Wavefunctions for Large Electronic Systems

Chapter

Abstract

Wavefunctions for large electron numbers suffer from an exponential growth of the Hilbert space which is required for their description. In fact, as pointed out by W. Kohn, for electron numbers \(N > N_0\) where \(N_0 \approx 10^3\) they become meaningless (exponential wall problem). Nevertheless, despite of the enormous successes of density functional theory, one would also like to develop electronic structure calculations for solids based on wavefunctions. This is possible if one defines the latter in Liouville space with a cumulant metric instead in Hilbert space. The cluster expansion of the free energy of a classical monatomic gas makes it transparent why cumulants are very well suited also for electronic structure calculations.

Notes

Acknowledgements

I would like to thank Hermann Stoll for many fruitful discussions and collaborations on subjects related to this article.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Max-Planck-Institut für Physik Komplexer SystemeDresdenGermany

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