Auxiliary basis sets for use in explicitly correlated MP2-F12 and CCSD-F12 methods, in which three- and four-electron integrals are approximated as products of two-electron integrals through the resolution of the identity (RI), have been optimized for the elements H, B-Ne, and Al-Ar. Fully matched to the recently constructed cc-pVnZ-F12 orbital basis sets, these new auxiliary basis sets result in very small RI errors, as exemplified by the calculated atomization energies of 42 molecules at the MP2-F12 level. Their utility in calculating smooth potential energy surfaces is also demonstrated in calculations of the spectroscopic properties of several diatomic molecules.

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Correlation consistent basis sets that are suitable for the correlation of the outer-core (n-1)spd electrons of the post-d elements Ga-Rn have been developed. These new sets, denoted by cc-pwCVXZ-PP (X=D,T,Q,5), are based on the previously reported cc-pVXZ-PP sets that were built in conjunction with accurate small-core relativistic pseudopotentials (PPs) and designed only for valence nsp correlation. These new basis sets have been utilized in benchmark coupled cluster calculations of the core-valence correlation effects on the dissociation energies and spectroscopic properties of several small molecules. As expected, the most important contribution is the correlation of the (n-1)d electrons. For example, in the case of the group 13 homonuclear diatomics (Ga(2),In(2),Tl(2)), this leads to a dissociation energy increase compared to a valence-only treatment from 1.5 to 3.2 kcal/mol, bond length shortenings from -0.076 to -0.125 Å, and harmonic frequency increases of 7-8 cm(-1). Even in the group 15 cases (As(2),Sb(2),Bi(2)), the analogous effects of (n-1)d electron correlation are certainly not insignificant, the largest values being +4.4 kcal/mol, -0.049 Å, and +9.6 cm(-1) for the effects on D(e), r(e), and ω(e), respectively. In general, the effects increase in magnitude down a group from 4p to 6p. Correlation of the outer-core (n-1)p electrons is about an order of magnitude less important than (n-1)d but larger than that of the (n-1)s. The effect of additional tight functions for Hartree-Fock and valence sp correlation was found to be surprisingly large, especially for the post-4d and post-5d elements. The pseudopotential results for the molecules containing post-3d elements are also compared to the analogous all-electron calculations employing the Douglas-Kroll-Hess Hamiltonian. The errors attributed to the PP approximation are found to be very small.

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An empirical dispersion correction is added to the range-separated hybrid density functionals HSE and HISS via parametrization versus a standard test bed of weakly bound complexes. The performance of the resulting HSE-D and HISS-D functionals is evaluated by calculating the equilibrium bond length, harmonic frequency, and dissociation energy for a number of rare gas dimers, and the lattice constants, band gaps, and sublimation energies of the rare gas solids. Both HSE-D and HISS-D are shown to provide accurate results for both molecules and extended systems, suggesting that the combination of a screened hybrid functional with an empirical dispersion correction provides an accurate, widely applicable method for use in solid-state and gas-phase electronic structure theory.