Physical Chemistry for Engineers
CHEM 4521
MO Theory Practice Problems
(1) Consider the molecules Cl2 and N2 .
(a) Write the minimum linear combination of atomic orbitals (LCAO) needed to
express the molecular orbitals (MOs) for:
(i) Cl2
(ii) N2
(b) Write the MO diagrams for:
(i) Cl2
(ii) N2
(c) Calculate the bond order for:
(i) Cl2
(ii) N2
(d) Which coefficients dominate in the LCAO for the:
(i) σ orbital of N2
(ii) π ∗ orbital of Cl2
(e) Explain in terms of your MO diagrams and calculations above which molecule
has a stronger bond N2 or Cl2 .
(2) Consider the molecules NaH and LiF.
(a) Write the minimum linear combination of atomic orbitals (LCAO) needed to
express the molecular orbitals for:
(i) NaH
(ii) LiF
(b) Determine which of the AOs will most significantly contribute to the bonding
of:
(i) NaH
(ii) LiF
(c) With the atomic orbitals you selected above, write a molecular orbital diagram
for:
(i) NaH
(ii) LiF
(d) For the bonding orbital of LiF, which coefficient(s) in the LCAO are largest?
(3) Consider the molecule vinyl-cyclobutadiene pictured below.
(a) Setup, but do not evaluate, the secular determinant for the electrons in the
conjugated π molecular orbitals. Use the approximations from Hückel theory
to simplify this determinant.
(b) How many molecular orbitals will be produced by solving the secular equation?
(c) Make a rough sketch of the solution for the lowest and highest energy molecular
orbitals of the conjugated π system.
(d) Given that none of the molecular orbitals in the conjugated π system of the
molecule are degenerate, how many of the molecular orbitals are occupied by
electrons in the ground state of the molecule?
Vinyl-cyclobutadiene