functions (6–31þG, 6–31þþG, 6–31þG and 6–31þþG) might be consid-
eredfairlylarge. A large basis set might have a doubly-split or even triply-split
valence shell withd,pandf, and maybe eveng, functions on at least the heavy
atoms. An example of a large (but not very large) basis set is the 6–311G (i.e.
6–311(d,p)) set. This is a split valence set with each valence orbital split into three
shells, composed of three, one and one Gaussian, while the core orbitals are
represented by one basis function composed of six Gaussians; each heavy atom
also has five (not six in this case) 3dfunctions and each hydrogen and helium has
three 2pfunctions. The 6–311G basis for carbon is then
1 s
2 s^02 p^02 p^02 p^0
2 s^002 p^00 2p^002 p^00
2 s^0002 p^000 2p^0002 p^000
3 d 3 d 3 d 3 d 3 d
18 Basis functions
and for hydrogen
1 s^0
1 s^00
1 s^000
2 p 2 p 2 p
Six basis functions
Unequivocally large basis sets would be triply-split valence shell sets withdand
ffunctions on heavy atoms andpfunctions on hydrogen. At the smaller end of such
sets is the 6–311G(df,p) basis, with five 3d’s and seven 4f’s on each heavy atom and
three 2p’s on each hydrogen and helium. For carbon this is
1 s
2 s^02 p^02 p^02 p^0
2 s^002 p^00 2p^002 p^00
2 s^0002 p^000 2p^0002 p^000
3 d 3 d 3 d 3 d 3 d
4 f 4 f 4 f 4 f 4 f 4 f 4 f
25 Basis functions
and for hydrogen
1 s^0
1 s^00
1 s^000
2 p 2 p 2 p
Six basis functions
A more impressive example of a large basis set would be 6–311G(3df,3pd). This
has for each heavy atom three sets of fivedfunctions and one set of sevenf
functions, and for each hydrogen and helium three sets of threepfunctions and
one set of fivedfunctions, i.e.
For carbon
1 s
2 s^02 p^02 p^02 p^0
5.3 Basis Sets 249