Molecular Orbital Modeling and Transition State Theory in Geochemistry

Abstract

Fundamental to the understanding of geochemical phenomena is the accurate determination of viable chemical reactions and their rates. The accurate determination of the rate constants of underlying chemical reaction are needed by numerous other areas of science and engineering as well, and it is no coincidence that predicting rate constants has become a major goal of computational chemistry. In this chapter, we discuss the possible determination of these rate constants and mechanisms in the geosciences through molecular orbital (MO) calculations and transition state theory. The rate constants and their temperature dependence are critical in geochemical kinetics. Knowledge of the temperature dependent rates allows the computation of reaction progress over a range of temperatures. Furthermore, if the forward and backward rate constants k f and k r are known for an elementary reaction, then the equilibrium constant K eq for that elementary reaction can be calculated as well, for \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathit{K}\_{\mathit{eq}}(\mathit{T}) = \mathit{k}\_{\mathit{f}} (\mathit{T})/\mathit{k}_{\mathit{b}}(\mathit{T})\] \end{document}(1) where ( T ) is used to emphasize the temperature dependence. Note that this enables the direct computation of the equilibrium isotope fractionation factors for overall reactions. In addition to knowing the rates of the reactions per se and calculating equilibrium constants for elementary reactions, knowledge of the thermal rate constants allows the prediction of phenomena such as kinetic isotope effects (KIE). For instance, the primary kinetic isotope effect of an elementary reaction may be evaluated using \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[KIE(\mathit{T}) = \mathit{k}\_{\mathit{f}}^{{\ast}}(\mathit{T})/\mathit{k}\_{\mathit{f}} (\mathit{T})\] \end{document}(2) assuming that the isotope is directly involved in the reaction and where the asterisk indicates the same reaction but with a different isotopic signature. Conventional transition state theory (TST) provides a formalism for predicting thermal rate constants by combining the important features of the potential energy surface (PES) with a statistical representation of the dynamics of the system. MO calculations, on the other hand, allow the numerical determination of the PES. Thus, MO theory used …