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8.3 Basis Set Symbolic Representation

8.3.1 Symbolic Representation Overview

(December 20, 2021)

Examples are given in the tables below and follow the standard format generally adopted for specifying basis sets. The single exception applies to additional diffuse functions. These are best inserted in a similar manner to the polarization functions; in parentheses with the light atom designation following heavy atom designation: (heavy, light), using a period as a placeholder in the unusual case that diffuse functions are to be added to hydrogen atoms but not to heavy atoms. See Table 8.1 for the general form and Table 8.3 for specific examples.

Basis Namea j mb nc
STO-j(k+,l+)G(m,n) 2,3,6 d p
j-21(k+,l+)G(m,n) 3 2d 2p
j-31(k+,l+)G(m,n) 4,6 3d 3p
j-311(k+,l+)G(m,n) 6 df, 2df, 3df pd, 2pd, 3pd
  • ak and l denote the number of sets of diffuse functions on heavy atoms and on hydrogen atoms, respectively.

  • bm denotes the number of sets of polarization functions on the heavy atoms.

  • cn denotes the number of sets of polarization functions on the hydrogen atoms.

Table 8.1: Summary of Pople-type basis sets available in Q-Chem.
Symbolic Name Atoms Supported
STO-2G H, He, LiNe, NaAr, K, Ca, Sr
STO-3G H, He, LiNe, NaAr, KKr, RbI
STO-6G H, He, LiNe, NaAr, KKr
3-21G H, He, LiNe, NaAr, KKr, RbXe, Cs
4-31G H, He, LiNe, PCl
6-31G H, He, LiNe, NaAr, KKr
6-311G H, He, LiNe, NaAr, GaI
G3LARGE H, He, LiNe, NaAr, KKr
G3MP2LARGE H, He, LiNe, NaAr, GaKr
Table 8.2: Atoms supported for Pople basis sets available in Q-Chem.
Symbolic Name Atoms Supported
3-21G H, He, Li Ne, Na Ar, K Kr, Rb Xe, Cs
3-21+G H, He, Na Cl, Na Ar, K, Ca, Ga Kr
3-21G* Na Ar
6-31G H, He, Li Ne, Na Ar, K Zn, Ga Kr
6-31+G H, He, Li Ne, Na Ar, Ga Kr
6-31G* H, He, Li Ne, Na Ar, K Zn, Ga Kr
6-31G(d,p) H, He, Li Ne, Na Ar, K Zn, Ga Kr
6-31G(.,+)G H, He, Li Ne, Na Ar, Ga Kr
6-31+G* H, He, Li Ne, Na Ar, Ga Kr
6-311G H, He, Li Ne, Na Ar, Ga I
6-311+G H, He, Li Ne, Na Ar
6-311G* H, He, Li Ne, Na Ar, Ga I
6-311G(d,p) H, He, Li Ne, Na Ar, Ga I
G3LARGE H, He, Li Ne, Na Ar, K Kr
G3MP2LARGE H, He, Li Ne, Na Ar, Ga Kr
Table 8.3: Examples of extended Pople basis sets.

Although not widely used in modern quantum chemistry, Dunning 293 Dunning Jr. T. H.
J. Chem. Phys.
(1971), 55, pp. 716.
Link
introduced an early set of basis sets denoted SV, DZ, and TZ; see Table 8.4. (These are not to be confused with the widely-used “correlation-consistent” basis sets, which are also associated with Dunning’s name.) The original Dunning basis sets can be extended with diffuse and polarization functions using a nomenclature similar to that used for Pople basis sets: name(k+,l+)(md,np), where k is the number of additional heavy atom diffuse functions, l is the number of additional light atom diffuse functions, m is the number of additional d polarization functions on heavy atoms, and n is the number of additional p polarization functions on light atoms. See Table 8.5 for examples of these basis sets.

Symbolic Name Atoms Supported
SV H, Li Ne
DZ H, Li Ne, Al Cl
TZ H, Li Ne
Table 8.4: Atoms supported in Q-Chem for the original Dunning basis sets. 293 Dunning Jr. T. H.
J. Chem. Phys.
(1971), 55, pp. 716.
Link
(These are different from the modern correlation-consistent Dunning basis sets.)
Symbolic Name Atoms Supported
SV H, Li Ne
SV* H, B Ne
SV(d,p) H, B Ne
SV(2+,+)(2d,p) H, B Ne
DZ H, Li Ne, Al Cl
DZ+ H, B Ne
DZ++ H, B Ne
DZ* H, Li Ne
DZ** H, Li Ne
DZ(d,p) H, Li Ne
DZ(2+,+)(2d,p) H, B Ne
TZ H, Li Ne
TZ+ H, Li Ne
TZ++ H, Li Ne
TZ* H, Li Ne
TZ** H, Li Ne
TZ(d,p) H, Li Ne
Table 8.5: Examples of extended Dunning basis sets.

The much more widely-used basis sets that are associated with Dunning are the correlation-consistent (“cc”) ones. 294 Dunning Jr. T. H.
J. Chem. Phys.
(1989), 90, pp. 1007.
Link
, 1234 Woon D. E., Dunning Jr. T. H.
J. Chem. Phys.
(1993), 98, pp. 1358.
Link
The basic ones and their augmented counterparts are listed in Table 8.6. Those appended with “-PP” are pseudopotential basis sets, defined for heavy elements only and intended to be used in conjunction with effective core potentials (ECPs), which are discussed in Section 8.10. Each correlation-consistent basis set (cc-name has an “augmented” counterpart (aug-cc-name) that includes diffuse functions.

Symbolic Name Atoms Supported
cc-pVDZ H Ar, Ca, Ga Kr
cc-pVDZ-full H Ar, Ca Kr
cc-pVDZ-PP Cu Rn
cc-pVTZ H Ar, Ca, Ga Kr
cc-pVTZ-full H Ar, Ca Kr
cc-pVTZ-PP Cu Rn
cc-pVQZ H Ar, Ca, Ga Kr
cc-pVQZ-full H Ar, Ca Kr
cc-pVQZ-PP Cu Rn
cc-pV5Z H Ar, Ca Kr
cc-pV6Z H Ar except Li, Na, Mg
cc-pCVDZ H Ar, Ca (H and He use cc-pVDZ)
cc-pCVTZ H Ar, Ca (H and He use cc-pVTZ)
cc-pCVQZ H Ar, Ca (H and He use cc-pVQZ)
cc-pCV5Z H, He, B Ar, Ca (H and He use cc-pV5Z)
cc-pwCVDZ B Ne, Al Ar
cc-pwCVTZ B Ne, Al Ar, Sc Zn
cc-pwCVQZ B Ne, Al Ar, Sc Zn, Br
cc-pwCVDZ-PP Cu Rn
cc-pwCVTZ-PP Cu Rn
cc-pwCVQZ-PP Cu Rn
aug-cc-pVDZa H Kr
aug-cc-pVDZ-PPb Cu Rn
aug-cc-pVTZa H Kr
aug-cc-pVTZ-PPb Cu Rn
aug-cc-pVQZa H Kr
aug-cc-pVQZ-PPb Cu Rn
aug-cc-pV5Z H Ar, Sc Kr
aug-cc-pV6Z H Ar except Li, Be, Na, Mg
aug-cc-pCVDZa H Ar (H and He use aug-cc-pVDZ)
aug-cc-pCVTZa H Ar (H and He use aug-cc-pVTZ)
aug-cc-pCVQZa H Ar (H and He use aug-cc-pVQZ)
aug-cc-pCV5Z H, He, B Ar (H and He use aug-cc-pV5Z)
aug-cc-pwCVDZc B Ne, Al Ar
aug-cc-pwCVTZc B Ne, Al Ar, Sc Zn
aug-cc-pwCVQZc B Ne, Al Ar, Sc Zn, Br
aug-cc-pwCVDZ-PPc Cu Rn
aug-cc-pwCVTZ-PPc Cu Rn
aug-cc-pwCVQZ-PPc Cu Rn
  • amay-, jun-, and jul-cc-p(C)VXZ variants are also available

  • bjun-cc-pVXZ-PP variant is also available

  • cjun-cc-p(w)VXZ(-PP) variant is also available

Table 8.6: Atoms supported in Q-Chem for correlation-consistent basis sets. For cc-pVXZ (X = D, T, Q), those names which do not end in “-full” correspond to the definitions with a segmented contraction scheme, 254 Davidson E. R.
Chem. Phys. Lett.
(1996), 260, pp. 514.
Link
and those that do end in “-full” correspond to the original optimized generally-contracted definitions. For all other basis sets, where there is no distinction, the only definition is from optimized general contraction. For the augmented basis sets, footnotes indicate the availability of “calendar” variants. 857 Papajak E., Truhlar D. G.
J. Chem. Theory Comput.
(2011), 7, pp. 10.
Link
, 1289 Zheng E. Papajak J. et al.
J. Chem. Theory Comput.
(2011), 7, pp. 3027.
Link

The correlation-consistent paradigm adds additional diffuse functions for each angular momentum class, meaning that for a second-row atom such as carbon, the aug-cc-pVDZ basis set contains diffuse s, p, and d functions (10 diffuse functions per atom), while hydrogen contains diffuse s and p functions. The aug-cc-pVTZ basis set also includes diffuse f functions for carbon (for a total of 20 diffuse functions per atom) and diffuse d functions for hydrogen. As compared to functions with tighter exponents, inclusion of diffuse functions is relatively expensive and prone to incur linear dependencies that hamper SCF convergence, as discussed in Section 8.3.2. At the same time, diffuse functions are often crucial to the description of anions, excited states, and noncovalent interactions but the high angular momentum diffuse functions included in aug-cc-pVXZ are not always necessary. In recognition of this fact. “calendar” versions of the correlation-consistent basis sets have been introduced (jul-, jun-, and may-name), 857 Papajak E., Truhlar D. G.
J. Chem. Theory Comput.
(2011), 7, pp. 10.
Link
, 1289 Zheng E. Papajak J. et al.
J. Chem. Theory Comput.
(2011), 7, pp. 3027.
Link
which systemically remove diffuse basis functions starting from aug-cc-name. The jul-cc-pVXZ basis set removes all diffuse functions from hydrogen, and is equivalent to using cc-pVXZ for hydrogen and aug-cc-pVXZ for heavy atoms. The jun-cc-pVXZ basis set additionally removes the highest angular momentum diffuse functions from each heavy atom, e.g., for a carbon atom the diffuse d functions are removed to make jun-cc-pVDZ and the diffuse f functions are removed to make jun-cc-pVTZ. The may-cc-pVXZ basis sets then remove the highest angular momentum diffuse functions that remain in jun-cc-pVXZ, so that for a carbon atom, may-cc-pVDZ is minimally augmented with only a single diffuse s function. Q-Chem includes may-, jun-, and jul-cc-pVXZ and similarly may-, jun-, and jul-cc-pCVXZ (for X = D, T, and Q in both cases). Also available are the jun-cc-pVXZ-PP parings of aug-cc-pVXZ-PP and the jun-cc-pwCVXZ(-PP) parings of aug-cc-pwCVXZ(-PP), again for X = D, T, or Q. If the user has questions as to what functions are included in any of these basis sets, simply set PRINT_GENERAL_BASIS = TRUE in the $rem section (as described in Section 8.3.2) to get a printout of the basis function information.

Symbolic Name Atoms Supported
TZV H Kr
VDZ H Kr
VTZ H Kr
Table 8.7: Atoms supported in Q-Chem for the original Ahlrichs basis sets. 993 Schäfer A., Horn H., Ahlrichs R.
J. Chem. Phys.
(1992), 97, pp. 2571.
Link
(Note that these are different from the more modern Karlsruhe “def2” basis sets, which are described in Table 8.8.)

The name Ahlrichs is also associated with two different collections of basis sets. The older set 993 Schäfer A., Horn H., Ahlrichs R.
J. Chem. Phys.
(1992), 97, pp. 2571.
Link
(TZV, VDZ, and VTZ) is listed in Table 8.7 but is no longer used. More widely used are the “def2” (i.e., second-generatiion) basis sets that are listed in Table 8.8, 1187 Weigend F., Ahlrichs R.
Phys. Chem. Chem. Phys.
(2005), 7, pp. 3297.
Link
, 946 Rappoport D., Furche F.
J. Chem. Phys.
(2010), 133, pp. 134105.
Link
and which are sometimes called “Karlsruhe” basis sets to distinguish them from the older basis sets developed by Ahlrichs and co-workers at the University of Karlsruhe. Finally, there is a set of basis sets associated with the name of Jensen 518 Jensen F.
J. Chem. Theory Comput.
(2008), 4, pp. 719.
Link
, 519 Jensen F.
Theor. Chem. Acc.
(2010), 126, pp. 371.
Link
(see Table 8.9), which were developed primarily for NMR calculations.

Symbolic Name Atoms Supported
def2-mSVP H–Kr,a Rb–Rn (with def2-ECP)
def2-SV(P), def2-SVP H–Kr; Rb–Rn (with def2-ECP)
def2-SVPD H–Kr; Rb–La, Hf-Rn (with def2-ECP)
def2-TZVP, def2-TZVPP H–Kr; Rb–Rn (with def2-ECP)
def2-TZVPD, def2-TZVPPD H–Kr; Rb–La, Hf-Rn (with def2-ECP)
def2-QZVP, def2-QZVPP H–Kr; Rb–Rn (with def2-ECP)
def2-QZVPD, def2-QZVPPD H–Kr; Rb–La, Hf–Rn (with def2-ECP)
UGBS H–Lr (except Pa–Np and Cm–Bk)
  • aNa–Kr are identical to def2-SV(P)

Table 8.8: Atoms supported in Q-Chem for the Karlsruhe “def2” basis sets 1187 Weigend F., Ahlrichs R.
Phys. Chem. Chem. Phys.
(2005), 7, pp. 3297.
Link
, 946 Rappoport D., Furche F.
J. Chem. Phys.
(2010), 133, pp. 134105.
Link
and for the universal Gaussian basis set (UGBS). 256 de Castro E. V. R., Jorge F. E.
J. Chem. Phys.
(1998), 108, pp. 5225.
Link
Symbolic Namea Atoms Supported
pcseg-n H Kr
pc-n H Kr
pcJ-n H Ar
psS-n H Ar
aug-pcseg-n H Kr
aug-pc-n H Kr
aug-pcJ-n H Ar
aug-psS-n H Ar
  • aFor n=0,1,2,3,4 in each case

Table 8.9: Atoms supported for Jensen polarization consistent basis sets available in Q-Chem. The pcseg-n sets should be preferred instead of pc-n, as they are more efficient in Q-Chem. The pcJ-n 519 Jensen F.
Theor. Chem. Acc.
(2010), 126, pp. 371.
Link
and pcS-n 518 Jensen F.
J. Chem. Theory Comput.
(2008), 4, pp. 719.
Link
basis sets are optimized for NMR spin-spin couplings and chemical shieldings, respectively.