Abstract
Recent description on density function (DF) sets of origin shifts is used in the present work to describe in a simple way Fukui functions. The present paper discusses first the possibilities and nuances of the origin shift in sets of three DF, formed by cation, neutral and anion functions; then uses quantum similarity techniques to analyze the resultant origin shifted DF sets. Extension of the origin shift in arbitrary sets of DF is also discussed, with a final application over the structure of a single DF itself in terms of the MO shape functions basis set.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The zero function might be defined as: \(\forall \mathbf{r}\in \mathbf{R}^{3}:0\left( \mathbf{r} \right)=0\).
This has to be seen as a general property of vector semispaces. Convex linear combinations of their elements belong to the semispace. That is the same to say that vector semispaces are closed upon convex linear combinations.
References
K. Fukui, T. Yonezawa, H. Shingu, J. Chem. Phys. 20, 722 (1952)
K. Fukui, T. Yonezawa, Ch. Nagata, H. Shingu, J. Chem. Phys. 22, 1433 (1954)
R.G. Parr, W. Yang, J. Am. Chem. Soc. 106, 4049 (1984)
P.W. Ayers, M. Levy, Perspective on “density functional approach to the frontier-electron theory of chemical reactivity”. Theor. Chem. Acc. 103, 353 (2000)
P.W. Ayers, R.G. Parr, J. Am. Chem. Soc. 122, 2010 (2000)
P. W. Ayers, W. Yang, L. J. Bartolotti, in Fukui Function, ed. by P. Chattaraj. Chemical Reactivity Theory: A Density Functional View (CRC Press, Boca Raton, 2009), pp. 255–267
P. A. Johnson, L. J. Bartolotti, P. W. Ayers, T. Fievez, P. Geerlings, in “Charge Density and Chemical Reactivity: A Unified View from Conceptual DFT”, ed. by C. Gatti, P. Macchi. Modern Charge Density Analysis (Springer, New York, 2012), pp. 715–764
P. Bultinck, D. Van Neck, G. Acke, P.W. Ayers, Phys. Chem. Chem. Phys. 14, 2408 (2012)
P. Bultinck, R. Carbó-Dorca, W. Langenaeker, J. Chem. Phys. 118, 4349 (2003)
P. Bultinck, R. Carbó-Dorca, J. Math. Chem. 34, 67 (2003)
R. Carbó-Dorca, A. Gallegos, Intl. J. Quant. Chem. 109, 2356 (2009)
P. Bultinck, D. Clarisse, P.W. Ayers, R. Carbó-Dorca, Phys. Chem. Chem. Phys. 13, 6110 (2011)
R. Carbó-Dorca, J. Math. Chem. 32, 201 (2002)
P. Bultinck, R. Carbó-Dorca, J. Math. Chem. 36, 191 (2004)
R. Carbó-Dorca, S. Van Damme, Afinidad 64, 147 (2007)
R. Carbó-Dorca, J. Math. Chem. 44, 628 (2008)
R. Carbó-Dorca, E. Besalú, J. Math. Chem. 50, 210 (2012)
R. Carbó-Dorca, E. Besalú, J. Math. Chem. 50, 1161 (2012)
P. Bultinck, X. Gironés, R. Carbó-Dorca, in “Molecular Quantum Similarity: Theory and Applications”, ed. by K.B. Lipkowitz, R. Larter, T. Cundari. Reviews in Computational Chemistry (Wiley, Hoboken, 2005), vol. 21, pp. 127–207
R. Carbó-Dorca, E. Besalú, L.D. Mercado, J. Comp. Chem. 32, 582 (2011)
R. Carbó-Dorca, J. Math. Chem. 49, 2109 (2011)
R. Carbó-Dorca, J. Math. Chem. 50, 734 (2012)
E. Durand, in “Solutions Numériques des Équations Algébriques Sistèmes de Plusiers Équations, Valeurs Propres des Matrices” (Masson et Cie, Paris, 1961), vol. II
R. Carbó-Dorca, J. Math. Chem. (2012). doi:10.1007/s10910-012-0083-x
Acknowledgments
The author wants to warmly thank professors Paul Ayers (Mc. Master University) and Patrick Bultinck (Ghent University) for valuable discussions and suggestions about this work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carbó-Dorca, R. A naïve geometrical perspective of Fukui functions: definition of Fukui function skew symmetric matrices described on density function sets. J Math Chem 51, 843–856 (2013). https://doi.org/10.1007/s10910-012-0120-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-012-0120-9