New aspects of the theory of electron transfer reaction dynamics

Citation

Onuchic, José Nelson (1987) New aspects of the theory of electron transfer reaction dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hcep-rh59. https://resolver.caltech.edu/CaltechETD:etd-02242006-162144

Abstract

This thesis deals basically with some new aspects of the electron transfer theory. It is divided into four parts: (1) Chapter I gives an introduction to the electron transfer problem; (2) Chapter II addresses the subject of how nuclear dynamics influences the electron transfer rate; (3) Chapter III explains how to calculate electron transfer matrix elements for non-adiabatic electron transfer systems, in particular protein systems; and (4) Chapter IV discusses some preliminary ideas about new problems I intend to work on the future.

In Chapter II the following dynamical problems are addressed. For the case of one overdamped reaction coordinate, the problem of adiabaticity and non-adiabaticity is considered in details. For an underdamped reaction coordinate, a preliminary discussion is given. All this formalism is developed using a density matrix formalism and path integral techniques. One of the advantages of using this formalism is that, by analyzing the spectral density, we can connect our microscopic Hamiltonian with macroscopic quantities. It also gives us a natural way of including friction in the problem. We also determine when the Hopfield semiclassical or the Jortner "quantum" models are good approximations to the "complete" Hamiltonian. In the limit that the reaction coordinates are "classical," we discuss how we can obtain the Fokker-Planck equation associated with the Hamiltonian.

By adding more than one reaction coordinate to the problem (normally two), several other problems are studied. The separation of "fast" quantum modes from "slow" semiclassical modes, where the fast modes basically renormalize the electronic matrix element and the driving force of the electron transfer reaction, is discussed. Problems such as exponential and non-exponential decay in time of the donor survival probability, and the validity of the Born-Oppenheimer and Condon approximations are also carefully addressed. This chapter is concluded with a calculation of the reaction rate in the inverted region for the extreme adiabatic limit.

In Chapter III we discuss calculations of electronic matrix elements, which are essential for the calculation of non-adiabatic rates. It starts with a discussion of why, through bond rather than through space, electron transfer is the important mechanism in model compounds. Also, it explains why tight-binding Huckel calculations are reasonable for evaluating these matrix elements, and why, through space and through bond, matrix element decays with distance have a different functional dependence on energy. Bridge effects due to different hydrocarbon linkers are also calculated.

This chapter concludes with a model for the calculation of matrix elements in proteins. The model assumes that the important electron transfer "pathways" are composed of both, through bond and through space parts. Finally, we describe how medium (bridge) fluctuations may introduce a new form of temperature dependence by modulating the matrix element.

In Chapter IV we discuss some experimental results obtained for electron transfer in the porphyrin-phenyl-(bicyclo[2.2.2]octane)_n-quinone molecule, and we propose some new experiments that should help to clarify our interpretation. It concludes with some preliminary discussions of how we can include entropy in the finite mode formalism described in Chapter II, and how we intend to use the formalism described in Chapter III in order to understand electron transfer in real protein systems.

Thesis Files