Computational Chemistry

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
3 d 3 d 3 d 3 d 3 d
3 d 3 d 3 d 3 d 3 d
4 f 4 f 4 f 4 f 4 f 4 f 4 f
35 Basis functions
and for hydrogen
1 s^0
1 s^00
1 s^000
2 p 2 p 2 p
2 p 2 p 2 p
2 p 2 p 2 p
3 d 3 d 3 d 3 d 3 d
17 Basis functions
Note that all these large basis sets can be made still bigger by adding diffuse
functions to heavy atoms (þ) or to heavy atoms and hydrogen/helium (þþ). The
number of basis functions on CH 2 using some small, medium and large bases is
summarized CþHþH):

STO#3G 5 þ 1 þ 1 ¼7 functions

3 #21G¼ 3 #21GðÞ$here

)*

9 þ 2 þ 2 ¼13 functions

6 #31G$ðÞ 6 #31G dðÞ 15 þ 2 þ 2 ¼19 functions

6 #31G** 6ðÞ#31G dðÞ;p 15 þ 5 þ 5 ¼25 functions

6 #311G$$ðÞ 6 #311G dðÞ;p 18 þ 6 þ 6 ¼30 functions

6 #311G dfðÞ;p 25 þ 6 þ 6 ¼37 functions

6 #311G 3dfðÞ;3pd 35 þ 17 þ 17 ¼69 functions

6 # 311 þþG 3dfðÞ;3pd 39 þ 18 þ 18 ¼75 functions

Large basis sets are used mainly for post-Hartree–Fock level (Section 5.4)
calculations, where the use of a basis smaller than the 6–31G seems to be
essentially pointless. At the Hartree–Fock level the largest basis routinely used is
the 6–31G or 6–31G* (augmented if appropriate by diffuse functions), and post-
HF geometry optimizations are frequently done using the 6–31G or 6–31G
basis too. Use of the larger bases (6–311G and up) tends to be confined tosingle-
pointcalculations on structures optimized with a smaller basis set (Section 5.5.2).
These are not firm rules: the high-accuracy CBS (complete basis set) methods

250 5 Ab initio Calculations