# 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-pV$X$Z 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.912 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. 912 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,909 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.