The electronic and structural properties of the (√3 x √3) R30° Ag/Si(111) and (√3 x √3) R30° Au/Si(111) surfaces are investigated using first principles total energy calculations. We have tested almost all experimentally proposed structural models for both surfaces and found the energetically most favorable model for each of them. The lowest energy model structure of the (√3 x √3) R30° Ag/Si(111) surface consists of a top layer of Ag atoms arranged as "honeycomb-chained-trimers" lying above a distorted "missing top layer" Si(111) substrate. The coverage of Ag is 1 monolayer (ML). We find that the honeycomb structure observed in STM images arise from the electronic charge densities of an empty surface band near the Fermi level. The electronic density of states of this model gives a "pseudo-gap" around the Fermi level, which is consistent with experimental results. The lowest energy model for the (√3 x √3) R30° Au/Si(111) surface is a conjugate honeycomb-chained-trimer (CHCT-1) configuration which consists of a top layer of trimers formed by 1 ML Au atoms lying above a "missing top layer" Si(111) substrate with a honeycomb-chained-trimer structure for its first layer. The structures of Au and Ag are in fact quite similar and belong to the same class of structural models. However, small variation in the structural details gives rise to quite different observed STM images, as revealed in the theoretical calculations. The electronic charge density from bands around the Fermi level for the (√3 x √3) R30° Au/Si(111) surface also gives a good description of the images observed in STM experiments;First principles calculations are performed to study the electronic and structural properties of a series of Ti-base binary alloys TiFe, TiNi, TiPd, TiMo, and TiAu in the B2 structure. Calculations are also done for Ti in bcc structure and hypothetical B2-structured TiAl, TiAg, and TiCu. Our results show correlation between the Martensitic transformation temperature (M[subscript]s) of these alloys and the electronic properties such as the total electronic density of states at the Fermi level, occupation of the Ti d states, and the degree of localization of the d states of the second element in the alloys. Angular momentum decomposition of the electronic states indicates that the bonding of d electrons of the two elements plays an important role in the stability of the binary alloys. Correlations between M[subscript]s and optimized structural parameters such as lattice constants and bulk moduli are also found.