The Acetylene Ground State Saga Michel Herman

The acetylene ground state saga Michel Herman

To cite this version:

Michel Herman. The acetylene ground state saga. Molecular Physics, Taylor & Francis, 2008, 105 (17-18), pp.2217-2241. 10.1080/00268970701518103. hal-00513123

HAL Id: hal-00513123 https://hal.archives-ouvertes.fr/hal-00513123 Submitted on 1 Sep 2010

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Molecular Physics

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The acetylene ground state saga

Journal: Molecular Physics

Manuscript ID: TMPH-2007-0155

Manuscript Type: Invited Article

Date Submitted by the 30-May-2007 Author:

Complete List of Authors: Herman, Michel; Université Libre de Bruxelles, Chimie quantique et Photophysique

acetylene, global picture, high resolution spectroscopy, Keywords: instrumental developments, intramolecular dynamics

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1 2 3 4 11 July 2010 5 Invited Manuscript 6 7 8 9 10 The acetylene ground state saga 11 12 13 14 15 Michel HERMAN 16 ServiceFor de PeerChimie quantique Review et Photophysique, Only CP 160/09 17 18 Université libre de Bruxelles (U.L.B.) 19 Ave. Roosevelt, 50. 20 21 B-1050 22 Brussels 23 24 Belgium 25 26 27 [email protected] 28 29 30 Pages : 57 31 32 Figures : 32 (including 2 colour figures) 33 Tables : 3 34 35 36 This ms was written using ‘‘century schoolbook’’ and, whenever necessary, 37 38 ‘‘symbol’’ fonts. A careful distinction was made between italic vee’s and 39 Greek nu’s both in the text and in formulas, that is important to respect. It 40 41 will only be visible if using ‘‘century schoolbook’’ as the major font to 42 visualize and print the text. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Abstract 5 6 7 8 The evolution of the high-resolution spectroscopic investigation of the 9 10 11 vibration-rotation energy states of acetylene in its ground electronic state 12 13 is presented, with focus on advances co-authored by the ULB group. The 14 15 16 emergenceFor of a global Peer picture Review accounting for all Only available spectroscopic 17 18 fingerprints, at their full accuracy, is highlighted. Contribution of this 19 20 21 research to various topics is illustrated, including instrumental 22 23 developments, local mode trends, quantum vs . classical correspondence, 24 25 26 energy vs . time approaches and nucleation processes. 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 1. Introduction 4 5 6 7 8 9 As reported by Miller in a book dedicated to acetylene [1], Edmund Davy 10 11 told the 1836 meeting of the British Association at Bristol that [2] 12 13 14 15 16 ‘‘in attemptingFor to Peer procure potassium Review by strongly Only heating a mixture of 17 18 calcined tartar and charcoal in a large iron bottle, I obtained a black 19 20 21 substance which readily decomposed water and yielded a gas which proved 22 23 to be a new compound of carbon and hydrogen. This gas burns in air with 24 25 26 a bright flame, denser and of greater splendour than even olefiant gas...In 27 28 contact with chlorine, instant explosion takes place, accompanied by a 29 30 31 large red flame and the deposition of much carbon…The new gas requires 32 33 for its complete combustion 2,5 volumes of oxygen gas, which are converted 34 35 36 into two volumes of carbonic acid and water, which are the only products of 37 38 its combustion... It is admirably adapted for the purposes of artificial light 39 40 41 if it can be procured at a cheap rate’’ 42 43 44 45 46 Edmund Davy identified this new gas as a "new (bi)carburet of hydrogen". 47 48 It was rediscovered in 1860 by French chemist Marcellin Berthelot, who 49 50 51 coined the name "acétylène." 52 53 54 55 56 As stated in an encyclopaedia: Acetylene (systematic name: ethyne) is 57 58 the simplest alkyne hydrocarbon, consisting of two hydrogen atoms and two 59 60 carbon atoms. Because it contains a triple bond, acetylene is an

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1 2 3 unsaturated chemical compound. The carbon-carbon triple bond leaves the 4 5 6 carbon atoms with two sp hybrid orbitals for sigma bonding, placing all 7 8 four atoms in the same straight line, with CCH bond angles of 180°. 9 10 11 Acetylene indeed provides the simplest example of carbon-carbon 12 13 triple bond and, as such, is referenced for its prototype geometrical 14 15 16 structure Forin textbooks, Peer with CH Review and CC bonds claimed Only to be 120 and 106 17 18 pm long. The latest equilibrium ( r ) and ground ( r ) internuclear distances 19 e 0 20 21 in acetylene, from [3], are, in pm: 22 23 24 25 26 rCH( )= 106.138(35); rCC ( ) = 120.292(13) e e (pm). 27 ( ) 105.756(52); ( ) 120.830(20) 28 rCH0 = rCC0 = 29 30 31 32 33 As such, they provide the most accurate values today available for the 34 35 basic CC triple bond and related CH distances. Interesting enough, these 36 37 38 bond lengths have not been optimally determined yet [4]. In addition, the 39 40 linear geometry refers to the ground electronic state and not to the first 41 42 43 and some additional excited electronic states. 44 45 46 47 48 The importance of acetylene in the ‘‘real world’’ dealt with in 49 50 encyclopaedias arises mainly from its application in synthetic organic 51 52 53 chemistry. Numerous prototype reaction mechanisms are well known and 54 55 of daily use to academic and industrial chemists . 56 57 58 Even in such ‘‘ordinary’’ chemistry, however, the detailed reaction 59 60 path may involve geometrical isomers of acetylene, such as vinylidene, a

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1 2 3 still evanescent species apparently resisting definite experimental 4 5 6 evidence. Furthermore, acetylene is present on Earth and in various other 7 8 planetary and also in stellar atmospheres, as well as in the interstellar 9 10 11 medium. As such, it is also a key species in astrochemistry. However, 12 13 related reaction mechanisms can often hardly be unravelled by textbook 14 15 16 knowledgeFor in organic Peer chemistry Review given the most Only specific experimental 17 18 conditions ruling astrochemistry. Acetylene chemistry is thus far from 19 20 21 mastered. Figure 1 presents previously unpublished spectra from the 22 23 Atmospheric Chemistry Experiment (ACE) mission demonstrating the 24 25 26 presence of acetylene in the Earth atmosphere. 27 28 29 30 31 Insert figure 1 32 33 34 35 36 37 38 Pure acetylene is a colourless, highly flammable gas with an 39 40 41 agreeable ethereal (ether-like) odour but the odour of the commercial purity 42 43 grade is distinctively garlic-like. 44 45 46 Reference to acetylene as a single species is misleading since for the 47 48 symmetric isotopologues, including 12 C H , there are two nuclear spin 49 2 2 50 51 isomers, ortho and para that seem not to interconvert easily, if they can 52 53 ever be forced to do so one day. One should therefore rather mention two 54 55 56 independent, coexisting acetylene molecules, each long lived and with 57 58 close but distinct thermodynamical properties, possibly specific chemistry 59 60 and, who knows, different smells? The lack of the expected 1:3, para :ortho

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1 2 3 intensity alternation in the ν fundamental vibration-rotation band in 4 3 5 12 6 C2H2 observed in the spectrum of figure 2, at specific J-values is typically 7 8 9 the observation that ‘‘spin-diggers’’ are searching for. It turns out, 10 11 however, that this peculiar observation is rather to be attributed to a 12 13 14 succession of emission-absorption schemes, thus not requiring any spin 15 16 conversionFor process, Peer as correctly Reviewinterpreted at the Onlytime. 17 18 19 20 21 Insert figure 2 22 23 24 25 26 27 28 29 30 31 Because, acetylene is important and stable, it is a very well known 32 33 34 chemical object, with numerous well documented properties in organic and 35 36 physical chemistry. Because acetylene is light and simple, it is an ideal 37 38 39 target to produce high quality spectroscopic data and elaborate quantum 40 41 models. Furthermore, with 7 vibrational degrees of freedom including two 42 43 44 doubly degenerate ones, acetylene supports complex intramolecular 45 46 mechanisms of direct relevance to the understanding of larger species. 47 48 49 Acetylene thus appears as a prototype vehicle to unravel macroscopic 50 51 properties at the microscopic level, i.e. to melt its Dr Jekyll and Mr Hyde 52 53 54 natures that we just illustrated. 55 56 57 58 59 Indeed, acetylene became over the years a privileged ground to 60 build theoretical concepts and develop very high-performance

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1 2 3 instrumental approaches, resulting in significant advances. At the same 4 5 6 time, the ever increasing amount and quality of data available kept 7 8 stimulating ever more powerful developments in a sort of catalytic process, 9 10 11 also feeding each time a giant virtual database. The set of high resolution 12 13 spectroscopy (HiReS) fingerprints on ground state acetylene presently 14 15 16 available Forin the literature Peer is probably Review one of the largest Only in all spectroscopy, 17 18 amounting to several ten of thousands vibration-rotation line energies and 19 20 21 very many intensities and broadening coefficients, and covering a very 22 23 extended excitation range. This data set is of primary importance to a 24 25 26 number of topics more traditionally connected to HiReS, including space 27 28 observation and metrology. 29 30 31 32 33 Ground state (GS) acetylene thus generated strong emulation, 34 35 36 fruitful collaboration and competition, and became over the years one of 37 38 the favourite target species of a number of research groups all over the 39 40 41 world, such as those headed by, in alphabetic order, Profs/Drs G. Blanquet 42 43 (FUNDP, Namur), A. Campargue (UJF Grenoble, France), F.F. Crim (U 44 45 46 Madison, USA), G. Di Lonardo and L. Fusina (Università di Bologna, 47 48 Italy), R.W. Field (MIT, USA), L. Halonen (U Helsinki, Finland), W.J. 49 50 51 Lafferty (NIST, USA), I.M. Mills (Reading, UK), B.J. Orr (McQuarrie, 52 53 Sydney/Australia), V. Perevalov (Tomsk, USSR), J. Plivà (Penn state U., 54 55 56 USA), K.N. Rao (Ohio State U., USA) and our group in Brussels, in 57 58 particular. Several hundreds of papers were published down the years, 59 60 including a number of reviews [8, 3, 9], giving birth to the ‘‘acetylene saga’’

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1 2 3 as the present paper is entitled. The reader is referred to these reviews for 4 5 6 a more exhaustive survey of the literature. In the present paper, only 7 8 some areas will be highlighted, from selected references corresponding to 9 10 11 matters in which the Brussels group has been more active. Our input was 12 13 actually initiated by the late Dr. Alec Douglas, from NRCC, Ottawa, who 14 15 16 provided For in the mid-seventies Peer Review Prof. Reg. Colin fromOnly ULB with original 17 18 spectroscopic plates recorded by Mr. Franz Alberti in the UV and far UV 19 20 21 on the high-performance Ottawa vacuum spectrograph. These data, 22 23 analyzed in collaboration with Prof. Ingvar Kopp, at the time at the 24 25 26 Physics Institute in Stockholm, brought information on Rydberg states 27 28 and Renner-Teller effects in various acetylene isotopologues [10, 11]. 29 30 31 Later, new plates reached Brussels through the same connection, which 32 33 were this time of primary interest to Dr. Jim Watson, from Ottawa. He 34 35 36 was the one to unravel from these spectroscopic data several remaining 37 38 % % 39 issues around the very peculiar A− X electronic transition [12-14], later 40 41 extended to additional isotopologues [15-19]. This study indirectly 42 43 44 highlighted perturbations in the bending vibrational ladder of states in GS 45 46 acetylene, isotopologue-specific [20-23]. These features in turn motivated 47 48 49 to a very large extent our present activity. 50 51 52 53 54 The present contribution thus focuses on the ULB contribution to the 55 56 acetylene saga, to respond precisely to the invitation. It is split into two 57 58 59 main sections, concerning vibrational clustering ---section 2- and the global 60 approach ---section 3-, each with several subsections. Various notations and

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1 2 3 conventions are recalled in subsections 2A and 3A. Final words are 4 5 6 provided in section 4. Various isotopologues will be considered in this 7 8 review, with the term isotopologue referring to a molecular entity that 9 10 12 12 11 differs only in isotopic composition, such as C2H2 and C2D2. It is 12 13 14 interesting to notice that isotopomers also exist in acetylene, i.e. isomers 15 16 having theFor same Peer number of eachReview isotopic atom Only but differing in their 17 18 19 positions, such as H 12 C13 CD and D 12 C13 CH. 20 21 22 23 24 25 26 27 28 29 2. Vibrational clustering 30 31 32 33 34 A. Normal modes, notations and conventions 35 36 37 Acetylene possesses 7 vibrational degrees of freedom giving rise to 5 38 39 normal modes of vibration represented in figure 3, for 12 C H . The 40 2 2 41 42 conventional labelling is thus ν1 and ν3 for the symmetric and asymmetric 43 44 CH stretches, respectively, ν for the CC stretching vibration, and ν 45 2 4 46

47 (trans ) and ν5 ( cis ) for the degenerate bends. Their symmetry is indicated 48 49 in figure 3, with the u/g label only valid for centro-symmetric 50 51 52 isotopologues. The same numbering is used for all isotopologues in the 53 54 literaturee. 55 56 57 58 59 Insert figure 3 60

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1 2 3 In the text, we shall label the vibrational states, using 4 5 6 7 8 l4 l5 9 (((vv1 2 v 3 v 4 v 5 ))) or (((vvvvv12345, ll 45 ))) or (((vvvv1234 v 5 ))) or (((vvvvv1 2 3 4 5 , k ))) 10 11 12 (2.1) 13 14 15 16 For Peer Review Only 17 with vi the vibrational quantum number for mode i, lb the bending 18 19 vibrational angular momentum quantum number and k = l +l . On some 20 4 5 21 22 occasions, commas will separate the vi’s in the labels. These different 23 24 notations are those in the various literature references from which the 25 26 27 figures selected for the present review originate. We shall on the other 28 29 hand strictly follow here the convention 30 31 32 33 34 Kkl≡=+≥ l0 andl ≥ 0 ifk = 0 (2.2) 35 4 5 4 36 37 38 39 Transitions will be labelled using various notations, as in the 40 41 42 literature. We shall sometimes detail the upper and then lower vibrational 43 44 quantum numbers of the states involved, such as, e.g. (01011)-(00000) or 45 46 1 −1 0 0 47 (0101 1 )-(0000 0 ). We shall also use ν2+ν4+ν5-GS, with GS for ground 48 49 50 state, or simply ν2+ν4+ν5 whenever the lower state is the ground state. 51 52 Thus, as an example, the band ν5-ν4 refers to the transition between the 53 54 1 0 0 1 55 (0001 0 ) lower and (0000 1 ) upper states. 56 57 58 59 % 0 60 The vibrational frequencies in figure 3 correspond to ωi values as

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1 2 3 determined from the following expansion: 4 5 6 7 8 9 Gvl0( , ) =++ω% 0 v xvv 0 gll + yvvv0 + yvll 0 + ∑∑ii ijij ∑ llbbb b ' ' ∑ ijmijm ∑ illibbb b ' ' 10 i=1,5 ij ≤ bb ≤= ' 4,5 ijm ≤≤ ibb, ≤ ' 11 (2.3) 12 zvvvv+ zvvll + z llll ∑ijmnijmn ∑ ijllb b ' ijbb' ∑ llllbbbbbb' b '' b ''' '''''' 13 ijmn≤≤≤ ijbb ≤≤,' bbbb ≤≤≤ '''''' 14 15 16 For Peer Review Only 17 18 Most of the terms in such expressions are not relevant for the remainder 19 20 21 of this paper. They are all defined in [28] and in the literature referred to 22 23 in that paper. Note that the gl l constants in Eq. (2.3), also used in our 24 b b ' 25 26 initial reports (see [12-14]), strictly correspond to x l l in [28]. As a rule, 27 t t ' 28 29 only the information on the theoretical models relevant to the discussion 30 31 32 will be provided in the text and the reader will be referred to the literature 33 34 for the full description of the vibration-rotation Hamiltonian [8]. The 35 36 37 values for the additional vibrational constants appearing in Eq.(2.3) are 38 39 listed in the references mentioned in Table 1, some of which are gathered 40 41 42 in [3]. 43 44 45 46 47 We need to mention the vibrational l-type resonance in this 48 49 introductory subsection, given by the following matrix element 50 51 52 53 54 1 ˆ m1 m m 2 55 llHl45 42,2 l 5±=4 rvlvl 454444()()()() ± + 2 vlvl 5555 ±+ 2  (2.4) 56 57 58 59 60 As an example, the combined role of the g45 and r 45 constants,

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1 2 3 respectively defined in eqs. (2.3) and (2.4) is demonstrated in figure 4. 4 5 6 7 8 Insert figure 4 9 10 11 12 13 As far as conventions are concerned, it is also worth pointing out 14 15 16 that anharmonicFor resonancesPeer willReview be referred toOnly in the text using the 17 18 corresponding coupling scheme, ij/kl or i/jkl or ii/jj, related to the coupling 19 20

21 parameters Kij/kl or Ki/jkl or Kii/jj , meaning that the interacting vibrational 22 23 states are such that v = v =± 1 and, simultaneously, v = v = m1 ; or 24 i j k l 25 26 v = ± 1 and v = v = v = m1 ; or v = ± 2 and v = m2 , respectively. 27 i j k l i j 28 29 The anharmonic resonances relevant for acetylene include e.g. 14/35, 3/245 30 31 32 and 44/55, as discussed in the forthcoming subsections. 33 34 As an example, the matrix element related to the first of these couplings is 35 36 37 38 1 39 l l % l ±1 l 1 2 vvvvvHvv,,,,4 5 ,−+− 1, v 1,( v 1),(4 v −=− 1)5 m 1 K ( v + 1)( vvlvlm )( ± ) 40 12345 12 3 4 58 3/2453[] 24455 41 (2.5) 42 43 with the content of the related coupling constants unravelled e.g. in [29]. 44 45 46 In agreement with a previous statement, the other relevant resonance 47 48 matrix elements as well as higher order terms and additional constants 49 50 51 required in the model are not further defined here and can be found e.g. in 52 53 [28] and in the literature referred to in that paper. All constants and 54 55 56 spectroscopic term values in the text will be given in cm −1 , independently 57 58 59 of the label used. 60

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1 2 3 The 5 normal modes of vibration, accounting for vibrational 4 5 6 frequencies and anharmonicities, generate numerous states with 7 8 increasing vibrational excitation. The integrated number of states in 12 C H 9 2 2 10 11 is shown in figure 5 (top), counting each substate with k ≠ 0 for 2 in the 12 13 14 sum. A seventh order polynomial expansion was adjusted to the top curve 15 16 in figure For 5, whose Peer coefficients Review are listed in the Only figure. The resulting 17 18 19 vibrational density can be easily inferred from this expression. It is 20 21 extrapolated to higher energy and presented in figure 5 (bottom). The 22 23 24 energy origin is set at the bottom of the potential hypersurface in figure 5 25 26 (top) and at the ground vibrational state in figure 5 (bottom), the 27 28 29 difference between the two origins corresponding to the zero point energy 30 31 (ZPE ~ 5672 cm −1 in 12 C H ). Some oscillation, amounting to a few tens of 32 2 2 33 34 states, was demonstrated by Zhilinskii to occur in the integrated number 35 36 of states [30]. It will be further referred to, later in the text. 37 38 39 40 41 Insert figure 5 42 43 44 45 46 47 48 49 50 51 B. The stretching states 52 53 54 The CH harmonic stretching frequencies in the various 55 56 %0 % 0 57 isotopologues scale in such a way that ω1 > ω 3 , with the first, symmetric 58 59 CH stretch frequency gaining importance from the contribution of the CC 60

stretch force constant ( f22 ), in a simple valence force field approximation ( f12

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1 2 3 = 0). The corresponding pure CH stretch states can be labelled either 4 5 6 using the normal mode picture, as defined in eq.(2.1), or using the local 7 8 mode notation 9 10 11 12 13 m, n =1  Ψ Ψ±Ψ Ψ  (2.6) 14 [ ]± 2 m n n m  15 16 For Peer Review Only 17 18 19 with m, n the number of quanta in each CH bond (see e.g . [31]). The local 20 21 22 mode character of the CH bond is known to increase upon vibrational 23 24 excitation and is often used to label the CH stretching states at higher 25 26 27 energy. It leads to interesting behaviour and was exploited in the 28 29 12 asymmetric C2HD species to proceed to bond selected photodissociation 30 31 32 [32]. 33 34 35 36 37 The intensity of vibrational CH overtone transitions, nνs, thus 38 39 between ground (GS) and vs = n states, have their transition moment given 40 41 42 by the following matrix element 43 44 45 46 2 2 47 Ψvib Ψ vib = R (2.7) 48 vns = α GS n ν s 49 50 51 52 53 in which the induced electric dipole moment operator can be developed as 54 55 a function of the undimensional normal vibrational coordinates q 56 s 57 58 59 60

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1 2 3 ∂  ∂2  4 =+e αq +1 α q q + ... (2.8) 5 α α ∑s2 ∑   s s ' s∂qs s≤ s '  ∂ q s ∂ q s '  6 e e 7 8 9 10 11 Thus, the well known pure vibrational matrix elements, see e.g. Table 7 in 12 13 [8], lead to the vs = n selection rule, with the relative intensity in an 14 15 16 overtone seriesFor controlled Peer by the Review following matrix Onlyelement and coefficient, 17 18 19 squared: 20 21 22

23 n 24 ∂ α  vib n vib   Ψvn= q s Ψ GS (2.9) 25 ∂q n s 26 s  e 27 28 29 30 31 Experimentally searching for successive overtone transitions 32 33 therefore requires more and more instrumental sensitivity since the 34 35 n 36 ∂  electric dipole numerical factor α  decreases with n. As shown in 37 ∂q n 38 s  e 39 40 figure 6 (top) for 12 C HD, this decrease is over one order of magnitude for 41 2 42 43 each additional quantum in the overtone series, here for CH excitation. 44 45 46 47 48 49 50 Insert figure 6 51 52 53 54 55 56 57 58 In the transition moment one needs accounting for electric 59 60 anharmonicity, as just performed, but one can also account for the

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1 2 3 mechanical anharmonicity. Each wavefunction can be developed into a 4 5 6 0 weighted sum of harmonic contributions ( Ψv ) 7 s 8 9 10 11 Ψvib =c Ψ 0 (2.10) 12 vns=∑ mvm s = 13 m 14 15 16 For Peer Review Only 17 18 As a result, various contributions can be distinguished in the 19 20 transition moment, depending on the order n of the electric dipole moment 21 22 23 derivative contribution, as defined in Eq.(2.9). These contributions were 24 25 12 unravelled by Liévin for C2HD stretching overtones, matching ab initio 26 27 28 results and experimental transition moments. The role and sign of the 29 30 contribution of each order m to two (n = 3 and 4) of the observed overtone 31 32 33 transitions is shown in figure 6 (bottom). The amount and signs of the 34 35 various contributions appear to be different for different overtones bands 36 37 38 (here 3 ν1 and 4 ν1) and actually, as shown in the referenced paper, also 39 40 between CH and CD excitation bands. 41 42 43 44 45 The intensity information in figure 6 is extracted from spectra 46 47 48 recorded at high resolution at ULB using Fourier transform spectroscopy 49 50 (FTS). Vibration-rotation bands were observed up to the visible range, 51 52 53 hence the denomination of ‘‘coloured’’ vibrations. The quality of the data is 54 55 illustrated in figure 7, which shows absorption to the 4th overtone of the 56

57 12 58 CH excitation (5 CH) in C2H2. For this recording, acetylene pressure was 59 60 250 mbar, absorption pathlength was 49.2m using a White type multipass

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1 2 3 cell, and 6900 scans recorded during some 96 hours were co-added. 4 5 6 7 8 Insert figure 7 9 10 11 12 13 Laser based experiments allow sensitivity to be boosted (see e.g. figure 68 14 15 16 (p.254) inFor [8]). The Peer highest energy Review CH overtone transitionOnly reported in the 17 18 −1 th 19 literature lies in the blue range, close to 24000 cm ! This 7 overtone ( n = 20 21 8) was recorded using intracavity optoacoustic laser spectroscopy [36] and, 22 23 24 more recently by the Grenoble group using the newly developed ‘‘cavity 25 26 enhanced spectroscopy’’ [37]. Numerous other acetylene spectra 27 28 29 demonstrating even higher sensitivity were recorded, as further discussed 30 31 in section 2D. 32 33 34 35 36 As a final word to this subsection, one can focus on the so-called x-K 37 38 39 relations, here applied to the CH stretchings. According to the local mode 40 41 picture, the various basic vibrational parameters associated to the CH 42 43 44 stretchings in the symmetric isotopologues are related through these x-K 45 46 relations and thus expected to fulfil the following approximate rule (see 47 48 49 e.g . [38]): 50 51 52

53 1 1 54 xx11= 33 =4 x 13 = 4 K 11/33 (2.11) 55 56 57 58 59 with the 11/33 anharmonic resonance connecting CH stretching states, 60

those with v1 =− v 3 =± 2 . Acetylene data allow this relation to be

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1 2 3 successfully checked, as demonstrated in table 1. These relations are 4 5 12 13 12 6 actually also well fulfilled in C CH 2 [39], but not in C2HD [27] because 7 8 of the decoupling of the CH and CD vibrations. As a result of the 11/33 9 10 11 resonance, the zero order wavefunctions are mixed up and severe labelling 12 13 problems may occur. These are often encountered in spectroscopy and will 14 15 16 be highlightedFor on Peer several other Review occasions in this Only review. It should be 17 18 noticed, however, that mixings between CH wavefunctions due to 11/33 19 20 12 21 are very limited, if not virtually non-existent in the case of C2D2, due to 22 23 the large offset between the ν and ν fundamental frequencies (see figure 24 1 3 25 26 2). 27 28 29 30 31 Insert table 1 32 33 34 35 36 C. The bending states 37 38 39 The normal mode bending motions can be understood as 40 41 symmetrically and antisymmetrically coordinated variations of the two 42 43 44 HCC angles. A look at the numbers in figure 3 shows that the two related 45 46 % 0 % 0 12 harmonic frequencies, ω4 and ω5 are almost degenerate in C2D2, as 47 48 12 49 further discussed below, while they are far apart in C2HD. In the latter 50 51 case ν and ν actually appear to be almost localised CCD and CCH bends, 52 4 5 53 54 respectively. As a rule the trans-bending frequency is lower than the cis- 55 56 bending one. A closer look at the anharmonicity corrections shows that the 57 58

59 series of trans - and cis -bending states do cross at high excitation, since x44 60

(>0) and x55 (<0) have opposite signs (see [40] for the latest values in

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1 2 3 12 C H ). This crossing occurs around v = 23 in 12 C H . Since a Darling 4 2 2 b 2 2 5 6 Dennison type resonance (44/55) occurs among the bends, with related 7 8 matrix elements accounting for l values, the mixing is maximal at that 9 10 11 stage and the labelling most problematic. It would be interesting to figure 12 13 out the structural evolution along this series of bending overtones. This 14 15 16 problem For could possiblyPeer be Review related to the Only acetylene-vinylidene 17 18 isomerization process already mentioned in the introduction. Along this 19 20 21 line of research, the stimulated emission pumping (SEP) and dispersed 22 23 laser induced fluorescence (DLIF) experimental techniques used by Field 24 25 26 (MIT) are most efficient ( e.g. [41]). Both use a two-step absorption scheme, 27 28 going through the first excited electronic states as an intermediate. 29 30 %%% 31 Thanks to the trans -geometry of this A state and the role of Franck 32 33 34 Condon factors, transitions towards highly excited bent states in the 35 36 ground electronic state are favoured and observed up to high excitation, as 37 38 39 will be exemplified in the next subsection. These investigations, however, 40 41 did apparently not bring definite information on the isomerization process, 42 43 44 yet. 45 46 47 48 49 The two bend frequencies are quite close and the related ν5-ν4 50 51 difference band was recorded in the far-infrared range using FTS by Johns 52

53 12 54 (NRC/Ottawa) and analysed in Bologna and Brussels for C2H2 [22, 42, 40] 55 56 and for 12 C D [23]. This closeness was examined by Zhilinskii and 57 2 2 58 59 Gaspard in terms of the related vibrational density and dynamics, 60 respectively [43]. The equilibrium vibrational frequencies in three

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1 2 3 symmetric isotopologues, reproduced from this reference, are provided in 4 5 6 Table 2, including the stretching vibrations for completeness. This Table 7 8 also lists the associated periods, calculated according to the relation 9 10 11 12 13 2πh 14 Ti = (2.12) 15 ωi 16 For Peer Review Only 17 18 19 20 with h = 5308.84 fs cm −1 . The analysis demonstrates that the bends, with 21 22 23 the slowest periodic orbits, have a major ‘‘bottleneck’’ contribution to the 24 25 vibrational dynamics in acetylene. In 12 C D , in particular, the two bends 26 2 2 27 −1 28 are separated by less than 30 cm and recurrence times are T = 65, 130 29 30 and 190 fs, with 31 32 33 34 35 T≈ nT ≈ nT and n, n = 1,1; 2,2;3,3 (2.13) 36 44 55 ( 4 5 ) ( ) ( ) ( ) 37 38 39 40 41 Insert Table 2 42 43 44 45 46 The major role of the bends in the internal vibrational dynamics was 47 48 demonstrated by Gaspard using vibrograms as presented in figure 8 for 49

50 12 51 C2D2. In these graphs, the energy (abscise), defined from the bottom of 52 53 the potential well, runs from −4000 to +9000 cm −1 , from left to right. The 54 55 56 integrated number of states is Fourier transformed over wide but 57 58 restricted energy windows, defining the time scale (see [43] for further 59 60 details). Translated to the energy picture, these time recurrences mean

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1 2 3 that all bend states, with their numerous l-components, accumulate in the 4 5 6 integrated number of states around multiples of the mean bend frequency, 7 8 i.e. about 500 cm −1 in 12 C D . This phenomenon actually leads to a slight 9 2 2 10 11 variation of the number of states at related regular energy spacing in the 12 13 14 integrated count compared to the regular fitted curve and, hence to small 15 16 oscillationsFor in this Peerquantity, as Reviewalready mentioned Only and presented in figure 17 18 19 8. In addition, because of this accidental near-degeneracy between the 20 12 21 bends, the Darling Dennison mixing is very efficient in C2D2 right from 22 23 24 the start of the bending vibrational ladder [23]. 25 26 27 28 29 Insert figure 8 30 31 32 33 34 35 36 37 38 39 D. The stretch-bend states 40 41 In addition to the 11/33 and 44/55 Darling Dennison resonances, 42 43 44 several other anharmonic coupling schemes occur in acetylene. 45 46 Resonances can be spotted from spectra using the concept of so-called 47 48 49 bright and dark states, or rather bright and dark transitions leading to 50 51 intensity borrowing. It is demonstrated in the sequence of schemes 52 53 54 gathered in Eq. (2.14) and in figure 9. All labels are explained in this 55 56 figure. 57 58 59 60

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1 2 3 2 2 2 4 0 0 0 2 0 ΨB GS ≠ 0 Ψ+ ≡()a ΨB +Ψ b D GS aΨB GS 5 → = (2.14) 2 2 2 6 Ψ0 GS = 0 0 0 b2Ψ 0 GS 7 D Ψ− ≡()b ΨB − a Ψ D GS B 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 Insert figure 9 18 19 20 21 22 23 24 25 Thus, intensity borrowing occurs, more or less efficiently depending 26 27 on the coupling and relative zero order energy schemes. This is illustrated 28

29 12 30 in figure 10, with the 1/255 resonance in C2HD. All pairs of states 31 32 fulfilling the 1/255 coupling schemes interact, with intensity borrowing 33 34 35 from the zero order bright to dark transitions. The relevant pairs of states 36 37 can actually be systematically predicted from the full set of energies, as 38 39 40 shown in figure 11. In this figure, the energy difference (E) between pairs 41 42 of states interacting through the selected resonance, here 1/255, is plotted 43 44 45 as a function of the state energy. Only one of the two interacting states is 46 47 identified on the figure, for clarity, using v v v v v . All those pairs with 48 1 2 3 4 5 49 50 values of E small enough and with one of the corresponding transitions 51 52 bright enough, can be expected to lead to intensity borrowing, as was 53 54 55 exemplified in figure 10, in a selected energy range. 56 57 58 59 60 Insert figures 10 and 11

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1 2 3 4 5 6 FT spectra, recorded over very broad ranges, such as those 7 8 displayed in figure 10, played a crucial role in highlighting anharmonic 9 10 11 resonances in acetylene. Additional resonances are usually accounted for 12 13 in the final vibrational fits, to improve the final residuals, provided they 14 15 16 do not affectFor the polyad Peer or cluster Review structure that willOnly be defined in section 17 18 3. Most of the acetylene FT spectra were recorded at ULB or in Bologna. 19 20 21 The ‘‘intracavity laser absorption spectroscopy (ICLAS)’’ data from 22 23 Grenoble ( e.g . [44-50], recently based on VeCSEL lasers [50], as well as 24 25 26 other laser-based methods such as the optoacoustic technique ( e.g. [51, 27 28 52]), NIR diode laser investigations ( e.g. [53]), and Raman-type 29 30 31 investigations ( e.g . [54, 55]) also provided a great deal of information on 32 33 the stretch-bend states up to high vibrational excitation. 34 35 36 37 38 In addition to relative intensities, absolute intensity measurements 39 40 41 provide even more refined insight into intramolecular coupling schemes, 42 43 as demonstrated in [56]. Furthermore, absolute intensities are of course 44 45 46 closely associated to the quantitative exploitation of spectral fingerprints 47 48 in the atmospheric and astrophysical contexts ( e.g. [40]). There again FT 49 50 51 data proved to be most relevant, not only in the lower infrared region, but 52 53 also in the overtone range ( e.g. [57]). The comparison with the FT data in 54 55 56 the paper just referred to stimulated the development at ULB of so-called 57 58 2T-FT-ICLAS experiments [58]. This technique was recently demonstrated 59 60 to provide accuracy better than 10% on absolute intensity measurements

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1 2 3 in the overtone range [59]. Figure 12 highlights the power of the 2T-FT- 4 5 6 ICLAS instrumental combination, thus merging the sensitivity of 7 8 intracavity absorption in a Ti:Sa laser and the broad spectral coverage of 9 10 11 high resolution FTS. The efficiency of the set-up, first developed at low 12 13 spectral resolution in Madrid [60], was significantly increased by 14 15 16 designingFor and building Peer a home Review made Ti:Sa Only laser for this specific 17 18 experiment. In ICLAS, one injects the pump laser into the Ti:Sa cavity for 19 20

21 a definite time, defining the generation time, tg, during which the 22 23 intracavity absorption occurs. The longer t , the longer the effective 24 g 25

26 absorption path leff in the cavity, with 27 28 29 30

31 leff= tclL g / (2.15) 32 33 34 35 36 with c the speed of light, l and L the lengths of the intracavity absorption 37 38 39 cell and of the Ti:Sa laser cavity, respectively. An interesting instrumental 40 41 challenge in the adaptation of ICLAS to FTS replacing spectrographs as in 42 43 44 the usual literature was to synchronize the pulsed character of the 45 46 technique to the FT sampling procedure. The ULB set-up is described in 47 48 49 [58], and applied in [61, 58, 27, 62, 59]. The technique was also developed 50 51 by other groups ( e.g. [63-65]). 52 53 54 55 56 Insert figure 12 57 58 59 60 As a final picture for the role of anharmonic resonances in the

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1 2 3 bright/dark issue, figure 13 reproduces a DLIF spectrum recorded at MIT 4 5 6 under jet-cooled conditions and interpreted at ULB [66]. In the zero order 7 8 picture, a simple two-line spectrum is expected. The eigenspectrum is, 9 10 11 however, composed of numerous peaks. All these additional features 12 13 happen to originate from an impressive fractionation of the zero order 14 15 16 bright transitionFor through Peer many Review intensity borrowing Only mechanisms (so-called 17 18 tier model). The simulation in figure 12 could actually be performed 19 20 21 almost independently of the observation, using the so-called cluster 22 23 picture developed in the next section. 24 25 26 27 28 Insert figure 13 29 30 31 32 33 34 35 36 37 38 E. Emergence of new constants of the motion 39 40 41 A key feature emerging from the numerous investigations that were 42 43 so far highlighted is that the ratios of the vibrational frequencies one to 44 45 46 another are close to being integers. These ratios in energy space, mirrored 47 48 in time space, are obviously isotopologue-dependent. Nevertheless, 49 50 51 harmonic frequencies are close enough in all three symmetric 52 53 isotopologues 12 C H 13 C H and 12 C13 CH , and one can check that, for all 54 2 2, 2 2 2 55 56 three species 57 58 59 60 1% 1 % 1 % 1 % 1 % 5ν1≈ 3 ν 2 ≈ 5 ν 3 ≈ 1 ν 4 ≈ 1 ν 5 (2.16)

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1 2 3 4 5 6 Thanks to this relationship, Kelman [67] could introduce an 7 8 approximate constant of the motion, N such that 9 r 10 11 12 13 N= v + v + vvv ++ (2.17) 14 r 51 3 2 5 345 15 16 For Peer Review Only 17 18 19 thus directly associated to the ratio of the time periods. All (vv1, 2 , v 3 , v 4 , v 5 ) 20 21 22 states sharing the same Nr value, either + or --- when k = 0, either u or g for 23 24 the symmetric isotopologues, define a vibrational polyad. As pointed out 25 26 27 by Zhilinskii [43], one can define a mean vibrational frequency 28 29 30 31 %1 %%%%% 1 1 2 2 32 νm ean =( 5 ννννν1 + 3 2 + 5 3 + 1 4 + 1 5 ) /7 (2.18) 33 34 35 36 37 whose value is close to 670 cm −1 in 12 C H . One can calculate in this 38 2 2 39 40 isotopologue all (vv1, 2 , v 3 , v 4 , v 5 ) vibrational state energies within a polyad 41 42 43 using the full set of vibrational constants from [24], and reduce them using 44 45 a weighted procedure accounting for the double degeneracy of all states 46 47 48 with k > 0, to a single average energy, a sort of ‘‘centre of gravity’’ of the 49 50 polyad ( ν%av (N ) ). These reduced energy values obey the simple relation 51 r 52 53 (2.19) 54 55 56 57 58 ν%av (N )= 672.95 N − 0.455 N 2 (2.19) 59 r r r 60

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1 2 3 in which N thus plays the role of a vibrational quantum number, with a 4 r 5 6 vibrational frequency (672.95 cm −1 ) quasi-identical to the mean vibrational 7 8 −1 9 frequency (670.0 cm ) defined in (2.18). As also discussed by Kelman [67], 10 11 Ns defines a further invariant of the Hamiltonian, with 12 13 14 15 16 For Peer Review Only Ns = v1 + v 2 + v 3 (2.20) 17 18 19 20 21 As it turns out, the { N ,N ,k} set of numbers, also accounting for +/- 22 s r 23 24 and u/g symmetries whenever relevant, unequivocally characterizes each 25 26 of the vibrational polyads. The remarkable feature is that all vibrational 27 28 29 states, most likely up to the top of visible energy range if not at even 30 31 higher energies, fit this model, hence the labelling of superpolyad or 32 33 34 cluster assessed at some stage by the MIT and ULB groups, respectively, 35 36 in the literature. As an example, figure 14 depicts the { N ,N ,k} = {2,10,0} 37 s r 38 12 39 cluster in C2H2. 40 41 42 43 44 Insert figure 14 45 46 47 48 49 This model was used to factorize the acetylene vibrational 50 51 Hamiltonian, thus into superpolyads or clusters, defining a block- 52 53 54 diagonalised matrix image of the molecule (MIME). The many known 55 56 vibrational energies were fitted to that MIME, in isotopologue-specific 57 58 12 12 13 12 12 13 59 procedures, for C2H2 [24], C2D2 [25], C2H2 [26], C2HD [27], and C CH 2 60 [39, 28], each time generating an extended set of vibrational constants.

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1 2 3 These parameters are fully effective. Typically, they allow the observed 4 5 6 vibrational energies to be matched within a few cm −1 , up to the bottom of 7 8 9 the visible range. Figure 15 details the internal structure of the many 10 12 11 vibrational energy states in C2H2 resulting from this effective but 12 13 %av 14 physically well-defined MIME, with respect to ν (N r ) and the similarly 15 16 %Forav Peer Review Only 17 defined ν (Nr , N s ) . A remarkable ordering emerges from this picture, 18 19 quite unexpected if one remembers the large integrated number of 20 21 22 vibrational states demonstrated in figure 5. It must also be emphasized 23 24 that the width of the various clusters becomes very large with increasing 25 26 27 energy, soon much larger than the energy separation between the ‘‘centres 28 29 of gravity’’ of the clusters. 30 31 32 33 34 Insert figure 15 35 36 37 38 39 40 41 42 43 44 3. Global picture. 45 46 47 48 49 Now that a reasonably coherent picture has emerged from the 50 51 52 investigation of the vibrational degrees of freedom, one can address the 53 54 rotational degrees of freedom. In some respects, these were already 55 56

57 considered, when including the role of the angular momenta l4 and l5 in the 58 59 MIME. The full inclusion of rotation in the MIME defines the so-called 60 global picture. Actually, rotational degrees of freedom were already

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1 2 3 completely and successfully included for various acetylene isotopologues, 4 5 6 including several thousands of vibration-rotation lines [15, 22, 42, 69, 70, 7 8 9 40]. However, only bend states, up to v = 4 , were considered in these 10 ∑ b vb 11 12 13 procedures. Extension towards high energy stretch-bend states was 14 15 attempted for 12 C H by Perevalov and coworkers, but with limited success 16 For2 Peer2 Review Only 17 18 [71]. ‘‘Real’’ global procedures, thus over a larger range of vibrational 19 20 excitations and including rotation, were published only for triatomic 21 22 23 species in the literature (see refs in [28]). One should also mention 24 25 attempts for a five-atom species, methane, 12 CH [72]. 26 4 27 28 29 30 The challenge we now face is thus building a global MIME for a 31 32 33 molecule larger than triatomic, acetylene, including rotation and valid 34 35 over a vibrational excitation range as extended as possible. Including 36 37 38 rotation obviously means accounting for, and reproducing all existing high 39 40 resolution data, at their full accuracy. 41 42 43 44 45 46 47 48 A. Rotation, notations and conventions 49 50 Several hundreds of publications in the literature since 1936 were 51 52 53 devoted to HiReS fingerprints of acetylene in the ground electronic state, 54 55 as reviewed in [8, 3, 9]. Their results, which formed the basis for the 56 57 58 vibrational MIME detailed in the previous section, of course include 59 60 detailed information on the so far undiscussed rotational structure. This

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1 2 3 structure was already highlighted in previous figures and also in figure 4 5 12 13 6 16, this time for C CH 2. To illustrate the richness of data such as those 7 8 presented in figure 16, one should stress that Di Lonardo and coworkers 9 10 11 identified more than 70 bands in the full range covered in this figure, thus 12 13 −1 14 from 5700 to 10000 cm [73, 74], some still to be published [75]. 15 16 For Peer Review Only 17 18 19 Insert figure 16 20 21 22 23 24 25 26 The rotation energies are given by 27 28 29 30 2 31 FJB()= JJ()() +−− 1 kD2  JJ +−+ 1 k 2  ... (3.1) 32 vvvvv1 2 3 4 5   vvvvv1 2 3 4 5  33 34 35 36

37 with, for the GS, B 00000 (or B 0) the principal rotational constant related to 38 39 the principal moment of inertia, and D (or D ) the lowest order 40 00000 0 41 42 distortion constant. As an example, the vibrational dependence of the 43 44 principal rotational constants is accounted for in the following way 45 46 47 48 49 BB=−+αγγ0 v 0 vv + ll + ε vvv + ε vll (3.2) 50 v0 ∑∑∑ ii ijij llbbb b ' ' ∑ ijmijm ∑ illibbb b ' ' 51 i ij≤ bb ≤' ijm ≤≤ ibb, ≤ ' 52 53 54 55 The latest values of B are listed for all studied isotopologues in table 3. 56 0 57 58 59 60 Insert table 3

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1 2 3 4 5 6 It is well known that rotation-vibration wavefunctions can be 7 8 symmetrized into e/f components, as defined in [80]: 9 10 11 12 13 1 14 vvlJe,,,,= vvlJ ,,, + vv ,,, − lJ  sbb sbb sbb  15 2 (3.3) 16 For Peer1 Review Only 17 vvlJf vvlJ vv lJ  sbb,,,,= sbb ,,, − sbb ,,, −  18 2 19 20 21 22 23 This separation is achieved using the Wang procedure summarized in 24 25 figure 17, here applied to the (00010) vibrational state selected as an 26 27 28 example. The 2-fold degeneracy of all rotational states within a vibrational 29 30 state with k ≥ 1 is lifted when accounting for the so-called rotational l-type 31 32 33 resonance interaction matrix element 34 35 36 37 1 1 1 38 ˆ 1 m 2 2 2 lHl±=24 qvlvl()() ±+ 211112  JJ()() +−± kk  JJ()()() +−±± k k  39 b b bbbbb    40 (3.4) 41 42 43 44 45 The expert reader will notice that the convention adopted in Eq. (3.3), that 46 47 leads to negative l-doubling parameters q and q , is different from most of 48 4 5 49 50 our own previous literature inputs but the most recent ones. This change 51 52 is to cope with the vibration-rotation matrix elements used in the 53 54 55 computer package building the global model discussed in section 3C. 56 57 58 59 60 The resulting rotational structure of selected transition-types is detailed

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1 2 3 in figure 18. It includes the role of nuclear spin statistics adapted to 12 C H , 4 2 2 5 6 to be later discussed. 7 8 9 10 11 Insert figures 17 and 18 12 13 14 15 16 For Peer Review Only 17 18 B. Including rotation in the MIME 19 20 21 Rotation can be included in the various vibrational interaction 22 23 schemes previously discussed, as exemplified in figure 19. 24 25 26 27 28 Insert figure 19 29 30 31 32 33 In this figure, the reduced rotational energy is plotted at the right, 34 35 36 as a function of J(J+1), as e.g. in [81, 28]. The value of J rather than 37 38 J(J+1) is indicated on the graphs for easier reading. This reduced energy 39 40 41 is defined as 42 43 44 45 2 46 EvJ(,)− BJJ()() +− 1 DJJ2 +−ν 1  % (3.5) 47 sel . 0  48 49 50 51 52 with the value of ν% selected to perform an adequate translation on the 53 54 energy axis and avoid dealing with large numbers and the value of B 55 sel . 56 57 selected to keep the dependency of the reduced energy of the states of 58 59 interest as horizontal as possible in the related graphs. If, for instance, the 60 rotational contribution from the GS state is subtracted from the energy, a

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1 2 3 horizontal line is expected for this state while a smooth variation from this 4 5 6 linear behaviour is expected to occur for the close vibrational states in 7 8 these reduced energy graphs, as observed in figure 19. 9 10 11 12 13 The energies in figure 19 result from the diagonalization of the 14 15 16 adequate For MIME, JPeer per J-value, Review built using the relatedOnly matrix elements, 17 18 such as appearing in eqs. (2.3), (2.4), (2.5), (3.1), (3.2) and (3.4). The 19 20 21 resulting matrix diagonalization leads to the eigenvalues presented in 22 23 figure 19, and also to the squared coefficients in the eigenvectors 24 25 26 associated to each of the zero order, basis states, detailed in figure 20 (see 27 28 [82] for further details). As illustrated in the latter graphs, a 1:1 mixing 29 30 12 + 31 occurs in C2H2 between these v3 = 1 and v2 = 1, v4 = 1, v 5 = 1, Σ states. As 32 33 34 a first result, the zero order bright ν3 band intensity is shared with the 35 36 zero order dark ν2+ν4+ν5 transition. As a second consequence, the zero 37

38 + 39 order forbidden k = 2, − Σ transition also emerges, now according to a 40 41 J-dependent mixing controlled by the rotational l-type resonance matrix 42 43 44 element detailed in Eq. (3.4). The latter effect is specifically highlighted in 45 46 figure 21. 47 48 49 50 51 Insert figures 20 and 21 52 53 54 55 56 Thus, a partial MIME can be built for this specific interaction 57 58 59 scheme, J value by J value, furthermore split into e and f states. Even 60 though the anharmonic resonance coupling mechanisms are J-

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1 2 3 independent (see eq. (2.5)), the rotational constants of the various 4 5 6 vibrational states within the same polyad are not identical, thus inducing 7 8 a variation with J of the energy separation between interacting levels, as 9 10 11 highlighted in the example just discussed. As a result, the amplitude of 12 13 the coupling effectively becomes J-dependent. This is a well-known 14 15 16 situation For which may Peer lead to dramaticReview effects on Only the relative band and 17 18 branch intensities, as e.g . discussed for the pure bends in 12 C H in [22]. 19 2 2 20 21 Another example of coupling is provided in figure 22. It highlights a 22 23 double avoided crossing affecting the (00300,00) zero order state in 24 25 12 13 26 C CH 2. 27 28 29 30 31 Insert figure 22 32 33 34 35 36 37 38 C. Global MIME 39 40 12 41 The strategy just highlighted for ν3/ν2+ν4+ν5 in C2H2 could be 42 43 44 applied to the full set of data available for this isotopologue. Each extra 45 46 datum brings another independent piece of relevant information, thus in 47 48 49 the end significantly improving the statistical quality of the global fit. On 50 51 the other hand, rotation-dependent interaction mechanisms show J- 52 53 54 dependence that will genuinely affect the coupling strength for increasing 55 56 J-values and, again, considering all rotation-vibration data will contribute 57 58 59 to better characterize the coupling schemes. Coriolis coupling schemes 60 different from rotational l-type resonance were actually identified in a

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1 2 3 number of cases for specific isotopologues, see e.g. [83, 28], though so far 4 5 6 not systematically. They are responsible of a limited number of local 7 8 perturbations and seem not to play a very systematic role in the spectral 9 10 11 pattern of acetylene. They are therefore not further addressed in this 12 13 review. 14 15 16 For Peer Review Only 17 18 A global MIME exploiting the vibrational cluster structure and 19 20 21 accounting for the l-dependent coupling terms was built to deal not only 22 23 with pure bending states in various isotopologues, as previously 24 25 26 mentioned. It was extended to the full set of available rotation-vibration 27 28 data in 12 C13 CH . The reason for selecting this specific isotopologue mainly 29 2 30 31 arises from the extensive set of data available. Since there is no restrictive 32 33 u/g selection rule, indeed, many more transitions are allowed, compared 34 35 12 36 to the symmetric C2H2 species. Another consequence of this absence of 37 38 symmetry is that the interaction scheme is also more complete, as 39 40 12 41 illustrated in figure 23. These specific features, compared to C2H2, define 42 43 additional constraints helping the fitting procedure to converge to a single 44 45 46 set of parameters, only. 47 48 49 50 51 Insert figure 23 52 53 54 55 12 13 56 The systematic investigation of C CH 2 using FT and FT-ICLAS 57 58 spectroscopy, in particular, allowed several thousands of rotation- 59 60 vibration lines to be assigned, up to the near infrared region (e.g. [70, 84,

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1 2 3 62, 73, 74]. Thus {N ,N ,J,e/f } clusters were built for each J-value, with the 4 s r 5

6 pseudo quantum numbers Ns and Nr defined as in (2.20) and (2.17), 7 8 respectively. The k-off diagonal matrix elements only couple states 9 10 11 differing by 2 in k and thus only even or odd k-states are present within a 12 13 single global cluster. A typical cluster matrix, with {N ,N } = {2,10}, is 14 s r 15 16 illustratedFor in figure Peer 24, only reproducingReview part ofOnly the full Hamiltonian. 17 18 Higher order terms defined in [85, 28] are included in the off-diagonal 19 20 21 coupling elements. 22 23 24 25 26 Insert figure 24 27 28 29 30 31 A fit was performed in [28] considering all 12703 vibration- 32 33 rotation lines assigned in 12 C13 CH up to 6750 cm −1 , weighted according to 34 2 35 36 the stated accuracy of the line positions (typically between 10 −2 and 10 −4 37 38 −1 39 cm ). Actually the limit was even systematically slightly decreased to 40 41 improve the quality of the fit. These lines reach about 4350 rotation states 42 43 44 from 158 different v/k vibrational states. The fit of 11738 of these lines 45 46 was successfully achieved with a dimensionless standard deviation of 0.99 47 48 49 using 216 parameters. The set of parameters include K11/33 , K1/244 , 50 51 K , K , K , K , K , K , K and K for 52 1/245 1/255 3/244 3/245 3/255 14/35 15/34 44/55 53 54 12 13 the anharmonic resonances. All 965 remaining lines in the C CH 2 fit 55 56 57 being discussed, thus those left outside from the procedure, are 58 59 recalculated within the initially stated wavenumber position accuracy, 60 before reducing it to improve the quality of the fit. It thus turns out that

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1 2 3 the cluster model, extended to include rotation, allows all assigned lines 4 5 −1 12 13 6 up to 6750 cm in C CH 2 to be satisfactorily reproduced, within or better 7 8 9 than the stated typical HiReS position accuracy. It is indeed, so far, a 10 11 successful story. 12 13 14 15 16 A For key issue Peer for the success Review of the global Only analysis, besides the 17 18 19 spectral analysis procedure already mentioned in the text, was the 20 21 package of highly efficient computer programs with very effective 22 23 24 graphical output achieved by Fayt and co-workers in Louvain (see e.g. [86, 25 26 81]). 27 28 29 30 12 13 31 The predictive power of the global model just discussed for C CH 2 32 33 34 proved critical in assigning some of the bands in the range considered in 35 36 the work just referred to. Actually 17 bands previously unspotted because 37 38 39 of their low intensity or not analysed because of their highly perturbed 40 41 rotational structure, could be identified and assigned thanks to the global 42 43 44 model, as discussed in [28]. This global procedure is now being extended 45 12 13 46 for C CH 2 towards higher excited regions, so far with success [75]. It is 47 48 also being applied, again so far successfully, to 12 C H [87]. Meanwhile, it 49 2 2 50 51 can be used to unravel various features in the observed spectra of both 52 53 54 isotopologues. As an example, figure 25 details the predicted set of 55 12 13 56 vibration-rotation states in a selected range in C CH 2, at high vibrational 57 58 59 excitation. Several avoided crossings can be spotted and assigned from 60 such graphs, as a possible help towards the detailed spectral analysis.

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1 2 3 This complex behaviour also illustrates the need for a more adequate basis 4 5 6 to deal with overtone states. 7 8 9 10 11 Insert figure 25 12 13 14 15 16 TheFor next step Peer in this globalReview process is toOnly reliably reproduce the 17 18 spectrum including relative and hopefully absolute intensity features. 19 20 21 Several investigations were carried on in the literature concerning 22 23 intensity simulations, however limited to sharply defined selected spectral 24 25 26 ranges (see e.g. [71]). We have also considered particular problems, such 27 28 as the determination of the transition dipole moment of ν -ν in 12 C H , of 29 5 4 2 2 30 31 relevance to space missions [40]. We are now attempting to simulate a 32 33 34 range as extended as possible, using the results of the global MIME to 35 36 account for all relevant couplings and produce reliable intensity 37 38 39 predictions. This step involves various model refinements, considering the 40 41 sign of the resonance parameters, in particular. 42 43 44 45 46 Another application of the global model is the spectral simulation of 47 48 49 absorption data at very high temperatures for astrophysical purposes, 50 51 thus back to the fingerprint issue of HiReS. Such a simulation requires 52 53 54 the a priori global knowledge of all state energies and coupling schemes, 55 56 while the zero order transition moments and their relative signs need to 57 58 59 be carefully estimated to reliably reproduce the intensity features. As a 60 flavour to these forthcoming developments, figure 26 shows a simulated

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1 2 3 absorption spectrum in the range of ν in 12 C H , under 500 K temperature 4 5 2 2 5 6 conditions, thus accounting for all relevant hot bands and related upper 7 8 9 state coupling mechanisms. 10 11 12 13 14 Insert figure 26 15 16 For Peer Review Only 17 18 19 20 21 Dreaming that such a spectral simulation can be systematically 22 23 −1 24 achieved, say on a range as extended as from 0 to 15000 cm , it would 25 26 cover the equivalent of a pulsed excitation of about 1 fs on the time scale. 27 28 29 This is another quite peculiar perspective stimulating the present purely 30 31 spectroscopic strategy of research. Altogether, the need for an appropriate 32 33 34 description of the highly excited vibration-rotation states, merging 35 36 quantum, dynamical and statistical issues, is still to be imagined. 37 38 39 40 41 42 43 44 D. Ultimate MIME 45 46 As a last input in this review, one should remember that, thanks to 47 48 49 the Pauli principle, nuclear spin isomers need be defined for the 50 51 symmetric acetylene isotopologues. Figure 27 summarizes the situation, 52 53 54 with the states with highest and lowest nuclear spin statistics labelled 55 56 ortho and para , respectively. The well known spectral intensity 57 58 59 alternation with J, illustrated in figure 28 is one of the striking 60 consequences of the existence of nuclear spin isomers in acetylene. It

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1 2 3 applies to all transitions in the symmetric isotopologues, with ortho to 4 5 6 para state transitions forbidden, as already illustrated in figure 18. The 7 8 global MIME ought obviously to include the role of nuclear spins, hence 9 10 11 the title ‘‘ultimate MIME’’ to the present subsection. 12 13 14 15 16 For PeerInsert Reviewfigures 27 and 28 Only 17 18 19 20 21 22 23 Literature on the role of spin-rotation interactions in acetylene, that 24 25 26 would be most relevant in this context, is lacking. We shall therefore here 27 28 only highlight some thoughts on related issues considering (i) nuclear spin 29 30 31 conversion, ( ii ) partition functions, (iii ) collision processes and, finally ( iv ) 32 33 formation of molecular complexes. 34 35 36 37 38 (i) Nuclear spin conversion: 39 40 41 Despite several conversion attempts between ortho and para species 42 43 (e.g. [89-92, 9]), it seems that such a nuclear spin isomerization process 44 45 46 was not observed in acetylene, so far. As a matter of fact, although it has 47 48 been investigated in some species, with interesting applications ( e.g. [93, 49 50 51 94]), this kind of conversion is known to be usually negligible, given the 52 53 smallness of the nuclear spin interaction terms that mix wavefunctions 54 55 56 from different nuclear spin isomers. The strategy to investigate nuclear 57 58 spin conversion first relies on the capacity to enrich a sample in one of the 59 60 isomers, before studying the return to statistical equilibrium. We recently

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1 2 3 reported [95] on a possible enrichment procedure, though accidental and 4 5 6 most indirect. We indeed noticed, as reported in figure 29, that the 7 8 absorption line profile of the first R( J) transitions in the ν +ν band of 9 1 3 10 12 11 C2H2 recorded with a tunable diode laser in an axisymmetric jet 12 13 14 presented a central dip. It could possibly partly due to the formation of 15 16 van der WaalsFor species Peer that is Review likely to be more favourableOnly in the colder, 17 18 19 central part of the jet beam thus removing monomer absorption. The 20 21 disappearance of this dip with increasing rotation, still to be confirmed 22 23 24 could possibly indicate that rotation hinders the formation of these 25 26 aggregates thus leading to recover the full amount of monomers. As a 27 28 29 result, the beam would then be specifically depleted in species with J = 0, 30 31 i.e . in para species. Thus very indirect enrichment in ortho species might 32 33 34 possibly occur in jet-cooled acetylene, under conditions used in the 35 36 experiments! As pointed out this interpretation is still most tentative and 37 38 39 calls for strict experimental evidence. 40 41 42 43 44 Insert figure 29 45 46 47 48 49 50 51 (ii ) Partition functions 52 53 54 The calculation of absolute line parameters and various other 55 56 properties rely on partition functions ( Q). Since ortho and para species do 57 58 59 not easily convert into each other, they ought to be considered as different 60 species in a number of processes and issues, including partition functions,

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1 2 3 as already stated e.g. by Dennison in 1927 {Dennison, 1974 #4631}. The 4 5 6 expressions for the two forms are presented in Eq. (3.6). 7 8 9 10 11   12 Qortho=3 g J exp − EE vJ, − GSJ ,= 1 / kT ∑ ortho( ortho )  13 J ortho 14 15 Q=1 g exp − EE − / kT  (3.6) 16 paraFor ∑Peer Jpara Review() vJ, para GSJ Only ,= 0 J   17 para 18 19 20 21 In these expressions we accounted for different lowest energy states 22 23 24 for the ortho and para nuclear isomers, respectively J = 1 and J = 0, to 25 26 stress the need for considering these two species separately. Obviously, 27 28 29 the proper calculation of the thermal population of each of the rotational 30 31 states, as performed in figure 26, requires the same selection for the 32 33 34 reference energies. The usual factor gJ (= 2 J+1) in these expressions 35 36 correspond to the spatial degeneracy. 37 38 39 40 41 The connection towards the usual partition function, as defined for 42

43 12 44 a single acetylene species C2H2 in most books, is achieved in Eqs. (3.7) 45 46 and (3.8). The distinction between different initial rotational states for the 47 48 49 two isomers is not made in these equations. First, one needs to merge the 50 51 contribution of both isomers, accounting for their respective abundance 52 53 54 under equilibrium conditions: 55 56 57 58 59 60

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1 2 3 4 3   Q=4 gJexp − E vJ, − EkT GS / 5 Total∑ ortho( ortho )  J ortho 6 (3.7) 7 1   8 +4 gexp − E − EkT / ∑ Jpara() vJ, para GS  9 J para 10 11 12 13 14 Next, assuming high temperature conditions, the sums on ortho and para 15 16 For Peer Review Only 17 states are each about identical, therefore leading to the final expression, 18 19 with the factor ½ presented as the symmetry factor in the usual 20 21 22 pedagogical literature. 23 24 25 26 27 T 1 Q≈2 gexp − EEkT − /  (3.8) 28 T otal ∑ J( vJ, GS )  J 29 30 31 32 33 Obviously, the proper calculation of the thermal population of each 34 35 36 of the rotational states, as performed in figure 26, requires the same 37 38 reference energies, different for ortho and para specie. 39 40 41 42 43 (iii ) Collision processes 44 45 46 We have only dealt with intramolecular features, so far. One can, 47 48 however, expect intermolecular issues to be affected by intramolecular 49 50 51 coupling schemes. Acetylene probably offers unique opportunities to 52 53 investigate how several of the features highlighted in this review may 54 55 56 influence or transfer into collision processes and aggregation mechanisms, 57 58 including nucleation. 59 60

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1 2 3 Concerning collisions, several line profile investigations were 4 5 6 reported in the literature in various groups (see review in [97]). We shall 7 8 only report here, as an illustration, on the abnormal self-pressure shift 9 10 12 11 effects affecting J = 18 in ν1+3ν3, C2H2. This specific vibration-rotation 12 13 14 state exhibits intramolecular perturbation and, as a result the R(17) and 15 16 P(19) linesFor accessing Peer that state Review are doubled as reported Only in several papers 17 18 19 including [98, 52, 99-101, 61]. The situation is schematized in figure 30. 20 21 At the time [61], the available global constants allowed first to unravel the 22 23 24 zero order composition of the ν1+3ν3 vibrational state, as indicated in 25 26 figure 30. Next, they suggested that the local perturbation affecting J = 18 27 28 29 could be assigned to a Coriolis-type, thus J-dependent interaction with a 30 31 state of Π symmetry involving significant bend excitation, also identified, 32 33 34 tentatively, on figure 30. As a result of the latter mixing, this vibration- 35 36 rotation state from a zero order pure stretch state carries bending 37 38 39 character. Since, in the overtone range, vibrationally-induced changes of 40 41 the mean geometrical structure become more significant, it is reasonable 42 43 44 to suggest that the collision mechanisms are significantly affected by 45 46 introducing this bend character, hence the different shift coefficients 47 48 49 measured for the lines reaching this J = 18 state in the ν1+3 ν3 band in 50 51 12 C2H2. Once obtained, the new global constant in this isotopologue, this 52 53 54 time including rotational degrees of freedom will be used to check the 55 56 nature of this specific wavefunction mixing. Actually, this statement about 57 58 59 geometrical structure changes in the overtone region supported 60 unfortunately unsuccessful attempts to perform laser drift experiments in

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1 2 3 acetylene in connection with nuclear spin conversion investigation [89]. 4 5 6 7 8 Insert figure 30 9 10 11 12 13 14 15 16 (iv )For Molecular Peer complexes Review Only 17 18 Concerning formation of complexes, we shall not review here the 19 20 21 literature around acetylene-containing van der Waals species, dimers and 22 23 multimers (see e.g. [9]). We shall only present two very recent results 24 25 26 obtained at ULB, illustrated in figures 31 and 32. The first is the 27 28 observation of the 12 C H -Ar complex at high resolution around 6500 cm −1 29 2 2 30 31 using cavity ring down spectroscopy [102], and the second is the probable 32 33 observation of multimers of 12 C H , possibly containing Ar, around 3300 34 2 2 35 36 cm −1 using Fourier transform spectroscopy ([103]). 37 38 39 40 41 Insert figures 31 and 32 42 43 44 45 46 We take this opportunity to highlight, following the FT recording of 47 48 49 coloured vibrations and the 2T-FT-ICLAS achievements previously 50 51 illustrated, another instrumental development stimulated at ULB by the 52 53 54 acetylene saga. The set-up used to record the spectra presented in figures 55 56 29, 31 and 32 is the next generation instrument to produce and 57 58 59 interrogate supersonic expansions. Our previous set-up combining a slit 60 jet and FTS proved to be very performing thanks to the use of a 16 cm long

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1 2 3 slit or multi nozzle (see [104] for a literature review on FT-jet 4 5 6 spectroscopy). A major drawback was the amount of gas injected, which 7 8 prevented us from using acetylene given its hazardous character. We have 9 10 11 very recently built a new set-up, named FANTASIO for ‘‘Fourier 12 13 trANsform, Tunable diode and quadrupole mAss spectrometers interfaced 14 15 16 to a SupersonicFor expansIOn’’. Peer The Review injection, through Only an axisymmetic or slit 17 18 nozzle, is now compatible with the use of acetylene, while a large 19 20 21 turbomolecular pumping group allows improved stagnation to residual 22 23 pressure ratios to be achieved. The sensitivity is boosted thanks to a 24 25 26 multipass sytem around the jet for FTS recording over very broad spectral 27 28 ranges and to thanks a cavity ring down system for tunable diode laser 29 30 31 investigations in the 1.5 m spectral region. Besides the recent detection 32 33 34 of complexes, as illustrated in figures 31 and 32, we are on our way 35 36 measuring absolute line intensities under jet cooled conditions [105]. We 37 38 39 also plan to inject a pump laser at the nozzle exit to perform double 40 41 resonance spectroscopy, hopefully also investigating the detailed 42 43 44 mechanism of acetylene nucleation. 45 46 47 48 49 50 51 52 53 54 4. Final words 55 56 57 58 59 The present paper was intended to respond to the invitation to 60 present the ULB contribution to the acetylene ground state investigation,

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1 2 3 or so-called acetylene saga. One should obviously grant the contribution of 4 5 6 many other research groups to this saga, several of them identified in the 7 8 introduction, whose contribution was accounted for in a previous review 9 10 11 [8]. The central issue in the acetylene saga as defined in the present paper 12 13 is the understanding, at the HiReS level of accuracy, of the molecular 14 15 16 behaviourFor in regions Peer of high vibrational Review excitation. Only Many basic questions 17 18 remain, including an appropriate zero order description involving 19 20 21 interplay between quantum, classical and dynamical pictures. The 22 23 probably complex response still to come is a key issue to unravel and to 24 25 26 master a number of important chemical mechanisms at the microscopic 27 28 level of investigation. 29 30 31 32 33 The research strategy along the acetylene saga fully relies on 34 35 36 HiReS, stimulating instrumental developments and, altogether generating 37 38 an impressive amount of first quality data also feeding more traditional 39 40 41 fingerprint type applications of HiReS. It is indeed interesting to point out 42 43 that all spectral data in the overtone ranges, initially generated to help 44 45 46 very fundamental research projects, today also support applied issues such 47 48 as trace detection relying on near infrared laser developments. The 49 50 51 acetylene saga thus contributed promoting HiReS as a major input to 52 53 modern and hot topics. This is a quite rewarding status in this period of 54 55 56 Science favouring interdisciplinary research…and often dismissing HiReS. 57 58 59 60 The acetylene saga is far from ended, and the so-called ultimate

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1 2 3 MIME in section 3D is, for sure, far from ultimate. The various research 4 5 6 tracks and questions that arose in the text and many others to come will 7 8 keep stimulating the activity of many research groups, including ours. 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 Acknowledgments 4 5 6 7 8 9 I wish to thank Prof. F. Merkt (ETH-Zurich), editor of Molecular Physics, 10 11 for inviting me to submit this review. It would simply not have existed 12 13 14 without the input of several collaborators and friends all over the world. I 15 16 wish to highlightFor thePeer acetylene Review co-authors active Only in Brussels during this 17 18 19 saga, namely Profs M. Godefroid, J. Liévin and Dr. J. Vander Auwera, as 20 21 well as Prof. P. Gaspard; also, as PhD students either at the time or still 22 23 24 now, M. Abbouti Temsamani, C. Depiesse, K. Didriche, I. El Idrissi, F. 25 26 Herreggodts, T. Huet, D. Hurtmans, C. Lauzin, S. Robert and, as postdoc 27 28 29 researchers, M. Hepp, Y. Kabbadj, S. Kassi and P. Macko. It is also my 30 31 pleasure to specifically thank Dr A. Campargue, from Grenoble, Profs G. 32 33 34 Di Lonardo and L. Fusina, from Bologna, Prof. A. Fayt from Louvain, Prof. 35 36 B.J. Orr, from Sydney, and Prof. B. Zhilinskii from Dunkerque, for a very 37 38 39 friendly collaboration about acetylene. I also thank Prof. Di Lonardo 40 41 (Bologna) for providing unpublished results listed in the present paper, 42 43 44 Drs Coheur and Herbin (ULB) for the figure on atmospheric acetylene, Dr 45 46 Demaison (Lille) for pointing out reference [96], Prof. Gaspard (ULB) for 47 48 49 useful comments on partition functions, Prof. Fayt (Louvain) and Séverine 50 51 Robert (Brussels), in particular, not forgetting Keevin Didriche and Badr 52 53 54 Amyay (Brussels) for various figures. Séverine Robert and Dr Vander 55 56 Auwera (ULB) also kindly commented on an earlier version of the 57 58 59 manuscript, while Profs Di Lonardo (Bologna), Fayt (Louvain), Sutcliffe 60 (Brussels) and Zhilinskii (Dunkerque) all reviewed the final version.

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1 2 3 Eventually, I wish to acknowledge the constant financial support of the 4 5 6 Belgian FRS-FNRS along these acetylene years as well as, more specific to 7 8 the present time period, support from the ‘‘Actions de recherches 9 10 11 Concertées de la Communauté française de Belgique’’, the ‘‘Laboratoire 12 13 Européen Associé HiReS’’, and the ‘‘European Union’’ (Quantitative 14 15 16 SpectroscopyFor for AtmosphericPeer Review and Astrophysical Only Research, QUASAAR, 17 18 contract MRTN-CT-2004-512202). 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 References 4 5 6 7 8 9 1. S. A. Miller, "Acetylene; Its properties, manufacture and uses, vol. I " 10 11 Ernest Benn Limited, London, (1965). 12 13 2. E. Davy, British. Ass. Reports, 62, (1836). 14 15 16 3. M. ForHerman, A.Peer Campargue, ReviewM. I. El Idrissi, and OnlyJ. Vander Auwera, J. Phys. 17 18 Chem. Ref. Data, 32, 921 (2003). 19 20 4. J. Demaison, private communication. 21 22 23 5. P. F. Coheur, B. Barret, S. Turquety, D. Hurtmans, J. Hadji-Lazaro, and C. 24 25 Clerbaux, J. Geophys. Res., 110, D24303 (2005). 26 27 28 6. P. F. Coheur, H. Herbin, D. Hurtmans, C. Wespes, C. Clerbaux, C. D. Boone, 29 30 P. F. Bernath, C. P. Rinsland, and J. Remedios, Geophys. Res. Letters, 31 32 submitted (2007). 33 34 35 7. M. Herman, D. Hurtmans, J. Vander Auwera, and M. Vervloet, J. Mol. 36 37 Spectrosc., 150, 293 (1991). 38 39 8. M. Herman, J. Liévin, J. Vander Auwera, and A. Campargue, Adv. Chem. 40 41 42 Phys., 108, 1 (1999). 43 44 9. B. J. Orr, Int. Rev. Phys. Chem., 25, 655 (2006). 45 46 10. R. Colin, M. Herman, and I. Kopp, Mol. Phys., 37, 1397 (1979). 47 48 49 11. M. Herman and R. Colin, Phys. Scr., 25, 275 (1982). 50 51 12. J. K. G. Watson, M. Herman, J. C. Van Craen, and R. Colin, J. Mol. 52 53 95, 54 Spectrosc., 101 (1982). 55 56 13. J. C. Van Craen, M. Herman, and R. Colin, J. Mol. Spectrosc., 111, 185 57 58 (1985). 59 60 14. J. C. Van Craen, M. Herman, R. Colin, and J. K. G. Watson, J. Mol.

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1 2 3 84. L. Fusina, G. Bramati, A. Mazzavillani, and G. Di Lonardo, Mol. Phys., 101, 4 5 6 513 (2002). 7 8 85. G. Di Lonardo and L. Fusina, private communication, (2007). 9 10 11 86. C. Vigouroux, A. Fayt, A. Guarnieri, A. Huckauf, H. Burger, D. Lentz, and D. 12 13 Preugschat, J. Mol. Spectrosc., 202, 1 (2000). 14 15 87. S. Robert, B. Amyay, M. Herman, and A. Fayt, unpublished results, (2007). 16 For Peer Review Only 17 18 88. M. Herman and J. Lievin, J. Chem. Edu., 59, 17 (1982). 19 20 89. P. Macko and M. Herman, Unreported experiments. 21 22 90. A. P. Milce and B. J. Orr, J. Chem. Phys., 112, 9319 (2000). 23 24 25 91. M. Metsälä, M. Nela, S. Yang, O. Vaittinen, and L. Halonen, Vib. Spectrosc., 26 27 29, 155 (2002). 28 29 92. M. Metsälä, S. Yang, O. Vaittinen, and L. Halonen, J. Chem. Phys., 117, 8686 30 31 32 (2002). 33 34 93. P. Cacciani, J. Cosléou, F. Herlemont, M. Khelkhal, and J. Lecointre, Phys. 35 36 69, 37 Rev. A, 032704 (2004). 38 39 94. M. Tudorie, P. Cacciani, J. Cosléou, F. Herlement, M. Khelkhal, C. Puzzarini, 40 41 S. Maret, and C. Kahane, A&A, 453, 755759 (2006). 42 43 44 95. M. Herman, K. Didriche, D. Hurtmans, B. Kizil, P. Macko, A. Rizopoulos, 45 46 and P. Van Poucke, Mol. Phys., 105, 843 (2007). 47 48 96. D. M. Dennison, American Journal of Physics, 42, 1051 (1974). 49 50 51 97. M. Lepère, G. Blanquet, J. Walrand, J. P. Bouanich, M. Herman, and J. 52 53 Vander Auwera, J. Mol. Spectrosc., 242 , 25 (2007)). 54 55 98. B. C. Smith and J. S. Winn, J. Chem. Phys., 94, 4120 (1991). 56 57 58 99. F. Herregodts, M. Hepp, D. Hurtmans, J. Vander Auwera, and M. Herman, J. 59 60 Chem. Phys., 111, 7961 (1999).

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1 2 3 100. F. Herregodts, D. Hurtmans, J. Vander Auwera, and M. Herman, J. Chem. 4 5 6 Phys., 111, 7954 (1999). 7 8 101. F. Herregodts, D. Hurtmans, J. Vander Auwera, and M. Herman, Chem. Phys. 9 10 316, 11 Lett., 460 (2000). 12 13 102. P. Macko, C. Lauzin, and M. Herman, unpublished results (2007). 14 15 103. Y.-C. Lee, V. Venkatesan, Y.-P. Lee, P. Macko, K. Didriche, and M. Herman, 16 For Peer Review Only 17 18 Chem. Phys. Lett., 435, 247 (2007). 19 20 104. M. Herman, R. Georges, M. Hepp, and D. Hurtmans, Int. Rev. Phys. Chem., 21 22 19, 277 (2000). 23 24 25 105. K. Didriche, P. Macko, M. Herman, J. Thiévin, A. Benidar, and R. Georges, 26 27 JQSRT, 105, 128 (2007). 28 29 106. S. Robert, PhD Thesis, ULB, in progress . 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 Figures 4 5 6 7 8 Figure 1 : Portion of the transmittance FT spectrum of the acetylene 9 recorded from space on October, 8 2005 above Mozambique (-6.85° lat; 10 11 39.42° long.) during the ACE mission (from [5, 6]). The upper spectrum 12 13 shows the simulated spectrum, the middle one presents the data as 14 recorded from space and the bottom spectrum shows the difference with 15 16 the spectrumFor calculated Peer under Reviewobservation conditions, Only the latter however 17 not including the acetylene contribution. This contribution is thus 18 19 highlighted in the bottom spectrum. Acetylene lines that seem to be 20 missing are actually buried into fully saturated regions. 21 22 23 24 25 26 27 28 29 30 31 32 33

34 Transmittance 35 36 37 38 39 40 41 42 3290 3292 3294 3296 3298 3300 3302 3304 3306 3308 3310 43 -1 Wavenumber (cm ) 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2

3 12 4 Figure 2 : Portion of the emission spectrum of C2H2 showing part of the R 5 branches of the ν3 and ν2+ν4+ν5 bands, recorded in emission from a 6 7 discharge (a). Intensity alternation is absent for those lines pointed out by 8 arrows, as highlighted from the comparison with an absorption spectrum 9 10 (b) (see dots). The figure is adapted from [7]. It is shown in this reference 11 that this phenomenon can be fully explained by a succession of 12 13 emission/absorption processes, allowing the emission temperature to be 14 15 inferred from the observations. 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 3: Normal modes of vibration in acetylene. The harmonic 5 % 0 12 frequencies (ωi ) are from El Idrissi et al ., 1999 [24] ( C2H2) ; Herman et 6 12 13 7 al ., 1998 [25] ( C2D2) ; Di Lonardo et al ., 1999 [26] ( C2H2); Herman et al ., 8 2004 [27] ( 12 C HD); and Fayt et al ., 2007 [28] ( 12 C13 CH ). 9 2 2 10 11 12 13 14 15 12 12 13 12 12 13 16 HHCCFor PeerCH Review CD CH Only CHD CCH 17 22 22 22 2 2 18 1 + − 1 19 σ(g ) 3397.12 2717.22 3374.90 3387.33 3389.12 cm 20 21 2 22 σ+ 1981.80 1768.07 1918.04 1859.36 1950.11 cm − 1 23 (g ) 24 3 25 + − 1 26 σ(u ) 3316.86 2455.11 3305.55 2605.83 3310.02 cm 27 28 4 29 −1 π(g ) 608.73 509.24 599.92 517.40 604.47 cm 30 31 5 32 −1 33 π(u ) 729.08 538.00 727.23 676.09 728.27 cm 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 4 : Role of the g45 and r45 interaction constants, exemplified on the 5 case of the v = v = 1 vibrational state in acetylene. Contribution from 6 4 5

7 terms involving g 44 and g 55 are identical for both k sublevels and are not 8 accounted for in the energy scheme. 9 10 11 12 E 13 14 15 ± ± 16 For Peer Review Only 17 18 19 20 +g 45 21 00011 22 − 23 Σ 24 -g45 25 l -type 26 -r45 27 vib. res. 28 ± 29 Σ +r 45 30 (r45 <0 ) 31 + 32 Σ 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2

3 12 4 Figure 5: Top: Integrated number of states, N(E) in C2H2, in function 5 of the vibrational energy up to 15000 cm −1 . The number was calculated 6 7 from the energies predicted using the extended set of vibrational constants 8 from [24], with each substate with k ≠≠≠ 0 counted for 2 in the sum, as 9 10 explained in [30]. The origin of the energy scale (E) is at the bottom of the 11 12 well; Bottom: Related density of vibrational states. The origin of the 13 energy is now the GS. 14 15 16 For Peer Review Only 17 18 70000 19 65000

20 4 5 7 60000 N (E) = 1 + α E + β E + γ E 21 aj 22 55000 −13 4 α = 4.4499 x 10 cm 23 50000 −17 5 β = 2.7573 x 10 cm 24 45000 −25 7 25 γ = 1.4290 x 10 cm 40000 26 35000 27 28 30000

29 25000 30 31 20000 32 15000

33 Integrated numberof states 10000 34 5000 35 36 0 0 2000 4000 6000 8000 10000 12000 14000 16000 37 38 E ( cm −1 ) 39

40 41 42 43 44 45 46 47 48 3 5 0 0 0 49 3 0 0 0 0 -1

50 2 5 0 0 0 51 2 0 0 0 0 52 53 1 5 0 0 0 54 1 0 0 0 0

55 5 0 0 0

56 / 100 cm density State 0 57 -5 0 0 0 58 0 5000 10000 15000 20000 25000 59 E (c m -1 ) 60

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1 2 3 4 Figure 6: Top: Variation of the absolute value of the electric dipole 5 transition moment (|R |) upon excitation along the nν (CH) overtone 6 v 1 12 7 series in C2HD (adapted from [33]). Triangles refer to measured 8 transition moments and squares to the sum of contributions from the 9 10 bright and related dark transitions; Bottom: Contribution to the transition 11 moment of the 3 ν and 4 ν bands in 12 C HD of the various orders in the 12 1 1 2 13 electric dipole development, accounting for mechanical anharmonicity in 14 15 the description of the wavefunctions (adapted from [34]). 16 For Peer Review Only 17 18 -2 19 3335 cm -1 20 21 22 -4 23 -1 24 6570 cm 25 26 | -6 27 v 9706 cm -1 28 29

30 ln |R -1 31 -8 12746 cm 32 33 15697 cm -1 34 35 -10 36 37 38 0.0 0.6 1.2 1.8 39 40 41 ln n 42 43 44 45 46 47 48 49 50 60 order 0 order 2 51 52 order 1 order 3

53 (in %)

v 40 54 55 R 56 57 20 58 59 60 0

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3 12 4 Figure 7: Vibration-rotation absorption FT spectrum of C2H2 in the 5 visible range showing the 4 th CH overtone band (adapted from [35]). (P = 6 acet 7 250 mbar; l = 49.2 m, 6900 scans co-added). 8 9 10 1.05 11 12 13

14 0.90 15

16 For Peer Review Only 17 18 19 0.75 20 Signal Detector 21

22 Absorption 5 ν 3 23 0.60 24 25 26 27 0.45 28 15650 15600 15550 15500 -1 29 Wavenumber (cm ) 15650 15600 15550 15500 30 31 cm −1 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 8 (IN COLOUR) : Statistical and dynamical role of the bending 5 vibrations in 12 C D (adapted from [43]): Top: Integrated number of states 6 2 2 7 (left ordinate) and residue between the predicted and calculated 8 integrated number of states (right ordinate) Bottom: Related Vibrogram 9 10 (see text) in which the energy (abscise), defined from the bottom of the 11 potential well, runs from −4000 to +9000 cm −1 , from left to right. 12 13 14 15 16 For Peer Review Only 17 18 19 20 N (E) Residue 21 80 80 22 2500025000 60 23 40 24 40 (E ) 20000 fit

20000 Residue 25 20 N 26 − 27 1500015000 0 0 28 -20 29 1000010000 30 -40-40

31 Residue N(E)= -60 32 50005000 Integrated num ber of states 33 -80-80 34 0 35 Integrated number of states -100 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -1 36 0 5000 10000 cm −1 37 E(cm ) 38 39 40 41 400 42 43 44 300 45 46 47 (fsec) 200 (fsec) 48 T 49 T 50 100 51 52 53 0 54 55 56 10000 57 58 59 60

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1 2 3 4 Figure 9: (a) Zero order picture in which two vibrational states with 5 0 0 identical energy ( ΨB and ΨD ) lead to very strong (bright) and very weak 6 7 (dark) transitions from GS, respectively; (b) a coupling results into two 8 eigenstates ( Ψ and Ψ ) with shifted energies and mixed wavefunctions; 9 + − 10 (c) the bright character is now equally shared by the two eigenstates. The 11 12 spectrum, restricted to a single bright transition in the zero order picture 13 (a/bottom) consists in two transitions each with half the initial intensity in 14 15 the eigen spectrum (c/bottom). 16 For Peer Review Only 17 18 19 E 20 ΨΨΨ ΨΨΨ 000 ΨΨΨ 0 ΨΨΨ 21 +++ = aaa BBB + bbb D +++ 22 23 24 Bright Dark 25 26 000 000 27 ΨΨΨBBB ΨΨΨDDD 28 29 30 ΨΨΨ ΨΨΨ 0 ΨΨΨ 0 ΨΨΨ 31 --- = bbb B --- aaa D --- 32 33 34 35 36 37 38 GS GS 39 40 (a) (b)(c) 41 42 43 44 45 46 ν% ν% 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 10 : Example of intensity borrowing through the 1/255 anharmonic 5 resonance in 12 C HD (adapted from [34]). Additional bands from 12 C H , 6 2 2 2 −1 7 with typical intensity alternation, are observed around 12700 cm in the 8 bottom spectrum. Zero order dark Q branches in Π − Σ + transitions are 9 10 identified on the top and middle figures, borrowing their intensity from 11 the zero order 3ν+ν (k = 1) and 3ν+ν (k = 1) bright transitions, 12 1 4 1 5 13 respectively. A zero order R branch borrowing intensity from the 4 ν1 14 + + 15 Σ − Σ bright transition is indicated in the bottom spectrum. 16 For Peer Review Only 17 18 19 20 21 22 23 -1 2 1 1 0 1 24 2ν1+ν2+( ν4 +2 ν5 ) 2ν1+ν2+( ν4 +2 ν5 ) 25 26 1 3ν1+ν4 cm −−−1−111 27 28 10212 10200 10188 29 30 31 32 33 34 35 3ν +ν 1 2ν +ν +3 ν 1 36 1 5 1 2 5 cm −−−1−111 37 38 10330 10320 10310 10300 39

40 41 42 3ν +ν +2 ν 0 43 1 2 5 44 45 4ν 1 12 C H 46 2 2 47 cm −−−1−111 48 12820 12780 12740 12700 12660 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 11 : Energy difference ( E = E( v1,v2,v3,v4,v5) - E( v1-1, v2+1, v3,v4,v5+2)) 5 between some pairs of states interacting through the 1/255 anharmonic 6 12 7 resonance in C2HD, plotted as a function of the approximate state energy. 8 Only one of the interacting states is identified with the help of the related 9

10 values of the vibrational quantum numbers, v1 to v5. The three sets of 11 interaction highlighted in figure 10 are framed. 12 13 14 Energy 15 *31042 -1 *40040 16 cm For*30122 Peer Review*31051 Only *41000 *32020 *30131 17 *30140 18 14000 *40011 *31022 *31031 19 *30102 *31040 20 *32000 *30120 *40010 *31012 *31030 *30042 21 *30101 *30051 *31011 *30110 *40000 22 *31020 *30032 *30041 23 *30100 *31001 *30050 24 12000 *30022 *31010 *30040 *30031 25 *31000 26 *30002 27 *30011 28 *30020 29 *30001 *30010 30 10000 31 *30000 32 *20041 33 34 *20031 35 36 8000 -1 37 -40 -20 0 20 40 cm 38 Energy difference [ E (v v v v v ) - E (v -1,v +1,v ,v ,v +2) ] 1 2 3 4 5 1 2 3 4 5 39 E 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3 12 4 Figure 12: Overtone spectrum of C2HD recorded using 2T-FT-ICLAS 5 (middle), showing a band not observed on the FT spectrum (bottom). The 6 7 product of absorption pathlength (14.64Km) and pressure (120 hPa) 8 conditions in the laser experiment is about 500 times larger than in the 9 10 FT experiment. The line assignment is indicated (middle) and the band 11 structure is simulated (upper) (adapted from [58]). 12 13 14 15 16 For Peer Review Only

17 1 .0 18

19 0 .8 20 21 0 .6 22 1 .0 23 24 25 e c n itta m s n ra T 0 .8 26 27 0 .6 28 29 0 .4

30 J 2 0 1 5 1 0 5 0 5 10 152025 31 0 .2 32 P (J) R (J)

33 0 .0 0 .5 4 8 34 Transmittance 35 36 0 .5 4 6

37 0 .5 4 4 38 39 0 .5 4 2 -1 40 cm 0 .5 4 0 41 13300.0 13320.0 13340.0 13360.0 13380.0 13400.0 42 13300W avenum 13400 ber (cm - 1 ) 13500 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 13 : Left: Scheme of bright/dark multiple intensity borrowing in a 5 straight absorption scheme; and, Right: dispersed fluorescence spectrum 6 12 −1 7 of C2H2 ranging over some 600 cm , observed (left) and simulated (right), 8 adapted from [66]. Each straight line in the simulation indicates, with 9 10 appropriate relative intensity, a predicted fractionation of the zero order 11 bright transition. 12 13 14 15 16 For Peer Review Only 000 17 ΨΨΨDDD Eigenstates 18 19 −1

20 cm 21 ΨΨΨ+/+/+/-+/ --- 22 23 24 25 26 27 −1 28 000 29 ΨΨΨBBB 30 Wbd 31 cm 600 32 33 34 35 36 37 38 8900 9000 9100 9200 9300 9400 39 40 41 42 43 44 GS 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3 12 4 Figure 14 : Scheme of the { Ns,Nr,k,+,u } = {2,10,0 ,+,u } cluster in C2H2, with 5 anharmonic resonance connecting vvvvl4 v l5 , Σ+ vibrational states 6 ((( 1234 5 ))) 7 identified (from [68]). 8 9 10 11 12 13 14 0 0 15 (101 0 0 ) 16 For Peer Review Only 17 18 3/245 1/255 1/244 19 20 21 1 1 0+ 0 0 0 0 22 (110 1 1 ) 14/35 (011 0 2 ) 44/55 (011 2 0 ) 23 24 25 1/255 3/245 3/245 26 1/244 27 28 1 1 0+ 29 (020 1 3 ) 44/55 (020 3 111)0+ 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 15: Evolution with the vibrational energy of the { Ns,Nr} clustering 5 of the states, in 12 C H . The average energies of the so-called sub-polyad 6 2 2 %av %av 7 ν (Nr , N s ) are taken with respect to each average polyad energy ν (N r ) 8 (adapted from [30]). 9 10 11 12 13 14 N 15 r 16 For1 Peer Review 10 Only 20 17 300 N = 0 18 s 19 )

20 -1 200 21 22 ) (cm ) 100 23 r N = 1 N s (

24 av 25 ν 0 ) - - )

26 s

27 N N = 2

, -100 s 28 r N 29 ( av 30 ν -200 Ns = 3 31 N = 4 32 s -300 33 Ns = 5 34 N = 6 35 -400 s 36 06000 2 4 6 12000 8 10 12 14 18000 16 18 20 22000 22 cm cm−1 −1 37 6000 12000 18000 22000 N 38 r 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3 12 13 4 Figure 16 : Portions of the FT-transmittance spectrum of C CH 2 5 recorded at ULB (adapted from [73]). The sample pressure was 5.05 mbar, 6 7 the temperature 273 K, and the absorption pathlength 55.1 m. The upper 8 and middle spectra range from about 5700 to 10000 and 5700 to 6000 cm −1 , 9 10 respectively. 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 6000 9000 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 5700 6000 42 Transmittance 43 44 45 46 1.0 47 48 49 50 51 52 53 54 55 56

57 0.90 58 59 5928 5932 5936 60 Wavenumber (cm -1)

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1 2 3 4 Figure 17 : Summary of the procedure to define e/f rotation-vibration 5 states in linear species, as defined in [80], applied to the v4=1, l 4 = 1 state 6

7 in acetylene. In this specific case, e levels are below f-ones (q 4<0). 8 9 10 11 l4 1−−− 1 12 v4 1 1 13 14 1 0 1 1 15 1Gv ((()( 1))) 2 qJJ4 ((()( +++ 1 ))) 16 For Peer Review Only 17 −1 1 0− 1 18 12 qJJ4 ((()( +++ 1))) G v ((()( 1 ))) 19 20 21 22 23 24 1 1 25 2 2  26 O ===   27 1−−− 1 28 2 2  29 30 31 32 33 34 t 1 1 35 OHO1, e 1, f 36 37 1 0 1 38 1,e Gv +2 qJJ4 ((()( + 10))) 39 40 1,1 00 1 1 41 f GqJJv −2 4 ((()( + ))) 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 18 : Detailed rotational structure, including the role of nuclear 5 spin statistics, for all Σ − Π transition-types in 12 C H (adapted from [10]). 6 2 2 7 Ortho /Para components are in full/dotted lines. 8 9 10 +++ −−− 11 J Σu − Π g J Σg − Π u 12 13 3 e 3 f 14 2 e 2 f 15 16 1 For Peere Review1 Only f 17 0 e 0 f 18 19 20 21 22 f f 23 2 e 2 e 24 1 f 1 f 25 e e 26 27 P P 28 Q Q 29 R R 30 31 32 33 −−− +++ 34 J Σu − Π g J Σg − Π u 35 3 f 3 e 36 37 2 f 2 e 38 1 f 1 e 39 40 0 f 0 e 41 42 43 44 45 f f 2 e 2 e 46 47 1 f 1 f 48 e e 49 P P 50 Q Q 51 52 R R 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 19 : Sequence of couplings, with main related parameters 5 highlighted at the bottom, affecting the v = 1 and v = v = v = 1 vibrational 6 3 2 4 5 7 states (left) and related reduced rotational energies (as defined in Eq. (3.5) 8 ) (right), in 12 C H . All states highlighted are of u symmetry. Other states 9 2 2 10 appear on the reduced energy graph, whose assignment is not given. 11 12 13 14 -6 2 2 -1 E - 1.172556 J(J+1) + 2.4993 10 J (J+1) (cm ) 15 VR 16 For Peer Review3310 Only 17 18 E e 19 ± 20 ± ± 01011, 1 1x 21 f 22 01011, 1-1f −−− 23 − − ΣΣΣ 01011 Σ Σ f 24 -1 25 26 ± Σ 00100, 0 0e 27 + +++ 30 cm 28 Σ ΣΣΣe 29 30 Σ+ + 31 00100 Σ 32 33 Σ+ 34 + +++ 35 Σ ΣΣΣe 36 01011, 1-1e 00032,-1 2x 00032, 3 0x 37 3280 38 0 102010 . 20 . 3030 . 40 (J) 39 J 40 % 41 wi, x ij gij r45 K 3 / 245 Bi, D i , q4 , q 5 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 20 : Eigenvector coefficients for the three interacting ( v1v2v3v4v5,l4l5) 5 zero order states in 12 C H identified in the graphs and pictured in figure 6 2 2 7 19. The labels •, • and ∇ refer to the (01011,11); (00100,00); and (01011,1- 8 1) zero order states, respectively (calculated from [82]) 9 10 11 (0 0 1 0 0, 0 0) (0 1 0 1 1, 1 -1) (0 1 0 1 1, 1 1) 12 1.0 1.0 1.0 1.0 13 3 01011, 1-1 3 01011, 1-1 14 2 01011, 1 1 2 01011, 1 1 1 00100, 0 0 1 00100, 0 0 15 16 0.8 0.8 For Peer 0.8Review Only0.8 17 3 01011, 1-1 18 2 01011, 1 1 19 1 00100, 0 0 20 0.6 0.6 0.6 0.6 21 22 23 24 0.4 0.4 0.4 0.4 25 26 Eigenvector coefficient 27 28 0.2 0.2 0.2 0.2 29 30 31 32 0 0 0 0.0 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 33 0MAT 10 35 NIV 1 20 0 1 0 1 30 1, 1 -1e 40 3281.899 50 0MAT 10 35 NIV 202 0 0 1 300 0, 0 0e 40 3294.840 50 0MAT 10 35 NIV 3 20 0 1 0 1 30 1, 1 1e 40 3303.018 50 34 J 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3 12 4 Figure 21 : Simulated portion of the infrared spectrum of C2H2 5 demonstrating the role of the various coupling schemes around ν in 6 3 + 7 making a zero order forbidden − Σ transition emerge, actually at higher 8 J-values, identified through stick lines drawn broader on the simulation 9 10 (adapted from [82]). 11 12 13 150 14 15 e+( e ) 16 For Peer Review Onlyu − Σ g 17 18 19 20 100 21 22 23 24 25 26 27 28 50 29 30 31 32 33 34 35 0 -1 36 3340 3345 3350 3355 cm 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 22 : Reduced energies, defined as in Eq. (3.5), as a function of J for l l 0 0 + 5 4 5 the observed vibration-rotation levels of the (vvvv1234 v 5 ) ≡ (0030 0 ) (Σ ) ( ■), 6 1 1 3 −1 13 12 7 (0213 1 ) ( ○) and (0303 3 ) ( ) ( ) states of CH CH, with all vibrational 8 labels corresponding to zero order assignments (adapted from [74]). 9 10 11 11 12 13 14 15 16 For Peer Review Only 17 18

19 ) 10 20 -1 21 22 23 24 25 26 27 9 28 29 30 Reduced energy (cm 31 32 33 34 8 35 36 37 38 39 0 5 10 15 20 25 30 35 J 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 23 : Portion of the { Ns,Nr} = {3,15} cluster in acetylene (adapted 5 from [39]). Arrows show the resonances, identified at the bottom of the 6

7 figure, connecting (v1v2v3v4v5) vibrational states. The two sets of states 8 separated by the horizontal dotted line are connected in 12 C13 CH but not in 9 2 12 10 C2H2 because of u/g selection rules forbidding the 1/245 and 3/244 11 couplings to occur. 12 13 14 15 16 For Peer Review Only 17 18 30000 21020 12040 19 20 (g) 21 22 12022 11111 10200 01220 23 24 25 26 21011 20100 11120 02140 27 28 29 (u) 30 03033 02122 01211 00300 31 32 33 34 35 36 1/245 3/245 11/33 1/244 3/244 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 24 : Illustration of the k-mixing in the global picture of acetylene, 5 from a portion of the {N ,N } = {2,10} vibration-rotation cluster in 12 C13 CH , 6 s r 2 7 in which higher order interaction terms, with upper/lower signs valid for 8 e/f symmetries are included, all defined in [28]. The symbol X indicates 9 10 the absence of coupling term. The matrix is symmetric. 11 12 13 v 1v 2v 3v 4v 5,l 4l 5 ... 02022, 0 0 02022, 0 2 02022, 2 -2 02022, 2 0 01111, 1 -1 01111, 1 1 00200, 0 0 ... 14 ... 15 02022, 0 0 E q r q K O X 16 For vrPeer5 Review45 4 Only3/245 3/245 17 02022, 0 2 Evr ± u 55 q455 ± q 4 r45 ± u 45 ± O3/245 K3/245 X 18 02022, 2 -2 Evr ± r 4455 q5 ± q 445 K3/245 X X

19 02022, 2 0 Evr ± u 44 O3/245 K3/245 X 20 01111, 1 -1 Evr ± r 45 q5 ± q 4 K3/245 21 01111, 1 1 E ± u O 22 vr 45 3/245 23 00200, 0 0 Evr 24 ... 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 25 (IN COLOUR) : Reduced energy graph, as defined in Eq. (3.5), 5 illustrating the complexity of the vibration-rotation energy pattern in the 6 12 13 7 overtone range in acetylene ( C CH 2). The energy behaviour is predicted 8 from the global picture presented in [28]. Full and doted lines indicate e 9 10 and f parity, respectively. Colours refer to different symmetries, with 11 those corresponding to interacting k = 1 (blue), 3 (purple) and 5 (black) 12 13 states highlighted. 14 15 16 EFor -11000 -Peer 1.137810 J( J+Review1) + 1.5567 10-6 J2( JOnly+1)2 (cm-1) 17 VR 18 19 11770770 20 13013,-1 1-1f 21 12034,cm 3 2x 22 23 24 25 04070,02202, 10 0x2x 26 27 28 12034,-1 4x 29 02134,11765 1765 4x 30 02125, 0 1x 31 03113, 1 3x 32 33 34 04015, 1-1e 35 04070, 3 0x 36 37 38 39 21032,11760 1760 2x 40 41 42 43 44 45 46 20112,-1 2x 47 02202, 0 0e 48 49 11755755 50 51 20112, 1 0x 52 53 54 55 56 21032,04070, 15 0x 57 58 03036,-3 6x 59 11750750 60 10 . 20 . 30 . 40 . 50 10 20 H23H30 4005/30/07 J 50 (J)

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1 2

3 12 4 Figure 26 : Simulated absorption spectrum of C2H2 (line-strengths) 5 around the ν region, corresponding to 500 K temperature conditions [87]. 6 5

7 Population on all excited states up to v4 = 5 was accounted for in the hot 8 band simulation [87]. 9 10 11 12 13 14 15 14 16 For Peer Review Only 17 19 18 12 19

20 )10 X 10 21 -2 22 23 8 24 25 26 6 27 28 29 /(molecule cm 4 -1 30

31 cm 2 32 33 34 0 35 600 650 700 750 800 850 cm -1 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 27 : Statistical weights ( gI) as a function of the e/f wavefunction 5 parity of the vibration-rotation energy states in various isotopologues of 6 7 acetylene. The result depends on the parity of J as well as on the 8 vibrational state-symmetry. 9 10 11 12 12 13 13 12 Parity J C H C D C H C D 13 2 2 2 2 2 2 2 2 + 14 even 1 6 10 15 Σg, Π g ,... e 15 16 For Peerodd Review3 3 Only6 21 17 18 − even 3 3 6 21 19 Σg, Π g ,... f 20 21 odd 1 6 10 15 22 23 24 25 Σ+ , Π ,... e even 3 3 6 21 26 u u 27 odd 1 6 10 15 28 29 − even 1 6 10 15 30 Σu, Π u ,... f 31 32 odd 3 3 6 21 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 28 Nuclear spin statistics and intensity alternation in R- 5 + + branches of Σ()u − Σ () g acetylene transitions (see [88]). The parity of J for 6 7 the stronger lines depends on the total nuclear spin function, while 8 9 intensity alternation does not occur for asymmetric isotopologues. 10 11 12 13 14 J even para gI =1 15 12 I(H)=1/2 16 For Peer ReviewC2H2 Only 17 J odd ortho g =3 18 I 19 6682,0 6670,0 6658,0 6646,0 6634,0 20 21 J even 22 23 12 24 C2HD 25 J odd 26 transmittance 27 4467,0 4454,5 4442,0 4429,5 4417,0 28

29 J even ortho gI =6 30 12 31 C2D2 I(D)=1 32 J para g 33 odd I =3 34 7760,0 7754,0 7748,0 7742,0 7736,0 35 Wavenumberwavenumber (cm -1 ) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 29 : Evolution of the absorption line profile of the first R( J) 5 transitions in the ν +ν band of 12 C H recorded at ULB with a tunable 6 1 3 2 2 7 diode laser in an axisymmetric jet (see experimental details in [95]. The 8 central dip is attributed to the formation of van der Waals species that is 9 10 more favourable in the central part of the jet beam. The evolution with J 11 may possibly indicate that rotation hinders the formation of these 12 13 molecular complexes. 14 15

16 For Peer Review Only -2 17 -3 2x10 3x10 R(0) R(1)

18 ) 0 2x10 -3 19 -2 1x10 20 1x10 -3 21 -ln(I/I 22 0 0 -2 23 1x10 -2 3x10 R(2) R(3)

24 ) -2 0 2x10 -3 25 5x10 26 1x10 -2 -ln(I/I 27 28 0 0 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 30 : Scheme of the perturbation mechanism possibly explaining 5 unusual self broadening coefficients affecting J = 18 in ν +3ν , 12 C H (see 6 1 3 2 2 7 text). ( adapted from [61]). 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2

3 12 4 Figure 31: Portion of the absorption spectrum of C2H2-Ar recorded using 5 jet-cooled cavity ring down spectroscopy at ULB. Lines in the K = 1•0 6 a 7 sub-band of the 2CH overtone band are assigned in terms of the usual 8 R/Q/P( J) notation, adapted from [102]. 9 10 11 12 K = 1 - 0 13 a 14 15 16 For Peer Review Only 17 18 -5 Q(1) 13 1x10 8 7 6 5 4 3 P(2) 19 20 R(0) 1 2 3 4 5 21 22 )

23 -1 24

25 (cm -6 26 α 5x10 27 28 29 30 31 32 33 0 34 35 * * * * * 36 6556.0 6556.5 6557.0 6557.5 37 -1 38 wavenumber (cm ) 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Figure 32: Absorption Fourier transform spectrum of jet-cooled acetylene 5 recorded at ULB demonstrating clustering effects (adapted from [103]). 6 7 8 9 10 0.030 11 12 (C H ) C H 13 2 2 n 2 2 14 0.025 15 16 For Peer Review Only 17 0.020 18 19 20 21 0.015 22 23 24 0.010 25 Absorbance 26 27 28 0.005 29 30 31 0.000 32 33 34 35 -0.005 36 3200 3220 3240 3260 3280 3300 3320 3340 37 -1 38 wavenumber / cm 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Tables 5 6 7 Table 1 : Check of x-K relations in symmetric acetylene isotopologues. 8 (Parameters from El Idrissi et al ., 1999 [24] ( 12 C H ); Herman et al ., 1998 9 2 2 12 13 10 [25] ( C2D2); Di Lonardo et al ., 1999 [26] ( C2H2)) 11 12 13 14 15 16 For Peer12 Review12 Only13 17 C H C D C H 18 2 2 2 2 2 2 19 20 21 22 x11 -24.8 -12.3 -25.4 23 24 25 26 27 28 29 x33 -27.6 -15.4 -26.7 30 31 32 33 34 35 36 x13 -107.5 -47.5 -104.3 37 38 39 40 41 42 43 K11/33 -105.7 -47.2 -103.4 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 Table 2: Periods associated to the normal mode vibrational frequencies 5 % e (ωi ) in symmetric acetylene isotopologues as published at the time (from 6 7 [43]). 8 9 10 11 12 13 14 15 Mode 12 13 12 16 For CPeer2H2 ReviewC2H2 OnlyC2D2 17 −1 −1 −1 18 i (cm ) (fsec) (cm ) (fsec) (cm ) (fsec) 19 20 1 3506.91 9.5 3481.14 9.6 2785.47 12.0 21 2 2012.56 16.6 1946.93 17.1 1787.44 18.7 22 23 3 3421.17 9.8 3404.99 9.8 2512.32 13.3 24 25 4 622.73 53.6 613.57 54.4 519.44 64.2 26 27 5 746.89 44.7 743.96 44.8 549.02 60.8 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 −1 4 Table 3: Principal rotational constants, B 0 in cm , of various 5 isotopologues of acetylene (from Cané et al ., 2002 [69] (13 C D ); Di Lonardo 6 2 2 13 12 13 13 12 7 et al ., unpublished [76] ( C2HD), (H C CD), and (H C CD); Di Lonardo et 8 al ., 1993 [77] ( 13 C H ); Wlodarczak et al ., 1989 [78] ( 12 C HD); Robert et al ., 9 2 2 2 12 12 13 12 10 2007 [40] ( C2H2); Huet et al ., 1991 [23] ( C2D2); [79] ( C CD 2), and Fayt 11 et al ., 2007 [28] ( 12 C13 CH )). 12 2 13 14 15 16 13 C D For0.817 Peer 872 206 Review 6 (4560) Only 17 2 2 18 13 19 C2HD 0.950 330 801 (617) 20 12 13 21 H C CD 0.975 271 02 (68) 22 13 12 23 H C CD 0.967 192 54 (82) 24 13 25 C2H2 1.119 574 687 (146) 26 12 27 C2HD 0.991 527 8 (3) 28 12 29 C2H2 1.176 646 18 (1) 30 12 31 C2D2 0.847 874 20 (24) 32 12 13 33 C CD 2 0.833 05 (4) 34 35 12 C13 CH 1.148 460 77 (1) 36 2 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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