Dual-Basis RI-MP2 Analytical Gradient
Collaboration with Rob Distasio

Two factors motivated our study of dual-basis RI-MP2 analytic derivatives:

• Accurate single-point energies were obtained for dual-basis MP2 (and RI-MP2). Furthermore, timings for these energies were approximately 10-20 times faster than convential MP2.
• Savings in the HF/DFT gradient were substantial. However, the one additional cost for these methods—the orbital response equations—is already present in MP2 derivatives.

Thus, it was possible to formulate the dual-basis MP2 derivative in a manner that allowed the already-present response equation to be cast in the small basis set alone. This result was particularly exciting, given the fact that we were taking an exact derivative of an approximate energy.

Accordingly, both timings and accuracy were excellent.

Reference:
"The analytical gradient of dual-basis resolution-of-the-identity second-order Moller-Plesset perturbation theory"
R. A. Distasio, Jr., R. P. Steele, and M. Head-Gordon. Mol. Phys. 105 2731–2742(2007).