Practical considerations

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:

#P  HF/6-31G(d)

If a non standard basis set is to be used, then the "GEN" directive is used instead of the basis set information in the keyword line and the basis set exponents and coefficients are given in fixed format after the geometry information (separated by one blank line):

#HF/GEN 6D

HF sp H2O using the 6-31G(d) basis set

0 1

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