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The Raman spectra of the methyldiboranes—I
Spectrochimica Acta, Vol. ZBA,pp. 1199 to 1214. Pergamon Press1970. Printedin Northern Ireland
The Raman spectra of the methyldiboranes-I. 1,Mimethyldiborane and tetramethykliborane J. H. CARPENTER* and W. J. JONES Departments of Theoretical and Physical Chemistry, University of Cambridge and R.
W.
JoTHtlMt and L.
H.
LONG
Department of Chemistry, University of Exeter (Rscskd 31 May 1969) Ab&act-The Raman spectra of liquid tetramethyldiborane and 1,l -dimethyldiborane at -70°C, together with qualitative states of polarisation,are presented. A vibrational assignment is given, using both infrared and Raman data. The effect of Fermi resonance on peaks in the 2000 cm-1 region is discussed.
THE methyldiboranes B2H6_,(CH3),, where n = 1, 2, 3, 4, are among the simplest boron-carbon compounds containing a boron-hydrogen bridge. The infrared spectra of these compounds have already been reported by other workers [l-4] but the Raman spectrum has been previously obtained only for tetramethyldiborane [5]. Because of the ease with which the methyldiboranes disproportionate, pure samples are readily obtainable only in small quantities and at low temperatures. Until recently, this has precluded the general application of Raman spectroscopy to these compounds. However, with the use of a laser source, we have obtained the spectra of methyldiboranes in the liquid phase at low temperatures, and are thus now able to present fuller vibrational assignments. In this paper we discuss the Raman spectra of the fully substituted diborane derivative tetramethyldiborane (hereafter referred to a,s TMDB) and of 1, l-dimethyldiborane (referred to as l,l-DMDB). It is convenient to deal with these two compounds together, as the latter shows features common to both TMDB and diborane, in that it contains both BH, and BMe, groups. EXPERIMENTAL TMDB and l,l-DMDB were prepared by equilibration [6] of intensely purified diborane and trimethylborane in ratios of 1:6 and 1: 1 respectively. This was conveniently accomplished in grease-free vessels, fist in the gas phase at low pressure for 16 hr, and secondly in the liquid phase under higher pressure for 3 hr in a vessel
* Present address: School of Chemistry, University of Newcastle-upon-Tyne. 7 Present Address: [l] [2] [3] [4] [5]
W. W. W. W. B. [6] H.
Depctrtment of Chemistry, University
of Sheffield.
J. LEHMANN, C. 0. WILSON and I. SRAPIRo, J. Chem. Phys. 32, 1088 (1900). J. LEE-N, C. 0. WILSON and I. SHAPIRO, ibid. 53, 690 (1960). J. LEEIIKANN,C. 0. WILSON ad I. SHAPIRO, ibid. 34, 476 (1901). J. LEHMANN, C. 0. WILSON and I. SHAPIRO, ibid. 34, 783 (1901). RICE, J. M. GONZALEZ BARREDO and T. F. YOUNQ, J. Am. Chenz. Sot. 78, 2306 (1951). I. SCHLESINGERand A. 0. WALKER, J. Am. Chem. Sot. 57, 621 (1935).
1199
1200
J. H. CARPENTER, W. J. JONES, JR. W. JOTEAM and L. H. LONQ
of smaller volume. The desired product was the major component of the resultant mixture and was isolated and purified by successive fractional condensations & ‘uctcuoat low temperatures until the obsemed vapour pressure was constant. For TMDB this was 48 mm Hg at 0°C and for 1,l-DMDB 44, 62 and 71 mmHg at -61.2, -66.7 and -63.2% respectively, values very close to those formerly reported [S]. The products were condensed at -196°C into the sample cells, which were then sealed and stored at the same ~mperat~e. Sample cells consisted of glass tubes of 15 mm internal bore, with rounded ends. While the spectra were being run, the tube was held in a special holder inside an evacuated Dewar vessel and cooled with acetone and dry ice to about -70 to -75°C. The holder was designed to prevent light scattered from liquid surfaces from reaching the collectiug lens. Transference of the tube from its storage Dewar vessel to the holder took less than one minute; the sample was thus above 0°C. for much less than this time, so no significant disproportionation was likely to have occurred.
Spec:;;+meter
M&itorphotocell
Loser tube. mirrors and wavelength selector
H&If gZ
Lens to focus laser beam into sample
Fig. 1. Schematiadiagramof the optical system (not to so&). A schematic diagram of the optical arrangement is given in Fig. 1. The spectrometer used was the Hilger E612 pho~eleot~c scanning spectrome~r, the low intensity Raman radiation being detected with an EM1 6094B photomultiplier tube. To eliminate variations in signal due to fluctuations in the source intensity, the laser source was monitored with a photocell used to generate the reference signal for a Cambridge Instrument Company Ratio Recorder. The laser source used was a d.c.-excited C.W.argon ion laser, giving up to 10 mW at 4880 A. The beam was focussed down into the sample, where its diameter was about 0~05-0~1mm. The scattered light was collected with a lens that was arranged so that it matched the aperture of the spectrometer, and subtended as large a solid angle at each scattering point in the sample as practicable. In this case, the lens had a diameter of 5 cm, and was at 5 cm from the sample and 40 cm from the spectrometer slit, With this geometry the image of the sample just overfilled the slit (which was about O*l-0.25 mm wide), so that most of the scattered light collected by the lens entered the spectrometer. Spectra were recorded with spectral slit widths of about 5-15 cm-l, with the electric vector of the incident beam either perpendicular or parallel to the scattering
The Raman spectra of the methyldiboranw-I
1201
direction. The spectrometer was calibrated with both a neon discharge lamp and the Raman spectra of carbon tetrachloride and toluene. For some spectra a t?lterwas placed in front of the slit to reduce the intensity at 4880 A. Measurement of wavenumber shift is correct to about 3 cm-l for sharp peaks; for weak, broad or overlapped features the accuracy is somewhat less.
RESULTS The Raman spectra of l,l-DMDB and TMDB are given in Tables 1 and 2. Representative spectra are illustrated in Figs. 2 and 3. In the tables the positions of the peaks are given, together with their intensities [measured as peak height relative to the strongest peak (at about 2900 cm-l) which is taken as 100; these are not corrected for the photomultiplier sensitivity], qualitative states of polarisation, and their assignments (see below). As well as the spectra taken at the low temperature the spectra subsequently taken at room temperature are included. These were taken with two objects in mind. Firstly the low temperature spectra became somewhat noisy at low wavenumber shifts from the exciting line because of thermal agitation of small particles in the sample ; this also prevented the accurate measurement of depolarization ratios. This effect was absent from the room temperature spectra, and so it was hoped that any peaks close to the exciting line which were missed at the low temperature would be observed at room temperature. Secondly the spectra taken after the samples had been at room temperature for some time gave semi-quantitative information about the extent of disproportionation of the samples. The table for TMDB also includes the results of RICE et al. [5]. This spectrum was recorded photographically and no polarization data were obtained. If the two spectra of TMDB are compared, it is seen that the agreement between them is good, though there are a few discrepancies. The peaks observed by us at 571, 743, 874, 1321 and 2047 cm-l, and not by Rice et al. are all fairly weak, one being a shoulder to a more intense peak; moreover, all except the peak at 743 cm-i are polarized, and with the plane polarized light from the laser beam the intensity of a polarized line is increased relative to that of a depolarized one, compared with their intensities for the conventional unpolarized light source used by Rice et al. The line at 651 cm-l in their spectrum is absent from ours and we conclude that it was not due to TMDB. The differences in the relative intensity of the lines between 2800 and 3000 cm-i in the two spectra cannot be fully explained as due to the different effect of the light sources on polarized and depolarized lines, and we cannot find a completely satisfactory explanation for this discrepancy. MOLECULARGEOMETRYAND SYMMETRYCO-ORDINATES An electron diffraction study [7] of TMDB suggests that the methyl groups have staggered conformations with respect to the B-C and B-H’ bonds from the boron atoms. Thus the molecular geometry is as shown in Fig. 4, and the point group of the molecule is D,. The barrier to internal rotation is estimated in Ref. [7] to be about 1 kcal/mole ; but even if there were free internal rotation the effective point group for vibrational assignments would still be D,,. The l,l-DMDB molecule is [7] B.L. CABROLL~~~L.
S. BARTELL,I~~~.C~~~. 7,219 (1968).
1202
J. H. CARPENTER, W. J. JONES, R. W. JOTELM and L. H. LONG Table 1. Infrared and Reman spectra of l,l-dimethyldiborane
Infrared spectrum* frequency notes (cm-l) intensity
Reman spectrum at - 70% frequency (cm-l) intensity notes
Ramem spectrum at 20% frequency intensity notes (cm-‘)
Assignment
317
829
85
A
923 976 1063 1064 1126
130 36
c
660 2
8
dp
613.
5
P
619
85
P
838
7
dp
:P ah P P P? P p. sh P tip?
VlB VlV V8V
t vaa. vao
%a Vll
VlO
6 3 2
dp? dp? P
PY dp
1165
3
?
9
dp
1133 1164
3 3
1163 1212 1316 1326 1441
260 26 480 130
A?
1646
1600
A
1533
1686 1764 1905 1985 2096
190 44
A?
1691 1675
VP
1053 1080 Ill6
1066
B A i 8, sh
5 4 2 1 4 2 82 41 1 2 5 4
V84
sh pip
253 312 324 385 610 674 613 624 691 801 831 850
1318
1
P
1317
1
P?
1434
9
dp
1433
5
dp?
3
dp
2
P? VW
1446 1456 1530 1662 1686
4 2 1 1 1
P P P
%a.vaa VQ8 v8
V6 VP +
Vll
2%0 VI1
sh 28 120
V-20
2091 2120 2152
14 14 20
P P P
2092 2117 2152
11 15 16
P P P
%a,
P
2500 2526 2674 2607
I50 11 6 3
P P dp dp
Va
P
2833
10
P
2%a
V4 v8+
v9
2304 2494
I8 460
2499
53
2571
470
2576
8
2740
ah. 2831
11
2909 2947
100 20
f;P
2911 2946
100 16
flP
vls*vlP
2970
IS
dp
2972
13
dp
%.%I
s, sh
2841
2958 3040 3610 3984
200 s, sh
dp
V18 2v, etc. va, van
25 11
* The infrared deta are from LEHXANN et al. 131. s = strong, m = medium, w = weak, b = broad, sh = shoulder, v = very, i = apparent intensity inareesed by overlap with other bends, p = polarized, dp = depolarized, ? = uncertain. A, B, C refer to infrared b-d oontQul%
100 40
w 140 60
860 146
400 260 eh w
172 80%
876 936 96% 986
1017 1066
Ill1 1147 1190 1260 1312 1324 1 1431
38
2%
360
:58 w w 8
18
sh
eh
sh
Pip
pip
b
A
sh
VW
m m
vs vs
2952
2985
w
w
8
w
m
w
w ve
2841 2886
2137
1987
1446
1100
1003
844
661
274 366 51%
b
b
RICE et al. [5] at -7O’C fr;zCI_y;Y intensity notes
2830 290%
2128
197% 2047
1321 1423 1441
1084 1108
1011
840 874
743
280 368 608 571
F
23 8
2966
2938
2832 2908
1%
23
dp?
dp?
E
P
2
1::
P
10 2129 2602
P P? b
P P? eb dP
g:
dp?
dp
B
dp, sh
7 3
I
E
4
2
4 10 3
6
f: t
7” $7
70 6
197% 2046
17342
1317 1434 1446
1091 1112 1163
1004
818 840 881
740
230 362 510 571
This work at 20’0 frequenay intensity notea (cm-l)
._
p = Polarized,
VI VZC
Vt
VCS
V4C
Assignment
i = apparent intensity inoreased by overlap with other bands.
dP
dp
P P
P
P P
P plsh dP
dP dP
dp
dP
P p
P
8
G 5
20
This work at -7O’C fr;?W&;Y intensity notes
* = strang, m = medium, w = wmk, b = broad, eb = shoulder, v = wry, dp = depoliwxsd, t = unoertain. A, l3. C refer to infrared band contours.
3049 3390 3448 3%%3
2958
2924
2174 2427 260% 2697 2688 2841
64
w 3G 18 18
2200
1606
1779 182s 1912 1972 2049 209%
200
1000
w
690
Infrared epeotrom [4] fr;qF$Y intensity notea c -
Table 2. Infrared and Ramm spectra of tetrmethyldiborme
.J.H. CAR~NTEGB,W. J. Jo-s,
1204
I
I
3000
2500
I
2000 Wavenumber
shift
R. W. JOTHBM[ and L. H. Loma
I
I
1
I
1500
IO00
5Oa
0
from exciting
line
Fig. 2. The Ramm epeotrum of I,I-~~ethyI~bo~ne at -?O% (a) Electric vector of lacer perpendiuulwto ebatteringdirection. (b) Electrio veotor parallel to scattering dire&ion.
here assumed to have the same staggered conformation and so is of point group c !&Piit can be obtained from Fig. 4 by substituting hydrogen atoms for the two methyl groups bonded to one of the boron atoms. The coordinate axes for both molecules are as shown in Fig. 4, and are consistent with those generally employed for diborane [8]. Symmetry species, vibrations and their approximate description sre given in Tables 3 and 4. The skeletal symmetry coordinates correspond to those used in diborane [8], while the methyl group vibrations are described in terms of the 1oc;al C,, symmetry of each methyl fragment.
The peaks observed in the Raman spectra c&n in many cases be assigned to normal modes which are numbered and approxim&ely described in Tables 3 and 4. This assignment is f&cilitated by the complementary information obtained from the infrared spectra of l,l-DMDB [3] and TMDB [4] for which partial assignments have been made. In addition the almost complete assignments for diborane [8] and boron trimethyl [9], which, in spite of the monomeric nature of the latter, may conveniently be regarded as end members of the series of methyldiboranes, indicate the regions of characteristio group vibrations. [S]
W.
L.
SMLTH
and 1. &f. ?&L&S,J. C%m. Pftys. 41, 1479 (1964). J. R. JEL+I;L, R. N. DIXON and N. SHEZPARD, ~~ec~~~~~. A&
[S]L. A. WOODWAXD, (1969).
26,249
1205
The Raman apeotraof the rnethyl~~~-I
I
3000
I
I
I
I
I 500
IO00
500
I
2000
2500
Wavenumber
shift
from exciting
I 0
line
Fig. 3. The Reman spectrum of tet~e~yl~bor~e. (a) Sampfe at -70%; ele&rio vector ~~n~aul~ to saMering direction. (b) Sample at room temper&ure; eleetrio vector perpendiwl~r to soattering direction (reduced gain conditions).
H\CkHH
q-C/” \ X/r
Y
=
Hw\H
“..
/
/B+B\
“/W,
Fig. 4. Molewlar geometry and co-ordinate sxes of t0t~ethyl~bor~ne.
Certain of the vibrations can readily be assigned to their respective modes. Thus the group around 2900 cm-l is assigned to the methyl stretching vibrations, of which there should be six which are Reman active, two of them polarized. In compounds containing the methyl group the symmetrio stretching vibration is at a lower frequency than the asymmetric vibrations, and where there are two or more methyl groups attached to the same atom there is little coupling between them [lo]. Hence the two peaks at 2941 and 2985 cm-l are assigned to the asymmetric stretching vibrations pl, yiS, yzs and ~4%; the four peaks overlap to give only two visible features. These peaks are almost certainly depolarized, although the fact
1206
J. H. CARFTWTER, W. J. JONEE, R. W. JOT.EAM and L. H.
LONG
Table 3. The vibrational modes of I,l-dimethyldiborane Approximate description va(CH,), in-plane 3 4 6 6 7 8 9 10 11 12
4
vs(CHs) MB&) v(BH’) sym.. in-phase v(BH’) aaym., out-of-phase &(CH,), in-plane ;gaH,: r F&z!? v&C,) v(B-B) 6(BC,)
frequency (cm-‘) 2970 2909 2499 2125 1646 1441 1326 1163 976 833 619 263
13 14 16 16 17 18
v&H,) $(@$))
Bl
19 20 21 22 23 24 26 26
K&H,) v(BH’) sym., out-of-phase v(BH’) eaym., out-of-phase S&H,) out-of-plane MCH,) MB&) NBC,) t(CH,)
2947 1986 1764 1434 (1066) 923 (317)
B,
27 28 29 30 31 32 33 34 36 36
v&CR,) in-plane vs(CH,) MB&) &(CH,), in-plane &(CHs) MBC,) r(CH,) r(BH,) MC,) ring pucker
2970 (2909) 2673 1434 1316 1126
t(BH,! t(BC,) WH,)
2947 1434 (1066) (317)
(317) (317)
that they are partially overlapped by the intense peak at 2906 cm-l made it impossible to measure their depolarization ratio accurately; it can be said, however, that their depolarization ratios are much higher than that of the 2906 cm-l peak, and are certainly close to the limiting ratio of 8. The polarized peak at 2906 cm-l is assigned to the in-phase symmetric stretching vibration Q; the other Raman active symmetric stretching vibration qB, which is expected in the same region and is depolarized, must be much less intense than y1 as the depolarization ratio of the 2906 cm-1 peak is small, about 0.05. The peak at 2830 cm-l is assigned to the first overtone of one or more of the asymmetric methyl deformation vibrations at 1423-1441 cm-l (see below). This has appreciable intensity because of Fermi resonance with the totally symmetric fundamental yz; such a situation occurs in the methyl halides [ll] and in most other compounds containing the methyl group [ 111 G. HERZBERQ,Infrared and Raman Spectra of Polyatomic Mo~Gu~~s. [12] N. SHEPPARD and D. M. SIWSON, Quart. Rev. 7, 19 (1963).
Van Nostrand
(1946).
1207
The Raman speotra of the methyldiboranea-I Table 4. The vibrational modes of tetramethyldiborcme Symmetry species
Running number
Approximate description v,(CH,), in-plane ~#=a) v(BH’) sym., in-phase &,(CH& in-plane MCH,) r(CH,) QW,) MB) &R%)
44
10 11 12 13 14
va(CH,), out-of-plane &(CH,), out-of-plane MCH,) ring twist WH,)
4,
16 16 17 I8 19 20 21
v&Ha), v&H,) &(CH& W=a) MB%) NH,) 0%)
B 1”
22 23 24 26 26 21
v&H& out-of-plane v(BH’) sym.. .&-of-phase &(CH& out-of-plane MCH,) w(BC,) WH,)
JL
28 29 30 31 32 33
vs(CH,), out-of-plme v(BH’) asym., out-of-phase 6&H,), out-of-plane o(CH,) NBC,) WH,)
34 36 36 37 38 39 40 41
va(CH,), in-plane vs(CH,) >{;K$$, in-plme
B 1n
42 43 44 46 46
va(CH,), out-of-plane B,(CH,), out-of-plane a#=,) ring twist WH,)
B su
47 48 49 60 61 62 63 64
va(CH,), in-plane ve(CH,) v(BH’) asym., in-phase &(CH,), in plane &(CH,) NH,) vs(B%) &RC,)
%I
3
in-plane in-plane
v:(RC:) NH,) r(BC,) ring pucker
Fundementpl frequency (cm-‘) 2986 2906 2060 1423 1321 a74 840 608 280
2986 (2906) 1423 1321 1108 (1011) (368) 2968 (1972) 1437 (936)
2941 1441 1011 (3‘3’3) 2968 2924 1437 1324 1147 (1017)
2941 1441 1084 743
2958 2924 1606 1437 1312 (1017) 172
1208
J.
H. CARPENTEZR, W. J. JONES, R. W. JOT~AMand L. H.
LONG
There are no peaks in the low temperature spectrum of TMDB in the 2500-2600 cm-l region. Peaks in this region are characteristic of terminal B-H stretching vibrations ; in diborane and all the methyldiboranes except TMDB itself intense peaks are observed [13] ; the absence here of any peaks demonstrates the very low concentration, if any, of disproportionation products. Vibrations of the B-H’ bridge bonds occur in the 1600-2200cm-l region [l-4,81. Two of these are expected to be Raman active, the symmetric in-phase vibration vagiving rise to a polarized peak and the asymmetric out-of-phase vibration vag giving a depolarized one. In the observed spectrum there are three polarized lines at 1976,2047 and 2128 cm-l, and none depolarized, in this region. Thus the asymmetric out-of-phase vibration vSOis not observed. The three peaks are due to the interaction by Fermi resonance between the symmetric in-phase fundamental va and two overtones or combination tones. This is discussed more fully below, where it is estimated that the unperturbed levels are at about 2016, 2050 and 2084 cm-l. The fundamental va is the central level; the level at 2016 cm-l is the first overtone of the Raman active methyl rocking vibration whose fundamental is observed at 1011cm-l, while the level at 2084 cm-l is the combination of the infrared active asymmetric BC, stretching vibration V~ at 772 cm-l and the symmetric methyl deformation vibration vsl at about 1312-1324cm-i [4]; each is of species B,, so their combination level is totally symmetric. In the 1400-1450 cm-l region there is a rather broad peak at 1441 cm-1 with a shoulder at 1426 cm-l. The whole feature extends from about 1400-1470 cm-l. Again it is not possible to be certain of the states of polarization, but from a comparison of the appearance of the peaks at the two states of polarization, it was found that the peak at lower frequency has a smaller depolarization ratio than the shoulder whose depolarization ratio is close to +. This region is characteristic of asymmetric methyl deformations, and in the Raman spectrum of this compound there should be one polarized fundamental, va, and three depolarized ones, vi?, vaOand v~. The peaks observed are assigned to these fundamentals, and it is probable that the vq vibration, of species A,, is at about 1426cm-l. The weak polarized line at 1321cm-l is assigned to the symmetric methyl deformation vibration vg of species A,. In common with many such compounds (e.g. the methyl halides [ll]), the symmetric methyl deformation vibrations give rise to weaker peaks in the Raman spectrum than the asymmetric deformation modes. This is in contrast to the methyl stretching vibrations, where the symmetric vibrations give rise to more intense scattering than the asymmetric. The opposite is true in the infrared [a], where the asymmetric stretching and the symmetric deformation vibrations give stronger absorption peaks than the symmetric stretching and asymmetric deformation vibrations respectively. In the region from 800 to 1200 cm-l there occur the various methyl rocking (in the plane of the B,C, skeleton) and wagging (out-of-plane) modes, as well as the B-C stretching modes. In the infrared spectra of the methyldiboranes [l-4] the asymmetric BC, stretching vibrations occur around 1100-1160cm-l, and are marked by a large lOBisotope shift of about 30 cm-l. In TMDB the infrared active [ 131J. H. CARPENTER, W. J. JONES,R.
W. JOTEAMand L. H. LONG, Chem. Commun. 881 (1968).
The Ramen ape&a of the methyldiboranes-I
1209
vibration v, occurs at 1147 cm-l. In the Raman spectrum there are two depolarized peaks in this region, at 1084 and 1108 cm- l, the lstter having a small shoulder at high frequency. One of these peaks is due to the asymmetric BC, vibration vls. It is possible that the shoulder is the l*B component of the vibration which would thus be assigned to the 1108 cm-l peak. The peak at 1084 cm-l is assigned to a methyl rocking or ws,gging vibration, as is that at 1011 cm-l. The two strong polarized peaks at 508 and 840 cm-l are assigned to the B-B stretching vibration vg and the symmetric BC, stretching vibration v7 respectively. LEHWUW et al. [4] show that this assignment gives better agreement with their Average Rule [14] than the opposite one. The B-B stretching vibration in diborane is s,t 788 cm-l (this is the llB component) and a drop of frequency on substitution of heavier methyl groups for terminal hydrogen is expected. There is no observable splitting due to boron isotopes in TMDB although for the components in diborane it is about 15 cm-l ; this decrease in splitting is also due to the greater mass of the termin&Xl groups. The peak at 368 cm-l is depolarized in the room temperature spectrum (its polarization could not be determined at the low temperature). This peak m&y be due to one of a number of BC, deform&ion or rocking vibrations. The peak at 280 cm-l, however, is polarized and so is to be assigned to the symmetric BC, deformation vibration v~, as this is the only totally symmetric fundamental which is expected in this region, and all the other A, vibrstions are accounted for. If the 368 cm-l line is assigned to the BC, rocking vibration val, then the average of these in-plane BC, deformstions for the Raman active vibrations is 324 cm-l. This compares with the value of 320 cm-l for the in-plane BC, deform&ion vibration of boron trimethyl [9]. However, in boron trimethyl the out-of-plane deformation vibration is at 336 cm-l, so the peak in TMDB could be due to the BC, wagging vibration vQI. This leaves the weak lines at 571, 743 snd 874 cm-l. The last is the in-plane methyl rocking vibration vs. The depolarized line at 743 cm-l might be the ring twisting vibrstion v~, which occurs at 1012 cm-l in diborane [8]. The line at 571 cm-l is polarized and hence is not a fundamental, since all the A, fundamentals in this region have been accounted for. It is probably the first overtone of the symmetric BC, deformation vg which occurs at 280 cm- l. The relatively high intensity for a non-fundamental is due to Fermi resonance with the fundamental at 608 cm-l. 2. l,l-dinzethyldiborane The peaks observed in the Raman spectrum can be assigned in a similar way to those of TMDB. However, because the molecule is of lower symmetry, most of the vibrations are active in both the in&red and Raman spectra. Hence more use can be made of the assignmenta of LEHMAXN et al. [3] for the infrared spectrum. The peaks at 2970 and 2947 cm-l are assigned to the asymmetric methyl stretching vibrations vz7, vr, V~ and vn,, the intense polarized peak at 2909 cm-l is assigned to the symmetric methyl stretching vibration ve, and the polarized peak at 2831 cm-l to the overtone of an asymmetric methyl deformation vibration. In the infrared spectrum peaks occur at 2968 and 2841 cm-l (the latter being a shoulder). [14] W. J. LEEXANN, J. Mol. &m&y 7, 1 (1961); W. J. LEE-, [M] V. N. KAPSSXTAL, Rum. J. Phy. Chmn. 40, 508 (1966).
ibid. 7, 261 (1961).
1220
J. EL CARPENTER,W.
J. Jomzs, R. W. JOTH~Mand L. H. Lor~a
The former corresponds to the two peaks at 2970 and 2947 cm-l in the Raman spectrum; the shoulder at 2841 cm-l is then probably a wwzbhuthn of asymmetric methyl deformation vibrations which is of the same symmetry species as the fundamental at 2958 am-l, and thus enhanced by Fermi resonance. The weak, rather broad, depolarized line at 2576 cm-l, and the strong polarized line at 2499 cm-l are due to the asymmetric and symmetric BH, stretching vibrations ySgand y3 respectively, and correspond to infrared frequencies of 2671 and 2494 cm-l. In the 1600-2200 cm-l region, there are again three polarized peaks and none depolarized. Two totally symmetric f~damentals ye and ye, and two depolarized, ~20and yzltwhich are all associa~ with the I&H, bridge, are expected in this region. Of the totally symmetric ones, the ~~metric in-phase vibration Q gives rise to the very strong absorption peak at 1546 cm-1 in the infrared spectrum; the very weak polarized Raman peak at 1533 em-l may correspond to this peak. The three peaks at 2152, 2120 and 2091 cm-l are therefore associated with the symmetric in-phase fundamental yq and overtones or combinations interacting by Fermi resonance, as for TMDB. It is shown below that the unperturbed levels are at about 2138, 2125 and 2104 cm-i. The interacting levels are thus probably the first overtone of one of the methyl rocking vibrations (the fundamentals of which occur at 1056 cm-l in the Raman spectrum, and at 1063 and 1064 cm-i in the infrared spectrum) in the case of the lower level, and the combination vE+ v. for the upper, the fundamental P* being at 2125 cm-l. We should expect the intensity pattern for this group to be similar in the infrared and Raman spectra; in the observed infrared spectra only one peak at 2096 cm-l is reported; in the spectrum illustrated [3] this peak is somewhat broader than other nearby peaks and covers the range of the Raman peaks. The broad depolarized peak at 1434 cm-l is due to the asymmetric methyl de. . 4 formation vibrations vu, y14,Ys2and y3,,. In the infrared spectrum the corresponding band is at 1441 cm-l. The weak polarized peak at 1318 cm-lis due to the symmetric methyl deformation vibration V?and the corresponding infrared bands are at 1326 and 1316 cm-l. The two peaks at 1133 and 1164 cm-l correspond to the two bands at 1126 and 1163 cm-l in the inf&red spectrum. L-X% et d. [3] assign the lower to the asymmetric BC, stretch~g vibration and the higher to the BH, deformation frequency. This assignment should be reversed, for the Raman peak at 1164 cm-l is definitely depolarized while that at 1133 cm-i, although having a fairly high depolarization ratio, is polarized. The medium intensity peak at 1056 cm-l, which has a shoulder at about 1070 cm-l, corresponds to the infrared bands at 1064 and 1053 cm-l. The Raman peak is depolarized. This region is characteristic of methyl rocking and wagging modes, and these peaks may be due to the methyl rocking mode y33or the wagging modes yls and y2& From a comparison with the Raman spectra of other methyldiboranes [13] the wagging modes seem more likely. The peak at 838 cm --1has a high depolarization ratio, but is polarized. The corresponding infrared peak at 829 cm-l is of type A ; the vibration is thus totally symmetric. The advent by L-m et al. [3] of this band to the sketch BC, stretching vibration y10is reasonable.
The Raman speotraof the methyldiboranes-I
1211
The very strong polarized peak at 619 cm-l is then naturally assigned to the B-B stretching vibration Q. This compares with the values of 788 cm-l for 11B2H, and 508 cm-l for TMDB ; all are intense peaks. In the room temperature spectrum the peak is seen to have two components; a stronger one at 613 cm-l with a shoulder at 624 cm-l. These are due to molecules containing llBH, and IOBH, groups respectively. In comparison the splitting in diborane is 14 cm-l (8), while it is not observed in TMDB. The peak at 317 cm-l observed at -70°C. is resolved in the room temperature spectrum into two components; a depolarized peak at 312 cm-l and a shoulder (whose polarization could not be determined) at 324 cm-l. In addition a peak is observed at 253 cm-l in the room temperature spectrum which, owing to the poorer signal-to-noise ratio close to the exciting line, was not observed at the lower temperature. The latter peak, which is polarized, is assigned to the symmetric BC, deformation vibration Q.; this is the only vibration of symmetry species A, which is expected in this frequency range. There is no unambiguous assignment for the other two peaks ; one may be due to the ring pucker vibration vse which occurs at 368 cm-l in diborane [8] and which is likely to decrease in frequency with increasing methyl substitution. Alternatively, one or both may be due to the BC, rocking vibration vQs,wagging vibration vs5,or twisting vibration vl,. This leaves the weak peaks at 513, 1591 and 1675 cm-l. The fist might just be due to tetramethyldiborane impurity, since there is an intense peak in the spectrum of the latter in this region; however, l,l-DMDB is easily isolated and relatively stable, and the absence of corresponding peaks due to other methyldiborane impurities and diborane make this unlikely. It is more likely due to the first overtone of the vibration at 253 cm-l. The two depolarized peaks due to the fundamentals vz,,and val are not observed. The weak peak at 1591 cm-l is too low in frequency to be due to either of them; it is assigned to a combination level of the B-B stretch vll at 619 cm-l with the methyl rocking vibration observed in the infrrtred spectrum at 975 cm-l. The very weak peak at 1675 cm-l is due to the first overtone of the symmetric BC, stretching vibration at 838 cm-l. FERMI
RESONANCE
IN
THE
1950-2200
cm-l
REGION
The interaction of two vibrational energy levels of the same symmetry species in a molecule, giving rise to a change in their energies and a mixing of the vibrational wave functions, is well known.* If the interaction is between a fundamental level (that is, one in which all the vibrational quantum numbers v are zero except one which is unity) and a combination or overtone level, then the mixing of wavefunctions means that the latter can “borrow” intensity from the former, and hence such an overtone or combination, which would not give rise to an infrared or Raman peak if the vibrations were harmonic, can now occur with appreciable intensity. * See,for instance, Ref. [ 111,p. 216 ff, also C. PLACZEK, The Rayleigh and Ram Scattering, translated by A. WERBIN (UCRL-!l!rana-626(L), chapter 20. U.S. Atomic Energy Commission (1969)).
1212
J. H. C~RPENTI~R, W. 5. JONPS, FL W. JOTEAMand L. H.
LONG
When there are three intera&ing levels, as in both these molecules, the system has fewer experimental data than interaction parameters. There is hence no unique solution, and so some simplifying assumptions must be made. Let the unperturbed energy levels be ,?Sr,E, and E, above the ground state, and the interaction energies be W1s, Wr, and W,,. Then, if the resonance is close, we may apply a perturbation method; the perturbed levels are then the eigenvalues of the matrix:
For any eigenvalue, the eigenvector gives the coefficients of the unperturbed wave functions in the eigenfunotions. Thus if all the intensity is due to the fundamental, the square of its coefficient in the three perturbed levels is proportional to the intensity of the line corresponding to that level. In the case of TMDB, the perturbed levels are at 1976, 2047 and 2128 cm-l, with intensities of 16: 8: 17 (i.e. approximately 2: 1: 2). The spacings are thus 71 and 81 cm-l between the central level and the other two, and the intensities of the latter are approximately the same. Because the energy level di&rences were roughly the same, and because of the intensity pattern, an unperturbed system in which the energy levels and their interactions were Ernest about the central peak was tried. Accordingly, the following gumptions were made: . g,
El = E, - E, = cl The central unperturbed level is the fundamental, and all the observed intensity is due to it. (iii) WI, = W2, = W, and WI8 = 0. WI, and W=, which are interactions between a fundamental and an overtone or combination, are due to cubic terms in the potential energy, while WB, which is an interaction energy between two levels which are not fundamentals, is due to a quartic term. It is thus plausible that the latter may be of a smaller order of magnitude than the former. The secular deter~~t now assumes the simple form:
E* -
E,+d--E
W
W
0
_E, - E
W
==o.
w
E, - a -
El
This can be solved analytically, giving the perturbed levels: E = I$, E2 f
q(2Wz + d2)
The normalised eigenve~~r matrix x, where Hx = SE (H being the pe~~bation
The Reman spectraof the methyldiboran~1
1213
matrix and E the diagonal eigenvalue matrix) is: X+d 2x
W
x-a-
x
2x
W
a
W
X
x
x
--
(X - 4 -2x
W
(X + 4
x
where X = 1/(2lP
2X
_
+ a*).
The second row of this gives the coefficients of the fundamental in the three perturbed levels, so the intensities of the three observed peaks should be in the ratio Ws:dz: W*. Using the observed energy levels and intensities, we find that d = 34 cm-l and W = 48 cm-l. Thus the unperturbed levels are at 2016, 2060 and 2084 cm-l, giving perturbedlevels at 1974, 2060 and 2126 cm-l, which compare with the observed values of 1976, 2047 and 2128 cm-l. The above solution is physically reasonable but is not unique, ss pointed out previously. It should be noted that the peak corresponding in energy to the unperturbed fundamental has least intensity, and indeed, if d -+ 0 its intensity falls to zero; that is, the perturbed level at this energy is a mixture of the two overtone levels only. In the spectrum of 1,l-DMDB there are again three polarized peaks in this region, at 2091, 2120 and 2152 cm-l, with intensity ratio of 14: 14: 20. These are again nearly equally spaced, with separations of 29 and 31 cm-l. However, the asymmetry of the system indicates that the situation is not the same as for TMDB. Values of the W’s and E’s were then tried on the assumption that again the central unperturbed level was the fundamental, that WI8 = 0 again, but now WI, # W,, and (Es - Ed # (Es - Es). It was found that if WI, > W, and (8, - E1) < (Es E,), then the separations remained roughly the same but the greatest intensity was in the highest frequency peak. The following values gave a reasonable fit with the observed results: E, = 2104 cm-l, E, = 2125 cm-l, E3 = 2139 cm-l, W,, = 21 cm-l, Wm = 17.5 cm -l. These gave perturbed levels at 2156, 2120 and 2091 cm-l, and relative intensities of 18.6, 14.1 and 15.3, compared with the experimental levels of 2162, 2120 and 2091 cm-i and relative intensities of 20, 14 and 14. Discussion
Comparing our assignments above with those of LEESMANN et ct.!.[3, 41, it can be seen that, with the exception of the slight change in the assignments of the methyl stretching vibrations, and the corrected values for the symmetric in-phase r(BH’) vibrations, our assignments are in agreement. Assignment of the fundamentals is included in Tables 1 and 2. The majority of the fundamentals have now been assigned but there are still some low frequency fundamentals which are not accounted for. The absence of infrared data below 650 cm-l also means that some of the Raman peaks cannot be assigned unambiguously. General force field calculations have been carried out on these molecules [16], and it is instructive to compare the calculated values with those observed. For most
1214
J. H.
(ktPRNTJ3R,
W. J. JONES, R. W. JOTHAN and L. H.
LONG
vibrations there is fairly good agreement. In particular, the calculated frequencies for the B-B stretching vibration are 502 cm-l in TMDB and 696 cm-l in 1,I-DMDB ; we observed 608 and 619 cm-l respectively. If we use the calculated frequencies to assign the lower frequency lines, then in the spectrum of l,l-DMDB the line at 317 cm-l is due to the ring pucker vibration vS8and/or the BCz rocking vibration vaa (or possibly the wagging vibration vzJ ; and the line at 253 cm-l is due to the BC, deformation vibration vls; this is as assigned. In TMDB the line at 365 cm-l corresponds either to the BC, wagging vibration vaz (calculated frequency = 439 cm-i) or the BC, rocking vibration vZ1(calculated frequency = 287 cm-l). The line at 280 cm-l, being polarized, is due to the BC, deformation which Kapshtal calculates at 188 cm-l. The agreement in this region for TMDB is rather poor; this is probably because force constants for these vibrations are not well characterized, and he was not able to apply any least-squares method to the vibrations for these molecules in this region as the infrared spectra did not extend below 660 cm-l.
The Raman spectra of the methyldiboranes-I. 1,Mimethyldiborane and tetramethykliborane J. H. CARPENTER* and W. J. JONES Departments of Theoretical and Physical Chemistry, University of Cambridge and R.
W.
JoTHtlMt and L.
H.
LONG
Department of Chemistry, University of Exeter (Rscskd 31 May 1969) Ab&act-The Raman spectra of liquid tetramethyldiborane and 1,l -dimethyldiborane at -70°C, together with qualitative states of polarisation,are presented. A vibrational assignment is given, using both infrared and Raman data. The effect of Fermi resonance on peaks in the 2000 cm-1 region is discussed.
THE methyldiboranes B2H6_,(CH3),, where n = 1, 2, 3, 4, are among the simplest boron-carbon compounds containing a boron-hydrogen bridge. The infrared spectra of these compounds have already been reported by other workers [l-4] but the Raman spectrum has been previously obtained only for tetramethyldiborane [5]. Because of the ease with which the methyldiboranes disproportionate, pure samples are readily obtainable only in small quantities and at low temperatures. Until recently, this has precluded the general application of Raman spectroscopy to these compounds. However, with the use of a laser source, we have obtained the spectra of methyldiboranes in the liquid phase at low temperatures, and are thus now able to present fuller vibrational assignments. In this paper we discuss the Raman spectra of the fully substituted diborane derivative tetramethyldiborane (hereafter referred to a,s TMDB) and of 1, l-dimethyldiborane (referred to as l,l-DMDB). It is convenient to deal with these two compounds together, as the latter shows features common to both TMDB and diborane, in that it contains both BH, and BMe, groups. EXPERIMENTAL TMDB and l,l-DMDB were prepared by equilibration [6] of intensely purified diborane and trimethylborane in ratios of 1:6 and 1: 1 respectively. This was conveniently accomplished in grease-free vessels, fist in the gas phase at low pressure for 16 hr, and secondly in the liquid phase under higher pressure for 3 hr in a vessel
* Present address: School of Chemistry, University of Newcastle-upon-Tyne. 7 Present Address: [l] [2] [3] [4] [5]
W. W. W. W. B. [6] H.
Depctrtment of Chemistry, University
of Sheffield.
J. LEHMANN, C. 0. WILSON and I. SRAPIRo, J. Chem. Phys. 32, 1088 (1900). J. LEE-N, C. 0. WILSON and I. SHAPIRO, ibid. 53, 690 (1960). J. LEEIIKANN,C. 0. WILSON ad I. SHAPIRO, ibid. 34, 476 (1901). J. LEHMANN, C. 0. WILSON and I. SHAPIRO, ibid. 34, 783 (1901). RICE, J. M. GONZALEZ BARREDO and T. F. YOUNQ, J. Am. Chenz. Sot. 78, 2306 (1951). I. SCHLESINGERand A. 0. WALKER, J. Am. Chem. Sot. 57, 621 (1935).
1199
1200
J. H. CARPENTER, W. J. JONES, JR. W. JOTEAM and L. H. LONQ
of smaller volume. The desired product was the major component of the resultant mixture and was isolated and purified by successive fractional condensations & ‘uctcuoat low temperatures until the obsemed vapour pressure was constant. For TMDB this was 48 mm Hg at 0°C and for 1,l-DMDB 44, 62 and 71 mmHg at -61.2, -66.7 and -63.2% respectively, values very close to those formerly reported [S]. The products were condensed at -196°C into the sample cells, which were then sealed and stored at the same ~mperat~e. Sample cells consisted of glass tubes of 15 mm internal bore, with rounded ends. While the spectra were being run, the tube was held in a special holder inside an evacuated Dewar vessel and cooled with acetone and dry ice to about -70 to -75°C. The holder was designed to prevent light scattered from liquid surfaces from reaching the collectiug lens. Transference of the tube from its storage Dewar vessel to the holder took less than one minute; the sample was thus above 0°C. for much less than this time, so no significant disproportionation was likely to have occurred.
Spec:;;+meter
M&itorphotocell
Loser tube. mirrors and wavelength selector
H&If gZ
Lens to focus laser beam into sample
Fig. 1. Schematiadiagramof the optical system (not to so&). A schematic diagram of the optical arrangement is given in Fig. 1. The spectrometer used was the Hilger E612 pho~eleot~c scanning spectrome~r, the low intensity Raman radiation being detected with an EM1 6094B photomultiplier tube. To eliminate variations in signal due to fluctuations in the source intensity, the laser source was monitored with a photocell used to generate the reference signal for a Cambridge Instrument Company Ratio Recorder. The laser source used was a d.c.-excited C.W.argon ion laser, giving up to 10 mW at 4880 A. The beam was focussed down into the sample, where its diameter was about 0~05-0~1mm. The scattered light was collected with a lens that was arranged so that it matched the aperture of the spectrometer, and subtended as large a solid angle at each scattering point in the sample as practicable. In this case, the lens had a diameter of 5 cm, and was at 5 cm from the sample and 40 cm from the spectrometer slit, With this geometry the image of the sample just overfilled the slit (which was about O*l-0.25 mm wide), so that most of the scattered light collected by the lens entered the spectrometer. Spectra were recorded with spectral slit widths of about 5-15 cm-l, with the electric vector of the incident beam either perpendicular or parallel to the scattering
The Raman spectra of the methyldiboranw-I
1201
direction. The spectrometer was calibrated with both a neon discharge lamp and the Raman spectra of carbon tetrachloride and toluene. For some spectra a t?lterwas placed in front of the slit to reduce the intensity at 4880 A. Measurement of wavenumber shift is correct to about 3 cm-l for sharp peaks; for weak, broad or overlapped features the accuracy is somewhat less.
RESULTS The Raman spectra of l,l-DMDB and TMDB are given in Tables 1 and 2. Representative spectra are illustrated in Figs. 2 and 3. In the tables the positions of the peaks are given, together with their intensities [measured as peak height relative to the strongest peak (at about 2900 cm-l) which is taken as 100; these are not corrected for the photomultiplier sensitivity], qualitative states of polarisation, and their assignments (see below). As well as the spectra taken at the low temperature the spectra subsequently taken at room temperature are included. These were taken with two objects in mind. Firstly the low temperature spectra became somewhat noisy at low wavenumber shifts from the exciting line because of thermal agitation of small particles in the sample ; this also prevented the accurate measurement of depolarization ratios. This effect was absent from the room temperature spectra, and so it was hoped that any peaks close to the exciting line which were missed at the low temperature would be observed at room temperature. Secondly the spectra taken after the samples had been at room temperature for some time gave semi-quantitative information about the extent of disproportionation of the samples. The table for TMDB also includes the results of RICE et al. [5]. This spectrum was recorded photographically and no polarization data were obtained. If the two spectra of TMDB are compared, it is seen that the agreement between them is good, though there are a few discrepancies. The peaks observed by us at 571, 743, 874, 1321 and 2047 cm-l, and not by Rice et al. are all fairly weak, one being a shoulder to a more intense peak; moreover, all except the peak at 743 cm-i are polarized, and with the plane polarized light from the laser beam the intensity of a polarized line is increased relative to that of a depolarized one, compared with their intensities for the conventional unpolarized light source used by Rice et al. The line at 651 cm-l in their spectrum is absent from ours and we conclude that it was not due to TMDB. The differences in the relative intensity of the lines between 2800 and 3000 cm-i in the two spectra cannot be fully explained as due to the different effect of the light sources on polarized and depolarized lines, and we cannot find a completely satisfactory explanation for this discrepancy. MOLECULARGEOMETRYAND SYMMETRYCO-ORDINATES An electron diffraction study [7] of TMDB suggests that the methyl groups have staggered conformations with respect to the B-C and B-H’ bonds from the boron atoms. Thus the molecular geometry is as shown in Fig. 4, and the point group of the molecule is D,. The barrier to internal rotation is estimated in Ref. [7] to be about 1 kcal/mole ; but even if there were free internal rotation the effective point group for vibrational assignments would still be D,,. The l,l-DMDB molecule is [7] B.L. CABROLL~~~L.
S. BARTELL,I~~~.C~~~. 7,219 (1968).
1202
J. H. CARPENTER, W. J. JONES, R. W. JOTELM and L. H. LONG Table 1. Infrared and Reman spectra of l,l-dimethyldiborane
Infrared spectrum* frequency notes (cm-l) intensity
Reman spectrum at - 70% frequency (cm-l) intensity notes
Ramem spectrum at 20% frequency intensity notes (cm-‘)
Assignment
317
829
85
A
923 976 1063 1064 1126
130 36
c
660 2
8
dp
613.
5
P
619
85
P
838
7
dp
:P ah P P P? P p. sh P tip?
VlB VlV V8V
t vaa. vao
%a Vll
VlO
6 3 2
dp? dp? P
PY dp
1165
3
?
9
dp
1133 1164
3 3
1163 1212 1316 1326 1441
260 26 480 130
A?
1646
1600
A
1533
1686 1764 1905 1985 2096
190 44
A?
1691 1675
VP
1053 1080 Ill6
1066
B A i 8, sh
5 4 2 1 4 2 82 41 1 2 5 4
V84
sh pip
253 312 324 385 610 674 613 624 691 801 831 850
1318
1
P
1317
1
P?
1434
9
dp
1433
5
dp?
3
dp
2
P? VW
1446 1456 1530 1662 1686
4 2 1 1 1
P P P
%a.vaa VQ8 v8
V6 VP +
Vll
2%0 VI1
sh 28 120
V-20
2091 2120 2152
14 14 20
P P P
2092 2117 2152
11 15 16
P P P
%a,
P
2500 2526 2674 2607
I50 11 6 3
P P dp dp
Va
P
2833
10
P
2%a
V4 v8+
v9
2304 2494
I8 460
2499
53
2571
470
2576
8
2740
ah. 2831
11
2909 2947
100 20
f;P
2911 2946
100 16
flP
vls*vlP
2970
IS
dp
2972
13
dp
%.%I
s, sh
2841
2958 3040 3610 3984
200 s, sh
dp
V18 2v, etc. va, van
25 11
* The infrared deta are from LEHXANN et al. 131. s = strong, m = medium, w = weak, b = broad, sh = shoulder, v = very, i = apparent intensity inareesed by overlap with other bends, p = polarized, dp = depolarized, ? = uncertain. A, B, C refer to infrared b-d oontQul%
100 40
w 140 60
860 146
400 260 eh w
172 80%
876 936 96% 986
1017 1066
Ill1 1147 1190 1260 1312 1324 1 1431
38
2%
360
:58 w w 8
18
sh
eh
sh
Pip
pip
b
A
sh
VW
m m
vs vs
2952
2985
w
w
8
w
m
w
w ve
2841 2886
2137
1987
1446
1100
1003
844
661
274 366 51%
b
b
RICE et al. [5] at -7O’C fr;zCI_y;Y intensity notes
2830 290%
2128
197% 2047
1321 1423 1441
1084 1108
1011
840 874
743
280 368 608 571
F
23 8
2966
2938
2832 2908
1%
23
dp?
dp?
E
P
2
1::
P
10 2129 2602
P P? b
P P? eb dP
g:
dp?
dp
B
dp, sh
7 3
I
E
4
2
4 10 3
6
f: t
7” $7
70 6
197% 2046
17342
1317 1434 1446
1091 1112 1163
1004
818 840 881
740
230 362 510 571
This work at 20’0 frequenay intensity notea (cm-l)
._
p = Polarized,
VI VZC
Vt
VCS
V4C
Assignment
i = apparent intensity inoreased by overlap with other bands.
dP
dp
P P
P
P P
P plsh dP
dP dP
dp
dP
P p
P
8
G 5
20
This work at -7O’C fr;?W&;Y intensity notes
* = strang, m = medium, w = wmk, b = broad, eb = shoulder, v = wry, dp = depoliwxsd, t = unoertain. A, l3. C refer to infrared band contours.
3049 3390 3448 3%%3
2958
2924
2174 2427 260% 2697 2688 2841
64
w 3G 18 18
2200
1606
1779 182s 1912 1972 2049 209%
200
1000
w
690
Infrared epeotrom [4] fr;qF$Y intensity notea c -
Table 2. Infrared and Ramm spectra of tetrmethyldiborme
.J.H. CAR~NTEGB,W. J. Jo-s,
1204
I
I
3000
2500
I
2000 Wavenumber
shift
R. W. JOTHBM[ and L. H. Loma
I
I
1
I
1500
IO00
5Oa
0
from exciting
line
Fig. 2. The Ramm epeotrum of I,I-~~ethyI~bo~ne at -?O% (a) Electric vector of lacer perpendiuulwto ebatteringdirection. (b) Electrio veotor parallel to scattering dire&ion.
here assumed to have the same staggered conformation and so is of point group c !&Piit can be obtained from Fig. 4 by substituting hydrogen atoms for the two methyl groups bonded to one of the boron atoms. The coordinate axes for both molecules are as shown in Fig. 4, and are consistent with those generally employed for diborane [8]. Symmetry species, vibrations and their approximate description sre given in Tables 3 and 4. The skeletal symmetry coordinates correspond to those used in diborane [8], while the methyl group vibrations are described in terms of the 1oc;al C,, symmetry of each methyl fragment.
The peaks observed in the Raman spectra c&n in many cases be assigned to normal modes which are numbered and approxim&ely described in Tables 3 and 4. This assignment is f&cilitated by the complementary information obtained from the infrared spectra of l,l-DMDB [3] and TMDB [4] for which partial assignments have been made. In addition the almost complete assignments for diborane [8] and boron trimethyl [9], which, in spite of the monomeric nature of the latter, may conveniently be regarded as end members of the series of methyldiboranes, indicate the regions of characteristio group vibrations. [S]
W.
L.
SMLTH
and 1. &f. ?&L&S,J. C%m. Pftys. 41, 1479 (1964). J. R. JEL+I;L, R. N. DIXON and N. SHEZPARD, ~~ec~~~~~. A&
[S]L. A. WOODWAXD, (1969).
26,249
1205
The Raman apeotraof the rnethyl~~~-I
I
3000
I
I
I
I
I 500
IO00
500
I
2000
2500
Wavenumber
shift
from exciting
I 0
line
Fig. 3. The Reman spectrum of tet~e~yl~bor~e. (a) Sampfe at -70%; ele&rio vector ~~n~aul~ to saMering direction. (b) Sample at room temper&ure; eleetrio vector perpendiwl~r to soattering direction (reduced gain conditions).
H\CkHH
q-C/” \ X/r
Y
=
Hw\H
“..
/
/B+B\
“/W,
Fig. 4. Molewlar geometry and co-ordinate sxes of t0t~ethyl~bor~ne.
Certain of the vibrations can readily be assigned to their respective modes. Thus the group around 2900 cm-l is assigned to the methyl stretching vibrations, of which there should be six which are Reman active, two of them polarized. In compounds containing the methyl group the symmetrio stretching vibration is at a lower frequency than the asymmetric vibrations, and where there are two or more methyl groups attached to the same atom there is little coupling between them [lo]. Hence the two peaks at 2941 and 2985 cm-l are assigned to the asymmetric stretching vibrations pl, yiS, yzs and ~4%; the four peaks overlap to give only two visible features. These peaks are almost certainly depolarized, although the fact
1206
J. H. CARFTWTER, W. J. JONEE, R. W. JOT.EAM and L. H.
LONG
Table 3. The vibrational modes of I,l-dimethyldiborane Approximate description va(CH,), in-plane 3 4 6 6 7 8 9 10 11 12
4
vs(CHs) MB&) v(BH’) sym.. in-phase v(BH’) aaym., out-of-phase &(CH,), in-plane ;gaH,: r F&z!? v&C,) v(B-B) 6(BC,)
frequency (cm-‘) 2970 2909 2499 2125 1646 1441 1326 1163 976 833 619 263
13 14 16 16 17 18
v&H,) $(@$))
Bl
19 20 21 22 23 24 26 26
K&H,) v(BH’) sym., out-of-phase v(BH’) eaym., out-of-phase S&H,) out-of-plane MCH,) MB&) NBC,) t(CH,)
2947 1986 1764 1434 (1066) 923 (317)
B,
27 28 29 30 31 32 33 34 36 36
v&CR,) in-plane vs(CH,) MB&) &(CH,), in-plane &(CHs) MBC,) r(CH,) r(BH,) MC,) ring pucker
2970 (2909) 2673 1434 1316 1126
t(BH,! t(BC,) WH,)
2947 1434 (1066) (317)
(317) (317)
that they are partially overlapped by the intense peak at 2906 cm-l made it impossible to measure their depolarization ratio accurately; it can be said, however, that their depolarization ratios are much higher than that of the 2906 cm-l peak, and are certainly close to the limiting ratio of 8. The polarized peak at 2906 cm-l is assigned to the in-phase symmetric stretching vibration Q; the other Raman active symmetric stretching vibration qB, which is expected in the same region and is depolarized, must be much less intense than y1 as the depolarization ratio of the 2906 cm-1 peak is small, about 0.05. The peak at 2830 cm-l is assigned to the first overtone of one or more of the asymmetric methyl deformation vibrations at 1423-1441 cm-l (see below). This has appreciable intensity because of Fermi resonance with the totally symmetric fundamental yz; such a situation occurs in the methyl halides [ll] and in most other compounds containing the methyl group [ 111 G. HERZBERQ,Infrared and Raman Spectra of Polyatomic Mo~Gu~~s. [12] N. SHEPPARD and D. M. SIWSON, Quart. Rev. 7, 19 (1963).
Van Nostrand
(1946).
1207
The Raman speotra of the methyldiboranea-I Table 4. The vibrational modes of tetramethyldiborcme Symmetry species
Running number
Approximate description v,(CH,), in-plane ~#=a) v(BH’) sym., in-phase &,(CH& in-plane MCH,) r(CH,) QW,) MB) &R%)
44
10 11 12 13 14
va(CH,), out-of-plane &(CH,), out-of-plane MCH,) ring twist WH,)
4,
16 16 17 I8 19 20 21
v&Ha), v&H,) &(CH& W=a) MB%) NH,) 0%)
B 1”
22 23 24 26 26 21
v&H& out-of-plane v(BH’) sym.. .&-of-phase &(CH& out-of-plane MCH,) w(BC,) WH,)
JL
28 29 30 31 32 33
vs(CH,), out-of-plme v(BH’) asym., out-of-phase 6&H,), out-of-plane o(CH,) NBC,) WH,)
34 36 36 37 38 39 40 41
va(CH,), in-plane vs(CH,) >{;K$$, in-plme
B 1n
42 43 44 46 46
va(CH,), out-of-plane B,(CH,), out-of-plane a#=,) ring twist WH,)
B su
47 48 49 60 61 62 63 64
va(CH,), in-plane ve(CH,) v(BH’) asym., in-phase &(CH,), in plane &(CH,) NH,) vs(B%) &RC,)
%I
3
in-plane in-plane
v:(RC:) NH,) r(BC,) ring pucker
Fundementpl frequency (cm-‘) 2986 2906 2060 1423 1321 a74 840 608 280
2986 (2906) 1423 1321 1108 (1011) (368) 2968 (1972) 1437 (936)
2941 1441 1011 (3‘3’3) 2968 2924 1437 1324 1147 (1017)
2941 1441 1084 743
2958 2924 1606 1437 1312 (1017) 172
1208
J.
H. CARPENTEZR, W. J. JONES, R. W. JOT~AMand L. H.
LONG
There are no peaks in the low temperature spectrum of TMDB in the 2500-2600 cm-l region. Peaks in this region are characteristic of terminal B-H stretching vibrations ; in diborane and all the methyldiboranes except TMDB itself intense peaks are observed [13] ; the absence here of any peaks demonstrates the very low concentration, if any, of disproportionation products. Vibrations of the B-H’ bridge bonds occur in the 1600-2200cm-l region [l-4,81. Two of these are expected to be Raman active, the symmetric in-phase vibration vagiving rise to a polarized peak and the asymmetric out-of-phase vibration vag giving a depolarized one. In the observed spectrum there are three polarized lines at 1976,2047 and 2128 cm-l, and none depolarized, in this region. Thus the asymmetric out-of-phase vibration vSOis not observed. The three peaks are due to the interaction by Fermi resonance between the symmetric in-phase fundamental va and two overtones or combination tones. This is discussed more fully below, where it is estimated that the unperturbed levels are at about 2016, 2050 and 2084 cm-l. The fundamental va is the central level; the level at 2016 cm-l is the first overtone of the Raman active methyl rocking vibration whose fundamental is observed at 1011cm-l, while the level at 2084 cm-l is the combination of the infrared active asymmetric BC, stretching vibration V~ at 772 cm-l and the symmetric methyl deformation vibration vsl at about 1312-1324cm-i [4]; each is of species B,, so their combination level is totally symmetric. In the 1400-1450 cm-l region there is a rather broad peak at 1441 cm-1 with a shoulder at 1426 cm-l. The whole feature extends from about 1400-1470 cm-l. Again it is not possible to be certain of the states of polarization, but from a comparison of the appearance of the peaks at the two states of polarization, it was found that the peak at lower frequency has a smaller depolarization ratio than the shoulder whose depolarization ratio is close to +. This region is characteristic of asymmetric methyl deformations, and in the Raman spectrum of this compound there should be one polarized fundamental, va, and three depolarized ones, vi?, vaOand v~. The peaks observed are assigned to these fundamentals, and it is probable that the vq vibration, of species A,, is at about 1426cm-l. The weak polarized line at 1321cm-l is assigned to the symmetric methyl deformation vibration vg of species A,. In common with many such compounds (e.g. the methyl halides [ll]), the symmetric methyl deformation vibrations give rise to weaker peaks in the Raman spectrum than the asymmetric deformation modes. This is in contrast to the methyl stretching vibrations, where the symmetric vibrations give rise to more intense scattering than the asymmetric. The opposite is true in the infrared [a], where the asymmetric stretching and the symmetric deformation vibrations give stronger absorption peaks than the symmetric stretching and asymmetric deformation vibrations respectively. In the region from 800 to 1200 cm-l there occur the various methyl rocking (in the plane of the B,C, skeleton) and wagging (out-of-plane) modes, as well as the B-C stretching modes. In the infrared spectra of the methyldiboranes [l-4] the asymmetric BC, stretching vibrations occur around 1100-1160cm-l, and are marked by a large lOBisotope shift of about 30 cm-l. In TMDB the infrared active [ 131J. H. CARPENTER, W. J. JONES,R.
W. JOTEAMand L. H. LONG, Chem. Commun. 881 (1968).
The Ramen ape&a of the methyldiboranes-I
1209
vibration v, occurs at 1147 cm-l. In the Raman spectrum there are two depolarized peaks in this region, at 1084 and 1108 cm- l, the lstter having a small shoulder at high frequency. One of these peaks is due to the asymmetric BC, vibration vls. It is possible that the shoulder is the l*B component of the vibration which would thus be assigned to the 1108 cm-l peak. The peak at 1084 cm-l is assigned to a methyl rocking or ws,gging vibration, as is that at 1011 cm-l. The two strong polarized peaks at 508 and 840 cm-l are assigned to the B-B stretching vibration vg and the symmetric BC, stretching vibration v7 respectively. LEHWUW et al. [4] show that this assignment gives better agreement with their Average Rule [14] than the opposite one. The B-B stretching vibration in diborane is s,t 788 cm-l (this is the llB component) and a drop of frequency on substitution of heavier methyl groups for terminal hydrogen is expected. There is no observable splitting due to boron isotopes in TMDB although for the components in diborane it is about 15 cm-l ; this decrease in splitting is also due to the greater mass of the termin&Xl groups. The peak at 368 cm-l is depolarized in the room temperature spectrum (its polarization could not be determined at the low temperature). This peak m&y be due to one of a number of BC, deform&ion or rocking vibrations. The peak at 280 cm-l, however, is polarized and so is to be assigned to the symmetric BC, deformation vibration v~, as this is the only totally symmetric fundamental which is expected in this region, and all the other A, vibrstions are accounted for. If the 368 cm-l line is assigned to the BC, rocking vibration val, then the average of these in-plane BC, deformstions for the Raman active vibrations is 324 cm-l. This compares with the value of 320 cm-l for the in-plane BC, deform&ion vibration of boron trimethyl [9]. However, in boron trimethyl the out-of-plane deformation vibration is at 336 cm-l, so the peak in TMDB could be due to the BC, wagging vibration vQI. This leaves the weak lines at 571, 743 snd 874 cm-l. The last is the in-plane methyl rocking vibration vs. The depolarized line at 743 cm-l might be the ring twisting vibrstion v~, which occurs at 1012 cm-l in diborane [8]. The line at 571 cm-l is polarized and hence is not a fundamental, since all the A, fundamentals in this region have been accounted for. It is probably the first overtone of the symmetric BC, deformation vg which occurs at 280 cm- l. The relatively high intensity for a non-fundamental is due to Fermi resonance with the fundamental at 608 cm-l. 2. l,l-dinzethyldiborane The peaks observed in the Raman spectrum can be assigned in a similar way to those of TMDB. However, because the molecule is of lower symmetry, most of the vibrations are active in both the in&red and Raman spectra. Hence more use can be made of the assignmenta of LEHMAXN et al. [3] for the infrared spectrum. The peaks at 2970 and 2947 cm-l are assigned to the asymmetric methyl stretching vibrations vz7, vr, V~ and vn,, the intense polarized peak at 2909 cm-l is assigned to the symmetric methyl stretching vibration ve, and the polarized peak at 2831 cm-l to the overtone of an asymmetric methyl deformation vibration. In the infrared spectrum peaks occur at 2968 and 2841 cm-l (the latter being a shoulder). [14] W. J. LEEXANN, J. Mol. &m&y 7, 1 (1961); W. J. LEE-, [M] V. N. KAPSSXTAL, Rum. J. Phy. Chmn. 40, 508 (1966).
ibid. 7, 261 (1961).
1220
J. EL CARPENTER,W.
J. Jomzs, R. W. JOTH~Mand L. H. Lor~a
The former corresponds to the two peaks at 2970 and 2947 cm-l in the Raman spectrum; the shoulder at 2841 cm-l is then probably a wwzbhuthn of asymmetric methyl deformation vibrations which is of the same symmetry species as the fundamental at 2958 am-l, and thus enhanced by Fermi resonance. The weak, rather broad, depolarized line at 2576 cm-l, and the strong polarized line at 2499 cm-l are due to the asymmetric and symmetric BH, stretching vibrations ySgand y3 respectively, and correspond to infrared frequencies of 2671 and 2494 cm-l. In the 1600-2200 cm-l region, there are again three polarized peaks and none depolarized. Two totally symmetric f~damentals ye and ye, and two depolarized, ~20and yzltwhich are all associa~ with the I&H, bridge, are expected in this region. Of the totally symmetric ones, the ~~metric in-phase vibration Q gives rise to the very strong absorption peak at 1546 cm-1 in the infrared spectrum; the very weak polarized Raman peak at 1533 em-l may correspond to this peak. The three peaks at 2152, 2120 and 2091 cm-l are therefore associated with the symmetric in-phase fundamental yq and overtones or combinations interacting by Fermi resonance, as for TMDB. It is shown below that the unperturbed levels are at about 2138, 2125 and 2104 cm-i. The interacting levels are thus probably the first overtone of one of the methyl rocking vibrations (the fundamentals of which occur at 1056 cm-l in the Raman spectrum, and at 1063 and 1064 cm-i in the infrared spectrum) in the case of the lower level, and the combination vE+ v. for the upper, the fundamental P* being at 2125 cm-l. We should expect the intensity pattern for this group to be similar in the infrared and Raman spectra; in the observed infrared spectra only one peak at 2096 cm-l is reported; in the spectrum illustrated [3] this peak is somewhat broader than other nearby peaks and covers the range of the Raman peaks. The broad depolarized peak at 1434 cm-l is due to the asymmetric methyl de. . 4 formation vibrations vu, y14,Ys2and y3,,. In the infrared spectrum the corresponding band is at 1441 cm-l. The weak polarized peak at 1318 cm-lis due to the symmetric methyl deformation vibration V?and the corresponding infrared bands are at 1326 and 1316 cm-l. The two peaks at 1133 and 1164 cm-l correspond to the two bands at 1126 and 1163 cm-l in the inf&red spectrum. L-X% et d. [3] assign the lower to the asymmetric BC, stretch~g vibration and the higher to the BH, deformation frequency. This assignment should be reversed, for the Raman peak at 1164 cm-l is definitely depolarized while that at 1133 cm-i, although having a fairly high depolarization ratio, is polarized. The medium intensity peak at 1056 cm-l, which has a shoulder at about 1070 cm-l, corresponds to the infrared bands at 1064 and 1053 cm-l. The Raman peak is depolarized. This region is characteristic of methyl rocking and wagging modes, and these peaks may be due to the methyl rocking mode y33or the wagging modes yls and y2& From a comparison with the Raman spectra of other methyldiboranes [13] the wagging modes seem more likely. The peak at 838 cm --1has a high depolarization ratio, but is polarized. The corresponding infrared peak at 829 cm-l is of type A ; the vibration is thus totally symmetric. The advent by L-m et al. [3] of this band to the sketch BC, stretching vibration y10is reasonable.
The Raman speotraof the methyldiboranes-I
1211
The very strong polarized peak at 619 cm-l is then naturally assigned to the B-B stretching vibration Q. This compares with the values of 788 cm-l for 11B2H, and 508 cm-l for TMDB ; all are intense peaks. In the room temperature spectrum the peak is seen to have two components; a stronger one at 613 cm-l with a shoulder at 624 cm-l. These are due to molecules containing llBH, and IOBH, groups respectively. In comparison the splitting in diborane is 14 cm-l (8), while it is not observed in TMDB. The peak at 317 cm-l observed at -70°C. is resolved in the room temperature spectrum into two components; a depolarized peak at 312 cm-l and a shoulder (whose polarization could not be determined) at 324 cm-l. In addition a peak is observed at 253 cm-l in the room temperature spectrum which, owing to the poorer signal-to-noise ratio close to the exciting line, was not observed at the lower temperature. The latter peak, which is polarized, is assigned to the symmetric BC, deformation vibration Q.; this is the only vibration of symmetry species A, which is expected in this frequency range. There is no unambiguous assignment for the other two peaks ; one may be due to the ring pucker vibration vse which occurs at 368 cm-l in diborane [8] and which is likely to decrease in frequency with increasing methyl substitution. Alternatively, one or both may be due to the BC, rocking vibration vQs,wagging vibration vs5,or twisting vibration vl,. This leaves the weak peaks at 513, 1591 and 1675 cm-l. The fist might just be due to tetramethyldiborane impurity, since there is an intense peak in the spectrum of the latter in this region; however, l,l-DMDB is easily isolated and relatively stable, and the absence of corresponding peaks due to other methyldiborane impurities and diborane make this unlikely. It is more likely due to the first overtone of the vibration at 253 cm-l. The two depolarized peaks due to the fundamentals vz,,and val are not observed. The weak peak at 1591 cm-l is too low in frequency to be due to either of them; it is assigned to a combination level of the B-B stretch vll at 619 cm-l with the methyl rocking vibration observed in the infrrtred spectrum at 975 cm-l. The very weak peak at 1675 cm-l is due to the first overtone of the symmetric BC, stretching vibration at 838 cm-l. FERMI
RESONANCE
IN
THE
1950-2200
cm-l
REGION
The interaction of two vibrational energy levels of the same symmetry species in a molecule, giving rise to a change in their energies and a mixing of the vibrational wave functions, is well known.* If the interaction is between a fundamental level (that is, one in which all the vibrational quantum numbers v are zero except one which is unity) and a combination or overtone level, then the mixing of wavefunctions means that the latter can “borrow” intensity from the former, and hence such an overtone or combination, which would not give rise to an infrared or Raman peak if the vibrations were harmonic, can now occur with appreciable intensity. * See,for instance, Ref. [ 111,p. 216 ff, also C. PLACZEK, The Rayleigh and Ram Scattering, translated by A. WERBIN (UCRL-!l!rana-626(L), chapter 20. U.S. Atomic Energy Commission (1969)).
1212
J. H. C~RPENTI~R, W. 5. JONPS, FL W. JOTEAMand L. H.
LONG
When there are three intera&ing levels, as in both these molecules, the system has fewer experimental data than interaction parameters. There is hence no unique solution, and so some simplifying assumptions must be made. Let the unperturbed energy levels be ,?Sr,E, and E, above the ground state, and the interaction energies be W1s, Wr, and W,,. Then, if the resonance is close, we may apply a perturbation method; the perturbed levels are then the eigenvalues of the matrix:
For any eigenvalue, the eigenvector gives the coefficients of the unperturbed wave functions in the eigenfunotions. Thus if all the intensity is due to the fundamental, the square of its coefficient in the three perturbed levels is proportional to the intensity of the line corresponding to that level. In the case of TMDB, the perturbed levels are at 1976, 2047 and 2128 cm-l, with intensities of 16: 8: 17 (i.e. approximately 2: 1: 2). The spacings are thus 71 and 81 cm-l between the central level and the other two, and the intensities of the latter are approximately the same. Because the energy level di&rences were roughly the same, and because of the intensity pattern, an unperturbed system in which the energy levels and their interactions were Ernest about the central peak was tried. Accordingly, the following gumptions were made: . g,
El = E, - E, = cl The central unperturbed level is the fundamental, and all the observed intensity is due to it. (iii) WI, = W2, = W, and WI8 = 0. WI, and W=, which are interactions between a fundamental and an overtone or combination, are due to cubic terms in the potential energy, while WB, which is an interaction energy between two levels which are not fundamentals, is due to a quartic term. It is thus plausible that the latter may be of a smaller order of magnitude than the former. The secular deter~~t now assumes the simple form:
E* -
E,+d--E
W
W
0
_E, - E
W
==o.
w
E, - a -
El
This can be solved analytically, giving the perturbed levels: E = I$, E2 f
q(2Wz + d2)
The normalised eigenve~~r matrix x, where Hx = SE (H being the pe~~bation
The Reman spectraof the methyldiboran~1
1213
matrix and E the diagonal eigenvalue matrix) is: X+d 2x
W
x-a-
x
2x
W
a
W
X
x
x
--
(X - 4 -2x
W
(X + 4
x
where X = 1/(2lP
2X
_
+ a*).
The second row of this gives the coefficients of the fundamental in the three perturbed levels, so the intensities of the three observed peaks should be in the ratio Ws:dz: W*. Using the observed energy levels and intensities, we find that d = 34 cm-l and W = 48 cm-l. Thus the unperturbed levels are at 2016, 2060 and 2084 cm-l, giving perturbedlevels at 1974, 2060 and 2126 cm-l, which compare with the observed values of 1976, 2047 and 2128 cm-l. The above solution is physically reasonable but is not unique, ss pointed out previously. It should be noted that the peak corresponding in energy to the unperturbed fundamental has least intensity, and indeed, if d -+ 0 its intensity falls to zero; that is, the perturbed level at this energy is a mixture of the two overtone levels only. In the spectrum of 1,l-DMDB there are again three polarized peaks in this region, at 2091, 2120 and 2152 cm-l, with intensity ratio of 14: 14: 20. These are again nearly equally spaced, with separations of 29 and 31 cm-l. However, the asymmetry of the system indicates that the situation is not the same as for TMDB. Values of the W’s and E’s were then tried on the assumption that again the central unperturbed level was the fundamental, that WI8 = 0 again, but now WI, # W,, and (Es - Ed # (Es - Es). It was found that if WI, > W, and (8, - E1) < (Es E,), then the separations remained roughly the same but the greatest intensity was in the highest frequency peak. The following values gave a reasonable fit with the observed results: E, = 2104 cm-l, E, = 2125 cm-l, E3 = 2139 cm-l, W,, = 21 cm-l, Wm = 17.5 cm -l. These gave perturbed levels at 2156, 2120 and 2091 cm-l, and relative intensities of 18.6, 14.1 and 15.3, compared with the experimental levels of 2162, 2120 and 2091 cm-i and relative intensities of 20, 14 and 14. Discussion
Comparing our assignments above with those of LEESMANN et ct.!.[3, 41, it can be seen that, with the exception of the slight change in the assignments of the methyl stretching vibrations, and the corrected values for the symmetric in-phase r(BH’) vibrations, our assignments are in agreement. Assignment of the fundamentals is included in Tables 1 and 2. The majority of the fundamentals have now been assigned but there are still some low frequency fundamentals which are not accounted for. The absence of infrared data below 650 cm-l also means that some of the Raman peaks cannot be assigned unambiguously. General force field calculations have been carried out on these molecules [16], and it is instructive to compare the calculated values with those observed. For most
1214
J. H.
(ktPRNTJ3R,
W. J. JONES, R. W. JOTHAN and L. H.
LONG
vibrations there is fairly good agreement. In particular, the calculated frequencies for the B-B stretching vibration are 502 cm-l in TMDB and 696 cm-l in 1,I-DMDB ; we observed 608 and 619 cm-l respectively. If we use the calculated frequencies to assign the lower frequency lines, then in the spectrum of l,l-DMDB the line at 317 cm-l is due to the ring pucker vibration vS8and/or the BCz rocking vibration vaa (or possibly the wagging vibration vzJ ; and the line at 253 cm-l is due to the BC, deformation vibration vls; this is as assigned. In TMDB the line at 365 cm-l corresponds either to the BC, wagging vibration vaz (calculated frequency = 439 cm-i) or the BC, rocking vibration vZ1(calculated frequency = 287 cm-l). The line at 280 cm-l, being polarized, is due to the BC, deformation which Kapshtal calculates at 188 cm-l. The agreement in this region for TMDB is rather poor; this is probably because force constants for these vibrations are not well characterized, and he was not able to apply any least-squares method to the vibrations for these molecules in this region as the infrared spectra did not extend below 660 cm-l.