#### Bridging the gap between theoretical and experimentally inferred reorganization energy

**Jonny Johannes**, Ehsan Zahedinejad, Dennis Salahub, Barry Sanders

- Institute for Quantum Science and Technology
- University of Calgary
- November 12, 2015
- PHAS Symposium 2015

## Overview

- Background
- Problem
- Motivation
- Methods
- Results
- Discussion

Photo credit: Richard Evans-Gowing at the University of East Anglia

## Background - Physical Chemistry

Marcus Theory

$$k_{\text{ET}} = \frac{2\pi}{\hbar}\left| H_{AB} \right|^2 \frac{1}{\sqrt{4 \pi k_{\text{B}} T}} \text{exp}\left(-\frac{\left( \lambda + \Delta G^\circ \right)^2}{4 \lambda k_{\text{B}} T}\right)$$

$$
\lambda_{\text{St}} = -\frac{\langle V_{\text{os}} \rangle}{2} \hspace{3cm}
\lambda_{\text{var}} = \lambda_{\text{St}} - \frac{\langle \delta V_{\text{o}s} \delta V_{\text{o}p} \rangle}{2k_{\text{B}}T}
$$
Martin, D and Matyushov, D. JCP, 2015.

## Problem

Disagreement between the theoretically calculated and experimentally inferred reorganization energy for the MADH-amicyanin complex.

## Motivation

Efficient, site-selective electron transfer is crucial for effective metabolic processes.

Diseases associated with free radical production.

Characterize efficient atomic scale wires.

- Apply the two-parameter model to the MADH-amicyanin system.

- Quantum calculations using density functional theory.

- Classical calculations using molecular mechanics, and molecular dynamics.

- Combined classical and quantum.

- Simulations allow us to probe inaccessible time and length scales.

- Fluctuations in how the protein rearranges itself and surrounding solvent is vital.

- $\lambda_{\text{var}}$ is an attempt to account for these fluctuations.

- Disagreement in theoretical and experimentally inferred $\lambda$ in MADH-amicyanin.

- Claim: two-paramenter model, accounting for statistics around protein-solvent electrostatic interactions can bridge the gap between theory and experiment.

- Novelty: application of the two-parameter model to MADH-amicyanin.