Page 52 - Mechanism and Theory in Organic Chemistry

Problems 41

(b) In each molecule that has a delocalized bonding system, identify the
orbitals that interact to form the delocalized molecular orbitals.
O\ /O
N-N
o/ \
0

KzCO3 Sodium nitrate
Allene (H3C)30BF4
Butadiene Benzyl cation
Sodium phenoxide Phenyl anion
Nitrobenzene 3,5-di-tert-butyl-4-nitrophenoxide
N-N-0
2. What kinds of symmetry are possible for interactions of d orbitals?
3. In the pentadienyl radical, predict the distribution of the unpaired electron
(a) from the resonance model, and (b) from the molecular orbital model.
4. Construct a complete orbital model for -HN3, showing both a and T molecular
orbitals, and giving an approximate energy-level diagram showing electron occupancy.
Compare the MO model with the resonance model.
5. Construct a MO model for twisted ethylene, in which the two CH, groups lie
in mutually perpendicular planes. Why does the molecule prefer coplanarity ?
6. Explain why dehydroannulenes, which have some of the double bonds of the
annulene replaced by triple bonds, can be considered in aromaticity theory as equivalent
to the parent annulene. What advantages might dehydroannulenes have over annulenes
in the study of aromaticity?
Problems 7-1 1 require the material in Appendix 1.
7. Verify that the hybrid orbital in Equation A1.9 (p. 46) is normalized for any
values of m, 8, 4.
8. Write the expression for a normalized spa hybrid orbital oriented along the line
from the origin to the point ( - 2, 3, - 1).
9. Write the expression for a normalized hybrid orbital with 28 percent s
character lying in the xy plane at an angle of 60" from the x axis.
10. If s, p,, p,, jz orbitals are to be hybridized, and the fractional s character of
three hybrids are specified, what remains to be specified before the hybrid set can be
written explicitly?
11. What are the fractional s and p characters of a pair of equivalent hybrids with
an angle of 100" between them? If the other two hybrids are required to be equivalent
to each other, what are their fractional s and p characters, and what is the angle be-
tween them ?

Problems 12 and 13 require the material in Appendix 2.
12. Find the Huckel energy levels and molecular orbitals for butadiene, cyclo-
butadiene, and pentatrienyl.
13. In the Huckel theory the T electron energy is defined as the sum of the orbital
energies of all the T electrons. Thus for ethylene, with two electrons in an orbital of
energy 8, the T electron energy is 28. Resonance energy is the difference between the
calculated T electron energy and the T electron energy the system would have if the
electrons were in localized ethylene double bonds. Find the resonance energies for the
systems in Problem 12.