Computational Chemistry

correlation-consistent (below) and Huzinaga sets, is given by Simons and Nichols
[ 41 ]. There is no one procedure for developing a basis set. One method is to
optimizeSlaterfunctions for atoms or small molecules, i.e. to find the values ofz
that give the lowest energy for these, and then to use a least-squares procedure to fit
contracted Gaussians to the optimized Slater functions [ 42 ]. Whatever the details of
their genesis, ab initio basis sets are constructed by some kind of mathematical
minimization procedure, and not by fitting them to reproduce experimental atomic
or molecular properties: they are not semiempirical.

5.3.3.1 STO-3G

This is called aminimal basis set, although some atoms actually have more basis
functions (which for this basis can be equated with atomic orbitals) than are needed

1 H

1 s

1 function

19 K– 20 Ca

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

4 s 4 p 4 p 4 p

13 functions

37 Rb– 38 Sr

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

4 s 4 p 4 p 4 p

5 s 5 p 5 p 5 p

3 d 3 d 3 d 3 d 3 d

22 functions

3 Li– 10 Ne

1 s

2 s 2 p 2 p 2 p

5 functions

11 Na– 18 Ar

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

9 functions

21 Sc– 30 Zn

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

4 s 4 p 4 p 4 p

3 d 3 d 3 d 3 d 3 d

18 functions

39 Y– 48 Cd

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

4 s 4 p 4 p 4 p

5 s 5 p 5 p 5 p

3 d 3 d 3 d 3 d 3 d

4 d 4 d 4 d 4 d 4 d

27 functions

2 He

1 s

1 function

31 Ga– 36 Kr

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

4 s 4 p 4 p 4 p

3 d 3 d 3 d 3 d 3 d

18 functions

49 In– 54 Xe

1 s

2 s 2 p 2 p 2 p

3 s 3 p 3 p 3 p

4 s 4 p 4 p 4 p

5 s 5 p 5 p 5 p

3 d 3 d 3 d 3 d 3 d

4 d 4 d 4 d 4 d 4 d

27 functions

a, STO-3G

Fig. 5.13(continued)

5.3 Basis Sets 239