A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed “quasiatomic minimal-basis-sets” is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn–Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.

1.
K. Ruedenberg has heard R. S. Mulliken make this remark in many discussions, public and private, in the early 1950s.
2.
K. Ruedenberg and K. R. Sundberg, in Quantum Science, edited by (J.-L. Calais, O. Goscinski, J. Linderberg, and Y. Öhrn (Plenum, New York, 1976), p. 505;
L. M.
Cheung
,
K. R.
Sundberg
, and
K.
Ruedenberg
,
J. Am. Chem. Soc.
100
,
8024
(
1978
);
L. M.
Cheung
,
K. R.
Sundberg
, and
K.
Ruedenberg
,
Int. J. Quantum Chem.
16
,
1103
(
1979
);
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
41
(
1982
);
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
51
(
1982
);
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
65
(
1982
);
D. F.
Feller
,
M. W.
Schmidt
, and
K.
Ruedenberg
,
J. Am. Chem. Soc.
104
,
960
(
1982
).
3.
P. E. H.
Siegbahn
,
A.
Heiberg
,
B. O.
Roos
, and
B.
Levy
,
Phys. Scr.
21
,
323
(
1980
);
B. O.
Roos
,
P. R.
Taylor
, and
P. E. M.
Siegbahn
,
Chem. Phys.
48
,
157
(
1980
);
B. O.
Roos
,
Int. J. Quantum Chem., Symp.
14
,
175
(
1980
);
P. E. M.
Siegbahn
,
J.
Almlöf
,
A.
Heiberg
, and
B. O.
Roos
,
J. Chem. Phys.
74
,
2384
(
1981
).
4.
(a)
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
41
(
1982
);
(b)
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
51
(
1982
);
(c)
K.
Ruedenberg
,
M. W.
Schmidt
,
M. M.
Gilbert
, and
S. T.
Elbert
,
Chem. Phys.
71
,
65
(
1982
);
(d)
S. S.
Xantheas
,
P.
Valtazanos
, and
K.
Ruedenberg
,
Theor. Chim. Acta
78
,
327
(
1991
).
5.
J. Ivanic and K. Ruedenberg (unpublished).
6.
See, e.g.,
T. R.
Cundari
and
M. S.
Gordon
,
J. Am. Chem. Soc.
113
,
5231
(
1991
).
7.
See, e.g., W. England, L. S. Salmon, and K. Ruedenberg, Topics in Modern Chemistry (Springer, Heidelberg, 1971), Vol. 23, p. 31.
8.
R. S.
Mulliken
,
J. Chem. Phys.
23
,
1833
(
1955
);
R. S.
Mulliken
,
J. Chem. Phys.
23
,
1841
(
1955
);
R. S.
Mulliken
,
J. Chem. Phys.
23
,
2338
(
1955
);
R. S.
Mulliken
,
J. Chem. Phys.
23
,
2343
(
1955
).
A review is given in R. S. Mulliken and W. C. Ermler, Diatomic Molecules (Academic, New York, 1977), Sec. II E.
9.
R. S.
Mulliken
,
J. Chem. Phys.
36
,
3428
(
1962
).
10.
E. R.
Davidson
,
J. Chem. Phys.
46
,
3320
(
1967
).
11.
K. R.
Roby
,
Mol. Phys.
27
,
81
(
1974
).
12.
R.
Heinzmann
and
R.
Ahlrichs
,
Theor. Chim. Acta
42
,
33
(
1976
);
C.
Ehrhardt
and
R.
Ahlrichs
,
Theor. Chim. Acta
68
,
231
(
1985
).
13.
W. H.
Adams
,
J. Chem. Phys.
37
,
2009
(
1962
);
W. H.
Adams
,
Chem. Phys. Lett.
12
,
295
(
1971
).
14.
P. W.
Anderson
,
Phys. Rev. Lett.
21
,
13
(
1968
);
J. D.
Weeks
,
P. W.
Anderson
, and
A. G. H.
Davidson
,
J. Chem. Phys.
58
,
1388
(
1973
).
15.
J. P.
Foster
and
F.
Weinhold
,
J. Am. Chem. Soc.
102
,
7211
(
1980
);
A. E.
Reed
,
R. B.
Weinstock
, and
F.
Weinhold
,
J. Chem. Phys.
83
,
735
(
1985
);
A. E.
Reed
and
F.
Weinhold
,
J. Chem. Phys.
83
,
1736
(
1985
);
L. A.
Curtiss
and
F.
Weinhold
,
Chem. Rev.
88
,
899
(
1988
).
16.
M. S.
Lee
and
M.
Head-Gordon
,
J. Chem. Phys.
107
,
9085
(
1997
);
M. S.
Lee
and
M.
Head-Gordon
,
Comput. Chem. (Oxford)
24
,
295
(
2000
).
17.
M. S.
Lee
and
M.
Head-Gordon
,
Int. J. Quantum Chem.
76
,
169
(
2000
).
18.
D.
Sanchez-Portal
,
E.
Artacho
, and
J. M.
Soler
,
J. Phys.: Condens. Matter
8
,
3859
(
1996
).
19.
I.
Mayer
,
Can. J. Chem.
74
,
939
(
1996
).
20.
J.
Cioslowski
and
A.
Liashenko
,
J. Chem. Phys.
108
,
4405
(
1998
).
21.
These quasiatomic orbitals thus satisfy the criterion postulated by J. Cioslowski and A. J. Liashenko in Ref. 20, inasmuch as their definition is not contingent upon the atom-centered basis functions used to calculate the molecular orbitals in practice.
22.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
);
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
);
W.
Kohn
,
Rev. Mod. Phys.
71
,
1253
(
1999
).
23.
S. F.
Boys
,
Rev. Mod. Phys.
32
,
300
(
1960
).
24.
K.
Fukui
,
J. Chem. Phys.
20
,
722
(
1952
);
K.
Fukui
,
Acc. Chem. Res.
4,
57
(
1971
);
K.
Fukui
,
Science
218
,
747
(
1982
);
R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry (Academic, New York, 1970). See also Chap. 1 of E. A. Halevi, Orbital Symmetry and Reaction Mechanism (Springer, Berlin, 1992).
25.
J. L.
Whitten
,
J. Chem. Phys.
56
,
5458
(
1972
);
J. L.
Whitten
,
Phys. Rev. B
21
,
4357
(
1979
);
Ch. W.
Bauschlicher
,
J. Chem. Phys.
72
,
880
(
1980
);
D.
Feller
and
E. R.
Davidson
,
J. Chem. Phys.
74
,
3977
(
1981
).
26.
W. C. Lu, C. Z. Wang, T. L. Chan, K. Ruedenberg, and K. M. Ho (unpublished).
27.
J. Ivanic and K. Ruedenberg (unpublished). This method of determining molecule-intrinsic directed quasiatomic hybrid orbitals is applicable regardless whether the QUAMBOs have been orthogonalized between atoms or not.
28.
Alternative bond order definitions have been given by
I.
Mayer
,
Int. J. Quantum Chem.
29
,
73
(
1986
);
I.
Mayer
,
Int. J. Quantum Chem.
29
,
477
(
1986
).
29.
J. E.
Lennard-Jones
and
J. A.
Pople
,
Proc. R. Soc. London, Ser. A
202
,
166
(
1950
);
C.
Edmiston
and
K.
Ruedenberg
,
Rev. Mod. Phys.
35
,
457
(
1963
);
R. C.
Raffenetti
,
K.
Ruedenberg
,
C. L.
Janssen
, and
H. F.
Schaefer
,
Theor. Chim. Acta
86
,
149
(
1993
).
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