The Journal of Chemical Physics

Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings

Gerrit Moritz, Bernd Artur Heß, Markus Reiher

Published Dec 20, 2004• 145 citations

Abstract

The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.

DOI: 10.1063/1.1824891

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