Basis Sets

Most methods require a basis set be specified; if no basis set keyword is included in the route section, then the STO-3G basis will be used. The exceptions consist of a few methods for which the basis set is defined as an integral part of the method; they are listed below:

The following basis sets are stored internally in the Gaussian 09 program (see references cited for full descriptions), listed below by their corresponding Gaussian 09 keyword (with two exceptions):

Adding Polarization and Diffuse Functions

Single first polarization functions can also be requested using the usual * or ** notation. Note that (d,p) and ** are synonymous—6-31G** is equivalent to 6-31G(d,p), for example—and that the 3-21G* basis set has polarization functions on second row atoms only. The + and ++ diffuse functions [Clark83] are available with some basis sets, as are multiple polarization functions [Frisch84]. The keyword syntax is best illustrated by example: 6-31+G(3df,2p) designates the 6-31G basis set supplemented by diffuse functions, 3 sets of d functions and one set of f functions on heavy atoms, and supplemented by 2 sets of p functions on hydrogens.

When the AUG- prefix is used to add diffuse functions to the cc-pVxZ basis sets, one diffuse function of each function type in use for a given atom is added [Kendall92, Woon93]. For example, the AUG-cc-pVTZ basis places one s, one d, and one p diffuse functions on hydrogen atoms, and one d, one p, one d, and one f diffuse functions on B through Ne and Al through Ar.

Adding a single polarization function to 6-311G (i.e. 6-311G(d)) will result in one d function for first and second row atoms and one f function for first transition row atoms, since d functions are already present for the valence electrons in the latter. Similarly, adding a diffuse function to the 6-311G basis set will produce one s, one p, and one d diffuse functions for third-row atoms.

When a frozen core calculation is done using the D95 basis, both the occupied core orbitals and the corresponding virtual orbitals are frozen. Thus while a D95** calculation on water has 26 basis functions, and a 6-31G** calculation on the same system has 25 functions, there will be 24 orbitals used in a frozen core post-SCF calculation involving either basis set.

The following table lists polarization and diffuse function availability and the range of applicability for each built-in basis set in Gaussian 09:

Basis Set    Applies to    Polarization Functions    Diffuse Functions
3-21G    H-Xe         +
6-21G    H-Cl    * or **    
4-31G    H-Ne    * or **    
6-31G    H-Kr    through (3df,3pd)    +,++
6-311G    H-Kr    through (3df,3pd)    +,++
D95    H-Cl except Na and Mg    through (3df,3pd)    +,++
D95V    H-Ne    (d) or (d,p)    +,++
SHC    H-Cl    *    
CEP-4G    H-Rn    * (Li-Ar only)    
CEP-31G    H-Rn    * (Li-Ar only)    
CEP-121G    H-Rn    * (Li-Ar only)    
LanL2MB    H-La, Hf-Bi         
LanL2DZ    H, Li-La, Hf-Bi         
SDD, SDDAll    all but Fr and Ra         
cc-pVDZ    H-Ar, Ca-Kr    included in definition    added via AUG- prefix (H-Ar, Sc-Kr)
cc-pVTZ    H-Ar, Ca-Kr    included in definition    added via AUG- prefix (H-Ar, Sc-Kr)
cc-pVQZ    H-Ar, Ca-Kr    included in definition    added via AUG- prefix(H-Ar, Sc-Kr)
cc-pV5Z    H-Ar, Ca-Kr    included in definition    added via AUG- prefix (H-Na, Al-Ar Sc-Kr)
cc-pV6Z    H, B-Ne    included in definition    added via AUG- prefix (H, B-O)
SV    H-Kr         
SVP    H-Kr    included in definition    
TZV and TZVP    H-Kr    included in definition    
QZVP    H-Rn    included in definition    
MidiX    H, C-F, S-Cl, I, Br    included in definition    
EPR-II, EPR-III    H, B, C, N, O, F    included in definition    
UGBS    H-Lr    UGBS(1,2,3)P    +,++,2+,2++
MTSmall    H-Ar         
DGDZVP    H-Xe         
DGDZVP2    H-F, Al-Ar, Sc-Zn         
DGTZVP    H, C-F, Al-Ar         
CBSB7    H-Kr    included in definition    +,++

STO-3G and 3-21G accept a * suffix, but this does not actually add any polarization functions.

Additional Basis Set-Related Keywords

The following additional keywords are useful in conjunction with these basis set keywords:

Other basis sets may also be input to the program using the ExtraBasis and Gen keywords. The ChkBasis keyword indicates that the basis set is to read from the checkpoint file (defined via the %Chk command). See the individual descriptions of these keywords later in this chapter for details.

Issues Arising from Pure vs. Cartesian Basis Functions

Gaussian users should be aware of the following points concerning pure vs. Cartesian basis functions:

Density Fitting Basis Sets

Gaussian 09 provides the density fitting approximation for pure DFT calculations [Dunlap83, Dunlap00]. This approach expands the density in a set of atom-centered functions when computing the Coulomb interaction instead of computing all of the two-electron integrals. It provides significant performance gains for pure DFT calculations on medium sized systems too small to take advantage of the linear scaling algorithms without a significant degradation in the accuracy of predicted structures, relative energies and molecular properties. Gaussian 09 can generate an appropriate fitting basis automatically from the AO basis, or you may select one of the built-in fitting sets.

The desired fitting basis set is specified as a third component of the model chemistry, as in this example:

# BLYP/TZVP/TZVPFit

Note that slashes must be used as separator characters between the method, basis set, and fitting set when a density fitting basis set is specified.

The following fitting sets keywords are available in Gaussian 09:

Density fitting sets can be generated automatically from the AO primitives within the basis set. This is requested using the Auto fitting set keyword. The program automatically truncates the set at a reasonable angular momentum: the default is Max(MaxTyp+1,2*MaxVal), where MaxTyp is the highest angular momentum in the AO basis, and MaxVal is the highest valence angular momentum. You can request that all generated functions be used with Auto=All, or request those up to a certain level with Auto=N, where N is the maximum angular momentum retained in the fitting functions. Finally, the PAuto form generates all products of AO functions on one center instead of just squares of the AO primitives, but this is typically more functions than are needed.

By default, no fitting set is used. Density fitting basis sets may be augmented with the ExtraDensityBasis keyword, defined in full with the Gen keyword, and optionally retrieved from the checkpoint file (use ChkBasis to do so). The options to the DensityFit keyword can be used to control some aspects of the fitting set used within calculations.


Last updated on: 9 Jun 2009