With increasing availability of good all‐electron LCAO MO (LCAO molecular orbital) wave functions for molecules, a systematic procedure for obtaining maximum insight from such data has become desirable. An analysis in quantitative form is given here in terms of breakdowns of the electronic population into partial and total ``gross atomic populations,'' or into partial and total ``net atomic populations'' together with ``overlap populations.'' ``Gross atomic populations'' distribute the electrons almost perfectly among the various AOs (atomic orbitals) of the various atoms in the molecule. From these numbers, a definite figure is obtained for the amount of promotion (e.g., from 2s to 2p) in each atom; and also for the gross charge Q on each atom if the bonds are polar. The total overlap population for any pair of atoms in a molecule is in general made up of positive and negative contributions. If the total overlap population between two atoms is positive, they are bonded; if negative, they are antibonded.

Tables of gross atomic populations and overlap populations, also gross atomic charges Q, computed from SCF (self‐consistent field) LCAO‐MO data on CO and H2O, are given. The amount of s‐p promotion is found to be nearly the same for the O atom in CO and in H2O (0.14 electron in CO and 0.15e in H2O). For the C atom in CO it is 0.50e. For the N atom in N2 it is 0.26e according to calculations by Scherr. In spite of very strong polarity in the π bonds in CO, the σ and π overlap populations are very similar to those in N2. In CO the total overlap population for the π electrons is about twice that for the σ electrons. The most easily ionized electrons of CO are in an MO such that its gross atomic population is 94% localized on the carbon atom; these electrons account for the (weak) electron donor properties of CO. A comparison between changes of bond lengths observed on removal of an electron from one or another MO of CO and H2, and corresponding changes in computed overlap populations, shows good correlation. Several other points of interest are discussed.

1.
C. C. J.
Roothaan
,
Revs. Modern Phys.
23
,
69
(
1951
).
2.
Breakdowns of the total charge into overlap and “net” atomic populations have been in use for some time, e.g.,
R. S.
Mulliken
,
Phys. Rev.
41
,
66
(
1932
);
R. S.
Mulliken
,
J. Chem. Phys.
3
,
573
(
1935
), Eqs. (38), (39), (42).
3.
The first of Eqs. (4) in general form was given by
R.
McWeeny
,
J. Chem. Phys.
19
,
1614L
(
1951
)
and
R.
McWeeny
,
20
,
920
(
1952
); what is here called “overlap population” he called “bond charge.” The former term is preferred here because it is more accurately, or at least more unambiguously, descriptive.,
J. Chem. Phys.
4.
The first of Eqs. (5) is given in reference 3, where n(i;rk) is called the “atom charge.”
5.
C. W.
Scherr
,
J. Chem. Phys.
23
,
569
(
1955
). See Appendix II for invariance theorems. Scherr has used the methods and notation of the present paper, which was prepared some time ago in preliminary form, in discussing his results on N2.
6.
R. S.
Mulliken
,
J. Chim. Phys.
46
,
675
(
1949
), Sec. 21. The present N(i;rk) is there called Fri: see Eq. (139) there.
7.
B. H.
Chirgwin
and
C. A.
Coulson
,
Proc. Roy. Soc. (London)
201A
,
196
(
1950
), who speak of “formal charges” for what are here called “gross populations.” Also reference 3.
8.
Reference 6, footnote 73.
9.
Reference 2, Eq. (39).
10.
R. S.
Mulliken
,
J. Phys. Chem.
56
,
295
(
1952
).
11.
J. F.
Mulligan
,
J. Chem. Phys.
19
,
347
(
1951
).
12.
R. C.
Sahni
,
Trans. Faraday Soc.
49
,
1
(
1953
).
13.
I.
Fischer
,
Arkiv Fysik
5
,
349
(
1952
).
14.
J.
Higuchi
,
J. Chem. Phys.
22
,
1339
(
1954
).
15.
A. B. F.
Duncan
,
J. Chem. Phys.
20
,
951
(
1952
);
A. B. F.
Duncan
,
J. Am. Chem. Soc.
77
,
2107
(
1955
).
16.
F. O.
Ellison
and
H.
Shull
,
J. Chem. Phys.
21
,
1420
(
L
(
1953
) and later full paper.
17.
R. C. Sahni (to be published).
18.
H. Kaplan, on p. 30 of Quarterly Progress Report for October 15, 1954 of the Solid‐State and Molecular Theory Group at the Massachusetts Institute of Technology, Cambridge, Massachusetts.
19.
See Sec. 6 of reference 6.
20.
R. S.
Mulliken
,
J. Am. Chem. Soc.
74
,
811
(
1952
), p. 822–823.
21.
C. A.
Coulson
,
Proc. Roy. Soc. (London)
207A
,
63
(
1951
).
22.
Similar results as to amounts of promotion in first‐row atoms have been obtained in reference 10 by use of the magic formula method, and (see survey in Sec. XII of reference 10) by other methods.
23.
D. F.
Heath
and
J. W.
Linnett
,
Trans. Faraday Soc.
44
,
556
(
1947
) on H2O;
Heath
,
Linnett
, and
Wheatley
,
Trans. Faraday Soc.
46
,
137
(
1950
), on H2O,H2S,H2Se,NH3,AsH3,CH4, etc.; ,
Trans. Faraday Soc.
T.
Simanouti
,
J. Chem. Phys.
17
,
245
,
734
(
1949
);
Heath
and
Linnett
,
J. Chem. Phys.
18
,
147
(
1950
).
This content is only available via PDF.
You do not currently have access to this content.