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Density Matrices and Density Functionals pp 21–49Cite as

Some Aspects on the Development of the Theory of Reduced Density Matrices and the Representability Problem

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Abstract

A brief historical review is given of the development of the theory of reduced density matrices in the 1950’s, the natural orbitals and natural geminals, the mirror theorem, and the constraints on the variation principle leading to the wave function and ensemble representability problems. The impact of John Coleman’s work on this field from the early 1960’s is briefly reviewed, and the properties of the second-order reduced density matrices with anomalously large eigenvalues are discussed. The absence of a representability problem in the electron-density-functional method based on Hohenberg-Kohn’s theorem is questioned and, as an example, the representability problems in the Hartree-Fock approximation is studied in some detail.

It is a very special privilege for me to be asked to give a lecture at this symposium in honor of Professor A. John Coleman, and I have been requested to give a brief historical review of the early development of the theory of the reduced density matrices as seen from my own limited personal point of view with some additional comments leading up to the present level of research. This is not an easy task, and I apologize from the very beginning for many omissions of important work.

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Author information

Authors and Affiliations

  1. Quantum Theory Project Departments of Chemistry and Physics, University of Florida, Gainesville, Florida, 32611, USA

    P. O. Löwdin (Professor Emeritus of Quantum Chemistry, NFCR Senior Investigator)

  2. Uppsala University, Uppsala, Sweden

    P. O. Löwdin (Professor Emeritus of Quantum Chemistry, NFCR Senior Investigator)

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  1. P. O. Löwdin
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Editor information

Editors and Affiliations

  1. Queen’s University, Kingston, Canada

    Robert Erdahl  & Vadene H. Smith Jr.  & 

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© 1987 D. Reidel Publishing Company

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Löwdin, P.O. (1987). Some Aspects on the Development of the Theory of Reduced Density Matrices and the Representability Problem. In: Erdahl, R., Smith, V.H. (eds) Density Matrices and Density Functionals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3855-7_3

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  • DOI: https://doi.org/10.1007/978-94-009-3855-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8214-3

  • Online ISBN: 978-94-009-3855-7

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