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.

By employing the Lanczos method, the effective valence bond model (EVB) is exactly solved for a series of conjugated hydrocarbons with four-membered rings. Several indices calculated from the EVB ground-state energies and wave functions are applied to interrelate with bond lengths, stabilities, and reactivities of these systems. Our results agree well with related experimental observations and deductions of molecular orbital theory. The failure of the classical valence bond theory in these systems is also exposed.

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.

A novel algorithm is introduced for coding all Slater determinants in the covalent space with conserved SZ, the z component of total spin S for a classical valence bond (VB) model. It effectively minimizes the search time and the storing space in the central memory of the computer. In cooperation with symmetry reductions based on molecular point group and spin inversion, the VB calculations have been extended to benzenoid hydrocarbons of up to 28 π-electrons that have 4×10 7 configurations. The low-lying states of benzenoids with 24, 26, and 28 π-electrons have been obtained for 62 species. To rationalize the aromaticity of benzenoids in a VB scheme, the resonance energy per hexagon (REPH) is defined. A linear correlation between the REPH and the energy gap of the ground (singlet) state and the first excited (triplet) state for 89 benzenoids is established.

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.