HF-SCF bases

I found some time to try out GAMESS a little bit more. What I was interested in is how a geometry optimisation changes with different bases.

I tried out most of the standard bases that GAMESS offers without any extra functions. The input looks like this (enter the base instead of ***). After evaluation I extracted the information with Visual Basic.

! Ethane staggered
!
 $CONTRL SCFTYP=RHF RUNTYP=Optimize $END
 $SYSTEM TIMLIM=30 $END
 $BASIS *** $END
 $GUESS GUESS=HUCKEL $END
 $DATA
Ethane...staggered...***
S2n 3

C           6.0   0.0000000000   0.0000000000  -0.7688320347
H           1.0  -1.0157199281   0.0000000000  -1.1532895468
 $END

This is the result. You see the C-C and C-H bond lengths (in Angstrom) and the C-C-H angle. The table is arranged according to the complexity of the base (information). In the first line are the literature values [1], in the other lines relative deviations.

Basis	C-C	C-H	C-C-H
Experimental	1.5351	1.0940	111.17°
MNDO	-0.0143	0.0152	0.0221°
AM1	-0.0348	0.0231	-0.4514°
PM3	-0.0306	0.0038	0.4605°
STO-2G	0.0029	-0.0020	-0.0537°
STO-3G	0.0026	-0.0080	-0.4380°
STO-4G	0.0002	-0.0116	-0.4738°
STO-5G	-0.0001	-0.0128	-0.4628°
STO-6G	-0.0004	-0.0125	-0.4612°
3-21G	0.0072	-0.0099	-0.3732°
6-21G	0.0064	-0.0099	-0.3084°
4-31G	-0.0062	-0.0106	-0.0081°
5-31G	-0.0054	-0.0098	0.0183°
6-31G	-0.0052	-0.0096	0.0236°
6-311G	-0.0070	-0.0113	0.0494°
DZV	0.0024	-0.0102	-0.1002°
TZV	-0.0047	-0.0109	-0.0096°

The first three are semiemperical methods. They show the worst results (as it is supposed to be).

It's more difficult to say things about the ab-initio calculations. It can be seen that bond lengths never differ much more than 0.01 (which is nice). Another interesting fact is that with a better basis, bond lengths tend to be shorter [2]. At the HF-SCF limit (self-consistent eigenfunctions of the Fock operator) bond lengths are usually too short (which is not nice). This is just shows a limitation of the method. Sometimes medium sized bases give better results than large bases. To overcome the problem, you need correlated calculations.

[1]Lide DR. Handbook of Chemistry and Physics 86^th Ed. 2005-2006. CRC
[2]Kutzelnigg W. Pure appl. Chem. 49, 981 (1977)