# Efficient Calculation of Electrostatic Energies for Large-Scale Nonadiabatic Molecular Dynamics in a Site Basis

## TL;DR

This paper introduces a more efficient method to calculate electrostatic energies in large-scale molecular simulations, improving accuracy and agreement with experimental results.

## Contribution

A new computational scheme for efficiently calculating electrostatic energies in nonadiabatic molecular dynamics simulations.

## Key findings

- Including electrostatic site energy fluctuations reduces hole delocalization and mobility in crystalline anthracene.
- Electrostatics improve agreement with experimental mobilities and anisotropy without changing the transport mechanism.
- Omitting electrostatic site energy disorder is reasonable for acenes but not sufficient for near-quantitative agreement with experiments.

## Abstract

Nonadiabatic molecular dynamics simulation of charge
and exciton
transport in molecular materials and biological systems are often
carried out in a (quasi-)­diabatic or site basis. Such simulations
require the calculation of the electrostatic site energy of all possible
charge or excited states of the system at each molecular dynamics
step, which quickly becomes computationally prohibitive when Ewald
summation is used. By combining the damped shifted force real space
electrostatic summation method with a suitable addition-subtraction
scheme, we show that the calculation of electrostatic energy and forces
for N
mol site energies can be carried
out at a small and system size independent overhead compared to the
calculation for a single site energy. This advance enables us to include
full electrostatic interactions in nonadiabatic molecular dynamics
simulations for charge and exciton transport. Applying our computational
scheme to hole transport in crystalline anthracene, we find that upon
inclusion of electrostatic site energy fluctuations (also sometimes
termed diagonal electrostatic disorder) the inverse participation
ratio measuring hole delocalization decreases from ∼5 to ∼4
concomitant with a decrease in the hole mobility by about 9% along
the b-crystallographic direction and by 30% along
the a-direction. Accounting for electrostatics improves
the agreement with experimental time-of-flight mobilities and mobility
anisotropy, but it does not alter the charge transport mechanism,
transient delocalization. Our work confirms that omission of electrostatic
site energy disorder is a reasonable approximation for acenes, yet
electrostatics is required to obtain near-quantitative agreement with
experiment, even for apolar systems.