The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems.

1.
G. N.
Lewis
,
J. Am. Chem. Soc.
38
,
762
(
1916
).
2.
R. F. W.
Bader
,
S.
Johnson
,
T. H.
Tang
, and
P. L. A.
Popelier
,
J. Phys. Chem.
100
,
15398
(
1996
).
3.
X.
Fradera
,
M. A.
Austen
, and
R. F. W.
Bader
,
J. Phys. Chem. A
103
,
304
(
1999
).
4.
R. J.
Gillespie
and
P. L. A.
Popelier
,
Chemical Bonding and Molecular Geometries: From Lewis to Electron Densities
(
Oxford University Press
,
New York
,
2001
);
R. J.
Gillespie
and
I.
Hargittai
,
The VSEPR Model of Molecular Geometry
(
Allyn and Bacon
,
Boston
,
1991
).
5.
C.
Edmiston
and
K.
Ruedenberg
,
Rev. Mod. Phys.
35
,
457
(
1963
);
S. F.
Boys
,
Rev. Mod. Phys.
32
,
296
(
1960
).
6.
R. F. W.
Bader
,
Chem. Rev. (Washington, D.C.)
91
,
893
(
1991
);
R. F. W.
Bader
,
Acc. Chem. Res.
18
,
9
(
1985
);
R. F. W.
Bader
,
Coord. Chem. Rev.
197
,
71
(
2000
).
7.
R. F. W.
Bader
,
Atoms in Molecules: A Quantum Theory
(
Clarendon
,
Oxford
,
1990
).
8.
R.
McWeeny
,
Methods of Molecular Quantum Mechanics
, 2nd ed. (
Academic
,
London
,
1976
);
E. R.
Davidson
,
Reduced Density Matrices in Quantum Chemistry
(
Academic
,
New York
,
1976
);
A. J.
Coleman
,
Int. J. Quantum Chem.
85
,
196
(
2001
);
J.
Cioslowski
,
Many-Electron Densities and Reduced Density Matrices
(
Kluwer Academic, Dordrecht/Plenum
,
New York
,
2000
).
9.
K.
Artmann
,
Z. Naturforsch.
1
,
426
(
1946
).
10.
J.
Lennard-Jones
,
Proc. R. Soc. London
198
,
1
(
1949
).
11.
R. F. W.
Bader
and
M. E.
Stephens
,
J. Am. Chem. Soc.
97
,
7391
(
1975
).
12.
K.
Ruedenberg
,
Rev. Mod. Phys.
34
,
326
(
1962
).
13.
E.
Wigner
and
F.
Seitz
,
Phys. Rev.
43
,
804
(
1933
).
14.
R. J.
Gillespie
,
D.
Bayles
,
J.
Platts
,
G. L.
Heard
, and
R. F. W.
Bader
,
J. Phys. Chem. A
102
,
3407
(
1998
).
15.
W. L.
Luken
and
J. C.
Culberson
,
Int. J. Quantum Chem.
16
,
265
(
1982
).
16.
V.
Tschinke
and
T.
Ziegler
,
J. Chem. Phys.
93
,
8051
(
1990
);
V. W.
Maslen
,
Proc. Phys. Soc., London, Sect. A
69
,
734
(
1956
);
W. L.
Luken
and
D. N.
Beratan
,
Theor. Chim. Acta
61
,
265
(
1982
);
E. V.
Ludeña
,
J. M.
Ugalde
,
L. X. J.
Fernández-Rico
, and
G.
Ramírez
,
J. Chem. Phys.
120
,
540
(
2004
);
[PubMed]
W.
Kutzelnigg
, in
Explicitly Correlated Wave Functions in Chemistry and Physics
, edited by
J.
Rychlewski
(
Kluwer Academic
,
Dordrecht
,
2003
), Vol.
13
, p.
3
;
M.
Ernzerhof
,
K.
Burke
, and
J. P.
Perdew
, in
Recent Developments and Applications of Modern Density Functional Theory
, edited by
J. M.
Seminario
(
Elsevier
,
Amsterdam
,
1996
), p.
207
;
D. L.
Cooper
and
C. N. M.
Pounder
,
Int. J. Quantum Chem.
17
,
759
(
1980
);
M. A.
Buijse
and
E. J.
Baerends
, in
Density Functional Theory of Molecules, Clusters and Solids
, edited by
D. E.
Ellis
(
Kluwer
,
Dordrecht
,
1995
), p.
1
;
E. J.
Baerends
and
O. V.
Gritsenko
,
J. Phys. Chem. A
101
,
5383
(
1997
);
R. F. W.
Bader
and
G. L.
Heard
,
J. Chem. Phys.
111
,
8789
(
1999
).
17.
A. D.
Becke
and
K. E.
Edgecombe
,
J. Chem. Phys.
92
,
5397
(
1990
).
18.
A.
Savin
,
R.
Nesper
,
S.
Wengert
, and
T. F.
Fassler
,
Angew. Chem., Int. Ed. Engl.
36
,
1809
(
1997
);
A.
Savin
,
A. D.
Becke
,
J.
Flad
,
R.
Nesper
,
H.
Preuss
, and
H. G.
Vonschnering
,
Angew. Chem., Int. Ed. Engl.
30
,
409
(
1991
).
19.
B.
Silvi
and
A.
Savin
,
Nature (London)
371
,
683
(
1994
).
20.
J.
Poater
,
M.
Duran
,
M.
Solà
, and
B.
Silvi
,
Chem. Rev. (Washington, D.C.)
105
,
3911
(
2005
).
21.
A. D.
Becke
,
Int. J. Quantum Chem.
23
,
1915
(
1983
).
22.
P. O.
Lowdin
,
Phys. Rev.
97
,
1474
(
1955
).
23.
A. D.
Becke
,
Int. J. Quantum Chem.
27
,
585
(
1985
).
24.
T. F.
Fassler
and
A.
Savin
,
Chem. Unserer Zeit
31
,
110
(
1997
).
25.
M.
Kohout
and
A.
Savin
,
Int. J. Quantum Chem.
60
,
875
(
1996
).
26.
M.
Kohout
and
A.
Savin
,
J. Comput. Chem.
18
,
1431
(
1997
).
27.
J.
Melin
and
P.
Fuentealba
,
Int. J. Quantum Chem.
92
,
381
(
2003
).
28.
J. C.
Santos
,
J.
Andrés
,
A.
Aizman
, and
P.
Fuentealba
,
J. Chem. Theory Comput.
1
,
83
(
2005
);
[PubMed]
J. C.
Santos
,
W.
Tiznado
,
R.
Contrearas
, and
P.
Fuentealba
,
J. Chem. Phys.
120
,
1670
(
2004
).
[PubMed]
29.
X.
Krokidis
,
S.
Noury
, and
B.
Silvi
,
J. Phys. Chem. A
101
,
7277
(
1997
);
S.
Berski
,
J.
Andrés
,
B.
Silvi
, and
L. R.
Domingo
,
J. Phys. Chem. A
107
,
6014
(
2003
).
30.
E.
Matito
,
J.
Poater
,
M.
Duran
, and
M.
Solà
,
ChemPhysChem
7
,
111
(
2006
).
31.
B.
Silvi
,
J. Phys. Chem. A
107
,
3081
(
2003
).
32.
M.
Kohout
,
K.
Pernal
,
F. R.
Wagner
, and
Y.
Grin
,
Theor. Chem. Acc.
112
,
453
(
2004
).
33.
M.
Kohout
,
Int. J. Quantum Chem.
97
,
651
(
2004
).
34.
J. F.
Dobson
,
J. Chem. Phys.
94
,
4328
(
1991
);
J. F.
Dobson
,
J. Chem. Phys.
98
,
8870
(
1993
).
35.
J. C.
Kimball
,
Phys. Rev. B
14
,
2371
(
1976
).
36.
M.
Kohout
,
K.
Pernal
,
F. R.
Wagner
, and
Y.
Grin
,
Theor. Chem. Acc.
113
,
287
(
2005
).
37.
A.
Scemama
,
P.
Chaquin
, and
M.
Caffarel
,
J. Chem. Phys.
121
,
1725
(
2004
).
38.
J.
Cioslowski
and
G. H.
Liu
,
J. Chem. Phys.
109
,
8225
(
1998
).
39.
J.
Poater
,
M.
Solà
,
M.
Duran
, and
X.
Fradera
,
Theor. Chem. Acc.
107
,
362
(
2002
).
40.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al, GAUSSIAN 03,
Gaussian, Inc.
, Pittsburgh, PA,
2003
.
41.
S.
Noury
,
X.
Krokidis
,
F.
Fuster
, and
B.
Silvi
,
Comput. Chem. (Oxford)
23
,
597
(
1999
).
42.
A.
Szabo
and
N. S.
Ostlund
,
Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory
(
McGraw-Hill
,
New York
,
1982
).
43.
K.
Raghavachari
and
J. A.
Pople
,
Int. J. Quantum Chem.
20
,
1067
(
1981
).
45.
H.
Schmider
,
R. P.
Sagar
, and
V. H.
Smith
,
J. Chem. Phys.
94
,
8627
(
1991
).
46.
R. P.
Sagar
,
A. C. T.
Ku
,
V. H.
Smith
, and
A. M.
Simas
,
J. Chem. Phys.
88
,
4367
(
1988
);
M.
Kohout
,
A.
Savin
, and
H.
Preuss
,
J. Chem. Phys.
95
,
1928
(
1991
).
47.
M.
Kohout
,
Int. J. Quantum Chem.
83
,
324
(
2001
).
48.
K. B.
Wiberg
,
C. M.
Hadad
,
T. J.
Lepage
,
C. M.
Breneman
, and
M. J.
Frisch
,
J. Phys. Chem.
96
,
671
(
1992
);
L. C.
Wang
and
R. J.
Boyd
,
J. Chem. Phys.
90
,
1083
(
1989
).
49.
R.
Daudel
,
H.
Brion
, and
S.
Odiot
,
J. Chem. Phys.
23
,
2080
(
1955
).
50.
R.
Ponec
and
J.
Chaves
,
J. Comput. Chem.
26
,
1205
(
2005
).
51.
A.
Gallegos
,
R.
Carbó-Dorca
,
F.
Lodier
,
E.
Cances
, and
A.
Savin
,
J. Comput. Chem.
26
,
455
(
2005
).
52.
M.
Solà
,
J.
Mestres
,
R.
Carbó
, and
M.
Duran
,
J. Chem. Phys.
104
,
636
(
1996
).
53.
L.
Horny
,
K. W.
Sattelmeyer
, and
H. F.
Schaefer
,
J. Chem. Phys.
119
,
11615
(
2003
).
54.
B. G.
Johnson
,
P. M. W.
Gill
, and
J. A.
Pople
,
J. Chem. Phys.
98
,
5612
(
1993
).
You do not currently have access to this content.