The Valence Bond Calculations on Conjugated Hydrocarbons of Medium to Infinite Sizes

Abstract

AbstractIn the past decade, we devoted time to the valence bond (VB) study of huge conjugated hydrocarbons by employing the Heisenberg model. Due to the dimension of the covalent space exponentially increasing with the size of molecule, the exact solution of the VB model for large molecules encounters a fundamental difficulty. Before 1990, Alexander and Schmalz published ground‐state energy results on a set of benzenoids of up to 24 π‐electrons using the graphical unitary group approach. Around 1995, we employed Lanczos technique to diagonalize the VB Hamiltonian and presented the low‐lying state energies and wave functions of benzenoids with up to 22 π‐centers. In terms of wave functions, the physical and chemical behaviors of these conjugated species have been discussed in detail. In succession, we generalized the VB calculation to larger systems by proposing an algorithm in coding all Slater determinants of the covalent space with conserved spin quantum number. The exact solutions of the VB model have been obtained for conjugated species with up to 30 π‐electrons. Recently, we broke through this limitation by extending the density‐matrix renormalization group (DMRG) method of White to the quasi‐one‐dimensional system. The VB energies of the ground states for two series of polycyclic aromatic hydrocarbons, polyacene and polyphenanthrene, of arbitrary lengths defined by the number of constituent hexagons have been obtained. The effective conjugated length for these infinite long‐chain polymers could be estimated.