Electron transport in real time from first-principles

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 (DFT), in recent years a few time-dependent approaches to transport have started to emerge. Among these, the driven Liouville-von Neumann equation [C. G. Sánchez et al., 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 allelectron 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. The equation of motion used in previous tight-binding implementations with massive electrodes has to be modified to produce a stable and unidirectional current during time propagation in time-dependent DFT simulations using much smaller leads. 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 lengths, with very promising prospects. Published by AIP Publishing. [http://dx

Chemical Reactivity and Spectroscopy Explored From QM/MM Molecular Dynamics Simulations Using the LIO Code

“…Aside from spectroscopic applications, real-time TDDFT offers the possibility to perform quantum transport simulations. Recently, we have implemented in LIO an approach to compute molecular conductance in open quantum conditions (Morzan et al, 2017 ). The combination of RT-TDDFT with a QM/MM framework provides a unique platform to investigate challenging phenomena related to electron dynamics in realistic environments, which are very difficult to address from the experimental side or even with other modeling strategies.…”

Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations

“…As mentioned above, the recently developed DLvN approach can eliminate this limitation by expanding the capabilities of the microcanonical approach to simulate truly open quantum systems. Similar to previous multi-lead implementations of the DLvN approach [42,14,43,44,46,45,56], the LvN equation of motion for the single-lead setup considered herein is augmented by sink and source terms that absorb outgoing electrons (thus avoiding reflections) and inject thermalized electrons near the system boundaries, respectively, as follows:…”

Driven Liouville–von Neumann Equation for Quantum Transport and Multiple-Probe Green’s Functions

“…In ref. 22 it has been reasoned that while DLvN-z represents a device between electronic reservoirs at equilibrium with well-defined chemical potentials, DLvN-e resembles the state of a charged capacitor, where the target density represents the equilibrium state of the entire finite junction model and not just the leads. This seems to be consistent with the origins of each of these schemes, that have now come to light.…”

“…It can be seen that deviations tend to be larger for DLvN-z, whereas the DLvN-e approach, inheriting the mathematical structure from F-HP, copes better with the shortening of the electrodes.To summarize, the two forms of the Driven Liouville-von Neumann equation produce similar results, reproducing the hairy probes method provided large values of Γ are avoided.The most noticeable difference is that, whereas DLvN-z observes Pauli's principle, DLvN-e does not. At the same time, in some situations the DLvN-e equation is more tolerant to a decrease of electrode size, as discussed in ref 22 ,. which is a consequence of the robustness of the HP method from which it is descended.8 Summary and final remarksIn this article, it was shown that the Green's functions based multiple-probes-or hairy probes-formalism, adopts a form equivalent to the heuristic Driven Liouville-von Neumann method as proposed in reference 22 (equation 4), plus an additional term involving a matrix…”