Problem Set 9

CHM 3411, Dr. Chatfield, Spring 2009

Due: Fri. Mar. 27

Suggested Discussion Question (Chapter 11): 1-6. Suggested Exercises (Chapter 11, all (b)): 1, 2, 4, 7, 10, 11, 12.

In this problem set, we explore molecular orbital theory.

1. Atkins Exercises 11.3b and 11.5b

2. Atkins Exercise 11.8b

3. W saw in class that a molecular orbital can be constructed as a linear combination of atomic orbitals (MO-LCAO). Below are unnormalized MOs expressed in this way. For a homonuclear diatomic molecule with the z axis coincident with the internuclear axis, characterize the MOs as s, p, or d; g or u; and bonding or antibonding. Sketch the AOs and resulting MO in each case. Note: although we did not discuss d MOs in class, they are analogous to d AOs; observed from along the z axis, d MOs look like d AOs.

a) 2p_y(A) + 2p_y(B) b) 2p_z(A) + 2p_z(B) c) 2p_z(A) – 2p_z(B)

d 2s(A) – 2s(B) e) 3d_xy(A) + 3d_xy(B) f)3d_z2(A) + 3d _z2 (B)

4. f_a and f_b are chosen to be a normalized set of basis functions for an MO-LCAO wave function for a one-electron homonuclear diatomic system. It is found that the values for the integrals involving these functions are

a.u. a.u.

a.u. a.u.

where is the molecular Hamiltonian. Find an upper bound for the ground state electronic energy for this system and the corresponding MO-LCAO normalized approximate wave function.

5. Atkins Exercise 11.12b

6. Atkins Problem 11.6

7. Write down secular determinants for the p-electron system (Huckel theory) for the following molecules (take careful note of the connectivity). Some of the carbons are numbered for convenience.