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.

The vibrational properties of atomic clusters are a fingerprint of their structures and can be used to investigate their thermodynamic behavior at low temperatures. In this work, we report a theoretical study, using density functional theory, on the vibrational spectrum and density of states (VDOS) of the cationic sodium cluster Na 139 + . Our study focuses on the most stable isomer, which corresponds to a truncated icosahedron. This isomer displays an electronic density of states that is in good agreement with photoelectron spectroscopy data previously published. After validation of the sodium cluster structure, its vibrational frequency spectrum was obtained in the harmonic approximation through a diagonalization of the dynamical matrix. The calculated vibrational frequencies were used to evaluate the cluster caloric curve and heat capacity at low temperatures. An excellent agreement was obtained between the calculated caloric curve and experimental data recently reported down to 6 K. A fit to the bulk Debye model of the calculated and measured cluster thermal energy yields a large variation at low temperatures of the equivalent Debye temperature as compared with a weaker temperature dependence found in bulk materials. Moreover, a further analysis shows that the calculated heat capacity of the 139-atom cationic sodium cluster does not follow the bulk Debye T 3 law at very low temperatures, due to the discreteness of the cluster frequency spectrum, and to the finite value of its acoustic gap (lowest frequency value). These results, indicating a finite size effect on the cluster vibrational spectrum, reflect the difference in the VDOS between clusters and bulk, and confirm the limitation of the bulk Debye model (and Debye temperature) to describe the low-temperature thermal behavior of metal clusters in the size range of around 139 atoms. The calculated vibrational frequency spectrum also provides the temperature dependence of the total vibrational excitation for the 139-atom sodium clusters, indicating that at 6 K, ∼ 92% of them are in their vibrational ground state.

The electronic band structure and electronic density of states of cubic SiC nanowires (SiCNWs) in the directions [001], [111], and [112] were studied by means of Density Functional Theory (DFT) based on the generalized gradient approximation and the supercell technique. The surface dangling bonds were passivated using hydrogen (H) atoms and OH radicals in order to study the effects of this passivation on the electronic states of the SiCNWs. The calculations show a clear dependence of the electronic properties of the SiCNWs on the quantum confinement, orientation, and chemical passivation of the surface. In general, surface passivation with either H or OH radicals removes the dangling bond states from the band gap, and OH saturation appears to produce a smaller band gap than H passivation. An analysis of the atom-resolved density of states showed that there is substantial charge transfer between the Si and O atoms in the OH-terminated case, which reduces the band gap compared to the H-terminated case, in which charge transfer mainly occurs between the Si and C atoms.

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