The Marcus dimension: identifying the nuclear coordinate for electron transfer from ab initio calculations

Area of Science:

• Physical Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The Marcus model is foundational for understanding electron transfer (ET).
• ET involves changes in diabatic potential energy surfaces along a nuclear coordinate.
• This coordinate, crucial for promoting ET, is often vaguely defined, hindering detailed analysis.

Purpose of the Study:

• To develop and demonstrate an *ab initio* method for quantitatively defining the electron transfer coordinate.
• To investigate the nature of nuclear motion driving ET in dinitroradical anions.
• To validate the identified coordinate against predictions of the Marcus-Hush theory.

Main Methods:

• Employed density functional theory (DFT) calculations combined with finite-temperature sampling.
• Quantified the ET coordinate using energy separation between potential energy surfaces and electron localization.
• Identified the precise nuclear motion as a linear combination of normal modes.

Main Results:

• Successfully quantified the electron transfer coordinate for dinitroradical anions.
• Demonstrated that evolution along this coordinate changes the diabatic state and optical excitation energy, consistent with the Marcus model.
• Found the energy barrier to be thin, suggesting significant heavy-atom tunneling during ET.

Conclusions:

• A single dimension of electron transfer, as described in Marcus-Hush theory, can be precisely defined as a specific nuclear motion.
• The developed *ab initio* approach effectively separates the intrinsic ET coordinate from other structural and environmental effects.
• The findings provide a quantitative tool for understanding ET pathways and highlight the role of tunneling.