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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 *$basis* section. The
smaller, secondary basis is placed in a similar *$basis*2 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* |

$$\begin{array}{cccccc}\hfill \text{H-He:}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill d\hfill \\ & \hfill p\hfill & \\ \hfill s\hfill & & \end{array}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill -\hfill \\ & \hfill -\hfill & \\ \hfill s\hfill & & \end{array}\hfill & \hfill \text{Li-Ne:}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill f\hfill \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & & \end{array}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill -\hfill \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & & \end{array}\hfill \\ & \hfill \text{cc-pVTZ}\hfill & \hfill \text{rcc-pVTZ}\hfill & & \hfill \text{cc-pVTZ}\hfill & \hfill \text{rcc-pVTZ}\hfill \end{array}$$ |

$$\begin{array}{cccccc}\hfill \text{H-He:}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill f\hfill \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & & \end{array}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill -\hfill & & \\ \hfill s\hfill & & \hfill -\hfill & \\ & \hfill p\hfill & & \hfill -\hfill \\ \hfill s\hfill & & \hfill -\hfill & \\ & \hfill -\hfill & & \\ \hfill s\hfill & & & \end{array}\hfill & \hfill \text{Li-Ne:}\hfill & \hfill \begin{array}{ccccc}\hfill s\hfill & & & & \\ & \hfill p\hfill & & & \\ \hfill s\hfill & & \hfill d\hfill & & \\ & \hfill p\hfill & & \hfill f\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \hfill g\hfill \\ & \hfill p\hfill & & \hfill f\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \\ & \hfill p\hfill & & & \\ \hfill s\hfill & & & & \end{array}\hfill & \hfill \begin{array}{ccccc}\hfill s\hfill & & & & \\ & \hfill p\hfill & & & \\ \hfill s\hfill & & \hfill d\hfill & & \\ & \hfill p\hfill & & \hfill -\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \hfill -\hfill \\ & \hfill p\hfill & & \hfill -\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \\ & \hfill p\hfill & & & \\ \hfill s\hfill & & & & \end{array}\hfill \\ & \hfill \text{cc-pVQZ}\hfill & \hfill \text{rcc-pVQZ}\hfill & & \hfill \text{cc-pVQZ}\hfill & \hfill \text{rcc-pVQZ}\hfill \end{array}$$ |

$$\begin{array}{cccccc}\hfill \text{H-He:}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill {s}^{\prime}\hfill & & \end{array}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \\ & \hfill -\hfill & \\ \hfill {s}^{\prime}\hfill & & \end{array}\hfill & \hfill \text{Li-Ne:}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill d\hfill \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill {d}^{\prime}\hfill \\ & \hfill {p}^{\prime}\hfill & \\ \hfill {s}^{\prime}\hfill & & \end{array}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill d\hfill \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill -\hfill \\ & \hfill {p}^{\prime}\hfill & \\ \hfill {s}^{\prime}\hfill & & \end{array}\hfill \\ & \hfill \text{aug-cc-pVDZ}\hfill & \hfill \text{racc-pVDZ}\hfill & & \hfill \text{aug-cc-pVDZ}\hfill & \hfill \text{racc-pVDZ}\hfill \end{array}$$ |

$$\begin{array}{cccccc}\hfill \text{H-He:}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill d\hfill \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill {d}^{\prime}\hfill \\ & \hfill {p}^{\prime}\hfill & \\ \hfill {s}^{\prime}\hfill & & \end{array}\hfill & \hfill \begin{array}{ccc}\hfill s\hfill & & \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill -\hfill \\ & \hfill p\hfill & \\ \hfill s\hfill & & \hfill -\hfill \\ & \hfill -\hfill & \\ \hfill {s}^{\prime}\hfill & & \end{array}\hfill & \hfill \text{Li-Ne:}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill f\hfill \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill {f}^{\prime}\hfill \\ \hfill s\hfill & & \hfill {d}^{\prime}\hfill & \\ & \hfill {p}^{\prime}\hfill & & \\ \hfill {s}^{\prime}\hfill & & & \end{array}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill -\hfill \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill -\hfill \\ \hfill s\hfill & & \hfill -\hfill & \\ & \hfill {p}^{\prime}\hfill & & \\ \hfill {s}^{\prime}\hfill & & & \end{array}\hfill \\ & \hfill \text{aug-cc-pVTZ}\hfill & \hfill \text{racc-pVTZ}\hfill & & \hfill \text{aug-cc-pVTZ}\hfill & \hfill \text{racc-pVTZ}\hfill \end{array}$$ |

$$\begin{array}{cccccc}\hfill \text{H-He:}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill f\hfill \\ \hfill s\hfill & & \hfill d\hfill & \\ & \hfill p\hfill & & \hfill {f}^{\prime}\hfill \\ \hfill s\hfill & & \hfill {d}^{\prime}\hfill & \\ & \hfill {p}^{\prime}\hfill & & \\ \hfill {s}^{\prime}\hfill & & & \end{array}\hfill & \hfill \begin{array}{cccc}\hfill s\hfill & & & \\ & \hfill p\hfill & & \\ \hfill s\hfill & & \hfill -\hfill & \\ & \hfill p\hfill & & \hfill -\hfill \\ \hfill s\hfill & & \hfill -\hfill & \\ & \hfill p\hfill & & \hfill -\hfill \\ \hfill s\hfill & & \hfill -\hfill & \\ & \hfill -\hfill & & \\ \hfill {s}^{\prime}\hfill & & & \end{array}\hfill & \hfill \text{Li-Ne:}\hfill & \hfill \begin{array}{ccccc}\hfill s\hfill & & & & \\ & \hfill p\hfill & & & \\ \hfill s\hfill & & \hfill d\hfill & & \\ & \hfill p\hfill & & \hfill f\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \hfill g\hfill \\ & \hfill p\hfill & & \hfill f\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \hfill {g}^{\prime}\hfill \\ & \hfill p\hfill & & \hfill {f}^{\prime}\hfill & \\ \hfill s\hfill & & \hfill {d}^{\prime}\hfill & & \\ & \hfill {p}^{\prime}\hfill & & & \\ \hfill {s}^{\prime}\hfill & & & & \end{array}\hfill & \hfill \begin{array}{ccccc}\hfill s\hfill & & & & \\ & \hfill p\hfill & & & \\ \hfill s\hfill & & \hfill d\hfill & & \\ & \hfill p\hfill & & \hfill -\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \hfill -\hfill \\ & \hfill p\hfill & & \hfill -\hfill & \\ \hfill s\hfill & & \hfill d\hfill & & \hfill -\hfill \\ & \hfill p\hfill & & \hfill -\hfill & \\ \hfill s\hfill & & \hfill -\hfill & & \\ & \hfill {p}^{\prime}\hfill & & & \\ \hfill {s}^{\prime}\hfill & & & & \end{array}\hfill \\ & \hfill \text{aug-cc-pVQZ}\hfill & \hfill \text{racc-pVQZ}\hfill & & \hfill \text{aug-cc-pVQZ}\hfill & \hfill \text{racc-pVQZ}\hfill \end{array}$$ |