Problem Set 9 Solutions

7
5 b.) continued
The third MO (which is unoccupied) is defined by the expression
φ 3 = c 13 f 1 + c 23 f 2 + c 33 f 3
= 0.0 f 1sLi − 0.820 f 2sLi + 0.493 f 1sH .
Here, we see that, like the second MO, the third MO consists of a combination of the 2s valence orbital on
Li and the 1s valence € orbital on H, φ 3 = −0.820 f 2sLi + 0.493 f 1sH . This appears to be an antibonding MO;
since one coefficient is positive and the other is negative, the atomic orbitals subtract to form an
antibonding MO with a node along the internuclear axis.
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c.) The molecular orbital energies are ε 1 = –2.426 a.u., ε 2 = –0.618 a.u., and
a.u. Do these results agree qualitatively with what you would expect
ε 3 = 0.085
The energies of the AOs in atomic units are
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ε 1sLi = − 2.478
ε 2sLi = − 0.196
ε 1sH = − 0.500.
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What do these atomic orbital energies suggest about the AOs that mix to form MOs
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We might expect the first MO, which represents something closely resembling the core 1s orbital on Li, to
be much lower in energy than the second MO, which represents the bonding MO. This is why we say that
the core atomic orbitals do not contribute to the bonding – they are generally too low in energy to
effectively combine with the valence atomic orbitals to form the bonds. Since MO1 consists solely of the
core 1s atomic orbital on Li, we would expect that the orbital energy of MO1 would be nearly the same as
the energy of the 1s atomic orbital, and it is. It is also much lower in energy than the other AOs or MOs.
We also would generally expect a bonding MO to have an orbital energy that is less than zero. A negative
orbital energy generally indicates a favorable interaction (since it is dominated by the Coulomb interaction,
which is negative in sign for an attractive interaction). The second MO consists of a linear combination of
the 2s orbital on Li and the 1s orbital on H, forming a bonding orbital. The energy of this MO is similar
to the energies of the two atomic orbitals from which it is formed, but the MO energy is a bit lower due to
the favorable bonding interaction, so this also makes sense.
Finally, we would expect an antibonding MO to have an orbital energy that is greater than zero. A positive
orbital energy generally indicates an unfavorable interaction. The third MO consists of a linear combination
of the 2s orbital on Li and the 1s orbital on H, forming an antibonding orbital. The energy of this MO is
higher than the energies of the two atomic orbitals from which it is formed, so this also makes sense.
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