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