We apply a finite-difference pseudopotential density functional theory in real space and the Langevin molecular dynamics annealing technique as well as the adiabatic time-dependent density functional theory within the local density approximation (TDLDA) to the descriptions of structures and optical absorption spectra of carbon clusters C8. It is shown that the odd-numbered clusters have the linear structures and most of the even-numbered clusters prefer cyclic structures. The calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.

We calculated the phase transition, elastic constants, full phonon dispersion curves, and thermal properties of molybdenum (Mo) for a wide range of pressures using density functional theory. Mo is stable in the bodycentered-cubic (bcc) structure up to 703 (19 GPa and then transforms to the face-centered close-packed (fcc) structure at zero temperature. Under high temperature and pressure, the fcc phase of Mo is more stable than the bcc phase. The calculated phonon dispersion curves accord excellently with experiments. Under pressure, we captured a large softening along H-P in the TA branches. When the volume is compressed to 7.69 A3, the frequencies along H-P in the TA branches soften to imaginary frequencies, indicating a structural instability. When the pressure increases, the phonon calculations on the fcc Mo predict the stability by promoting the frequencies along Γ to X and Γ to L symmetry lines from imaginary to real. The thermal equation of state was also investigated. From the thermal expansion coefficient and the heat capacity, we found that the quasiharmonic approximation was valid only up to about melting point at zero pressure. However, under pressure, the validity can be extended to a much higher temperature.

The intermolecular interaction potentials of methane (CH4) dimer are calculated within the density functional theory in the local density approximation (LDA). It is found that the calculated potentials have minima when the intermolecular distance of (CH4) dimer is about 7.0 a.u., which is in good agreement with the experiment. The depth of the potential is 0.017 eV. The results obtained by our LDA calculations seem to agree well with those obtained by MP2, MP3, and CCSD from the M