The Hirshfeld-I method: atoms in molecules and chemical bonding perspective

Abstract

The Hirshfeld method for the atom in the molecule (AIM) was born from crystallography and relies on the use of a so-called promolecule [1]. The promolecule is composed of all atoms in their respective locations in the molecule and a promolecular density is obtained as the sum of all isolated atomic densities. At every point in space, the share of an (isolated) atom in the promolecular density can be easily computed via their ratio and the key element of the Hirshfeld method is that this ratio is then used to extract an AIM density from the molecular electron density . That is: Unfortunately, the results of Hirshfeld analysis depend heavily on the isolated atom states used to compute the AIM weight functions. In the improved Hirshfeld-I method, the Hirshfeld process is repeated until self consistency is reached. In other words: the charge on the AIM and the isolated atom are the same. In this presentation the information theoretic context of Hirshfeld-I is sketched, performance of the method compared to regular Hirshfeld analysis discussed, its impact on the nature of atom condensed Fukui functions described, and its use for good quality monopole approximation electrostatic potentials is shown [2-6]. Electron delocalization indices, as obtained using the Hirshfeld-I method, are described [7] and the excellent Hirshfeld-I AIM charge performance in electronegativity equalization methods discussed [9]. Finally, based on Hirshfeld-I derived density matrices [10], an AIM is formulated in momentum space. [1] F.L. Hirshfeld, Theor. Chim. Acta, 1977, 44, 129. [2] P. Bultinck, C. Van Alsenoy, P.W. Ayers, and R. J. Carbo-Dorca, J. Chem. Phys., 2007, 126, 144111. [3] P. Bultinck, P. Faraday Discussions, 2007, 135, 244. [4] P. Bultinck, P.W. Ayers, S. Fias, K. Tiels, C. Van Alsenoy, Chem. Phys. Lett., 2007, 444, 205. [5] P. Bultinck, P., S. Fias, C. Van Alsenoy, P.W. Ayers, and R. Carbo-Dorca, J. Chem. Phys., 2007, 127, 034102. [6] S. Van Damme, P. Bultinck, and S. Fias, J. Chem. Theory and Comput., 2009, 5, 334. [7] Heyndrickx, W.; Matito, E.; Salvador, P.; Sola, M.; Bultinck, P. J. Comput. Chem., 2011, 32, 386. [9] Verstraelen, T.; Bultinck, P.; Van Speybroeck, V.; Ayers, P.W.; Van Neck, D.; Waroquier, M. J. Chem. Theor. Comput. In press, 2011. [10] Vanfleteren, D.; Van Neck, D.; Bultinck, P.; Ayers, P.W.; Waroquier, M. J. Chem. Phys., 2010, 132, 164111.