The vibrational energy levels in acetylene. III. [sup 12]C[sub 2]D[sub 2]

The vibrational energy levels in acetylene. III. 12C2D2

M. Herman,a) M. I. El Idrissi, and A. Pisarchikb)

Laboratoire de Chimie Physique CP160/09, Universite´ Libre de Bruxelles, Ave. Roosevelt, 50, 1050-B,Belgium

A. Campargue, A.-C. Gaillot, and L. BiennierLaboratoire de Spectrome´trie Physique (UMR 5588),c) UniversiteJoseph Fourier de Grenoble, B.P. 87,38042 Saint-Martin d’He`res Cedex, France

G. Di Lonardo and L. FusinaDipartimento di Chimica Fisica e Inorganica, Universita` di Bologna, Viale Risorgimento, 4, I-40136,Bologna, Italy

~Received 16 July 1997; accepted 21 August 1997!

We have performed the rovibrational analysis of the absorption spectrum of12C2D2 between 5150and 8000 cm21, recorded by Fourier transform absorption spectroscopy, and between 12 800 and16 600 cm21, recorded by intracavity laser absorption spectroscopy. Respectively 10 and 9 bandsare reported for the first time in each range. Improved or new rovibrational parameters wereobtained for 34 vibrational levels altogether. The vibrational energies we obtained, together withthose reported in the literature, were taken into account to model the vibrational energy pattern in12C2D2(X

1Sg1). The analysis was performed in successive steps, inferring each time suitable

parameters. The 44/55, 11/33, 12/33, and 1/244 quartic order anharmonic resonances wereintroduced during the procedure. They altogether define vibrational clusters which are characterizedby only two dynamical constants of motion,Ns5V11V21V3 andk5 l 41 l 5 . © 1998 AmericanInstitute of Physics.@S0021-9606~97!03044-4#

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I. INTRODUCTION

Acetylene isotopomers altogether have providedground for the study of the vibrational energy pattern inpolyatomic molecule within the same electronic state, uphigh excitation energy.1–3 The12C2H2 and12C2HD moleculeswere the most systematically studied species in this contThe main isotopomer has stimulated many experimentalvestigations which provide extensive coverage of the sptrum up to high excitation energy, using in particular toptoacoustic4,5 ~OA! technique, intracavity laser absorptiospectroscopy6 ~ICLAS!, stimulated emission and laser induced resolved fluorescence spectroscopies.7 Theoreticalmodels were developed, based in particular on the validitnew quantum numbers associated to the multiresonant vtional structure,8–10 including the rotation-vibrationinteractions.11 These studies also highlighted, among othfeatures, the role of the bending vibrations on bothspectroscopy12 and the intramolecular dynamics.13,14 In thecase of12C2HD, the absorption spectrum was also expementally investigated over a broad range,4,5,15 leading to in-formation on the dynamics and on the evolution of thesorption intensity among the overtones.15 A fair amount ofwork was also devoted to the rovibrational energy levels13C2H2, including the range of the lower overtone vibrationalthough most results are not published yet.16

The spectrum of dideuteroacetylene in its ground el

a!Electronic mail: [email protected]!Permanent address: B.I.Stepanov Institute of Physics; Belarus Academ

Sciences, Skaryna Ave., 70, 220072 Minsk, Belarus.c!Associated with the CNRS.

J. Chem. Phys. 108 (4), 22 January 1998 0021-9606/98/108(4)/1

Downloaded 17 Feb 2004 to 128.97.89.5. Redistribution subject to AIP

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tronic state,12C2D2(X1Sg

1), was studied in specific rangeThe first bending levels were investigated initially using mcrowave and far-infrared~FIR! data,17,18 then, indirectly, us-ing ultraviolet spectrographs.19 This latter contribution re-vealed for the first time in acetylene the importance ofbend–bend interaction of Darling–Dennison~DD! type.20

This work stimulated a much more complete investigationthe bending vibrations based on FIR Fourier transform~FT!data, by Huetet al.21 which considered in full details thecontribution of this anharmonic resonance. Many other sties were devoted to the Raman,22–24 infrared,25–37

near-infrared,38–41 and visible4 energy ranges of the rovibrational spectrum, yielding extensive sets of parameters, cacterizing the individual bands investigated. The informaton the stretch energy levels available at the time were csidered by Halonenet al.1 and by Herman and Pisarchik.40

Besides the more recent modelling proposed by Bramet al.,3 who considered all isotopomers simultaneously,complete set of vibrational parameters on12C2D2(X

1Sg1),

considering stretching and bending degrees of freedom,only produced in the early days by Talley and Nielsen,27 in1954, and Allenet al.,28 in 1956. A stretch–stretch DD interaction was commented on at the time28 and received laterstrong theoretical support.42

In the present investigation we first aimed at extendthe experimental information on the vibrational energy levof 12C2D2. We have reconsidered FT data we had reporearlier40 and analysed absorption bands in a range we hadpreviously considered, between 5150 and 8000 cm21. Wehave also applied, for the first time in C2D2, ICLAS ~Ref.43! and reinvestigated the higher energy range of the sp

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license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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1378 Herman et al.: Vibrational energy levels in acetylene. III

trum, previously studied using OA laser techniques.4 Oursecond motivation in this joint study was to produce paraeters allowing the vibrational energy levels in the molecto be modelled. All known experimental information o12C2D2 were therefore gathered to build an adequate Hamtonian. Interesting comparisons with the reference situain 12C2H2 can be anticipated.

II. EXPERIMENTS

A. FT data

Absorption spectra were recorded using a BruIFS120HR FT interferometer. A 1.7 m White-type multipaabsorption cell was used, set to 41 m total absorption pwith 11.6 kPa total pressure of a sample containing 912C2D2. The resolution was 0.025 cm21. The spectra werealready reported in a previous contribution,40 but not fullyanalyzed in the energy range presently considered, i.e.,tween 5150 and 8000 cm21. The reader is referred to thapaper by Herman and Pisarchik40 for further details on theexperimental conditions. We have calibrated the line wanumbers in the present investigation, using reference msurements on H2O ~Ref. 44! and C2H2 ~Ref. 45! present as animpurity in the sample. It resulted in decreasing0.0035 cm21 all measurements provided by the FT interncalibration procedure. We applied the same correction toband origins which we previously reported in Ref. 40 sinwe did not apply any calibration procedure at the time.

B. ICLAS data

The experimental apparatus for ICLAS has already bdescribed in detail earlier.43 Briefly, the ICLAS technique isbased on the high sensitivity of a broadband laser to intavity losses, e.g., absorption due to the sample containethe intracavity cell. The laser spectrum is dispersed by a hresolution grating spectrograph and recorded by a 1024 ptodiode array. The absorption lines appear superimposethe broadband spectrum of a dye laser pumped by an aion laser. The dye spectrum is time resolved and the timtg

spent from the beginning of the generation~the time whenthe gain in the cavity becomes larger than the losses! to thetime of observation of the spectrum gives directly tequivalent absorption pathlength

l eq5~ l /L !ctg , ~1!

wherec is the speed of light andl /L is the occupation ratioof the cavity, i.e., the ratio of the cell length to the opticlength of the laser cavity~l /L50.55 in this recording!. In thecurrent experiments, we used generation timestg between 95and 200ms leading to equivalent pathlength ranging betweof 15.7 and 33 km.

The intracavity sample cell was filled with dideuteroacetylene12C2D2 ~Advanced Research in Chemistry 99purity! at pressures varying from 18.3 to 30 kPa. Dye sotions of Styryl 8, Pyridine 2, DCM, and Rhodamine 59were used to explore the spectrum between 12 80016 600 cm21. We focused our experiments on speci

J. Chem. Phys., Vol. 108,


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ranges selected on the basis of previous observations4 and ofpredictions based on known Dunham coefficients.40 In someranges, it was necessary to fill the laser cavity with drytrogen or argon in order to remove the relatively strongmospheric absorption, due to H2O and O2, obscuring theC2D2 spectrum. A new, improved procedure is usedGrenoble for the wavenumber calibration. The spectrumrecorded with an intracavity etalon whose fringes provideinternal calibration, for each elementary range of typica15 cm21 corresponding to one grating position in the spetrograph. Two reference lines provide the absolute calibtion. We used for this purpose either atmospheric lineswater or oxygen46 or an extracavity iodine cell.47 In one spe-cific range (13 160– 13 210 cm21), the line positions ofstronger rovibrational lines of12C2D2 previously recorded aBrussels,39 were used to calibrate weaker lines only observin the ICLAS spectrum. The precision of the ICLAS mesurements is believed to be better than 0.01 cm21, aschecked from ground state combination differences. Tagreement between the rotational transition wavenumbgiven by Hall4 is generally satisfactory, except for the banat 15 685 cm21 for which discrepancies as large a0.17 cm21 are noticed.

12C2HD was detected as an impurity in the sample. Twrelated absorption bands already reported in the literatur4,15

were observed, at 15 282 and 15 697 cm21. They are strongrelative to the nearby C2D2 bands, despite the much lowerelative abundance of C2HD in the sample. This is to beattributed to the relative strength of the CH and CD tyvibrational excitations. It is interesting to point out that thmeasured wavenumbers for these two bands on the preICLAS spectra agree with literature measurements repoby Herman and co-workers15 but, again not with those oHall.4 This calibration problem for C2HD occurs in the sameenergy range as the one just mentioned for C2D2.

C. Status of the experimental observations

We observed 23 bands including 5 hot bands inrange 5150– 8000 cm21, on the FT spectrum. Seven of thewere already present in the literature,40 while 10 of the re-maining bands, including 2 hot bands, were not previoureported. Most of the other bands were only reported inearly literature.27,28 In the range probed by ICLAS12 800– 16 600 cm21, we observed 14 cold bands and 4 hbands, 9 of them being reported for the first time. The othinclude all bands previously reported by Hall,4 but the oneoutside of the range recorded here, at 17 694 cm21.

All the bands we have observed are listed in Table11

which also gathers all the information available in the liteture on the vibrational bands in12C2D2. The informationbelieved to be the most reliable is printed first, for each baIt includes the band origin (n0), the band type, the experimental technique and the literature reference. All othererature investigations mentioning the band are listed in ecase, but for the very early works. We already used6 thispresentation for12C2H2. The bands specifically investigatein the present work are highlighted in bold character. T

No. 4, 22 January 1998


1379Herman et al.: Vibrational energy levels in acetylene. III

TABLE I. Vibrational bands origins~n0 in cm21! determined for12C2D2(X1Sg

1) together with those reported in the literature.

n0 Band type Tech.a Ref.b n0 Band type Tech.a Ref.b

16.676 Su1 –Sg

1 FTS huet9117.282 Su

1 –Dg FTS huet9123.558 Du–Sg

1 FTS huet9124.164 Du–Dg FTS huet9126.764 Dg–Du FTS huet9127.105 Pu–Pg FTS huet91

MIC laff7729.371 Sg

1 –Su1 FTS huet91

486.420 Dg–Pu FTS huet91487.026 Sg

1 –Pu FTS huet91510.628 Pg–Sg

1 RAM kost80RAM fast72

527.085 II Pu–Sg1 FTS huet91

527.690 II Pu–Dg FTS huet91528.550 Pu–Dg FTS huet91530.807 Su

1 –Pg FTS huet91FTS huha79

SPEC bald72SPEC tall54

532.826 Pu–Sg1 FTS huet91

532.86 Dg–Pu SPEC tall54533.073 Sg

1 –Pu FTS huet91FTS huha79

SPEC bald72536.765 IPu–Sg

1 FTS huet91536.918 Fu–Dg FTS huet91

FTS huha79537.348 Dg–Pu FTS huet91

FTS huha79SPEC bald72

537.370 IPu–Dg FTS huet91537.549 Fu–Dg FTS huet91537.689 Du–Pg FTS huet91

FTS huha79SPEC bald72

537.786 Pu–Sg1 FTS huet91

FTS huha79SPEC bald72SPEC over55SPEC tall54

537.982 Su2 –Pg FTS huet91

FTS huha791036.171 Pg–Pu SPEC hurl71

SPEC gher711041.247 Pu–Pg SPEC hurl71

SPEC gher711041.495 Su

1 –Sg1 SPEC hurl71

SPEC gher71SPEC palm69SPEC over55SPEC tall54

1226.9 Sg1 –Pu SPEC tall54

1595.0 Dg–Pu SPEC tall541599.0 Sg

1 –Pu SPEC tall541603.692 Pu–Sg

1 SPEC hurl71SPEC gher71SPEC tall54

1764.796 Sg1 –Sg

1 RAM kost80RAM fast72

1919.93 Pu–Dg SPEC tidw621928.563 Su

1 –Pg SPEC hurl71SPEC gher71SPEC tidw62SPEC alle56SPEC over55

SPEC tall542152.07 Pu–Dg SPEC tidw622152.212 Pg–Du SPEC hurl71

SPEC gher68b2153.7 ••• SPEC tall542159.1 ••• SPEC tall542159.639 Pg–Su

1 SPEC hurl71SPEC gher68bSPEC tidw62

2163.906 Pu–Sg1 SPEC hurl71

SPEC gher68bSPEC tidw62

2167.43 Sg1 –Pu SPEC hurl71

SPEC gher68bSPEC tidw62SPEC alle56SPEC over55SPEC tall54

2279.7 ••• SPEC tall542293.28 Su

1 –Pg DL alan87SPEC tall54

2300.04 Du–Pg DL alan872300.37 Su

1 –Pg DL alan872300.91 Sg

1 –Pu DL alan872304.23 Pu–Sg

1 DL alan87SPEC tall54

2305.35 Dg–Pu DL alan87SPEC tall54

2425.368 ••• SPEC gher682425.44 ••• SPEC tidw622427.924 Sg

1 –Su1 SPEC gher68

2427.988 Du–Dg SPEC gher68SPEC tidw62

2428.135 Su1 –Sg

1 SPEC hurl71SPEC gher68SPEC tidw62

2428.762 Du–Dg SPEC hurl71SPEC gher68

2428.862 Su1 –Sg

1 SPEC hurl71SPEC gher68

2429.011 Dg–Du SPEC hurl71SPEC gher68

2433.639 Pu–Pg SPEC hurl71SPEC gher71SPEC gher68SPEC tidw62SPEC alle56SPEC over55

2434.079 Pg–Pu SPEC hurl71SPEC gher71SPEC gher68SPEC tidw62

2439.244 Su1 –Sg

1 SPEC hurl71SPEC gher68SPEC tidw62SPEC alle56SPEC over55SPEC tall54

2658.5 Pu–Sg1 SPEC tall54

2662.77 Pg–Pu SPEC tidw622674.21 ••• SPEC tidw622705.160 Sg

1 –Sg1 RAM kost80

RAM fast722931.912 Sg

1 –Pu SPEC hurl71SPEC gher68b

J. Chem. Phys., Vol. 108, No. 4, 22 January 1998

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TABLE I. ~Continued.!


SPEC tall542938.708 Dg–Pu SPEC hurl71

SPEC gher68bSPEC tidw62

2938.786 Fu–Dg SPEC gher68bSPEC tidw62


SPEC gher68b2941.512 Du–Pg SPEC hurl71

SPEC gher68bSPEC tidw62SPEC tall54

2941.662 Su1 –Pg SPEC hurl71

SPEC gher68bSPEC tidw62SPEC tall54


SPEC gher68bSPEC tidw62SPEC alle56SPEC over55SPEC tall54

3219.363 Fu–Dg SPEC gher68b3219.765 Du–Pg SPEC hurl71

SPEC gher68b3221.596 Sg

1 –Pu SPEC hurl71SPEC gher68b

3226.139 Dg–Pu SPEC hurl71SPEC gher68bSPEC tidw62



SPEC gher71SPEC gher68bSPEC tidw62SPEC alle56SPEC tall54

4181.256 Pu–Pg SPEC hurl71SPEC gher71

4187.065 Pg–Pu SPEC hurl71SPEC gher71

4190.638 Su1 –Sg

1 SPEC hurl71SPEC gher71SPEC alle56SPEC tall54

4283.9 Pu–Sg1 SPEC tall54


4684.65c Su1 –Pg SPEC tall54

4688.05c Du–Pg SPEC tall544692.34 Pu–Sg

1 SPEC tall544848.67 Sg

1 –Pu SPEC tall545076.121 Pu–Pg SPEC hurl71

SPEC gher715083.812 Pg–Pu SPEC hurl71

SPEC gher71SPEC alle56

5097.195 Su1 –Sg

1 SPEC hurl71SPEC gher71SPEC alle56SPEC tall54

5196.241 Du–Sg1 FTS herm97

5197.799 Su1–Sg

1 FTS herm97SPEC alle56

5376.533 Pu–Sg1 FTS herm97

5466.740 Su1–Sg

1 FTS herm97


SPEC tall545907.618 Pu–Sg

1 FTS herm97SPEC alle56SPEC tall54


SPEC tall545969.332 Pu–Sg

1 FTS herm97SPEC tall54

6079.791 Du–Sg1 FTS herm97

6080.672 Su1–Sg

1 FTS herm976381.287 Su

1–Sg1 FTS herm97

6803.024 Pu–Pg FTS herm976816.285 Pg–Pu FTS herm976828.141 Su

1–Sg1 FTS herm97

SPEC alle56SPEC tall54

6933.483 Su1–Sg

1 FTS herm977212.616 Pu–Pg FTS herm947230.036 Su

1 –Sg1 FTS herm94


7697.178 Pu–Pg FTS herm947712.466 Pg–Pu FTS herm947734.003 Su

1 –Sg1 FTS herm94

SPEC alle56SPEC tall54

7805.518 Su1 –Sg

1 FTS herm947979.210 Pu–Sg

1 FTS herm948207.861 Pu–Sg

1 FTS herm948550.142 Su

1 –Sg1 FTS herm94

SPEC saks528931.932 Pu–Pg FTS herm948938.485 Pg–Pu FTS herm948952.887 Su

1 –Sg1 FTS herm94

SPEC saks529444.434 Su

1 –Sg1 FTS herm94

LS sini929794.074 Su

1 –Sg1 FTS herm94

SPEC saks529963.76 Pu2(g

1 LS sini9210347.92 Su

1 –Sg1 SPEC saks52

11146.074 Su1 –Sg

1 FTS pisa93SPEC saks52

11455.843 Pu–Pg FTS pisa93SPEC saks52

11492.719 Su1 –Sg

1 FTS pisa93SPEC saks52

11875.045 Pu–Pg DL gros9511878.01 Pg–Pu DL gros9511905.369 Su

1 –Sg1 FTS pisa93

DL gros95OA hall84

SPEC saks5211965.697 Pu–Sg

1 DL gros9511980.004 Pu–Pg DL gros9512009.279 Pg–Pu DL gros9512036.950 Su

1 –Sg1 FTS pisa93

DL gros95SPEC saks52

12295.231 Pu–Pg DL gros9512312.595 Pg–Pu DL gros9512344.537 Su

1 –Sg1 FTS pisa93

DL gros95SPEC saks52

12934.436 Su1–Sg

1 ICLAS herm97



toacoustic


TABLE I. ~Continued.!


12962.052 Su1–Sg

1 ICLAS herm9713160.801 Pg–Pu ICLAS herm9713181.997 Su

1–Sg1 ICLAS herm97

FTS pisa93OA hall84

SPEC saks5213563.761 Pu–Pg ICLAS herm9713597.580 Su


OA hall8413717.309 Su


OA hall8413768.982 Su


13966.693 Pu–Pg ICLAS herm9713989.229 Pg–Pu ICLAS herm9714019.722 Su


OA hall8414377.736 Su


OA hall8414861.293 Su


14878.400 Su1–Sg

1 ICLAS herm9715280.615 Su


OA hall8415685.433 Su


OA hall8416041.042 Su


OA hall8416536.970 Su


OA hall8417694.21 Su

1 –Sg1 OA hall84

aDL, diode laser; FTS, Fourier transform spectroscopy; ICLAS, intracavity laser absorption spectroscopy; MIC, microwave spectroscopy; OA, oplaser absorption spectroscopy; RAM, Raman spectroscopy; SPEC, spectrograph; LS, laser spectroscopy.

balan87~Ref. 37!; alle56~Ref. 28!; bald72~Ref. 35!; fast72~Ref. 23!; gher68~Ref. 31!; gher68b~Ref. 32!; gher71~Ref. 34!; gros95~Ref. 41!; hall84 ~Ref.4!; herm94~Ref. 40!; herm97 this work; huet91~Ref. 21!; huha79~Ref. 36!; hurl71 ~Ref. 33!, kost80~Ref. 24!; laff77 ~Ref. 17!; over55~Ref. 26!; palm69~Ref. 30!; pisa93~Ref. 39!; saks52~Ref. 38!; tall54 ~Ref. 27!; tidw62 ~Ref. 29!; sini92 ~see note added in proof!.

cDGV5GV82GV9 .

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band origin mentioned in Table I is related to the vibrationenergies (GV) considered in the next section using the retion,

n05~GV82GV9 !1~BV9 l 922BV8 l 82!. ~2!

We sometimes had to adapt the information in the literatuwhenever possible, to reliably fulfil this rule. Some of tbands mentioned in the literature could not be identifiedthe authors did not mention the band type. These arecluded in Table I but will not be further considered. A feothers early observations were either vibrationally reassigaccording to the analysis presented in the next sectionassumed to be identical to bands reinvestigated later, evtheir listed origin was shifted up to a couple of wavenubers.

III. BAND BY BAND ROTATIONAL ANALYSIS

We have performed the rotational analysis of all bannewly reported on the FT and on the ICLAS spectra, incluing two bands of12C2HD.

The conventional model was used to represent the rbrational energy levels,

TV5GV~V1 ,V2 ,V3 ,V4l 4,V5

l 5!1FV~J!, ~3!

whereGV andFV are the vibrational and rotational contributions to the energy, respectively, and

FV~J!5BV@J~J11!2k2#2DV@J~J11!2k2#2

1HV@J~J11!2k2#3, ~4!

wherek5 l 41 l 5 is the quantum number of the total vibrational angular momentum taking into account the contribtions from thepg , trans (V4) and pu , cis (V5) bendings.



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The other normal modes,V1(sg1), V2(sg

1) andV3(su1) cor-

respond respectively to the symmetric CD, the CC, andantisymmetric CD stretching vibrations.

The rotationall -type doubling contribution to the rotational energy is

7~1/2!@qV1qVJ J~J11!1qV

JJJ2~J11!2#J~J11!, ~5!

where the2 and1 signs correspond to thee and f compo-nents, respectively, as defined in Ref. 48.

The upper state parameters or the variation of the pareters from the ground state were fitted, for FT and ICLAdata, respectively. In all cases, the lower state paramewhich are listed at the top of Table II, were constrained froHuet et al.21

The results of the rotational analysis are reportedTable II. All upper vibrational levels listed in that table aobserved through one of the bands highlighted in boldTable I. Concerning theP levels in Table II, those at 53775588, 5908, 5960, and 5970 cm21 were observed throughP –S1 bands and all others through hot bands.

For the previously characterized states, the numberotational levels observed and assigned from the presentexceeds the previously reported information, both forbands recorded by FT spectroscopy and by ICLAS and lto improve the known rovibrational parameters. The relaliterature is referenced to in Table I. The relative intensitythe bands observed on the FT spectrum, reported in thecolumn of Table II, was measured from the transmittancetheR(10) line in all but 2 cases, and normalized to the strogest band. For the levels at 7315 and 7355 cm21, the nor-malized intensity was measured for theR(6) lines, with eand f components. A detailed analysis of the rotational prameters listed in Table II reveals irregular features in thdependence on the vibrational excitation. This is rather



stsity of the

ates


TABLE II. Rovibrational parameters (cm21) of the analyzed12C2D2 vibrational levels. The uncertainties~1s! are given in parentheses in units of the laquoted digit. The number of lines used in the fitting procedure is given with, in parentheses, the total number of lines assigned. The relative intenbands is indicated for the FT spectra.

V1V2V3V4V5 Sym.a Gv Bv

DV(3106)Hv(3109)b

qV(3102)qv

J(3108) Liness

(3103) I rel

0 0 0 0 0 Sg1 0.0 0.84787420 0.80229

0.0004990 0 0 1 0 Pg 511.536 0.84993494 0.82875 0.324200

0.00011320 0 0 0 1 Pu 538.636 0.8500594 0.82814 0.327567

0.00682

0 1 1 2 0 Su1 5197.79941~26! 0.8442718~85! 26.253(64) 35~69! 0.7 26.3

26.47(13)0 1 1 2 0c,f Du

e 5199.6029~51! 0.844168~67! 7.21~27! 17~36! 0.9 1.85.29~34!

0 0 2 0 1f Pu

5377.37460~13! 0.84109737~52! 0.80766~39! 0.310473~65! 96~105! 0.6 7.222.155(60)

1 1 0 1 1f Su1 5466.74019~25! 0.8432558~31! 2.8176~89! 54~67! 0.8 3.2

0.4695~69!1 0 1 1 0 Pu 5587.64002~22! 0.8395964~23! 0.8450~23! 0.32857~14! 73~83! 0.8 0.5

0.0183~32! 22.84(16)2 0 0 0 1 Pu 5908.45676~21! 0.8383357~14! 0.8402~20! 0.34192~19! 69~70! 0.8 12.6

22.82(35)1 1 0 2 1 Pu 5960.12996~65! 0.8449775~94! 2.335~35! 0.39216~65! 22~33! 0.9 0.2

0.257~35! 244.8(15)1 1 0 2 1 Pu 5970.17650~48! 0.8449590~92! 21.086(48) 20.09787(89) 42~45! 0.8 0.3

20.420(72) 74.7~64!d1 0 1 2 0f Su

1 6080.67181~31! 0.841801~14! 210.82(15) 30~64! 0.7 2.5217.09(41)

1 0 1 2 0c,f Due 6083.1544~19! 0.840874~32! 6.96~15! 20~37! 1 0.4

5.87~21!2 0 0 1 1f Su

1 6381.28723~23! 0.8407634~55! 2.779~31! 41~58! 0.6 0.60.407~45!

1 1 1 0 0 Su1 6828.14050~20! 0.8343977~15! 0.8135~28! 77~87! 0.8 100

0.0115~13!0 2 1 2 0f Su

1 6933.48338~33! 0.8410305~71! 23.597(38) 37~53! 0.8 0.822.511(53)

1 1 1 1 0f Puf 7314.54701~33! 0.8365462~26! 0.8349~52! 0.333430~41! 80~116! 0.3(e)

20.0042(29) 0.15(f )1 1 1 0 1f Pg

f 7354.90742~88! 0.8365883~78! 0.851~15! 0.32878~11! 73~115! 0.1(e)0.0206~76! 0.2(f )

2 1 0 0 1f Puf 7636.33203~19! 0.8353430~12! 0.8651~13! 0.35394~13! 56~71! 0.7 0.5

23.58(20)

4 0 1 0 0f Su1 12934.4364~44! 0.824215~50! 0.80229e 11~18! 13

3 1 1 2 0f Su1 12962.0516~32! 0.824217~3! 20.937(52) 38~42! 9

1 2 3 0 0 Su1 13181.9973~18! 0.822568~15! 0.753~19! 37~37! 7

0 1 5 0 0 Su1 13597.5800~28! 0.822428~19! 0.771~25! 55~56! 10

1 2 3 0 1f Pg 13699.4122~62! 0.824925~43! 0.786~55! 0.305~1! 17~20! 103 2 1 0 0 Su

1 13717.3093~18! 0.821007~12! 0.856~13! 55~56! 72 3 1 2 0f Su

1 13768.9815~26! 0.826707~29! 20.736(61) 28~29! 82 1 3 0 0 Su

1 14019.7219~22! 0.819824~16! 0.956~20! 57~58! 80 1 5 1 0f Pu 14075.2706~30! 0.823745~30! 21.142(49) 0.331~5! 9~12! 101 0 5 0 0 Su

1 14377.7359~16! 0.818922~13! 0.763~18! 53~53! 62 1 3 1 0f Pu

1 14478.2012~34! 0.821891~32! 0.82875e 0.348~1! 37~45! 132 1 3 0 1f Pg 14527.8369~31! 0.821682~43! 27.502(11) 0.243~2! 25~37! 111 3 3 0 0f Su

1 14861.2933~27! 0.819776~10! 0.80229e 42~43! 123 0 3 0 0f Su

1 14878.4001~30! 0.816521~17! 0.649~46! 46~46! 90 2 5 0 0 Su

1 15280.6155~32! 0.819729~30! 0.772~55! 35~43! 92 2 3 0 0 Su

1 15685.4330~29! 0.817059~22! 0.586~33! 44~49! 81 1 5 0 0 Su

1 16041.0420~25! 0.816244~25! 0.674~48! 41~49! 83 1 3 0 0 Su

1 16536.9698~22! 0.815940~18! 0.5007~29! 47~52! 8

aThe parameters for the ground andV451 andV551 levels are taken from Huetet al. ~Ref. 21!. qVJJ parameters are available for the fundamental bend st

but were not included in the fitting procedure.bH9 was not included for the bands observed at higher energies.cObserved from aD–S band which was rotationally analyzed as aS–S band~see text!.dqV

JJ50.133(11)31028.eConstrained to the lower state value.fLevel previously not reported in the literature.



rstan

thsewd

o

enth

thlehes

erno

hefi

diosal

in

-tos

n

eII.iniv

na

-

’’he

.-

d in

h

nalob-ab-d to

n-


vious from the variation in the sign of distortion parametefrom one level to another. Many of the FT rovibrational dacorresponding to higherJ values, could not be included ithe fitting procedure using the set of parameters in Eq.~4!.Only the introduction of higher order distortion terms, withe J dependence up to the twelve power in some camade them fit within the experimental precision. We hoever arbitrarily decided to limit the expansion as presenteEq. ~4! and Table II, to provide comparable results in the twenergy ranges investigated.

An apparently random scatter of the values of the ctrifugal distortion parameters and, to some respect, ofprincipal rotation constants was also pointed out11 in 12C2H2.It was demonstrated that this effect originates fromstrong anharmonic resonances put forward in the molecu11

It is most likely that the same explanation applies in tpresent case. The responsible anharmonic resonance12C2D2 will be characterized in the next section. Howevwe shall not much detail the consequences of the vibratioperturbations on the rotational structure, in the present ctribution.

We wish to stress the observation of twoDue–Sg

1 ‘‘per-turbation allowed’’ bands in the lower energy range of tspectrum. This assignment is based on several features;both bands are only observed at highJ values; next they arevery close to other, much stronger bands, ofSu

1 –Sg1 type

(n055197.80 and 6080.67 cm21!. In addition, the vibra-tional parameters reported in the next section only preoneSu

1 level in each concerned range. It is therefore almcertain that these extra bands, which we initially identifiedSu

1 –Sg1 , arise from the contribution of the rotationa

l -doubling connecting thee rotational levels in theS andDsublevels of a manifold characterized by a multiple bendexcitation. TheSu

1 levels of interest were identified as (V2

1V312V4) and (V11V312V4) and must indeed be connected to aDu

e level nearby. The intensity borrowing, duetheJ-dependent rotationall -doubling mixing terms, transfersome of the allowed character of theSu

1 –Sg1 band to the

zero order forbiddenDue–Sg

1 one. This process has beefully detailed in previous contributions13,49 devoted to12C2H2. We have analyzed the forbidden bands as if thwere ofSu

1 –Sg1 symmetry. The results are listed in Table

We have also fitted them together with their correspondclose companion. The fit was actually better converging, ging rise to the following values in cm21, with all parameters,but gV , defined in the previous equations from conventiomodels:21

EV55 197.799 58(20); BV50.844 289 1(18);DV50.854 3(32)31026; HV50.005 9(16)31029;gV50.448 69(10); qV50.324 146(69)31022;qV

J 52.492(69)31028 ~rmslines50.7731023; 99 transitionsfitted among 106 identified!; and EV56 080.672 89(23);BV50.841 775 8(27); DV50.896 3(59)31026;HV50.029 0(37)31029; gV50.610 07(13);qV50.326 474(95)31022; qV

J 53.37(12)31028

~rmslines50.8131023; 85 transitions fitted among 101 identified!.

Figure 1 shows theSu1 –Sg

1 and theDue–Sg

1 bands in



,,

s,-in

-e

e.

in,aln-

rst,

ctts

g

y

g-

l

the 6030– 6130 cm21 range. Only theSu1 –Sg

1 is clearly vis-ible owing to the weakness of the ‘‘perturbation allowedband. An enlargement of the spectrum in t6100– 6112 cm21 region in the lower part of the figureshows a portion of theR(J) branches for both bands. In Fig2 then11n21n3 , Su

1 –Sg1 transition has been reported. Ex

amples of the spectra recorded using ICLAS are reporteFigs. 3 and 4. They present the 2n11n213n3 and 2n1

12n213n3 Su1 –Sg

1 bands, respectively.

IV. VIBRATIONAL PARAMETERS

The vibrational energies reported in Table III, whicwere extracted using Eq.~2! from the information listed inTable I, have been used to determine a set of vibratioparameters. As pointed out before, some of the previousservations could not be considered reliable, given thesence of information on the rotational structure. Comparethe situation we dealt with10 in 12C2H2, there is less experi-

FIG. 1. ~a! The FT spectrum of then11n313n4 band of C2D2 containingthe Su

1 –Sg1 and the Du

e–Sg1 ‘‘perturbation allowed’’ subbands in the

6030– 6130 cm21 range. A fewR(J) and P(J) transitions of the strongerSu

1 –Sg1 band have been identified.~b! An enlargement of the spectrum in

the 6100– 6112 cm21 range, containing a fewR(J) transitions of bothSu1

and Due components of the (V1V2V3V4V5)5(1,0,1,2,0) manifold. Experi-

mental conditions: path length, 41 m; pressure, 11.6 kPa.

FIG. 2. The FT spectrum of then11n21n3 Su1 –Sg

1 band of C2D2 centeredat 6828.14 cm21 with associatedn11n21n31n42n4 Pu–Pg andn11n2

1n31n52n5 Pg–Pu weaker hot bands. A fewR(J) andP(J) transitionsof the more intenseSu

1 –Sg1 band have been identified. Experimental co

ditions: path length, 41 m; pressure, 11.6 kPa.



w,s

t fealethu

llypr

ra

ag

ra-

pa-miteen

n

d

ron

anrgy.pos-e of

refter-eron-

ghingn

theal

ost

gwe

etchrix

rpthir

rphi


mental information available and, besides the well kno44/55 DD resonance already put forward in the literature21

there is no strong evidence for any other anharmonic renance to be taken into account. The model in12C2H2,

10 helpsselecting the other quartic resonances of potential interesdealing with12C2D2. However, in the dideutero molecule thpairs of possibly resonating levels are not as systematicclose as in the main isotopomer. One can thus expectpronounced effects on the energy of the levels and onintensity of the bands, and the resonances are therefore mmore difficult to be reliably assessed.

In view of these elements, we proceeded very carefuin successive steps, before attempting a global fit. Thecedure is described hereafter.

A. Bending levels

Concerning the pure bending levels, rotational and vibtional parameters were simultaneously determined21 by fit-ting 1608 rovibrational and rotational line energies tomodel including in full details the 44/55 DD couplin

FIG. 3. The ICLAS spectrum of the 2n11n213n3 Su1 –Sg

1 band centeredat 14 019.722 cm21 of 12C2D2. The pressure was 19.6 kPa and the absotion equivalent pathlength of about 22 km. Two hot bands arising frombending modesV451 and V551 are observed, the arrows indicate thecentres at 13 989.229 and 13 966.71 cm21, respectively.

FIG. 4. The ICLAS spectrum of the 2n112n213n3 Su1 –Sg

1 band centeredat 15 685.433 cm21 of 12C2D2. The pressure was 28.4 kPa and the absotion equivalent pathlength of about 16 km. The weak band observed atenergy is assigned to the 5n3 overtone transition of12C2HD centered at15 697.03 cm21 present in minor quantity in our sample.



n

o-

or

llyssech

,o-

-

scheme. The quality of the fit, which reproduced the rovibtional line wavenumbers within 1024 cm21, was excellent.We decided to constrain the corresponding vibrationalrameters to the values previously obtained in order to lithe degrees of freedom in the procedure. They have breported with an asterisk in Table IV. The labels45 of theDD coupling constant has been changed inK44/55, which hasalso been used for12C2H2.

10,11 The previous work21 on thebending levels in12C2D2 included the levelsV4 , V5 , 2V4 ,2V5 , V41V5 , 3V5 , and 2V41V5 . Information was alsoavailable at the time onV412V5 but was not included. TableI lists pure bending levels at even higher energy~up to 5V5!from Talley and Nielsen,27 which were also not considered ithe present procedure.

B. Stretching levels

Concerning the pure stretching levels, we initially fittethem separately to a Dunham expansion of the type,

GVs 5(

svs

0Vs1 (s<s8

xss80 VsVs8

1 (s<s8<s9

yss8s9VsVs8Vs9 . ~6!

with s51 – 3.We selected the coefficientsy to be determined afte

initial fits excluding them. All parameters in the expansiwere considered, provided they could be determined witherror not exceeding their fitted value. The stretching enelevels were reproduced within 1 cm21 using this procedureThe only evidence for an inadequate model, because ofsibly missing anharmonic resonances, appeared in the sizsome of the third order,y anharmonic parameters. Pustretching anharmonic resonances were introduced, ahaving removed ally’s. These were later carefully reintroduced, checking that they did not significantly affect neiththe present, nor the next step in the procedure, which csiders the stretch–bend levels and is described below.

The good quality of the fit obtained without considerinany anharmonic resonance connecting the pure stretclevels is a confirmation of the low vibrational interactiostrengths, relative to the situation in both12C2H2 and13C2H2.

The first anharmonic resonance we considered is11/33 DD coupling, according to the following conventionmatrix element:

^V1 ,V2 ,V3 ,V4l 4,V5

l 5uh11/33/hcuV122,V2 ,V312,V4l 4,V5

l 5&

5 14 K11/33@V1~V121!~V311!~V312!#1/2. ~7!

Thex–K relations42 predict thatK11/33 must be close tox13,whose value could be readily determined from the first, mlikely unperturbed, corresponding stretching levels,V1 , V3 ,and V11V3 . To reach a satisfactory result both providinlow obs.-calc. values and responding the latter criteria,found necessary to include an extra, 12/33 stretch–strinteraction, corresponding to the following interaction matelement:

-e

-gh



ne.h-tingm-

nwer

in-tlyWe

c-to

no

s fitra-


TABLE III. Vibrational energy levels of12C2D2(X1Sg

1) included in theglobal fitting procedure~GV and obs.-calc. values in cm21!. All levels re-ported in this work are highlighted in bold. Pure bending levels arelisted.

V1 V2 V3 V4l 4 V5

l 5 Sym GVobs O-C Ref.a

0 1 0 00 00 Sg1 1764.796 20.03 kost80

0 1 0 00 11 Pu 2305.079 0.35 alan870 0 1 00 00 Su

1 2439.244 20.60 gher681 0 0 00 00 Sg

1 2705.160 0.24 alan870 1 0 11 121 Su

1 2803.965 20.46 alan870 1 0 121 11 Su

2 2811.055 20.55 alan870 1 0 11 11 Du 2814.126 20.59 alan870 1 0 00 20 Sg

1 2838.696 0.86 alan870 1 0 00 22 Dg 2846.536 0.86 alan870 0 1 11 00 Pu 2945.17 20.32 gher710 0 1 00 11 Pg 2972.70 20.37 bald721 0 0 11 00 Pg 3201.98 1.02 gher68b1 0 0 00 11 Pu 3235.61 0.10 gher710 0 1 20 00 Su

1 3452.35 20.56 hurl710 0 1 22 00 Du 3455.60 20.09 hurl710 0 1 11 121 Sg

1 3469.417 20.63 gher680 0 1 11 11 Dg 3480.776 0.44 gher680 0 1 00 20 Su

1 3499.72 0.05 gher680 0 1 00 22 Du 3507.286 20.05 gher681 0 0 11 11 Du 3733.84 0.68 gher68b1 0 0 00 20 Sg

1 3759.38 0.17 bald721 0 0 00 22 Dg 3767.30 0.16 bald720 0 1 31 00 Pu 3965.21 0.44 gher68b0 0 1 33 00 Fu 3970.63 0.21 gher68b0 1 1 00 00 Su

1 4190.638 0.07 hurl711 0 0 00 31 Pu 4284.75 0.55 tall540 1 1 11 00 Pu 4692.77 20.29 gher710 1 1 00 11 Pg 4725.68 0.57 bald720 0 2 00 00 Sg

1 4848.786 20.88 tall541 0 1 00 00 Su

1 5097.195 20.39 hurl710 1 1 20 00 Su

1 5197.800b 0.32 herm970 1 1 22 00 Du 5199.594b 20.52 herm970 0 2 00 11 Pu 5377.375 20.16 herm972 0 0 00 00 Sg

1 5386.456 0.19 tall541 1 0 11 121 Su

1 5466.740 20.99 herm971 0 1 11 00 Pu 5587.640 20.11 herm971 0 1 00 11 Pg 5622.42 20.39 bald722 0 0 00 11 Pu 5908.457 20.41 herm971 1 0 22 121 Pu 5960.130 0.02 herm971 1 0 20 11 Pu 5970.176 20.18 herm971 0 1 20 00 Su

1 6080.673b 0.75 herm971 0 1 22 00 Du 6083.113b 0.69 herm972 0 0 11 121 Su

1 6381.287 0.51 herm971 1 1 00 00 Su

1 6828.141 20.20 herm970 2 1 20 00 Su

1 6933.483 0.13 herm970 0 3 00 00 Su

1 7230.036 20.15 herm941 1 1 11 00 Pu 7314.547 20.85 herm971 1 1 00 11 Pg 7354.907 0.06 herm972 1 0 00 11 Pu 7636.332 22.11 herm970 0 3 11 00 Pu 7724.139 0.24 herm942 0 1 00 00 Su

1 7734.003 20.05 herm941 1 1 20 00 Su

1 7805.520 0.97 herm941 0 2 00 11 Pu 7980.045 20.11 herm942 0 1 11 00 Pu 8208.694 20.17 herm942 0 1 00 11 Pg 8251.086 20.22 herm941 2 1 00 00 Su

1 8550.142 20.26 herm940 1 3 00 00 Su

1 8952.887 0.83 herm940 1 3 11 00 Pu 9443.452 0.89 herm942 1 1 00 00 Su

1 9444.434 0.38 herm940 1 3 00 11 Pg 9477.105 1.22 herm941 0 3 00 00 Su

1 9794.074 0.63 herm943 0 1 00 00 Su

1 10347.92 20.46 saks52



^V1 ,V2 ,V3 ,V4l 4,V5

l 5uh12/33/hcuV121,V221,V312,

V4l 4,V5

l 5&5 14 K12/33@V1V2~V311!~V312!#1/2. ~8!

This interaction was not previously determined in acetyleIt was only predicted10 to be of some importance at higexcitation energy in12C2H2 because of the anticipated decrease in the energy difference between pairs of resonalevels, with increasing vibrational energy. The related cobination of fundamental frequencies, i.e.,v11v2 and 2v3 ,are much closer in12C2D2 and this anharmonic perturbatiocan therefore be expected to affect the pattern at much lovibrational energies than in12C2H2. Both matrix elements,from Eqs.~7! and~8! were thus simultaneously consideredthis initial step. The selectedy coefficients, as described previously, have been retained in the fit because they slighreduce the final obs.-calc. values on the energy levels.attempted introducing they123 Dunham coefficient. In thatcase the value ofK12/33 was extremely sensitive to the seletion of bands included in the fit. We therefore decided

t

TABLE III. ~Continued.!

V1 V2 V3 V4l 4 V5

l 5 Sym GVobs O-C Ref.a

2 2 1 00 00 Su1 11146.074 0.83 pisa93

1 1 3 00 00 Su1 11492.719 20.10 pisa93

0 0 5 00 00 Su1 11905.369 20.18 pisa93

1 1 3 11 00 Pu 11967.356 20.27 pisa933 1 1 00 00 Su

1 12036.950 0.33 pisa932 0 3 00 00 Su

1 12344.537 0.42 pisa930 0 5 11 00 Pu 12386.560 20.35 gros950 0 5 00 11 Pg 12416.624 20.62 gros953 1 1 11 00 Pu 12491.516 21.72 gros953 1 1 00 11 Pg 12547.891 0.81 gros952 0 3 11 00 Pu 12806.742 20.08 gros952 0 3 00 11 Pg 12851.205 0.45 gros954 0 1 00 00 Su

1 12934.443 25.64c herm973 1 1 20 00 Su

1 12962.052 9.86c herm971 2 3 00 00 Su

1 13181.997 21.34 herm970 1 5 00 00 Su

1 13597.580 0.23 herm971 2 3 00 11 Pg 13699.412 20.98 herm973 2 1 00 00 Su

1 13717.309 1.51 herm972 3 1 20 00 Su

1 13768.982 0.72 herm972 1 3 00 00 Su

1 14019.722 0.11 herm970 1 5 11 00 Pu 14075.271 20.09 herm971 0 5 00 00 Su

1 14377.736 6.10c herm972 1 3 11 00 Pu 14478.201 21.06 herm972 1 3 00 11 Pg 14527.836 0.36 herm971 3 3 00 00 Su

1 14861.293 20.45 herm973 0 3 00 00 Su

1 14878.400 20.11 herm970 2 5 00 00 Su

1 15280.615 0.22 herm972 2 3 00 00 Su

1 15685.433 20.60 herm971 1 5 00 00 Su

1 16041.042 0.98 herm973 1 3 00 00 Su

1 16536.970 6.93c herm971 2 5 00 00 Su

1 17694.210 24.98c hall84

aalan87 ~Ref. 37!; bald72 ~Ref. 35!; gher68 ~Ref. 31!; gher71 ~Ref. 34!;gher68b~Ref. 32!; gros95 ~Ref. 41!; hall84 ~Ref. 4!; hurl71 ~Ref. 33!;herm94~Ref. 40!; herm97, this work; kost80~Ref. 24!; pisa93~Ref. 39!;saks52~Ref. 38!; tall54 ~Ref. 27!; see also note added in proof.

bVibrational energies were extracted from the results of the simultaneouof the D–S andS–S rovibrational bands with the same upper state vibtional identification, presented in the text.

cNot included in the fit.



e

nt

nt

odetent

t,uc-

ed

k arwan

c

tels

dceininrs

itblbla

sle

ab

al.

eanbe

t in-est

ivengofcitedin-ies

by

tat-

entnde

,f thech a

stedthisnes

t is

di-of its

byT

ce.ra-

ndslar

ing


keepK11/33andK12/33but to excludey123. Although only theabsolute value of theK ’s parameters matters for the fit, thsign of K11/33, which is predicted from thex–K relations tobe identical to the one ofx13, was adopted. The agreemebetween these two parameters is extremely good.

C. Stretch–bend levels

In the final step of this initial procedure the stretch–belevels have been considered. All parameters concerningpure bending and the pure stretching vibrations were cstrained to their value determined during the previouslyscribed steps. All but a few stretch–bend data were fittaking into account in the diagonal, Dunham-type elemethe following extra term:

GVsb5(

s,bxsbVsVb , ~9!

with s51 – 3 andb54,5. One of the criteria used in the fiin addition to the overall obs.-calc. value, was the reprodtion of the parameterx25, whose value could be independently calculated from the following unperturbed bands:n5 ,n22n5 , andn21n5 . The sign of this constant was expectto be opposite~i.e., positive! to all otherxsb mixed anharmo-nicities. Except for two bands reported in the present wor12 934.443 and 12 962.052 cm21 and, to a minor extent, fothree other bands at higher energy, the result of the fitmost satisfactory. Four bands reported by Talley aNielsen,27 at 5793.65, 7211.15, 5875.45, and 5892.69 cm21,have not been listed neither in Table I nor in Table III. In fathe first two were observed by us and assigned to the C2HDmolecule, while the other two belong probably to C2D4 or tosome other partially deuterated isotopomer. It is also inesting to note that all these bands have very large residuathe analysis of Ref. 27.

D. Global fit

Several stretch–bend levels do bring significant adtional information concerning the anharmonic resonan11/33 and 12/33 introduced when fitting the pure stretchlevels. A global fit of all bands was then performed, adoptthe following restrictions:~i! the pure bending parametewere constrained from Huetet al.,21 and~ii ! no extra param-eter, in particular no extray was included in the model, inaddition to those whose role was assessed during the inprocedure. The results of the global fit are provided in TaIII and the related vibrational parameters are listed in TaIV. Twenty-one parameters were fitted to reproduce 88 dwith a standard deviation of 0.72 cm21 and 17 parameterwere constrained from the literature. Five stretch–bendels were excluded from the fit and no pure bending level wconsidered in the procedure. None of those is listed in TaIII.

E. Discussion

The very same few levels gave rise to large obs.-cvalues both in the step by step and global fit procedures



dhen--ds,

-

t

sd

t

r-in

i-sgg

ialeeta

v-sle

c.In

particular, three levels at 14 378, 16 537, and 17 694 cm21,present obs.-calc. values significantly larger than the mvalue but no other zero order assignment, however, canpossibly suggested. As a consequence, they were nocluded in the fitting procedure. They are among the highenergy levels observed in12C2D2. It would be useful to char-acterize close and, if possible resonating extra levels, to gthem more weight in the fitting procedure, before attributithe problem to any, still unidentified interaction. The rolethe anharmonic parameters also increases for such exvibrational levels and slight changes might significantlyfluence the quality of the prediction. Similar discrepancwere observed when applying the12C2H2 parameters10 topredict the highest energy levels reported in that speciesHall.4

Two other levels, at 12 934 and 12 962 cm21, assignedto ~4,0,1,0,0! and~3,1,1,2,0! respectively, show a significandeviation from their calculated energy and deserve moretention. They are reported for the first time in the preswork, from the ICLAS data, and are listed in Tables II aIII, but were not included in the fitting procedure. As thobs.-calc. value is negative (25.64 cm21) for the lower en-ergy one and positive (9.86 cm21) for the higher energy onewe suggest that an additional anharmonic resonance, otype 1/244, is required to interpret these observations. Suresonance occurs10 also in 12C2H2. The related matrix ele-ment,

^V1 ,V2 ,V3 ,V4l 4,V5

l 5uh1/244/hcuV111,V221,V3 ,~V422! l 4,

V5l 5&5 1

4 K1/244@~V111!V2~V422 l 4

2!#1/2 ~10!

connects the~4,0,1,0,0! and ~3,1,1,2,0! levels. It is easy toestimate the interaction parameter,K1/244, since the unper-turbed energies can be predicted from the parameters liin Table IV and both perturbed levels are observed. Onbasis, a simple two by two matrix model allows to determiK1/244512.4 cm21. As a result of the coupling, the mixing iabout 50/50 and the intensities, as well as theBV values, arestrongly affected. This latter aspect will be detailed later. Iinteresting to notice that the 3n11n21n312n4 band carriesthe strongest intensity, in the ratio of about 25:10. This incates that this band possesses some significant intensityown, compared to the 4n11n3 band, despite the very highexcitation involved~7 quanta!. As a matter of fact the 4n1

1n3 band is not expected to be relatively strong, asn1 doesnot carry much intensity.

Further evidence in the 1/244 coupling is obtainedconsidering the levels reported in Table II, now from the Fdata. The levels within two pairs,~1,0,1,0,0!/~0,1,1,2,0! and~1,1,1,0,0!/~0,2,1,2,0! are connected by the 1/244 resonanWithin each pair, one of the levels has two additional vibtional quanta, i.e.,~0,1,1,2,0! at 5198 cm21 and~0,2,1,2,0! at6933 cm21. None of these should be observed through baas strong as indicated in Table II. In addition, other, similevels such as~0,1,1,0,2! and~0,2,1,0,2! are not observed. Itmust be the 1/244 resonance that allows intensity borrow




Downloaded 17 F

TABLE IV. Vibrational parameters (cm21) determined for12C2D2(X1Sg

1). The uncertainties~1s! are given inparentheses, in units of the last quoted digit, except for those constrained from the literature.

Dunham parameters

v1052717.22(39) x115212.30(17) x125217.20(32) x24523.16(15)

v2051768.07(74) x22522.69(74) x135247.52(32) x2551.30(25)

v3052455.11(37) x335215.42(22) x145215.49(15) x34525.881(93)

v405509.237901a x4451.8428a x15528.01(15) x35525.37(12)

v505537.9979a x55521.6173a x235213.54(38) x45521.6381a

g440 50.4512a g55

0 52.2670a g450 53.1823674a

y222520.55(18) y33350.157(33) y13350.34(11) y233520.568(89)y445520.00275a y4

4550.16871a y555520.0484a y5

44520.09990a

y55550.03718a

Interaction parameters

r 450 525.497a r 44550.0708a r 45550.884a

K44/55527.963a K44550.569a

K11/335247.2(14) K12/335u54.4(20)u K1/244512.4b

aConstrained from Huetet al. ~Ref. 21!.bNot included in the global fitting procedure~see text!.

in

een-he

to-

th

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from the other, much stronger band in each pair, involvthe ~1,0,1,0,0! or ~1,1,1,0,0! levels at 5097 and 6828 cm21,respectively.

Besides the~4,0,1,0,0!/~3,1,1,2,0! dyad, one can estimatthat the 1/244 resonance is rather inefficient in terms ofergy perturbation, about 1 cm21, given the much larger energy difference between the interacting levels in the otobserved pairs. Actually two other levels,~3,2,1,0,0! and~2,3,1,2,0! are close enough~GV513 717 and 13 769 cm21,respectively! that the predicted shift due to 1/244 raisesabout 7 cm21. It is interesting to point out that the corresponding obs.-calc. values obtained without including1/244 resonance, listed in Table III, are around 1 cm21 only.This confirms that, despite our careful step by step produre, the higher order parameters do absorb some ofenergy perturbations. This comment certainly also appliethe role of other resonances, such as 3/245 and 1/255 wwe were unable to reliably point out. Highly correlated prameters, with increased uncertainty, would have resultedtaking into account the 1/244 resonance, which thereforenot included in the global fit. We rather used the most snificant information to estimateK1/244, which is listed inTable IV. It brings very interesting insight into the clusterinof the vibrational levels, discussed in the next section.

V. LEVEL CLUSTERING

The notion of cluster extends the well known onepolyad to the whole vibrational energy pattern in the mecule. It block diagonalises the effective vibrational Hamtonian, leading to define a better suited basis set, represeby new quantum numbers. The formation of vibrational cluters and the related quantum numbers were adopted antensively discussed for12C2H2 ~Refs. 6, 8–10! and used forN2O.50


eb 2004 to 128.97.89.5. Redistribution subject to AIP

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A. Three quantum number clusters

Vibrational clusters are uniquely defined by the setanharmonic resonances we have discussed in the prevsection. In a first step, one can deal with only the 44/11/33, and 12/33 resonances included in the global fit andvibrationall -type doubling coupling. The latter was includein the model as discussed in the analysis of the pure benlevels.21 As for 12C2H2,

10 one can associate a vector to eaof these resonances. It can be easily demonstrated thafour interactions are expressed by linearly independent vtors. Therefore, as shown by Kellman,8 (3N25)24, i.e., 3quantum numbers can be defined, with 3N25 the number ofnormal modes in the molecule. They areNs5V11V21V3 ,Nsb5V11V21V31V41V5 , andk5 l 41 l 5 .

The fitting procedure in the previous section was acally adapted to this clustering scheme and interaction maces were build for each relevant combination of quantnumbers. The same procedure was used for12C2H2, with,however, a slightly different set of quantum numbers, givthe difference in the relevant resonances to be considere10

B. Two quantum number clusters

If the 1/244 anharmonic resonance is included incluster scheme, then another resonance vector that hapto be linearly independent of all others in the basis justfined, is introduced. As a consequence, the quantum numNsb disappears and only 2 quantum numbers can be defiNs5V11V21V3 andk5 l 41 l 5 . Besides the symmetry, implicitly contained ink, the bending excitation becomes therfore irrelevant. The size of the clusters is significantly elarged, and, already at very low excitation energy, the pictis getting much closer to chaos than in12C2H2. The termchaos is used here for total absence of relevant vibratioquantum numbers. The size of the clusters to be dealt wand the very limited number of significant information wi



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regard to the 1/244 resonance practically forbids a glofitting procedure including 1/244 in addition to the other coplings found to be relevant.

One should point out a rather unique feature in the cltering process occurring in12C2D2. For each cluster, there iat least one level with the adequate quantum numberNs andsymmetry (k) which does not interact with any other leveFor k50 clusters, there is one such level, with valu(V1V2V3) defined as (0,Ns21,1) and (0,Ns,0), for Su

1 andSg

1 symmetry, respectively. For instance, within the clusNs56 with Su

1 symmetry, the level~0,5,1! is not interactingwith any of the other levels in the cluster through the 44/11/33, 12/33, 1/244 or vibrationall -type couplings. It wouldbe most interesting to characterize the dynamical propeof such levels.

C. Rotational parameters

As previously discussed, the mixing induced by the aharmonic resonances in12C2D2 within the 3-quantum num-ber clusters is, besides 44/55, not very significant. The eigvectors resulting from the matrix diagonalization show ththe zero order character, again besides the pure benlevels,21 is kept in most cases at more than 90% in theserved eigenstates. Thus, although the whole vibrationalture is more scrambled than in normal acetylene, the mixiare less severe. As a result, the rotational constantsBV can inmost cases be reliably extrapolated up to high vibratioexcitation, provided their vibrational dependencies (a i) areknow. The parametersa i have been determined using literture values for theB parameters in the fundamental leveaccording to the relation,

BV5Be2 (i 51,5

a i~Vi1di /2!, ~11!

TABLE V. Vibrational dependencies of the rotational constants12C2D2(X

1Sg1).

Mode a (cm21) Ref.a

1 0.005585 kost802 0.003133 kost803 0.004488 gher684 20.00208127 huet915 20.00215884 huet91

agher68~Ref. 31!; huet91~Ref. 21!; kost80~Ref. 24!.

TABLE VI. Observed and calculatedBV parameters and contribution of thzero-order wave function in12C2D2 for all reported pure stretching vibrational levels withNs56. All energies and constants are in cm21.

V1V2V3V4V5 Gn(obs) Bn

(obs) Bn(cal) %

1 2 3 0 0 13181.997 0.82257 0.8225 890 1 5 0 0 13597.580 0.82243 0.8222 923 2 1 0 0 13717.309 0.82100 0.8204 912 1 3 0 0 14019.722 0.81982 0.8201 821 0 5 0 0 14377.736 0.81892 0.8197 883 0 3 0 0 14878.400 0.81652 0.8177 84



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with i 51 – 5, anddi51,2 for i 51 – 3 and 4, 5, respectivelyThe values ofa i are listed in Table V. In some cases, th

mixing between the zero order states is more pronouncedcan be taken into account to reproduce the observedBV val-ues, as described for12C2H2.

10 The correction is howeveonly just significant. As an example Table VI lists the oserved and predicted rotational constants for all pure streing levels corresponding toNs56. The calculation takes intoaccount only the 11/33 and 12/33 anharmonic contributiowithin the 3-quantum number cluster model. The agreemis very satisfactory. The contribution of the zero order wafunction, corresponding to the identification provided in ttable, is given in the last column.

The BV values for the~4,0,1,0,0! and ~3,1,1,2,0! levelsdeserve further comments: the predictedBV , using the de-pendencies listed in Table V, are respectively, 0.82110.8277 cm21. The rotational analysis of the bands leadsrespectivelyBV50.824 17 and 0.824 21 cm21, which arehalfway between the calculated values. The rotational pareters thus confirm the 50/50 mixing between the levelsbring a definite support to the introduction of the 1/244 renance in the model required for unravelling the observvibrational energy pattern in12C2D2.

VI. CONCLUSION

The experimental information available on the rovibrtional energy levels in12C2D2(X

1Sg1) has been extende

using Fourier transform and ICLA spectroscopy. Ninetevibrational levels, up to high excitation energy, have becharacterized for the first time. The knowledge of the vibtional energy pattern has been greatly improved usingsame procedure as in12C2H2,

10 i.e., based on the block diagonalization of the vibrational Hamiltonian into clusterThe selection of relevant resonances includes, besides44/55 and vibrationall -couplings previously studied indetails,21 also the 11/33 and 12/33 couplings. The introdution of the 1/244 interaction was motivated by one expemental observation, and supported by various other featin the spectrum. Altogether, the five linearly independecouplings result into the definition of only 2 quantum numbers associated to the vibrational energy clusters. Imporconsequences were pointed out, concerning the size ofclusters, as well as the presence of peculiar states within ecluster. Although the situation appears in theory more coplex than in12C2H2, the extent of mixing between zero ordestates is less pronounced, because of larger differencestween the vibrational energies, and predictions at varilevels are therefore more straightforward. Investigations12C2D2 may therefore help finding unusual features, due eto isomerization processes, more easily and reliably thaother isotopomers. We therefore hope that the presentsults, including the detailed rotational investigations, wstimulate further experiments based on dideutero acetyl~All rovibrational line wave numbers resulting from thpresent rovibrational analysis are available from the autho!

Note added in proof:C2D2 bands were also reported bL. Sinitsa @J. Quant. Spectrosc. Radiat. Transf.48, 721



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~1992!#, which were included in Table I but not considerein Table III. The level at 9963.76 cm21, not reported else-where in the literature, is assigned to~2110°11! and recalcu-lated with an O.-C. value of 1.22 cm21, using the parameterof Table IV.

ACKNOWLEDGMENTS

The ULB group acknowledges financial support frothe Fonds National de la Recherche Scientifique~FNRS-Belgium, contracts FRFC 9.4504.93 and FRFC 2.4504.!,and the Communaute´ Francaise de Belgique~contract ARC‘‘Quantum keys for reactivity’’ ARC 93/98-166!. They areindebted to all previous workers at ULB, including Dr. Abbouti Temsamani, who contributed to the package of pgrams we have used. The UB group acknowledges the fincial support received from the Universita` di Bologna and theMinistero dell’Universitae della Ricerca Scientifica e Tecnologica. M.H. gratefully thanks the University of Bolognfor an invited professorship which stimulated the present claboration. A.C. and M.H. are indebted to the CNRS aFNRS/CGRI for a collaborative research grant.

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Documents

The vibrational energy levels in acetylene. III. [sup 12]C[sub 2]D[sub 2]