C566 Master Lecture Notes
Lecture 6
Review of Molecular Symmetry (pp 181-201, Hollas)
Elements of Symmetry
(0)
Identity, E
E(x,y,z) = (x,y,z)
z
y
x
z
y
x
1
0
0
0
1
0
0
0
1
(1)
n
-fold axis of symmetry, C
n
.
Rotation of molecule by 2
/
n
radians (n = 1, 2, …,
)
results in a nuclear arrangement that is indistinguishable from the initial state.
1
0
0
0
2
cos
2
sin
0
2
sin
2
cos
2
n
n
n
n
n
R
z
In cylindrical coordinates, it can be represented as:
C
n
(r,
, z) = (r,
+2
/
n
, z)
(2)
Plane of symmetry,
:
Reflection of the nuclei through a plane of symmetry resultes
in a molecular structure (nuclear arrangement) that is indistinguishable from the initial
structure.
Convention:
Highest-n C
n
axis is the principle (or primary) axis, called z
v
is || to the principle axis
h
is
to the principle axis
v
,
xz
, perpendicular to plane:
xz
(x, y, z) = (x, -y, z)
v,yz
parallel to plane:
yz
(x, y, z) = (-x, y, z)