Chapter 5 Molecular Orbitals 79
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larger than those on oxygen.
The 3 orbitals also show the influence of electronegativity, this time with the lobe
extending to the left from the less electronegative atom being the largest, with CO once
more showing the greatest effect. This can be viewed in part as a consequence of the 3
orbital being a better match for the energy of the less electronegative atom’s 2s orbital
which, together with the 2p
z
orbital of the same atom, interacts with the 2p
z
orbital of the
more electronegative atom (the atom shown on the right).
c. The results vary greatly depending on the software used. The results using one approach,
AM1, are shown below (numerical values are energies in electron volts).
*
π*
π
*
LUMO HOMO
CN
–
14.7 0.13 –3.13 –5.10 –9.37
–28.0
CO 5.28 0.94 –13.31 –16.30 –22.00 –41.2
N
2
6.03 1.00 –14.32 –16.19 –21.43 –41.39
NO
+
–4.42 –9.62 –26.13 –28.80 –35.80 –56.89
In this table, the energies decrease as the atomic numbers increase (with CO and N
2
giving mixed results). There is considerable mixing of the orbitals, a phenomenon
that may raise the energy of the (HOMO) orbital above the energy of the π orbitals–
as is the case in each of these examples.
5.38 Among the trends that should be observed is the effect on the shapes of the π and π* orbitals
(see orbitals of CO labeled as 1π and 1π* in Figure 5.13) as the difference in electronegativity
between the atoms increases (this trend is also observed in Problem 37). For BF and BeNe, the
lobes of the π orbitals should become increasingly concentrated on the more electronegative
atoms, and the lobes of the π* orbitals should become increasingly concentrated on the less
electronegative atoms (a pattern that has begun with CO, if the orbital shapes for CO are
compared with those of the isoelectronic N
2
).
An additional effect is that the size of the protruding orbital lobe of the less electronegative atom
should increase as the difference in electronegativity between the atoms increases; this can be see
in the 3 orbital of CO in Figure 5.13. Additional trends in the other molecular orbitals can also
be noted.
5.39
In one bonding orbital, the H s orbitals have the same sign and add to the Be s orbital in the
HOMO–1 orbital. Subtracting the Be s orbital results in the antibonding LUMO. The difference
between the two H s orbitals added to the Be p
z
orbital results in the HOMO; subtracting the Be
p
z
results in the LUMO+3 orbital. LUMO+1 and LUMO+2 are the Be p
x
and p
y
orbitals and are
nonbonding (and degenerate) in BeH
2
. For an energy level diagram, see the solution to Exercise
5.8 in Appendix A.
5.40
BeF
2
is similar to BeH
2
, with the addition of π and π* orbitals from the p
x
and p
y
orbitals,
extending over all three atoms. The F p
x
orbitals with opposite signs do not combine with the Be
orbitals, and neither do the p
y
orbitals; the p
x
and p
y
orbitals form the HOMO and HOMO+1 pair.