7.3.5.4 Electronegativity, Hardness, Softness and the Fukui Function:
Electron Density Reactivity Indexes
The idea of electronegativity was born as soon as chemists suspected that the
formation of chemical compounds involved electrical forces (before the discovery
of the electron): metals and nonmetals were seen to possess opposite appetites for
the “electrical fluid(s)” of eighteenth century physics. This “electrochemical dual-
ism” is most strongly associated with Berzelius [ 136 ], and is clearly related to
our qualitative notion of electronegativity as the tendency of a species to attract
electrons. Parr and Yang have given a sketch of attempts to quantify the idea [ 137 ].
Electronegativity is a central notion in chemistry.
Hardness and softness as chemical concepts were presaged in the literature as
early as 1952, in a paper by Mulliken [ 138 ], but did not become widely used till they
were popularized by Pearson in 1963 [ 139 ]. In the simplest terms, the hardness of a
species, atom, ion or molecule, is a qualitative indication of how polarizable it is,
i.e. how much its electron cloud is distorted in an electric field. The adjectives hard
and soft were said to have been suggested by D.H. Busch [ 140 ], but they appear in
Mulliken’s paper [ 138 ], p. 819, where they characterize the response to spatial
separation of the energy of acid-base complexes. The analogy with the conventional
use of these words to denote resistance to deformation by mechanical force is clear,
and independent extension, by more than one chemist, to the concept of electronic
resistance, is no surprise. The hard/soft concept proved useful, particularly in
rationalizing acid-base chemistry [ 141 ]. Thus a proton, which cannot be distorted
in an electric field since it has no electron cloud (we ignore the possibility of nuclear
distortion) is a very hard acid, and tends to react with hard bases. Examples of soft
bases are those in which sulfur electron pairs provide the basicity, since sulfur is a
big fluffy atom, and such bases tend to react with soft acids. Perhaps because it was
originally qualitative, the hard-soft acid-base (HSAB) idea met with skepticism
from at least one quarter: Dewar (of semiempirical fame) dismissed it as a “mystical
distinction between different kinds of acids and bases” [ 142 ]. For a brief review of
Pearson’s contributions to the concept, which has been extended beyond strict
conventional acid-base reactions, see [ 143 ].
The Fukui function or frontier function was introduced by Parr and Yang in 1984
[ 144 ]. They generously gave it a name associated with the pioneer of frontier
molecular orbital theory, who emphasized the roles of the HOMO and LUMO in
chemical reactions. In a reaction a change in electron number clearly involves
removing electrons from or adding electrons to the HOMO or LUMO, respectively,
i.e. thefrontier orbitalswhose importance was emphasized by Fukui.^4 The mathe-
matical expression (below) of the function defines it as the sensitivity of the
electron density at various points in a species to a change in the number of electrons
in the species. If electrons are added or removed, how much is the electron density
(^4) Kenichi Fukui, born Nara, Japan, 1918. Ph.D. Kyoto Imperial University 1948, Professor Kyoto
Imperial University 1951. Nobel Prize 1981. Died 1998.
7.3 Applications of Density Functional Theory 497