Ab initio Density Matrix Renormalization Group Theory for Multireference Quantum Chemistry

Abstract

A major challenge in molecular electronic structure theory arises from chemical systems where the mean-field picture based upon a single electronic connguration fails to properly describe mechanics of many electrons. Such complex electronic states should be accounted for using a correlated superposition of multiple determinants and are referred to as multireference in quantum chemistry. Application domain of traditional multireference methods is severely limited to systems containing a small number of correlated electrons because of their exponential complexity. In recent years, much attention has been drawn to the density matrix renormalization group (DMRG) theory as a promising alternative. It has been introduced in ab initio quantum chemistry calculations and shown to be a highly-scalable multireference method that can handle full quantum degrees of freedom for the strongly-correlated wavefunction with unprecedented large connguration space. In this article, we provide an explicative introduction to the underlying theory and formalism built into the DMRG method and give a brief overview of our methodological extensions that combine DMRG and active-space correlation models. 1. | = | + | | g u Figure 1 H 2 g u g g u t U H = t + U t > U HOMO-LUMO | t < U HOMO-LUMO HOMO LUMO | Figure 1. With the stretched H-H bond, orbital energy levels become quasi-degenerate. With decreasing strength of ligand field, the role of electron correlation is increasingly more important (t