Computational Chemistry

ignored (set equal to zero) are determined from the extent to whichdifferential

overlapis neglected. Differential overlapdSis the differential of the overlap

integral (e.g. Section4.3.3)S:

S¼

Z

frð 1 Þfsð 1 Þdv 1 (*6.3)

dS¼frð 1 Þfsð 1 Þdv 1 (*6.4)

Semiempirical methods differ amongst themselves in, amongst other ways, the
criteria for settingdS¼0, i.e. for applyingzero differential overlap, ZDO.
4.The overlap matrix.SCF-type semiempirical methods take the overlap matrix as
a unit matrix,S¼ 1 , soSvanishes from the Roothaan-Hall equationsFC¼SCe
without the necessity of using an orthogonalizing matrix to transform these
equations into standard eigenvalue formFC¼Ceso that the Fock matrix can
be diagonalized to give the MO coefficients and energy levels (Sections4.4.3
and 4.4.1; Section5.2.3.6.2).
We begin our examination of specific SCF-type semiempirical methods with the
simplest, the Pariser-Parr-Pople method.

6.2.2 The Pariser-Parr-Pople (PPP) Method

The first semiempirical SCF-type method to gain widespread use was the Pariser-
Parr-Pople method (1953) [ 12 , 13 ]. Like the simple H€uckel method, PPP calcula-
tions are limited topelectrons, with the other electrons forming asframework to
hold the atomicporbitals in place. The Fock matrix elements are calculated from
Eq.6.1¼5.82; for a PPP calculationHcorers represents the nuclei plus all non-p-
system electrons,Ptuis calculated from the coefficients of thosepAOs contributing
to thepsystem, and the two-electron repulsion integrals refer to electrons in thep
system. The one-center core integralsHcorerr are estimated empirically from the
ionization energy of a2pAO and (see below) the two-electron integral (rr|ss).
The two-center core integralsHrscoreare calculated from

Hrscore¼khifrð 1 Þjfsð 1 Þ r¼ 6 s ð 6 : 5 ¼ 5 : 82 Þ

wherekis an empirical parameter chosen to give the best agreement with experi-
ment of the wavelength of UV absorption bands, and the overlap integralhfr|fsiis
calculated from the basis functions, with the proviso that iffrandfsare on atoms
that are not connected then the integral is taken as zero.
The two-electron integrals are evaluated by applying the ZDO approximation
(above) to all different orbitalsrands:

dS¼frð 1 Þfsð 1 Þdv 1 ¼0 forr 6 ¼s (6.6)

396 6 Semiempirical Calculations