Using the absorption frequencies measured by Robinson and DiGiorgio, a rotational analysis of the 0+←0 and 1+←0 bands of the 3A21A1 transition in H2CO has been performed. Each band contains a number of overlapping subbands which are themselves made up of several branches consisting of individual rotational lines. Despite the overlapping, it was found possible to give assignments to a large number of lines. All branches are q‐type branches; that is, only ΔK = 0 transitions are observed. The positions of the triplet‐state rotational levels relative to the lowest rotational level of the ground vibronic state were obtained with the aid of the very accurate ground‐state rotational levels determined interferometrically by Parkin and Poole. These triplet‐state levels were found to fit accurately the Hamiltonian proposed by Van Vleck for an asymmetric‐rotor molecule in a triplet electronic state provided that further terms were added to take account of rotational distortion.

Values of the rotational constants, rotational distortion constants, and spin‐interaction constants of the 3A2(0+) and 3A2(1+) states have been determined. The rotational constants for the 3A2(1+) state are as follows: A = 8.6275 (±0.0008) cm−1; B = 1.1491 (±0.0001) cm−1; and C = 1.0343 (±0.0001) cm−1. The results for the 3A2(0+) state are very similar. From these constants it is possible to show that the equilibrium nuclear geometry of formaldehyde in this state is highly nonplanar, the geometrical parameters having the following values: r(C–H) = 1.10 Å; r(C–O) = 1.28 Å; ∠HCH = 118°; out‐of‐plane angle = 36°. The spin‐interaction constants, which determine the extent of the triplet splitting of the rotational levels, take account not only of spin—molecular rotation, spin—orbit, spin—other‐orbit, and spin—spin interactions, but also of the effect of rotational asymmetry upon these interactions. The observed relative intensities of the rotational lines agree very well with those predicted by the recent theory of Hougen. In particular, the almost complete absence in the spectrum of transitions to the F2 component of the triplet state is understandable in the light of this theory. As a consequence of the fact that only ΔK = 0 transitions are observed (the theoretically possible ΔK = ±2 transitions were not detected), it is possible to deduce with the aid of Hougen's theory that it is a 1A1 state that, by spin—orbit coupling with the 3A2 state, permits the formally forbidden triplet←singlet bands to occur. This result is in complete agreement with the theoretical deductions of Sidman made some years ago.

1.
In describing transitions between two states, we adopt the convention of writing the upper state first and the lower state second.
2.
G. W. Robinson, in Experimental Methods of Molecular Physics, edited by D. Williams (Academic Press Inc., New York, 1962), Vol. 3, p. 208.
3.
G. W.
Robinson
and
V. E.
DiGiorgio
,
Can. J. Chem.
36
,
31
(
1958
).
4.
V. E.
DiGiorgio
and
G. W.
Robinson
,
J. Chem. Phys.
31
,
1678
(
1959
).
5.
V. E. DiGiorgio, thesis, Johns Hopkins University, 1959.
6.
A. J.
Merer
,
Discussions Faraday Soc.
35
,
127
(
1963
).
7.
G.
Herzberg
and
R. D.
Verma
,
Can. J. Phys.
42
,
395
(
1964
).
8.
J. H.
Van Vleck
,
Rev. Mod. Phys.
23
,
213
(
1951
).
9.
D. W.
Posener
and
M. W. P.
Strandberg
,
Phys. Rev.
95
,
374
(
1954
);
D. W.
Posener
and
M. W. P.
Strandberg
,
96
,
1714
(
1954
).,
Phys. Rev.
10.
W. T.
Raynes
,
J. Chem. Phys.
41
,
3020
(
1964
).
11.
J. T.
Hougen
,
Can. J. Phys.
42
,
433
(
1964
).
12.
See Table III of Ref. 3.
13.
H. J.
Bernstein
and
G.
Herzberg
,
J. Chem. Phys.
16
,
30
(
1948
).
14.
This situation probably arises because of a large dipole‐moment reduction upon excitation. Such a reduction is known to occur in the A12A11 transition [
D. E.
Freeman
and
W.
Klemperer
,
J. Chem. Phys.
40
,
604
(
1964
)]. A statistical average over the dipole‐dipole contribution to the transition energy would contribute to the line broadening.
15.
F. S.
Tomkins
and
M.
Fred
,
J. Opt. Soc. Am.
41
,
641
(
1951
);
G. H.
Dieke
,
D.
Dimock
, and
H. M.
Crosswhite
,
J. Opt. Soc. Am.
46
,
456
(
1956
).,
J. Opt. Soc. Am.
16.
R. S.
Mulliken
,
J. Chem. Phys.
3
,
564
(
1935
).
17.
H. L.
McMurry
and
R. S.
Mulliken
,
Proc. Natl. Acad. Sci. U.S.
26
,
312
(
1940
).
18.
H. L.
McMurry
,
J. Chem. Phys.
9
,
231
(
1941
).
19.
A. D. Walsh, J. Chem. Soc. 1953, 2306.
20.
See, for example,
J. M.
Foster
and
S. F.
Boys
,
Rev. Mod. Phys.
32
,
303
(
1960
).
21.
Compare, for example, the orbital descriptions given here (based on Ref. 20) with the ones given on p. 32 of Ref. 3 which were obtained from a combination of what was thought to be the “best” parts of Refs. 16–19.
22.
J. C. D. Brand, J. Chem. Soc. 1956, 858.
23.
G. W.
Robinson
,
Can. J. Phys.
34
,
699
(
1956
).
24.
A. D.
Cohen
and
C.
Reid
,
J. Chem. Phys.
24
,
85
(
1956
).
25.
W. H.
Eberhardt
and
H.
Renner
,
J. Mol. Spectry.
6
,
483
(
1961
).
26.
J. W.
Sidman
,
J. Chem. Phys.
29
,
644
(
1958
).
27.
D. A. Ramsay, in The Determination of Organic Structures by Physical Methods, edited by F. C. Nachod and W. D. Phillips (Academic Press Inc., New York, 1962), p. 245.
28.
J. C. D.
Brand
and
D. G.
Williamson
,
Advan. Phys. Org. Chem.
1
,
365
(
1963
).
29.
J. H.
Callomon
and
K. K.
Innes
,
J. Mol. Spectry
,
10
,
166
(
1963
). In references dating earlier than this one, for example, Refs. 3, 5, 22, 27, and 28, the Vibrational analysis of the A121A1 transition of formaldehyde is apparently incorrect. The previous upper‐state Vibrational assignments were based wholly on a comparison with known ground‐state fundamentals, since at that time no rotational analysis near the center of the bands had been carried out. This reasoning led to the assignments ν3 = 1321 cm−1 and ν1 = 1321 cm−1 for the totally symmetric CH2 “in‐plane” bend and the totally symmetric CH stretch in the A12 excited electronic state of H2CO. In the A11 ground state of H2CO the corresponding values are ν3 = 1503 cm−1 and ν1 = 2780 cm−1. However, a closer examination of the bands supposedly involving these modes led Callomon and Innes to the conclusion that they were not Type B, as expected on the basis of the earlier assignments, but instead were Type C. A reassignment consistent with the findings of Callomon and Innes would give the following A12 fundamentals for H2CO:ν1 =  (not yet observed); ν2 = 11777 cm−1, unchanged from previous assignments; ν3 =  (not yet observed); ν4 = inversion, unchanged from previous assignments; ν5 = 2968 cm−1; and ν6 = 1445 cm−1. [For comparison of assignments, note that Callomon and Innes have adopted the numbering of Brand,22 while we adhere to the scheme recommended by Mulliken.30 Compare the schemes (a) and (d) in the footnote on p. 699 of Ref. 23.] In the A11 ground state ν2 = 1738 cm−1,ν5 = 2874 cm−1, and ν6 = 1280 cm−1. Note that, according to the new assignment, both ν5 and ν6 increase in magnitude upon excitation.
30.
R. S.
Mulliken
,
J. Chem. Phys.
23
,
1997
(
1955
).
31.
S. E.
Hodges
,
J. R.
Henderson
, and
J. B.
Coon
,
J. Mol. Spectry.
2
,
99
(
1958
).
32.
G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Company, Inc., New York, 1945), p. 51.
33.
J. T.
Hougen
,
J. Chem. Phys.
39
,
358
(
1963
).
34.
G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., New York, 1950).
35.
J. E. Parkin and H. G. Poole, University College London (unpublished results).
36.
H. G. Poole, W. T. Raynes, and B. C. Stace, in Advances in Molecular Spectroscopy, edited by A. Mangini (Pergamon Press Ltd., London, 1962). Vol. 3, p. 1343.
37.
As used in the present paper this expression denotes the mean of the deviations when the signs of these deviations are all made positive.
38.
Reference 34, p. 191.
39.
G. W.
King
,
R. M.
Hainer
, and
P. C.
Cross
,
J. Chem. Phys.
11
,
27
(
1943
).
40.
G. W. Robinson (private communication).
41.
G. H.
Dieke
and
G. B.
Kistiakowsky
,
Phys. Rev.
45
,
4
(
1934
);
and unpublished results given to G. W. Robinson by G. H. Dieke.
42.
T.
Oka
,
H.
Hirakawa
, and
K.
Shimoda
,
J. Phys. Soc. Japan
15
,
2265
(
1960
);
T. Oka, ibid., p. 2274.
43.
J. E. Parkin, thesis, University of London, 1962.
44.
J. M.
Dowling
,
J. Mol. Spectry.
6
,
550
(
1961
).
45.
L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, New York, 1960), 3rd ed., p. 231.
46.
The neglect of the Vibrational contribution to the inertial defect results in the calculated out‐of‐plane angle being somewhat smaller than the correct value. This problem has been discussed by
T.
Oka
and
Y.
Morino
[
J. Mol. Spectry.
6
,
472
(
1961
);
T.
Oka
and
Y.
Morino
,
11
,
349
(
1963
)], but the theory for a molecule which can undergo inversion doubling has not yet been developed.
Nevertheless with the aid of the “uniform coupling” approximation of
D. R.
Herschbach
and
V. W.
Laurie
[
J. Chem. Phys.
40
,
3142
(
1964
)],
T. Oka (private communication) has been able to estimate that the contribution of Vibrational motion to the inertial defect in H2CO is 0.045 amu⋅Å2. From this it can be deduced that better values for the out‐of‐plane angle for the triplet state are as follows: 39° for the A12(0+) state and 37° for the A32(1+) state.
47.
J. A.
Pople
and
J. W.
Sidman
,
J. Chem. Phys.
27
,
1270
(
1957
).
48.
M. McCarty, V. E. DiGiorgio, and G. W. Robinson, work reported in DiGiorgio’s thesis (Ref. 5), pp. 20‐21. In that work, an analysis by M. McCarty, Jr., showed that the lower state of these transitions is the ground Vibronic state of formaldehyde. It showed no electric‐quadrupole branches, and further it showed no anomalous K subband intensities thus eliminating the idea that the bands arise from a rotational‐electronic interaction (Ref. 47). Symmetry arguments coupled with the observed intensity then lead to the magnetic‐dipole interpretation. A similar line of thought was used by Callomon and Innes29 in their more extensive analysis.
49.
See the brief discussion on p. 451 of Ref. 11. The central point is that the symmetry properties with respect to exchange of protons depend only on the space part of the eigenfunction and not on the total space×electron spin eigenfunction.
50.
A. E.
Douglas
and
E. R. V.
Milton
,
J. Chem. Phys.
41
,
357
(
1964
).
51.
J. T.
Hougen
,
J. Chem. Phys.
41
,
363
(
1964
).
52.
R. S.
Henderson
,
Phys. Rev.
100
,
723
(
1955
);
C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (McGraw‐Hill Book Company, Inc., New York, 1955), pp. 192–193; see also Ref. 2, pp. 202–203.
53.
Reference 2, p. 203 when the factor (hc)−1 is incorporated.
54.
For a near‐symmetric rotor, wτJ(b)≈K2. A good discussion can be found in C. H. Townes and A. L. Schawlow, Ref. 52; see Chap. 4.
55.
G. W.
Robinson
,
J. Chem. Phys.
27
,
1227
(
1957
).
56.
See, for example,
G.
Herzberg
and
K. K.
Innes
,
Can. J. Phys.
35
,
842
(
1957
).
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