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Calculations of the hyperpolarizability are typically much more difficult toconverge with basis set size than the linear polarizability. In order tounderstand these convergence issues and hence obtain accurate ab initio values,we compare calculations of the static hyperpolarizability of the gas-phasechloroform molecule (CHCl_3) using three different kinds of basis sets:Gaussian-type orbitals, numerical basis sets, and real-space grids. Althoughall of these methods can yield similar results, surprisingly large, diffusebasis sets are needed to achieve convergence to comparable values. Theseresults are interpreted in terms of local polarizability andhyperpolarizability densities. We find that the hyperpolarizability is verysensitive to the molecular structure, and we also assess the significance ofvibrational contributions and frequency dispersion.

Basis set effects on the hyperpolarizability of CHCl_3: Gaussian-type orbitals, numerical basis sets and real-space grids