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Basis-Set Input

The basis set to be used in a calculation is specified via

BASIS=basis

There are predefined choices for basis such as

a) Pople basis sets

STO-3G
3-21G
4-31G
6-31G
6-311G
6-31G*
6-31G**
6-31G*
6-311G**

b) Dunning-Huzinaga basis sets

DZ
DZP
TZ2P

c) Karlsruhe basis sets

svp
dzp
tzp
tz2p
qz2p
pz3d2f
13s9p4d3f

d) correlation-consistent basis sets

cc-pVXZ (x=D,T,Q,5,6)
cc-pCVXZ (x=D,T,Q,5,6)
cc-pwCVXZ (X=D,T,Q,5,6)
aug-pVXZ (X=D,T,Q,5,6)
d-aug-pVXZ (X=D,T,Q,5,6)
aug-pCVXZ (X=D,T,Q,5,6)

e) Atomic Natural Orbital (ANO) basis sets

ANO0
ANO1
ANO2

f) Widmark-Malmqvist-Roos (WMR) basis sets

WMR

g) polarized basis sets of Sadlej et al

PBS

h) ccJ-pVXZ sets for the calculation of spin-spin couplings

ccJ-pVDZ
ccJ-pVTZ
ccJ-pVQZ
ccJ-pV5Z

The corresponding basis sets are known to CFOUR and usually supplied via the GENBAS file (for availability see section Basis-set file GENBAS). However, if one wants to use a non-predefined basis set, this can be accomplished via

BASIS=SPECIAL

together with a specification of the used sets for each atom after the CFOUR keyword list. In the following example

   input of non-standard basis sets
   O
   H 1 R  
   H 1 R 2 A

   R=1.
   A=100.

   *CFOUR(CALC=SCF,BASIS=SPECIAL)

   O:DZP
   H:DZ
   H:DZ

a DZP basis is requested for oxygen and DZ sets are requested for hydrogen (note that the order of the specified sets must correspond to the ZMAT ordering; no basis sets are to be specified for dummy atoms (X), while a basis set must be given for ghost atoms (GH)).

The use of non-standard basis sets often requires that a corresponding entry in the GENBAS file is made, as a set with the corresponding label must exit in the supplied GENBAS file (for adding a basis set to the GENBAS file, see section Basis-set file GENBAS).

Uncontracted basis sets

Uncontracted versions of a given contracted basis set can be obtained by specifying CONTRACTION=UNCONTRACTED. Note that in case of the cc-p(w)CVXZ sets, the corresponding cc-p(w)CVXZ-unc sets (without the steep s- and p- functions in the case of first- and second-row, without the steep s-, p- , and d-functions in the case of third-row elements) are used to avoid linear dependencies.

BASIS=EVEN_TEMPERED

Even tempered basis sets can be generated automatically by specifying BASIS=EVEN_TEMPERED in the ZMAT. After the keyword list, the section %EVEN_TEMPERED is needed which is constructed as shown in the following example:

   input for even tempered basis sets
   H
   CL 1 R

   R=0.9157993311

   *CFOUR(BASIS=EVEN_TEMPERED)

   %EVEN_TEMPERED
   H=VARIANT FACNUM
   s 0.2 1.7 5
   p 0.2 1.7 4
   END

   CL=VARIANT FACNUM
   s 0.3 2.3 16
   p 0.2 2.0 5
   d 0.2 2.0 3
   END

A definition section for all atoms in the molecule has to be provided.
Line #1: atom-symbol=VARIANT FACNUM
This means that aside from the angular momentum (ang=s,p,d etc. ) and the smallest exponent (expmin), the factor (fac) and the total number of exponents (totexp) are given in order to calculate the exponents for the basis set. Only this variant is currently implemented.

Line #2 (and following): ang expmin fac totexp

Last line (for each atom): END

Note:

• The described procedure generates an uncontracted basis set.
• It is possible to use BASIS=SPECIAL and define even tempered set just for some atoms of the molecule (i.e. H:PVDZ, F:EVEN_TEMPERED).

Cartesian versus Spherical Gaussians

By default, all calculations with CFOUR are performed with Spherical Gaussians (keyword SPHERICAL=ON; 5d, 7f 9g, ...) which uses for the polarization functions the pure set of d-, f-, g-, ... functions. If one wants to use Cartesian Gaussians (usually known as 6d, 10f, ...), this can be accomplished via the keyword

SPHERICAL=OFF

Note that care is here required, as some basis sets have been constructed (and should be therefore used) with Cartesian Gaussians (e.g., 6-31G**) and others (actually most) with Spherical Gaussians.

Used definition of spherical Gaussians

Order of basis functions

Normalization of basis functions