Lectures 7 and 8:
Molecular Orbital Theory
Molecular orbitals
are regions of highest probability for locations of electrons in
molecules.
They are composed of contributions (“linear combinations”) of atomic
orbitals, or of other molecular orbitals.
Remember that the function ψ is a solution of the Schroedinger equation associated with
an energy, and that ψ
2
is the probability density for the electron to be located in a specific
part of the volume around an atom.
The integral of ψ
2
over all of space must equal one!
Combinations of ψ are also solutions
to the Schroedinger equation as long as the
resulting set of probability densities remains normalized.
For example, let us imagine two hydrogen atoms H
a
and H
b
that each have atomic orbitals
1s, given by wave functions ψ
a
and ψ
b
.
We can combine these two wave functions to make two new ones:
Cψ
a
+ Cψ
b
and Cψ
a

Cψ
b
.
If we add up the two probability densities, we get
C
2
(2ψ
a
2
+ 2ψ
b
2
)
.
If we set C = 1/√2
then the result is what we had with the two individual atoms, so this checks out!
Note:
the text oversimplifies by omitting the coefficient C.
The two new wave functions are the two molecular orbitals for the H
2
molecule.
The symmetric combination has lower energy than the sum of the two atomic orbitals,
and a high probability that the electrons are between the two H atoms.
This is the
bonding
orbital.
The unsymmetric combination has higher energy, and has a node
between the two atoms with a low probability that the electrons are between the atoms.
This is the
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 Spring '09
 KATZ
 Atom, Atomic Orbitals, Electron, Molecule

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