The use of the basis set library supplied with DALTON is indicated by the word BASIS or ATOMBASIS on the first line of the molecular input.
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: 2 2 X Y Z 1.00D-15 6: 6. 2 7:C1 1.379495419 .0 0.975450565 8:C2 .0 1.379495419 -.975450565 9: 1. 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. [77]. 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, thight or polarizing basis functions. Returning to tetrahedrane, we could for instance use the 6-31G* basis sets on carbon and the 4-31G** basis sets on 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: 2 2 X Y Z 1.00D-15 5: 6. 2 6-31G* 6:C1 1.379495419 .0 0.975450565 7:C2 .0 1.379495419 -.975450565 8: 1. 2 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, following right after the number of symmetry-distinct atoms of this type. Everything following position 15 (the number of symmetry-distinct atoms) is in free format.
The string Pol denotes that the rest of the line specifies diffuse, thight 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).
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: 2 2 X Y Z 1.00D-15 5: 6. 2 ano-1 3 2 0 0 Pol 3 0.8 6:C1 1.379495419 .0 0.975450565 7:C2 .0 1.379495419 -.975450565 8: 1. 2 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 [76] was constructed in order to provide, in electronic form, a basis set compilation very similar to original set of van Duijneveldt [78] . 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: 2 2 X Y Z 1.00D-15 5: 6. 2 NQvD 8 4 3 2 Pol 3 0.8D0 6:C1 1.379495419 .0 0.975450565 7:C2 .0 1.379495419 -.975450565 8: 1. 2 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 no further explanantion 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 dumping a standard basis set
to DALTON.BAS using the keyword .MOLPRI
, and then adding
functions to this set.