Skip to main content
SpringerLink
Log in

Mathematical aspects of the LCAO MO first order density function (5): centroid shifting of MO shape functions basis set, properties and applications

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

In MO SCF theory and related computational levels, the first order density function (DF) can be considered as a linear combination of the MO shape functions (ShF) set. This work studies the possibility of constructing a centroid function from the ShF set elements using it to perform a ShF set origin shift, while permitting the DF decomposition in two well defined function terms. The properties and consequences of such a simple operation are analyzed in deep.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Carbó-Dorca R.: Mathematical aspects of the LCAO MO first order density function (1): atomic partition, metric structure and practical applications. J. Math. Chem. 43, 1076–1101 (2008)

    Article  Google Scholar 

  2. Carbó-Dorca R.: Mathematical aspects of the LCAO MO first order density function (2): relationships between density functions. J. Math. Chem. 43, 1102–1118 (2008)

    Article  Google Scholar 

  3. Carbó-Dorca R., Bultinck P.: Mathematical aspects of the LCAO MO first order density function (3): a general localization procedure. J. Math. Chem. 43, 1069–1075 (2008)

    Article  Google Scholar 

  4. Carbó-Dorca R., Besalú E.: Mathematical aspects of the LCAO MO first order density function (4): notes on the connection of Taylor series of electronic density (TSED) function with the holographic electronic density theorem (HEDT) and the Hohenberg–Kohn theorem (HKT). J. Math. Chem. 49, 836–842 (2011)

    Article  Google Scholar 

  5. Carbó-Dorca R., Besalú E.: Centroid origin shift of quantum object sets and molecular point clouds: description and element comparisons. J. Math. Chem. 50, 11161–11178 (2012)

    Google Scholar 

  6. Carbó-Dorca R., Besalú E.: Shells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces. J. Math. Chem. 50, 210–219 (2012)

    Article  Google Scholar 

  7. Carbó-Dorca R.: Diagonal coefficient representation of density functions and quantum similarity measures. J. Math. Chem. 44, 621–627 (2008)

    Article  Google Scholar 

  8. Constans P., Carbó R.: J. Chem. Inf. Comp. Sci. 35, 1046–1053 (1995)

    CAS  Google Scholar 

  9. P. Constans, X. Fradera, L. Amat, R. Carbó, Quantum molecular similarity measures (QMSM) and the atomic shell approximation (ASA), in Proceedings of the 2nd Girona Seminar on Molecular Similarity. Advances in Molecular Similarity, July 1995, vol. 1. (Jai Press Inc., Greenwich, CT, 1996), pp. 187–211

  10. Amat L., Carbó-Dorca R.: J. Comput. Chem. 18, 2023–2029 (1997)

    Article  CAS  Google Scholar 

  11. Amat L., Carbó-Dorca R.: J. Comput. Chem 20, 911–920 (1999)

    Article  CAS  Google Scholar 

  12. B.N. Plakhutin, E.V. Gorelik, N.N. Breslavskaya, J. Chem. Phys. 125, 204110-10 (2006)

    Google Scholar 

  13. Plakhutin B.N., Davidson E.R: J. Phys. Chem. A 113, 12386–12395 (2009)

    Article  CAS  Google Scholar 

  14. Davidson E.R, Plakhutin B.N.: J. Chem. Phys. 132, 184110–184114 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Química Computacional, Universitat de Girona, 17071, Girona, Catalonia, Spain

    Ramon Carbó-Dorca

Authors
  1. Ramon Carbó-Dorca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramon Carbó-Dorca.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carbó-Dorca, R. Mathematical aspects of the LCAO MO first order density function (5): centroid shifting of MO shape functions basis set, properties and applications. J Math Chem 51, 289–296 (2013). https://doi.org/10.1007/s10910-012-0083-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-012-0083-x

Keywords

Search

Navigation