Redox Free Energies from Vertical Energy Gaps: Ab Initio Molecular Dynamics Implementation

Abstract

The development of methods for the exploration of reaction paths in condensed molecular systems (solutions and biopolymers) and the computation of the corresponding reaction free energies and kinetic parameters remains at the center of research in computational chemistry. Much has happened in recent years. It is the subject of a good number of the chapters in this book, which give an up to date overview of the enormous progress that has been made. We mention the development of the transition path sampling method by the group of Chandler at Berkeley (see the chapters by Dellago, Bolhuis and Geissler, where also the references to the original literature can be found). An alternative approach with a somewhat different purpose and scope is the metadynamics method developed by the Parrinello group (see the chapter by Laio and Parrinello). Transition path sampling and metadynamics studies to date have focused mostly on dynamical processes which never leave the adiabatic ground state potential energy surface (PES). However barriers for chemical reactions often coincide with an avoided crossing, or, alternatively, can be seen as the result of the coupling between two intersecting diabatic surfaces (see Fig. 1). The diabatic perspective offers certain advantages. This applies in particular to activation energies with a strong solvent contribution. An instructive example of such a reaction is electron transfer (ET). For outer sphere transfer the barrier is almost 100 percent due to rearrangement of the solvent polarization. This observation is a key idea in the Marcus theory of electron transfer [1–4]. In the original formulation of the theory [1] the polarization was described by the linear response of a dielectric continuum. How to quantify solvent polarization by a microscopic order parameter? Polarization is a highly collective quantity with a configurational component (the orientation of molecules) and electronic component (induced polarization).