Inorganic Chemistry

Identifying the Marcus dimension of electron transfer from ab initio calculations

Authors

Abstract

The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an ab initio approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then be obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus--Hush theory can be found in the real systems as an intuitive nuclear motion. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.

Version notes

Figures and captions updated; some text edits

Content

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Supplementary material

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Supporting Information for Identifying the Marcus dimension of electron transfer from ab initio calculations
This file includes IVCT spectra, relevant normal modes, depictions for Marcus dimensions, multideterminantal calculations, scans along the Marcus dimensions, properties of the Marcus dimension, parameterisation of the Marcus model, estimates of heavy atom tunnelling