Physical Chemistry Third Edition

21.10 More Advanced Treatments of Molecular Electronic Structure. Computational Chemistry 907

Table 21.5 Comparison of Semiempirical Molecular Orbital

Methods

H EH PPP CNDO INDO NDDO MNDO MINDO

1p v p v v v v v

2p g p g g g g g

3n n y y y y y y

4e a a a a a a a

5y n n n n n n n

6z c z z z z z z

7n n y y y y y y

8n n c c i d d i

9n y y y y y y y

Methods considered:

H = Hückel, EH = extended Hückel, PPP = Pariser–Pople–Parr, CNDO = complete

neglect of differential overlap, INDO = intermediate neglect of differential overlap,

NDDO = neglect of diatomic differential overlap, MNDO = modified neglect of

differential overlap, MINDO = modified intermediate neglect of differential overlap.

Note: AM1 and PM3 are MNDO methods that differ only in the way constants are

chosen to approximate various integrals.

Characteristics considered:

1. Type of electrons explicitly treated (p =πonly, v = valence only)


2. Molecular geometry that can be treated (p = planar only, g = general)


3. Is it a self-consistent field calculation? (y = yes,n=no)


4. How are matrix elements of Heffobtained? (a = approximated by some formula,
   e = fit from experimental data)


5. Are some off-diagonal matrix elements of Heffassumed to vanish?


6. How are overlap integrals treated? (z = assumed to vanish, c = calculated)


7. Are electron–electron repulsions included in the Hamiltonian? (y = yes,n=no)


8. How are electron–electron repulsion terms handled? (n = not included, c = zero
   differential overlap (ZDO) approximation applied to all integrals, i = ZDO not applied
   to one-center integrals, d = ZDO not applied to one-center integrals nor to a two-center
   integral if both orbitals of an electron are on the same nucleus)


9. Can the method be used to optimize molecular geometry? (y = yes,n=no)

orbitals, which are the best possible set of orbitals. Various kinds of basis functions are

in common use. An important criterion is the speed with which computers can evaluate

the integrals occurring in the calculation. It is found that Slater-type orbitals (STOs)

require less computer time than hydrogen-like orbitals. These orbitals contain the same

spherical harmonic functions as the hydrogen-like orbitals, but their radial factors are

exponential functions multiplied by powers ofrinstead of by polynomials inr. There

are rules for guessing appropriate values for the exponents.^17

In addition to Slater-type orbitals,Gaussian orbitalshave been widely used. The

correct spherical harmonic functions are used for the angular factors, but the radial

factor is approximated by

R(r)∝e−br

2

(21.10-3)

wherebis a constant. Such Gaussian functions are not very good representations of

radial factors, but allow for even more rapid computer evaluation of integrals than

Slater-type orbitals. Some basis sets contain linear combinations of several Gaussian

(^17) I. N. Levine,op. cit., p. 624 (note 2).