Biomedical Engineering Reference
In-Depth Information
that the compound undergoes effective DEA within a low-energy resonant feature
at 1 eV and a further resonance peaking at 8 eV. The DEA reactions are associated
with the direct cleavage of the C-O and the P-O bonds but also the excision of
the PO
,PO
3
and H
2
PO
3
units. They propose that the most direct mechanism of
single strand breaks occurring in DNA is due to DEA directly to the phosphate
group.
Low-energy electron collisions with molecules can result in a variety of different
processes [
46
]. A common feature of all these processes is that they can be
considered to go via an intermediary,
AB
. One of the methods used to consider
low-energy electron-molecule collisions is the R-matrix method [
10
,
11
,
45
], which
is built around obtaining accurate wave functions for this intermediary and hence
gives a theoretical framework capable of modelling all the above processes.
In this chapter we describe the application of R-matrix calculations to DNA
and RNA constituents. A particular advantage of this method is its ability to
treat not only shape resonances, which have been widely studied by a vari-
ety of methods, but also Feshbach resonances. Feshbach resonances have been
found to be important experimentally [
2
,
3
] but have received much less attention
theoretically.
The size of these molecules and, in particular, the complexity of their electronic
wavefunctions makes such calculations very challenging. So far the study of each
system has necessitated the consideration of a number of models in order to obtain
reliable results. We have completed studies on electron collisions with uracil [
13
],
phosphoric acid [
9
], adenine, guanine, cytosine and thymine which consider these
issues in turn for each molecule. Here, instead, we present a set of results for
electron collisions with the bases calculated using a single model, which facilitates
intercomparison between these species.
6.2
The R-matrix method
The basis of our calculations is the R-matrix method. The topic of electron-molecule
collision calculations has been extensively reviewed by one of us [
45
] and only a
flavor of the method will be given here.
The underlying physical model used in R-matrix calculations is the division of
space into an inner region, contained within a sphere of radius
and centered on
the target center-of-mass, and an outer region. The inner region is designed to be
large enough to contain the entire electron density of the molecular target, including
those for excited states in calculations which consider electronic excitation. This can
be an issue for the biomolecules considered since they are considerably larger than
the small molecules traditionally studied using this methodology. In the inner region
the scattering electron and target electrons are treated as being indistinguishable and
all interactions, including electron-electron correlation and exchange, are explicitly
considered. Conversely, in the outer region the scattering electron is only affected
a
