The density matrix renormalization group method: Application to the low-lying electronic states in conjugated polymers

Abstract

Conjugated organic systems have occupied the center stage of activity in chemistry. This is because of their unique properties such as high reactivity, unusually large anisotropic diamagnetic susceptibility, and long wavelength electronic absorption. It has been observed that many conjugated systems can be doped to high electrical conductivities and/or can intrinsically possess large luminescence, electroluminescence, and nonlinear optical responses, as well as, in some cases, the ability to lase when optically or electrically pumped. These properties point to the distinct possibility of their role in molecular electronics as well as optoelectronics or photonics devices. The chapter describes an innovative way for solving the model Hamiltonians, which goes beyond the conventional techniques and is based on the density matrix renormalization group (DMRG) theory. The method, which overcomes the difficulty of exploding dimensionalities, is the renormalization-group technique in which one systematically throws out the degrees of freedom of a many-body system. The Density Matrix Renormalization Group (DMRG) method has proved to be an accurate technique for obtaining a few low-lying states of interacting model Hamiltonians with short-range interactions in low-dimensions. This technique would find wide applications in the electronic structure studies of conjugated polymers and donor–acceptor systems, if excited eigenstates in different symmetry subspaces can be obtained.