Physical Chemistry Third Edition

908 21 The Electronic Structure of Polyatomic Molecules

functions that simulate Slater-type orbitals. For example, in the STO-3G basis set,

each Slater-type orbital is represented approximately by a linear combination of three

Gaussian functions.

Since the best single-configuration product of molecular orbitals still contains the

correlation error, configuration interaction (CI) is used to improve the energies. This

means that the wave function, instead of being a Slater determinant corresponding

to a particular electron configuration, is a linear combination of Slater determinants,

each corresponding to a different configuration. The CI procedure appears to con-

verge slowly, and numerous configurations are required to obtain nearly complete

elimination of the correlation energy. Up to a million configurations have been used

in some calculations, but the use of many configurations requires a large amount of

computer time.

Most of the methods we have mentioned rely on the Hartree–Fock–Roothaan

method. The principal shortcoming of this method is that the only way to eliminate the

correlation error is by using configuration interaction, which is rather inefficient. We

now mention some computational methods that have been devised to provide a more

efficient way to eliminate the correlation error.

The Density Functional Method

This method was mentioned in Chapter 19, and has become a common method in

quantum chemical research. Detailed discussion of it is beyond the scope of this book.^18

It has been found that the approximation schemes that have been developed work at

least as well as Hartree–Fock–Roothaan methods with configuration interaction for

most molecular properties such as bond lengths and energies of molecular ground

states.

The Møller-Plesset Perturbation Method

The Møller-Plesset perturbation method was introduced around 1975. It differs from

the ordinary perturbation method introduced in Chapter 19 in that the unperturbed

wave function is taken to be the Hartree–Fock wave function without configuration

interaction. The perturbation term is taken as the difference between the Hartree–Fock

potential and the actual interelectron repulsion potential.^19 Calculations are usually

carried out to second order but calculations to the fourth order have been done.

The Coupled-Cluster Method

This method introduces electron correlation by expressing configuration interaction in

a particular way. The correct wave functionΨis represented as

Ψexp(̂T)Φ 0 (21.10-4)

whereΦ 0 is the ground-state Hartree–Fock wave function. The exponential of the

operator̂Tis represented by a Taylor series expression, as mentioned in Problem 16.4

(^18) I. N. Levine,op. cit., p. 573ff (note 2) and references cited therein.
(^19) I. N. Levine,op. cit., p. 563ff (note 2) and references cited therein.