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The infrared spectrum of the ν10 band of allene
.IOl’ltN
\ 1. OF
MOLk:(‘t-L.\R
38, 503-507
SPliCTROSCOPT
The Infrared
Spectrum
(1971)
of the vlo band
of Allene
J. M. R. STONEI Division
of Physics,
Xational
Research. Council of Canada,
Ottawa, Canada.
Some new experimental and theoretical results are presented for the Y,” fundamental band of allene-hr An explanation of the anomalously broad PQ~ branch is suggested in terms of an l-type doubling in t,he K = 1 (- 1) levels band is proposed. mid a reassignment of the hot bands near the ~10fundamental 1. INTRODUCTION
The vy and v16fundament.al bands of allene were studied by 3lills, Smith and Durlcan (1) in 1965, and they showed that the unusual rotational structure \zithin the bands was due to a strong Coriolis interaction, about the figure axis, betn-een the vibrational levels (21~= 1, u10 = 0) and (us = 0, Llln= 1). They developed the necessary theory required to analyse these bands and hence obtained the molecular parameters An, VY, VI0, I$‘), (:x’ and / {hf?n1. In the present, paper we attempt to resolve some of the questions posed by the previous authors. In the observed spect’rum of the vi0 fundamental the ‘Q? branch is very much broader than the Q branches in the rest of t,he band and in Section 2 an explanat iotl of this in terms of an Z-type doubling of the K = 1 (- 1) levels in the u1n = 1 state is suggested.’ Also a reassignment of the branches associated \vith the hot band (vl(, + vll - ~11) is given in Section 4. 2. THE
PQq BRANCH
OF THE
~10 FU?il)AMENTAL
The term “I-type doubling” is used to refer to the interaction which connects rovibrational energy levels of a symmetric top molecule in a degenerate vibr;ttional state 21,, say, according to the rules Ak = f 2, A/, = f’l. This interaction removrs the degeneracy of the K = 1 j+?) levels in an E vibrationally excited state. l;or molecules with a fourfold axis of symmetry there is :I second kind of ltype doubling interaction which connects rovibrationnl energy levels differing by Ak = f2, Al, = ~2 (2). This second kind of l-type doubling provides ti mechanism for splitt.ing the K = 1 (- 1) levels in an E vibrational state and hence any transition which involves this pair of levels (for example PQZ) may be esprcted to she\\- the effects of this splitting. From the work of Hougrn (3 ) we de1K.l:.C.C. Postdoctoral 2 We denote hy K = [ k .I :tbollt the molecule-fisedz
Fellow
1969-71.
1the modulus of the component, axis. 503
of the total :Lngular momentum
STONE
504
V,, = 1 (E)
FIG. 1. Energy levels involved in the p&z(J) transition.
,‘Q6iA,A2- Ei
,‘I,;Q~A,A,-E) 1 .^ b%_\,L~“., ,I,_? 1 n,0
j_ j ‘ii.,
., >.A’i?,‘.‘,\\L.,I,,,,.. \,.Yx
P 1. ,. 1__ 1,:/XII _._>.L .,‘__\__,,_\__‘_,? _ ‘--. ‘-. I ~~~~~ ~_.___ __+ 800cl+
FIG. 2. Infrared spect,rum of nllene-ha in the region of the ~~0fundamental.
duce that allowed transitions occur between rovibrational levels connected by the species B1, and, therefore, if such a splitting occurs, the ‘Q2 branch should be split or broadened (see Fig. 1). Figure 2 shows the spectrum in the region of t#he ‘Q2 branch of the vlo fundamental of allene with a resolution of ~0.1 cm-‘, taken on the infrared spectrometer previously described by Douglas and Sharma (4). We denote the constant which characterises the usual l-type doubling as qt+ and that which characterises the second kind of l-type doubling as qte. In principle, it is possible to calculate the splitting of the AlA, levels. For allene in an excit’ed state of an E vibration, labelled tit , the l-type doubling expression for the levels k = ---It = *l is T (A,)
-
T (AZ) = ?,$qt- (- 1)” Cut+ 1 >J (J + 11,
(1)
505
~10BAND OF ALLENE
where T (Al), etc, is the term value of the rovibrational level of symmetry A 1, etc. The usual /-type doubling expressions for the levels h- = $1, = fl is ?‘(R,)
-
T(B2)
= l,;q,+(-l)“(Z+
+ l)J(J
+ 1).
(‘I) _,
These expressions were first derived by Grenier-Benson (5). For the sake of clarity, n-e can separat.e t,his new l-type doubling constant into three contributions, which have the same origins as the normal l-type doubling, and tlwsr arc nritten out below: _ Pt = qt- (harmonic, a) + qt- (harmonic, {) + qt- (anharmonic), where qt- (harmonic,
qt- (harmonic,
a)
<)
q,- (anharmonic)
The parameters in the above expressions, wit,h the except,ion of the anharmonic constants, are obtained from the resulm of previous studies on allene. The derivat*ives of the moments of inertia with respect to the normal coordinates ai@) and t.he Coriolis coupling constants [i,z’ require knowledge of t.he L matrices. These are obt’ained from force constant calculations on t,he separate symmet.ry species, see, for example, Nemes, Duncan and Mills (6). We then calculate 410 (harmonic,
a) = -3.438
q& (harmonic,
{) = - X.OM
X lo-’ cm-.‘, X lo-* cm-~‘.
I;ntil t’he cubic anharmonic force const,ant,s are known, this is as far as we can carry t,he calculation; but the maximum of intensity witShin the ‘Q2 branch occurs at .I - 20, and then these terms alone give a splitting of about. 1 cm- ‘. 4. HOT BANDS AHSOCIATP;Il WITH VI,, The spect)rum shown in Fig. 2 is under a higher resolutSion than that obtained by Mills, Smit’h and Duncan (I ), and on the low frequency side of each Q branch of t,he ~10fundamental t,here now appears a weak side branch. We assign t,hese weak branches as hot bands and thereby correct, the hot band assignment given in Ref. (I ).
STONE
506
TABLE Q BUNCH
-__ -__
R&18 RQ~? R&H
~~~SIMA
VI0 ~.. E+-A1
(YKI + VI1- 01) A,Az+- E _~
BlBz+E ____~
928.31 923.35
R&I0 RQ9 R&s R&l RQ6 RQ.a R&4 R&3 R&Z R&l R&O
918.28 913.05 907.61 901.92 895.98 889.65 883.16 876.29 869.05 861.44 853.36 845.31
P&l
836.52
P&2 P&3 PQ4 P&Z P&B P&i
827.52 818.05 SOS.32 798.28 787.97 777.40
Since ~11for allen&
I
ASSIGNMENTS IN THE VIOBa~u OF ALLICNF,-~~ (cm-l) -____AND
907.36 901.61 895.75 889.48 882.90 876.01 868.77 861.15 853.24 (845.50 js44.49 ‘836.21 827.13 817.75 808.05 798.07 787.82
914.34 908.97 903.21 897.32 891.00 884.52 877.70 870.52 862.96 855.09 846.85 838.18 jS30.18 jS28.46 '820.03 810.44 800.45 790.25 779.80
is only 355 cm-l, \ye expect. t.o see t,he hot band (y10 + with t,he fundament.al band vlo . The upper state of such a hot band has vibrational symmetry E X E = AI + A2 + BI + B2 .These four vibrational states will be nearly degenerate for K = 0, except for small perturbations due to anharmonicity. For K # 0 a strong Coriolis interact’ion will occur between the A1 and A2 stat#es and between the B1 and Bs stat,es making the A1 + E and AZ +- E transitions appear as a single perpendicular band and the RI+-E and Bz+ E transitions appear as a second perpendicular band. Hence we should see two series of subsidiary Q branches associated with t,he fundamental. The previous authors having suggested an assignment were puzzled by t.he fact t,hat t)he BIB2+- E and AlAt+- E components were not, of equal intensity. It is now suggested that the AlAz+- E component, was wrongly assigned, and t)his assignment should be applied t’o the series of side bands seen to the low frequency side of the vlo fundamental Q branches. As pointed out by Mills, et al. (I), transitions involving K = 0 in the upper state will show only the effects of anharmonicity and ‘&I subbands should be Vll- vll)associated
split, into a doublet. The AlAz + h’ component of the ‘&I subband occurs near the “Qo branch of the ~10fundamental and is split, by 1.01 cm-‘. The B&z - E component appears near the ‘Qz fundamental Q branch and is split by 1.73 cm -‘. The measured line positions of all the Q branches in the ~10 band and the ( vln + ~11- ~11)hot bands are presented in Table I. It is noted t,hat, the Q branch separat,ion in both series of hot, bands slowly increases towards the wings of the band. This is similar to the behaviour of t)he fundamentals vy and vlo and is due I o a Coriolis interaction about the figure axis between (uy = 1, ~11= 1) and (VI,, = 1, 1111= 1). We have no argument with the assignments of the hot bands in the vy fundamental band and indeed the disposition of the hot’ bands is very similar to that proposed here for t’he vlo band. The lines which had been previously assigned as the Q branches of the A9, + fi components of t,he hot band are not] so clearly identifiable under higher resolut,ion and arr probably due to an accidental “pile up” of the rotational .J structure. ACKNOWLEDGMENTS I am grateful rllssions. I~ECEIVED
:
to Professor
Sovember
I. M. Mills
and Dr. J. Ii. (:. Watson
for many helpful
30, 1970
f. J. &I. hIILLS, w. L. SMITH AND J. L. I)uNCAN, J. fife/. ~~w~WC. 16,349 (1965) A_ 0 J. DE HEER, Phys. Rev. 83, 741 (1951). 3. .J. T. HOUGE:N, J. Chen~. Phys. 37, 1433 (1962,. 4. A. 1’. I)O~JGLAS AND I>.SHARMA, J. Chem. Phys. 21, -LB (1953). 5. M. L. GRENIEH-BESSON, J. Phys. Radium 21, 555 (1960). 6. I,. NEMES, J. L. I~CNCAN .WD I.M. MILLS, Spectrochiw Ac!n A23, 1803 (1967,.
dis-
\ 1. OF
MOLk:(‘t-L.\R
38, 503-507
SPliCTROSCOPT
The Infrared
Spectrum
(1971)
of the vlo band
of Allene
J. M. R. STONEI Division
of Physics,
Xational
Research. Council of Canada,
Ottawa, Canada.
Some new experimental and theoretical results are presented for the Y,” fundamental band of allene-hr An explanation of the anomalously broad PQ~ branch is suggested in terms of an l-type doubling in t,he K = 1 (- 1) levels band is proposed. mid a reassignment of the hot bands near the ~10fundamental 1. INTRODUCTION
The vy and v16fundament.al bands of allene were studied by 3lills, Smith and Durlcan (1) in 1965, and they showed that the unusual rotational structure \zithin the bands was due to a strong Coriolis interaction, about the figure axis, betn-een the vibrational levels (21~= 1, u10 = 0) and (us = 0, Llln= 1). They developed the necessary theory required to analyse these bands and hence obtained the molecular parameters An, VY, VI0, I$‘), (:x’ and / {hf?n1. In the present, paper we attempt to resolve some of the questions posed by the previous authors. In the observed spect’rum of the vi0 fundamental the ‘Q? branch is very much broader than the Q branches in the rest of t,he band and in Section 2 an explanat iotl of this in terms of an Z-type doubling of the K = 1 (- 1) levels in the u1n = 1 state is suggested.’ Also a reassignment of the branches associated \vith the hot band (vl(, + vll - ~11) is given in Section 4. 2. THE
PQq BRANCH
OF THE
~10 FU?il)AMENTAL
The term “I-type doubling” is used to refer to the interaction which connects rovibrational energy levels of a symmetric top molecule in a degenerate vibr;ttional state 21,, say, according to the rules Ak = f 2, A/, = f’l. This interaction removrs the degeneracy of the K = 1 j+?) levels in an E vibrationally excited state. l;or molecules with a fourfold axis of symmetry there is :I second kind of ltype doubling interaction which connects rovibrationnl energy levels differing by Ak = f2, Al, = ~2 (2). This second kind of l-type doubling provides ti mechanism for splitt.ing the K = 1 (- 1) levels in an E vibrational state and hence any transition which involves this pair of levels (for example PQZ) may be esprcted to she\\- the effects of this splitting. From the work of Hougrn (3 ) we de1K.l:.C.C. Postdoctoral 2 We denote hy K = [ k .I :tbollt the molecule-fisedz
Fellow
1969-71.
1the modulus of the component, axis. 503
of the total :Lngular momentum
STONE
504
V,, = 1 (E)
FIG. 1. Energy levels involved in the p&z(J) transition.
,‘Q6iA,A2- Ei
,‘I,;Q~A,A,-E) 1 .^ b%_\,L~“., ,I,_? 1 n,0
j_ j ‘ii.,
., >.A’i?,‘.‘,\\L.,I,,,,.. \,.Yx
P 1. ,. 1__ 1,:/XII _._>.L .,‘__\__,,_\__‘_,? _ ‘--. ‘-. I ~~~~~ ~_.___ __+ 800cl+
FIG. 2. Infrared spect,rum of nllene-ha in the region of the ~~0fundamental.
duce that allowed transitions occur between rovibrational levels connected by the species B1, and, therefore, if such a splitting occurs, the ‘Q2 branch should be split or broadened (see Fig. 1). Figure 2 shows the spectrum in the region of t#he ‘Q2 branch of the vlo fundamental of allene with a resolution of ~0.1 cm-‘, taken on the infrared spectrometer previously described by Douglas and Sharma (4). We denote the constant which characterises the usual l-type doubling as qt+ and that which characterises the second kind of l-type doubling as qte. In principle, it is possible to calculate the splitting of the AlA, levels. For allene in an excit’ed state of an E vibration, labelled tit , the l-type doubling expression for the levels k = ---It = *l is T (A,)
-
T (AZ) = ?,$qt- (- 1)” Cut+ 1 >J (J + 11,
(1)
505
~10BAND OF ALLENE
where T (Al), etc, is the term value of the rovibrational level of symmetry A 1, etc. The usual /-type doubling expressions for the levels h- = $1, = fl is ?‘(R,)
-
T(B2)
= l,;q,+(-l)“(Z+
+ l)J(J
+ 1).
(‘I) _,
These expressions were first derived by Grenier-Benson (5). For the sake of clarity, n-e can separat.e t,his new l-type doubling constant into three contributions, which have the same origins as the normal l-type doubling, and tlwsr arc nritten out below: _ Pt = qt- (harmonic, a) + qt- (harmonic, {) + qt- (anharmonic), where qt- (harmonic,
qt- (harmonic,
a)
<)
q,- (anharmonic)
The parameters in the above expressions, wit,h the except,ion of the anharmonic constants, are obtained from the resulm of previous studies on allene. The derivat*ives of the moments of inertia with respect to the normal coordinates ai@) and t.he Coriolis coupling constants [i,z’ require knowledge of t.he L matrices. These are obt’ained from force constant calculations on t,he separate symmet.ry species, see, for example, Nemes, Duncan and Mills (6). We then calculate 410 (harmonic,
a) = -3.438
q& (harmonic,
{) = - X.OM
X lo-’ cm-.‘, X lo-* cm-~‘.
I;ntil t’he cubic anharmonic force const,ant,s are known, this is as far as we can carry t,he calculation; but the maximum of intensity witShin the ‘Q2 branch occurs at .I - 20, and then these terms alone give a splitting of about. 1 cm- ‘. 4. HOT BANDS AHSOCIATP;Il WITH VI,, The spect)rum shown in Fig. 2 is under a higher resolutSion than that obtained by Mills, Smit’h and Duncan (I ), and on the low frequency side of each Q branch of t,he ~10fundamental t,here now appears a weak side branch. We assign t,hese weak branches as hot bands and thereby correct, the hot band assignment given in Ref. (I ).
STONE
506
TABLE Q BUNCH
-__ -__
R&18 RQ~? R&H
~~~SIMA
VI0 ~.. E+-A1
(YKI + VI1- 01) A,Az+- E _~
BlBz+E ____~
928.31 923.35
R&I0 RQ9 R&s R&l RQ6 RQ.a R&4 R&3 R&Z R&l R&O
918.28 913.05 907.61 901.92 895.98 889.65 883.16 876.29 869.05 861.44 853.36 845.31
P&l
836.52
P&2 P&3 PQ4 P&Z P&B P&i
827.52 818.05 SOS.32 798.28 787.97 777.40
Since ~11for allen&
I
ASSIGNMENTS IN THE VIOBa~u OF ALLICNF,-~~ (cm-l) -____AND
907.36 901.61 895.75 889.48 882.90 876.01 868.77 861.15 853.24 (845.50 js44.49 ‘836.21 827.13 817.75 808.05 798.07 787.82
914.34 908.97 903.21 897.32 891.00 884.52 877.70 870.52 862.96 855.09 846.85 838.18 jS30.18 jS28.46 '820.03 810.44 800.45 790.25 779.80
is only 355 cm-l, \ye expect. t.o see t,he hot band (y10 + with t,he fundament.al band vlo . The upper state of such a hot band has vibrational symmetry E X E = AI + A2 + BI + B2 .These four vibrational states will be nearly degenerate for K = 0, except for small perturbations due to anharmonicity. For K # 0 a strong Coriolis interact’ion will occur between the A1 and A2 stat#es and between the B1 and Bs stat,es making the A1 + E and AZ +- E transitions appear as a single perpendicular band and the RI+-E and Bz+ E transitions appear as a second perpendicular band. Hence we should see two series of subsidiary Q branches associated with t,he fundamental. The previous authors having suggested an assignment were puzzled by t.he fact t,hat t)he BIB2+- E and AlAt+- E components were not, of equal intensity. It is now suggested that the AlAz+- E component, was wrongly assigned, and t)his assignment should be applied t’o the series of side bands seen to the low frequency side of the vlo fundamental Q branches. As pointed out by Mills, et al. (I), transitions involving K = 0 in the upper state will show only the effects of anharmonicity and ‘&I subbands should be Vll- vll)associated
split, into a doublet. The AlAz + h’ component of the ‘&I subband occurs near the “Qo branch of the ~10fundamental and is split, by 1.01 cm-‘. The B&z - E component appears near the ‘Qz fundamental Q branch and is split by 1.73 cm -‘. The measured line positions of all the Q branches in the ~10 band and the ( vln + ~11- ~11)hot bands are presented in Table I. It is noted t,hat, the Q branch separat,ion in both series of hot, bands slowly increases towards the wings of the band. This is similar to the behaviour of t)he fundamentals vy and vlo and is due I o a Coriolis interaction about the figure axis between (uy = 1, ~11= 1) and (VI,, = 1, 1111= 1). We have no argument with the assignments of the hot bands in the vy fundamental band and indeed the disposition of the hot’ bands is very similar to that proposed here for t’he vlo band. The lines which had been previously assigned as the Q branches of the A9, + fi components of t,he hot band are not] so clearly identifiable under higher resolut,ion and arr probably due to an accidental “pile up” of the rotational .J structure. ACKNOWLEDGMENTS I am grateful rllssions. I~ECEIVED
:
to Professor
Sovember
I. M. Mills
and Dr. J. Ii. (:. Watson
for many helpful
30, 1970
f. J. &I. hIILLS, w. L. SMITH AND J. L. I)uNCAN, J. fife/. ~~w~WC. 16,349 (1965) A_ 0 J. DE HEER, Phys. Rev. 83, 741 (1951). 3. .J. T. HOUGE:N, J. Chen~. Phys. 37, 1433 (1962,. 4. A. 1’. I)O~JGLAS AND I>.SHARMA, J. Chem. Phys. 21, -LB (1953). 5. M. L. GRENIEH-BESSON, J. Phys. Radium 21, 555 (1960). 6. I,. NEMES, J. L. I~CNCAN .WD I.M. MILLS, Spectrochiw Ac!n A23, 1803 (1967,.
dis-