Appendix 1
99
There are seven quartic centrifugal distortion constants for a planar asymmetric top
for which the symmetry plane is ab: T aa , T bb , T cc , T ab , T bc , T ca , and T
∗
ab = τ abab
4
(Note that τ caca = τ bcbc = 0).
The constants T 1 and T 2 are linear combinations of the last four constants of the
former set
T 1 = T ab + T bc + T ca + 2T
∗
ab
(4.50)
T 2 = AT bc + BT ca + CT ab + 2CT
∗
ab
(4.51)
To obtain all the constants, the planarity relations have to be used (Dowling 1961)
T bc =
1
2
B
2 C
2
−
T aa
A 4 +
T bb
B 4 +
T cc
C 4
(4.52)
T ca =
1
2
C
2 A
2
T aa
A 4 −
T bb
B 4 +
T cc
C 4
(4.53)
and
T ab =
1
2
A
2 B
2
−
T aa
A 4 −
T bb
B 4 +
T cc
C 4
(4.54)
And
T
∗
ab may be obtained from Eq. (4.50)
(4.55)
Actually, there are different ways to determine T
∗
ab , and they are discussed by
Yamada and Winnewisser (1976).
Appendix 2
Expression for the moments of inertia of some simple molecules (the symmetry
group and one example are given in parentheses.