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.

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.

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.

AM1 calculations are performed to study the non-linear optical (NLO) properties of push-pull quinones. The variations of molecular structure, linear (a) and NLO polarizabilities (b, c) for a set of push-pull quinones are discussed in terms of quinoid-benzenoid character (QBC), and the strength of donor-acceptor pairs The parameter already used for the polyene (dDA). dDA, bridge, is still valid in rationalizing the donor»acceptor strength for quinoid derivatives. In addition, we examined how an external electric-eld created by ìSparklesœ in the MOPAC package drives a quinoid molecule from the quinoid limit to the benzenoid limit, and how it aÜects the NLO properties. The results show that the eÜect produced by Sparkles is qualitatively similar to that of donor»acceptor pairs.

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.