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Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method

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Theoretical Chemistry in Belgium

Part of the book series: Highlights in Theoretical Chemistry ((HITC,volume 6))

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Abstract

The variational procedure of the Hartree–Fock and Kohn–Sham methods can be modified by adding one or more constraints that fix the number of electrons in a given number of molecular fragments. The corresponding Euler–Lagrange equations lead to a modified Fock matrix, where the contribution from the constraints only depends on the overlap matrix, when using the Mulliken or Hirshfeld atoms-in-molecules method. For all compounds in the test set, the energy shows a quadratic dependence on the fixed charges. This behavior provides a procedure to obtain the atomic electronegativity and hardness parameters in the electronegativity equalization method.

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References

  1. Mortier WJ, Ghosh SK, Shankar S (1986) J Am Chem Soc 108:4315–4320

    Article  CAS  Google Scholar 

  2. Mortier WJ (1987) In: Sen KD, Jorgensen CK (eds) Electronegativity. Springer, Berlin

    Google Scholar 

  3. Baekelandt BG, Mortier WJ, Schoonheydt RA (1992) In: Sen KD (ed) Chemical hardness. Springer, Berlin

    Google Scholar 

  4. Blanco MA, Martín–Pendás A, Francisco E (2005) J Chem Theory Comput 1:1096–1109

    Article  CAS  Google Scholar 

  5. Vanfleteren D, Ghillemijn D, Van Neck D, Bultinck P, Waroquier M, Ayers PW (2011) J Comput Chem 32:3485–3496

    Article  CAS  Google Scholar 

  6. Mayer I (2007) Faraday Discuss 135:439–450

    Article  CAS  Google Scholar 

  7. Parr RG, Yang W (1989) Density functional theory of atoms and molecules. New York, Oxford

    Google Scholar 

  8. Politzer P, Weinstein H (1979) J Chem Phys 71:4218–4220

    Article  CAS  Google Scholar 

  9. Sanderson RT (1951) Science 114:670

    Article  CAS  Google Scholar 

  10. Sanderson RT (1983) Polar CoValence. Academic Press, New York

    Google Scholar 

  11. Baekelandt B, Mortier W, Lievens J, Schoonheydt R (1991) J Am Chem Soc 113:6730–6734

    Article  CAS  Google Scholar 

  12. Rappe A, Goddard W (1991) J Phys Chem 95:3358–3363

    Article  CAS  Google Scholar 

  13. Menegon G, Shimizu K, Farah JPS, Dias LG, Chaimovich H (2002) Phys Chem Chem Phys 4:5933–5936

    Article  CAS  Google Scholar 

  14. Bultinck P, Langenaeker W, Lahorte P, De Proft F, Geerlings P, Waroquier M, Tollenaere JP (2002) J Phys Chem A 106:7887–7894

    Article  CAS  Google Scholar 

  15. Bultinck P, Langenaeker W, Lahorte P, De Proft F, Geerlings P, Van Alsenoy C, Tollenaere JP (2002) J Phys Chem A 106:7895–7901

    Article  CAS  Google Scholar 

  16. Bultinck P, Vanholme R, Popelier P, De Proft F, Geerlings P (2004) J Phys Chem A 108:10359–10366

    Article  CAS  Google Scholar 

  17. Verstraelen T, Van Speybroeck V, Waroquier M (2009) J Chem Phys 131:044127

    Article  Google Scholar 

  18. Verstraelen T, Bultinck P, Van Speybroeck V, Ayers PW, Van Neck D, Waroquier M (2011) J Chem Theory Comput 7:1750–1764

    Article  CAS  Google Scholar 

  19. Bultinck P, Carbó–Dorca R (2002) Chem Phys Lett 364:357–362

    Article  CAS  Google Scholar 

  20. Bultinck P, Langenaeker W, Carbó–Dorca R, Tollenaere JP (2003) J Chem Inf Comput Sci 43:422–428

    Google Scholar 

  21. York DM, Yang W (1996) J Chem Phys 104:159–172

    Article  CAS  Google Scholar 

  22. Chelli R, Procacci P, Righini R, Califano S (1999) J Chem Phys 111:8569–8575

    Article  CAS  Google Scholar 

  23. Warshel A, Kato M, Pisliakov AV (2007) J Chem Theory Comput 3:2034–2045

    Article  CAS  Google Scholar 

  24. van Duin ACT, Strachan A, Stewman S, Zhang Q, Xu X, Goddard WA (2003) J Phys Chem A 107:3803–3811

    Article  Google Scholar 

  25. Szabo A, Ostlund NS (1982) Modern quantum chemistry. Macmillan, New York

    Google Scholar 

  26. Mulliken RS (1955) J Chem Phys 23:1833–1840

    Article  CAS  Google Scholar 

  27. Dederichs PH, Blü gel S, Zeller R, Akai H (1984) Phys Rev Lett 53:2512–2515

    Article  CAS  Google Scholar 

  28. Wu Q, Van Voorhis T (2005) Phys Rev A 72:024502

    Article  Google Scholar 

  29. Wu Q, Van Voorhis T (2006) J Chem Theory Comput 2:765–774

    Article  CAS  Google Scholar 

  30. Kaduk B, Kovalczyk T, Van Voorhis T (2012) Chem Rev 112:321–370

    Article  CAS  Google Scholar 

  31. Cioslowski J, Stefanov BB (1993) J Chem Phys 99:5151–5162

    Article  CAS  Google Scholar 

  32. Hirshfeld FL (1977) Theor Chim Acta 44:129–138

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, 09340, Mexico, DF, Mexico

    Andrés Cedillo

  2. Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000, Ghent, Belgium

    Andrés Cedillo & Patrick Bultinck

  3. Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052, Zwijnaarde, Belgium

    Dimitri Van Neck

Authors
  1. Andrés Cedillo
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  2. Dimitri Van Neck
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  3. Patrick Bultinck
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Corresponding author

Correspondence to Patrick Bultinck .

Editor information

Editors and Affiliations

  1. Laboratory of Theoretical Chemistry, University of Namur, Namur, Belgium

    Benoît Champagne

  2. Research Group of Theoretical Chemistry and Molecular Modeling, Hasselt University, Diepenbeek, Belgium

    Michael S. Deleuze

  3. Faculteit Wetenschappen, Free University of Brussels, Brussels, Belgium

    Frank De Proft

  4. Laboratory of Crystal Engineering Inst.of Condensed Matter and Nanoscience, Catholic University of Louvain, Louvain-La-Neuve, Belgium

    Tom Leyssens

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Cedillo, A., Van Neck, D., Bultinck, P. (2014). Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method. In: Champagne, B., Deleuze, M., De Proft, F., Leyssens, T. (eds) Theoretical Chemistry in Belgium. Highlights in Theoretical Chemistry, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41315-5_3

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