Quantum-chemical perspective of nanoscale Raman spectroscopy with three-dimensional phonon confinement model

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.