4.7 Dual-Basis Self-Consistent Field Calculations

4.7.3 Basis-Set Pairings

We recommend using basis pairings in which the small basis set is a proper subset of the target basis (6-31G into 6-31G*, for example). They not only produce more accurate results; they also lead to more efficient integral screening in both energies and gradients. Subsets for many standard basis sets (including Dunning-style cc-pVXZ basis sets and their augmented analogs) have been developed and thoroughly tested for these purposes. A summary of the pairings is provided in Table 4.2; details of these truncations are provided in Figure 4.1.

A new pairing for 6-31G*-type calculations is also available. The 6-4G subset (named r64G in Q-Chem) is a subset by primitive functions and provides a smaller, faster alternative for this basis set regime.868 A case-dependent switch in the projection code (still OVPROJECTION) properly handles 6-4G. For DB-HF, the calculations proceed as described above. For DB-DFT, empirical scaling factors (see Ref. 868 for details) are applied to the dual-basis correction. This scaling is handled automatically by the code and prints accordingly.

As of Q-Chem version 3.2, the basis set projection code has also been adapted to properly account for linear dependence,865 which can often be problematic for large, augmented (aug-cc-pVTZ, etc.) basis set calculations. The same standard keyword (LIN_DEP_THRESH) is used to determine linear dependence in the projection code. Because of the scheme used to account for linear dependence, only proper-subset pairings are now allowed.

Like single-basis calculations, user-specified general or mixed basis sets may be employed (see Chapter 8) with dual-basis calculations. The target basis specification occurs in the standard $basis section. The smaller, secondary basis is placed in a similar $basis2 section; the syntax within this section is the same as the syntax for $basis. General and mixed small basis sets are activated by BASIS2 = BASIS2_GEN and BASIS2 = BASIS2_MIXED, respectively.

BASIS BASIS2
cc-pVTZ rcc-pVTZ
cc-pVQZ rcc-pVQZ
aug-cc-pVDZ racc-pVDZ
aug-cc-pVTZ racc-pVTZ
aug-cc-pVQZ racc-pVQZ
6-31G* r64G, 6-31G
6-31G** r64G, 6-31G
6-31++G** 6-31G*
6-311++G(3df,3pd) 6-311G*, 6-311+G*
Table 4.2: Summary and nomenclature of recommended dual-basis pairings
H-He:spsdpssps--sLi-Ne:spsdpfsdpsspsdp-sdpscc-pVTZrcc-pVTZcc-pVTZrcc-pVTZ
H-He:spsdpfsdpss-s-p-s--sLi-Ne:spsdpfsdgpfsdpsspsdp-sd-p-sdpscc-pVQZrcc-pVQZcc-pVQZrcc-pVQZ
H-He:spspssps-sLi-Ne:spsdpsdpsspsdps-psaug-cc-pVDZracc-pVDZaug-cc-pVDZracc-pVDZ
H-He:spsdpsdpssps-ps--sLi-Ne:spsdpfsdpfsdpsspsdp-sdp-s-psaug-cc-pVTZracc-pVTZaug-cc-pVTZracc-pVTZ
H-He:spsdpfsdpfsdpssps-p-s-p-s--sLi-Ne:spsdpfsdgpfsdgpfsdpsspsdp-sd-p-sd-p-s-psaug-cc-pVQZracc-pVQZaug-cc-pVQZracc-pVQZ
Figure 4.1: Structure of the truncated basis set pairings for cc-pV(T,Q)Z and aug-cc-pV(D,T,Q)Z. The most compact functions are listed at the top. Primed functions depict diffuse function augmentation. Dashes indicate eliminated functions, relative to the paired standard basis set. In each case, the truncations for hydrogen and heavy atoms are shown, along with the nomenclature used in Q-Chem.