3.8 Definition of the Different Structures
69
I 0 =
h
8π 2
1
B
0
−
1
B 0
= I e +
h
16π 2
α e
B 2
e
α
e
α e
B
2
e
B 2
e
− 1
(3.61)
But as from (3.51)
α
e
α e
=
B
2
e
B 2
e
ω
ω =
B
e
B e
3/2
(3.62)
Then
I 0 = I e +
h
16π 2
α e
B 2
e
B e
B
e
1/2
− 1
= I e
1 +
α e
4B e
(3.63)
and the r s value is
r s =
I 0
μ
= r e
1 +
α e
8B e
(3.64)
which leads to (3.65)
r e = 2r s − r 0
(3.65)
and, as α e > 0
r e < r s < r 0
(3.66)
3.8.4 Zero-Point Structure r z (or r 0
α )
This structure is the distance between average nuclear positions in the ground vibrational state at 0 K. This r z structure is interesting for two reasons: (i) It has a welldefined physical meaning, contrary to the r 0 or r s structures; (ii) it is also determinable
by electron diffraction by conversion of the r g parameters taking into account the
harmonic vibrational effects.
The spectroscopic definition was given by Herschbach and Laurie (Herschbach
and Laurie 1961). The B 0 rotational constant is transformed into a B z constant
B z = B 0 +
α
harm
e
2
= B e −
α
anharm
e
2
with α
harm
e
= −6
B
2
e
ω e
(3.67)
To calculate this structure, it is enough to know the harmonic force field. The
relation between r e and r z is