  Density functional theory based calculations and experimental analysis on a
limited number of real samples are performed to study how the presence of
silver intercalated in the van der Waals gap of few-layer MoS$_2$ affects the
low-frequency Raman active modes of this material. Silver is found to
predominantly affect the breathing-like and shear-like vibrational modes of
MoS$_2$. These modes correspond to quasi-rigid movements of each individual
layer with a restoring force (and, in turn, frequency) that is determined by
modulations in the weak interlayer interactions. Noticeable red-shifts with
increasing Ag concentration are found for all low-frequency modes. This finding
indicates the potential for low-frequency vibrations as useful gauges for
practical determination of silver concentration using low-frequency Raman
spectroscopy. This work also describes a semi-classical linear chain model that
allows to extrapolate results to a large number of layers. Further,
first-principles calculations show how Raman spectroscopy can be used to
characterize the quality of the two-dimensional interface between MoS$_2$ and a
silver substrate.
