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.

In earlier theoretical studies, it has been widely noticed that the electron correlation effect played an important role in determining the excitation energies of low-lying π→π* excited states for neutral polyenes and their radical cations and dications. In this paper, neutral and doped polyene oligomers of medium to large sizes are investigated with the Pariser-Parr-Pople model, and the π-electron correlation effect is fully taken into consideration by virtue of the density-matrix renormalization group method. The excitation properties in the polymer limit are also obtained by exponential extrapolation from the finite oligomers. The reasonable agreement of our results with the available experimental observations and advanced ab initio calculations is witnessed. It is also observed that while charge doping can significantly lower the exciting energy, the odd-charged oligomers show lower excitation energies than the even-charged ones.

We have carried out density matrix renormalization group calculations on the T1 state of linear polyenes applying the Pariser-Parr-Pople (PPP) Model. The geometry optimization for the polyene oligomers C2nH2n12 (n54,5,6,...,15) shows that the S0 to T1 excitation region is composed of a soliton-antisoliton pair located symmetrically away from the center of the chain and leads to singleand double-bond interconversions in between. The distance between the soliton and antisoliton centers in T1 state changes with the length of the chain, contradictory to earlier conclusions obtained with PPP-SDCI or ab initio SCI methods. The inconsistency most possibly comes from the insufficient consideration of the electron correlations in small-scale CI methods.

We describe an alternative multireference coupled cluster (MRCC) method, pair-correlated coupled cluster (PCCC) theory, for treating the ground state of closed-shell systems with degeneracy or quasidegeneracy. With the separated electron pair (SEP) wave function as a reference, the PCCC wave function is truncated according to how many electron pairs are explicitly correlated. The inclusion of only two-pair correlation defines the PCCC2 scheme, and the inclusion of up to three-pair correlation gives the PCCC3 scheme. The PCCC theory is well defined within the natural orbital (of the SEP reference) description and size extensive. We present the formalism of the PCCC theory by taking the PCCC2 scheme as an example, and implement the PCCC2 and PCCC3 schemes at the ab initio level with various basis sets. Then illustrative applications are presented for systems such as the perpendicular insertion reaction path of Be into H2, the simultaneous bond stretching in AlH3 and H2O. The results show that the overall performance of PCCC methods is competitive to that of the RCCSD (T) or UCCSD (T) method at stretched geometries, but slightly inferior to that of the CCSD (T) method at the equilibrium geometry.

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.