Computational Chemistry

(Chapter 6) are perhaps more likely to be used nowadays in preliminary investiga-
tions, and to obtain reasonable starting structures for ab initio optimizations, but for
systems significantly different from those for which the semiempirical methods
were parameterized one might prefer to use the STO-3G basis. As for examining
atomic contributions to bonding, interpreting bonding in terms of hybrid orbitals
and the contribution of particular atoms to MO’s is simpler when each atom has
just one conventional orbital, rather than split orbitals (as in the basis sets to be
discussed). Thus an analysis of the electronic structure of three- and four-membered
rings used the STO-3G basis explicitly for this reason [ 44 ], as did an interpretation
of the bonding in the unusual molecule pyramidane [ 45 ].
The shortcomings (and virtues) of the STO-3G basis are extensively documented
throughout ref. [ 1 g]. Basically, the drawbacks are that by comparison with the
3–21G basis, which is not excessively more demanding of time, it gives signifi-
cantly less accurate geometries and energies (this was the reason for the call to
abandon this basis [ 43 ]). Actually, even for second-row atoms (Na–Ar), where the
defects of such a small basis set should be, and are, quite apparent, the STO-3G
basis supplemented with fivedorpolarizationfunctions (the STO-3G basis;
polarization functions are discussed below) can give results comparable to those
of the 3–21G basis set. Thus for the S–O bond length of Me 2 SO we get (A ̊):
STO-3G, 1.820; STO-3G, 1.480; 3–21G, 1.678; 3–21G(), 1.490; exp., 1.485,
and for NSF [ 46 ] the geometries shown in Fig.5.14. Nevertheless, the STO-3G
basis is not in the normally-used repertoire.

5.3.3.2 3–21G and 3–21G* Split Valence and Double-Zeta Basis Sets

First consider what we could denote as the “simple” 3–21G basis set. This splits
each valence orbital into two parts, an inner shell and an outer shell. The basis
function of the inner shell is represented by two Gaussians, and that of the outer
shell by one Gaussian (hence the “21”); the core orbitals are each represented by
one basis function, each composed of three Gaussians (hence the “3”). Thus H and
He have a 1s orbital (the only valence orbital for these atoms) split into 1s^0 (1s
inner) and 1s^00 (1s outer), for a total of two basis functions. Carbon has a 1sfunction
represented by three Gaussians, an inner 2s,2px,2pyand 2pz(2s^0 ,2px^0 ,2py^0 ,2pz^0 )

1.611 1.654

N 101.2

S

F

STO-3G

1.468 1.570

N 114.4

S

F

STO-3G* 1.448 116.9 1.643

N

S

F

1.567 1.672 experiment

N 107.8

S

F

3-21G

1.440 1.609

113.8

N

S

F

3-21G*

Fig. 5.14 Some STO-3G, STO-3G, 3–21G and 3–21G geometries

5.3 Basis Sets 243