I' Diatomic Molecules

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I. Diatomic Molecules
1. General Properties
O stands for high order interactions, name,
spin-orbital and so on.
Three motions

• Energy Time
• Electronic energy 10 eV 100 as
• (b) Vibrational energy 0.1 eV 10 fs
• (c) Rational energy 0.001 eV 1 ps

Note
Translation, vibration and rotation terms
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I. Diatomic Molecules
Born-Oppenheimer approximation
With
Note that BO approximation is valid for most
molecules, not only the diatomic molecules
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I. Diatomic Molecules
2. Symmetry and designation of electronic states
of diatomic molecules
If we use a cylindrical coordinate and make
transformation
(a)
(b) Total electron spin S,
(c) Reflection on a plane contains the molecular
axis,
(d) Reflection at the origin for homonuclear
molecules,
For homonculear molecules
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I. Diatomic Molecules
Depend on the system
Symmetry
(a)
(b)
Note for ? ? 0, the energies of ? states are
degenerate.
(c)
(d)
notation
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I. Diatomic Molecules
3. Born-Oppenheimer approximation
The exact total wave can be written as
with
Born-Oppenheimer approximation requires that
with
Thus, we separate the electron and nuclear
motions.