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Journal of Chemical Physics / Volume 135 / Issue 24 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 135, 244111 (2011); http://dx.doi.org/10.1063/1.3671388 (14 pages)

An algebraic operator approach to electronic structure

Neil Shenvi and Weitao Yang

Department of Chemistry, Duke University, Durham, North Carolina 27708, USA

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(Received 15 August 2011; accepted 1 December 2011; published online 30 December 2011)

In this paper, we introduce an algebraic approach to electronic structure calculations. Our approach constructs a Jordan algebra based on the second-quantized electronic Hamiltonian. From the structure factor of this algebra, we show that we can calculate the energy of the ground electronic state of the Hamiltonian operator. We apply our method to several generalized Hubbard models and show that we can usually obtain a significant fraction of the correlation energy for low-to-moderate values of the electronic repulsion parameter while still retaining the O(L3) scaling of the Hartree-Fock algorithm. This surprising result, along with several other observations, suggests that our algebraic approach represents a new paradigm for electronic structure calculations which opens up many new directions for research.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
    1. Jordan algebras and the calculation of eigenvalues
    2. Krylov subspaces and building the algebra
    3. Many-body operators and Valdemoro's approximation
    4. Particle number and effective chemical potentials
    5. Outline of the algorithm
  3. APPLICATIONS
  4. DISCUSSION
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

algebra, ground states, HF calculations, Hubbard model, mathematical operators

PACS

  • 31.15.xr

    Self-consistent-field methods

  • 02.10.-v

    Logic, set theory, and algebra

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3671388

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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    E. Neuscamman, T. Yanai, and G. K.-L. Chan, J. Chem. Phys 130, 124102 (2009)JCPSA6000130000012124102000001.

    C. Halboth and W. Metzner, Phys. Rev. Lett. 85, 5162 (2000).


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