Fluctuation formulas for the external potential v(r) are introduced in a modified Legendre‐transformed representation of the density functional theory of electronic structure (isomorphic ensemble). A new (nuclear/geometric) reactivity index h(r), having the same status as the electronic Fukui function in the canonical ensemble, is thereby identified, h(r)=(1/N)[δμ/δσ(r)]N,T=(1/kT) [〈μ⋅v(r)〉−〈μ〉〈v(r)〉], where μ is the electronic chemical potential, σ is the shape factor of the electron density distribution, N is the number of electrons, 〈...〉 denotes the ensemble average of a quantity, and 〈v(r)〉 is the ensemble averaged external potential. This new local quantity is shown to be an inverse of the local softness, and to provide a useful definition of a local hardness.

1.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev. B
136
,
864
(
1964
).
2.
R. G.
Parr
and
W.
Yang
,
J. Am. Chem. Soc.
104
,
4049
(
1984
).
3.
W.
Yang
and
R. G.
Parr
,
Proc. Natl. Acad. Sci. USA
82
,
6723
(
1985
).
4.
M.
Berkowitz
and
R. G.
Parr
,
J. Chem. Phys.
88
,
2554
(
1988
).
5.
(a)
S. K.
Ghosh
and
M.
Berkowitz
,
J. Chem. Phys.
83
,
2976
(
1985
);
(b)
M.
Berkowitz
,
S. K.
Ghosh
, and
R. G.
Parr
,
J. Am. Chem. Soc.
107
,
6811
(
1985
);
(c)
S. K.
Ghosh
,
Chem. Phys. Lett.
172
,
77
(
1990
).
6.
M. H.
Cohen
,
M. V.
Ganduglia-Pirovano
, and
J.
Kudrnovsky
,
J. Chem. Phys.
101
,
8988
(
1994
).
7.
B. G.
Baekelandt
,
G. O. A.
Janssens
,
H.
Toufar
,
W. J.
Mortier
,
R. A.
Schoonheydt
, and
R. F.
Nalewajski
,
J. Phys. Chem.
99
,
9784
(
1995
).
8.
G. O. A. Janssens, B. G. Baekelandt, H. Toufar, W. J. Mortier, and R. A. Schoonheydt, Int. J. Quantum Chem. (in press).
9.
W.
Yang
and
R. G.
Parr
,
Proc. Natl. Acad. Sci. USA
82
,
6723
(
1985
).
10.
M. K.
Harbola
,
P. K.
Chattaraj
, and
R. G.
Parr
,
Isr. J. Chem.
31
,
395
(
1991
).
11.
P. K.
Chattaraj
and
R. G.
Parr
,
Struct. Bond. Chem. Hardness
80
,
11
(
1993
).
12.
R. G.
Parr
and
P. K.
Chattaraj
,
J. Am. Chem. Soc.
113
,
1854
(
1991
).
13.
P. K.
Chattaraj
,
H.
Lee
, and
R. G.
Parr
,
J. Am. Chem. Soc.
113
,
1855
(
1991
).
14.
N. D.
Mermin
,
Phys. Rev. A
137
,
1441
(
1965
).
15.
R. F.
Nalewajski
and
R. G.
Parr
,
J. Chem. Phys.
77
,
399
(
1982
).
16.
R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, The International Series, Monographs in Chemistry (Oxford University, New York, 1989), Vol. 15.
17.
L. M.
Falicov
and
G.
Somorjai
,
Proc. Natl. Acad. Sci. USA
82
,
2207
(
1985
).
18.
W. J. Mortier, in Theoretical Aspects of Heterogeneous Catalysis, edited by J. B. Moffat (Van Nostrand Reinhold, New York, 1990), pp. 135–159.
19.
R. F. Nalewajski (personal communication).
20.
R. G.
Parr
and
L. J.
Bartolotti
,
J. Phys. Chem.
87
,
2810
(
1983
).
21.
A.
Cedillo
,
Int. J. Quantum Chem. Chem. Symp.
28
,
231
(
1994
).
22.
R. G.
Parr
and
R. G.
Pearson
,
J. Am. Chem. Soc.
105
,
7512
(
1983
).
23.
See, e.g., D. A. McQuarrie, Statistical Mechanics, edited by S. A. Rice (Harper & Row, New York, 1976).
24.
B. G. Baekelandt, Ph.D. thesis, K. U. Leuven, 1989.
25.
M.
Berkowitz
,
S. K.
Ghosh
, and
R. G.
Parr
,
J. Am. Chem. Soc.
107
,
6811
(
1985
).
26.
R. G.
Pearson
,
J. Phys. Chem.
98
,
1989
(
1994
).
27.
W. J.
Mortier
,
S. K.
Ghosh
, and
S.
Shankar
,
J. Am. Chem. Soc.
108
,
4315
(
1986
).
28.
L.
Uytterhoeven
,
W. J.
Mortier
, and
P.
Geerlings
,
J. Phys. Chem. Solids
50
,
479
(
1989
).
29.
B. G.
Baekelandt
,
W. J.
Mortier
,
J. L.
Lievens
, and
R. A.
Schoonheydt
,
J. Am. Chem. Soc.
113
,
6730
(
1991
).
30.
B. G.
Baekelandt
,
W. J.
Mortier
, and
R. A.
Schoonheydt
,
Struct. Bond. Chem. Hardness
80
,
187
(
1993
).
31.
R. F.
Nalewajski
,
Z. Naturforsch.
43A
,
65
(
1988
).
32.
R. F.
Nalewajski
,
Struct. Bonding Chem. Hardness
80
,
115
(
1993
), and references therein.
This content is only available via PDF.
You do not currently have access to this content.