Basis Sets
Last Update: 6/26/2001

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:

• All semi-empirical methods (including Zindo for excited states)

• All molecular mechanics methods

• G1, G2 and G2MP2

• CBS-4, CBS-Lq, CBS-Q, CBS-QB3, and CBS-APNO

The following basis sets are stored internally in the Gaussian 98 program (see references cited for full descriptions), listed below by their corresponding Gaussian 98 keyword (with two exceptions):

• STO-3G [159-160]

• 3-21G [161,162,163,293,294,295]

• 6-21G [161-162]

• 4-31G [164,165,166,167]

• 6-31G [164,165,166,167,168]

• 6-31G† and 6-31G††: Gaussian 98 also includes the 6-31G† and 6-31G†† basis sets of George Petersson and coworkers, defined as part of the Complete Basis Set methods [75,169]. These are accessed via the 6-31G(d') and 6-31G(d',p') keywords, to which single or double diffuse functions may also be added.

• 6-311G: Specifies the 6-311G basis for first-row atoms and the MacLean-Chandler (12s,9p) (621111,52111) basis sets for second-row atoms [170-171] (note that the basis sets for P, S, and Cl are those called "negative ion" basis sets by MacLean and Chandler; these were deemed to give better results for neutral molecules as well), the Wachters-Hay [172-173] all electron basis set for the first transition row, using the scaling factors of Raghavachari and Trucks [174], and the 6-311G basis set of McGrath, Curtiss and coworkers for most of the rest of the third row (note that K and Ca are not currently defined) [290,291,292].

Note that Raghavachari and Trucks recommend both scaling and including diffuse functions when using the Wachters-Hay basis set for first transition row elements. You will need to use the 6-311+G keyword form to include the diffuse functions recommended in their paper (see reference [174]). MC-311G is a synonym for 6-311G.

• D95V: Dunning/Huzinaga valence double-zeta [175].

• D95: Dunning/Huzinaga full double zeta [175].

• SHC: D95V on first row, Goddard/Smedley ECP on second row [175-176]. Also known as SEC.

• CEP-4G: Stephens/Basch/Krauss ECP minimal basis [177, 359, 360].

• CEP-31G: Stephens/Basch/Krauss ECP split valance [177, 359, 360].

• CEP-121G: Stephens/Basch/Krauss ECP triple-split basis [177, 359,360]

Note that there is only one CEP basis set defined beyond the second row, and all three keywords are equivalent for these atoms.

• LanL2MB: STO-3G [159-160] on first row, Los Alamos ECP plus MBS on Na-Bi [178,179,180].

• LanL2DZ: D95 on first row [175], Los Alamos ECP plus DZ on Na-Bi [178,179,180].

• SDD:D95 on the first row [175] and Stuttgart/Dresden ECP's on the remainder of the periodic table [364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387].

• cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z, cc-V6Z: Dunning's correlation consistent basis sets [181,182,183, 356, 357] (double, triple, quadruple, quintuple-zeta, and sextuple zeta, respectively). These basis sets have had duplicate functions removed and have been rotated [358] in order to increase computational efficiency. As so altered they produce identical energetic results to the cc* basis sets in Gaussian 94.

These basis sets include polarization functions by definition. The following table lists the valence polarization functions present for the various atoms included in these basis sets:

These basis sets may be augmented with diffuse functions by adding the AUG- prefix to the basis set keyword (rather than using the + and ++ notation--see below).

*However, the elements He, Mg, Li, Be, and Na do not have diffuse functions defined within these basis sets.

• Dcc-pVDZ and Dcc-pVTZ: Dunning's correlation consistent basis sets as above using Davidson's contraction scheme [358] which reduces the number of primitives in the s and p contracted functions. Energies computed with these basis sets will differ slightly from those computed with the corresponding standard cc basis set.

• SV, SVP and TZV of Ahlrichs and coworkers [361, ]

• Midi! of Truhlar and coworkers [363]. The MidiX keyword is used to request this basis set.

• Epr-IIand EPR III: The basis sets of Barone [274] which are optimized for the computation of hyperfine coupling constants by DFT methods (particularly B3LYP). EPR-II is a double zeta basis set with a single set of polarization functions and an enhanced s part: (6,1)/[4,1] for H and (10,5,1)/[6,2,1]for B to F. EPR-III is a triple zeta basis set including diffuse functions, double d-polarizations and a single set of f-polarization functions. Also in this case the s-part is improved to better describe the nuclear region: (6,2)/[4,2] for H and (11,7,2,1)/[7,4,2,1] for B to F.

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 [184] are available with some basis sets, as are multiple polarization functions [185]. 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-pV*Z basis sets, one diffuse function of each function type in use for a given atom is added [181-182]. 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 98:

*Note: cc-pV5Z does not include He.

ADDITIONAL BASIS SET-RELATED KEYWORDS

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

• 5D and 6D: Use 5 or 6 d functions (pure vs. Cartesian d functions), respectively.

• 7F and 10F: Use 7 or 10 f functions (pure vs. Cartesian f functions), respectively. These keywords also apply to all higher functions (g and beyond).

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:

• All of the built-in basis sets use pure f functions. Most also use pure d functions; the exceptions are 3-21G, 6-212G, 4-31G, 6-31G, 6-31G†, 6-31G††, D95 and D95V. The preceding keywords may be used to override the default pure/Cartesian setting. Note that basis functions are generally converted to the other type automatically when necessary, for example, when a wave function is read from the checkpoint file for use in a calculation using a basis consisting of the other type.
• Cartesian and pure functions of the same angular momentum (i.e., d vs f and highter) may not be mixed within a single calculation in Gaussian 98.
• When using the ExtraBasis and Gen keyword, the basis set explicitly specified in the route section always determines the default form of the basis functions (for Gen, these are 5D and 7F). For example, if you use a general basis set taking some functions from the 3-21G and 6-31G basis sets, pure function will be used unless you explicitly specify 6D in the route section in addition to Gen. Similarly, if you add basis functions for a transition metal form the 6-311G(d) basis set via ExtraBasis to a job that specifies the 6-31G(d) basis sets in the route section, Cartesian d functions will be used. Likewise, if you want to add basis functions for Xe from the 3-21G basis set to the 6-311 basis set via the ExtraBasis keyword, the Xe basis functions will be pure functions.

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