100
4 Rotation of the Polyatomic Molecule
Molecule
Moments of inertia a
Linear
X
1 X
2
· · · X
a
N
(C
∞υ , HC
≡ CF)
I
=
1
M
n
i≥ j
m
X
i m
X
j r 2
X
i X
j
Spherical
XY
4
(T d
, CH
4
)
I
=
8
3 m
Y r 2
XY
XY
6
(O h
, SF
6
)
I
= 4m
Y r 2
XY
Symmetric
planar, XY
3
(D 3h
, BF
3
)
I
z
= 3m
Y r
2
XY
I
x
= I
y
= I
z
/2
pyramidal, XY
b
3
(C 3v
, NH
3
)
I
x
= I
y
= 2m
Y r
2
XY sin
2 θ
2
+
m
X m
Y
M
r
2
XY
3
− 4 sin
2 θ
2
I
z
= 4m
Y r
2
XY sin
2 θ
2
planar, XY
4
(D 4h
, XeF
4
)
I
z
= 4m
Y r
2
XY
I
x
= I
y
= I
z
2
XY
5
(D 3h
, PF
5
)
c
I
z
= 3m
Y r
2
eq
I
x
= I
y
= 3m
Y r
2
eq + 2m
Y r
2
ax
(continued)