Electron transport in real time from first-principles

TL;DR

This paper develops a real-time, first-principles approach to electron transport in molecular systems using a density functional theory framework, addressing stability issues and removing dependence on arbitrary parameters.

Contribution

It adapts the driven Liouville-von Neumann equation to DFT, ensuring particle conservation and parameter independence for large molecular systems.

Findings

The modified equation improves stability of electron dynamics.

The method accurately predicts current-voltage characteristics.

It is suitable for large, complex molecular systems.

Abstract

While the vast majority of calculations reported on molecular conductance have been based on the static non-equilibrium Green's function formalism combined with density functional theory, in recent years a few time-depedent approaches to transport have started to emerge. Among these, the driven Liouville-von Neumann equation (J. Chem. Phys. 124, 214708 (2006)) is a simple and appealing route relying on a tunable rate parameter, which has been explored in the context of semi-empirical methods. In the present study, we adapt this formulation to a density functional theory framework and analyze its performance. In particular, it is implemented in an efficient all-electron DFT code with Gaussian basis functions, suitable for quantum-dynamics simulations of large molecular systems. At variance with the case of the tight-binding calculations reported in the literature, we find that now the initial perturbation to drive the system out of equilibrium plays a fundamental role in the stability of the electron dynamics, and that the equation of motion used in previous tight-binding implementations has to be modified to conserve the total number of particles during time propagation. Moreover, we propose a procedure to get rid of the dependence of the current-voltage curves on the rate parameter. This method is employed to obtain the current-voltage characteristic of saturated and unsaturated hydrocarbons of different lenghts, with very promising prospects.