Breathing mode of nanoclusters: Definition and comparison to a continuous medium model

Breathing modes are closely related to many physical properties of nanoclusters. Decades of research, however, failed to formulate a general and unambiguous definition. Here we present a straightforward and widely applicable definition of breathing modes based on power spectra of geometric quantities, namely, surface area, volume, etc. Applying group theory, normal-mode analysis, and molecular dynamics simulations, we have explored breathing modes of several Aln clusters with high and low symmetries. The results suggest that our definition is able to cover not only common breathing modes but also some hidden modes. Our consistent definition also allows us to make a comprehensive and in-depth comparison with Lamb's continuous medium model, which reveals some high-frequency breathing modes are explicable only at the atomic level.