modeling chemical reactions - Cobalt

[Note that some of what follows is additional to what is found in the text – in particular,the importance of anisotropy and solute contributions in solvation free energy, and someparts of the discussion of slow-growth methods, are new. As well, material has been rearrangedfor (I hope) clarity. – Jason ]Non-electrostatic contributions to solvation free energy• Recall: ∆G sol=∆G elec+∆G vdW+ ∆G cav• The 1 st term (∆G elec) has been treated. Here we consider the non-electrostaticterm ∆G vdW+∆G cav, which can be treated in two different ways.As separate terms• ∆G vdWand ∆G cavcan be treated separately by models approximating theirphysical origin.• ∆G vdWcan be approximated by a continuous distribution function [Floris, F. andTomasi, J.; Journal of Computational Chemistry, 10 (1989), 616].• ∆G cavis treated by scaled-particle theory, in which the solute cavity is “growninto” the solvent.By linear approximation• The first solvation shell is expected to account for most of the van der Waalsinteraction energy. The number of solvent molecules in the first solvation shell –and therefore ∆G vdW, assuming each molecule interacts with the solute in asimilar manner – is therefore expected to be approximately proportional to thesolvent-accessible surface area A of the solute.• ∆G cavmight be expected to follow a similar trend, since the solvent moleculesmost strongly affected by cavity formation are those at the cavity surface. If, as inthe scaled particle method, the cavity is “grown” into the solvent:

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1. We begin by choosing a model, and therefore determining the form of theenthalpic surface.2. The desired transition state (a saddle point with steepest-descent paths leadingto products and reactants) and the intrinsic reaction path (IRP, the union ofthose steepest-descent paths) are determined.3. The system is warmed to a finite temperature. While the remaining degrees offreedom are allowed to evolve freely, the component along the IRP is slowly“dragged” from products to reactants. In this way, the space surrounding theIRP is sampled and the ensemble-average force required to maintain theconstraint can be evaluated at each location along the IRP.4. The mean force is integrated to give a free energy profile for the reaction.• The process is illustrated schematically below.→Enthalpic surfaceIRP↓←Reaction coordinateIntegration of mean forceSampling

Potential of mean force: An application• The application of slow-growth IRC methods to the SN 2 reaction of methylchloride with the chloride anion, as investigated by Artur Michalak of the Zieglergroup, will be discussed.• Of particular interest (in addition to the quality of the predicted energies) is theevident rotational freedom of the reactants relative to one another at coordinatesquite close to the transition state – a phenomenon not observed in enthalpic IRCcalculations.Empirical Approaches• Force field methods have been developed to treat reactions.• As an example: The reaction of enol boronates with aldehydes, shown below,was investigated:OBL 2OH R 2OOHR 1R 1 R 2Each conformer of the starting material can go through one of two transitionstates – the “chair” conformation, or the “boat” conformation. These transitionstates are shown below for the trans starting material:OR1BOR 2OOO OBR 2 BR 2R 1 R 1

R 2OOOB OB OB ODepending on the relative orientations of the two reactant molecules (R 2 axial orequatorial), each transition state can, in turn, give one of two productconformations. Both reactions shown above lead to the product given below:OOHR 1 R 2In this study, empirical parameters were fit to match experimentally-determinedtransition state structures where R 1 = R 2 = H. These parameters were then usedsuccessfully to predict product ratios for other substituents, whose interactionsthrough the reaction were primarily steric.