Complete Basis Set Extrapolation and Hybrid Schemes for Geometry Gradients of Noncovalent Complexes

In this paper, we focus on the performance of popular WFT (MP2, MP2.5, MP3, SCS(MI)-MP2, CCSD(T)) and DFT (M06-2X, TPSS-D) methods in optimizations of geometries of noncovalent complexes. Apart from the straightforward comparison of the accuracy of the resulting geometries with respect to the most accurate, computationally affordable, reference method, we have also attempted to determine the most efficient utilization of the information contained in the gradient of a particular method and basis set. Essentially, we have transferred the ideas successfully used for noncovalent interaction energy calculations to geometry optimizations. We have assessed the performance of the hybrid gradients (for instance, MP2 and CCSD(T) calculated in different basis sets), investigated the possibility of extrapolating gradients calculated with a particular method in a series of systematically built basis sets, and finally compared the extrapolated gradients with the counterpoise(CP)-corrected optimizations, in order to determine which of these approaches is more efficient, in terms of their convergence toward the CBS geometry for the respective calculation cost. Further, we compared the efficiency of the CP-corrected, extrapolated, and hybrid gradients in terms of the rate of convergence with respect to basis set size. We have found that CCSD(T) geometries are most faithfully reproduced by the MP2.5 and MP3 methods, followed by the comparably well performing SCS(MI)-MP2 and MP2 methods, and finally by the worst performing DFT-D and M06 methods. Basis set extrapolation of gradients was shown to improve the results and can be considered as a low-cost alternative to the use of CP-corrected gradients. A hybrid gradient scheme was shown to deliver geometries close to the regular gradient reference. Analogously to a similar hybrid scheme, which nowadays is routinely used for the calculation of interaction energies, such a hybrid gradient scheme can save a huge amount of computer time, when high accuracy is desired.