Chapter 5 - Density matrix renormalization group with orbital optimization

Abstract

Ab initio density matrix renormalization group (DMRG) provides a useful tool for describing electronic structure properties of strongly correlated molecules that require large complete active spaces composed of up to ~100 active orbitals, which are not accessible by conventional quantum chemistry methods. However, the multiconfigurational wave functions also depend greatly on the choice of selected active molecular orbitals (MOs) in an active space with a given size, and accordingly multiconfigurational self-consistent field (SCF) (MCSCF) calculation usually has to be performed, in which both configuration interaction coefficients and MOs are variationally optimized. In this chapter, we will introduce the first-order and second-order algorithms of MCSCF and its implementation in DMRG-SCF for orbital optimization. Consequently, we provide exemplary application of DMRG and DMRG-SCF algorithms for geometry optimization, calculations of excited states, molecular spectra, and non-Born–Oppenheimer (nonadiabatic) effects.