Spin delocalization in hydrogen chains described with the spin-partitioned total position-spread tensor

  • Muammar El Khatib
  • Oriana Brea
  • Edoardo Fertitta
  • Gian Luigi Bendazzoli
  • Stefano EvangelistiEmail author
  • Thierry Leininger
  • Beate Paulus
Regular Article
Part of the following topical collections:
  1. 9th Congress on Electronic Structure: Principles and Applications (ESPA 2014)


The formalism of the spin-partitioned total position spread (SP-TPS) tensor is applied to model systems treated at ab initio level. They are hydrogen linear chains having different geometries and showing qualitatively different behaviors. Indeed, the SP-TPS behavior depends in a crucial way on the entanglement properties of the chain wave function. It is shown that the SP-TPS tensor gives a measure of the spin delocalization in the chain. This is very low in the case of isolated fixed-length dimers and maximal for chains of equally spaced atoms. The present formalism could be used to describe, for instance, the spin fluctuation associated with spintronic devices.


Hydrogen chains Total position spread Full CI  Spintronics Spin fluctuation 



We thank the University of Toulouse and the French CNRS for financial support. MEK and EF acknowledge the ANR-DFG action (ANR-11-INTB-1009 MITLOW PA1360/6-1) for their PhD grant. OB thanks to the Spanish “Ministerio de Educación Cultura y Deporte” for her PhD grant. We acknowledge the support of the Erasmus Mundus programme of the European Union (FPA 2010-0147). This work was supported by the Programme Investissements d’Avenir under the program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT. We thank Prof. R. Cimiraglia of the University of Ferrara for using his 4-index transformation code. Finally, we also thank the HPC resources of CALMIP under the allocation 2011-[p1048].

Supplementary material

214_2015_1625_MOESM1_ESM.pdf (178 kb)
Supplementary material 1 (pdf 178 KB)


  1. 1.
    Wunderlich T, Akgenc B, Eckern U, Schuster C, Schwingenschlögl U (2013) Modified Li chains as atomic switches. Sci Rep 3:2605CrossRefGoogle Scholar
  2. 2.
    Scheer E, Agraït N, Cuevas JC, Yeyati AL, Ludoph B, Martín-Rodero A, Bollinger GR, van Ruitenbeek JM, Urbina C (1998) The signature of chemical valence in the electrical conduction through a single-atom contact. Nature 394:154–157CrossRefGoogle Scholar
  3. 3.
    Sinitskiy AV, Greenman L, Mazziotti D (2010) Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method. J Chem Phys 133:014104CrossRefGoogle Scholar
  4. 4.
    Kohanoff J, Hansen JP (1995) Ab initio molecular dynamics of metallic hydrogen at high densities. Phys Rev Lett 74:626–629CrossRefGoogle Scholar
  5. 5.
    Kohn W (1964) Theory of the insulating state. Phys Rev 133:A171–A181CrossRefGoogle Scholar
  6. 6.
    Resta R, Sorella S (1999) Electron localization in the insulating state. Phys Rev Lett 82:370–373CrossRefGoogle Scholar
  7. 7.
    Sgiarovello C, Peressi M, Resta R (2001) Electron localization in the insulating state: application to crystalline semiconductors. Phys Rev B 64:115202CrossRefGoogle Scholar
  8. 8.
    Resta R (2002) Why are insulators insulating and metals conducting? J Phys Condens Matter 14:R625–R656CrossRefGoogle Scholar
  9. 9.
    Resta R (2005) Electron localization in the quantum hall regime. Phys Rev Lett 95:196805CrossRefGoogle Scholar
  10. 10.
    Resta R (2011) The insulating state of matter: a geometrical theory. Eur Phys J B 79:121–137CrossRefGoogle Scholar
  11. 11.
    Resta R (2006) Polarization fluctuations in insulators and metals: new and old theories merge. Phys Rev Lett 96:137601CrossRefGoogle Scholar
  12. 12.
    Resta R (2006) Kohns theory of the insulating state: a quantum-chemistry viewpoint. J Chem Phys 124:104104CrossRefGoogle Scholar
  13. 13.
    Souza I, Wilkens T, Martin R (2000) Polarization and localization in insulators: generating function approach. Phys Rev B 62:1666–1683CrossRefGoogle Scholar
  14. 14.
    Brea O, El Khatib M, Angeli C, Bendazzoli GL, Evangelisti S, Leininger T (2013) Behavior of the position–spread tensor in diatomic systems. J Chem Theory Comput 9:5286–5295CrossRefGoogle Scholar
  15. 15.
    Ángyán JG (2009) Electron localization and the second moment of the exchange hole. Int J Quantum Chem 109:2340–2347CrossRefGoogle Scholar
  16. 16.
    Ángyán J (2011) Linear response and measures of electron delocalization in molecules. Curr Org Chem 15:3609–3618CrossRefGoogle Scholar
  17. 17.
    Bendazzoli GL, Evangelisti S, Monari A, Paulus B, Vetere V (2008) Full configuration-interaction study of the metal-insulator transition in model systems. J Phys Conf Ser 117:012005CrossRefGoogle Scholar
  18. 18.
    Vetere V, Monari A, Bendazzoli GL, Evangelisti S, Paulus B (2008) Full configuration interaction study of the metal-insulator transition in model systems: LiN linear chains (N = 2, 4, 6, 8). J Chem Phys 128:024701Google Scholar
  19. 19.
    Bendazzoli GL, Evangelisti S, Monari A, Resta R (2010) Kohns localization in the insulating state: one-dimensional lattices, crystalline versus disordered. J Chem Phys 133:064703CrossRefGoogle Scholar
  20. 20.
    Bendazzoli GL, Evangelisti S, Monari A (2011) Full-configuration-interaction study of the metal- insulator transition in a model system: Hn linear chains \(\text{ n }=4,6,\ldots,16\). Int J Quantum Chem 111:3416–3423CrossRefGoogle Scholar
  21. 21.
    Giner E, Bendazzoli GL, Evangelisti S, Monari A (2013) Full-configuration-interaction study of the metal-insulator transition in model systems: Peierls dimerization in H(n) rings and chains. J Chem Phys 138:074315CrossRefGoogle Scholar
  22. 22.
    Vetere V, Monari A, Scemama A, Bendazzoli GL, Evangelisti S (2009) A theoretical study of linear beryllium chains: full configuration interaction. J Chem Phys 130:024301CrossRefGoogle Scholar
  23. 23.
    Evangelisti S, Bendazzoli GL, Monari A (2010) Electron localizability and polarizability in tight-binding graphene nanostructures. Theor Chem Acc 126:257–263CrossRefGoogle Scholar
  24. 24.
    Bendazzoli GL, El Khatib M, Evangelisti S, Leininger T (2014) The total position spread in mixed-valence compounds: a study on the H4+ model system. J Comput Chem 35:802–808CrossRefGoogle Scholar
  25. 25.
    Monari A, Bendazzoli GL, Evangelisti S (2008) The metal-insulator transition in dimerized Hückel chains. J Chem Phys 129:134104CrossRefGoogle Scholar
  26. 26.
    Bendazzoli GL, Evangelisti S, Monari A (2012) Asymptotic analysis of the localization spread and polarizability of 1-D noninteracting electrons. Int J Quantum Chem 112:653–664CrossRefGoogle Scholar
  27. 27.
    Horodecki R, Horodecki M, Horodecki K (2009) Quantum entanglement. Rev Mod Phys 81:865–942CrossRefGoogle Scholar
  28. 28.
    Gühne O, Tóth G (2009) Entanglement detection. Phys Rep 474:1–75CrossRefGoogle Scholar
  29. 29.
    El Khatib M, Brea O, Fertitta E, Bendazzoli L, Evangelisti S, Leininger T (2014) The total position–spread tensor : spin partition (submitted to JCP)Google Scholar
  30. 30.
    Peierls RE (1955) Quantum theory of solids. Clarendon Press, OxfordGoogle Scholar
  31. 31.
    Mott NF (1968) Metal-insulator transition. Rev Mod Phys 40:677–683CrossRefGoogle Scholar
  32. 32.
    Kubo R (1962) Generalized cumulant expansion method. J Phys Soc Jpn 17:1100–1120CrossRefGoogle Scholar
  33. 33.
    El Khatib M, Leininger T, Bendazzoli GL, Evangelisti S (2014) Computing the position–spread tensor in the CAS-SCF formalism. Chem Phys Lett 591:58–63CrossRefGoogle Scholar
  34. 34.
    NEPTUNUS is a FORTRAN code for the calculation of FCI energies and properties written by Bendazzoli GL, Evangelisti S with contributions from Gagliardi L, Giner E, Monari A, Verdicchio M.
  35. 35.
    Bendazzoli GL, Evangelisti S (1993) A vector and parallel full configuration interaction algorithm. J Chem Phys 98:3141CrossRefGoogle Scholar
  36. 36.
    Bendazzoli GL, Evangelisti S (1993) Computation and analysis of the full configuration interaction wave function of some simple systems. Int J Quantum Chem 48:287–301CrossRefGoogle Scholar
  37. 37.
    Gagliardi L, Bendazzoli GL, Evangelisti S (1997) Direct-list algorithm for configuration interaction calculations. J Comput Chem 18:1329–1343CrossRefGoogle Scholar
  38. 38.
    Tunega D, Noga J (1998) Static electric properties of LiH: explicitly correlated coupled cluster calculations. Theor Chim Acta 100:78–84CrossRefGoogle Scholar
  39. 39.
    Angeli C, Bendazzoli GL, Evangelisti S (2013) The localization tensor for the H2 molecule: closed formulae for the Heitler–London and related wavefunctions and comparison with full configuration interaction. J Chem Phys 138:054314CrossRefGoogle Scholar
  40. 40.
    Dalton A Molecular electronic structure program See:
  41. 41.
    Oliphant TE (2007) Python for scientific computing. Comput Sci Eng 9:10–20CrossRefGoogle Scholar
  42. 42.
    Millman KJ, Aivazis M (2011) Python for scientists and engineers. Comput Sci Eng 13:9–12CrossRefGoogle Scholar
  43. 43.
    van der Walt S, Colbert SC, Varoquaux G (2011) The NumPy array: a structure for efficient numerical computation. Comput Sci Eng 13:22–30CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Muammar El Khatib
    • 1
  • Oriana Brea
    • 1
    • 2
  • Edoardo Fertitta
    • 3
  • Gian Luigi Bendazzoli
    • 4
  • Stefano Evangelisti
    • 1
    Email author
  • Thierry Leininger
    • 1
  • Beate Paulus
    • 3
  1. 1.Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMCUniversité de Toulouse (UPS) et CNRS (UMR-5626)Toulouse CedexFrance
  2. 2.Departamento de Química, Facultad de Ciencias, Módulo 13Universidad Autónoma de MadridMadridSpain
  3. 3.Institut für Chemie und Biochemie - Freie Universität BerlinBerlinGermany
  4. 4.Dipartimento di Chimica Industriale “Toso Montanari”Università di BolognaBolognaItaly

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