The bending vibrations in 12C2H2 : Global vibration-rotation analysis

Transcription

1 The bending vibrations in CH : Global vibration-rotation analysis Séverine Robert, Michel Herman, Jean Vander Auwera, Gianfranco Di Lonardo, Luciano Fusina, Ghislain Blanquet, Muriel Lepère, André Fayt To cite this version: Séverine Robert, Michel Herman, Jean Vander Auwera, Gianfranco Di Lonardo, Luciano Fusina, et al.. The bending vibrations in CH : Global vibration-rotation analysis., Taylor Francis, 00, 0 (0-0), pp.-. <0.00/00000>. <hal-000> HAL Id: hal Submitted on Sep 00 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 The bending vibrations in CH : Global vibration-rotation analysis Journal: Manuscript ID: TMPH R Manuscript Type: Full Paper Date Submitted by the Author: -Oct-00 Complete List of Authors: Robert, Séverine; Université libre de Bruxelles, Chimie quantique et Photophysique Herman, Michel; Université Libre de Bruxelles, Chimie quantique et Photophysique Vander Auwera, Jean; Université libre de Bruxelles, Chimie quantique et Photophysique di Lonardo, Gianfranco; Università di Bologna Fusina, Luciano; Università degli Studi di Bologna Blanquet, Ghislain; Facultés Universitaires Notre Dame de la Paix, Laboratoire de Spectroscopie Moléculaire Lepère, Muriel; Facultés Universitaires Notre Dame de la Paix, Laboratoire de Spectroscopie Moléculaire Fayt, André; Université catholique de Louvain Keywords: acetylene, bendings, global fit, high resolution spectroscopy, astrophysics

3 Page of The bending vibrations in C H : Global vibration-rotation analysis Revised version John Brown s special issue S. Robert *, M. Herman and J. Vander Auwera ** G. Di Lonardo and L. Fusina G. Blanquet and M. Lepère *** A. Fayt Service de Chimie quantique et Photophysique CP0/0 Université Libre de Bruxelles Av. Roosevelt, 0 B-00, Bruxelles Belgium Dipartimento di Chimica Fisica e Inorganica Università di Bologna Viale Risorgimento, I-0, Bologna Italy Laboratoire de Spectroscopie Moléculaire Facultés Universitaires Notre-Dame de la Paix B-000, Namur Belgium Laboratoire de Spectroscopie Moléculaire Université Catholique de Louvain Chemin du Cyclotron, B- Louvain-La-Neuve Belgium * FRIA researcher **Senior Research Associate with the Fonds National de la Recherche Scientifique (Belgium) *** Research Associate with the Fonds National de la Recherche Scientifique (Belgium) Number of pp.: Number of Figures: Number of Tables: All correspondence to be sent to Prof. M. Herman (mherman@ulb.ac.be)

4 Page of Abstract A total of vibration-rotation line positions providing accurate information on all known vibration-rotation states up to 000 cm in C H were gathered from the literature. Additional lines were assigned on new spectra. The full data set was simultaneously fitted using an appropriate Hamiltonian, with refined parameters. A dimensionless standard deviation equal to 0., accounting for % of the lines, was achieved. The vibrational transition dipole moment of the v = v = band observed in the far-infrared was estimated to be µ = 0. D with 0 % accuracy, from absolute intensity measurements for a few Q-branch lines.

5 Page of Introduction Since the pioneering contribution of Plíva (, ), a number of experimental and theoretical studies have concerned the bending vibrations in acetylene, C H (-). Of particular interest to the present investigation is the global modeling of the bending vibration-rotation levels in C H, first performed by Plíva (, ) who addressed the problem of l-type doubling associated to the two degenerate bending vibrations in this species, ν (transbending) and ν (cis-bending). This work was later extended by considering additional experimental data and/or terms in the Hamiltonian, by (, -, ) and also additional isotopologues of this molecule (-). In their contribution on C H, Kabbadj et al. () achieved a global vibration-rotation fit considering vibration-rotation lines from bands involving bending vibrational states up to v b, with b the bending vibrations, as well as the b v = vibrational state, with ν the CC stretch. We have since accessed to new pure bending vibrational transitions among the same states and to new vibration-rotation lines of previously assigned vibrational transitions, by refining the analysis of the Fourier transform spectra presented in (). Additional new bands also became available in the literature, at higher energy, either again connecting differently the states previously observed, or involving upper stretch (ν )-bend combination states not previously considered (). All these new bands add

6 Page of relevant information on the pure bend states of interest to the present investigation. There was therefore room for improving the global vibrationrotation fit on the bends, which we have performed using a dedicated package of computer programs. The Hamiltonian and the data set are presented in section and the results are detailed in section. This contribution is actually part of a much larger effort in the global analysis of the known vibration-rotation data of acetylene, up to the overtone range. The program package allows relative vibration-rotation line intensities to be predicted accounting for all terms in the energy Hamiltonian. We have used these facilities to estimate, in section, the induced dipole moment of the v = v = (named ν - ν ) band observed in the far-infrared (FIR), of interest to astrophysical detection.. Global Hamiltonian and data set The previous work on the global fitting of the vibration-rotation lines in the bending range of acetylene was achieved using the Hamiltonian defined in (, ) and a computer program written at ULB and refined in Bologna. A different computer program was used in the present work, developed at Louvain-La-Neuve and dedicated to both energy and intensity

7 Page of treatments (0-). The form of the Hamiltonian is different from the one previously used and presented in table. The initial data set we considered was identical to the one in (, ), resulting from the analysis of FTIR spectra recorded in Ottawa at the Herzberg Institute of Astrophysics. Vibration-rotation lines involving the CC strech, ν, were observed in the same range as highly excited pure bending vibrations, and were also considered at that time. Information on the related experimental conditions can be found in (, ). The analysis in the spectral region around 00 cm - was later extended in Bologna. New pure bending vibrational transitions as well as additional vibration-rotation lines in vibrational transitions previously assigned could be identified in a spectrum recorded with longer path length. This spectrum was recorded in Ottawa with a modified Bomem DA.00 FT interferometer, in the 0 0 cm range, at K, with an absorption path length of 0 m and a sample pressure of 0 Pa. The instrument was equipped with a Cu-Ge detector cooled to liquid He temperature and the achieved resolution was 0.00 cm. Table lists this new information. The related line list can be obtained from the Bologna authors. The data set presently considered was thus extended to include all these additional lines. Besides, vibration-rotation lines reported in () from a spectrum recorded in a higher energy range compared to the one in () were also added. They mainly concern hot bands towards higher excited bend states as well towards stretch (ν )-bend combination states.

8 Page of The full data set amounts to vibration-rotation lines, with from (), from assignments performed on the new spectra and from (). All related vibrational transitions are identified in figure, which updates figure of (). They are detailed in table, which summarizes the full data set used in the global fit.. Results A weighted least-squares fitting procedure was adopted, accounting for the experimental accuracy, estimated to be 0 cm for the data from () and for the new data and 0 cm for those from (). As usual in such procedures, the selection of higher order terms in the model is delicate given the high correlation between some of the parameters. We included only those higher order constants which seemed most efficient in reducing the standard deviation of the fit, while keeping a reasonable value compared to the corresponding ones of lower order in the development. The fitting procedure led to a set of parameters listed in table, with dimensionless standard deviation of 0. on fitted lines out of assigned transitions. lines presenting anomalously large (obs. calc.) values were excluded from the fit. They correspond to very weak and/or

9 Page of blended lines. As already mentioned in (), a few rejected transitions probably suggest local Coriolis perturbation effects, which have not been included in the model Hamiltonian. It is interesting to point out that the bending Darling-Dennison anharmonic resonance /, discussed e.g. in (), had to be included in the Hamiltonian defined in table in order to achieve the presently obtained standard deviation. It could not be previously determined in (). This resonance is known to significantly contribute in higher excited ranges of the vibrational ladder, where the related interacting states are closer in energy. The accuracy of the present data combined with the inclusion of higher excited bend states in the procedure, compared to the data set in (), explains the need for introducing the / resonance. The related parameter, K / =. cm, is very close the value of. cm determined in (). Compared to previous results (), more lines are fitted in the present work ( against 0), as well as more bands. The R.M.S. error on the lines previously considered is actually much better (0.000 cm compared to cm ) while the number of determined parameters is similar ( against 0 previously reported). In fact, of the additional parameters (x, x, γ, γ ) arise from the inclusion of the two stretch-bend states (v +v and v +v ),

10 Page of not previously considered. All corresponding parameters in the Hamiltonian have very close values in both sets of results. The resulting vibrational term values are provided in table, for each k- substate. They correspond to calculated rotationless energies, G C defined as G = G 0 v ' C with k = l + l. The ν - ν band B k v ' D k () v ' The ν - ν FIR band was previously reported in () and the observed vibration-rotation transitions were included in the present global fit. This band is of interest for the detection of acetylene in the FIR range, with obvious astrophysical applications (). The line positions, already included in the Cologne Database (, ), see are not repeated here. As values for absolute intensities would obviously help in this context we decided to estimate the related transition dipole moment, µ, using existing information. The absolute intensity of Q-branch lines observed in the range.. cm was measured by fitting a synthetic spectrum to

11 Page of the observed transmittance spectrum presented in figure of (). This spectrum was recorded at K, with an absorption path length of m and a sample pressure of 00 Pa. The synthetic spectrum was computed by application of Beer's law, using a Voigt function to model the observed line profiles and including instrumental distortion resulting from the finite maximum optical path difference achieved ( cm) and source aperture diameter of the interferometer (. mm). Figure shows the spectra observed and calculated at the end of the fit. From the measured absolute line intensities, we determined using usual methods () the value of the vibrational transition dipole moment of the ν ν band to be µ = 0. D. Its accuracy is not expected to be better than 0%.. Conclusions We have gathered all the accurate spectral information observed in the lower energy range of the infrared spectrum concerning the bending vibration-rotation states on C H reported in the literature. During the present investigation, new bands and additional vibration-rotation lines in some known bands were assigned on new spectra recorded at longer path length and included in the data set. A total of vibration-rotation lines were successfully fitted to a set of parameters of a global Hamiltonian. They were determined with previously unmatched precision, with a

12 Page 0 of dimensionless standard deviation of the fit equal to 0.. They were used to simulate, among others, the ν -ν FIR band, of astrophysical relevance. The comparison with the observed transmittance spectrum of this band allowed the related transition dipole moment to be determined. Acknowledgments The authors are very pleased to contribute to this special issue dedicated to John Brown. They thank Dr. J.W.C. Johns (Ottawa) for the recording of FTIR spectra, Dr. V. Perevalov (Tomsk) for providing a list of wavenumbers and Mrs Progneaux for some calculations. This work was sponsored, in Italy, by the University of Bologna and MIUR (PRIN «Dinamiche molecolari») and, in both Namur and Brussels, by the Fonds National de la Recherche Scientifique (FNRS, contracts FRFC and IISN) and, at ULB specifically, by the «Action de Recherches Concertées de la Communauté française de Belgique». It is also performed within the LEA HiRes collaboration between ULB, UCL and FUNDP, and was earlier supported by a bilateral scientific collaboration between the «Communauté française de Belgique» and FNRS (Belgium) and Italy. ULB acknowledges financial support from the European Union (Quantitative Spectroscopy for Atmospheric and Astrophysical Research, QUASAAR, contract MRTN-CT-00-0). 0

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19 Page of Figure Legends Figure. Vibrational states and transitions in C H taken into account in the present investigation, with the following labels: ( ) from (); (- - -) presently newly assigned; (. ) from (). The states are identified with the values of the bend quantum numbers (v v ) or with ν +ν / for the stretchbed combination states. Figure. Spectrum of the ν ν band of C H near the band origin, recorded at the National Research Council Canada (Ottawa) and presented in Fig. of () (T = K, l = m, P = 00 Pa). In the upper part of the figure, the solid line and the symbols represent respectively the spectra observed and calculated at the end of the fit. The lower part of the figure shows the corresponding residuals.

20 Page of Table Captions Table. Terms in the Hamiltonian used to perform the global vibration-rotation fit in C H. a Table. Bands of C H newly measured. Table. Summary of the full data set used in the global vibrationrotation fit of the bending states in C H. Table. Vibration-rotation parameters in C H (cm ). a Table. Calculated vibrational term values G C (cm ) of all v,l sublevels in C H lower than 0 cm.

21 Page of Table G = % ω v + x v v + x l l + y v v v + y v l l + z v v v v + z v v l l + z l l l l v i i ij i j lblb ' b b ' ijm i j m ilblb ' i b b' ijm n i j m n ijlblb ' i j b b ' lblb ' lb '' lb ''' b b ' b '' b''' i=, i j b b ' =, i j m i, b b ' i j m n i j, b b ' b b' b '' b ''' ( )( )( )( ) % m ± = ± m + m ± + l, l H l, l r v l v l v l v l () i ( i δi δi ) ij ( i δi δi )( j δ j δ j ) l ( )( ) ( ) blb ' b b J () r = r + r v + r v v + r l ± l ± + r J J + 0,, ' i i j b b ' r = r + r ( v δ δ ) () 0 J J J, i i i i i ( ) ( ) ( ) 0 0 rv = v + v + v + + v + E G B J J k D J J k H J J k () B = B α v + γ v v + γ l l + ε v v v + ε v l l () v 0 i i ii ' i i ' lblb ' b b ' ii ' i" i i ' i" ilblb ' i b b ' i i i ' b b ' i i ' i " i, b b ' () D = D + β v + β v v + β l l 0 v 0 i i ii ' i i ' lblb ' b b ' i i i ' b b ' H H () v = 0 ( )( ) l b H lb ± = q b vb m lb vb ± lb + F± ( J, k ) F± ( J, k ± ) () 0 qb = qb + qbi ( vi δib ) + qbj J ( J + ) (0) i, ( ) () q = q + q v δ 0 bj bj bj i i ib i ( )( )( )( )( )( ) l b, lb ' H lb ±, l m b ' = q ' bbb vb lb vb ± lb + vb lb vb ± lb + vb ' ± lb ' vb ' lb ' + F± ( J, k) F± ( J, k ± ) m m m () l ( )( )( )( ) b H lb ± = ubb vb m lb vb ± lb + vb m lb vb ± lb + F± ( J, k ) F± ( J, k ± ) F± ( J, k ± ) F± ( J, k ± ) () ()

22 Page 0 of ( )( )( )( ) ( ) ( ) ( ) ( ) l blb ' H lb ±, lb ' ± = ubb ' vb mlb vb ± lb + vb ' m lb ' vb ' ± lb ' + F± J, k F± J, k ± F± J, k ± F± J, k ± () (, ) = ( + ) ( ± ) F ± J k J J k k () v % + = [ ], v, l, l H v, v, l, l K / ( v l )( v l )( v l )( v l ) () i ( i δ ) i J ( ) () K = K + K v + K J J + k 0 / / /, /, i [ ] ' v, v, l, l H% v +, v, l ±, l m = K / ( v ± l + )( v ± l + )( v ± l )( v ± l ) () i ( i δ ) i J ( ) () K = K + K v + K J J + k ' '0 ' ' / / /, /, i a In the terms, i, j, m, n refer to the five modes of vibration, b and b specifically to the bending ones and k = l + l. The notation δ ij is the usual notation for the delta of Kronecker function. 0

23 Page of Table Transition Symmetry ν a C ν ν ν ν + ν ν + ν ν + Σ g g Π g Π g Π g Φ g II Π u II Π u I Π u I Π u Φ u a The band center (in cm ) is ν C = G 0 v ' b Assigned Transitions Π u 0. b P e-e (-); R e-e (-); Q e-f (-) Π u. b P e-e (-); R e-e (-); Q e-f (-) + u P f-f (-); R f-f (-); Q f-e (-) Σ. P e-e (-); R e-e (-); Q f-e (-) Σ.0 b P f-f (-); R f-f (0-); Q e-f (-) u u. b P e-e (-); R e-e (-); Q e-f (-) P f-f (-); R f-f (-); Q f-e (-) u 0. b P e-e (-); R e-e (-); Q e-f (-) + Σ g 0. Q f-e (-) P f-f (-); R f-f (-); Q f-e (-0) g.0 P e-e (-); R e-e (-); Q e-f (-) P f-f (-); R f-f (-); Q f-e (-) + Σ g 0.0 P e-e (-); R e-e (0-); Q f-e (-) g 0. P e-e (-); R e-e (-); Q e-f (-) P f-f (-0); R f-f (-); Q f-e (-) g 0. P e-e (-); R e-e (-); Q e-f (-0) Bv ' k P f-f (-); R f-f (-); Q f-e (-) Dv ' k ( v G 0 " Bv " k Dv " k ) Band previously observed in Ref. (). The range of the J values has been extended.

24 Table Upper state Lower state Lines Jmax Ref. v v, l l e/f v v, l l e/f 0, 0 e 0 0, 0 0e 0 a 0, 0 e 0, 0e a 0, 0 e 0, 0f 0 0 a 0, 0 f 0, 0e a 0, 0 f 0, 0f a 0, 0 f 0 0, 0 0e 0 a 0, 0 0e 0, 0 e b 0, 0 0e 0, 0 f 0 b 0, 0e 0, 0 e b 0, 0e 0, 0 f b 0, 0f 0, 0 f b 0, 0f 0, 0 e b, -e 0, 0e a, -e 0, 0f a, -e 0, 0 0e a, -e 0 0, 0 0e a, -f 0, 0f a, -f 0, 0e a, e 0, 0e 0 a, e 0, 0f a, e 0, 0e a, e 0 0, 0 0e 0 a, f 0, 0f a, f 0, 0e a, f 0, 0f a 0, 0 0e 0, 0 e a 0, 0 0e 0, 0 f a 0, 0 0e, -e a 0, 0 e 0, 0 e 0 a 0, 0 e 0, 0 f a 0, 0 e, e a 0, 0 f 0, 0 f 0 a 0, 0 f, f 0 a 0, 0 f 0, 0 e a 0, 0e, -f b 0, 0e, -e b 0, 0e, e b 0, 0e, f b 0, 0f, -f 0 b 0, 0f, -e b 0, 0f, e b 0, 0f, f b 0, 0e, e b 0, 0e, f b 0, 0f, e 0 b 0, 0f, f b, -e 0, 0e 0 a, -e 0, 0e a, -e 0, 0f 0 0 a, -e 0, 0 e b, -e 0, 0 f b, -f 0, 0 0e b, -f 0, 0f a, -f 0, 0 e b, -f 0, 0 f b, -f 0, 0 0e a Page of 0

25 Page of , -f 0, 0e a, -f 0, 0f 0 a, 0 e 0, 0 0e a, 0 e 0, 0f a, 0 e 0, 0e a, 0 e 0, 0 0e b, 0 e 0, 0 e b, 0 e 0, 0 f b, 0 f 0, 0f a, 0 f 0, 0 0e b, 0 f 0, 0 f b, 0 f 0, 0 e b, e 0, 0e a, e 0, 0f 0 a, e 0, 0 e b, e 0, 0 f 0 b, f 0, 0 f b, f 0, 0f a, f 0, 0e a, f 0, 0f a, f 0, 0 e 0 b, 0 e 0 0, 0 0e c, 0 f 0 0, 0 0e c, -e 0 0, 0 0e c, -f 0 0, 0 0e c, 0e, -e a, 0e 0, 0 e a, 0f, -e a, 0f 0, 0 f a,- e 0, 0 e a,- e, -f 0 a,- f, -f 0 a,- f 0, 0 f a, e, e a, e, f a, f, e a, f, f 0 a 0, 0 e 0, 0 0e 0 a 0, 0 e 0, 0 e a 0, 0 e 0, 0 f a 0, 0 f 0, 0 0e a 0, 0 f 0, 0 e a 0, 0 f 0, 0 f a 0, 0 e 0, 0 e a 0, 0 f 0, 0 f a 0, 0 e 0 0, 0 0e c 0, 0 f 0 0, 0 0e c, -e 0, 0 0e 0 a, -e 0, 0e a, -f 0, 0f a, -e 0, 0e c, -f 0, 0f c, e 0, 0e c, f 0, 0f c, -e, -e a, -f, -f a, -f, f a, 0e, e a, 0f, f 0 a, 0f, -f a, -e 0, 0 e c, -e 0, 0 f c, -f 0, 0 f c

26 , 0f 0, 0 f c, -e 0, 0 0e a, e 0, 0 e a, f 0, 0 f a, -e 0, 0e c, -e 0, 0f c, -f 0, 0f c, -f 0, 0e c, e 0, 0e c, f 0, 0e c, f 0, 0f c, e 0, 0f c,- e 0, 0e c,- f 0, 0e c,- f 0, 0f c,- e 0, 0f 0 c 0, 0 0e 0, 0 e c 0, 0 0e 0, 0 f c 0, 0 e 0, 0 e c 0, 0 f 0, 0 e c 0, 0 f 0, 0 f c 0, 0 e 0, 0 f c Upper state Lower state Lines Jmax Ref. v v v v v, l l e/f v v v v v, l l e/f , 0 0e , 0 e a , 0 0e , 0 f a 0 0 0, 0e , 0 e c 0 0 0, 0f , 0 f c 0 0 0, 0 e , 0e 0 c 0 0 0, 0 f , 0f 0 c All labels are identified in the text. Ref. a is Kabbadj et al (); Ref. b is the present work; Ref. c is Jacquemart et al. (). Page of 0

27 Page of Table ν.0() omega 0.0() omega.() x -.0() x -.() x.() x -.() x -.() xll 0.(0) xll.0() xll.() y 0.0(0) y 0.0() y 0.0() y 0.0(0) yll -0.00() yll 0.0() yll 0.00() yll -0.00(0) yll 0.0() yll -0.00() z -0.00() z -0.00() zll 0.00() zll 0.00(0) zl () B0.() E-0 alpha.0() E-0 alpha -.() E-0 alpha -.() E-0 gam -.() E-0 gam -.() E-0 gam -0.() E-0 gam -.0() E-0 gam.() E-0 gll -.() E-0 gll -.() E-0 gll -0.() E-0 eps 0.0() E-0 eps 0.() E-0 eps -0.() E-0 epsl 0.00() E-0 epsl 0.0(0) E-0 epsl 0.() E-0 epsl -0.() E-0 epsl -0.() E-0 epsl -0.() E-0 D0.() E-0 beta.() E-0 beta.() E-0 H0.(0) E- q -.00(0) E-0 qv -0.0() E-0 qv 0.00() E-0 qv -0.0(0) E-0 qj.() E-0 qjv 0.() E-0 q -.() E-0

28 qv 0.00() E-0 qv -0.(0) E-0 qv -0.00() E-0 qv -0.() E-0 qj.0() E-0 qjv 0.() E-0 q 0.() E-0 q 0.() E-0 u -0.0() E-0 u -0.() E-0 u -0.0() E-0 r -.() rv 0.0() rv -0.0() rv -.() E-0 rv.() E-0 rl -.0() E-0 rj.() E-0 rjv -0.0() E-0 rjv 0.() E-0 k -.() kv 0.() kv 0.() kj.() E-0 kp.() kpv 0.() kpj -.() E-0 a The standard deviation (σ) is indicated in parentheses, in the units of the last quoted digit. The parameters are labeled in agreement with the model defined in table. Page of 0

29 Page of Table v v v v v, l l e/f k G C (cm ) , 0 0 e , 0 * , 0 * , 0 * , 0 0 e , - e , - f , * , 0 0 e , 0 * , 0 * , 0 * , - * , 0 * , * , 0 0 e , 0 * , - * , * , 0 * , 0 * , 0 * , 0 * , 0 0 e , - * , - e , 0 * , - f , * , * , - e , - f , 0 * , 0 0 e , 0 * , * , 0 * , - e , * , - f , - * , * , 0 0 e , 0 * , 0 * , 0 * , 0 * , 0 * , - * , - * , 0 * , * , * , - * , 0 * 0.

30 Page of , - *.0 0 0, - e , - f , * , 0 * , * , * , 0 * , - * , * , 0 * , 0 * , * , - * , - * , 0 * , * , * , 0 * , 0 * , 0 *.0 * Identical value for e and f components

31 Page of Figure E (cm - ) (0) (0) I Σ u u II u Σ Φ u Π u g Σ + g + u IΠ g (0) IIΠ g Π g Φ g () (v v ) (00) Φ g () () Π Π u g u II g Σ IIΣ Σ Σ u + u + g g + Σg () g + Σg () (0) I u Σ II u Π u + Π u g Φ u () IΠ u IIΠ u (0) (0) Σ + g g ν + ν ν + ν Σ + g ν (0)

32 Page 0 of Figure.0 0. O C ( 00) Transmittance Wavenumber (cm ) 0