Driven Liouville von Neumann Approach for Time-Dependent Electronic Transport Calculations in a Nonorthogonal Basis-Set Representation

Abstract

A non-orthogonal localized basis-set implementation of the driven Liouville von Neumann (DLvN) approach is presented. The method is based on block-orthogonalization of the Hamiltonian and overlap matrix representations, yielding non-overlapping blocks that correspond to the various system sections.An extended Hückel description of the Gold/benzene-dithiol/Gold junction is used to demonstrate the performance of the method. The presented generalization is an important milestone towards using the DLvN approach for performing accurate dynamic electronic transport calculations in realistic model systems, based on density functional theory packages that rely on atom-centered basis set representations.

Parameter-free driven Liouville-von Neumann approach for time-dependent electronic transport simulations in open quantum systems

“…Furthermore, the steady-state current corresponds well with the Landauer current (X mark) calculated using the procedure described in Ref. [31]. The broadening factors, plotted in the inset of Fig.…”

“…Next, we turn to examine the performance of the PF-DLvN method for non-orthogonal basis-set representations of molecular junctions, within the framework of extended Hückel (EH) theory. [31] To this end, a Slater orbital basis-set is introduced to evaluate the overlap and Hamiltonian matrix representation elements using the procedure and parameters described in Ref. [31].…”

“…[31] To this end, a Slater orbital basis-set is introduced to evaluate the overlap and Hamiltonian matrix representation elements using the procedure and parameters described in Ref. [31]. First, we consider a hydrogen chain junction model equivalent to the TB chain model discussed above.…”

“…[29][30] [31][32] Furthermore, the method was shown to accurately describe dynamic currents in junctions subjected to time-dependent perturbations. [23] The success of the DLvN approach suggests that it offers an efficient and physically motivated methodology for time-dependent charge transport in molecular junctions.…”

Electron transport in real time from first-principles

“…20 Very recently, these authors generalized this approach to non-orthogonal localized basis sets using an extended Hückel model. 21 Our goal in the present study is to realize a first-principles implementation of the driven Liouville-von Neumann equation discussed in the previous paragraph, suited for transport simulations in realistic molecular systems. We find that when this equation of motion, either in its original or in its modified form, is integrated in a Kohn-Sham setting with Gaussian basis functions, several issues arise which render it inapplicable to transport calculations.…”