The ferroelectricity of BaTiO3 is investigated with the plane-wave pseudopotential method and the LCAO quantum chemical approach in the framework of density functional theory (DFT). Potential energy surfaces of various atomic displacements and the influence of lattice strain and lattice volume on the surfaces are examined. On the basis of the potential surfaces, phonon frequencies are also computed, which are in agreement with experiment results. The obtained potential energy surfaces show that the ferroelectric phase transition (from the cubic to the tetragonal phase) is decisively controlled by Ti displacement. The larger the lattice volume and the ratio c/a, the deeper the potential well. The calculated electronic populations and static charges show that from cubic to tetragonal phases Ti and O1 lose charges whereas Ba and O2 gain charges. The bond orders reveal that Ba-O has some extent of covalency, and during the phase transition the chemical bonding between metal and oxygen atoms, especially the Ti-O1 bond, is enhanced. Our results seem consistent with the vibronic theory about the origin of ferroelectricity of BaTiO3.

The effects of charge-doping and boron and phosphorus substitution on the electronic structures and band gaps of polysilane, poly(vinylenedisilanylene), and poly(butadienylenedisilanylene) were theoretically investigated by using density functional theory and time-dependent density functional theory. Band gaps of polymers were estimated both by extrapolations from excitation energies of oligomers up to 30 units and by calculations with the periodic boundary condition. It was found that charge-doping in the polysilane decreases the band gap more significantly than B and P substitutions. However, Si-Si bonds are easily broken by charge-doping. In contrast, B and P substitutions exert little influence on the strength of Si-Si bonds. From natural bond orbital analysis, it was concluded that charge-doping and heteroatom substitution bring about a lowering of the band gap in

The low-lying excited states of benzenoid hydrocarbons with up to 22

The Lanczos method is employed to solve the valence bond model exactly for n-electronic systems of benzenoid hydrocarbons. The exact valence bond ground-state wave functions have been obtained for benzenoid hydrocarbons of up to 20 n centers. By defining a set of local indices which can be easily calculated from these wave functions, bond lengths, reactivity, and local aromaticity of these benzenoid hydrocarbons have been discussed in a systematic way. The results are in excellent agreement with the known experimental facts and related predictions from molecular orbital theory.

The chain length dependence of excitation energies of oilgomers of polyene, p-phenylene, pentafulvene, cyclopentadiene, pyrrole, furan, silole, phosphole, and thiophene was studied employing the time-dependent density functional theory with B3LYP functional. Band gaps and effective conjugation lengths of the corresponding polymers were obtained by extrapolating vertical excitation energies of trimers through pentamers to infinite chain length. Polypentafulvene, polycyclopentadiene, polysilole, and polyphosphole were predicted to have smaller band gaps than polythiophene, and polypentafulvene has the smallest band gap. Among the studied cyclopentadiene-based polymers, those with the third row heteroatoms were found to have narrower band gaps than their second row counterparts.