8/12/2019 HSAB_2
1/1
J . A m . C h e m . S O C .1985 107, 6801-6806 6801Absolute
Electronegativity and Absolute Hardness of LewisAcids and
BasesRalph G . PearsonContribution fr om the Chemistry Department,
University of California,Santa Barbara, California 93106. Received
April 15 1985
Abstract: Th e relationship of x o he absolu te
electronegativity, and 7 , the absolute hardness, to chemical
bonding in Lewisacid-base complexes is examin ed. This is done by
using semiempirical MO theory in which the same experime ntal param
etersappe ar. The a priori electron egativity of a Lewis acid or
base is shown to be ( I + A ) / 2 . For any two atom s, ions, or
molecules,the direction of net electron flow is determined by the
difference in x o values. For a specific pair of react ants, the
effectivevalue of x o can range from A A or a pure electron
acceptor to I , for a pure electron dono r. The most common
situation willhave electron transfer in both directions u plus
bonding). Then x o will be a weighted mean of I and A for both acid
andbase. Th e absolute hardness, q = I A ) / 2 ,determines the mag
nitude of the total electron transfer, both u and H Smallvalues of
vA and 7, lead to the greatest amount of covalent bonding. For
neutral molecules and cations, values of I and Afor the species are
used. For anions it is both necessary and theoretically logical to
use values of I and A for the correspondingneutral atoms or
radicals.Recent w ork based on density f unctional theory h as
developedthe concepts of absolute electronegativity, x ] nd
absolutehardness, 7. The defini t ions are
Where E is the electronic energy of a molecule, ato m, or ion,is
the number of electrons, and Z is a fixed set of nuclear
charges.The absolute electronegativity is also equal to the
electronicchemical potential, k with chang e in sign. The
operational (andapproximate) definitions arex = y2(Z A ) ; 7 = )
>(I A ) ( 2 )
where Z s the ionization potential, and A is the electron
affinity.The absolute electronegativity is the sa me as the
Mulliken value.W e assume that for small changes in N , we can
writew = w + 27AN 3)If we have two chemical species, A an d B,
which ar e allowed toreact, the re will be a shift of electrons
from the less electronegativemolecule, B, to the more
electronegative molecule, A. The con-dition of equilibrium is that
the chemical potentials, p and pBbecome equaL3 This leads to a
shift in charge, A N , from B toA .
X O A X O BA N =2 ?A -k 7B
Electron transfer leads to an energy lowering, given by2(4)
(5 )Note in (4) and (5) th at electronegativity difference drive
theelectron transfer, and the sum of hardness parame ters inhibit
it .The hardness is the resistance of the chemical potential to
changein the number of electrons. Th at is, 27 = (aw/aN),.The
chemical potential and the absolute electronegativity aremolecular
properties and not orbita l properties. However, inconsidering the
transfer of electrons from B to A, it becomes
(1) Parr , R. G ;Donnelly, R. A, ;Levy, M .; Palke, W . E. J .
Chem. Phys.1978 68 3801. See also: Iczkowski, R. P.; Margra ve, J.
L . J . Am Chem.S O C . 961 83 3547.(2 ) Parr, R . G.; Pearson, R .
G . Am Chem. SOC 983 105 7512. Seealso: Huheey, J E. J . Phys .
Chem. 1965 85, 148.(3) This condition was first given by Sanderson
as the postulate of elec-tronegativity equalization. Sanderson, R.
T Science (Washington,D . C . ) 1951114 670. It is provable in
density functional theory (ref 1).
necessary to consider th e electrons as coming from definite
oc-cupied orbitals in B and going into definite empty orbitals in
A.This defines the relative orientations of A and B, to give
thegreate st possible overlap between these frontier orbital^.^
Alsoand x are stat e functions, and while ground states are most
oftenconsidered, sometimes it is useful to consider valence states
orexcited states, particularly for th e reactions of
atoms.Equations 4 and are obviously incomplete. T he
chemicalpotential is also a func tion of changing external fields,
so that iA (or B) is charged, this will affect wL or w A as a
function ofthe distance between A and B.5 Also there is no
indication ofthe delocalization of electron density corresponding
to covalentbonding.In spite of these shortcomings, eq 4 and are
very appealing.They have th e great virtue (an d weakness) of
trying to predictchemical behavior with a minimum num ber of
paramet ers. Valuesof I ar e becoming available for more and more
molecules.6 Values
of A are still few in number. In fact for most molecules,
theelectron affinity canno t be detected. In such cases A is set
equalto zero, meaning that E is a minimum when the electron is
atinfinity. Clea rly this is inconsistent with the idea of
electronstransferring t o definite orbitals. It suggests instead
negative valuesof A , related to, but not equal to, the energy of
appropriate emptyorbitals.Th e use of eq 4 and actually predates
the development ofdensity functional theory.* Attem pts have also
been made toinclude the effects of Coulombic interactions (ionic
bonding) andof covalent bonding. Howev er, this earlier work
considered onlyatoms and radicals with one valence electron to
contribute to abond. Also the interest was in estimatin g the
percent of ioniccharacter in the bond, and t he results are not
convenient for bondenergies.In this paper we will consider the
interaction of a Lewis acidand a base:
( 6 ):B - :B4) Parr, R. G. ; Yang, W. J . Am . Ch em . SOC. 984
106 4049.5 ) Nalewajski, R. F. J . Am . Ch em . S O C. 984 106
944.(6) Rosenstock, H . M. et al. J . Phys. C hem. ReJ Dura 1977 6,
suppl. no.7 ) Lowe (Lowe, J P. J . Am . Ch em . S O C.1977 99,
5557) gives a useful
(8) Hinze, J ; Whitehead, M. A, ; Ja ff e ; H . H . J . Am Chem.
SOC. 963(9) Iczkowski. R. P. J . Am . Ch em . SOC. 964. 86 2329.
Evans. R. S.:
1.discussion of the electron affinities of small molecules.85,
148.Huheey, J E. J. Inorg. Nucl . Chem. 1970 32. 373 , Reed, J L. J
Phys.Chem. 1981 85 148.
0002-7863/85/1507-6801 01.50/0 985 American C hemical
Society
