  It has been puzzling that the Raman optical modes shift to lower frequency
(or termed as optical mode softening) associated with creation of Raman
acoustic modes that shift to higher energy (or called as acoustic hardening)
upon nanosolid formation and size reduction. Understandings of the mechanism
behind the size-induced acoustic hardening and optic softening have been quite
controversial. On the basis of the recent bond order-length-strength (BOLS)
correlation [Phys. Rev. B 69 045105 (2004)], we show that the optical softening
arises from atomic cohesive energy weakening of surface atoms and the acoustic
mode hardening is predominated by intergrain interaction. Agreement between
predictions and observations has been reached for Si, CdS, InP, TiO2, CeO2, and
SnO2 nanostructures with elucidation of vibration frequency of the
corresponding isolated dimers. Findings further evidence the impact of bond
order loss to low-dimensional systems and the essentiality of the BOLS
correlation in describing the behavior of nanostructures.
