Derivation of interpretative models for long range electron transfer from constrained density functional theory

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Abstract

The constrained DFT approach of Wu and Van Voorhis is a promising tool for the study of long range biological electron transfers within Marcus theory. This approach allows one to define chemically relevant non-adiabatic states and to compute the three key parameters entering the rate constant expression; the driving force (ΔG°), the reorganization energy (λ) and the electronic coupling HDA. Here we present the implementation of the method in deMon2k and we then successively use it to derive new parameters for the pathway model which is one of the most common interpretative models used in biochemistry to relate the HDA amplitude to the composition of proteins. This original application of CDFT also opens the door towards more elaborate models.

Section snippets

Introduction and background

Long range electron transfer (LRET) plays a major role in numerous biochemical processes [1]. Prominent examples are given by the cell’s respiratory chain or the photosynthetic system, where electrons are shuttled by means of a succession of electron jumps from the energy source (light or nutrient) toward the ATP synthases [2]. Various enzymes also provide examples of such processes: it is common that electrons have to be supplied to enzymes to enable them to fulfil their catalytic role. In the

Empirical approaches for HDA

In the present paper we focus on the electronic coupling HDA and explore the possibility of deriving interpretative models from CDFT computations. The electronic coupling is one of the key parameters of long range electron transfer rates. Whereas ΔG° and λ are mainly related to the structural characteristics of the cofactors, HDA is essentially related to the chemical composition of the intervening medium (the “bridge”). A great deal of effort has been spent in the past years to discover the

Implementation

We first briefly recall the principle of constrained DFT. As explained above the main objective is to enable the user to impose a charge or a spin density on a group of atoms during the SCF procedure [33]. In the case of LRET this constraint may apply for instance to the donor or the acceptor charges or, equivalently, to the charge difference between D and A. Of course the method presupposes the choice of an electronic population scheme and various proposals have been made. We have implemented

Application

All computations were done with the PBE functional [38] and the DZVP-GGA orbital basis set. To ensure a proper spanning of the intermolecular space the basis set was augmented by a set of diffuse p orbitals on oxygen atoms [39]. The GEN-A2 auxiliary basis set was used to fit the orbital density. We estimated HDA following the approach proposed by Van Voorhis. The Becke population scheme was chosen. Several trials have been made to test the robustness of the reported values depending on the

Summary

In summary, CDFT appears as a valuable tool to derive interpretative models for tunnelling pathways. To our knowledge this original use of CDFT is the first attempt to perform such a parameterization. The results presented are rather encouraging. First of all, our results confirm the intrinsic exponential behaviour of the electronic coupling with the distance separating D and A or, within the pathway paradigm, between two bridging atoms along the pathway. This is to be related to the remarkable

Acknowledgements

We thank Andreas Köster for illuminating correspondence on the implementation. We are grateful to NSERC-Canada for ongoing support and to WestGrid for computational resources.

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