Biomedical Engineering Reference
In-Depth Information
50
100
Adenine :
A
Adenine :
A
40
80
30
60
20
40
10
20
0
2
4
6
8
10
12
0
2
4
6
8
10
12
SE
SEP
CC
40
Guanine :
A
160
120
80
40
0
Guanine :
A
30
20
10
0
0
2
4
6
8
10
12
0
2
4
6
8
10
E
(
eV
)
E
(
eV
)
Fig. 6.1
Calculated elastic cross sections for the purine bases adenine and guanine. See text for
details of the models used
performing exceptionally large CC expansions, tends to overestimate resonance
positions. The uncontracted approach leads to systematically lower resonance
positions. However it is not clear that this approach is completely balanced [
43
]
and therefore it is possible to obtain resonances which are too low in energy or
even become bound states. Furthermore, fully uncontracted calculations can become
very large, requiring either unacceptably long times for the calculations or further
compromises to be made on the size of the model wavefunctions chosen. For
a more thorough discussion of the differences between these models, including
full technical details, the reader is referred to our study on uracil [
13
]. The CC
calculations reported here retained the lowest 32 states for uracil (U), 16 states for
guanine (G), adenine (A) and thymine (T) and 20 states for cytosine (C).
Our previous study of resonances in phosphoric acid [
9
] revealed that the
resonances showed little sensitivity to isomerisation. Our calculations suggest that
this insensitively even extends between molecules with similar structures. Thus our
calculations show a total of four
-type shape resonances for the purine bases, while
the pyrimidines all have three.
The effect of these resonances can clearly be seen in the elastic cross sections.
Figures
6.1
and
6.2
summarize our calculated elastic cross sections for the purine
and pyrimidine DNA bases respectively. It should be noted that for strongly dipolar
systems, such as the ones considered here, higher partial waves have a profound
effect on the total elastic cross section, particularly at low energy. It is possible to
correct for this using the Born approximation [
56
], which we have indeed done
elsewhere [
13
]. However this correction is so big that it obscures the resonance
