Chemistry Reference
In-Depth Information
The adiabatic approximation includes in U
e
(q) the third term in (9.6),
which describes the effect of the nuclear Laplacian
r
2
a
on the electronic
wavefunction
Y
e
. Both small vibronic terms in (9.6) can be included in a
variational or perturbative way in a refined calculation of the molecular
energy as a function of nuclear coordinates, and are responsible for
interesting fine structural effects in the vibrational spectroscopy of polya-
tomic molecules (Jahn-Teller and Renner effects).
9.2 THE HYDROGEN MOLECULE H
2
Electrons and nuclei in the H
2
molecule are referred to the interatomic
coordinate system of Figure 9.1. At A and B are the two protons (charge
รพ
1), a distance R apart measured along the z-axis; at 1 and 2 are the two
electrons (charge
1). The bottom part of the figure shows the overlap
x
2
r
12
1
1
r
2
r
1
r
A2
r
B1
z
B
A
R
y
A
B
b
(
r
)
S
a
(
r
)
Figure 9.1 Interatomic coordinate system (top) and overlap S between spherical AOs
(bottom)
