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New approaches in electronic structure theory: The density matrix renormalization group

Markus Reiher - ETH Zürich


Chemical processes are governed by the interaction of electrons in the external field of atomic nuclei changing their configuration. At the core of all theoretical attempts to describe chemical reactions is therefore electronic structure theory, a research field that has emerged since the early 1950s when Roothaan and Hall proposed to solve one-electron Schrodinger-type partial  differential equations by basis-set expansion techniques. Since that time, many important developments have produced a standard tool box of methods, which was recognized by the Nobel Prize in Chemistry in 1998.
Quite recently, an approach very different from any traditional one, namely the density matrix renormalization group (DMRG) algorithm, has emerged as a competitive method for the theoretical description of the correlated motion of electrons that allows us to access large active orbital spaces beyond the capabilities of traditional approaches. An advantage of DMRG is the iterative nature of the algorithm. While this could be viewed as a drawback (many iterations are needed and convergence can feature plateaus with little change in energy), the qualitative nature of the DMRG wave function is well reproduced already after comparatively few iterations. 
This knowledge can be exploited for solving the active-space selection problem in MCSCF approaches. Recently, we have shown that concepts from quantum information theory can be used to classify active orbital spaces so that they can be constructed from partially converged DMRG calculations.