A Green's function approach to long-range electron transfer in macromolecules

Abstract

We applied the formalism of double-time Green's functions to the problem of electron transfer from donor (D) to acceptor (A) through large macromolecules. The finite size of a system does not allow the use of momentum representation. For a tight-binding (Huckel-like) Hamiltonian we obtained the Dyson equation. The equation for Green's functions is linear and does not require one to go to higher order ones, which makes analysis of large protein molecules quite feasible. In this paper we analyze the structure of important double-time correlation functions, which will allow us to investigate time-dependent features of long-range electron transfer. We find explicit solutions of Dyson equations for some special cases. Our next 'vhich will provide a useful tool to investigate the general case of large paper will be dkdicaied to a graphical technique macromolecules.Electron transfer between localized sites is an important problem in some physical, chemical, and biological phenomena.' It is found that in living systems electron transfer occurs over large distances. For example, in the case of the photosynthesis the absorption of light by chlorophyll promotes an electron along an electrontransport chain mode up of a sequence of sites. We consider these sites to correspond to the structure of polypeptide chains. The chemical and biological problems deal with electron propagation from one center of an individual molecule to an acceptor. The problem is to estimate the rate of this transfer.The many-body technique, developed in solid-state physics and statistical mechanics, may successfully be applied to the problem under investigation. Especially promising will be (we believe) the application of so-called double-time Green's functions developed some time ago. They are especially effective in the case of nonequilibrium quantum statistical mechanics, and electron transport is essentially a nonequilibrium quantum mechanical process. The difference in technique which we will describe here and usually used in the solid-state many-body technique is that we cannot use the momentum representation but must, rather, work in direct spatial representation.da Gama was the first to use Green's function formalism in a model for the through-bond electronic interaction between electron donor and acceptor in proteins.I0The model which we adopt here is that of an electron donor (D), an electron acceptor (A), and a chain of amino acids. For each group we will assign a site of the chain and a subsequent orbital energy Ti. We will use the grand canonical ensemble, and therefore, chemical potentials enters here. The electron intersite interaction is not restricted to first neighbors and is represented by the hopping transfer potentials 6) In this paper we concern ourselves with only the electronic part of the Hamiltonian. We will discuss the ionic part elsewhere.In what follows we will adopt a tight-binding (Huckel-like) Hamiltonian, written in secondary quantized form 'Hopping" integrals vj are taken here to be nonrandom functions of r y Here we ...

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