With the exception of semiemipirical
methods such as AM1, MNDO, and PM3, and compound methods such as G2 any basis
set can be combined with any quantum mechanical method (not all combinations
are meaningfull, though). In most cases, the basis set will be called from a
library contained in quantum mechanics programs through an acronym such as
"6-31G(d)". In the input file format used in Gaussian 98, quantum
mechanical method and basis set information are separated by a "/".
The following example requests a Hartree-Fock calculation using the 6-31G(d)
basis set:
O1
H2 1 r2
H3 1 r2
2 a3
r2=0.94733729
a3=105.50796079
O 1
S 6 1.00
0.5484671660D+04 0.1831074430D-02
0.8252349460D+03 0.1395017220D-01
0.1880469580D+03 0.6844507810D-01
0.5296450000D+02 0.2327143360D+00
0.1689757040D+02 0.4701928980D+00
0.5799635340D+01 0.3585208530D+00
SP 3 1.00
0.1553961625D+02 -0.1107775490D+00
0.7087426820D-01
0.3599933586D+01
-0.1480262620D+00 0.3397528390D+00
0.1013761750D+01
0.1130767010D+01 0.7271585770D+00
SP 1 1.00
0.2700058226D+00
0.1000000000D+01 0.1000000000D+01
D 1 1.00
0.8000000000D+00 0.1000000000D+01
****
H 0
S 3 1.00
0.1873113696D+02 0.3349460434D-01
0.2825394365D+01 0.2347269535D+00
0.6401216923D+00 0.8137573262D+00
S 1 1.00
0.1612777588D+00 0.1000000000D+01
****
The basis set information is given
for each element separated by a line containing four stars. If this type of
input is used, the program does not check whether all atoms have received basis
functions. If, for example, the basis set
information for hydrogen is deleted from the last example, the calculation will
still run as usual, but without any basis functions at hydrogen - with
desasterous results! Also some care has to be taken in specifying the
correct number of d-orbitals (five pure d-type
orbitals vs. six cartesian d-functions). If no additional information is
given Gaussian 98 assumes the use of five d-type functions. This can be
specified more explicitely using the keywords "5D" and
"6D". In a similar fashion, the program can be directed to use either
"7F" or "10F" polarization
functions. The combination of a standard basis set and some additional
basis functions is most easily achieved using the "GEN" keyword. In the
following example the 6-31G basis set is called from the basis set library for
all carbon and hydrogen atoms and an extra d-type polarization function is then
added onto atom No. 1 (oxygen). Using an exponent of 0.8 for the six d-type
functions reproduces exactly what is otherwise described as Pople's
"6-31G(d)" basis set.
#HF/GEN 6D
HF sp H2O using the 6-31G basis + additional d-type
functions (6D)
0 1
O1
H2 1 r2
H3 1 r2
2 a3
r2=0.94733729
a3=105.50796079
O H 0
6-31G
****
1 0
D 1 1.00
0.8000000000D+00 0.1000000000D+01
****
A listing of basis sets in a
format appropriate for input as a general basis set can be obtained in two
ways. (i) The first is using Gaussian
itself to produce a listing of the currently used basis set. This can be
achieved using the keyword gfinput e.g.
#P HF/6-31G(d,p) gfinput
This results in basis set
information given for each single center contained in the system.
(ii) An alternative source of
basis set information is provided by the EMSL Gaussian Basis Set Library at
http://www.emsl.pnl.gov/forms/basisform.html which also
provides a number of basis sets not provided as a standard basis set by Gaussian.
Literatur
1) W. J. Hehre, R. F.
Stewart, J. A. Pople, Self-Consistent Molecular-Orbital Methods. I. Use of
Gaussian Expansions of Slater-Type Orbitals. J. Chem. Phys. 1969, 51, 2657. [STO-nG basis sets]
2) J. S. Binkley, J. A. Pople,
W. J. Hehre, Self-Consistent Molecular Orbital Methods. 21. Small Split-Valence
Basis Sets for First-Row Elements. J. Am.
Chem.
Soc. 1980, 102, 939. [3-21G and 6-21G basis sets]
3) M. S. Gordon, J. S.
Binkley, J. A. Pople, W. J. Pietro, W. J. Hehre, Self-Consistent Molecular
Orbital Methods. 22. Small Split-Valence Basis Sets for Second-Row Elements. J. Am. Chem. Soc. 1982, 104, 2797. [3-21G, 2nd row elements]
4) W. J. Pietro, M. M.
Francl, W. J. Hehre, D. J. DeFrees, J. A. Pople, J. S. Binkley, Self-Consistent
Molecular Orbital Methods. 24. Supplemental Small Split-Valence Basis Sets for
Second-Row Elements. J. Am. Chem. Soc.
1982, 104, 5039. [Polarization for 3-21G, 2nd row elements]
5) R. Ditchfield, W. J.
Hehre, J. A. Pople, Self-Consistent Molecular-Orbital Methods. IX. An Extended
Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 1971, 54, 724. [4-31G
basis set]
6) W. J. Hehre, R.
Ditchfield, J. A. Pople, Self-Consistent Molecular Orbital Methods. XII. Further
Extensions of Gaussian-Type Basis Sets for Use in Molecular-Orbital Studies of
Organic Molecules. J. Chem. Phys. 1972, 56, 2257. [6-31G basis set]
7) T. H. Dunning, Jr.,
Gaussian Basis Functions for Use in Molecular Calculations. I. Contraction of
(9s5p) Atomic Basis sets for the First-Row Atoms. J. Chem. Phys. 1970, 53,
2823. [D95 basis]
8) T. H. Dunning Jr, P. J.
Hay, in Modern Theoretical Chemistry,
Ed. H. F. Schaefer, III, Plenum Press, New York, 1976, Vol. 3, p.1. [D95 basis]
9) S. Huzinaga, J. Chem. Phys. 1965, 42, 1293.
[Uncontracted 9s5p basis]
10) P. C. Hariharan, J. A.
Pople, The Influence of Polarization Functions on Molecular Orbital
Hydrogenation Energies. Theor. chim.
Acta. 1973, 28, 213. [polarization functions for 6-31G]
11) D. J. DeFrees, B. A.
Levi, S. K. Pollack, W. J. Hehre, J. S. Binkley, J. A. Pople, Effect of
Electron Correlation on Theoretical Equilibrium Geometries. J. Am. Chem. Soc. 1979, 101, 4085.
[HF/6-31G(d) and MP2/6-31G(d) results for small organics]
12) G. W. Spitznagel, T. Clark,
J. Chandrasekhar, P. v. R. Schleyer, Stabilization of Methyl Anions by
First-Row Substituents. The Superiority of Diffuse Function-Augmented Basis
Sets for Anion Calculations. J. Comp.
Chem. 1982, 3, 363.
13) T. Clark, J.
Chandrasekhar, G. W. Spitznagel, P. v. R. Schleyer, Efficient Diffuse
Function-Augmented Basis Sets for Anion Calculations. III. The 3-21+G Basis Set
for First-Row Elements, Li-F. J. Comp.
Chem. 1983, 4, 294.
14) R. Krishnan, J. S.
Binkley, R. Seeger, J. A. Pople, Self-Consistent Molecular Orbital Methods. XX.
A basis set for correlated wave functions. J.
Chem. Phys. 1980, 72, 650. [6-311G** basis set]
15) T.H. Dunning, Jr.,
Gaussian basis stes for use in correlated molecular calculations I. The atoms
boron through neon and hydrogen. J. Chem.
Phys. 1989, 90, 1007. [cc basis sets]
16) R. A. Kendall, T. H.
Dunning, Jr., R. J. Harrison, J. Chem.
Phys. 1992, 96, 6796. [augmented cc basis sets]
last changes: 01.04.2008, AS questions & comments to: axel.schulz@uni-rostock.de