Chem 481L
Fall 2009
Lab Module #2
Molecular Orbital Treatment of H
2
+
Due Date:
Noon, Tuesday, September 15
Submit via Blackboard
Goal:
The goal of this week’s module is to use Mathcad to evaluate the overlap, resonance and
Coulomb integrals from molecular orbital theory that describe interactions between the various
bodies in H
2
+.
These integrals will then be put together to produce the potential energy curves
for ground level bonding and antibonding orbitals of H
2
+.
Research questions:
Can we use Mathcad to replicate molecular orbital theory’s treatment of
the ground level bonding and antibonding orbitals for H
2
+?
Introduction
H
2
+ consists of two nuclei a distance R apart and one electron which is r
A
away from nucleus A
and r
B
away from nucleus B.
At each extreme, the electron can be thought of as interacting
solely with either A or B.
In these limits, the orbitals that describe the electron motion are
hydrogen 1s atomic orbitals centered on A and B, as shown in Atkins textbook (or wikipedia!)
φ
A
=
φ
B
=
where a
0
is the Bohr radius.
We can make a linear combination of the atomic orbitals (LCAO) situated on A and B which will
then provide us with a model of the electron when it is interacting with both nuclei (see Atkins
handout).
Ψ
+
= N(φ
A
+
φ
B
)
where N is a normalization constant.
Note that r
A
and r
B
are not independent; according to the law of cosines:
r
B
2
=
r
A
2
+ R
2
– 2 r
A
R cos θ
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 Spring '07
 PIELAK
 Atom, Electron, Mole, Chem 481L Lab, Molecular Orbital Treatment

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