Size and Shape Dependence of the Vibrational Spectrum and Low-Temperature Specific Heat of Au Nanoparticles

The vibrational spectra of metal nanoparticles are a signature of their structures and determine the low-temperature behavior of their thermal properties. In this work, we report a theoretical study on the size evolution of the vibrational spectrum and density of states (VDOS) of Au nanoparticles in the range of 1–4 nm. Our study focuses on truncated octahedral (FCC), decahedral, and icosahedral nanoparticles. The structural optimization was performed through atomistic simulations using molecular dynamics and the many-body Gupta potential, whereas the vibrational frequency spectrum was obtained within the harmonic approximation through a diagonalization of the dynamical matrix. The calculated frequency spectra are discrete, have a finite acoustic gap (lowest frequency value), and extend up to a maximum frequency in the range of ∼140–185 cm^–1, depending on the nanoparticle morphology. The VDOS evolves from a multiple-peak line shape for small sizes to a characteristic profile for the larger nanoparticles that anticipates the well-known VDOS of the bulk Au metal. The frequency spectrum was used to quantify the specific heat at low temperatures for the Au nanoparticles, displaying small variations with size and shape. Further analysis of these results indicates that the acoustic gap is responsible of a slight reduction in the specific heat with respect to bulk in the temperature range, 0 < T < T_r, (T_r ≈ 5 K for Au nanoparticles with size ∼1.4 nm). Also, the well-known increment in the specific heat of metal nanoparticles with respect to the bulk value, caused by the enhancement of the VDOS at low frequencies, is recovered for T_r < T < T_s (T_s ≈ 35–45 K). Moreover, it is also found that for T > T_s the calculated specific heat of all Au nanoparticles under study is again smaller than the bulk value. This oscillating behavior in the specific heat of Au nanoparticles is related to the differences in their VDOS line shape with respect to the one of the bulk phase. The usefulness of the equivalent (temperature-dependent) Debye temperature of Au nanoparticles to describe the temperature behavior of their specific heat is also discussed.