Structural, Electronic, and Superconducting Properties of Solids.

A first-principles pseudopotential method is used to calculate structural, electronic, and lattice vibrational properties for various types of solids. Applications of the pseudopotential method are extended to more complicated systems with superconducting states. Much of emphasis is placed on successful applications for calculating electron -phonon coupling parameters and predicting new superconducting states. A study of the relationship between soft phonon modes, structural phase transitions, and superconductivity is presented. The results are compared with available experimental data and the good agreements with experiments are found. Investigations of the phase stability for Si and Ge are given. New high pressure phases similar to those found in Si are predicted for Ge. For both crystals, the soft phonon modes are closely related to the phase transitions. High pressure phases for SiC, BeO, and MgO are also studied. Rhombohedral phase stability relative to simple cubic is investigated for the group-VA elements. This stability decreases with either increasing pressure or decreasing covalency. The electronic structures of CdS, BeO, and MgO are examined. Incorporating the Cd d state into the valence band improves substantially the main valence band width for CdS. The band structures for the hexagonal and cubic structures are compared. By studying the pressure variations of band gaps in semiconductors and insulators, it is demonstrated that although the local density approximation underestimates the band gaps, the pressure coefficients of band gaps are correctly estimated and are insensitive to the use of different functional forms for the exchange-correlation potential. The lattice dynamical properties such as the phonon frequency and the pressure dependence of the frequency are examined for AlAs. From the averaged electro-static potential, the longitudinal effective charges are estimated and satisfy the acoustic sum rule. Applying the pseudopotential method for calculating electron-phonon coupling parameters, superconducting solutions are found for the high pressure metallic phases of Si. The soft phonon modes near the structural phase transitions for Si and black phosphorus are found to significantly enhance the superconducting transition temperature. For metallic Si, Ge, and Sn, the following correlation is found: with increasing electron concentration, the phonon frequencies, force constants, phonon linewidths, and electron-phonon interactions increase. This calculation suggests that the Debye temperature dominates in determining the superconducting critical temperature.