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