Ring Frequencies.-- 1x1 tlie isolated D 3 1 ~ cyanuric both increases in intensity and shifts slightly to acid molecule one should expect four ring stretching higher frequency. The small frequency shift frequencies, of which two, of symmetry class AI' could be accounted for by an interaction between and Az', are inactive in the infrared. Of the two the two vibrations. Presumably the only out of doubly degenerate E' pairs one should probably be plane fundamentals which could lie in this region quite active and tlu other only moderately so. are the N-H and C=O bendings. We tentatively l i the ring were stripped of peripheral atoms this ascribe 807 cm-' to the former, though the frevibration would become virtually inactive due to quency seems rather low for this mode, and 765 tlie near equality of the inasses of nitrogen and to the latter. I n a previous investigations the out carbon atoms. In the reduced symmetry oi the of plane C=O bend in urea was ascribed to i n 0 crj-stal, the vibration derived from AI' might be- cm. - I c'oiiie weakly active, but the At' mode should Conclusion warcely be expected to gain significant activity. As has been shown above the infrared observaA s was mentioned above, the splitting of the 11' lions are compatible with it previous X-ray struc~ u i r siiiight well be rather small. L1 e ascribe the single intense arid unpolarized ture determination as Ear 2s the presence uE an essetitially sytiinirtric~alring is concerned ; biit arc t u i i t l a t 1470 CIII. * to one of these pairs mcl the perpendicularly polarized narrow doublet a t 1050 in disagreement in regard to the periphery of the and LO65 c m - ' to the other. Sone of these bands cyanuric acid molecule. In contradiction to the shows appreciable shift on deuteration. The last X-ray determiriation i t appears very probable that nientioned doublet, however, appears to suffer all C-0 distances ar,e nearly equal and are not significant decrease in intensity on deuteriuni greater than the 1.25 A. found in diketopiperazine. substitution, though our observations are very The N-H...O hydrogen bond distances, on the qualitative. This is perhaps not surprising since other hand, are probably not all equal. The for reasons mentioned above one of the E' pairs stronger bond appears to be formed in the case iiiay owe a considerable portion of its moderate when the C=O and N...O directions make an angle intensity to the small motions of peripheral atoms, of around 124" with each other. The bonds tlie amplitudes of which may be significantly parallel to the b axis must be lengthened corresponding to the shortening of the C=O distance, and tbe affected by deuteration. Out of Plane Vibrations.-From their relatively S-H.s.0 distance is probably not less than 2.87 A. Acknowledgment.-We are indebted to Dr. R. A. high intensity in the powder spectrum as compared with that of the (101) crystal, it is probable that Pasternak for the X-ray measurements made in 807 and 765 cni.-' correspond to out of plane vibra- connection with the verification of the orientation of the cyanuric acid crvstals. tions. The foriiier appears to shift to 570 cni. mi deuteration (807 570 = 1.4), while the latter PASADEYA 1,CALIFORUIA
[ C O N T R I R l T I O S FROM 'THE b'IALLINCKRODT CFIEMICAL L A R O R A T O R Y , ITARVARn T'NIVBRSITY
]
The Microwave Spectrum and Structure of Methylene Fluoride' BY DAVIDR.LIDE,JR.' RECEIVED A P R I L 9, 1952 The IC-band microwave spectrum of the slightly asymmetric rotor CH~FD. has been recorded and analyzed. Many of the lines appear as close doublets which are due to asymmetry splitting of levels which would be degenerate in the limiting synimetric rotor. The rotational constants determined from the three lines of lowest J values are a = 49,138.4 mc.; b = 10,603.89 nic.; and c = 9249.20 y c . With the aid of twojines of Cl3HaF*the following structural parameters have bee11 calculated: 7CF = 1.358 f 0.001 A . , ~ C H= 1.092 f 0.003 A . , L FCF = 108" 17' f 6', LHCH = 111' 52' f 25'. Stark rffect measurements give a dipole moment of 1.96 f 0.02 debye units.
The structure of methylene fluoride, CH2F2, has previously been studied by electron diffraction3 and by high-resolution infrared spectroscopy, with results in rather poor agreement. The dipole moment has not been reported. The structure of this molecule is of interest in connection with recent radio-frequency and microwave spectroscopic investigations of other halogenated methanes, which have yielded useful information on the nature of the chemical bond. The available structural information indicated 1 ) 1 he resedrch r e p o r t e d i n t h i \ p a p e r wd, mdde p o w b l e b y slip port r x t e u d e d I l a r b d r d 7 u i r e r s i t y h v the 0 8 i r r u[ Y L \i l Kr\cariIi ,iildrr 0 h ' R C o n t r a c t Niori 7b 'I a\k Order \ 1) \ t d n d a r d Oil of C d i f o r m n Predoctordl 1 rllow 7 I 0 Hrochwav J Phv\ hrnr 4 1 1 R i l I q 7 7 4 11 I 3 \ I C ) > Gri i u t l I I II \ I C I c i i / ' I ] Kc 76 I 4 0 I i i I
-
that CHZF, should be a slightly asymmetric rotor (K -0.93) with dipole moment in the axis of intermediate moment of inertia (the C2symmetry axis). The magnitude of the reciprocal moments of inertia was such that the only transitions likely to fall below 40,000 mc. would be of the type A J = 1, AK = - 1. (The notation of King, Hainer and Cross5will be used, with K understood to mean XI.) Since transitions of this type are very sensitive to the exact values of the structural parameters, it was impossible to predict with any certainty the transitions which would fall in the .tccessible frequency region, sample of CH2F2wxs kindly provided by 17r.
+
( ? I
'7
(:
144 L
lk
hatir, 1< \ I
I l A t i i r r diu1
t'
(*
('rw\
I ( l i r i o f'tiv\
11
Application of the Wang splitting formula then cotifirmed the existence of a true series, as well as providing a value of the asymmetry parameter p. It is seen from the Wang formula that the ratio A V J , K / A V J + ~ , Kis+ ~proportional to /3. The five experimental splitting ratios formed in this way should therefore be predictable from a single value of p, provided that the J and K values of the beginning doublet are properly assigned. Calculations showed that consistency in this one parameter problem could be obtained only for a small number of assignments. The number was further limited by consideration of the absolute value of the splittings, the intensity alternation of the doublets, the actual intensities of the lines, and finally by tising the liiie frequencies to calculate a set of rough rotational constants. The discovery of another series of doublets a t lower frequency was also of help in the analysis. I t was possible with this information to make an unambiguous assignment of quantum numbers to each series, The original series ran from J,K = 20,s -+ l9,B to J , K = 40,lO -+ 39,11. IVhile the identification of the doublet series was the key to the analysis of the spectrum, the large centrifugal distortion a t these high J values made it impossible to obtain accurate rotational constants, However, the series did provide a good value of the parameter p, and this knowledge permitted a relatively easy trial-and-error fitting of the lines whose J values had been tentatively identified by Stark effects. A set of rotational constants was thus obtained which explained practically all of the thirty-odd lines observed, while predicting no unobserved lines in the region searched. The correctness of this analysis was further confirmed by Stark measurements on four lines. The observed Stark effects of the 21 2 3 0 , 3 , 51,6-+ where 42.2, 82 6 -+ 91,9,and 9?.1-+ 101.lotransitions agreed ( J + K)! quite well with the calculated pattern. Since the F(J,K) = 8 ( J - K ) ! ( K - l)!i calculations are sensitive to a large number of perc __ turbing levels, this agreement provides excellent p = _ _b_- _ a = h,'8r21,, etc. verification for the assignments. 2ia - ' / n ( b GI1 I n view of the uncertainty in methods for correctIt is apparent from this formula that the chief ing for centrifugal distortion in general asymmetric contribution to the line splitting will come from the level of smaller K . Rough calculations made by rotor transitions, it was decided not to attempt such means of Golden's Mathieu function procedure* a correction a t the present time. Instead, the indicated that the doublets above J = 20 should frequency range was extended to include the 41,3 -+ I , 3 2 . 2 transition a t 31,543.75 mc., and this line was tend to fall into series of the type J , K -+ J K - 1; J 4,K 1 -+ J 5, K ; etc., in which used with the 2 1 2 --+ 3 0 3 and 5 1 5 -+ 42.2 lines to the doublet splitting decreased monotonically with calculate the three rigid-rotor constants. Since increasing J . The reason for such a grouping, in centrifugal distortion should b e quite low a t these which J increases by four for each unit increase in J values, it is felt that the constants determined in K , can be seen from the very approximate equation this way are accurate enough for all present physical applications. ( I t should be mentioned that an for the frequency of the transition J,K -+ J alternative set of rigid-rotor constants, calculated 1,K-1 from a least squares fit of six lines of J < 10, v(mc ) -20,000 ( J + 1) - 40,000 (2R - 1) differed from these by only 0.008%.) The conWith this suggestion as a guide, i t was possible stants obtained from these three lines are given iri to pick out of the observed spectrum a series of six Table I ; this table also includes the approximate doublets, spaced about 2000 mc. apart, which rotational constants of Cl3H2F2, whose determinaseetned likely to satisfy the above requirements. tion is outlined in the next section. (6) K I3 McAfee, J r , R XI Hughe5 and F ~ L B Wtlsau Tr Rev In Table TI the observed frequencies of all lines S c r I n r f r u m c n l s , 10, 821 (19491 are conipared with rigid in the spectrum of C12H2F2 ( 7 ) s c W d n g PhVT Hlu 34, 243 (1929) rotor frrquencieq calct~lcitetlTro1n the constants 131 \ ( h l i l r r i I Clwiii Phv\ 16, 75 (1948)
D. E. Kvalnes of the Jackson Laboratory of E. I. du Pont de Nemours and Company. It was reported t o contain less than 0.3% impurities; no further purification was attempted. The spectrum was observed on a Stark modulation spectrographs which employed 100 kc. square wave modulation. The measured frequencies should be good to a t least 0.10 mc. Analysis of the Spectrum An initial search of the region from 17,000 to 31,000 mc. yielded approximately thirty lines of reasonable intensity. Stark effects indicated that most of these lines had fairly high J values. The most prominent feature of the spectrum was the tendency of the strongest lines to occur as close doublets. Since no hyperfine structure should be expected in CH2F2, the only reasonable explanation was that these doublets resulted from the asymmetry splitting of levels which would be degenerate in the limiting prolate symmetric rotor. Confirmation of this hypothesis was provided by the intensity variation bf the doublets; this agreed well with the 10:6 ratio expected from the nuclear spin weights which result from the equivalent hydrogen and fluorine atoms. On the basis of partially resolved Stark effects tentative J values could be assigned to three lines. Considering the complexity of the calculations and the large number of transitions which could still be assigned to these lines, a trial and error fit on the basis of this information alone was not practical. Consequently, attention was turned to the doublets in the spectrum. The asymmetry splitting of the J,K level of an almost prolate rotor has been given to first order by Wang? in the very convenient form
---f
+
+
+
+
+
+
in Table I. The final calculations were made with continued fraction^,^ and should be accurate to one or two units in the last figure for lhe transitions of J < 30. For the higher J levels, where the convergence was very slow, the computational errors should not exceed 10 mc. TABLE I ROTATIONAL e o S s T A N r S Ob C I ~ J F , L'2Ii:I 11
l) C I (1,
h
- (h
-t
I 1
+ c)/2 2
47, 720 10,604 O,I9X
: i i , 820 9,1!01 -I! !)270
9:i2077
TABLE I1 OBSERVED A N D CALCULATED SPECTRUM OF CH2F2 Observed f r e q u t n r ] , mc.
17,411 86 17,429 8'1 18,972 13 IQ,(J34 89 19,(139 76 20,237 69 20,199 85 20,500 3s 20,570 cid 20,571 99 21,423 30 21,934 33 21,980 68 22,135 41 22,137 33 22,204 18 22,579 40 23,188 45 23,864.92 23,871 82 24,297 52 24,760 40 25,669 29 25,694 13 27,516 98 27,603,66 29,268 90 29,339.38 29,624.66 29,630 87 30,679.01 30,962 OS 31,543 75 31,777 75
TABLE 111 DOUBLET SERIES
C'sIlzl't, mc
t i il1L
49,138.4 I O ,6(J;3 89 9,240 20 39,211 8 9,926 54 -0
Table I11 also gives a comparison of the observed doublet splittings with those calculated from the Wang formula. The discrepancy here is due partly to centrifugal distortion and partly to the nature of the Wang approximation. Exact calculations by means of continued fractions on the more widely split doublets gave splittings about 4% lower than the \Vmg fnrmula.
Calculated irequeiicy
18,707 18,727 16,674 20,816 20,822 20,226.4 18 800 18,801 22,943 22,947 ~
25,067 21,996.1 20 ,922 20,924 (22,204.18) 27,193 23 ,030 23 ,038 29,303 24,871 25,132 25,157 27,197 27,286 (29,268.90) 29,165 29,875 29,463 30,694.9 30,884
(31,543.75) 31,755
The properties of the two series of doublets are presented more clearly in Table 111. It is seen that the discrepancy between observed and calculated frequencies, which must be due almost entirely to centrifugal distortion, increases within mch series in a roughly exponential manner with increasing K . This variation is smooth enough to pemiit identification of the unresolved doublets at the end of each series, even though thev are shifted by thousands of rneg:ii.j~les from the rigid-rut or
Aucalcll./ Auobsd.
APOlie.d.,
J,K*
mc.
l!), 6 171 305.70 291.49 1.06 23, 7 319 93.15 SO. 66 1.07 57,8 537 27.27 24.84 1.10 875 7.81 6.90 1.13 31.9 35, 10 1213 2.20 1.91 1.15 1700 0.61 0.53 1.15 39,ll 43, 12 2298 0.17 .... 33, 9 - 1297 20,78 18.02 1.15 37, 10 - 1782 5.89 4.87 1.21 - -3375 1.64 1.36 1.21 41,ll 4&12 - 3 133 0.45 .... .. 4
TABLE IV
STRUCTURAL PARAMETERS OF CIILF2 This research II'I
1s
Infrarede
Electron diffractiond
1.3m 1.357 1 . 3 2 f 0 . 0 1 1.36'50.02 108" 14' 108" 20' 107" 0' f 30' 110' rt 1 " YCH, -4. 1.091 1.094 (1.094)" L x I r 1120 6' 111038' ( i i o o y a From 21.2 -+ 30,3 of C ~ ~ H Z F ~ From . 51.5 -+ 4%,tof Ci3112F?. Reference 4. Reference 3. a Assumed values. YCF,A.
LFCF
Structural Parameters and Dipole Moment If the atomic massesg are assumed to be known, the three moments of inertia obtained by fitting the spectrum of CH2F3provide three equations in the four parameters which determine the geometrical structure oi the rigid molecule. Upon proper choice of coordinate system, these equations can give explicit solutions for two of the parameters; i n particular, it can easily be shown that the F-F and H-13 distances are given by ?nFd2FF = It,f IC - I. ?f7Hd2HH = I a 4I b - IC These relations give ~ F F= 2.2005 f 0.0001 A. and d H H = 1.5105 f 0.0008 A. A single equation now relates the two remaining parameters, which may conveniently be taken as the altitudes of the HCH and FCF triangles. I n practice i t is convenient to assume approximate values for these two quantities and to carry linear correction terms as the two unknowns. A complete solution (in the rigid approximation) now requires one additional relation, which is in principle provided by a single transition of any isotopically substituted species.
-
(9) Atomic masses used were: 1I = 1.008123, F = 19,00450,C'z 12.0038%.Cl* = 13.00751. ?'Le conversion factor between moments of inertia auti rotvtioual courtants was taken as 5.05425.106 mc. (X.U.1
July 20, 1'352
SPECTRUM AND STRUCTURE OF METHYLENE
If the carbon atom of CHzJ?2 is substituted, the computation is simplified by the following theoremlo: For any rigid rotor, if an isotopic substitution is made on an atom located on a symmetry axis (and therefore on a principal axis), the new principal moments of inertia are given b y (if the symmetry axis is labeled b) I' = I. 1; = I b I' = I,
+ TJ*Anz(M/hf') + q2Am(Al/Llf')
Here primes denote the substituted molecule, Af is the total mass, Am = M' - Af, and q is the distance of the substituted atom from the center of mass of the original molecule. If the original moments are known, the measurement of a single isotopic transition thus permits calculation of the quantity q. I n the case of substitution of the carbon atom in CHzF2 the equation relating 7 to the molecular parameters chosen above gives the additional relation that is needed for a complete solution of the structure. It was possible by searching with a pen and ink recorder to locate in natural abundance the 21,~+ 30,3 and 51,6 -+ 42,~transitions of C13HzFz. These lines appeared a t 23,501.2 f 0.4 mc. and 25,829.9 f 0.4 mc., respectively. Since no other lines of low J values could fall in the region accessible t o highsensitivity searching, i t was not possible to make a n independent determination of the rotational constants of CI3HzF2. However, each of these lines may be used to calculate a set of structural parameters in accordance with the procedure outlined above; the discrepancy between the two sets then gives an estimate of the validity of the rigid-rotor approximation. The results of this calculation are given in Table I V ; the electron diffraction and infrared results are included for comparison. It is seen that the agreement between microwave and electron diffraction parameters is satisfactory, while the infrared C-F distance is out of line. This discrepancy is a consequence of the disagreement in rotational constants. While the infrared value of 39,059 & 150 mc. for a - '/z(b c) agrees fairly well with the microwave result, the value 10,671 f 150 mc. for '/&I c) is sufficiently far from our value of 9976.55 mc. t o produce this difference in C-F distance. The dipole moment of CHzFz was determined from Stark effect measurements on the hf = 1 component of the 21,2 ---f 30,3transition. The Stark coefficients for this transition were calculated by the method of Golden and Wilson l l ; the direction cosine matrix eleiiients involved were evaluated by a perturbation treatment around the limiting symmetric rotor. Calibrations12 were carried out by measurements on the OCS line at 24,325.92 mc. The dipole moment obtained i n this way is 1.OG f 0.02 debye units. Discussion of Structure The structural parameters of the simple chlorin-
+
+
(10) This relation w a s originally given by Dr. D. K Coles for linear and symmetric rotor molecules. See "Advances in Electrooics," 1'01. 11, Academic Press, New York, 1950, p. 316. (11) S. Golden and E. B. Wilson, Jr., J. Chcm. Phys., 16, 669 (19481. (12) R . G. Shulmaa and C. H. Townes, P h y s . Rcu., 77, 500 (1950).
FLUORIDE
3551
ated and fluorinated rnethanes for which microwave data are available are listed in Table V. The most obvious regularity in this series is the shortening of the carbon-halogen distance, in a roughly linear manner, as an additional halogen is added to the molecule. Such a shortening was originally explained by Pauling13 by the assumption of resonance structures of the type H
I
H-C=>;
f
xThe fact that the C-F shortening is niore markcd than the C-C1 is attributed to the greater tendency of fluorine to form double bonds. The contribution of structures of this type is also compatible with the increase in the HCH angle as a second halogen is added. However, this simple picture provides no ready explanation of the shortening of the C-H distance, which is especially pronounced in the chlorine case. In this connection it would be interesting to have information on the C-H distance in CHX, molecules. TABLE V
STRUCTURE OF HALOGENATED METHANES rex, A.
