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The Role of the N-Representability in One-Particle Functional Theories

  • M. Piris
Chapter

Abstract

The purpose of this chapter is to analyze the role of the N-representability in one-particle functional theories, that is, in theories where the ground-state energy is represented in terms of the first-order reduced density matrix (1RDM) \(\Gamma \) or simply its diagonal part: the density \(\rho \). I have chosen to write on this topic to honor Norman H. March since he has always been interested on the subject. Throughout these years during his visits to the Donostia International Physics Center, Professor March has encouraged me to emphasize the importance of the functional N-representability, an issue that has not received enough attention in the literature. This has led us to recently write several articles together (Piris and March, Phys Chem Liq 52(6):804, 2014, [1]; Piris and March, Phys Chem Liq 53(6):696, 2015, [2]; Piris and March, J Phys Chem A 119(40):10190, 2015, [3]; Piris and March, Phys Chem Liq 54(6):797, 2016, [4]; Piris and March, Int J Quantum Chem 116(11):805, 2016, [5]) using what is so far the only known natural orbital functional, namely PNOF5 (Piris et al, J Chem Phys 134(16):164102, 2011, [6]; Piris et al, J Chem Phys 139(23): 234109, 2013, [7]), which even including the electronic correlation, maintains a one-to-one correspondence with the energy obtained from an N-particle wavefunction (Pernal, Comput Theor Chem 1003:127, 2013, [8]; Piris, J Chem Phys 139(6):064111, 2013, [9]).

Notes

Acknowledgements

Financial support comes from Eusko Jaurlaritza (Ref. IT588-13) and Ministerio de Economía y Competitividad (Ref. CTQ2015-67608-P). The SGI/IZO–SGIker UPV/EHU is gratefully acknowledged for generous allocation of computational resources.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Donostia International Physics Center (DIPC)Donostia, EuskadiSpain
  2. 2.Euskal Herriko Unibertsitatea (UPV/EHU)Donostia, EuskadiSpain
  3. 3.Basque Foundation for Science (IKERBASQUE)Bilbao, EuskadiSpain

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