Hirshfeld Partitioning of the Electron Density:
Atomic Dipoles and their Relation
with Functional Group Properties
F. DE PROFT,
1
R. VIVAS–REYES,
1
A. PEETERS,
2
C. VAN ALSENOY,
2
P. GEERLINGS
1
1
Eenheid Algemene Chemie, Vrije Universiteit Brussel (VUB), Faculteit Wetenschappen,
Pleinlaan 2, 1050 Brussels, Belgium
2
Department of Chemistry, University of Antwerp (UIA), Universiteitsplein 1,
B-2610 Antwerpen, Belgium
Received 28 June 2002; Accepted 23 September 2002
Abstract: Atomic dipole moments, derived within the Hirshfeld partitioning of the molecular electron density, have
been studied for compounds of the type H—X and Cl—X, for a series of functional groups X frequently encountered
in organic molecules. In the case of the H—X compounds, the component of the atomic dipole moment on H along the
axis connecting H with the central atom in X is found to be linearly correlated with the electronegativity of X, the
hardness of X playing no significant role. In the case of the Cl—X compounds, the situation is less clear. However,
evidence seems to point to the conclusion that for these compounds, also the group hardness plays an important role.
© 2003 Wiley Periodicals, Inc. J Comput Chem 24: 463– 469, 2003
Key words: Hirshfeld partitioning; atomic dipoles; group electronegativity; group hardness
Introduction
Chemists often use the concept of atoms in molecules (AIM) to
rationalize molecular properties on the basis of their constituent
atoms or functional groups. Unfortunately, no unique manner to
partition the molecular space in atomic regions is available. A
diversity of methods have been proposed in the past. The majority
of these methods are based on the use of the molecular electron
density of the system (r). One of the most popular definitions of
atoms in molecules is the one due to Bader, based on the topology
of the electron density.
1
In this approach, an atomic region (or an
atomic basin
A
) is defined as to be enclosed by the so-called
zero-flux surfaces, defined as
r n = 0 (1)
where n is the normal vector. The atomic population can then be
calculated as
N
A
=
A
rdr (2)
Similar investigations concerning the topology of the molecular
electrostatic potential have been conducted.
2
Another way to partition the molecular electron density is due
to Stewart et al.,
3–5
and was revisited recently by Gill et al.
6
In this
approach, a sum of spherically symmetric atom centered electron
densities
A
, termed Stewart atoms, is constructed such that their
sum best fits the moleculair electron density in a least-square
sense. This, in practice, results in the minimization of the follow-
ing functional:
Z =
r -
A
A
r - R
A
r - r r
-
A
A
r - R
A
drdr (3)
where (r - r') is an operator depending on the relative positions
of the two electrons, and which, in most cases is set to l/|r - r'|.
These Stewart atoms can be considered as radially perturbed
isolated atoms. Gill introduced the approximation that the valence
part of the Stewart atoms can be written as a Slater exponential and
thus introduced the Stewart–Slater atoms, which were shown to
provide atoms and charges in agreement with chemical intuition.
6
Recently, however, there has been a renewed interest in the
Hirshfeld partitioning
7
of the molecular electron density.
8 –12
It
Correspondence to: P. Geerlings; e-mail: pgeerlin@vub.ac.be
Contract/grant sponsor: University of Antwerp; contract/grant number:
GOA-BOF-UA-23
© 2003 Wiley Periodicals, Inc.