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.
References
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)
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)
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)
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)
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)
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)
Carbó-Dorca R.: Diagonal coefficient representation of density functions and quantum similarity measures. J. Math. Chem. 44, 621–627 (2008)
Constans P., Carbó R.: J. Chem. Inf. Comp. Sci. 35, 1046–1053 (1995)
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
Amat L., Carbó-Dorca R.: J. Comput. Chem. 18, 2023–2029 (1997)
Amat L., Carbó-Dorca R.: J. Comput. Chem 20, 911–920 (1999)
B.N. Plakhutin, E.V. Gorelik, N.N. Breslavskaya, J. Chem. Phys. 125, 204110-10 (2006)
Plakhutin B.N., Davidson E.R: J. Phys. Chem. A 113, 12386–12395 (2009)
Davidson E.R, Plakhutin B.N.: J. Chem. Phys. 132, 184110–184114 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-012-0083-x