  Raman spectroscopy of crystalline/molecular systems is well backed with
quantum chemical calculations and group theory, making it a unique
characterization tool. For the "intermediate" case of nanoscale systems,
however, the use of Raman spectroscopy is limited by the lack of such
theoretical bases. Here, we suggest to couple a scaled quantum-mechanical (SQM)
calculation with the phonon confinement model (PCM) to construct a universal
and physically consistent basis for nanoscale Raman spectroscopy. Unlike the
commonly used one-dimensional dispersion PCM, we take into account the
confinement along all the three dimensions of the k-space. We apply it to
diamond nanoparticles of sub-50nm size, a system with pronounced anisotropy of
dispersion for which the use of three-dimensional dispersion is a requisite.
The model excellently reproduces size-sensitive spectral features, including
the peak position, bandwidth and asymmetry of the sp3 C-C Raman band. This
fundamental approach can be easily generalized to other nanocrystalline solids
to hopefully contribute the future development of quantitative nanoscale Raman
spectroscopy.
