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.

Quantumchemistry and molecular mechanics calculations are performed to study formation mechanisms and packing structures of octadecanal and octadecene monolayers on Si(111). The radical chain mechanism is investigated by density functional theory with cluster models. Transition states of key steps involving abstracting a neighboring hydrogen atom from the surface are confirmed with the six-membered ring structures. Energy barriers for abstractions of the surface H to form new reactive surface Si radicals in the substitution of Si(111) via Si-O and Si-C linkages are 18.05 and 14.97 kcal/mol, respectively. Based on the radical chain mechanism, we investigate the linear and zigzag acking structures of alkoxyl chains on Si(111) with substitution percentages of 50%, 66.7%, and 75% using a series of two-dimensional repeating cells. By comparison of packing energies of octadecanoyl chains at different substitution percentages, 66.7% is predicted to be an optimal substitution ercentage, which agrees with experimental observations. At this surface substitution, packing structures of the monolayer such as tilt angles and film thickness are well correlated with experimental data. The difference in packing structures between monolayers on Si(111) via Si-Oand Si-C linkages is rationalized by their different van der Waals radii of surface linkage groups and tilt angles of chains.

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 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 ground-state energies of polyacenes and polyphenanthrenes are obtained with the density-matrix renormalization group method from finite up to infinite lengths under the classical valence bond theory. In comparison with the exact valence bond results, numerical errors of retaining various numbers of states are all less than 10-5 J. Meanwhile, the linear equations in terms of the chain length are deduced for the groundstate energies of these two homologous series. And the energy gaps between the lowest singlet and triplet states (S-T gap) are also evaluated. On the other hand, the relative local hexagon energy converges as the chain length increases, and leading to an effective conjugated length of n=12 for polyacene and polyphenanthrene.