Using basis set libraries

The use of predefined basis sets is indicated by the word BASIS or ATOMBASIS on the first line of the molecular input. (If you want Z-matrix input you must use BASIS.)

The specified basis set(s) are searched for in the following directories:

• all user specified basis set directories (with dalton -b dir1 -b dir2 ...
• the job directory
• the basis set library supplied with DALTON.

If BASIS is used, a common basis set is used for all atoms in the molecule, and the name of this basis set is given on the second line. If we want to use one basis set for all the atoms in a molecule, the molecule input file can be significantly simplified, as we may delete all the input information regarding the basis set. Thus, the input in the previous section for tetrahedrane with the 6-31G** basis will, if the basis set library is used, be reduced to:

 1:BASIS
 2:6-31G**
 3:        Tetrahedrane, Td_symmetric geometry
 4:                 4-31G** basis
 5:Atomtypes=2 Generators=2 X Y Integrals=1.00D-15
 6:Charge=6.0 Atoms=2
 7:C1    1.379495419          .0                 0.975450565
 8:C2     .0                 1.379495419         -.975450565
 9:Charge=1.0 Atoms=2
10:H1    3.020386510         .0                  2.1357357837
11:H2     .0                 3.020386510         -2.1357357837

The use of the basis set library is indicated by the presence of the BASIS word in the beginning of MOLECULE-file instead of INTGRL.

An alternative approach would be to use different basis sets for different atoms, e.g. the concept of locally dense basis sets introduced in NMR calculations by Chesnut et al. [129]. This is for instance also required when using the ANO or NQvD basis sets. Another option is to use standards basis sets from the basis set library and add your own sets of diffuse, tight or polarizing basis functions. Returning to tetrahedrane, we could for instance use the 6-31G* basis set for carbon and the 4-31G** basis set for hydrogen. This could be achieved as

 1:ATOMBASIS
 2:        Tetrahedrane, Td_symmetric geometry
 3:    Mixed basis (6-31G* on C and 4-31G** on H)
 4:Atomtypes=2 Generators=2 X Y Integrals=1.00D-15
 5:Charge=6.0 Atoms=2 Basis=6-31G*
 6:C1    1.379495419          .0                 0.975450565
 7:C2     .0                 1.379495419         -.975450565
 8:Charge=1.0 Atoms=2 Basis=4-31G Pol 2 0.75D0
 9:H1    3.020386510         .0                  2.1357357837
10:H2     .0                 3.020386510         -2.1357357837

Thus, when using ATOMBASIS the name of the basis set for a given set of identical atoms is given on the same line as the nuclear charge, indicated by the keyword ``Basis=''.

The string Pol denotes that the rest of the line specifies diffuse, tight or polarizing functions, all which will be added as segmented basis functions. For each basis function, its ``angular momentum'' ($l+1$) and its exponent must be given. Thus, in the above input we indicate that we add a $p$ function with exponent 0.75 to the hydrogen basis set. The order of these functions are arbitrary (that is, a $p$ function can be given before an $s$ function and so on).

Augmenting the correlation-consistent sets of Dunning [68] is a straight-forward process in DALTON. The aug-cc-pVXZ and aug-cc-pCVXZ basis sets are extended in an even-tempered manner (in the manner of Dunning [68]) by including a 'd-', 't-' or 'q-' prefix to give doubly, triply or quadruply augmented basis sets, respectively. For example, specifying t-aug-cc-pVDZ will produce a triply augmented cc-pVDZ basis. The aug-ecp basis sets may be augmented in the same manner by using the same prefixes, eg d-aug-ecp. Note that these basis sets are not listed explicitly in the basis library directory, but are automatically generated within DALTONfrom the respective aug-cc-pVXZ and aug-ecp basis sets.

The ANO basis sets require that you give the number of contracted functions you would like to use for each of the primitive sets defined in the basis sets. Thus, assuming we would like to simulate the 6-31G** basis set input using an ANO basis set but with the polarization functions of the 6-31G** set, this could be achieved through an input like

 1:ATOMBASIS
 2:        Tetrahedrane, Td_symmetric geometry
 3:    Mixed basis (6-31G* on C and 4-31G** on H)
 4:Atomtypes=2 Generators=2 X Y Integrals=1.00D-15
 5:Charge=6.0 Atoms=2 Basis=ano-1 3 2 0 0 Pol 3 0.8
 6:C1    1.379495419          .0                 0.975450565
 7:C2     .0                 1.379495419         -.975450565
 8:Charge=1.0 Atoms=2 Basis=ano-1 2 0 0 Pol 2 0.75D0
 9:H1    3.020386510         .0                  2.1357357837
10:H2     .0                 3.020386510         -2.1357357837

This input will give a [3s2p0d0f] ANO basis set on carbon, with a polarizing $d$ function with exponent 0.8, and a [2s0p0d] ANO basis set on hydrogen with a polarizing $p$ function with exponent 0.75 as above.

Note that the number of contracted functions in the ANO set has to be given for all primitive blocks, even though you do not want any contracted functions of a given quantum number. Here also, Pol separates the number of contracted functions from polarization functions.

The NQvD basis set [128] was constructed in order to provide, in electronic form, a basis set compilation very similar to original set of van Duijneveldt [130]. The sets are in general as good, or slightly better, than the original van Duijneveldt basis, with only minor changes in the orbital exponents.

In the NQvD basis set, you need not only to pick the number of contracted functions, but also your primitive set. The contracted basis set will be constructed contracting the (NPRIM-NCONT + 1) tightest functions with contraction coefficients based on the eigenvectors from the atomic optimization, keeping the outermost orbitals uncontracted.

NOTE: As is customary, the orbital exponents of all hydrogen basis functions are automatically multiplied by a factor of 1.44.

Thus, an input for tetrahedrane employing the NQvD basis set might look like

 1:ATOMBASIS
 2:        Tetrahedrane, Td_symmetric geometry
 3:    Mixed basis (6-31G* on C and 4-31G** on H)
 4:Atomtypes=2 Generators=2 X Y Integrals=1.00D-15
 5:Charge=6.0 Atoms=2 Basis=NQvD 8 4 3 2 Pol 3 0.8D0
 6:C1    1.379495419          .0                 0.975450565
 7:C2     .0                 1.379495419         -.975450565
 8:Charge=1.0 Atoms=2 Basis=NQvD 4 2 Pol 2 0.75D0
 9:H1    3.020386510         .0                  2.1357357837
10:H2     .0                 3.020386510         -2.1357357837

This input will use an (8s4p/4s) primitive basis set on carbon and hydrogen respectively, contracting it to a [3s2p/2s] set. The polarization functions should not require further explanation at this stage.

The only limitations to the use of polarization functions when ATOMBASIS is used, is that the length of the line must note exceed 80 characters. If that happens, we recommend collecting a standard basis set from the file DALTON.BAS, and then adding functions to this set.