Ab initio calculation of temperature effects in the optical response of open-shell sodium clusters

Many properties of atomic clusters have been found to be size dependent, e.g., the optical response. There are, however, factors other than size that can also play an important role in determining the properties of nanoscale systems. Temperature, in particular, has been shown to have a strong effect on the optical response of open-shell sodium clusters. We incorporate the temperature effect on the optical absorption spectra by combining pseudopotentials, Langevin molecular dynamics, and time-dependent density functional theory. We have done calculations for several open-shell sodium clusters, Na(4) (+), Na(7) (+), and Na(11) (+), for which experimental data are available for comparison. We find that the positions of the lower energy peaks of the calculated spectra correspond very well to the peaks in the experimental spectra, although the local density approximation tends to overestimate the gap of the smaller clusters by up to 0.2 eV and underestimate the gap of the largest cluster by 0.4 eV. We fit the width of the peaks in the lower-temperature calculations to the corresponding experimental result to obtain the instrumental linewidth. We then use this same width for the high-temperature calculations and find very good agreement with experiment. Finally, we analyze the transitions that contribute to the observed peaks in the absorption spectra and we plot the effective valence charge density for specific transitions for each cluster. We find that for the two smaller clusters the absorption spectra are dominated by transitions from the occupied levels to a few (three for Na(4) (+) and five for Na(7) (+)) empty levels, although the contribution from transitions to other empty levels can still be significant. In contrast, the absorption spectra for Na(11) (+) come from a greater mixture of transitions as evidenced in the analysis as well as in the plot of the effective valence charge density.