量子化学作业 第十一章（2016）
11‒5. Use molecular orbital theory to explain why the dissociation energy of N2 is
greater that of [N2]+, but the dissociation energy of [O2]+ is greater than that of O2.
11-8. Predict the relative bond strengths and bond lengths of diatomic carbon, C2, and
its negative ion, C2 .
11‒11. In Section 11.2, we constructed molecular orbitals for homonuclear diatomic
molecules using the n = 2 atomic orbitals on each of the bonded atoms. In this
problem, we will consider the molecular orbitals that can be constructed from n = 3
atomic orbitals. These orbitals are important in describing diatomic molecules of the
first row of the transition metals. Once again we chooser the z axis to lie along the
molecular bond. What are the designations for the 3sA ± 3sB and 3pA ± 3pB molecular
orbitals? The n = 3 shell also contains a set of five 3d orbitals. (The shapes of the 3d
atomic orbitals are shown in Figure 7.8.) Given that molecular orbitals with two nodal
planes contain the internuclear axis are called δ orbitals, show that ten 3dA ± 3dB
molecular orbitals consist of a bonding σ orbital, a pair of bonding π orbitals, a pair of
bonding δ orbitals and their corresponding antibonding orbitals.
Figure 7.8
11‒12. Determine the largest bond order for a first‒row transition‒metal homonuclear
diatomic molecule. (See the previous problem. )
11‒16. In this problem, we consider the heternuclear diatomic molecules CO. The
ionization energies of an electron from the valence atomic orbitals on the carbon atom
and the oxygen atom are listed below:
Atom
O
Valence orbital
Ionization energy/(MJ·mol‒1)
2s
3.116
2p
1.524
C
2s
1.872
2p
1.023
Use these data to construct a molecular orbital energy‒level diagram for CO. What
are the symmetry designations of the molecular orbitals of CO? What is the electron
configuration of the ground‒state of CO? What is the bond order of CO? Is CO
paramagnetic or diamagnetic?
11‒24. Determine the ground‒state molecular term symbols of O2, N2, [N2]+, and
[O2]+.
11‒26. The highest occupied molecular orbitals for an excited electronic configuration
of the oxygen molecule are (1πg)1(3σu)1. What are the molecular term symbols for
oxygen with this electronic configuration?
11-27. Show that the  molecular orbital corresponding to the energy for E    
ethene is   
1
(2 pz1  2 pz 2 ) .
2
11 - 30. Show that
x
1
0
0
1
x
1
0
0
1
x
1
0
0
0
1
x
gives the algebraic equation x 4  3x 2  1  0 .
11‒37. Calculate the Hückel π‒electronic energies of cyclobutadiene. What do Hund’s
rules say about the ground state of cyclobutadiene? Compare the stability of
cyclobutadiene with that of two isolated ethylene molecules.