Biomedical Engineering Reference
In-Depth Information
computational basis were complete [
32
,
33
]. Comparison of the oscillator strengths
calculated in the different formulations thus gives a measure of the completeness of
the computational basis.
12.3
Calculation of Shell Corrections
In order to obtain
C
2
for calculation of the shell corrections in (
12.8
), (
12.7
)
was fitted to calculated shell correction data for H, C, N, and O [
34
]. That data [
11
]
is given in Table
12.1
.
C
1
and
12.4
Calculational Details
In order to obtain ground state geometries, we have optimized the geometries of the
five nucleobases [
14
] at the density functional theory (DFT) level with the B3LYP
functional [
35
]andthe6-31
G(d,p) [
36
] one-electron basis set using the Gaussian
program, starting from geometries which had already been optimized at the MP2/6-
31G
level [
37
]. After the geometry optimization the molecules were oriented in
such a way that the heterocycles are placed in the xy-plane as in Fig.
12.1
and
Fig.
12.2
.
Using the minimum energy molecular geometries of the nucleobases, the vertical
singlet excitation energies and associated electronic transition dipole moments were
calculated with the TURBOMOLE program [
38
,
39
] using linear response or polar-
ization propagator methods [
17
]attheRPAlevel[
14
]. As the cc-CVTZ
C
C
(3df,p)&
s
C
p
C
d-recontracted basis developed for glycine [
24
] produced excellent results,
Table 12.1
Atomic Shell
Correction Parameters for use
in (
12.8
)
Atom
C
1
C
2
H
1.50
1.00
C
0.14
0.20
N
0.15
0.21
O
0.26
0.33
x
f
x
f
x
f
2
2
11
9
9
12
2
7
8
3
3
7
3
7
4
6
4
6
10
4
8
6
5
10
13
8
9
5
11
5
12
11
12
10
14
13
Fig. 12.1
Optimized geometries of the pyrimidine nucleobases thymine
(a)
, cytosine
(b)
,and
uracil
(c)
. The molecules lie in the xy-plane with the y-axis point upwards and the x-axis to the right
