Abstract
The socalled driven Liouville−von Neumann equation is a
dynamical formulation to simulate a voltage bias across a molecular system and to
model a timedependent current in a grandcanonical framework. This approach
introduces a damping term in the equation of motion that drives the charge to a
reference, out of equilibrium density. Originally proposed by Horsfield and coworkers, further work on this scheme has led to different coexisting versions of
this equation. On the other hand, the multipleprobe scheme devised by Todorov
and collaborators, known as the hairyprobes method, is a formal treatment based
on Green’s functions that allows the electrochemical potentials in two regions of
an open quantum system to be fixed. In this article, the equations of motion of
the hairyprobes formalism are rewritten to show that, under certain conditions,
they can assume the same algebraic structure as the driven Liouville−von
Neumann equation in the form proposed by Morzan et al. (J. Chem. Phys. 2017, 146, 044110). In this way, a new formal ground
is provided for the latter, identifying the origin of every term. The performances of the different methods are explored using
tightbinding timedependent simulations in three trial structures, designated as ballistic, disordered, and resonant models. In
the context of firstprinciples Hamiltonians, the driven Liouville−von Neumann approach is of special interest, because it does
not require the calculation of Green’s functions. Hence, the effects of replacing the reference density based on the Green’s
function by one obtained from an applied field are investigated, to gain a deeper understanding of the limitations and the range
of applicability of the driven Liouville−von Neumann equation.
Original language  English 

Pages (fromto)  1254212555 
Number of pages  14 
Journal  The Journal of Physical Chemistry C 
Volume  123 
DOIs  
Publication status  Published  30 Apr 2019 
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Profiles

Daniel Dundas
 School of Mathematics and Physics  Senior Lecturer
 Atomistic Simulation Centre (ASC)
Person: Academic