906 21 The Electronic Structure of Polyatomic Molecules
An approximation calledzero differential overlapis invoked to set some of these
integrals to zero. The name is somewhat confusing because the approximation is not
applied to overlap integrals but to these electron–electron repulsion integrals. This
approximation sets integrals like that of Eq. (21.10-2) equal to zero, unlessrt
andsu.
When the LCAOMOs are substituted into the Hartree–Fock equations and the above
approximations are applied, a set of equations for the coefficients in the linear combina-
tions is obtained. These equations are called the Roothaan equations.^13 The Roothaan
equations are solved by iteration, and the results are the orbital energies and the values
of the coefficients for each of the LCAOMOs.Other Semiempirical Methods
There are a number of other semiempirical methods that use the Hartree–Fock–Roothaan
self-consistent field approach. They differ from each other in the scheme used to decide
which integrals to approximate by zero and in the scheme used to assign values to
the other integrals. Some methods are named according to the type of integrals that
are assumed to vanish, such as the CNDO method (complete neglect of differential
overlap), the INDO method (intermediate neglect of differential overlap), the NDDO
method (neglect of diatomic differential overlap), MNDO (modified neglect of differ-
ential overlap), and the MINDO method (modified intermediate neglect of differential
overlap). Two common methods that are based on the MNDO method are the AM1^14
and PM3^15 methods, which are included in a package of programs called MOPAC.^16
The CAChe software package contains the MOPAC package as well as additional pro-
grams. Other methods are named for approximations of different sorts, such as the
PCILO method (perturbative configuration interaction using localized orbitals) and the
DIM method (diatomics in molecules). Table 21.5 summarizes some characteristics of
several semiempirical methods.Exercise 21.22
Using a software package, such as CAChe or Spartan, that contains either the AM1 or PM3
method, find the equilibrium conformation of the molecules in Exercise 21.21. Construct and
view the orbital regions and compare your results with the results using the extended Hückel
method.Ab Initio Methods
The principal differences between ab initio and semiempirical calculations is that ab
initio methods evaluate all of the integrals numerically instead of relying on experi-
mental information to assign values to integrals. The term ab initio means “from the
beginning.” If a large enough set of well-chosen basis functions is used, the results of
ab initio Hartree–Fock–Roothaan calculations can nearly replicate the Hartree–Fock(^13) I. N. Levine,op. cit., p. 429ff (note 2).
(^14) M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, J. J. P. Stewart,J. Am. Chem. Soc., 107 , 3902 (1985).
(^15) J. J. P. Stewart,J. Comp. Chem., 10 , 209 (1989); 10 , 221 (1989).
(^16) The MOPAC package of programs was originally available from the Quantum Chemistry Program
Exchange at Indiana University, and is included in the CAChe package.