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Infrared spectra of deuterated methanols and force field
Spectrochtmlca Acts, Vol. 3OA, pp. 1133 to 1145. Pergamon Press 1974. Printed in Northern Ireland
T.t,ared spectra of deuterated methanols and force field P. D. i~AT.LINSON* a n d D. C. M c K E A N Department of Chemistry, Universityof Aberdeen, Aberdeen A B 9 2 U E (Received 7 August 1973) Abstracb---Infrared spectra have been obtained in argon matrices at 20 K from CHD2OH, CDaOD and CDaOH. The two CH stretching frequencies seen in CHD$OH reveal the presence of t w o types of CH bond whose lengths are predicted to be 1"094 and 1.100 A respectively. A harmonic force field is calculated, based on matrix frequencies for eight isotopic species determined here or in the previous work of BARm'mS and HAT+LAM,and employing 29 parameters, including two hybrid orbital force field constraints. The CH and CD stretching frequencies were analyzed both by full (12 x 12) and by limited (3 × 3) refinement procedures, and the presence e r a 20 cm-x Fermi resonance shift on the lower A'CH s stretching mode deduced. The 3 × 3 treatment with constrained stretch-stretch interaction constantsf, a' = fas', appears to predict satisfactorily the positions of nearly all of the uncertain CH and CD stretching frequencies. Further work is needed to locate all the fundamental frequencies and to improve the isotopic shift data. INTRODUCTION ALTHOUaH t h e force field of m e t h a n o l has been studied t h r e e times in the last t w e l v e years [1-3], all these investigations h a v e been based on d a t a f r o m t h e gas p h a s e which for this molecule are u n u s u a l l y unreliable, due to t h e g r e a t complexity, e x t e n t o f overlapping a n d in certain cases, t h e weakness o f t h e bands. Moreover no a c c o u n t could be t a k e n o f t h e effects o f F e r m i resonance in t h e C H or CD stretching regions, or o f possible differences in C H b o n d strength, n o r was t h e r e available a n y e x a c t knowledge o f t h e positions o f C H s a n d CD a d e f o r m a t i o n a n d rocl~iug modes. T h e a d v e n t o f t h e m a t r i x isolation technique, which offers considerable a d v a n tages for t h e e x a c t location o f f u n d a m e n t a l bands, gave hope o f g r e a t e r insight i n t o t h e force field, a n d t h e present s t u d y is based largely on t h e frequencies observed in argon matrices a t 20 K b y BAR~C~.Sand HALLAM [4] for t h e species CI~sOH, I ~ H s O H , CHaOD, CHalSOD a n d CDaOD(H ). To the d a t a for t h e a b o v e species we here a d d a s t u d y o f C H D 2 0 H a n d CDaOH. ~ T h e C H stretching region of the f o r m e r species will, on t h e one h a n d , indicate d i r e c t l y w h e t h e r t h e r e are two t y p e s o f C H b o n d present [5, 6] a n d on t h e other, m a y be helpful in elucidating t h e e x t e n t o f F e r m i resonance affecting t h e lower C t t a a n d CD3 stretching modes. This l a t t e r use has been discussed b y one o f us previously for t h e case o f c o m p o u n d s containing s y m m e t r i c a l m e t h y l groups [7J, a n d m e t h a n o l is a n a p p r o p r i a t e model s y s t e m to investigate, t o see i f t h e * Present address: Department of Chemistry, University of Reading, Reading, England. J" Barnes and Hallam only observed bands due to CD8OH as impurities in their spectra of CDsOD. [1] [2] [3] [4] [5] [6] [7] 5
M. MA.RGOTTIN-:MACLOU, g'. Phys. Radium 21, 634 (1960). M. F~L~ and E. WH~LT.~Y,d. Chem. Phys. 34, 1554 (1961). G. Z ~ I , J. OVm~END and B. L. CP~W~ORD, J. Chem. Phys. ~ , 122 (1963). A. J. BAP,m~s and H. E. YIAT.T.~L~,Trans. Faraday See. 66, 1920 (1970). D. C. McKEAN, Chem. Commun., 1373 (1971). D. C. M c K E ~ , J. L. DUNCAN and L. BATT, Spectrochim. Acts, ~gA, 1037 (1973). D. C. McKEAI% Spectroehim. Acts, 29A, 1559 (1973). 1133
1134
P. I). 1WAT.T.rNSO~and D. C. McKEAN
CHD 2 method for assessing Fermi resonances is applicable also in the case of asymmetric ones. I t was hoped initially that a general force field might be determinable for methanol, as was achieved for the methyl halides [8, 9]. Although this hope has not been fulfilled, the results concerning the assessment of Fermi resonance are encouraging. EXPERIMENTAL Samples of CD30D and CHD20t{, quoted as being 99~o isotopically pure, were obtained from CIBA and Prochem Ltd., respectively. CD30H was prepared from the CD30D b y exchange with phenol Spectra were recorded on a Perkin-Elmer 225 infrared spectrometer calibrated with frequencies from the I.U.P.A.C. tables. Argon matrices of M/A ratios varying from 200 to 1000 were deposited on a CsI window a t 20 K in an Air Products AC-3L Cryotip apparatus. Some of these spectra are illustrated in Figs. 2, 3 and 4 for the CHD20H, CDaOD and CD30H respectively. The vapour phase spectrum of the latter in the CH stretching region is shown in Fig. 1. In general the degree of isolation achieved at the higher M/A ratios was apparently not as good as that of Barnes and Hallam. A~SSIGNMENTS The presence of bands due to dimers and multimers at the highest M/A ratios continues to present difficulties, especially since hydrogen bond formation can cause considerable changes in intensity and frequency in modes other than OH stretching and bending ones. In CD30H and CD30D only points of difference between ourselves and [4] will be noted. CHD20H In the CI-I stretching region, in the gas phase, shown in Fig. 1, two Q branches are seen, at 2978.7 and 2919.3 cm-* respectively, from which we infer the existence of two kinds of CH bond whose lengths are 1.094 and 1-100 A respectively from the correlation graph of [6]. The intensities of the corresponding matrix bands at 2986.4 and
I 3050
I 3000
t 2950
] 2900
K 2850
Fig. 1. Infrared spectrum o f O H D s O H , vapour phase, 80 m m pressure in 10 c m cell. [8] J. L. DUNCAN, A. ALLA~ and D. C. M C K E ~ , Mol. Phys. 18, 289 (1970). [9] J. L. D u n c A n , D. C. McKEA~ and G. K . SPEIRS, Mo~. Phys. 24, 553 (1972).
Infrared spectra of deuterated methanols and force field
1135
MIA=900 ~ 1 ~
3800
'
1400
3()00 CM-1
25'00
2000
1200
1(~0
8~)0
CM-1 Fig. 2. Infrared spectra of CHD2OH (23 p mole) in argon matrices at 20 K.
2931.0 cm -1 (Fig. 2) are in keeping with the expected distribution of 2 weak (trans t o oxygen unshared pairs) and one strong bond (trans to OH).* Thus the higher frequency m a y be assigned to the s species of CHD2OH, the lower to the as one. I n t he region 2300-2100 cm -1, six bands are found, viz 2242.3, 2208.1, 2197, 2186, 2134-2 and 2113.3 cm -1, of which the two at 2197 and 2186 cm -1 are assigned as first overtones of the bands at 1095.5 and 1090-8 cm-L Since the as species has one weak and one strong CD bond, whereas the s species has two weak ones, the following assignments are readily made: as 2242.3, 2134.2 cm-l: s 2208.1 [a ~] 2113.3 cm -~ [a']. There are perhaps small Fermi resonances involving t he two overtone bands with the lower-lying fundamentals (see further below). I n the region 1500-1200 em -~ 6 absorptions due to OH and CH bending modes are expected to appear. U n f o r t u n a t e l y most of the bands here are broad and very weak. A band of medium strength a t 1268 cm -1 has the appearance like t h a t of an OH bend in the other isotopic species, and is so assigned, to bot h s and as species, although the refinement calculations place the as mode 18 cm -1 lower at 1250 cm-L Amongst * Although such intensities can be misleading, the evidence for t r a n s effects of this kind is now
overwhelming as for example in (CH8)90 [10]. [10] A. A z ~ , (1971).
D. C. M c ~ ,
J-P. l~mC~AuD and M-L. JoszE~, Spectrochirn. Ac~a 27,%, 1409
1136
P . D . MALLINSON and D. C. MCKEA_~
-•-• I
3800
14oo
'
M/A=900
30'00 CM-1
12'oo
'
1(:;oo
2500
'
2000
8~o
CM-1 Fig. 3. Infrared spectra of CDaOD in argon matrices at 20 K : M/A 900-23 p mole, M/A 200-14 p mole.
other absorptions at 1414, 1376, 1355 and 1318 cm -1, only two are compatible with the force field, 1355 as ~5 in the as species, 1318 cm -I as ~10(a') in the ~. However it seems likely t h a t there is extensive interference here from multimer bands, and further work is needed both to confirm the above assignments and to locate the missing monomer fundamentals, whose positions are predicted to be 1431 (~5, s) and 1290 (Vlo, as). I n the region 1100-1000 cm -1, we expect the CD~ scissors and CO stretching modes. Two pairs of bands are seen, at 1095-5[1090.8 and 1040.3/1013.3 respectively. The force field calculations show t h a t both pairs of modes are strongly mixed in character, the proportion of CO stretching being greater in the lower. They also indicate the as frequencies to be 1090.8 and 1040.3 cm -~, the other two, s, which is also in keeping with their relative intensities. In the region 1000-800 cm -~, 4 bands are seen, at 947.9, 926.7, 874.2 and 870.4 cm -~ respectively, of which the second is very weak. The first band is readily assigned as the CD~ wag of the as species, but the other three present some difficulty. The fact t h a t the very weak baud at 926.7 cm -~ increased in intensity on passing from M/A = 200 to 900 suggested t h a t this was a monomer baud, and initially this was assigned as the CD 2 wag of the s species. The other two lower frequencies were then attributed to the CD 2 rocks of the two species. However this gave a product rule
Infrared spectra of deuterated methanols and force field
1137
M/A=200
MIA=900 .
3900
1400
3500 '
30'00 CM-1
1200
CM-1
25'00
1000
~
'
2000
800
Fig. 4. Infrared spectra of CDsOH in argon matrices at 20 K : 23 p mole deposited.
discrepancy of about --10% in the a' class of the 8 species (relative to C H 3 0 H ) which is unreasonably high, and in addition, attempts at refinlug to these assignments threw out several quite trustworthy frequencies in the other species.* I t was finally concluded that the 926.7 cm -1 band probably arises from the CD~ wag of dimeric a8 --CHD~OH* and that the lower two bands represented three fundamentals. In particular the CD 2 rocks of both molecular species were predicted to lie within 0-2 cm -1 of each other, and the CD 2 wag of the a about 16 cm -1 higher, near 883 cm -x. Accordingly the former were assigned to the 870.4 cm -~ band, the latter to that at 874.2 c m - L t The torsional mode occurs in the 200 cm -a region and according to [4] is overlapped b y the hydrogen bond stretching bands of multimers, as well as being split into A and E components. No investigation was therefore made here. CD30D The matrix spectra are shown in Fig. 3. The monomer frequencies found here differ only slightly from those in [4]. Due to the slightly poorer quality of our spectra, the a' CDs rock could not be identified here, and the value of 1055 from [4] is accepted, although the refinement value is 13 cm -~ higher. I t is interesting to note that of the * A t t e m p t s to find a CH2DOH mode to suit this frequency also failed. t Although this is 9 em -1 below the computed value (Table 1), it is considerable nearer t h a n the 926.7 cm -1 band.
1138
P . D . MATZ.~NSONand D. C. MCKEA~
two a' frequencies in this region, 1030.8 a n d 1055-0 cm -1, t h e higher b a n d is in fact calculated t o be t h e CD8 rock coupled to OD bending as previously surmised [4]. I n the CD stretching region, the assignments in [4] o f 2254 cm -~ as a ~, 2219 as a' modes, are here reversed, so t h a t the sequence a' > a ~ > a ' n o r m a l to a m e t h y l g r o u p containing two weak a n d one strong b o n d is observed.* CD30H F i g u r e 4 shows t h e m a t r i x spectra o f this species. Several b a n d s in t h e s p e c t r u m of CD30D a t t r i b u t e d t o " s e c o n d site" m o n o m e r s in [4], were here shown to arise from C D 3 0 H , for example, t h e a'CD 3 s y m m e t r i c d e f o r m a t i o n ~5 a n d t h e CO s t r e t c h ~8. T h e a'Oa,CD ~ m o d e a t 1031-3 cm -1 in [4] was n o t observed b y us in our 100% C D 3 0 H s p e c t r u m a l t h o u g h a possible sign of it was seen in a 70~o CD30D/30~/o C D 3 0 H film n e a r 1039 c m - l . ~ Below 900 cm -~, C D 3 0 H shows a p r o m i n e n t m o n o m e r b a n d a t 860.7 cm -1 w i t h a possible v e r y w e a k m i n o r c o m p o n e n t a t 866.5 cm -1. These are assigned to the a" a n d a~PcD8 modes ~11 a n d ~ respectively, a l t h o u g h the order o f m a g n i t u d e is reversed b y t h e f.f. calculations (see Table 1). I t would be possible t o i n t e r c h a n g e t h e assignments, b u t o n l y a t t h e expense of f u r t h e r increasing t h e p r o d u c t ratio discrepancy (see below). A f u r t h e r consideration is t h a t ~11 is p r e d i c t e d a t identical positions in the CDsOH and CD30D a n d since the 860-7 cm -~ b a n d is seen in b o t h cases, i t m u s t therefore be ~11.$ F i n a l l y we n o t e t h a t t h e higher a'CD stretching m o d e lies at 2259.9 cm -1 in C D 3 0 H , which is 6 cm -1 higher t h a n its position in C D 3 0 D (2253.9 cm-~). Since 2~ 5 for these two molecules is e x p e c t e d a t a b o u t 2 × 1 1 2 7 - 2 - 10 = 2244-4 a n d 2 × 1 1 3 2 - 0 - 10----2254 cm -~ respectively, it is possible t h a t the a b o v e shift derives f r o m a F e r m i resonance.§ Failing the latter, a n a l t e r n a t i v e e x p l a n a t i o n involves coupling to t h e OD s t r e t c h a t 2705 cm -~, a l t h o u g h this would require a n i n t e r a c t i o n force c o n s t a n t n o t i n c o r p o r a t e d so far into t h e force field.
Torsional frequencies of all species T h e values q u o t e d in [4] are incompatible with each other. This is p r o b a b l y due to overlapping of the E c o m p o n e n t in C H 3 0 H a n d of t h e A c o m p o n e n t in CH3OD b y the dimer h y d r o g e n b o n d stretching bands. F o r refinement purposes we t o o k t h e A c o m p o n e n t f r e q u e n c y in C H 3 0 H o f 272 cm -1 a n d assumed t h a t the corresponding C H 3 0 D f r e q u e n c y was 213 cm -1, these two frequencies being compatible. * This sequence is found generally for cases where the stretch-stretch interaction force constant f o r f ~ is small, as in all cases of CH bonds. t This apparent paradox we can only explain in terms of the accidental comb'mation of two factors: (1) that the degree of isolation in the 100~o film was poorer than usual: (2) that the ~aaCD3(a~) intensity is extremely low, especially in the multimeric species. The latter appears to be true in CD3OD at least. + It is just possible however that the presence of this 860-7 cm-1 band in the CD3OD spectrum is due to OH impurity in the latter. The band at 894.7 em-1 in [4], assigned as v7 of CDsOH is very broad and weak and probably arises from multimers. § Multimer bands obscure the region where 2~5 is expected to occur.
Infrared
Table
spectra
1. C o m p a r i s o n
of deuterated
of observed
3667.3 3005.3 2847"9 1474.1 1451.4 1335.0 1076.7 1034-0 2961-9 1465.8 1109.0 272.0
rI rs r3 rt r6 r6 r7 rs ro rio ~l i ~
17.2 ----4.0 -25-5 -----
frequencies
37 30 1000 15 15 13 11 10 30 15 11 10
--0.7 --0-1 (2861.5) -~-0.1 --1.1 --4-0 ~-1-8 --0.7 --2.7 --3-5 --1-5 -I-1"7
-9.9 4.8 1.1 5.6 8.0 6.5 15.5 8"9 ----
-0.2 5-0 1.0 0.2 2.0 0.2 0.4 2.0
CHsOD
(0.0) 0.0 - - 1-3 ~-0.2 0.0 --~-0.3 0.0 0-0 --]-0.7 (2.1) (8-2) (0.0)
/~v c
0-4
-I- 0"1 (0-0) (0.0) (0.1) (1.1) 0.0 (5.3) --0.2 (0-0) (0.25) (2.9) (1.2)
0.1 0.5
~Obll 3666-0 2259.9 2076.4 (1030-8) 1127.2 1293"4 866"5 t 989-4 2217.1 1067-8 860.7t --
rob.
~,
3665.8 2896.4 2113.3 1095.5 -1268.2 874.2 1013.3 2208-1 1317-7 870-4
37 30 21 11 13 9 10 22 13 9
27 30 1000 15 15 9 12 10 30 15 11 10
-I-3"1 --I-1.4 (2861.7) -{-6-8 ~-6.7 --0.3 -~7.0 --4.7 --2.8 --3.5 --1.5 (215-2)
CDsOD
O'v
A°-c
robs
37 23 21 10 11 13 9 10 22 11 9
--2.0 -~- 12.1 --6.7 --7.9 --5.0 --6.8 ~-8.3 --2.5 ~4.2 -~-0.8 --5.2 (256.5)
2704.8 2253.9 2077.0 1030.8 1132.0 776.5 1055.0 984.5 2217.8 1067.6 860.7t
s-CHDsOH
rI •s 1,I rt rs re r7 v8 rs rio ~'lx rxl
2706.1 3006-6 2845.5 1472.7 1451.4 864-9 1227-3 1042.8 2961.9 1465.8 1109.0 213-0
CDsOH
O'AV
1139
for methanols
~SCHsOH
CHslSOD A1~obS
and force field
and calculated*
CHsOH
~x rs rs rt ~s re r7 ~s ~s ~1o vlt r~s
methanols
O'V 27 23 21 10 11 8 10 10 22 11 9
AOv-O -t-2-0 -I-6"6 --6.0 --1.3 --0.1 -~-2.1 --13.1 --5.2 -~-4.9 -I-0.6 --5.2 (197-5)
a~-CHDIOH
A?-~ --2.2 0.0 --2.1 ~-4.9 (1430.7) --0.5 --9.0 ~2.9 - - 5-5 -+- 8.6 -I-2.6 (260.2)
rob.
~,
A?-~
3665.8 2931.0 2134.2 1090-8 13557 1268.2 947.9 1040.3 2242.3 -870.4 --
37 29 21 11
--2.2 0-0 -L-3"7 ~-7.9 (1352.2) -t- 18.2 -+-6-2 -+-5.9 ~ 0.6 (1290.0) --t-2-4 (259.3)
13 10 10 22 -9
~O-C ~ 1%bserved_~calculated e x c e p t for b r a c k e t e d values, w h i c h a r e t h e ca/cu/ated frequencies: similarly for * F o r c e field of T a b l e 5. Calculated frequencies w e r e ' d e h a x m o n i z e d ' a f t e r r e f i n e m e n t w a s complete, for display here. t A l t e r n a t i v e l y , ~n(pcDs, a n) could lie a t 866.5 c m -1 in b o t h C D s O H a n d CDsOD , in w h i c h case Ao-c w o u l d b e -I-0,6 c m -1, w i t h vT(pcDs a') a t 860.7 c m -1, A ° - c t h e n b e i n g -{-2.5 c m -1. H o w e v e r t h e p r o d u c t rule ' o v e r s h o o t ' w o u l d t h e n be e v e n g r e a t e r t h a n before.
P . D . MAT.T.~SONand D. C. MoKEAN
1140
CHsOH and CHsOD a" rock, ~9 The refinement calculations below indicated t h a t the assignment in [4] of r9 to the v e r y weak and broad absorptions at 1157 and 1160 cm -1 respectively in CHsOH and CHsOD was incompatible with other more reliable data, quite apart from the fact t h a t these frequencies offend the Rayleigh rule. A single spectrum of CHaOH obtained here at 2ILIA = 175 suggested t h a t the absorption at 1109 cm -x was more likely to be duo to monomers, and this frequency is nicely compatible with the other data. The calculated values of r~ are identical in C H 3 0 H and CHsOD.
Anharmonicity corrections and Troduct ratio8 Anharmonicity corrections were applied, as before, [8, 9] using ])ennison's rule and x factors of 0.04 for OH and C t t stretching, 0-02 for OH and Ctt bending and 0.01 for C - - O stretching. Since several fundamental frequencies are still unknown, " r e d u c e d " ratios were calculated in which the contribution made b y the missing frequencies was estimated from the force field and then removed from the ratio. This was necessary for a number of the h e a v y isotopic shifts, for several Ct t bending modes in CHD~OtI, and for all the torsions. The results are shown in Table 2. Here it is seen t h a t while the observed ratios HD/H H are in all cases larger t h a n the theoretical ones, the "h ar mo n ized " ones are appreciably smaller t h a n what t h e o r y predicts for t he CDsOtt, CDaOD and s-CI-ID20H a' species. P a r t of this overshoot m a y derive from the fact t h a t the lower a'CIt stretching frequency has been raised b y 20 cm -~ to allow for Fermi resonance and t h a t no such allowance has been made in the corresponding CD stretch. An upward shift of 10 cm -~ in the latter could in fact be accommodated Table 2. Product ratios for frequencies of methanols in argon matrices* A' Symmetry species Ratio
Obsd.
~aCHsOH/CHsOH CHaOD/CH3OH CHalS0D/CHaOH CDsOH/CHsOH CDaOD/CHsOH s-CHD2OH/CHsOH
0.963911 0.548820 0-529536
A u Symmetry speciest
"Harmonized" Theory
0.220512 0-118557 0.411155~
0.963256 0.540590 0.521339 0.212409 0-112477 0-402430~
0-963330 0.536435 0.514803 0.215397 0-114847 0.406513~ 0"400777
Obsd. 0"996995 1.0 1.0 0.423205 0-423259 0.525990
"Harmonized" Theory 0.996872 1.0 1.0 0-414617 0.414672 0.517134
0.987886 1.000012 0.997259 0.414103 0.414092 0.511155
A Symmetry speciest Ratio
Obsd.
as-CHD~OH]CHaOH 0.268388§
"Harmonized" 0.260865§
Theory 0.251187 § 0-204704
* Calculated from data of Table 1. Where freq. shifts axe unobserved the corresponding freq. of the "Master" isotope is used. 20 cm-1 added to ~a in CHaOH and CHaOI). t Less torsion. Less CH out-of-CD2-plane bend. § Less CH bends.
I n f r a r e d s p e c t r a o f d e u t e r a t e d m e t h a n o l s a n d force field
1141
by the force field, which would raise the product ratios by ½ per cent. This however still leaves a discrepancy of 1-2 $/o unexplained. No acceptable way of distributing the discrepancy by interchanging a' and a" assignments could be found. Indeed the only plausible exchange, noted above in u~ and ~zz of CDaOH, had the effect of worsening the a' discrepancy. The only likely candidates for assignment revision would appear to be the 5~,CDa modes in CDaOH and CD30D, and the CH bending ones of CHD~Ott. We are reluctant to attribute the overshoot to failure of the anharmonicity correction procedure, but this m a y prove to be necessary. F O R C E F I E L D CALCULATIONS
The s y m m e t r y coordinates and molecular geometry assumed are given in Table 3. The data employed consisted of the harmonized frequencies for the eight species CFIaOH, zsCHaOtt, Ctta0D, CHaZS0D, CDaOH, CDa0D, s and as-CHD~OH determined either in this work or in [4]. As before, the zaC and zaO data were included as shifts. Although centrifugal distortion data also exist for CHa0H, CHaOD and CDaOH [11] these were not employed for several reasons. Firstly, the observed D~ °, D ~ ° and D ~ ° were determined through the symmetric top approximation for the rotational levels of what are asymmetric tops, whereas the calculated values are 'true' "asymmetric rotor" ones. Secondly the calculated ones are for the equilibrium configuration in the matrix, and not for the ground state of the gaseous molecule.* T a b l e 3. I n t e r n a l s y m m e t r y c o - o r d i n a t e s a n d g e o m e t r y for methanol* § A'
~z =
~Z =
Al 1]V"6 ( 2 A t I -- Ar~ -- Ara)
s s -- 1/~/~ (Ar~ + Ar 2 + Ar~) AIVg (2A~s8 - h ~ l s -- 5 ~ 1 )
8, =
- A V 1 + _~
$6 = A(AT) , ~ = AR A"
~
= 1l~
* geometry:
Ars)
(At2 -
A
,5':t =
HzCO
=
107°2',
f12 =
fla =
110°54',
A
~tg. = HxCH~ = ~ a = ~ a = 108°38' y = H O C = 108032 ' rCH = 1"0936)x, R c o = /OH = 0-9451 .~ [11].
t K
=
3 sin t~cos/~[sin ~ (Assuming/~1 =
1-426)x, ,82 =
88)
T ~ = d i h e d r a l a n g l e H~COH. § All a n g l e b e n d c o - o r d i n a t e s scaled w i t h u n i t )x l e n g t h : = 10-z° m * T h e effect o f c h a n g e i n g e o m e t r y u p o n c a l c u l a t e d v a l u e s o f D ' s c a n b e significant c o m p a r e d w i t h c h a n g e s i n t h e force field [8]. [11] R . M. LEES a n d J . G. BAKER, Or. Glwm. P h y s . 48, 5299 (1968).
1142
P . D . I~ALLINSONand D. C. MCKEA~
Thirdly the D's are most sensitive to the torsion and torsion-rock interaction force constants, and all attempts to define these failed. Most refinements were carried out with 1 ~/o uncertainties on each absolute frequency, and commensurate errors in the shifts [8, 9], except for doubtful cases such as the torsions and CH bending modes of CHD20H where rather greater error was assumed. However the CH and CD stretching frequencies were treated differently, as discussed below. Preliminary exploration indicated t h a t there was as yet no information to define the following interaction constants: (a) all 3 torsion interactions: (b) all 7 OH stretching interactions: (c) interactions involving vas with ~, ~OH, VCOand vswith ~OH, P and Veo, all in the a' species. All these 17 constants were therefore constrained to be zero. I n addition, the hybrid orbital force field constraint t h a t the interactions va,/~, and v~,/p be equal and opposite in sign [12] was applied in both a' and a" species (two constraints). Out of a total of 46 possible parameters therefore, 29 were use d, of which 27 were independent. A further constraint results amongst the diagonal CH stretching constraints, %/2F2.3 ---- F~.2 -- Fa.9, if the two possible valence force field stretch-stretch interactions f ~ ' and f~a' are equated to each other.*
Treatment of CH and CD stretching frequencies The main objects here were to extract the maximum amount of information concerning Fermi resonance, and to test the applicability of the 3 × 3 refinement procedure used in [7]. The latter involves treating the CH and CD stretching motions in isolation from all others in the molecule, using merely principal and interaction stretching constants. For an asymmetric molecule such as methanol, the constants are four in numberfa,fs,f~ ~' a n d f ~ ' . Observed frequencies are used, but the mutual incompatibility between CH and CD stretching due to anharmonicity is alleviated by dividing all observed CD stretches by 1.011 before input, and remultiplying the refined ones by this factor before making a final comparison with the observed values. The prediction of unperturbed CH and CD stretching frequencies is based on the assumption t h a t only the four constants noted above are important in determining the separations of various CH stretching modes from each other, fa and f~ are essentially determined by the ~CHfrequencies in CHD20H: f j andfa~' can then be found if one a' and one a" frequency in either the CH, or CD3 species can be trusted to be free of Fermi resonance. For such modes uncertainties of ± 1 cm -1 were assumed, and much larger ones used where Fermi resonance was suspected. All CD stretches however are given uncertainties of at least 4-10 cm -1, to allow for error inherent in the 1.011 factor. The highest CH 3 stretching mode appeared to be least affected by Fermi resonance and was therefore given an error of 1 cm-L The a"CH s stretch was considered to be more uncertain, and given 4-10 cm -1. Refinements were carried out with these errors using both the complete (12 x 12) and limited (3 x 3) procedures, and the results are * These are the constants which are the equivalent offald in [7]. [12] I. M. MILLS,Spectrochirn. Acta 19, 1585 (1963).
Infrared spectra of deuterated methanols a n d force field
1143
Table 4. Analysis of CH s and CD s stretching frequencies in methanols Av(obs-calc), 12 x 12" Species
%bs
3005"3 2961.9 2847"9 2253.9 CDaOD 2217.8 2077.0 as-CI-r._.D20H 2931.0 2242-3 2134.2 2986.4 s-CHD~OH 2208.1 2113.3 fa fs fas t faa t
CHsOH
av (a') (a") (a t) (a') (a") (a')
(a t) (a") (a')
A
1 --0-1 10 --2.8 1000 --13-6 10 +6.6 10 +4.9 21 --6.0 1 0.0 10 +0.6 10 + 3 . 7 1 0.0 10 --5.5 10 --2.1 4.729 4.911 --0"016/ --0.033J
Av(obs-calc), 3 x 3t
B
A
--0.2 +1.4 --18.2 +6.6 -t-4"3 --6.4 0.0 +0-7 +3.1 --0-1 --5.7 --3.4 4.726 4.912 --0.012
0.0 +2.1 --23.6 +1.7 --1.9 --8.0 +0.2 +4.1 --0-7 0.0 --1.6 --7.2 4-694 -4- 0.002 4.874 4- 0.002 0.004 4- 0-003 / 0.012 -4- 0.011/
B +0.1 --0.3 --20.8 +1.9 --3.7 --6-0 +0.2 --4.4 0.0 0-0 --13.4 --4.9 4.693 ± 0-002 4.875 ± 0.002 0.003 -4- 0"003
* Complete refinement based on harmonized frequencies. Valence force constants 'deharmonized' b y factor (0.96)2: A. fas' ~ faa' (force field of Table 5): B. fas t = faa" t Refinement of CH and CD stretches only, the latter divided b y 1.011 before input, remultiplied b y 1.011 after refinement. A . fas' # faa': B . fas' = faa"
shown in Table 4. Here the 12 x 12 calculated frequencies and (observed calculated) error vector are both "deharmonized" for the direct comparison with the 3 x 3 results.* I n each case the effect of the constraintf,,' = f ~ ' was also tested (results B in Table 4) the importance of this lying in the fact t h a t very seldom wiU it be possible to determine these two constants independently. Although in both 12 x 12 and 3 × 3 procedures, without this constraint, refinement proceeds to give f , , ' =f=f ~ ' , the difference between the two is within the experimental error, of which the greater part lies in f~', deriving from the 10 em -1 uncertainty in the a" frequency. Moreover the order of magnitude is different in the two treatments; f , , ' > f ~ ' in the 12 x 12, but < f ~ ' in the 3 x 3. We conclude t h a t there is no evidence as yet for a significant difference between f ~ ' and f~,', and comparison of the error vectors shows t h a t the frequencies predicted by the constrained and unconstrained force fields differ but little.t We see further t h a t the constrained 12 x 12 and 3 x 3 force fields (B) predict upwards shifts of 18 and 21 cm -1 on the lower a'CH8 mode and therefore agree in attributing a Fermi resonance shift here of about 20 cm -1. A rather smaller shift could exist on the corresponding CD8 mode of up to 10 cm-~.~ * Similarly the valence stretching constants derived in the 12 x 12 calculation are scaled down b y (0.96) s in this table. t Differences in the abso/atte rrmgn/tude o f f ' between different procedures do not appear to affect appreciably the prediction of fundamental frequencies [7]. ++The only major inconsistency revealed in the comparison above concerns the a" mode of s-CHDs, which in the 3 x 3 B calculation is 13 cm-1 above the observed value. I t m a y be observed t h a t both 12 x 12 and 3 x 3 calculations place a"CD s and s-CHDg, modes very close together, or coincident, and t h a t the puzzle here is really why the observed values of these two modes should differ b y 9.7 cm-L
1144
P . D . MAT,T,INSONand D. C. MeKEA~ Table 5. Symmetry harmonic force constants for methanol* F
171.1 Fz. 2 Fs,a F2. 4
Fu.v Fa. a Fa.5 174.4 F4.5 F4., F4,7 174.s Fs. 5 Fs. 6
Fa. 7
8.147 5.274 +0-102 --0.188# (--0.120) +0-188~ (+0.161) 5.151 +0.128 (+0"203) 0.568 +0.041 +0.022 --0-060 (--0.055) +0.031 0.661 --0.012 -0.093
~(F)
0.028 0.043 --0-039 0-034 0.034 0.043 0"096 0.006 0-004 0.008 0-007 0.013 0.007 0.006 0-007
F
Fs. s Fe. e Fe.v Fe. s FT.7 FT.s Fs. 8 Fg. 0 F0.10 Fg.n Flo.,o Flo.n Fn, n F19.1~
--0-583 (--0.610) 0.772 + 0.103 +0.421 0-981 + 0-063 5.450 5-168 --0-2091' (--0.210) +0.209T (+0.161) 0-590 --0.024 (--0.055) 0.799 0-0270
~(F)
0.011 0.005 0.004 0-009 0.011 0.015 0.023 0.034 0.053 0.053 0.005 0.009 0-005 0.001
* All values in mdyn ~-1 (= ajA-1) ? Constrained values: /'2,4 = --E2.~; F9.10 = --Fg,n
Harmonic force fieZd: general considerations F o r simplicity we q u o t e in Table 5 t h e 29 p a r a m e t e r h a r m o n i c force field f r o m which t h e 12 x 12 (A) results o f Table 4 were taken. A l t h o u g h this was defined b y artificially small errors on certain C H stretching modes, those errors were released t o t h e n o r m a l 1 % ones in t h e last cycle, to give t h e more realistic a values o f Table 5. O f t h e 29 p a r a m e t e r s , all b u t one, F3,s, t h e ~,/0 s i n t e r a c t i o n c o n s t a n t , are fairly well defined. I n general t h e values o f those i n t e r a c t i o n c o n s t a n t s which are c o m m o n to b o t h m e t h a n o l a n d m e t h y l fluoride agree well with each o t h e r (CHaF values b r a c k e t e d in T a b l e 5), e x c e p t perhaps for F3.5 which is illdefined here. T h e la(3 a n d is0 isotopic shifts were well-reproduced at all stages in t h e refinement a n d t h e r e f o r e c o n t r i b u t e d little to the latter.* This was largely due t o t h e experim e n t a l errors associated w i t h t h e m . T h e discrepancy between the observed 1~3 shift o f 4.8 em -~ on t h e 2847-9 cm -1 b a n d of CHaOH a n d the p r e d i c t e d one of 3.5 cm -~ confirms t h e presence o f F e r m i resonance here (2~ 5 is calculated to h a v e a shift o f 2 x 5.6 = 11.2 em-a). Table 6 shows t h e observed a n d calculated values o f D j , D j K a n d D ~ for CHaOH, CH3OD, a n d CDaOH. T h e a g r e e m e n t m u s t be considered satisfactory in t h e light o f t h e considerations discussed above, t F u r t h e r i m p r o v e m e n t s in the force field should result with (a) location o f t h e remaining unobserved, or insecure, f u n d a m e n t a l s , (b) more accurate h e a v y isotopic shifts. I t seems likely t h a t t h e m a j o r obstacle to a d v a n c e is the basic 1 ~/o u n c e r t a i n t y resulting f r o m a n h a r m o n i c i t y . T h u s the a r b i t r a r y elevation o f C H bending modes b y 2~/o a n d o f CO stretching b y 1 ~/o m a y seriously d i s t o r t t h e force field where these * Their main value lay in assigning ~8 and (~8(CHs). t Further details concerning the centrifugal distortion parameters calculated here for all species may be obtained on application to the authors.
I n f r a r e d spectra of d e u t e r a t e d m e t h a n o l s a n d force field
1145
Table 6. O b s e r v e d a n d calculated v a l u e s of centrifugal distortion co-efflcients (MHz)
D j obs.* calc. D j K obs.* calc. D K obs.* calc.
CHsOH
CHsOD
CDsOH
0"0492 ± 0"002 0"0531 0"2864 4- 0"0058 0.3087 1.27 4- 0-06 1-191
0-0464 4- 0"0086 0"0483 0"1900 ± 0"022 0.2551 -0.999
0"0289 4- 0"0003 0"0311 0"1594 -4- 0"0019 0-1685 -0.296
* F r o m reference [11]
modes are in fact strongly coupled to each other. This might be circumvented b y the use of more, and more precise, heavy isotopic shifts and possibly also b y a similar refinement to the small shifts such as those in ~a,(CDs), p(CDs) or ~ o between CD30H and CD30D etc. Acknow/e~gen~ent~-We are v e r y g r a t e f u l to Dr. J . L. DU~CA~ for assistance in calculating t h e B a n d G e l e m e n t s for this molecule. W e t h a n k t h e Science R e s e a r c h Council for a g r a n t t o w a r d s t h e p u r c h a s e of isot~pically labelled c o m p o u n d s a n d for a s t u d e n t s h i p g r a n t to one o f us [P. D. M.].
T.t,ared spectra of deuterated methanols and force field P. D. i~AT.LINSON* a n d D. C. M c K E A N Department of Chemistry, Universityof Aberdeen, Aberdeen A B 9 2 U E (Received 7 August 1973) Abstracb---Infrared spectra have been obtained in argon matrices at 20 K from CHD2OH, CDaOD and CDaOH. The two CH stretching frequencies seen in CHD$OH reveal the presence of t w o types of CH bond whose lengths are predicted to be 1"094 and 1.100 A respectively. A harmonic force field is calculated, based on matrix frequencies for eight isotopic species determined here or in the previous work of BARm'mS and HAT+LAM,and employing 29 parameters, including two hybrid orbital force field constraints. The CH and CD stretching frequencies were analyzed both by full (12 x 12) and by limited (3 × 3) refinement procedures, and the presence e r a 20 cm-x Fermi resonance shift on the lower A'CH s stretching mode deduced. The 3 × 3 treatment with constrained stretch-stretch interaction constantsf, a' = fas', appears to predict satisfactorily the positions of nearly all of the uncertain CH and CD stretching frequencies. Further work is needed to locate all the fundamental frequencies and to improve the isotopic shift data. INTRODUCTION ALTHOUaH t h e force field of m e t h a n o l has been studied t h r e e times in the last t w e l v e years [1-3], all these investigations h a v e been based on d a t a f r o m t h e gas p h a s e which for this molecule are u n u s u a l l y unreliable, due to t h e g r e a t complexity, e x t e n t o f overlapping a n d in certain cases, t h e weakness o f t h e bands. Moreover no a c c o u n t could be t a k e n o f t h e effects o f F e r m i resonance in t h e C H or CD stretching regions, or o f possible differences in C H b o n d strength, n o r was t h e r e available a n y e x a c t knowledge o f t h e positions o f C H s a n d CD a d e f o r m a t i o n a n d rocl~iug modes. T h e a d v e n t o f t h e m a t r i x isolation technique, which offers considerable a d v a n tages for t h e e x a c t location o f f u n d a m e n t a l bands, gave hope o f g r e a t e r insight i n t o t h e force field, a n d t h e present s t u d y is based largely on t h e frequencies observed in argon matrices a t 20 K b y BAR~C~.Sand HALLAM [4] for t h e species CI~sOH, I ~ H s O H , CHaOD, CHalSOD a n d CDaOD(H ). To the d a t a for t h e a b o v e species we here a d d a s t u d y o f C H D 2 0 H a n d CDaOH. ~ T h e C H stretching region of the f o r m e r species will, on t h e one h a n d , indicate d i r e c t l y w h e t h e r t h e r e are two t y p e s o f C H b o n d present [5, 6] a n d on t h e other, m a y be helpful in elucidating t h e e x t e n t o f F e r m i resonance affecting t h e lower C t t a a n d CD3 stretching modes. This l a t t e r use has been discussed b y one o f us previously for t h e case o f c o m p o u n d s containing s y m m e t r i c a l m e t h y l groups [7J, a n d m e t h a n o l is a n a p p r o p r i a t e model s y s t e m to investigate, t o see i f t h e * Present address: Department of Chemistry, University of Reading, Reading, England. J" Barnes and Hallam only observed bands due to CD8OH as impurities in their spectra of CDsOD. [1] [2] [3] [4] [5] [6] [7] 5
M. MA.RGOTTIN-:MACLOU, g'. Phys. Radium 21, 634 (1960). M. F~L~ and E. WH~LT.~Y,d. Chem. Phys. 34, 1554 (1961). G. Z ~ I , J. OVm~END and B. L. CP~W~ORD, J. Chem. Phys. ~ , 122 (1963). A. J. BAP,m~s and H. E. YIAT.T.~L~,Trans. Faraday See. 66, 1920 (1970). D. C. McKEAN, Chem. Commun., 1373 (1971). D. C. M c K E ~ , J. L. DUNCAN and L. BATT, Spectrochim. Acts, ~gA, 1037 (1973). D. C. McKEAI% Spectroehim. Acts, 29A, 1559 (1973). 1133
1134
P. I). 1WAT.T.rNSO~and D. C. McKEAN
CHD 2 method for assessing Fermi resonances is applicable also in the case of asymmetric ones. I t was hoped initially that a general force field might be determinable for methanol, as was achieved for the methyl halides [8, 9]. Although this hope has not been fulfilled, the results concerning the assessment of Fermi resonance are encouraging. EXPERIMENTAL Samples of CD30D and CHD20t{, quoted as being 99~o isotopically pure, were obtained from CIBA and Prochem Ltd., respectively. CD30H was prepared from the CD30D b y exchange with phenol Spectra were recorded on a Perkin-Elmer 225 infrared spectrometer calibrated with frequencies from the I.U.P.A.C. tables. Argon matrices of M/A ratios varying from 200 to 1000 were deposited on a CsI window a t 20 K in an Air Products AC-3L Cryotip apparatus. Some of these spectra are illustrated in Figs. 2, 3 and 4 for the CHD20H, CDaOD and CD30H respectively. The vapour phase spectrum of the latter in the CH stretching region is shown in Fig. 1. In general the degree of isolation achieved at the higher M/A ratios was apparently not as good as that of Barnes and Hallam. A~SSIGNMENTS The presence of bands due to dimers and multimers at the highest M/A ratios continues to present difficulties, especially since hydrogen bond formation can cause considerable changes in intensity and frequency in modes other than OH stretching and bending ones. In CD30H and CD30D only points of difference between ourselves and [4] will be noted. CHD20H In the CI-I stretching region, in the gas phase, shown in Fig. 1, two Q branches are seen, at 2978.7 and 2919.3 cm-* respectively, from which we infer the existence of two kinds of CH bond whose lengths are 1.094 and 1-100 A respectively from the correlation graph of [6]. The intensities of the corresponding matrix bands at 2986.4 and
I 3050
I 3000
t 2950
] 2900
K 2850
Fig. 1. Infrared spectrum o f O H D s O H , vapour phase, 80 m m pressure in 10 c m cell. [8] J. L. DUNCAN, A. ALLA~ and D. C. M C K E ~ , Mol. Phys. 18, 289 (1970). [9] J. L. D u n c A n , D. C. McKEA~ and G. K . SPEIRS, Mo~. Phys. 24, 553 (1972).
Infrared spectra of deuterated methanols and force field
1135
MIA=900 ~ 1 ~
3800
'
1400
3()00 CM-1
25'00
2000
1200
1(~0
8~)0
CM-1 Fig. 2. Infrared spectra of CHD2OH (23 p mole) in argon matrices at 20 K.
2931.0 cm -1 (Fig. 2) are in keeping with the expected distribution of 2 weak (trans t o oxygen unshared pairs) and one strong bond (trans to OH).* Thus the higher frequency m a y be assigned to the s species of CHD2OH, the lower to the as one. I n t he region 2300-2100 cm -1, six bands are found, viz 2242.3, 2208.1, 2197, 2186, 2134-2 and 2113.3 cm -1, of which the two at 2197 and 2186 cm -1 are assigned as first overtones of the bands at 1095.5 and 1090-8 cm-L Since the as species has one weak and one strong CD bond, whereas the s species has two weak ones, the following assignments are readily made: as 2242.3, 2134.2 cm-l: s 2208.1 [a ~] 2113.3 cm -~ [a']. There are perhaps small Fermi resonances involving t he two overtone bands with the lower-lying fundamentals (see further below). I n the region 1500-1200 em -~ 6 absorptions due to OH and CH bending modes are expected to appear. U n f o r t u n a t e l y most of the bands here are broad and very weak. A band of medium strength a t 1268 cm -1 has the appearance like t h a t of an OH bend in the other isotopic species, and is so assigned, to bot h s and as species, although the refinement calculations place the as mode 18 cm -1 lower at 1250 cm-L Amongst * Although such intensities can be misleading, the evidence for t r a n s effects of this kind is now
overwhelming as for example in (CH8)90 [10]. [10] A. A z ~ , (1971).
D. C. M c ~ ,
J-P. l~mC~AuD and M-L. JoszE~, Spectrochirn. Ac~a 27,%, 1409
1136
P . D . MALLINSON and D. C. MCKEA_~
-•-• I
3800
14oo
'
M/A=900
30'00 CM-1
12'oo
'
1(:;oo
2500
'
2000
8~o
CM-1 Fig. 3. Infrared spectra of CDaOD in argon matrices at 20 K : M/A 900-23 p mole, M/A 200-14 p mole.
other absorptions at 1414, 1376, 1355 and 1318 cm -1, only two are compatible with the force field, 1355 as ~5 in the as species, 1318 cm -I as ~10(a') in the ~. However it seems likely t h a t there is extensive interference here from multimer bands, and further work is needed both to confirm the above assignments and to locate the missing monomer fundamentals, whose positions are predicted to be 1431 (~5, s) and 1290 (Vlo, as). I n the region 1100-1000 cm -1, we expect the CD~ scissors and CO stretching modes. Two pairs of bands are seen, at 1095-5[1090.8 and 1040.3/1013.3 respectively. The force field calculations show t h a t both pairs of modes are strongly mixed in character, the proportion of CO stretching being greater in the lower. They also indicate the as frequencies to be 1090.8 and 1040.3 cm -~, the other two, s, which is also in keeping with their relative intensities. In the region 1000-800 cm -~, 4 bands are seen, at 947.9, 926.7, 874.2 and 870.4 cm -~ respectively, of which the second is very weak. The first band is readily assigned as the CD~ wag of the as species, but the other three present some difficulty. The fact t h a t the very weak baud at 926.7 cm -~ increased in intensity on passing from M/A = 200 to 900 suggested t h a t this was a monomer baud, and initially this was assigned as the CD 2 wag of the s species. The other two lower frequencies were then attributed to the CD 2 rocks of the two species. However this gave a product rule
Infrared spectra of deuterated methanols and force field
1137
M/A=200
MIA=900 .
3900
1400
3500 '
30'00 CM-1
1200
CM-1
25'00
1000
~
'
2000
800
Fig. 4. Infrared spectra of CDsOH in argon matrices at 20 K : 23 p mole deposited.
discrepancy of about --10% in the a' class of the 8 species (relative to C H 3 0 H ) which is unreasonably high, and in addition, attempts at refinlug to these assignments threw out several quite trustworthy frequencies in the other species.* I t was finally concluded that the 926.7 cm -1 band probably arises from the CD~ wag of dimeric a8 --CHD~OH* and that the lower two bands represented three fundamentals. In particular the CD 2 rocks of both molecular species were predicted to lie within 0-2 cm -1 of each other, and the CD 2 wag of the a about 16 cm -1 higher, near 883 cm -x. Accordingly the former were assigned to the 870.4 cm -~ band, the latter to that at 874.2 c m - L t The torsional mode occurs in the 200 cm -a region and according to [4] is overlapped b y the hydrogen bond stretching bands of multimers, as well as being split into A and E components. No investigation was therefore made here. CD30D The matrix spectra are shown in Fig. 3. The monomer frequencies found here differ only slightly from those in [4]. Due to the slightly poorer quality of our spectra, the a' CDs rock could not be identified here, and the value of 1055 from [4] is accepted, although the refinement value is 13 cm -~ higher. I t is interesting to note that of the * A t t e m p t s to find a CH2DOH mode to suit this frequency also failed. t Although this is 9 em -1 below the computed value (Table 1), it is considerable nearer t h a n the 926.7 cm -1 band.
1138
P . D . MATZ.~NSONand D. C. MCKEA~
two a' frequencies in this region, 1030.8 a n d 1055-0 cm -1, t h e higher b a n d is in fact calculated t o be t h e CD8 rock coupled to OD bending as previously surmised [4]. I n the CD stretching region, the assignments in [4] o f 2254 cm -~ as a ~, 2219 as a' modes, are here reversed, so t h a t the sequence a' > a ~ > a ' n o r m a l to a m e t h y l g r o u p containing two weak a n d one strong b o n d is observed.* CD30H F i g u r e 4 shows t h e m a t r i x spectra o f this species. Several b a n d s in t h e s p e c t r u m of CD30D a t t r i b u t e d t o " s e c o n d site" m o n o m e r s in [4], were here shown to arise from C D 3 0 H , for example, t h e a'CD 3 s y m m e t r i c d e f o r m a t i o n ~5 a n d t h e CO s t r e t c h ~8. T h e a'Oa,CD ~ m o d e a t 1031-3 cm -1 in [4] was n o t observed b y us in our 100% C D 3 0 H s p e c t r u m a l t h o u g h a possible sign of it was seen in a 70~o CD30D/30~/o C D 3 0 H film n e a r 1039 c m - l . ~ Below 900 cm -~, C D 3 0 H shows a p r o m i n e n t m o n o m e r b a n d a t 860.7 cm -1 w i t h a possible v e r y w e a k m i n o r c o m p o n e n t a t 866.5 cm -1. These are assigned to the a" a n d a~PcD8 modes ~11 a n d ~ respectively, a l t h o u g h the order o f m a g n i t u d e is reversed b y t h e f.f. calculations (see Table 1). I t would be possible t o i n t e r c h a n g e t h e assignments, b u t o n l y a t t h e expense of f u r t h e r increasing t h e p r o d u c t ratio discrepancy (see below). A f u r t h e r consideration is t h a t ~11 is p r e d i c t e d a t identical positions in the CDsOH and CD30D a n d since the 860-7 cm -~ b a n d is seen in b o t h cases, i t m u s t therefore be ~11.$ F i n a l l y we n o t e t h a t t h e higher a'CD stretching m o d e lies at 2259.9 cm -1 in C D 3 0 H , which is 6 cm -1 higher t h a n its position in C D 3 0 D (2253.9 cm-~). Since 2~ 5 for these two molecules is e x p e c t e d a t a b o u t 2 × 1 1 2 7 - 2 - 10 = 2244-4 a n d 2 × 1 1 3 2 - 0 - 10----2254 cm -~ respectively, it is possible t h a t the a b o v e shift derives f r o m a F e r m i resonance.§ Failing the latter, a n a l t e r n a t i v e e x p l a n a t i o n involves coupling to t h e OD s t r e t c h a t 2705 cm -~, a l t h o u g h this would require a n i n t e r a c t i o n force c o n s t a n t n o t i n c o r p o r a t e d so far into t h e force field.
Torsional frequencies of all species T h e values q u o t e d in [4] are incompatible with each other. This is p r o b a b l y due to overlapping of the E c o m p o n e n t in C H 3 0 H a n d of t h e A c o m p o n e n t in CH3OD b y the dimer h y d r o g e n b o n d stretching bands. F o r refinement purposes we t o o k t h e A c o m p o n e n t f r e q u e n c y in C H 3 0 H o f 272 cm -1 a n d assumed t h a t the corresponding C H 3 0 D f r e q u e n c y was 213 cm -1, these two frequencies being compatible. * This sequence is found generally for cases where the stretch-stretch interaction force constant f o r f ~ is small, as in all cases of CH bonds. t This apparent paradox we can only explain in terms of the accidental comb'mation of two factors: (1) that the degree of isolation in the 100~o film was poorer than usual: (2) that the ~aaCD3(a~) intensity is extremely low, especially in the multimeric species. The latter appears to be true in CD3OD at least. + It is just possible however that the presence of this 860-7 cm-1 band in the CD3OD spectrum is due to OH impurity in the latter. The band at 894.7 em-1 in [4], assigned as v7 of CDsOH is very broad and weak and probably arises from multimers. § Multimer bands obscure the region where 2~5 is expected to occur.
Infrared
Table
spectra
1. C o m p a r i s o n
of deuterated
of observed
3667.3 3005.3 2847"9 1474.1 1451.4 1335.0 1076.7 1034-0 2961-9 1465.8 1109.0 272.0
rI rs r3 rt r6 r6 r7 rs ro rio ~l i ~
17.2 ----4.0 -25-5 -----
frequencies
37 30 1000 15 15 13 11 10 30 15 11 10
--0.7 --0-1 (2861.5) -~-0.1 --1.1 --4-0 ~-1-8 --0.7 --2.7 --3-5 --1-5 -I-1"7
-9.9 4.8 1.1 5.6 8.0 6.5 15.5 8"9 ----
-0.2 5-0 1.0 0.2 2.0 0.2 0.4 2.0
CHsOD
(0.0) 0.0 - - 1-3 ~-0.2 0.0 --~-0.3 0.0 0-0 --]-0.7 (2.1) (8-2) (0.0)
/~v c
0-4
-I- 0"1 (0-0) (0.0) (0.1) (1.1) 0.0 (5.3) --0.2 (0-0) (0.25) (2.9) (1.2)
0.1 0.5
~Obll 3666-0 2259.9 2076.4 (1030-8) 1127.2 1293"4 866"5 t 989-4 2217.1 1067-8 860.7t --
rob.
~,
3665.8 2896.4 2113.3 1095.5 -1268.2 874.2 1013.3 2208-1 1317-7 870-4
37 30 21 11 13 9 10 22 13 9
27 30 1000 15 15 9 12 10 30 15 11 10
-I-3"1 --I-1.4 (2861.7) -{-6-8 ~-6.7 --0.3 -~7.0 --4.7 --2.8 --3.5 --1.5 (215-2)
CDsOD
O'v
A°-c
robs
37 23 21 10 11 13 9 10 22 11 9
--2.0 -~- 12.1 --6.7 --7.9 --5.0 --6.8 ~-8.3 --2.5 ~4.2 -~-0.8 --5.2 (256.5)
2704.8 2253.9 2077.0 1030.8 1132.0 776.5 1055.0 984.5 2217.8 1067.6 860.7t
s-CHDsOH
rI •s 1,I rt rs re r7 v8 rs rio ~'lx rxl
2706.1 3006-6 2845.5 1472.7 1451.4 864-9 1227-3 1042.8 2961.9 1465.8 1109.0 213-0
CDsOH
O'AV
1139
for methanols
~SCHsOH
CHslSOD A1~obS
and force field
and calculated*
CHsOH
~x rs rs rt ~s re r7 ~s ~s ~1o vlt r~s
methanols
O'V 27 23 21 10 11 8 10 10 22 11 9
AOv-O -t-2-0 -I-6"6 --6.0 --1.3 --0.1 -~-2.1 --13.1 --5.2 -~-4.9 -I-0.6 --5.2 (197-5)
a~-CHDIOH
A?-~ --2.2 0.0 --2.1 ~-4.9 (1430.7) --0.5 --9.0 ~2.9 - - 5-5 -+- 8.6 -I-2.6 (260.2)
rob.
~,
A?-~
3665.8 2931.0 2134.2 1090-8 13557 1268.2 947.9 1040.3 2242.3 -870.4 --
37 29 21 11
--2.2 0-0 -L-3"7 ~-7.9 (1352.2) -t- 18.2 -+-6-2 -+-5.9 ~ 0.6 (1290.0) --t-2-4 (259.3)
13 10 10 22 -9
~O-C ~ 1%bserved_~calculated e x c e p t for b r a c k e t e d values, w h i c h a r e t h e ca/cu/ated frequencies: similarly for * F o r c e field of T a b l e 5. Calculated frequencies w e r e ' d e h a x m o n i z e d ' a f t e r r e f i n e m e n t w a s complete, for display here. t A l t e r n a t i v e l y , ~n(pcDs, a n) could lie a t 866.5 c m -1 in b o t h C D s O H a n d CDsOD , in w h i c h case Ao-c w o u l d b e -I-0,6 c m -1, w i t h vT(pcDs a') a t 860.7 c m -1, A ° - c t h e n b e i n g -{-2.5 c m -1. H o w e v e r t h e p r o d u c t rule ' o v e r s h o o t ' w o u l d t h e n be e v e n g r e a t e r t h a n before.
P . D . MAT.T.~SONand D. C. MoKEAN
1140
CHsOH and CHsOD a" rock, ~9 The refinement calculations below indicated t h a t the assignment in [4] of r9 to the v e r y weak and broad absorptions at 1157 and 1160 cm -1 respectively in CHsOH and CHsOD was incompatible with other more reliable data, quite apart from the fact t h a t these frequencies offend the Rayleigh rule. A single spectrum of CHaOH obtained here at 2ILIA = 175 suggested t h a t the absorption at 1109 cm -x was more likely to be duo to monomers, and this frequency is nicely compatible with the other data. The calculated values of r~ are identical in C H 3 0 H and CHsOD.
Anharmonicity corrections and Troduct ratio8 Anharmonicity corrections were applied, as before, [8, 9] using ])ennison's rule and x factors of 0.04 for OH and C t t stretching, 0-02 for OH and Ctt bending and 0.01 for C - - O stretching. Since several fundamental frequencies are still unknown, " r e d u c e d " ratios were calculated in which the contribution made b y the missing frequencies was estimated from the force field and then removed from the ratio. This was necessary for a number of the h e a v y isotopic shifts, for several Ct t bending modes in CHD~OtI, and for all the torsions. The results are shown in Table 2. Here it is seen t h a t while the observed ratios HD/H H are in all cases larger t h a n the theoretical ones, the "h ar mo n ized " ones are appreciably smaller t h a n what t h e o r y predicts for t he CDsOtt, CDaOD and s-CI-ID20H a' species. P a r t of this overshoot m a y derive from the fact t h a t the lower a'CIt stretching frequency has been raised b y 20 cm -~ to allow for Fermi resonance and t h a t no such allowance has been made in the corresponding CD stretch. An upward shift of 10 cm -~ in the latter could in fact be accommodated Table 2. Product ratios for frequencies of methanols in argon matrices* A' Symmetry species Ratio
Obsd.
~aCHsOH/CHsOH CHaOD/CH3OH CHalS0D/CHaOH CDsOH/CHsOH CDaOD/CHsOH s-CHD2OH/CHsOH
0.963911 0.548820 0-529536
A u Symmetry speciest
"Harmonized" Theory
0.220512 0-118557 0.411155~
0.963256 0.540590 0.521339 0.212409 0-112477 0-402430~
0-963330 0.536435 0.514803 0.215397 0-114847 0.406513~ 0"400777
Obsd. 0"996995 1.0 1.0 0.423205 0-423259 0.525990
"Harmonized" Theory 0.996872 1.0 1.0 0-414617 0.414672 0.517134
0.987886 1.000012 0.997259 0.414103 0.414092 0.511155
A Symmetry speciest Ratio
Obsd.
as-CHD~OH]CHaOH 0.268388§
"Harmonized" 0.260865§
Theory 0.251187 § 0-204704
* Calculated from data of Table 1. Where freq. shifts axe unobserved the corresponding freq. of the "Master" isotope is used. 20 cm-1 added to ~a in CHaOH and CHaOI). t Less torsion. Less CH out-of-CD2-plane bend. § Less CH bends.
I n f r a r e d s p e c t r a o f d e u t e r a t e d m e t h a n o l s a n d force field
1141
by the force field, which would raise the product ratios by ½ per cent. This however still leaves a discrepancy of 1-2 $/o unexplained. No acceptable way of distributing the discrepancy by interchanging a' and a" assignments could be found. Indeed the only plausible exchange, noted above in u~ and ~zz of CDaOH, had the effect of worsening the a' discrepancy. The only likely candidates for assignment revision would appear to be the 5~,CDa modes in CDaOH and CD30D, and the CH bending ones of CHD~Ott. We are reluctant to attribute the overshoot to failure of the anharmonicity correction procedure, but this m a y prove to be necessary. F O R C E F I E L D CALCULATIONS
The s y m m e t r y coordinates and molecular geometry assumed are given in Table 3. The data employed consisted of the harmonized frequencies for the eight species CFIaOH, zsCHaOtt, Ctta0D, CHaZS0D, CDaOH, CDa0D, s and as-CHD~OH determined either in this work or in [4]. As before, the zaC and zaO data were included as shifts. Although centrifugal distortion data also exist for CHa0H, CHaOD and CDaOH [11] these were not employed for several reasons. Firstly, the observed D~ °, D ~ ° and D ~ ° were determined through the symmetric top approximation for the rotational levels of what are asymmetric tops, whereas the calculated values are 'true' "asymmetric rotor" ones. Secondly the calculated ones are for the equilibrium configuration in the matrix, and not for the ground state of the gaseous molecule.* T a b l e 3. I n t e r n a l s y m m e t r y c o - o r d i n a t e s a n d g e o m e t r y for methanol* § A'
~z =
~Z =
Al 1]V"6 ( 2 A t I -- Ar~ -- Ara)
s s -- 1/~/~ (Ar~ + Ar 2 + Ar~) AIVg (2A~s8 - h ~ l s -- 5 ~ 1 )
8, =
- A V 1 + _~
$6 = A(AT) , ~ = AR A"
~
= 1l~
* geometry:
Ars)
(At2 -
A
,5':t =
HzCO
=
107°2',
f12 =
fla =
110°54',
A
~tg. = HxCH~ = ~ a = ~ a = 108°38' y = H O C = 108032 ' rCH = 1"0936)x, R c o = /OH = 0-9451 .~ [11].
t K
=
3 sin t~cos/~[sin ~ (Assuming/~1 =
1-426)x, ,82 =
88)
T ~ = d i h e d r a l a n g l e H~COH. § All a n g l e b e n d c o - o r d i n a t e s scaled w i t h u n i t )x l e n g t h : = 10-z° m * T h e effect o f c h a n g e i n g e o m e t r y u p o n c a l c u l a t e d v a l u e s o f D ' s c a n b e significant c o m p a r e d w i t h c h a n g e s i n t h e force field [8]. [11] R . M. LEES a n d J . G. BAKER, Or. Glwm. P h y s . 48, 5299 (1968).
1142
P . D . I~ALLINSONand D. C. MCKEA~
Thirdly the D's are most sensitive to the torsion and torsion-rock interaction force constants, and all attempts to define these failed. Most refinements were carried out with 1 ~/o uncertainties on each absolute frequency, and commensurate errors in the shifts [8, 9], except for doubtful cases such as the torsions and CH bending modes of CHD20H where rather greater error was assumed. However the CH and CD stretching frequencies were treated differently, as discussed below. Preliminary exploration indicated t h a t there was as yet no information to define the following interaction constants: (a) all 3 torsion interactions: (b) all 7 OH stretching interactions: (c) interactions involving vas with ~, ~OH, VCOand vswith ~OH, P and Veo, all in the a' species. All these 17 constants were therefore constrained to be zero. I n addition, the hybrid orbital force field constraint t h a t the interactions va,/~, and v~,/p be equal and opposite in sign [12] was applied in both a' and a" species (two constraints). Out of a total of 46 possible parameters therefore, 29 were use d, of which 27 were independent. A further constraint results amongst the diagonal CH stretching constraints, %/2F2.3 ---- F~.2 -- Fa.9, if the two possible valence force field stretch-stretch interactions f ~ ' and f~a' are equated to each other.*
Treatment of CH and CD stretching frequencies The main objects here were to extract the maximum amount of information concerning Fermi resonance, and to test the applicability of the 3 × 3 refinement procedure used in [7]. The latter involves treating the CH and CD stretching motions in isolation from all others in the molecule, using merely principal and interaction stretching constants. For an asymmetric molecule such as methanol, the constants are four in numberfa,fs,f~ ~' a n d f ~ ' . Observed frequencies are used, but the mutual incompatibility between CH and CD stretching due to anharmonicity is alleviated by dividing all observed CD stretches by 1.011 before input, and remultiplying the refined ones by this factor before making a final comparison with the observed values. The prediction of unperturbed CH and CD stretching frequencies is based on the assumption t h a t only the four constants noted above are important in determining the separations of various CH stretching modes from each other, fa and f~ are essentially determined by the ~CHfrequencies in CHD20H: f j andfa~' can then be found if one a' and one a" frequency in either the CH, or CD3 species can be trusted to be free of Fermi resonance. For such modes uncertainties of ± 1 cm -1 were assumed, and much larger ones used where Fermi resonance was suspected. All CD stretches however are given uncertainties of at least 4-10 cm -1, to allow for error inherent in the 1.011 factor. The highest CH 3 stretching mode appeared to be least affected by Fermi resonance and was therefore given an error of 1 cm-L The a"CH s stretch was considered to be more uncertain, and given 4-10 cm -1. Refinements were carried out with these errors using both the complete (12 x 12) and limited (3 x 3) procedures, and the results are * These are the constants which are the equivalent offald in [7]. [12] I. M. MILLS,Spectrochirn. Acta 19, 1585 (1963).
Infrared spectra of deuterated methanols a n d force field
1143
Table 4. Analysis of CH s and CD s stretching frequencies in methanols Av(obs-calc), 12 x 12" Species
%bs
3005"3 2961.9 2847"9 2253.9 CDaOD 2217.8 2077.0 as-CI-r._.D20H 2931.0 2242-3 2134.2 2986.4 s-CHD~OH 2208.1 2113.3 fa fs fas t faa t
CHsOH
av (a') (a") (a t) (a') (a") (a')
(a t) (a") (a')
A
1 --0-1 10 --2.8 1000 --13-6 10 +6.6 10 +4.9 21 --6.0 1 0.0 10 +0.6 10 + 3 . 7 1 0.0 10 --5.5 10 --2.1 4.729 4.911 --0"016/ --0.033J
Av(obs-calc), 3 x 3t
B
A
--0.2 +1.4 --18.2 +6.6 -t-4"3 --6.4 0.0 +0-7 +3.1 --0-1 --5.7 --3.4 4.726 4.912 --0.012
0.0 +2.1 --23.6 +1.7 --1.9 --8.0 +0.2 +4.1 --0-7 0.0 --1.6 --7.2 4-694 -4- 0.002 4.874 4- 0.002 0.004 4- 0-003 / 0.012 -4- 0.011/
B +0.1 --0.3 --20.8 +1.9 --3.7 --6-0 +0.2 --4.4 0.0 0-0 --13.4 --4.9 4.693 ± 0-002 4.875 ± 0.002 0.003 -4- 0"003
* Complete refinement based on harmonized frequencies. Valence force constants 'deharmonized' b y factor (0.96)2: A. fas' ~ faa' (force field of Table 5): B. fas t = faa" t Refinement of CH and CD stretches only, the latter divided b y 1.011 before input, remultiplied b y 1.011 after refinement. A . fas' # faa': B . fas' = faa"
shown in Table 4. Here the 12 x 12 calculated frequencies and (observed calculated) error vector are both "deharmonized" for the direct comparison with the 3 x 3 results.* I n each case the effect of the constraintf,,' = f ~ ' was also tested (results B in Table 4) the importance of this lying in the fact t h a t very seldom wiU it be possible to determine these two constants independently. Although in both 12 x 12 and 3 × 3 procedures, without this constraint, refinement proceeds to give f , , ' =f=f ~ ' , the difference between the two is within the experimental error, of which the greater part lies in f~', deriving from the 10 em -1 uncertainty in the a" frequency. Moreover the order of magnitude is different in the two treatments; f , , ' > f ~ ' in the 12 x 12, but < f ~ ' in the 3 x 3. We conclude t h a t there is no evidence as yet for a significant difference between f ~ ' and f~,', and comparison of the error vectors shows t h a t the frequencies predicted by the constrained and unconstrained force fields differ but little.t We see further t h a t the constrained 12 x 12 and 3 x 3 force fields (B) predict upwards shifts of 18 and 21 cm -1 on the lower a'CH8 mode and therefore agree in attributing a Fermi resonance shift here of about 20 cm -1. A rather smaller shift could exist on the corresponding CD8 mode of up to 10 cm-~.~ * Similarly the valence stretching constants derived in the 12 x 12 calculation are scaled down b y (0.96) s in this table. t Differences in the abso/atte rrmgn/tude o f f ' between different procedures do not appear to affect appreciably the prediction of fundamental frequencies [7]. ++The only major inconsistency revealed in the comparison above concerns the a" mode of s-CHDs, which in the 3 x 3 B calculation is 13 cm-1 above the observed value. I t m a y be observed t h a t both 12 x 12 and 3 x 3 calculations place a"CD s and s-CHDg, modes very close together, or coincident, and t h a t the puzzle here is really why the observed values of these two modes should differ b y 9.7 cm-L
1144
P . D . MAT,T,INSONand D. C. MeKEA~ Table 5. Symmetry harmonic force constants for methanol* F
171.1 Fz. 2 Fs,a F2. 4
Fu.v Fa. a Fa.5 174.4 F4.5 F4., F4,7 174.s Fs. 5 Fs. 6
Fa. 7
8.147 5.274 +0-102 --0.188# (--0.120) +0-188~ (+0.161) 5.151 +0.128 (+0"203) 0.568 +0.041 +0.022 --0-060 (--0.055) +0.031 0.661 --0.012 -0.093
~(F)
0.028 0.043 --0-039 0-034 0.034 0.043 0"096 0.006 0-004 0.008 0-007 0.013 0.007 0.006 0-007
F
Fs. s Fe. e Fe.v Fe. s FT.7 FT.s Fs. 8 Fg. 0 F0.10 Fg.n Flo.,o Flo.n Fn, n F19.1~
--0-583 (--0.610) 0.772 + 0.103 +0.421 0-981 + 0-063 5.450 5-168 --0-2091' (--0.210) +0.209T (+0.161) 0-590 --0.024 (--0.055) 0.799 0-0270
~(F)
0.011 0.005 0.004 0-009 0.011 0.015 0.023 0.034 0.053 0.053 0.005 0.009 0-005 0.001
* All values in mdyn ~-1 (= ajA-1) ? Constrained values: /'2,4 = --E2.~; F9.10 = --Fg,n
Harmonic force fieZd: general considerations F o r simplicity we q u o t e in Table 5 t h e 29 p a r a m e t e r h a r m o n i c force field f r o m which t h e 12 x 12 (A) results o f Table 4 were taken. A l t h o u g h this was defined b y artificially small errors on certain C H stretching modes, those errors were released t o t h e n o r m a l 1 % ones in t h e last cycle, to give t h e more realistic a values o f Table 5. O f t h e 29 p a r a m e t e r s , all b u t one, F3,s, t h e ~,/0 s i n t e r a c t i o n c o n s t a n t , are fairly well defined. I n general t h e values o f those i n t e r a c t i o n c o n s t a n t s which are c o m m o n to b o t h m e t h a n o l a n d m e t h y l fluoride agree well with each o t h e r (CHaF values b r a c k e t e d in T a b l e 5), e x c e p t perhaps for F3.5 which is illdefined here. T h e la(3 a n d is0 isotopic shifts were well-reproduced at all stages in t h e refinement a n d t h e r e f o r e c o n t r i b u t e d little to the latter.* This was largely due t o t h e experim e n t a l errors associated w i t h t h e m . T h e discrepancy between the observed 1~3 shift o f 4.8 em -~ on t h e 2847-9 cm -1 b a n d of CHaOH a n d the p r e d i c t e d one of 3.5 cm -~ confirms t h e presence o f F e r m i resonance here (2~ 5 is calculated to h a v e a shift o f 2 x 5.6 = 11.2 em-a). Table 6 shows t h e observed a n d calculated values o f D j , D j K a n d D ~ for CHaOH, CH3OD, a n d CDaOH. T h e a g r e e m e n t m u s t be considered satisfactory in t h e light o f t h e considerations discussed above, t F u r t h e r i m p r o v e m e n t s in the force field should result with (a) location o f t h e remaining unobserved, or insecure, f u n d a m e n t a l s , (b) more accurate h e a v y isotopic shifts. I t seems likely t h a t t h e m a j o r obstacle to a d v a n c e is the basic 1 ~/o u n c e r t a i n t y resulting f r o m a n h a r m o n i c i t y . T h u s the a r b i t r a r y elevation o f C H bending modes b y 2~/o a n d o f CO stretching b y 1 ~/o m a y seriously d i s t o r t t h e force field where these * Their main value lay in assigning ~8 and (~8(CHs). t Further details concerning the centrifugal distortion parameters calculated here for all species may be obtained on application to the authors.
I n f r a r e d spectra of d e u t e r a t e d m e t h a n o l s a n d force field
1145
Table 6. O b s e r v e d a n d calculated v a l u e s of centrifugal distortion co-efflcients (MHz)
D j obs.* calc. D j K obs.* calc. D K obs.* calc.
CHsOH
CHsOD
CDsOH
0"0492 ± 0"002 0"0531 0"2864 4- 0"0058 0.3087 1.27 4- 0-06 1-191
0-0464 4- 0"0086 0"0483 0"1900 ± 0"022 0.2551 -0.999
0"0289 4- 0"0003 0"0311 0"1594 -4- 0"0019 0-1685 -0.296
* F r o m reference [11]
modes are in fact strongly coupled to each other. This might be circumvented b y the use of more, and more precise, heavy isotopic shifts and possibly also b y a similar refinement to the small shifts such as those in ~a,(CDs), p(CDs) or ~ o between CD30H and CD30D etc. Acknow/e~gen~ent~-We are v e r y g r a t e f u l to Dr. J . L. DU~CA~ for assistance in calculating t h e B a n d G e l e m e n t s for this molecule. W e t h a n k t h e Science R e s e a r c h Council for a g r a n t t o w a r d s t h e p u r c h a s e of isot~pically labelled c o m p o u n d s a n d for a s t u d e n t s h i p g r a n t to one o f us [P. D. M.].