The primary purpose of the present series of papers is to give more explicit mathematical form to the theory of Mulliken and Hund, and in some instances to the alternative theories of Pauling and Slater and of Heitler and Rumer, for valence in carbon compounds. A critical comparison is given of the Slater‐Pauling and Hund‐Mulliken concepts of CH4, which are based respectively on localized bonds (``electron pairs'') with the Heitler‐London method, and on one‐electron wave functions (Mulliken's ``orbitals'') for a self‐consistent field with tetrahedral symmetry. The H‐M procedure avoids hybridization of the carbon 2s and 2p wave functions, but allows two (though never three or more) electrons to accumulate on one H atom, as well as up to eight on a C atom. Inadequate cognizance is thus taken of the tendency of inter‐electronic Coulomb forces to keep two electrons apart. The S‐P procedure avoids this excessive accumulation, but at the expense of not letting an individual wave function be of a symmetry type (irreducible group representation) appropriate to a tetrahedral field. In particular, its s‐p hybridization ``undiagonalizes'' the internal energy of the C atom. These points are illustrated by explicit exhibition of the secular determinant, which is the main new feature. Because inter‐electronic repulsions make the dynamical problem more complicated than a one‐electron one, the tetrahedral symmetry need only be preserved in the properties of the total wave function of the entire system rather than that of one electron, but the departures from individual tetrahedral symmetry should be less than in the Slater‐Pauling theory if the Hartree self‐consistent field is really a good approximation. Thus both the H‐M and S‐P methods, though qualitatively exceedingly illuminating, have their own characteristic drawbacks from a quantitative standpoint unless refined by inclusion of higher approximations which ultimately merge the two methods but which practically are very difficult to make.

1.
A preliminary account was given at the Washington meeting of the American Physical Society, April, 1932, (abstract in
Phys. Rev.
40
,
1037
(
1932
)).
2.
Since we are here confining our attention to theories of directed or orbital valence, we do not need to include in the present discussion the Heitler‐Rumer treatment of carbon compounds, in which the directional properties exist only in virtue of the repulsions between the atoms attached by the central carbon atom. This Heitler‐Rumer method must not, however, be overlooked and will be compared with the other methods in Part III.
3.
J. C.
Slater
,
Phys. Rev.
37
,
481
;
J. C.
Slater
,
38
,
1109
(
1931
).,
Phys. Rev.
4.
L.
Pauling
,
J. Am. Chem. Soc.
53
,
1367
,
3225
(
1931
).
5.
M.
Born
,
Zeits. f. Physik
64
,
729
;
M.
Born
,
65
,
718
(
1930
).
6.
F.
Hund
,
Zeits. f. Physik
73
,
1
,
565
;
F.
Hund
,
74
,
429
(
1931–2
).
7.
R. S.
Mulliken
,
Phys. Rev.
40
,
55
;
R. S.
Mulliken
,
41
,
49
(
1932
).,
Phys. Rev.
8.
H.
Bethe
,
Ann. d. Physik
3
,
133
(
1929
).
9.
A. S.
Coolidge
has recently made a calculation of H2O by the Slater‐Pauling method without the use of as many approximations as (a)‐(e); (
Phys. Rev.
42
,
189
(
1932
)). Unfortunately the accord with experiment is poor, suggesting that the close agreement achieved with the less refined calculations is perhaps somewhat accidental.
10.
In unpublished work, Mulliken has also independently found that the functions ψ1,ψ2,ψ3,ψ4 defined in (3) are linear combinations of the H wave functions appropriate to the tetrahedral symmetry. Mulliken’s method of obtaining the combinations was a study of general symmetry properties rather than of the secular determinant. He has also thus deduced independently the trigonal wave functions to be given in Eq. (29) of Part II.
11.
J. C.
Slater
,
Phys. Rev.
34
,
1293
(
1929
).
12.
See discussion by
R. S.
Mulliken
,
Phys. Rev.
41
,
69
71
(
1932
)
based on a calculation by
Slater
,
Phys. Rev.
35
,
514
515
(
1930
).,
Phys. Rev.
13.
Do not confuse our references to the higher and lower roots of an individual determinant of (4) with the upper and lower choices of sign which yield the two determinants.
14.
Here, as usual, the notation ψg,ψu means wave functions respectively even and odd with respect to reflection in the midpoint of the internuclear axis. The corresponding notation in reference 12 is φ0,φ1.
15.
W.
Heitler
and
G.
Herzberg
,
Zeits. f. Physik
53
,
52
(
1929
).
16.
The location of the remaining term sp33S is unknown.
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