Basis set limits of the second order Møller-Plesset correlation energies of water, methane, acetylene, ethylene, and benzene

Explicitly Correlated Methods within the ccCA Methodology

The prediction of energetic properties within "chemical accuracy" (1 kcal mol(-1) from well-established experiment) can be a major challenge in computational quantum chemistry due to the computational requirements (computer time, memory, and disk space) needed to achieve this level of accuracy. Methodologies such as coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) combined with very large basis sets are often required to reach this level of accuracy. Unfortunately, such calculations quickly become cost prohibitive as system size increases. Our group has developed an ab initio composite method, the correlation consistent Composite Approach (ccCA), which enables such accuracy to be possible, on average, but at reduced computational cost as compared with CCSD(T) in combination with a large basis set. While ccCA has proven quite useful, computational bottlenecks still occur. In this study, the means to reduce the computational cost of ccCA without compromising accuracy by utilizing explicitly correlated methods within ccCA have been considered, and an alternative formulation is described.

Explicitly correlated second-order Møller-Plesset perturbation theory employing pseudospectral numerical quadratures

We implemented explicitly correlated second-order Møller-Plesset perturbation theory with numerical quadratures using pseudospectral construction of grids. Introduction of pseudospectral approach for the calculation of many-electron integrals gives a possibility to use coarse grids without significant loss of precision in correlation energies, while the number of points in the grid is reduced about nine times. The use of complementary auxiliary basis sets as the sets of dealiasing functions is justified at both theoretical and computational levels. Benchmark calculations for a set of 16 molecules have shown the possibility to keep an error of second-order correlation energies within 1 milihartree (mH) with respect to MP2-F12 method with dense grids. Numerical tests for a set of 13 isogyric reactions are also performed.

Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.