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# 4.7.1 Introduction

(December 20, 2021)

The dual-basis approximation 687 Liang W. Z., Head-Gordon M.
J. Phys. Chem. A
(2004), 108, pp. 3206.
, 1072 Steele R. P. et al.
J. Chem. Phys.
(2006), 125, pp. 074108.
, 1075 Steele R. P. et al.
J. Phys. Chem. A
(2006), 110, pp. 13915.
, 275 DiStasio, Jr. R. A., Steele R. P., Head-Gordon M.
Mol. Phys.
(2007), 105, pp. 2731.
, 1074 Steele R. P., Head-Gordon M.
Mol. Phys.
(2007), 105, pp. 2455.
, 1071 Steele R. P., DiStasio, Jr. R. A., Head-Gordon M.
J. Chem. Theory Comput.
(2009), 5, pp. 1560.
to self-consistent field (HF or DFT) energies provides an efficient means for obtaining large basis set effects at vastly less cost than a full SCF calculation in a large basis set. First, a full SCF calculation is performed in a chosen small basis (specified by BASIS2). Second, a single SCF-like step in the larger, target basis (specified, as usual, by BASIS) is used to perturbatively approximate the large basis energy. This correction amounts to a first-order approximation in the change in density matrix, after the single large-basis step:

 $E_{\text{total}}=E_{\text{small basis}}+\mbox{tr}[(\Delta\mathbf{P})\mathbf{F}% ]_{\text{large basis}}\;.$ (4.56)

Here $\mathbf{F}$ (in the large basis) is built from the converged (small basis) density matrix. Thus, only a single Fock build is required in the large basis set. Currently, HF and DFT energies (SP) as well as analytic first derivatives (FORCE or OPT) are available.

Note:  As of version 4.0, first derivatives of unrestricted dual-basis DFT energies—though correct—require a code-efficiency fix. We do not recommend use of these derivatives until this improvement has been made.

Across the G3 set 244 Curtiss L. A. et al.
J. Chem. Phys.
(1991), 94, pp. 7221.
, 243 Curtiss L. A. et al.
J. Chem. Phys.
(1998), 109, pp. 7764.
, 242 Curtiss L. A. et al.
J. Chem. Phys.
(2000), 112, pp. 7374.
of 223 molecules, using cc-pVQZ, dual-basis errors for B3LYP are 0.04 kcal/mol (energy) and 0.03 kcal/mol (atomization energy per bond) and are at least an order of magnitude less than using a smaller basis set alone. These errors are obtained at roughly an order of magnitude savings in cost, relative to the full, target-basis calculation.