Why are diffuse atomic orbitals needed for accurate electronic wave functions of even neutral molecules?
An accurate description of electron correlation energies in molecules requires either basis set extrapolation or the use of explicitly-correlated wave functions that address the deficiencies of standard determinantal expansions at short interelectronic distances. Practical and robust explicitly-correlated F12 methods require the use of standard or specialized atomic orbital (AO) basis sets that include diffuse AOs, even for neutral species. Although modern reduced-scaling formulations of explicitly-correlated many-body methods have become routinely applicable to molecules with hundreds of atoms, application of F12 methods to large molecular systems can be severely hampered due to the onset of ill-conditioning spurred by the presence of diffuse AOs in the F12-appropriate orbital basis sets. Here we re-examine why diffuse AOs are necessary for application of F12 methods. To help such an investigation, we developed a dual-basis formulation of traditional and F12 coupled-cluster singles and doubles (CCSD) methods in which the reference (occupied) and correlating (virtual) orbitals are expanded in separate AO basis sets. Our conclusion is that diffuse AOs are fundamentally important for the traditional (non-F12) description of dynamical correlation; the necessity of diffuse AOs in F12 calculations arises indirectly due to the dramatic reduction of the basis set error by the F12 terms such that the error due to the lack of diffuse AOs becomes comparable to the residual basis set incompleteness. The dual-basis CC methods are suggested as an important candidate formalism for accurate (in particular, F12) reduced-scaling many-body methods in extended systems.