The dual-basis approximation can also be used for the reference energy of a correlated second-order Møller-Plesset (MP2) calculation.910, 909 When activated, the dual-basis HF energy is first calculated as described above; subsequently, the MO coefficients and orbital energies are used to calculate the correlation energy in the large basis. This technique is particularly effective for RI-MP2 calculations (see Section 6.6), in which the cost of the underlying SCF calculation often dominates.
Furthermore, efficient analytic gradients of the DB-RI-MP2 energy have been developed223 and added to Q-Chem. These gradients allow for the optimization of molecular structures with RI-MP2 near the basis set limit. Typical computational savings are on the order of 50% (aug-cc-pVDZ) to 71% (aug-cc-pVTZ). Resulting dual-basis errors are only 0.001 Å in molecular structures and are, again, significantly less than use of a smaller basis set alone.