- Email: [email protected]
High-Resolution Photoacoustic Overtone Spectrum of Monobromoacetylene, HCCBr, above 11 600 cm−1
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
187, 193–199 (1998)
MS977477
High-Resolution Photoacoustic Overtone Spectrum of Monobromoacetylene, HCCBr, above 11 600 cm01 Olavi Vaittinen,* ,1 Markku Ha¨ma¨la¨inen,* Peter Jungner,* Kirsi Pulkkinen,* Lauri Halonen,* Hans Bu¨rger,† and Oliver Polanz† *Laboratory of Physical Chemistry, P.O. Box 55 (A. I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland; and †FB9-Anorganische Chemie, Universita¨t Gesamthochschule, D-42097 Wuppertal, Germany Received October 6, 1997
Photoacoustic overtone spectra of monobromoacetylene, HCCBr, have been recorded in the wavenumber region 11600–13400 cm01 using a titanium:sapphire ring laser spectrometer. All together, eight overtone bands of HCC 79Br and eight bands of HCC 81Br have been observed in the rotational analysis. A Fermi resonance model based on conventional normal coordinate theory has been used to vibrationally assign the rotationally analyzed bands. The resonance model employed reproduces well the observed vibrational band origins and rotational constants. q 1998 Academic Press 1. INTRODUCTION
Monobromoacetylene, HCCBr, is a useful molecule for experimental and theoretical work in high-resolution overtone spectroscopy. By possessing just one C–H bond, it is an ideal object for studies on rovibrational couplings in the overtone region, and thus for studies on the energy flow within a molecule. From the practical point of view, because HCCBr is a linear molecule, the rotational analysis is usually simple. Previously, the vibration –rotation spectra of HCCBr in the fundamental and overtone region, up to the third overtone of the C– H stretch, have been studied using highresolution FTIR and photoacoustic spectroscopy (1 –4 ). We aim to expand the previous analysis to cover all the band systems measurable by our sensitive titanium:sapphire ring laser spectrometer in the overtone region from 10800 to 14500 cm01 . In this study, we have used a phase-sensitive intracavity detection method to record high-resolution vibration–rotation spectra of HCCBr at 11600–13400 cm01 with the exception of the 4n1 band system around 12 600 cm01 , which has been recorded and analyzed earlier (4). The spectra are rotationally analyzed by standard vibration–rotation theory, and a Fermi resonance model based on rectilinear normal coordinate theory is used to vibrationally assign the observed bands. 2. EXPERIMENTAL DETAILS
HCCBr was synthesized as described in Ref. ( 5) by dehydrobromination of 1,2-dibromoethene with KOH/KCN and purified by fractional condensation in vacuo. 1
To whom correspondence should be addressed. E-mail: vaittine@ fkbond.pc.helsinki.fi.
The overtone spectra were recorded employing an intracavity photoacoustic detection method using a Coherent 89921 titanium:sapphire ring laser which is pumped by a Coherent Innova 200/20-4 argon ion laser as described in detail previously (6, 7). The sample was placed inside a 20-cmlong resonant photoacoustic cell, which is equipped with a copper waveguide and a Knowles microphone BT1759. Pressure waves are created inside the sample cell by mechanically chopping the laser beam. The photoacoustic signal is enhanced by placing the cell inside the ring-laser cavity, and the signal is detected with a phase-sensitive method using a lock-in amplifier EG&G 5109. The spectra were measured at room temperature. The Doppler limited spectra were calibrated by simultaneously recording an iodine absorption spectrum (8). In the procedure, a 25-cm-long cell made of quartz and containing solid I2 was placed inside an oven whose temperature was maintained around 6007C. The absolute accuracy achieved by our calibration procedure is estimated to be better than 0.01 cm01 , limited mainly by the quality of the I2 spectrum. In order to survey all of the vibration–rotation bands appearing inside the optical gain curve of the laser, low-resolution spectra (resolution of about 1 cm01 ) were obtained by removing the intracavity e´talons and the Brewster plate from the standard ring-laser cavity. The wavenumber scale was attached to these spectra using a Burleigh wavemeter, model WA-4500. The sample pressure in the low-resolution measurements was chosen to be about 50 mbar compared with about 15 mbar used in the high-resolution work. 3. RESULTS
The low-resolution spectrum of HCCBr in the wavenumber region 10800–14500 cm01 is presented in Fig. 1. All of
193 0022-2852/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.
AID
JMS 7477
/
6t26$$$$81
01-30-98 11:49:47
mspa
194
VAITTINEN ET AL.
FIG. 1. The low-resolution photoacoustic spectrum of monobromoacetylene in the wavenumber region 10800–14500 cm01 is shown. The sample pressure has been about 50 mbar, and the spectral resolution is about 1 cm01 . The laser power variation has not been taken into account in plotting the spectrum. It might have an effect on the relative intensities of some of the bands. The notation is such that n1 is the CH stretch, n2 is the CC stretch, n3 is the CBr stretch, and n5 is the CCBr bend.
the observed band systems belong to HCCBr, except for the ones at about 12400 cm01 and at about 13800 cm01 , which are both due to water. As expected, the ‘‘pure’’ hydrogen stretching overtone band 4n1 ( n1 is the C–H stretch) is the strongest feature in the spectrum. Almost as strong is the 3n1 / n2 ( n2 is the CGC stretch) band system. An order of magnitude weaker are the 4n1 / n3 ( n3 is the C–Br stretch) and 4n1 / n5 ( n5 is the CGC–Br bend) band systems. Overviews of the 4n1 / n5 and 4n1 / n3 band systems recorded with high resolution are shown in Figs. 2 and 3, respectively. In Fig. 2, a sequence of Q branches is observed as a result of perpendicular transitions. The vibration–rotation upper states associated with the whole band system are thought to form a mutually resonating group, and the corresponding transitions gain their oscillator strength originally from the 4n1 / n5 transition. The rest of the observed bands appear as parallel bands being S – S transitions originating from the ground vibrational state. The rotational analyses are based on the standard energy level expression of a linear molecule (9) Ev /hc Å Gv / Fv (J, k) Å Gv / Bv[J(J / 1) 0 k 2 ]
[1]
0 Dv[J(J / 1) 0 k 2 ] 2 ,
where Gv is the vibrational term value, Bv is the rotational
constant, and Dv is the quartic centrifugal distortion constant of the vibrational state v. J is the total angular momentum quantum number, and k Å (t lt Å l4 / l5 is the total vibrational angular momentum quantum number. To refine the upper state parameters, it is convenient to fit the rotational lines in terms of reduced energy transitions because this method constrains the lower state parameters to their given values and optimizes only the upper state parameters. The observed line positions can be converted to reduced energy transitions as nI red Å nI 0 B 9v [J * (J * / 1) 0 k * 2 ] / B 9v [J 9 (J 9 / 1) 0 k 9 2 ] / D 9v [J * (J * / 1) 0 k * 2 ] 2 0 D 9v [J 9 (J 9 / 1) 0 k 9 ]
Å DG / DB[J * (J * / 1) 0 k * 2 ] 0 DD[J * (J * / 1) 0 k * 2 ] 2 ,
where nI is the transition wave number, DG Å G *v 0 G 9v , DB Å B *v 0 B 9v , and DD Å D *v 0 D 9v . The coefficient optimization is done by the linear least-squares method. The constrained lower state rotational parameters are taken from Ref. (3). The lower state assignments of this study were
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
[2]
2 2
mspa
OVERTONE SPECTRUM OF BROMOACETYLENE
195
FIG. 2. The high-resolution photoacoustic spectrum of the (4n1 / n5 )-band system of monobromoacetylene. The spectral resolution is about 0.03 cm01 and the sample pressure has been about 15 mbar.
confirmed by the ground-state combination difference method (9). We have been able to assign practically all of the strong and medium-strong lines in the spectrum. The blended and
perturbed lines were excluded from the fits. The results of the rotational analyses are given in Tables 1 and 2. The uncertainties of the upper state parameters given in these tables were obtained by assuming that the lower state param-
FIG. 3. The high-resolution photoacoustic spectrum of the (4n1 / n3 )-band system of monobromoacetylene. The spectral resolution is about 0.03 cm01 and the sample pressure has been about 15 mbar.
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
mspa
196
VAITTINEN ET AL.
TABLE 1 Rotational Analysis of HCC 79Br
eters do not possess any uncertainties. Thus, they reflect the uncertainties of the differences between upper and lower state parameters. The standard deviations of some fits are unusually large as a result of perturbations, which appear locally (so-called crossover perturbations) or for high J values (so-called global perturbations). Unfortunately, due to the lack of data, it is impossible to sort out the unknown perturbers. For the vibrational analysis we have used standard vibration–rotation theory formulated in terms of rectilinear normal coordinates. The diagonal matrix elements of our model Hamiltonian take the usual form (9, 10) » vÉHvib /hcÉv … Å
∑ nI *r vr / ∑ x*rr (v 2r 0 vr ) r
/
r
∑ x*rr =vrvr = / ∑ g*tt (l 2t 0 vt ) [3] r õr =
/
t
bers nI r* are used instead of harmonic wavenumbers vr . x* rr , x* rr = , g* tt , and g* tt = are anharmonic parameters, which are functions of cubic and quartic force constants in the normal coordinate representation. vr is the standard vibrational quantum number, and lt (t Å 4 or 5) is the vibrational angular momentum quantum number associated with the doubly degenerate bending modes n4 and n5 . The summation indices r and r * span all five normal modes, whereas the indices t and t * span only the bending modes. The doubly degenerate modes are counted only once. The superscript star indicates that the Fermi resonance has been included explicitly in the model. The wavenumbers of the fundamental vibrations ( n1 É 3336 cm01 , n2 É 2091 cm01 , n3 É 620 cm01 , n4 É 617 cm01 , and n5 É 291 cm01 ) are such that they give rise to several resonances. The off-diagonal Fermi resonance matrix elements included are (4) l
∑ g*tt = ltlt = ,
l
Å k355[v3 (v5 / l5 / 2)(v5 0 l5 / 2)/8] 1 / 2 ,
tõt =
where v on the left-hand side denotes all of the vibrational quantum numbers, and fundamental vibrational wavenum-
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
[4]
the matrix elements due to the Darling–Dennison-type resonance are (11)
Copyright q 1998 by Academic Press
AID
l
» v1v2v3v 44v 55 ÉH/hcÉv1v2 (v3 0 1)v 44 (v5 / 2) l5 …
mspa
197
OVERTONE SPECTRUM OF BROMOACETYLENE
TABLE 2 Rotational Analysis of HCC 81Br
l
l
l
» v1v2v3v 44v 55 ÉH/hcÉ(v1 0 1) (v2 / 1)v3 (v4 / 2) l4v 55 … Å 14 K1244[v1 (v2 / 1)(v4 / l4 / 2)
[5]
1 (v4 0 l4 / 2)]
1/2
,
confirm that this limitation has an insignificant effect on the results. The differences DB between upper state ( Bv ) and ground state ( B0 ) rotational constants are obtained from the equation ( 4 )
and the off-diagonal vibrational l-resonance matrix elements are (10) l4 4
l5 5
» v1v2v3v v ÉH/hcÉv1v2v3v
( l40 2 ) 4
v
( l5/ 2 ) 5
DB Å B0 0 Bv Å 0
[6]
1 [(v5 / 1) 2 0 (l5 / 1) 2 ]} 1 / 2 ,
where k355 , K1244 , and r45 are parameters which describe the strength of these interactions. Only the states with the same symmetry and with the same polyad quantum number V Å 11v1 / 7v2 / 2v3 / 2v4 / v5
[7]
are coupled together in our model. Consequently, the Hamiltonian matrix is factorized to a large number of smaller matrices (4). For practical reasons, we have decided to restrict the sizes of the matrix blocks by including only the closest interacting states by limiting the maxima of the individual quantum numbers vr and lt (4). Test calculations
/
6t26$$$$82
iÅ1
r Å1
[8]
where ci is the eigenvector element attached to a specific vibrational state (a specific basis function), ar describes the vibrational dependence of the rotational constants of the fundamentals (9), and N is the number of interacting states (the size of the matrix block in question). The calculated values have been computed using the eigenvectors obtained by diagonalizing the resonance Hamiltonian matrices. The values for the parameters in Eqs. [3] – [8] are taken from Ref. (4). Tables 3 and 4 contain the results for the vibrational term values and rotational constants for both isotopic species. 5. DISCUSSION
Generally, the anharmonic model we have used to interpret the vibrational and rotational data yields trustworthy results. About half of the calculated vibrational origins are
Copyright q 1998 by Academic Press
JMS 7477
5
…
Å 14r45 {[(v4 / 1) 2 0 (l4 0 1) 2 ]
AID
N
∑ c 2i ∑ arvr ,
01-30-98 11:49:47
mspa
198
VAITTINEN ET AL.
TABLE 3 Vibrational Analysis of HCC 79Br
within two wavenumbers of the observed ones. Most of the rotational constants are also well reproduced. This applies particularly to the ‘‘bright’’ states such as É401 0 0 0 0 … after which the band systems are named. The larger differences between the model and the observations appear with the states with unusual quantum labels like É041 8 0 0 0 … . It may thus be argued that the resonances included in the model are not adequate to precisely reproduce the energies of these strongly mixed states. We believe, however, that the quantum labels are the most reasonable ones, because although the mixing ratios may be imperfectly computed, there are no other justifiable candidates in the neighbourhood of these states in the calculations. In a similar case of monofluoroacetylene, it was found out that diminutive changes in the parameters can cause substantial effects on the mixing of the states (12). The Darling–Dennison resonance term in K1244 appears to be sufficient to justify all except one of the observed vibration–rotation bands in the spectrum. The exception is the band at 11667.5 cm01 for HCC 79Br and at 11666.9 cm01 for HCC 81Br labelled as É043 2 0 2 0 … . In that case, it is possible to observe a Darling–Dennison resonance sequence É310 0 0 0 0 … r É220 2 0 0 0 … r É130 4 0 0 0 … r É040 6 0 0 0 … , which explains the vibrational quanta of the v1 and v2 excitations. Our model does not include any resonances
which would account for the energy transfer from the Darling–Dennison coupled group of states to the É043 2 0 2 0 … state. The relatively large intensity of the observed band, however, seems to hint that a new type of resonance may exist. Another aspect worth mentioning is that the sign of the Darling–Dennison constant K1244 depends on the chosen positive sense of the coordinates q1 and q2 (11). Therefore, the absolute signs of K1244 and k355 are not meaningful in our study. The relative signs of these parameters, in contrast, are important because both of them appear in off-diagonal matrix elements. The current study has reinforced the importance of the Darling–Dennison resonance in the intramolecular energy flow of HCCBr. The Fermi resonance seems to play no obvious role in the overtone region of this molecule. Analogous results have also been obtained in the case of iodoacetylene, HCCI (13). On the other hand, with fluoroacetylene, HCCF, several Fermi resonances are needed to explain the overtone spectrum (11, 12). Chloroacetylene, HCCCl, is an interesting example where the effects of anharmonic resonances are quite small in the first overtone band of the C– H stretch (14). However, the resonances reappear en masse in the third overtone region as demonstrated by the photoacoustic experiment (15). Unfortunately, that study does not
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
mspa
OVERTONE SPECTRUM OF BROMOACETYLENE
199
TABLE 4 Vibrational Analysis of HCC 81Br
include a vibrational analysis, which would account for the observed phenomena. ACKNOWLEDGMENTS The authors thank the DAAD/Academy of Finland and the Rector of the University of Helsinki for financial support. We are grateful to Mr. Robert Brotherus for the use of his visual spectrum analysis program.
REFERENCES 1. O. Vaittinen, L. Halonen, H. Bu¨rger, and O. Polanz, J. Mol. Spectrosc. 167, 55–70 (1994). 2. M. Halonen, J. Mol. Spectrosc. 167, 225–230 (1994). 3. O. Vaittinen, T. Lukka, L. Halonen, H. Bu¨rger, and O. Polanz, J. Mol. Spectrosc. 172, 503–519 (1995). 4. O. Vaittinen, Chem. Phys. Lett. 238, 319–326 (1995). 5. G. R. Hunt and M. K. Wilson, J. Chem. Phys. 34, 1301–1306 (1961).
6. X. Zhan, E. Kauppi, and L. Halonen, Rev. Sci. Instrum. 63, 5546–5550 (1992). 7. X. Zhan, Ann. Acad. Sci. Fenn. Ser. A 252, 1–38 (1993). 8. S. Gerstenkorn, J. Verges, and J. Chevillard, ‘‘Atlas du Spectre d’absorption de la molecule d’iode,’’ Laboratoire Aime´-Cotton, CNRS II, Orsay, 1982. 9. G. Herzberg, ‘‘Infrared and Raman Spectra of Polyatomic Molecules,’’ Van Nostrand, New York, 1945. 10. J. K. Holland, D. A. Newnham, I. M. Mills, and M. Herman, J. Mol. Spectrosc. 151, 346–368 (1992). 11. A. F. Borro, I. M. Mills, and E. Venuti, J. Chem. Phys. 102, 3938– 3944 (1995). 12. O. Vaittinen, M. Saarinen, L. Halonen, and I. M. Mills, J. Chem. Phys. 99, 3277–3287 (1993). 13. J. Lummila, O. Vaittinen, P. Jungner, L. Halonen, and A.-M. Tolonen, J. Mol. Spectrosc. 185, 296–303 (1997). 14. A. F. Borro, I. M. Mills, and A. Mose, Chem. Phys. 190, 363–371 (1995). 15. M. Saarinen, L. Halonen, and O. Polanz, Chem. Phys. Lett. 219, 181– 186 (1994).
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$83
01-30-98 11:49:47
mspa
187, 193–199 (1998)
MS977477
High-Resolution Photoacoustic Overtone Spectrum of Monobromoacetylene, HCCBr, above 11 600 cm01 Olavi Vaittinen,* ,1 Markku Ha¨ma¨la¨inen,* Peter Jungner,* Kirsi Pulkkinen,* Lauri Halonen,* Hans Bu¨rger,† and Oliver Polanz† *Laboratory of Physical Chemistry, P.O. Box 55 (A. I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland; and †FB9-Anorganische Chemie, Universita¨t Gesamthochschule, D-42097 Wuppertal, Germany Received October 6, 1997
Photoacoustic overtone spectra of monobromoacetylene, HCCBr, have been recorded in the wavenumber region 11600–13400 cm01 using a titanium:sapphire ring laser spectrometer. All together, eight overtone bands of HCC 79Br and eight bands of HCC 81Br have been observed in the rotational analysis. A Fermi resonance model based on conventional normal coordinate theory has been used to vibrationally assign the rotationally analyzed bands. The resonance model employed reproduces well the observed vibrational band origins and rotational constants. q 1998 Academic Press 1. INTRODUCTION
Monobromoacetylene, HCCBr, is a useful molecule for experimental and theoretical work in high-resolution overtone spectroscopy. By possessing just one C–H bond, it is an ideal object for studies on rovibrational couplings in the overtone region, and thus for studies on the energy flow within a molecule. From the practical point of view, because HCCBr is a linear molecule, the rotational analysis is usually simple. Previously, the vibration –rotation spectra of HCCBr in the fundamental and overtone region, up to the third overtone of the C– H stretch, have been studied using highresolution FTIR and photoacoustic spectroscopy (1 –4 ). We aim to expand the previous analysis to cover all the band systems measurable by our sensitive titanium:sapphire ring laser spectrometer in the overtone region from 10800 to 14500 cm01 . In this study, we have used a phase-sensitive intracavity detection method to record high-resolution vibration–rotation spectra of HCCBr at 11600–13400 cm01 with the exception of the 4n1 band system around 12 600 cm01 , which has been recorded and analyzed earlier (4). The spectra are rotationally analyzed by standard vibration–rotation theory, and a Fermi resonance model based on rectilinear normal coordinate theory is used to vibrationally assign the observed bands. 2. EXPERIMENTAL DETAILS
HCCBr was synthesized as described in Ref. ( 5) by dehydrobromination of 1,2-dibromoethene with KOH/KCN and purified by fractional condensation in vacuo. 1
To whom correspondence should be addressed. E-mail: vaittine@ fkbond.pc.helsinki.fi.
The overtone spectra were recorded employing an intracavity photoacoustic detection method using a Coherent 89921 titanium:sapphire ring laser which is pumped by a Coherent Innova 200/20-4 argon ion laser as described in detail previously (6, 7). The sample was placed inside a 20-cmlong resonant photoacoustic cell, which is equipped with a copper waveguide and a Knowles microphone BT1759. Pressure waves are created inside the sample cell by mechanically chopping the laser beam. The photoacoustic signal is enhanced by placing the cell inside the ring-laser cavity, and the signal is detected with a phase-sensitive method using a lock-in amplifier EG&G 5109. The spectra were measured at room temperature. The Doppler limited spectra were calibrated by simultaneously recording an iodine absorption spectrum (8). In the procedure, a 25-cm-long cell made of quartz and containing solid I2 was placed inside an oven whose temperature was maintained around 6007C. The absolute accuracy achieved by our calibration procedure is estimated to be better than 0.01 cm01 , limited mainly by the quality of the I2 spectrum. In order to survey all of the vibration–rotation bands appearing inside the optical gain curve of the laser, low-resolution spectra (resolution of about 1 cm01 ) were obtained by removing the intracavity e´talons and the Brewster plate from the standard ring-laser cavity. The wavenumber scale was attached to these spectra using a Burleigh wavemeter, model WA-4500. The sample pressure in the low-resolution measurements was chosen to be about 50 mbar compared with about 15 mbar used in the high-resolution work. 3. RESULTS
The low-resolution spectrum of HCCBr in the wavenumber region 10800–14500 cm01 is presented in Fig. 1. All of
193 0022-2852/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.
AID
JMS 7477
/
6t26$$$$81
01-30-98 11:49:47
mspa
194
VAITTINEN ET AL.
FIG. 1. The low-resolution photoacoustic spectrum of monobromoacetylene in the wavenumber region 10800–14500 cm01 is shown. The sample pressure has been about 50 mbar, and the spectral resolution is about 1 cm01 . The laser power variation has not been taken into account in plotting the spectrum. It might have an effect on the relative intensities of some of the bands. The notation is such that n1 is the CH stretch, n2 is the CC stretch, n3 is the CBr stretch, and n5 is the CCBr bend.
the observed band systems belong to HCCBr, except for the ones at about 12400 cm01 and at about 13800 cm01 , which are both due to water. As expected, the ‘‘pure’’ hydrogen stretching overtone band 4n1 ( n1 is the C–H stretch) is the strongest feature in the spectrum. Almost as strong is the 3n1 / n2 ( n2 is the CGC stretch) band system. An order of magnitude weaker are the 4n1 / n3 ( n3 is the C–Br stretch) and 4n1 / n5 ( n5 is the CGC–Br bend) band systems. Overviews of the 4n1 / n5 and 4n1 / n3 band systems recorded with high resolution are shown in Figs. 2 and 3, respectively. In Fig. 2, a sequence of Q branches is observed as a result of perpendicular transitions. The vibration–rotation upper states associated with the whole band system are thought to form a mutually resonating group, and the corresponding transitions gain their oscillator strength originally from the 4n1 / n5 transition. The rest of the observed bands appear as parallel bands being S – S transitions originating from the ground vibrational state. The rotational analyses are based on the standard energy level expression of a linear molecule (9) Ev /hc Å Gv / Fv (J, k) Å Gv / Bv[J(J / 1) 0 k 2 ]
[1]
0 Dv[J(J / 1) 0 k 2 ] 2 ,
where Gv is the vibrational term value, Bv is the rotational
constant, and Dv is the quartic centrifugal distortion constant of the vibrational state v. J is the total angular momentum quantum number, and k Å (t lt Å l4 / l5 is the total vibrational angular momentum quantum number. To refine the upper state parameters, it is convenient to fit the rotational lines in terms of reduced energy transitions because this method constrains the lower state parameters to their given values and optimizes only the upper state parameters. The observed line positions can be converted to reduced energy transitions as nI red Å nI 0 B 9v [J * (J * / 1) 0 k * 2 ] / B 9v [J 9 (J 9 / 1) 0 k 9 2 ] / D 9v [J * (J * / 1) 0 k * 2 ] 2 0 D 9v [J 9 (J 9 / 1) 0 k 9 ]
Å DG / DB[J * (J * / 1) 0 k * 2 ] 0 DD[J * (J * / 1) 0 k * 2 ] 2 ,
where nI is the transition wave number, DG Å G *v 0 G 9v , DB Å B *v 0 B 9v , and DD Å D *v 0 D 9v . The coefficient optimization is done by the linear least-squares method. The constrained lower state rotational parameters are taken from Ref. (3). The lower state assignments of this study were
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
[2]
2 2
mspa
OVERTONE SPECTRUM OF BROMOACETYLENE
195
FIG. 2. The high-resolution photoacoustic spectrum of the (4n1 / n5 )-band system of monobromoacetylene. The spectral resolution is about 0.03 cm01 and the sample pressure has been about 15 mbar.
confirmed by the ground-state combination difference method (9). We have been able to assign practically all of the strong and medium-strong lines in the spectrum. The blended and
perturbed lines were excluded from the fits. The results of the rotational analyses are given in Tables 1 and 2. The uncertainties of the upper state parameters given in these tables were obtained by assuming that the lower state param-
FIG. 3. The high-resolution photoacoustic spectrum of the (4n1 / n3 )-band system of monobromoacetylene. The spectral resolution is about 0.03 cm01 and the sample pressure has been about 15 mbar.
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
mspa
196
VAITTINEN ET AL.
TABLE 1 Rotational Analysis of HCC 79Br
eters do not possess any uncertainties. Thus, they reflect the uncertainties of the differences between upper and lower state parameters. The standard deviations of some fits are unusually large as a result of perturbations, which appear locally (so-called crossover perturbations) or for high J values (so-called global perturbations). Unfortunately, due to the lack of data, it is impossible to sort out the unknown perturbers. For the vibrational analysis we have used standard vibration–rotation theory formulated in terms of rectilinear normal coordinates. The diagonal matrix elements of our model Hamiltonian take the usual form (9, 10) » vÉHvib /hcÉv … Å
∑ nI *r vr / ∑ x*rr (v 2r 0 vr ) r
/
r
∑ x*rr =vrvr = / ∑ g*tt (l 2t 0 vt ) [3] r õr =
/
t
bers nI r* are used instead of harmonic wavenumbers vr . x* rr , x* rr = , g* tt , and g* tt = are anharmonic parameters, which are functions of cubic and quartic force constants in the normal coordinate representation. vr is the standard vibrational quantum number, and lt (t Å 4 or 5) is the vibrational angular momentum quantum number associated with the doubly degenerate bending modes n4 and n5 . The summation indices r and r * span all five normal modes, whereas the indices t and t * span only the bending modes. The doubly degenerate modes are counted only once. The superscript star indicates that the Fermi resonance has been included explicitly in the model. The wavenumbers of the fundamental vibrations ( n1 É 3336 cm01 , n2 É 2091 cm01 , n3 É 620 cm01 , n4 É 617 cm01 , and n5 É 291 cm01 ) are such that they give rise to several resonances. The off-diagonal Fermi resonance matrix elements included are (4) l
∑ g*tt = ltlt = ,
l
Å k355[v3 (v5 / l5 / 2)(v5 0 l5 / 2)/8] 1 / 2 ,
tõt =
where v on the left-hand side denotes all of the vibrational quantum numbers, and fundamental vibrational wavenum-
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
[4]
the matrix elements due to the Darling–Dennison-type resonance are (11)
Copyright q 1998 by Academic Press
AID
l
» v1v2v3v 44v 55 ÉH/hcÉv1v2 (v3 0 1)v 44 (v5 / 2) l5 …
mspa
197
OVERTONE SPECTRUM OF BROMOACETYLENE
TABLE 2 Rotational Analysis of HCC 81Br
l
l
l
» v1v2v3v 44v 55 ÉH/hcÉ(v1 0 1) (v2 / 1)v3 (v4 / 2) l4v 55 … Å 14 K1244[v1 (v2 / 1)(v4 / l4 / 2)
[5]
1 (v4 0 l4 / 2)]
1/2
,
confirm that this limitation has an insignificant effect on the results. The differences DB between upper state ( Bv ) and ground state ( B0 ) rotational constants are obtained from the equation ( 4 )
and the off-diagonal vibrational l-resonance matrix elements are (10) l4 4
l5 5
» v1v2v3v v ÉH/hcÉv1v2v3v
( l40 2 ) 4
v
( l5/ 2 ) 5
DB Å B0 0 Bv Å 0
[6]
1 [(v5 / 1) 2 0 (l5 / 1) 2 ]} 1 / 2 ,
where k355 , K1244 , and r45 are parameters which describe the strength of these interactions. Only the states with the same symmetry and with the same polyad quantum number V Å 11v1 / 7v2 / 2v3 / 2v4 / v5
[7]
are coupled together in our model. Consequently, the Hamiltonian matrix is factorized to a large number of smaller matrices (4). For practical reasons, we have decided to restrict the sizes of the matrix blocks by including only the closest interacting states by limiting the maxima of the individual quantum numbers vr and lt (4). Test calculations
/
6t26$$$$82
iÅ1
r Å1
[8]
where ci is the eigenvector element attached to a specific vibrational state (a specific basis function), ar describes the vibrational dependence of the rotational constants of the fundamentals (9), and N is the number of interacting states (the size of the matrix block in question). The calculated values have been computed using the eigenvectors obtained by diagonalizing the resonance Hamiltonian matrices. The values for the parameters in Eqs. [3] – [8] are taken from Ref. (4). Tables 3 and 4 contain the results for the vibrational term values and rotational constants for both isotopic species. 5. DISCUSSION
Generally, the anharmonic model we have used to interpret the vibrational and rotational data yields trustworthy results. About half of the calculated vibrational origins are
Copyright q 1998 by Academic Press
JMS 7477
5
…
Å 14r45 {[(v4 / 1) 2 0 (l4 0 1) 2 ]
AID
N
∑ c 2i ∑ arvr ,
01-30-98 11:49:47
mspa
198
VAITTINEN ET AL.
TABLE 3 Vibrational Analysis of HCC 79Br
within two wavenumbers of the observed ones. Most of the rotational constants are also well reproduced. This applies particularly to the ‘‘bright’’ states such as É401 0 0 0 0 … after which the band systems are named. The larger differences between the model and the observations appear with the states with unusual quantum labels like É041 8 0 0 0 … . It may thus be argued that the resonances included in the model are not adequate to precisely reproduce the energies of these strongly mixed states. We believe, however, that the quantum labels are the most reasonable ones, because although the mixing ratios may be imperfectly computed, there are no other justifiable candidates in the neighbourhood of these states in the calculations. In a similar case of monofluoroacetylene, it was found out that diminutive changes in the parameters can cause substantial effects on the mixing of the states (12). The Darling–Dennison resonance term in K1244 appears to be sufficient to justify all except one of the observed vibration–rotation bands in the spectrum. The exception is the band at 11667.5 cm01 for HCC 79Br and at 11666.9 cm01 for HCC 81Br labelled as É043 2 0 2 0 … . In that case, it is possible to observe a Darling–Dennison resonance sequence É310 0 0 0 0 … r É220 2 0 0 0 … r É130 4 0 0 0 … r É040 6 0 0 0 … , which explains the vibrational quanta of the v1 and v2 excitations. Our model does not include any resonances
which would account for the energy transfer from the Darling–Dennison coupled group of states to the É043 2 0 2 0 … state. The relatively large intensity of the observed band, however, seems to hint that a new type of resonance may exist. Another aspect worth mentioning is that the sign of the Darling–Dennison constant K1244 depends on the chosen positive sense of the coordinates q1 and q2 (11). Therefore, the absolute signs of K1244 and k355 are not meaningful in our study. The relative signs of these parameters, in contrast, are important because both of them appear in off-diagonal matrix elements. The current study has reinforced the importance of the Darling–Dennison resonance in the intramolecular energy flow of HCCBr. The Fermi resonance seems to play no obvious role in the overtone region of this molecule. Analogous results have also been obtained in the case of iodoacetylene, HCCI (13). On the other hand, with fluoroacetylene, HCCF, several Fermi resonances are needed to explain the overtone spectrum (11, 12). Chloroacetylene, HCCCl, is an interesting example where the effects of anharmonic resonances are quite small in the first overtone band of the C– H stretch (14). However, the resonances reappear en masse in the third overtone region as demonstrated by the photoacoustic experiment (15). Unfortunately, that study does not
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$82
01-30-98 11:49:47
mspa
OVERTONE SPECTRUM OF BROMOACETYLENE
199
TABLE 4 Vibrational Analysis of HCC 81Br
include a vibrational analysis, which would account for the observed phenomena. ACKNOWLEDGMENTS The authors thank the DAAD/Academy of Finland and the Rector of the University of Helsinki for financial support. We are grateful to Mr. Robert Brotherus for the use of his visual spectrum analysis program.
REFERENCES 1. O. Vaittinen, L. Halonen, H. Bu¨rger, and O. Polanz, J. Mol. Spectrosc. 167, 55–70 (1994). 2. M. Halonen, J. Mol. Spectrosc. 167, 225–230 (1994). 3. O. Vaittinen, T. Lukka, L. Halonen, H. Bu¨rger, and O. Polanz, J. Mol. Spectrosc. 172, 503–519 (1995). 4. O. Vaittinen, Chem. Phys. Lett. 238, 319–326 (1995). 5. G. R. Hunt and M. K. Wilson, J. Chem. Phys. 34, 1301–1306 (1961).
6. X. Zhan, E. Kauppi, and L. Halonen, Rev. Sci. Instrum. 63, 5546–5550 (1992). 7. X. Zhan, Ann. Acad. Sci. Fenn. Ser. A 252, 1–38 (1993). 8. S. Gerstenkorn, J. Verges, and J. Chevillard, ‘‘Atlas du Spectre d’absorption de la molecule d’iode,’’ Laboratoire Aime´-Cotton, CNRS II, Orsay, 1982. 9. G. Herzberg, ‘‘Infrared and Raman Spectra of Polyatomic Molecules,’’ Van Nostrand, New York, 1945. 10. J. K. Holland, D. A. Newnham, I. M. Mills, and M. Herman, J. Mol. Spectrosc. 151, 346–368 (1992). 11. A. F. Borro, I. M. Mills, and E. Venuti, J. Chem. Phys. 102, 3938– 3944 (1995). 12. O. Vaittinen, M. Saarinen, L. Halonen, and I. M. Mills, J. Chem. Phys. 99, 3277–3287 (1993). 13. J. Lummila, O. Vaittinen, P. Jungner, L. Halonen, and A.-M. Tolonen, J. Mol. Spectrosc. 185, 296–303 (1997). 14. A. F. Borro, I. M. Mills, and A. Mose, Chem. Phys. 190, 363–371 (1995). 15. M. Saarinen, L. Halonen, and O. Polanz, Chem. Phys. Lett. 219, 181– 186 (1994).
Copyright q 1998 by Academic Press
AID
JMS 7477
/
6t26$$$$83
01-30-98 11:49:47
mspa