Biomedical Engineering Reference
In-Depth Information
which are responsible for starting the nucleation into water droplets and can
lead to the formation of clouds, fog, the deposition of nitrogen, acidification of
precipitations, etc.. In addition, molecular clusters have been observed in interstellar
media.
In general, clusters are present in a variety of dense gaseous media, where they
form spontaneously; in this environment, many studies have analysed the interaction
between electrons and clusters, particularly focusing on the effect clusters have in
electron transport and on the attachment, ionisation and fragmentation processes.
Clusters of biophysically relevant molecules solvated by water molecules are being
investigated as models for
in vivo
proteins, RNA, DNA, etc. (see, for example, [
4
]).
In spite of the pervasiveness of molecular clusters, and the importance of low
energy electron scattering in a variety of environments as initiators of chemical
processes [
5
], theoretical work on electron collisions with molecular clusters is
scarce. Studies have been restricted mostly to dimers [
6
-
8
]. An exception to this
is the work of Fabrikant and collaborators, who have concentrated on electron
attachment and vibrational Feshbach resonances [
9
].
It is therefore highly desirable to have available a theoretical approach for
electron collisions with molecular clusters. Evidently, standard electron scattering
techniques can be used. However, as the size of the cluster increases, the compu-
tational requirements of these calculations, particularly
ab initio
ones, increases
significantly: currently, the biggest
ab initio
calculations tackle collisions with
targets formed by
20-25 atoms. A 10 monomer cluster of triatomic or larger
molecules will be bigger and require more resources.
A method has been developed [
8
,
10
], based on multiple-scattering ideas, to treat
elastic low energy electron collisions with molecular clusters within the fixed-nuclei
approximation. This approach was initially proposed by Caron and Sanche ([
11
]
and references therein). The method is based on the assumption that the potential
of a complex target can be separated into non-overlapping regions each of which
contains a single scatterer. In the current approach, and in contrast to earlier work
on electron scattering [
12
], each molecule in the cluster (i.e. each monomer) is taken
as a scatterer.
In this chapter, we will review the theory underlying the technique, summarise
some practical issues regarding its application and present some results.
'
7.2
Multiple-scattering approach
The purpose of the method is to provide information on the electron-molecular
cluster collision process by combining scattering information for each of the
molecular sub-units. In order to do this, we need to derive an expression linking
cluster scattering data with monomer scattering data.
