Appendix 2
101
(continued)
Molecule
Moments of inertia a
axial, ZXY
3
b
(C 3v
, CH
3 F)
I
x
= I
y
= 2m
Y r
2
XY sin
2 θ
2
+
3m
Y
M
(m X
+ m
Z
)r
2
XY
1
−
4
3
sin
2 θ
2
+
m
Z r
XZ
M
(3m Y
+ m
X
)r XZ
+ 6m
Y r
XY
1
−
4
3
sin 2 θ
2
I
z
= 4m
Y r
2
XY sin
2 θ
2
Asymmetric
planar, ZXY
2
b,d
(C 2v
, H
2 CO)
I
z
= 2m
Y r
2
XY sin
2 θ
2
I
x
=
1
M
[m
Z
(2m Y
+ m
X
)r
2
XZ + 2m
Y
(m X
+ m
Z
)r
2
XY cos
2 θ
2
+ 4m
Y m
Z r
XZ r
XY cos
θ
2
a
r
ij is the distance between atoms i
and j, m
i is the mass of atom i, M
is the total mass of the molecule, and z
the figure axis (principal symmetry axis)
b
θ is the YXY angle
c
Trigonal bipyramidal molecule, r
eq and r
ax are the equatorial and axial bond length, respectively
d
The y-axis
is perpendicular to the xz
plane, with z
the C
2 axis. I
y
= I
z
+ I
x