Chemistry Reference
In-Depth Information
have developed a new local view of electrostatic interactions. In this approach,
the electric field is the physical quantity of interest, and the canonical partition
function is written in terms of this field. The Hamiltonian for the total electro-
static energy is then a grid sum of the field variable squared, times a constant.
The field has a value for each neighbor link on the grid. The basic algorithm
consists of solution of Gauss's law for a starting charge configuration, provides
updates of the fields by shifts of the link variables, and updates the particle
locations using a Monte Carlo procedure. This algorithm has been modified
to overcome sampling difficulties inherent in the original approach.
237-239
Transport Problems
Most of the problems considered above involved solving for the electron
distribution given a static nuclear configuration or solving for the static Pois-
son or equilibrium PB electrostatic potential. In the field of ab initio simula-
tion, the nuclei are propagated classically in real time based on forces
determined by the other nuclear locations and the electron distribution, but
the electrons are generally assumed to move on the ground-state surface. In
many important physical systems, such as molecular electronic devices and
membrane proteins, the system exists out of equilibrium, however. Thus,
we must deal with electron or ion transport. These nonequilibrium cases are
at a much earlier stage of development than their equilibrium counterparts,
both in terms of fundamental theory and numerical applications. Here we
briefly review some recent progress in modeling electron and ion transport
through nanosystems.
Modeling electron transport requires a quantum treatment, as discussed
in the introduction to this chapter. It is beyond the scope of this review to dis-
cuss details of the nonequilibrium Green's function approach, which is the
most rigorous ab initio method at the present time.
51
Suffice it to say that
the Green's function methods allow for modeling of a molecular device
coupled to electrodes at the DFT level. Several computational methods have
been developed to carry out the transport calculations.
43,44,46-48,175
Real-
space methods are ideally suited for this purpose because the physical system
involves two semi-infinite metal surfaces, with a localized molecule sand-
wiched between them. The use of a localized-orbital representation allows
for relatively easy construction of the necessary Green's functions that enter
the Landauer theory of transport. An alternative is to set up the electrode
system as a scattering problem, with incident, penetrating, and reflected waves
that assume a plane-wave form in the bulk electrodes. A clear description of
this second approach is detailed by Hirose et al.,
158
along with its relationship
to the Green's function method (with a further discussion of the alternative
Lippman-Schwinger scattering theory
240
). Real-space methods have found
application in both the Green's function and scattering wave function
approaches.
