Chapter 3 - Density matrix renormalization group for semiempirical quantum chemistry

Abstract

Inspired by the great success of density matrix renormalization group (DMRG) for solving physical models in one-dimensional strongly correlated systems, DMRG was soon applied to the accurate solution of semiempirical quantum chemical Hamiltonians (such as the Pariser–Parr–Pople model) for clarifying the puzzling electronic structure issues in one-dimensional conjugated polymers. This is also considered as the beginning of DMRG quantum chemistry. In this chapter, we first give a brief introduction to the model Hamiltonians that have been largely employed in the study of conjugated molecules. Then, the symmetrized DMRG algorithm, including the electron-hole symmetry, spin-flip symmetry, and C2h point group symmetry, is described. Finally, we review several DMRG applications for the study of the electronic structures of conjugated oligomers and polymers, including the electronic structure of ground state and excited states, the exciton binding energy, the linear and nonlinear optical properties, and the effect of electron–lattice interaction on the electronic structure.