Biomedical Engineering Reference
In-Depth Information
Tabl e 7. 2 Overview of the
6-particle states of benzene,
sorted by S z and symmetry.
Orbitals with A -and B -type
of symmetry show no
degeneracy, while E -type
orbitals are doubly
degenerate. From [ 20 ]
Number
of states
States with given
symmatry
NS z [
h
]
6
3
1
1 B 1 u
2
26
4 A 1 g
2 A 2 g
2
6 E 2 g
4 B 1 u
2 B 2 u
2 × 6 E 1 u
×
1
225
16 A 1 g
20 A 2 g
2 × 36 E 2 g
22 B 1 u
17 B 2 u
2
×
39 E 1 u
0
400
38 A 1 g
30 A 2 g
2
66 E 2 g
38 B 1 u
30 B 2 u
2
×
×
66 E 1 u
.
1
225
2
36
3
1
the equilibrium chemical potential
μ 0 =
0. We specialize the tunnelling Hamiltonian
( 7.4 ) to the following form
d
χσ
χ k σ
c
χ
H tun =
t
c
σ +
d χσ
,
(7.28)
χ
k
k
σ
where we define d
χσ
as the creator of an electron in the benzene carbon atom which
. In particular d
d ,
d
=
is closest to the lead
χ
:
, respectively, in the para and
meta configuration, while d
d
:
=
in both setups (see Fig. 7.6 for the numbering
of the benzene carbon atoms).
7.4.2
Symmetry of the Benzene Eigenstates
In this section, we will review the symmetry characteristics of the eigenstates of the
interacting Hamiltonian of benzene, focusing on the symmetry operations
σ v and
C n which have a major impact on the electronic transport through the molecular I-
SET. Benzene belongs to the D 6 h point group. Depending on their behavior under
symmetry operations, one can classify the molecular orbitals by their belonging to a
 
Search WWH ::




Custom Search