Physical Chemistry Third Edition

904 21 The Electronic Structure of Polyatomic Molecules

21.61Tell which of the following molecules and ions will have
nonzero dipole moments:
a.SO^24 −
b. BF 3
c.HClO 4
Explain your answers.

21.62Tell which of the following molecules and ions will have
nonzero dipole moments:

a. H 2 CCCH 2

b. NO 2

c.CO 2

21.63Show geometrically that the dipole moment of a

tetrahedral molecule such as carbon tetrachloride

vanishes. Place the bonds on alternate diagonals of a cube

centered at the origin and with faces perpendicular to the

Cartesian coordinate axes.

21.10 More Advanced Treatments of Molecular

Electronic Structure. Computational

Chemistry

Our discussion of molecular electronic structure has been extremely crude compared

with current quantum chemistry practice. Over the past several decades modern digital

computers have made calculations possible that previously could only be dreamed

of. Dewar and Storch have written a review article comparing the results of different

semiempirical and ab initio methods in calculating enthalpy changes of reactions.^10

At the time this article was published (1985), no method had given accuracy that is

adequate for quantitative chemical purposes for anything but a few small molecules.

However, considerable progress has been made since that time.

Semiempirical Methods

There are a number of semiempirical methods, each with its own set of approximations.

These methods are analogous to the Hückel method described in Section 21.6 but are

more sophisticated. Some use the variation method, but more use the Hartree–Fock–

Roothaan method. All of them represent the molecular orbitals as linear combinations

of a set of basis functions. There are simultaneous equations to be solved for the

coefficients in the linear combinations. These equations contain numerous integrals,

including matrix elements of one-electron Hamiltonians such as those in Appendix H for

the Hückel method, overlap integrals, and integrals representing expectation values of

electron–electron repulsions. These integrals contain only basis functions, so that they

can be evaluated numerically if the Hamiltonian is known. In semiempirical methods

approximations are used to avoid explicit calculation of some or all of the integrals. Two

types of approximations are invoked: The first is the assumption that certain integrals

can be approximated by zero, and the second is a scheme to assign approximate values

to other integrals such that results agree with experimental data, as was done in the

Hückel method.

The Extended Hückel Method

The extended Hückel method was pioneered by Wolfsberg and Helmholz.^11 It is not

restricted to the electrons in pi orbitals and can treat molecules that are not planar

(^10) M. J. S. Dewar and D. M. Storch,J. Am. Chem. Soc., 107 , 3898 (1985).
(^11) M. Wolfsberg and L. Helmholz,J. Chem. Phys., 20 , 837 (1952).