6.2 Diatomic Molecules
261
Fig. 6.1 Illustration of
potential energy curves for a
diatomic molecule as a
function of internuclear
separation R. D e ≡ D e is the
depth, D 0 the dissociation
energy, for the AB pair in the
ground electronic state
R e
massive than typical nuclei in the molecule, so that the corresponding velocities
differ by approximately two orders of magnitude. This approximation is sometimes
known as the ‘clamped nuclei’ approximation, but is more commonly known as the
Born–Oppenheimer approximation. It is only within this Born–Oppenheimer (BO)
approximation that the concept of a potential function holds. Three types of potential
energy curve are illustrated in Fig. 6.1: an interaction with an attractive well, typified
by a diatomic molecule AB formed from two ground state neutral atoms A and B,
a purely repulsive interaction, and an upper (attractive) curve corresponding to a
diatomic molecule AB ∗ formed from a ground state atom A and an excited state
atom B ∗ , as indicated by the higher-energy asymptote.
The Schrödinger equation for a diatomic molecule can be expressed in the
generic form
H(r, R) = EE(r, R) ,
(6.2.1)
with r referring (collectively) to electron coordinates and R to nuclear coordinates.
Now if the total energy E for the molecule can be split into two parts, one
corresponding to nuclei, the other to electrons, we may write E as
E = E nuclear motions + E electron motions ,
(6.2.2)