  Metallic transition metal dichalcogenides like tantalum diselenide
(TaSe$_{2}$) exhibit exciting behaviors at low temperatures, including the
emergence of charge density wave (CDW) states. In this work, density functional
theory (DFT) is used to investigate how structural, electronic, and Raman
spectral properties of the CDW configuration change as a function of thickness.
Such findings highlight the influence of dimensionality change (from 2D to 3D)
and van der Waals (vdW) interactions on the system properties. The vdW effect
is most strongly present in bulk TaSe$_{2}$ in the spectral range 165 cm$^{-1}$
to 215 cm$^{-1}$. The phonons seen in the experimental Raman spectra are
compared with the results calculated from the DFT models as a function of
temperature and layer number. The matching of data and calculations
substantiates the model's description of the CDW structural formation as a
function of thickness, which is shown in depth for 1L through 6L systems. These
results highlight the importance of understanding interlayer interactions,
which are pervasive in many quantum phenomena involving two-dimensional
confinement.
