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

Gerrit Moritz1, Bernd Artur Hess, Markus Reiher

  • 1Lehrstuhl für Theoretische Chemie, Universität Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany.

The Journal of Chemical Physics
|January 11, 2005
PubMed
Summary

Optimizing orbital ordering is crucial for the density-matrix renormalization group (DMRG) method in quantum chemistry. This study presents genetic algorithms and integral-based methods to improve DMRG convergence for complex systems like chromium dimer.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Materials Science

Background:

  • The density-matrix renormalization group (DMRG) is a powerful ab initio method for quantum chemistry.
  • Routine application of DMRG is hindered by challenges, including orbital ordering.
  • Orbital ordering significantly impacts the convergence of DMRG calculations.

Purpose of the Study:

  • To develop and evaluate methods for optimizing orbital ordering in DMRG.
  • To improve the efficiency and reliability of DMRG for complex electronic structures.

Main Methods:

  • Genetic algorithm optimization of orbital orderings.
  • Derivation of orderings from one- and two-electron integrals.
  • Application to the chromium dimer, a system with complex electronic structure.

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Main Results:

  • Demonstrated that optimized orbital orderings enhance DMRG convergence.
  • Compared the performance of genetic algorithm and integral-based ordering methods.
  • Analyzed the convergence behavior for various orderings on the chromium dimer.

Conclusions:

  • Optimized orbital ordering is essential for efficient DMRG calculations.
  • Both genetic algorithms and integral-based approaches offer viable strategies for optimization.
  • Further development is needed for routine DMRG application in quantum chemistry.