  Anharmonic vibrational calculations can already be computationally demanding
for relatively small molecules. The main bottlenecks lie in the construction of
the potential energy surface and in the size of the excitation space in the
vibrational configuration interaction (VCI) calculations. To address these
challanges, we use localized-mode coordinates to construct potential energy
surfaces and perform vibrational self-consistent field (L-VSCF) and L-VCI
calculations [P. T. Panek, Ch. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all
vibrational modes of two prototypical test cases, the ethene and furan
molecules. We find that the mutual coupling between modes is reduced when
switching from normal-mode coordinates to localized-mode coordinates. When
using such localized-mode coordinates, we observe a faster convergence of the
$n$-mode expansion of the potential energy surface. This makes it possible to
neglect higher-order contributions in the $n$-mode expansion of the potential
energy surface or to approximate higher-oder contributions in hybrid potential
energy surfaces, which reduced the computational effort for the construction of
the anharmonic potential energy surface significantly. Moreover, we find that
when using localized-mode coordinates, the convergence with respect to the VCI
excitation space proceeds more smoothly and that the error at low orders is
reduced significantly. This makes it possible to devise low-cost models for
obtaining a first approximation of anharmonic corrections. This demonstrates
that the use of localized-mode coordinates can be beneficial already in
anharmonic vibrational calculations of small molecules, and provides a possible
avenue for enabling such accurate calculations also for larger molecules.
