Biomedical Engineering Reference
In-Depth Information
Table 16.1
Population of the
molecular orbitals used in the
CNDO description of the
H
2
O molecule
Molecular orbital
Population
1a
1
2O(1s)
2a
1
1.48 O(2s)
C
0.52 H(1s)
1b
2
1.18 O(2p)
C
0.82 H(1s)
3a
1
1.44 O(2p)
C
0.34 H(1s)
C
0.22 O(2s)
1b
1
2 O(2p)
Furthermore, let us note that this description was also used in the binary-
encounter-dipole (BED) model developed by Kim and Rudd [
34
,
35
] for providing
ionization cross sections for a large set of molecules impacted by electrons.
Finally, we propose here a third description of the water molecule which
has been successfully applied for treating the ionization of simple molecules
like CH
4
; NH
3
and H
2
O by electrons [
36
] as well as by light-ion impact,
namely, H
C
; He
2
C
and C
6
C
ions [
2
,
37
-
39
]. In these works, we have used the
molecular description provided by Moccia who reported one-center ground state
wave functions for molecules of the type XH
n
, namely, for HF, CH
4
and SiH
4
[
40
], for NH
3
; NH
4
; PH
3
and PH
4
[
41
], and for H
2
O; H
2
SandHCl[
42
]. The
molecular orbitals were expressed in terms of Slater-like functions all centered
at a common origin coinciding with the X nucleus since the electronic density
was - for these molecules - mainly governed by a “central” atom. Thus, providing
suitable analytical wave functions was quite similar to the atomic case. Furthermore,
note that the problem of evaluation of multi-center integrals depends on the type of
basis functions used. Indeed, although it appears that there are no convenient and
practical ways to evaluate such integrals for more than two non-aligned centers
when Slater-type functions are used, it is worth noting that the use of Gaussian
functions for the radial part decreases the difficulties even if it is clear that the
Gaussian basis set needs probably 40% more such functions to achieve comparable
results [
40
]. Under these conditions, the ten bound electrons of the water molecule
were distributed among five one-center molecular wave functions corresponding to
the five molecular orbitals of the water molecule (for more details concerning the
coefficients needed for this kind of molecular description, we refer the reader to our
previous works [
2
,
4
,
36
,
38
] and to the supplementary material online at
http://www.
aip.org/pubservs/epaps.html
[
43
]).
Finally, it is important to note that these molecular wave functions refer to the
calculated equilibrium configurations,
i.e
. to the geometrical configurations which,
among many others considered, give the minimum of the total energy and agree
with the experimental data in terms of HOH angle, bound O-H length, 1
st
ionization
potential and electric dipole moment as reported in [
42
].
