Absorption spectra for small sulfur clusters Sn (n = 2-8) are calculated using an adiabatic time-dependent density-functional formalismwithin the local density approximation (LDA). We compare the calculated spectra with those calculated using the simple LDA approach. The calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations. In addition, we also obtain a significant threshold absorption, which can distinguish different ground states of the sulfur clusters.

We report a detailed first-principles calculation to investigate the structures, elastic constants, and phase transition of Ti. The axial ratios of both a-Ti and w-Ti are nearly constant under hydrostatic compression, which confirms the latest experimental results. From the high pressure elastic constants, we find that the a-Ti is unstable when the applied pressures are larger than 24.2 GPa, but the w-Ti is mechanically stable at all range of calculated pressure. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening around point of w-Ti. When the pressure is raised to 35.9 GPa, the frequencies around the point along-M-K and -A in transverse acoustical branches become imaginary, indicating a structural instability. Within quasiharmonic approximation, we obtained the full phase diagram and accurate thermal equations of state of Ti. The phase transition w-Ti→a-Ti→b-Ti at zero pressure occurs at 146K and 1143K, respectively. The predicted triple point is at 9.78 GPa, 931 K, which is close to the experimental data. Our thermal equations of state confirm the available experimental results and are extended to a wider pressure and temperature range.

We have investigated the structures and the elastic constants of hcp MgB2 at high pressures using the full-potential linearized muffin-tin orbital (FP-LMTO) scheme within the generalized gradient approximation correction (GGA) in the frame of density functional theory (DFT). The obtained normalized volume dependence of the resulting pressure is in excellent agreement with experiment. The elastic constants and acoustic anisotropy as a function of the applied pressure are presented. An analysis for the calculated parameters has been made to reveal the anisotropy of MgB2.