  In the last years, Infrared Reflection-Absorption Spectroscopy (IRRAS) became
a standard technique to study vibrational excitations of molecules. These
investigations are strongly motivated by perspective applications in monitoring
chemical processes. For a better understanding of the adsorption mechanism of
molecules on dielectrics, the polarization-dependence of an interaction of
infrared light with adsorbates at dielectric surfaces is commonly used. Thus,
the peak positions in absorption spectra could be different for s- and
p-polarized light. This shift between the peak positions depends on both the
molecule itself and the dielectric substrate. While the origin of this shift is
well understood for infinite two-dimensional adsorbate layers, finite-size
samples, which consist of 2D islands of a small number of molecules, have never
been considered. Here, we present a study on polarization-dependent finite-size
effects in the optical response of such islands on dielectric substrates. The
study uses a multi-scale modeling approach that connects quantum chemistry
calculations to Maxwell scattering simulations. We distinguish the optical
response of a single molecule, a finite number of molecules, and a
two-dimensional adsorbate layer. We analyze CO and CO$_2$ molecules deposited
on CeO$_2$ and Al$_2$O$_3$ substrates. The evolution of the shift between the
polarization-dependent absorbance peaks is firstly studied for a single
molecule, which it does not exhibit for at all, and for finite molecular
islands, which it increases with increasing island size for, as well as for an
infinite two-dimensional adsorbate layer. In the latter case, the agreement
between the obtained results and the experimental IRRAS data and more
traditional three/four-layer-model theoretical studies supports the predictive
power of the multi-scale approach.
