N Lamarre

C Falvo

C Alcaraz

B Cunha De Miranda

S Douin

A Flütsch

C Romanzin

J.-C Guillemin

S Boyé-Péronne

B Gans

Photoionization spectroscopy of CH 3 C 3 N in the vacuum-ultraviolet range

Keywords: cyanopropyne, methylcyanoacetylene, 2-butynenitrile, CH 3 C 3 N, synchrotron radiation, TPES, dissociative photoionization, DFT calculations

Using vacuum-ultraviolet (VUV) synchrotron radiation, threshold and dissociative photoionization of cyanopropyne (CH 3 C 3 N) in the gas phase have been studied from 86000 cm -1 up to 180000 cm -1 by recording Threshold-PhotoElectron Spectrum (TPES) and PhotoIon Yield (PIY). Ionization energies of the four lowest electronic states X+ 2 E, Ã+ 2 A 1 , B+ 2 E and C+ of CH 3 C 3 N + are derived from the TPES with a better accuracy than previously reported. The adiabatic ionization potential of CH 3 C 3 N is measured as 86872 ± 20 cm -1 . A description of the vibrational structure of these states is proposed leading to the first determination of the vibrational frequencies for most modes. The vibrational assignments of the X+ state are supported by density functional theory calculations. In addition, dissociative photoionization spectra have been recorded for several cationic fragments in the range 12-15.5 eV (96790-125000 cm -1 ) and they bring new information on the photophysics of CH 3 C 3 N + . Threshold energies for the cationic dissociative channels leading to CH 2 C 3 N + , CHC 3 N + , HC 3 H + , HCNH + and CH + 3 have been measured for the first time and are compared with quantum chemical calculations.

Introduction

Cyanopropyne CH 3 -C≡C-C≡N (or 2-butynenitrile) is the methylated derivative of cyanoacetylene HC 3 N, an important astrophysical species. Although the chemical and physical properties of HC 3 N have been extensively studied (see for instance Ref. [START_REF] Leach | Ionization photophysics and spectroscopy of cyanoacetylene[END_REF] and references therein), cyanopropyne has been much less investigated. Less ubiquitous than HC 3 N, which has been observed in several molecular clouds of the Interstellar Medium (ISM), in Titan and in comets, cyanopropyne was detected in 1984 in the molecular cloud TMC-1 and more recently in Sgr B2 [START_REF] Broten | The detection of interstellar methylcyanoacetylene[END_REF][START_REF] Belloche | Complex organic molecules in the interstellar medium: IRAM 30 m line survey of Sagittarius B2(N) and (M)[END_REF]. Twelve years after its first detection, an isomer, the cyanoallene (2,3-butadienenitrile, H 2 C=C=CHCN) was found in TMC-1 [START_REF] Lovas | Hyperfine Structure Identification of Interstellar Cyanoallene toward TMC-1[END_REF] but in lower amounts: a 0.25 ratio compared to cyanopropyne, as it has been often observed for thermodynamically less stable compounds [START_REF] Lattelais | Interstellar Complex Organic Molecules and the Minimum Energy Principle[END_REF].

Even if it has never been unambiguously detected up to now in the atmosphere of Titan, the presence of cyanopropyne was found in several atmosphere simulations of this satellite using a plasma discharge in N 2 -CH 4 mixtures at low pressures [START_REF] Thompson | Plasma discharge in N 2 + CH 4 at low pressures: Experimental results and applications to Titan[END_REF][START_REF] Coll | Experimental laboratory simulation of Titans atmosphere: aerosols and gas phase[END_REF][START_REF] Molina-Cuberos | Nitriles produced by ion chemistry in the lower ionosphere of Titan[END_REF]. Note that Vuitton et al. reported the detection of a C 4 H 3 N species in the atmosphere of Titan by mass spectrometry [START_REF] Vuitton | Ion chemistry and N-containing molecules in Titan's upper atmosphere[END_REF] but did not specify the corresponding molecular structure.

To explain its formation in the ISM as well as how it could be formed in the atmosphere of Titan, the addition of the CN radical on propyne (a gas observed in the ISM as well as in the atmosphere of Titan) has been proposed. Corresponding studies have been performed via a neutral-neutral reaction under single collision conditions in a crossed molecular beam experiment to yield the expected product and the cyanoallene isomer [START_REF] Kaiser | The Formation of Nitriles in Hydrocarbon-Rich Atmospheres of Planets and Their Satellites: Laboratory Investigations by the Crossed Molecular Beam Technique[END_REF][START_REF] Balucani | Laboratory investigation on the formation of unsaturated nitriles in Titans atmosphere[END_REF][START_REF] Huang | Crossed beam reaction of the cyano radical, CN(X 2 Σ + ), with methylacetylene, CH 3 CCH(X 1 A 1 ): Observation of cyanopropyne, CH 3 CCCN(X 1 A 1 ), and cyanoallene, H 2 CCCHCN(X 1 A ′ )[END_REF]. However other approaches starting from cyanoacetylene might also be proposed for its synthesis in these media.

Cyanopropyne is a prolate symmetric top which has a neutral ground state configuration [core](1a 1 ) 2 (2a 1 ) 2 (3a 1 ) 2 (4a 1 ) 2 (5a 1 ) 2 (1e) 4 (2e) 4 (6a 1 ) 2 (3e) 4 , leading to a X 1 A 1 state in the C 3v point group. This molecule has 12 vibrational modes: 6 symmetric modes of a 1 symmetry (ν 1 to ν 6 ) and 6 degenerate modes of e symmetry (ν 7 to ν 12 ). The vibrational structure of the electronic ground state has been studied by infrared spectroscopy [START_REF] Tubino | Vibrational Spectrum and VibroRotational Analysis of Cyanopropyne[END_REF][START_REF] Cerceau | Infrared spectra of gaseous mononitriles: Application to the atmosphere of Titan[END_REF][START_REF] Khlifi | Infrared intensifies and frequencies of 2butynenitrfie: Application to the atmosphere of Titan[END_REF]. The rotational structure of the vibronic ground state [START_REF] Sheridan | Microwave Spectrum of Methyl-Cyanoacetylene[END_REF][START_REF] Moïses | Millimeterwave spectrum of methylcyanoacetylene[END_REF][START_REF] Bester | Rotational spectrum of methylcyanoacetylene. A new millimiter wave spectrometer[END_REF] and of the v 12 fundamental vibrational level [START_REF] Yamada | Pure rotational spectrum of cyanopropyne in the v12 = 1 vibrational state[END_REF] have also been determined by microwave spectroscopy.

Concerning the electronic spectroscopy of cyanopropyne, Bruston et al. recorded a UV absorption spectrum at roomtemperature between 185 and 250 nm and made the first vibronic analysis of the transition to the first valence state [START_REF] Bruston | UV spectroscopy of Titan's atmosphere, planetary organic chemistry, and prebiological synthesis: I. Absorption spectra of gaseous propynenitrile and 2-butynenitrile in the 185-to 250-nm region[END_REF]. On the other hand, the highly-excited electronic stucture is still to be unveiled since no vacuum-ultraviolet (VUV) absorption nor multiphoton excitation spectra of CH 3 -C≡C-C≡N have been reported to date.

As for the cyanopropyne cation, very little information is cur-rently available. This information has been obtained by He(I) and He(II) photoelectron spectroscopy [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF][START_REF] Åsbrink | 30.4-nm He(II) Photoelectron spectra of organic molecules: Part II. Aza-compounds (C, H, N[END_REF][START_REF] Kuhn | Photoelectron-photon coincidence studies of the A and B excited electronic states of X-CC-CN+, X = CH3, CD3, Cl, Br, I[END_REF] in the gas phase or by neon matrix absorption spectroscopy [START_REF] Fulara | Electronic absorption spectra of cyanogen cation (NCCN + ), cyanoacetylene cation (HCCCN + ), and methylcyanoacetylene cation (MeCCCN + ) in neon matrixes[END_REF]. From these studies, ionization energies of the six lowest electronic states have been extracted and only a few vibrational frequencies of the three lowest electronic states of the cation have been measured with consequent error bars.

Finally, only three theoretical studies have been reported to our knowledge: in 1982, Niessen et al. calculated ionization energies of CH 3 C 3 N by a Green's function method [START_REF] Niessen | Ionization energies of some molecules found in interstellar clouds calculated by a green's function method[END_REF], in the 90's Siam et al. optimized the geometry of the neutral species using Hartree-Fock calculations [START_REF] Siam | Ab initio calculations of structural features not easily amenable to experiment: Part 68. Structural trends in some substituted nitriles and acetylenes[END_REF] and Moliner et al. obtained the rotational constant and the dipole moment of the vibronic ground state with second-order-Møller-Plesset (MP2) and density-functional-theory (DFT) calculations [START_REF] Moliner | Rotational constants and dipole moments of interstellar polyynes: a comparative {MP2} and density functional (BP86) study[END_REF].

The present work is focused on the CH 3 -C≡C-C≡N cationic species which might be involved in the ion-neutral chemistry of astrophysical media, as for instance the ISM and the upper atmosphere of Titan. The first part of this paper is devoted to an accurate description of the vibronic structure of the cation reached by direct ionization from the neutral ground state. Vibrational assignment of the X+ spectrum is guided by exploratory density functional theory (DFT) calculations. In the second part of this paper, dissociative ionization is studied through observation of appearance energies for the different cationic fragmentation channels of CH 3 C 3 N + . They are compared with estimated thresholds obtained by DFT calculations.

Experiment

2-Butynenitrile (cyanopropyne) has been prepared in a twostep sequence starting from ethyl butynoate (Alfa-aesar) used as a precursor of 2-butynamide, as previously reported [START_REF] Strübing | A facile and efficient synthesis of enyne-reaction precursors by multicomponent reactions[END_REF]. Then, in a flask under nitrogen, 2-butynamide (5g, 60 mmol) was mixed with sea sand (30 g) and phosphorus pentoxide (33.8 g, 240 mmol). The flask was fitted on a vacuum line (0.1 mbar) equipped with two traps. The first one was immersed in a bath cooled at -10 • C (to trap the high boiling-temperature impurities) and the second one in a bath at -50 • C. The flask was heated up to 170 • C in approximately 1 hour. The 2-butynenitrile sample produced during this process was vaporized as it was formed and selectively condensed in the second trap. Thanks to these trapping temperatures, 2-butynenitrile was obtained in a 77% yield (3.0 g, 46 mmol) with a very high purity (∼99%) checked by NMR spectroscopy.

The experiments were carried out on the DESIRS Vacuum-UltraViolet (VUV) beamline at the SOLEIL synchrotron facility in St. Aubin (France) [START_REF] Nahon | DESIRS: a state-of-the-art VUV beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL[END_REF] operating in the 8-bunch mode. This beamline is equipped with a 6.65 m normal incidence monochromator and a gas filter to eliminate the higher harmonics of the undulator [START_REF] Mercier | Experimental and theoretical study of a differentially pumped absorption gas cell used as a low energy-pass filter in the vacuum ultraviolet photon energy range[END_REF]. The VUV photon flux was monitored independently by a calibrated gold grid VUV detector in order to normalize the spectrum intensities.

The experimental setup CERISES used in this work was installed on the DESIRS beam line and has already been described previously [START_REF] Alcaraz | Dutuit, 15 N + + CD 4 and O + + 13 CO 2 State-Selected IonMolecule Reactions Relevant to the Chemistry of Planetary Ionospheres[END_REF]. Here we limit the description to the specific details of our experiment. Briefly, the CH 3 C 3 N gaseous molecules were introduced in a very low-pressure chamber (≈ 2 × 10 -6 mbar) at room temperature where they were excited by the VUV synchrotron radiation. Ions produced by the direct or dissociative ionization processes were mass-selected and guided towards the micro channel plate detector using a first quadrupolar mass filter, two octopolar guides and a second quadrupolar mass filter. The photoelectrons with near zero-kinetic energy (so-called threshold photoelectrons) were collected in the opposite direction and selected by geometrical and temporal discrimination criteria. The photon resolution of the TPES was approximately 4 meV below 15.5 eV and 10 meV above 15.5 eV. The corresponding overall resolution of the spectra, including the resolution of the photons and of the photoelectrons, was measured at 10 meV (around 80 cm -1 ) below 15.5 eV and about 15 meV above 15.5 eV in the present experimental conditions. For the dissociative ionization study, the fragment ion yields were recorded at lower resolution (15 meV). The photon energy scale of all spectra was calibrated with an accuracy of 1 meV (8 cm -1 ) using the argon and neon absorption lines observed in the ion signals due to their presence in the beamline gas filter. Note that these rare gas absorptions were not fully corrected by the normalisation procedure since the photon flux was recorded with a different spectral resolution.

Theoretical calculations

All electronic structure calculations were carried out using the Gaussian09 suite of programs [START_REF] Frisch | Gaussian 09 Revision D.01[END_REF]. Equilibrium geometries and vibrational harmonic frequencies were computed for the neutral and cation electronic ground states using DFT with the hybrid functional B97-1 [START_REF] Hamprecht | Development and assessment of new exchange-correlation functionals[END_REF], in combination with the basis set aug-cc-pvtz (AVTZ) and a grid of size (99,590).

Equilibrium geometries and vibrational frequencies for

the electronic ground states 1.

N C C C C H H H
The symmetry of the equilibrium geometry of the neutral ground state of CH 3 C 3 N was found to belong to the C 3v point group. The optimised equilibrium geometry of the cation ground state was found to be of C s symmetry due to distorsion resulting from a Jahn-Teller interaction. Note that a similar situation is encountered in the propyne cation ground state (CH 3 C 2 H + ) [START_REF] Marquez | On the Photoionization Spectrum of Propyne: A Fully ab Initio Simulation of the Low-Energy Spectrum Including the JahnTeller Effect and the SpinOrbit Interaction[END_REF]. The calculated equilibrium geometries of neutral and cationic CH 3 C 3 N are detailed in Table 1 with the labels defined in Fig. 1 corresponding to the molecular geometry in the C s symmetry group. They are compared with earlier experimental [START_REF] Sheridan | Microwave Spectrum of Methyl-Cyanoacetylene[END_REF] and theoretical [START_REF] Siam | Ab initio calculations of structural features not easily amenable to experiment: Part 68. Structural trends in some substituted nitriles and acetylenes[END_REF] values obtained for the neutral species. The present calculated structure for neutral CH 3 C 3 N is in very good agreement with the geometrical structure determined by microwave rotational spectroscopy [START_REF] Sheridan | Microwave Spectrum of Methyl-Cyanoacetylene[END_REF]. [START_REF] Sheridan | Microwave Spectrum of Methyl-Cyanoacetylene[END_REF] In Table 2, the calculated vibrational frequencies of CH 3 C 3 N and CH 3 C 3 N + in their electronic ground states are reported. Their respective geometries belonging to different point groups (C 3v and C s ) imply different labels for the vibrational normal modes. The normal modes in the cation are strongly modified with respect to the neutral normal modes. These modes are related to the eigenstates χ i,p of the force constant matrix D i j = h i j / √ m i m j where h i j = ∂ 2 V/∂r i ∂r j is the second derivative of the potential forming the Hessian matrix and m i the mass of atom i. Each of the two charge states, neutral and cation, gives rise to one set of eigenstates χ i,d,p and χ ′ i,p , respectively, where the index d for the neutral molecule is an index over the degeneracy of vibrational mode p corresponding to the C 3v symmetry group. To quantify how much the normal modes in the cation are modified with respect to the neutral molecule, we introduce the Squared Dushinsky (SD) matrix defined as

|∆ p,q | 2 = d i χ i,d,p χ ′ i,q 2 (1)
In Fig. 2, a map plot of the SD matrix is shown as a function of the neutral and cation mode number. Among the symmetric normal modes of the neutral species (of a 1 symmetry), one can see that the ν 2 , ν 3 , ν 5 and ν 6 normal modes correlate almost exclusively to the ν + 3 , ν + 4 , ν + 7 and ν + 9 normal modes of the cation, respectively. For the degenerate e mode of the neutral species, only the ν 10 and ν 12 modes can be associated in good approximation with the couples of mode (ν + 10 , ν + 15 ) and (ν + 12 , ν + 18 ) of the cation, respectively. Note that the calculated vibrational frequencies corresponding to these couples are degenerate or quite close (see Table 2). The other normal modes of the neutral molecule (ν 1 , ν 4 , ν 7 , ν 8 , ν 9 and ν 11 ) are more delocalised over the normal modes of the cation. Thus, one cannot easily compare these latter vibrational modes between the neutral and the cation without crude approximations. The correlations between the normal modes of the neutral species and the cation are summarized in Table A.10 of Appendix A. From the harmonic frequencies and normal modes in the neutral and cation ground states, the Franck-Condon (FC) factors have been calculated for the X+ 2 E ← X 1 A 1 transition using the harmonic approximation for the potential energy surfaces and the Condon approximation for the dipole moment. The FC integrals were computed, including the Duschinsky effect, using recursive formulae already implemented in Gaussian09 [START_REF] Barone | Fully Integrated Approach to Compute Vibrationally Resolved Optical Spectra: From Small Molecules to Macrosystems[END_REF]. The strongest Franck-Condon factors are reported in Table B.11 of Appendix B. From the Franck-Condon factors, the TPES at 0 K was computed by convoluting the stick spectrum with a Gaussian line shape of 160 cm -1 full-width at half maximum (FWHM), which reproduces well the observed band widths resulting from the spectral resolution and the rotational band profile.

Dissociative ionization thresholds

CH 3 C 3 N ionization energy and product dissociative ionization thresholds were calculated and corrected for zero-point energies (ZPE). The thresholds were calculated only for the channels leading to the lower electronic states of the fragments (S 0 singlet or T 1 triplet states for fragments with odd spin multiplicity, and D 0 doublet states for even spin multiplicity). Note that the present calculations have been carried out at 0 K and thus do not take into account the temperature dependence of the threshold. The observed appearance energies might also be affected by possible activation barriers which are not included in the calculations. Nevertheless, these crude approximations allowed us to identify the observed dissociative channels (see section 4.2).

Results and discussion

Photoionization of cyanopropyne

The CH 3 C 3 N + ion yield and the threshold photoelectron spectrum of CH 3 C 3 N have been recorded in the [86000-180000 cm -1 ] region for the first time and are displayed in Fig. 3.

The TPES spectrum is quite similar to the PES spectrum reported by Bieri et al. [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF], leading to observation of six electronic states. The assignments of the different electronic states have been determined in Ref. [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF] and are reported in Fig. 3. The ionization thresholds measured in the present work towards the different electronic states of the cation are summarized in Table 3 and compared with previous studies. The three lowest electronic states, X+ 2 E, Ã+ 2 A 1 and B+ 2 E, exhibit a sharp peak at their origin followed by vibrational progressions. Their origins are located at 86872 ± 20 cm -1 , 105354 ± 20 cm -1 and 107848 ± 20 cm -1 , respectively (see Table 3), in good agreement with Bieri et al. values within their error bars [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF]. The disagreement with the results of Åsbrink et al. is suspected to come from their calibration procedure in which they only used one argon line for the calibration of the entire range of the spectrum (from 9 to 27 eV) [START_REF] Åsbrink | 30.4-nm He(II) Photoelectron spectra of organic molecules: Part II. Aza-compounds (C, H, N[END_REF]. The three next states C+ , D+ and Ẽ+ are much broader and unresolved, except for the C+ state. This indicates a predissociative character for the D+ and Ẽ+ states and important alterations in the geometry of the C+ state with respect to the ground state of the neutral species. It is of interest to mention that the measured ionization thresholds towards the X+ and B+ states of cyanopropyne cation (10.77 eV and 13.37 eV, respectively) are very close to the first ionization threshold of propyne (10.37 eV [START_REF] Xing | Rovi-brationally selected and resolved pulsed field ionization-photoelectron study of propyne: Ionization energy and spin-orbit interaction in propyne cation[END_REF]) and hydrogen cyanide (13.6 eV [START_REF] Baker | High resolution molecular photelectron spectroscopy. III. Acetylenes and aza-acetylenes[END_REF]), respectively. This situation is similar to what was encountered in the case of cyanoacetylene [START_REF] Mendes | Rydberg states of cyanoacetylene investigated by (3+1) REMPI spectroscopy in the 77,000 90,000 cm -1 energy range[END_REF] for which the ionization thresholds were close to the one of acetylene and hydrogen cyanide. This trend was explained for cyanoacetylene by the removal of a π electron more localised on the C≡C bond for the X + state or on the C≡N bond for the B + state. By analogy, we propose that the removal of an electron from the (3e) molecular orbital leading to the X+ 2 E state of cyanopropyne cation is more localised on the C≡C bond. Similarly, the B+ 2 E state is formed by the ejection of an electron from the (2e) molecular orbital more localised on the C≡N bond. Above the first ionization threshold (86872 cm -1 ), the ion yield shown in Fig. 3 exhibits sharp structures up to 105000 cm -1 which correspond to autoionization of Rydberg series converging to the Ã+ and B+ excited electronic states of the cation. The assignments of these series will be discussed in a forthcoming paper. Above 109300 cm -1 , the ion yield significantly decreases up to 120000 cm -1 . This range corresponds to the gap between the B+ and C+ electronic states and no Rydberg series converging to the C+ electronic state is observed. Therefore we attribute this drop in the CH 3 C 3 N + ion yield to the opening of different dissociative ionization channels (see section 4.2). The ion signal increases again around 120000 cm -1 corresponding to the opening of the C+ ionization channel.

An important remark concerns the mode labelling adopted throughout this paper. Indeed, the vibrational modes are different between the neutral and cation electronic ground state in their respective point group, as discussed in section 3, and the same situation is probably encountered in the other electronic states. In earlier works, the C 3v notations were used. Here, all electronic structure calculations are limited to the X+ electronic ground state. Consequently, the proposed assignment for the vibronic transitions to the X+ electronic ground state is derived from our calculations of the vibronic structure of X+ state in the C s symmetry but the labels are converted into the C 3v notation (see Fig. 2 andTable A.10 of Appendix A). The proposed assignment for the vibronic transitions to the Ã+ , B+ and C+ states are derived only by comparison with the vibrational structure of the neutral electronic ground state.

Hence, we choose in this paper to use the vibrational mode labels of the neutral species in the C 3v point group for the transitions to the cation vibronic states. For example, Fig. 4 a) shows the TPES spectrum of the X+ 2 E ← X 1 A 1 transition, which exhibits a progression in the symmetric C≡N and C≡C stretches. Using the C 3v labels (neutral symmetry), this corresponds to the ν 2 mode, but in the C s symmetry of the ion, this mode would correspond to the ν + 3 mode (as defined in Table 2). The assignments of the vibronic transitions to the four lowest electronic states of the cation are presented below.

4.1.1. The X+ 2 E ← X 1 A 1 transition
Figs. 4 a) and 4 b) display the experimental TPES spectrum (in black) in the vicinity of the X+ electronic ground state of CH 3 C 3 N + and the corresponding calculated spectrum (in red). Only an horizontal shift has been applied to the calculated spectrum to match the 0 0 band position of the experimental spectrum. Although DFT being monoconfigurational is not fully appropriate to describe the CH 3 C 3 N + electronic ground state which is affected by Jahn-Teller effect, the overall agreement between the calculated and experimental spectra is quite good. The main discrepancies are the positions of the 9 1 and 2 1 bands (and therefore the combination bands involving these modes) which can be explained by anharmonic effect, and the band intensities in the 87750-89000 cm -1 range (see Fig. 4 b)) which will be discussed later in this section. In the Born-Oppenheimer approximation, a transition between the neutral vibronic ground state and a vibronic state of the cation is allowed only if the product of the vibrational wavefunctions contains a symmetric component. Therefore, in C 3v symmetry, the modes of e symmetry should be reached only with even quanta of excitation whereas the modes of a 1 symmetry should be reached with even and odd quanta of excitation. In the present case, the e modes correlate with a ′ + a ′′ components in the C s point group. Consequently, the transition to odd quanta of excitation is allowed for the e modes through the a ′ components.

In Fig. 4 a), one can see the main vibrational progression due to the ν 2 mode (C≡N and C≡C stretches in phase, with a 1 symmetry) due to the changes of the C≡N and C≡C bond lengths upon ionization (see Table 1). The corresponding vibrational wavenumber is decreased (from 2271 cm -1 in the neutral species to 2178 ± 20 cm -1 in the cation) which is consistent with the predicted increases of these bond lengths. The calculated TPES spectrum confirms the observed progression in the ν 2 mode (with the neutral notation in the C 3v point group) but the calculated vibrational wavenumber and intensity of the 2 n bands are slightly overestimated. Close to the 2 1 band, one can see (Fig. 4 b)) that the 3 1 band (which corresponds to the C≡N and C≡C stretches in opposite phase) is observed in the experimental spectrum unlike in the calculated spectrum. We suspect that the ν 2 and ν 3 normal modes or the C≡C and C≡N bond lengths are not well described with our calculations and that the calculated intensity of the 2 1 band is actually spread over the 2 1 and 3 1 observed bands.

The intensity disagreement around the position of the 5 1 band can also be attributed to the limited validity of our calculation. In addition, the TPES intensity in this region is likely affected by autoionization. Indeed, in the ion yield spectrum displayed in Fig. 3, one can see a very strong line located at the same energy (88100 cm -1 ) which is the signature of an efficient autoionization process.

The other bands are quite well reproduced but their labels are not trivial. As mentioned above, we use the C 3v notation for the vibrational mode labelling but the calculation results are given with the C s notation labels. The calculated band that we label 11 2 is actually the 17 2 band in C s notation (see Table A.10 in Appendix A). In Fig. 2, the SD matrix shows that the projection of the ν + 17 cation normal mode over the normal modes of the neutral species is actually spread over the ν 11 mode (with the higher contribution) and the ν 9 and ν 8 modes. For the same reason, the band which overlaps in the calculated spectrum with the band that we label 6 1 (9 1 in the C s notation) is the 16 1 17 1 band. From the map plot of the SD matrix, we cannot derive a corresponding mode in the C 3v notation. That is why we use the question mark in Fig. 4 b). The last ambiguous band is the one labeled 4 1 /8 1 . Indeed the calculated spectrum gives a transition at this energy with corresponds to the 5 1 transition in the C s notation. Again, from the SD matrix, this normal mode of the cation is associated to the ν 4 and ν 8 normal modes of the neutral species.

The position of the bands with their labels in the C 3v notation are listed in Table 4. The corresponding vibrational wavenum-bers are compared with the earlier work of Bieri et al. [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF] in Table 8. We find that the values for the ν 2 and ν 9 vibrational modes obtained by Bieri et al. are in good agreement with the present results within the error bars. a IP( X+ ) = 86872 cm -1

4.1.2. The Ã+ 2 A 1 ← X 1 A 1 transition
The region of the TPES spectrum which includes the vibronic transitions to the Ã+ state is displayed in Fig. 5. Similarly to the transition to the X+ state, the ν 2 mode is active upon ionization and the transition towards v 2 = 2 vibrational state is probably hidden in the region of the transitions to the B+ states. The proximity of these two electronic states might lead to vibronic interactions. The other observed bands are assigned to transitions involving the 5 1 , 6 1 , 8 1 , 9 1 and 11 2 transitions. The vibrational structure of this electronic transition being quite similar to the one involving the electronic ground state of the cation, we can suppose that the two lowest electronic states ( X+ and Ã+ ) have close equilibrium geometry. Higher-level calculations such as Complete Active Space Self-Consistent Field (CASSCF) would be necessary to confirm this hypothesis. The positions of the vibronic transitions presented in Fig. 5 are summarized in Table 5. The comparison of the derived vibrational wavenumbers with the work of Bieri et al. [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF] and Fulara et al. [START_REF] Fulara | Electronic absorption spectra of cyanogen cation (NCCN + ), cyanoacetylene cation (HCCCN + ), and methylcyanoacetylene cation (MeCCCN + ) in neon matrixes[END_REF] is reported in Table 8. Within the error bars, our value for the ν 6 vibrational mode is consistent with the one obtained by Bieri et al.. The disagreement with the results of Fulara et al. probably comes from matrix effects. In addition, the authors mentioned that the fluorescence spectrum is strongly affected by non-radiative relaxation of the B+ state towards the Ã+ state.

The B+ 2 E ← X 1 A 1 transition

The TPES spectrum in the vicinity of the B+ 2 E ← X 1 A 1 transition is also displayed in Fig. 5. Unlike for the transition to the X+ and Ã+ electronic states, the main vibrational progression is assigned to the ν 5 mode (≡C-C≡ stretch) with a vibra- tional wavenumber of 1132±20 cm -1 . The other transitions are mainly associated with the ν 3 , ν 6 , ν 11 and ν 12 vibrational modes and their combination bands with the ν 5 mode.

On the right part of the spectrum, two broad features are observed around 110500 and 111700 cm -1 . The assignments of these bands is not trivial. In this region, too many combination bands involving the Ã+ and B+ electronic states could be reasonably consistent with the overall vibronic structure of these two states. High-resolution spectra and more sophisticated calculations are necessary to unambiguously assign these bands and thus no attempt is made to do so. Table 6 summarizes the positions of the assigned bands of the B+ 2 E ← X 1 A 1 transition. The derived vibrational wavenumbers are reported in Table 8. A good agreement is found with the ν5 and ν6 values measured by Bieri at al. [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF] and Fulara et al. [START_REF] Fulara | Electronic absorption spectra of cyanogen cation (NCCN + ), cyanoacetylene cation (HCCCN + ), and methylcyanoacetylene cation (MeCCCN + ) in neon matrixes[END_REF] within their error bars. distinguish the C+ and the D+ states which strongly overlap as was observed already by Åsbrink et al. [START_REF] Åsbrink | 30.4-nm He(II) Photoelectron spectra of organic molecules: Part II. Aza-compounds (C, H, N[END_REF]. Surprisingly, these states seem more distinguishable in the spectrum of Bieri et al. although the resolution is less than ours [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF]. Nevertheless, an extended vibrational progression is clearly observed on the red side of the broad band with a first intense peak at 119390 ± 50 cm -1 . We propose to assign this peak to the origin of the C+ state regarding the sharp rise for this first peak with respect to the background signal and the evolution of the peak intensities over the band. If a vibronic transition with a smaller Franck-Condon factor existed at lower wavenumber, our signalto-noise ratio would allow us to observe it. It is clear in our spectrum that no such transition occurs. We assign the vibrational progression to the ν 8 mode (CH 3 asymmetric deformation) with combination band with the ν 6 mode (C-C stretches in phase) by comparing the corresponding vibrational wavenumbers with the ones of the three lowest electronic states of the cation (see Table 8). The peak positions of this extended series are listed in Table 7.

The vibronic structure of this spectrum demonstrates a change in geometry of the C+ state with respect to the X neutral ground state. The same trend was observed for the C+ state of HC 3 N + by Baker and Turner [START_REF] Baker | High resolution molecular photelectron spectroscopy. III. Acetylenes and aza-acetylenes[END_REF].

Note that the origin of the D+ ← X 1 A 1 transition is not observed. Nevertheless, a very tentative value of 130160 ± 500 cm -1 for the vertical ionization threshold can be derived from the maximum of the broad bump reached before the drop of the signal (see Fig. 6). In the PES spectrum of Bieri et al., which exhibits a different energy profile for this band, they peaked the maximum of the transition to the D+ state at 131468 cm -1 [START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF].

Table 8: Experimental and calculated (in italics) vibrational wavenumbers of the electronic ground state of CH 3 C 3 N and the four lowest electronic states of CH 3 C 3 N + . All values are in cm -1 and error bars are given in parenthesis. When no unambiguous correlation between the neutral and cation normal mode can be drawn, the calculated value is replaced by a question mark.

Dissociative ionization of cyanopropyne

Mass spectra recorded at 12, 15.5 and 20 eV are presented in Figs. 7 a), b) and c), respectively. The mass spectrum of Fig. 7 a) (at 12 eV) exhibits only two peaks corresponding to the CH 3 C 3 N + parent ion (m/q=65) and its natural 13 C isotopologue (m/q=66). The mass spectrum of Fig. 7 b) (at 15.5 eV) already starts to show evidences for dissociative ionization with two main fragments at m/q = 38 and m/q = 64 and very weak signals at m/q = 15, m/q = 28 and m/q = 63 (hardly visible on the scale of this spectrum, see spectrum of panel c) at 20 eV). The mass spectrum of Fig. 7 c) (at 20 eV) presents the same fragments and in addition m/q = 37. All the other ion signals are due to 13 C isotopologues or impurities (see below).

Let us examine first the mass signals which are not directly relevant for the present study.

The signals at m/q = 18 and m/q = 17 in Figs. 7 b) and c) correspond to H 2 O and its OH dissociative ionization fragment since water was a residual by-product of the CH 3 C 3 N synthesis.

Between masses 40 and 55, we observe residual impurities coming from other samples studied with the same experimental setup in the past. The masses observed at m/q = 44, 50 and 51 can be assigned without any ambiguity to CD 3 CN, CH 3 Cl and HC 3 N, respectively, comparing the observed ion yields (not shown here) with earlier works [START_REF] Schwell | {VUV} photophysics of acetonitrile: Fragmentation, fluorescence and ionization in the 722 eV region[END_REF][START_REF] Locht | About the photoionization of methyl chloride. A threshold photoelectron spectroscopic and photoionization mass spectrometric investigation[END_REF][START_REF] Leach | Ionization photophysics and spectroscopy of cyanoacetylene[END_REF].

The mass spectrum of Fig. 7 b) exhibits a peak at m/q = 62 which might be assigned to the C 4 N + fragment at first sight. However, the appearance energy measured for this mass was lower (≈ 12.1 eV) than the ones of H-and H 2 -loss channels (see below). We rather assign it to a dissociative ionization fragment of CH 3 C 5 N traces, which had been studied during the same experimental beamtime. Indeed, the excitation of CH 3 C 5 N at 15.5 eV produces a strong ion signal at m/q = 62 corresponding to C 4 N + (see mass spectrum in Appendix C). No dissociative ion yield has been recorded for this molecule but the complete dis- sociative photoionization study of CH 3 C 5 N will be investigated in details soon. Finally, the signal observed at m/q = 27 is attributed to photoionization of HCN by comparing the ion yield measured in this work with the one of Ref. [START_REF] Baker | High resolution molecular photelectron spectroscopy. III. Acetylenes and aza-acetylenes[END_REF]. The neutral HCN molecule responsible for this signal is suspected to be a product of either photolysis or dissociative photoionization of cyanopropyne.

During our experimental beamtime, we only measured the appearance energies of the fragments which are below 15.5 eV. Thus, the data corresponding to masses 64, 63, 38, 28 and 15 are discussed below and their corresponding ion yields are presented in Figs. 8 a) to e). The observed appearance energies are marked by arrows in these figures and summarized in Table 9. In this table, the experimental measurements are compared with the calculated thresholds which allows us to propose a corresponding dissociative ionization process for each fragment.

As mentioned in section 3, the calculated thresholds only give a rough idea of the corresponding appearance energies. For instance, the calculated ionization energy of CH 3 C 3 N is 10.22 eV whereas the experimental value is 10.77 eV (86872 cm -1 ), which gives a discrepancy of 0.55 eV. One should also keep in mind that the calculations do not take into account the temperature dependence and the possible activation barrier of the dissociative channels, as explained in section 3. Thus, we roughly estimate that the calculated thresholds are reasonably representative of the observed appearance energies within 1 eV.

In Table 9, one can see that the channels producing ions with m/q = 64 and m/q = 63 (seen in Fig. 8 a) and b)) are easily assigned to the CH 2 C 3 N + (S) + H and CHC 3 N + (D) + H 2 dissociative channels and that the calculations are in good agreement with the observed appearance energies. The appearance energy measured for m/q = 38 (see Fig. 8 c)) is close to the calculated threshold for the HC 3 H + (D) + HCN(S) channel. This channel is quite surprising and complex mechanisms have to be involved in the dissociative ionization processes to lead to these reorganised fragments. Similar molecular rearrangements have to be invoked to understand the m/q = 37 fragment formation (production of C 3 H + , see Table 9). As mentioned above, the corresponding ion yield has not been measured but the mass spectra of Figs. 7 b) and c) allow to give lower and upper limit values: between 15.5 and 20.0 eV. Unfortunately, the calculated thresholds of the three possible channels lie in this range and we cannot conclude on the process responsible for this C 3 H + fragment.

Finally, the fragments at m/q = 28 and 15 are the two minor products. The measured appearance energies are close to the threshold of the lowest dissociative channel calculated for these two masses and involving ion-pair formation (HCNH + (S) + HC 3 -(S) and CH + 3 (S) + C 3 N -(S)). One can remark that the ion yields corresponding to the proposed ion-pair formations have weaker intensities by 1 or 2 order of magnitudes compared to the other fragments (see vertical scales of Fig. 8) which is consistent with the usual ion-pair formation efficiency. One could argue that the experimental appearance energy for m/q = 15 is quite high with respect to the calculated one compared with the overall agreement for the other channels. However, ionpair potential curve minima are not located at the same equilibrium geometry as the ground state of the molecule [START_REF] Suits | Ion pair dissociation: Spectroscopy and dynamics[END_REF]. Therefore, a photon excitation (which is a vertical excitation) brings the molecule in the Franck-Condon region of the ion-pair potential curve which is often higher than the ion-pair dissociative threshold. This could explain the consequent difference of 1.7 eV observed between the experimental and calculated energies. In the case of the m/q = 28 channel, the excess energy is only about 0.1 eV. A possible explanation is that the ion-pair dissociation process is different. Indeed, unlike in the CH + 3 + C 3 N -channel which seems to proceed through a direct dissociation process, the HCNH + + HC 3 -channel necessitates an important atomic rearrangement probably involving intermediates which might be coupled to the ion-pair potential curve [START_REF] Suits | Ion pair dissociation: Spectroscopy and dynamics[END_REF] leading to a near-threshold dissociation.

Conclusion

Photoionization spectroscopy of cyanopropyne has been investigated by TPES for the first time over a wide energy range at SOLEIL synchrotron facility thanks to the VUV tunability of the DESIRS beamline. New values of the ionization thresholds towards the four lowest electronic states of the cation have been measured with improved accuracy. The vibrationally-resolved spectra combined with DFT calculations bring new insights on the complex vibronic structure of CH 3 C 3 N + . The DFT calculations performed in this work predict for the first time the geometry of the electronic ground state of the cation and account for the vibrational progression observed in our experimental spectrum. This geometry was found to be of C s symmetry due to a Jahn-Teller interaction. Higher resolved experiments should be a The corresponding ion yield was not measured in this work. From Fig. 7, a threshold is expected between 15.5 and 20 eV which does not allow to draw any conclusion about the corresponding process.

carried out to highlight a clear signature of this interaction. In the ground and the second excited electronic states ( X+ 2 E and B+ 2 E) of the cation, a spin-orbit coupling of non-negligible magnitude is also expected. Indeed, in the HC 3 N + cation, a spin-orbit splitting of 44 cm -1 has been measured [START_REF] Pfi-Zeke | study of HC 3 N will[END_REF]. In CH 3 C 3 N + , we can suspect a spin-orbit splitting of the same order of magnitude, slightly decreased by the off-axis H atoms [START_REF] Mcclure | Spin-orbit interaction in aromatic molecules[END_REF][START_REF] Herzberg | Molecular spectra and molecular structure III. Electronic spectra and electronic structure of polyatomic molecules[END_REF]. Thus, higher-resolved spectra of the X+ 2 E ← X 1 A 1 transition should exhibit a complex rovibronic structure due to the combination of the Jahn-Teller effect and spin-orbit coupling like in propyne [START_REF] Marquez | On the Photoionization Spectrum of Propyne: A Fully ab Initio Simulation of the Low-Energy Spectrum Including the JahnTeller Effect and the SpinOrbit Interaction[END_REF][START_REF] Xing | Rovi-brationally selected and resolved pulsed field ionization-photoelectron study of propyne: Ionization energy and spin-orbit interaction in propyne cation[END_REF] and the 2-butyne [START_REF] Jacovella | Internal rotation, spin-orbit coupling, and low-frequency vibrations in the X 2 E ground state of CH 3 -CC-CH + 3 and CD 3 -CC-CD + 3[END_REF] cations. Pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy would be perfectly suited for this purpose. In addition vibronic coupling between the Ã+ and B+ electronic states is expected from their vicinity. More sophisticated multiconfigurational ab initio calculations of the excited electronic states of CH 3 C 3 N + , such as CASSCF approaches, are required to deepen our understanding of this cation. Appearance energies for the dissociative photoionization channels below 15.5 eV have been measured for the first time and the proposed channels are guided by quantum chemical calculations. Interestingly, two channels tentatively associated with ion-pair formation (CH + 3 + C 3 N -and HCNH + + C 3 H -) are observed through the detection of the positive ion fragment. Experiments combining the detection of the positive and negative ions in coïncidence would allow to definitely confirm these channels.

Figure 1 :

 1 Figure 1: CH 3 C 3 N molecule structure. The labels correspond to the ones used in Table1.

2 Figure 2 :

 22 Figure 2: Map plot of the Squared Dushinsky matrix of CH 3 C 3 N (see text for more details). The color scale indicates the correlation degree between the neutral and cation normal modes in the ground states.

Figure 3 :

 3 Photon energy / eV

Figure 4 :

 4 Figure 4: Panel a) Experimental threshold photoelectron spectrum of CH 3 C 3 Nin the vicinity of the X+ 2 E ← X 1 A 1 transition (in black) with the calculated TPES spectrum (in red). The calculated stick spectrum has been convoluted with a gaussian line shape (FWHM=160 cm -1 ) for clarity. Panel b) Zoom of the same spectra between 86250 and 90750 cm -1 . The assignments of the X+ vibrational states are given with the neutral normal mode notations. For clarity, the calculated spectrum is shifted down. The question mark accounts for normal modes of the cation which have no equivalent in the C 3v point group (see text for details).

Figure 6 :

 6 Figure 6: Threshold photoelectron spectrum of CH 3 C 3 N in the vicinity of the C+ ← X 1 A 1 and D+ ← X 1 A 1 transitions with the assignments of the C+ vibrational states. The tentative vertical ionization threshold of D+ state is marked by an arrow.

  / a.m.u.

Figure 7 :

 7 Figure 7: Mass spectra obtained with photon energies of a) 12 eV, b) 15.5 eV and c) 20 eV.

  Photon energy / eV

Figure 8 :

 8 Figure 8: Fragment ion yields of the dissociative photoionization of CH 3 C 3 N. Note that the vertical scale is identical for all fragments. The arrows indicate the appearance energy of each fragment. See text for more details.

  arb. units) m/q / a.m.u.

Figure C. 9 :

 9 Figure C.9: Mass spectra obtained with photon energies of a) 12 eV and b) 15 eV in the photoionization study of CH 3 C 5 N.

Table 1 :

 1 Calculated and experimental bond distances (Å) and angles (degrees) for CH 3 C 3 N in neutral and cationic electronic ground states. The values from this work are in bold font.

	calc. a	CH 3 C 3 N (C 3v ) calc. b exp c	CH 3 C 3 N + (C s ) calc. b
	1.132 1.388 1.183 1.466 1.086 1.086 180.0 180.0 180.0 110.0 110.0 108.9 108.9 a HF/4-21G*, calculated values from Ref. [26] 1.159 1.157 N≡C 1 1.369 1.379 C 1 -C 2 1.207 1.203 C 2 ≡C 3 1.452 1.458 C 3 -C 4 1.093 1.10 C 4 -H 1 1.093 1.10 C 4 -H 2 180.0 180.0 N≡C 1 -C 2 180.0 180.0 C 1 -C 2 ≡C 3 180.0 180.0 C 2 ≡C 3 -C 4 110.5 -C 3 -C 4 -H 1 110.5 -C 3 -C 4 -H 2 108.4 108.5 H 1 -C 4 -H 2 108.4 108.5 H 2 -C 4 -H 2	1.179 1.335 1.243 1.414 1.110 1.097 180.0 180.1 179.1 107.0 111.5 107.0 112.5
	b B971/AVTZ, this work
	c Experimental values from Ref.

Table 2 :

 2 Calculated harmonic frequencies for CH 3 C 3 N in neutral and cationic electronic ground states in the C 3v and C s point group, respectively. The symmetry of the modes and their approximate description are also reported. All values are in cm -1 .

	mode	CH 3 C 3 N (C 3v ) description	symmetry	ν	CH 3 C 3 N + (C s ) description	symmetry	ν+
	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18	CH 3 sym. stretch C≡N, C≡C stretches (in phase) C≡N, C≡C stretches (opposite phase) CH 3 sym. deformation C-C stretches (opposite phase) C-C stretches (in phase) CH 3 asym. stretch CH 3 asym. deformation CH 3 rock C-C≡C-C≡N skeleton bend C-C≡C-C≡N skeleton bend C-C≡C-C≡N skeleton bend	a 1 a 1 a 1 a 1 a 1 a 1 e e e e e e	3023 2384 2252 1403 1174 670 3090 1464 1042 537 357 146	CH 3 stretch CH 3 stretch C≡N, C≡C stretches (in phase) C≡N, C≡C stretches (opposite phase) CH 3 deformation CH 3 deformation C-C stretches (opposite phase) CH 3 rock C-C stretches (in phase) C-C≡C-C≡N skeleton bend C-C≡C-C≡N skeleton bend C-C≡C-C≡N skeleton bend CH 3 stretch CH 3 deformation C-C≡C-C≡N skeleton bend + CH 3 def. C-C≡C-C≡N skeleton bend + CH 3 def. C-C≡C-C≡N skeleton bend + CH 3 def. C-C≡C-C≡N skeleton bend	a ′ a ′ a ′ a ′ a ′ a ′ a ′ a ′ a ′ a ′ a ′ a ′ a ′′ a ′′ a ′′ a ′′ a ′′ a ′′	3016 2901 2275 2018 1413 1305 1224 3021 1233

Table 3 :

 3 Ionization thresholds towards the different electronic states of CH 3 C 3 N + . All values are in cm -1 and correspond to adiabatic energies unless specified. Experimental error bars are given in parenthesis.

	X+ 2 E Ã+ 2 A 1 B+ 2 E C+ D+ Ẽ+	This work 86872(20) 105354(20) 107848(20) 119390(50) 130160(500) a,b 164300(500) b	Bieri et al. [21] Åsbrink et al. [22] 86947(160) 88318(160) 105336(160) 105336(160) 107836(160) 109046(160) 121790(800) b 122596(800) b 131468(800) b 133081(800) b 165344(800) b 165344(800) b

a Tentative value (see text). b Value for the vertical ionization threshold derived from the position of the band maximum.

Table 4 :

 4 Band wavenumbers and assignments of the X+ 2 E ← X 1 A 1 vibronic transitions observed in the TPES. All values are in cm -1 .

	Wavenumber Wavenumber -IP( X+ ) a	Upper level assignment
	86872 87320 87525 87889 88100 88253 88805 89050 89674 90070 90270 91246 93182	0 448 653 1017 1228 1381 1933 2178 2802 3198 3398 4374 6310	0 0 11 2 6 1 and ? 9 1 5 1 4 1 / 8 1 3 1 2 1 2 1 6 1 and 2 1 ? 2 1 9 1 2 1 5 1 2 2 2 3

Table 5 :

 5 Band wavenumbers and assignments of the Ã+ 2 A 1 ← X 1 A 1 vibronic transitions observed in the TPES. All values are in cm -1 .

	Wavenumber Wavenumber -IP( Ã+ ) a	Upper level assignment
	105354	0	0
	105830	476
	106009	655	6
	106280	926	9
	106513	1159	5
	106688	1334	6
	106975	1621	8
	107600	2246	2

a IP( Ã+ ) = 105354 cm -1

Table 6 :

 6 Band wavenumbers and assignments of the B+ 2 E ← X 1 A 1 vibronic transitions observed in the TPES. All values are in cm -1 .Figure5: Threshold photoelectron spectrum of CH 3 C 3 N in the vicinity of the Ã+ 2 A 1 ← X 1 A 1 and B+ 2 E ← X 1 A 1 transitions with the assignments of the Ã+ (in black) and B+ (in gray) vibrational states.

	Wavenumber Wavenumber -IP( B+ ) a	Upper level assignment
	107848 107970 108252	0 122 404	0 12 1 11 2
	108541	693	6
	108980 109350 109615	1132 1502 1767	5 5 1 10 1 5 1
	109835	1987	3
	110070 111033	2222 3185	5 5 1
	111120	3272	5

a IP( B+ ) = 107848 cm -1 4.1.4. The C+ ← X 1 A 1 and D+ ← X 1 A 1 transitions

In Fig.

6

, the TPES in the region of the C+ and D+ states is shown. In our spectrum, we are not able to unambiguously

  Average value of the R and P branch positions. d 2ν 4 band position divided by 2. e wavenumbers corresponding to either ν 1 or ν 7 modes. f wavenumbers corresponding to either ν 4 or ν 8 modes. g From PES experiment of Ref.[START_REF] Bieri | Electronic states of substituted haloacetylene and cyanoacetylene radical cations[END_REF]. h From EAS experiment of Ref.[START_REF] Fulara | Electronic absorption spectra of cyanogen cation (NCCN + ), cyanoacetylene cation (HCCCN + ), and methylcyanoacetylene cation (MeCCCN + ) in neon matrixes[END_REF]. i Derived from the 11 2 band position.

		X 1 A 1	this work	X+ 2 E	literature	this work	Ã+ 2 A 1 literature	this work	B+ 2 E literature	C+ this work
	ν1	2938.5 a,c	-		-	-	-	-	-	-
		3023	?
	ν2	2271 a,c	2178(20)		2100(80) g	2246(30)	2332(30)? h	-	-	-
		2384	2275
	ν3	2168 a,c	1933(30)		-	-	-	1987(30)	-	-
		2252	2018
	ν4	1373.5 a,d	(1381(30) f )	-	-	-	-	-	-
		1403	?
	ν5	1156 a,c	1228(20)		-	1159(40)	-	1132(20)	1100(80) g	-
		1174	1224						1105(30) h
	ν6	642.5 a,c	653(30)		-	655(30)	560(80) g	693(30)	700(80) g	705(40)
		670	680				545(30) h		676(30) h
	ν7	2987 a	-		-	-	-	-	-	-
		3090	?
	ν8	1445 a	(1381(30) f )	-	1621(20)	-	-	-	1586(40)
		1464	?
	ν9	1030 a	1017(30)		930(80) g	926(30)	-	-	-	-
		1042	?
	ν10	499 a	-		-	-	-	-	-	-
		537	?
	ν11	339 a	224(30) i		-	238(30)	-	202(30)	-	-
		357	?
	ν12	144.75 b,c	-		-	-	-	122(40)	-	-
		146	133

a Ref.

[START_REF] Tubino | Vibrational Spectrum and VibroRotational Analysis of Cyanopropyne[END_REF]

. b Ref.

[START_REF] Khlifi | Infrared intensifies and frequencies of 2butynenitrfie: Application to the atmosphere of Titan[END_REF]

. c

Table 7 :

 7 Band wavenumbers and assignments of the C+ ← X 1 A 1 vibronic transitions observed in the TPES. All values are in cm -1 .

	Wavenumber Wavenumber -IP( C+ ) a	Upper level assignment
	119390 120095 120976 121628 122318 123083 123864 124536 125176 125975 126507 127225 127982 128793	0 705 1586 2238 2928 3693 4474 5146 5786 6585 7117 7835 8592 9403	0 0 6 1 8 1 8 1 6 1 8 2 8 2 6 1 8 3 8 3 6 1 8 4 8 4 6 1 8 5 8 5 6 1 8 6 8 6 6 1

a IP( C+ ) = 119390 cm -1

Table 9 :

 9 Calculated thresholds and experimental appearance energies of dissociative ionization channels of CH 3 C 3 N. The uncertainties of the experimental values are about 0.10 eV. (S) and (T) denote the singlet or triplet spin multiplicity of the fragments (the fragments are in doublet states when it is not specified). See text for more details.

	m/q / a.m.u.	channel	AE calc / eV	AE exp / eV
	64	CH 2 C 3 N + (S) + H	12.7	12.35
	63	CHC 3 N + + H 2 (S) CHC 3 N + + 2H	12.6 16.9	12.09
	38	HC 3 H + + HCN(S) HC 3 H + + HNC(S) H 2 C + 3 + HCN(S) H 2 C + 3 + HNC(S)	12.4 13.0 13.9 14.5	12.14
	37	HC + 3 (S) + H 2 CN HC + 3 (S) + HCNH HC + 3 (S) + H 2 (S) + CN	15.5 16.1 17.9	-a -a -a
	28	HCNH + (S) + HC 3 HCNH + (S) + HC 3 -(S) H 2 CN + (T) + HC 3 -(T) HCNH + (T) + HC 3 -(T) H 2 CN + (T) + HC 3	12.1 13.8 16.8 16.8 18.6	12.21
	15	CH + 3 (S) + C 3 N -(S) CH + 3 (S) + C 3 N CH + 3 (T) + C 3 N -(T) NH + + C 4 H 2 (S) CH + 3 (T) + C 3 N	11.1 15.4 18.1 18.7 18.8	12.80

Table A .

 A 10: Correlation between the normal modes of the ground states of CH 3 C 3 N and CH 3 C 3 N + .

		ν 9 / ν 11
	ν + 18	ν 12

Table B .

 B 11: Calculated wavenumbers with respect to IP( X+ ) and FC factors of the X+ 2 E ← X 1 A 1 transition. All transitions are from the vibronic ground state of the neutral and only the transitions with a FC factor greater than 0.008 are reported. the CH 3 C 3 N experiment (see section 4.2) are also observed in the present mass spectra recorded prior to the CH 3 C 3 N photoionization study.

		51 detected in
	Upper level assignment wavenumber / cm -1 (C s notation) 0 0 0 11 1 346 17 2 478 16 1 17 1 679 9 1 680 8 1 913 7 1 1224 5 1 1413 3 1 2275 3 1 17 2 2753 3 1 16 1 17 1 2954 3 1 9 1 2954 3 1 8 1 3188 3 2 4550	FC factor 0.4201 0.0108 0.0294 0.0205 0.0156 0.0338 0.0097 0.0082 0.1745 0.0122 0.0085 0.0090 0.0134 0.0326

Acknowledgments

We acknowledge SOLEIL for provision of synchrotron radiation facilities. This work was performed on the DESIRS beamline under proposal number 20131102. J.-C. G. thanks the Centre National d'Etudes Spatiales (CNES) for financial support. The authors acknowledge the computating facility GMPCS of the LUMAT federation (FR LUMAT 2764). The authors would also like to thank J. Lievin for useful discussions.

Appendix A. Correlation between the normal modes of the neutral and cationic species

The approximate correlation between the normal modes of the neutral species and of the cation in the C 3v and C s point groups, respectively, are presented in the following Table A.10. This correlation is derived using the SD matrix displayed in Fig. 2 and only the main contributions (SD matrix elements greater than 0.2) are taken into account.

The FC factors used in the calculated TPES spectrum of ) exhibits a very strong signal at m/q = 62 which probably comes from the CH 3 C 5 N + hν → CH 3 C + C 4 N + + e -channel. The CH 3 C 5 N was present in the experiment of our CH 3 C 3 N study as residual impurity. Thus, these mass spectra justify our argumentation about the observed m/q = 62 signal. Note that the impurities at m/q = 44, 50 and

Highlights

Threshold photoelectron spectrum of cyanopropyne has been recorded for the first time between 86000 and 180000 cm -1 .

Analysis of the vibronic structure of the four lowest electronic states of the cyanopropyne cation has been performed.

We report on the first observation of the dissociative photoionization channels below 120000 cm -1 .


H Rabiei

F Richard

M Roth

J.-L Anton

O Coulon

J Lefèvre

The graph windowed Fourier transform: a tool to quantify the gyrification of the cerebral cortex

Keywords: gyrification index, spectral analysis, windowed Fourier transform, Laplace-Beltrami operator, computational anatomy

The Gyrification Index (GI) quantifies the amount of folding of a cortical surface. In this paper, we show the efficiency of spectral analysis to perform such a task, and in particular we explain how the graph windowed Fourier transform can be used as a tool to define new GIs with multiscale properties. We propose two different GIs and study their effect on a set of subjects whose cortical surfaces are modeled with triangular meshes.

Introduction

The human cerebral cortex, as a geometric object, has a highly convoluted shape. The study of this shape and its complexity is of great interest in order to understand normal and pathological cortical development but is made difficult by the very large inter-subject variability. Much research has been aimed to quantify the complexity of human cerebral cortex. To our best knowledge, the first quantitative study [START_REF] Jerison | Quantitative analysis of evolution of the brain in mammals[END_REF] has been presented in 1961 in which the cortical folding was measured by using a surface ratio of the cortical surface area over the perimeter of the brain, measured on two-dimensional coronal sections. Zilles et al. [START_REF] Zilles | The human pattern of gyrification in the cerebral cortex[END_REF] computed a global 2D gyrification index (GI) via the ratio of pial surface perimeter in a given coronal slice and the perimeter of its convex hull in that slice. Using 2D sections may cause a bias in perimeter mesurements because of slice orientation and some buried sulci might be ignored. Schaer et al. [START_REF] Schaer | A surface-based approach to quantify local cortical gyrification[END_REF] argued that in addition to slice orientation sensitivity, the standard deviation of results obtained by Zilles's GI is too high to reveal group differences. By using 3D triangulated surfaces of the cerebral cortex, they extended the Zilles's GI to a global 3D GI based on the area of cortical mesh and that of its convex hull. They also defined a local version as the ratio between the area of regions of interest on the convex hull and that of corresponding regions on the pial surface. At the same time, Toro et al. [START_REF] Toro | Brain size and folding of the human cerebral cortex[END_REF] introduced a local measure of cortical folding through computing the surface ratio between a part of cerebral cortex contained in a sphere and the great circle of that sphere. Schaer's and Toro's GIs are conceptually similar and yielded similar results.

Nevertheless, these GIs based on comparing the surface areas may sometime fail in measuring the amount of folding. Indeed, by using these techniques, deep folds and a set of more shallow but oscillating folds with equal surface areas have an equal degree of folding while the latter is intuitively more folded (See Fig. 1(a)).

Another natural way to quantify the quantity of folding of a surface is its mean curvature. Normal curvatures measure the local bending of a surface in all directions and the mean curvature is the average of all these quantities. Mean curvature maps, however, are too local to deliver a helpful insight into the surface foldedness. Luders et al. [START_REF] Luders | A curvature-based approach to estimate local gyrification on the cortical surface[END_REF] used a heat kernel smoothing filter to smooth the absolute mean curvature of the cerebral cortex in order to define a localized degree of folding but the resulting maps give a very low frequency information. Instead, in [START_REF] Germanaud | Larger is twistier: spectral analysis of gyrification (SPANGY) applied to adult brain size polymorphism[END_REF], a Fourier-like analysis was applied to the mean curvature of triangulated cortical surfaces. By binning the global frequency distribution in several frequency bounds and computing the dominant and the determinant bands, they derived two metrics of folding that can discriminate primary, secondary and tertiary folds.

In this paper, we pursue the same line of research and adapt a local spectral method, called graph windowed Fourier transform, to quantify the degree of folding of the cerebral cortex. In the following section, we present the windowed Fourier transform on graphs and show how it can be used to define relevant GIs. In Section 3, we present experiments on a set of 20 subjects.

Method

The surface of the cerebral cortex is a highly folded closed surface in IR 3 which can be approximated by triangulation. The triangulated surface can be analyzed by the spectral theory which is based on the spectrum of the discretized Laplace-Beltrami operator associated with the triangle mesh.

Formally, let G = {V, E, w} be a triangulation where V is the set of vertices with V = {P 1 , P 2 , . . . , P N }, |V | = N < ∞, E is the set of edges and w : E → IR + is the weight function which assigns a positive weight to each edge. Meyer et al. [START_REF] Meyer | Discrete differential-geometry operators for triangulated 2-manifolds[END_REF] established a discretization of Laplace-Beltrami operator based on linear finite element formula/finite volume method (Voronoi cell) on the triangulation:

(Lf )(P i ) = ∑ Pj ∈N (Pi) -1 2A(P i ) ( cot(α ij ) + cot(β ij ) )( f (P i ) -f (P j ) ) , (1)
where N (P i ) is the set of vertices which are connected directly to vertex P i , A(P i ) is obtained from the area of Voronoi cell around P i and α ij and β ij are the angles opposite to the edge P i P j in two triangles sharing this edge. There are also other discretization of the Laplaca-Beltrami operator on the mesh [START_REF] Reuter | Discrete Laplace-Beltrami operators for shape analysis and segmentation[END_REF].

The discretized Laplace-Beltrami operator L is a positive semi-definite matrix with real eigenvalues 0 = λ 1 < λ 2 ≤ . . . ≤ λ N and complete orthonormal eigenvectors {χ j } N j=1 in IR N which serves as Fourier atoms on triangulation. Indeed, if f is a function defined on vertices of the triangulation, Fourier transform of this function is computed by f (l) = ⟨f, χ l ⟩ where the inner product is in IR N . It gives global information about frequency distribution of the function i.e. it is local in frequency domain but global in spatial domain.

To have local information in time domain, in 1946, Gabor [START_REF] Gabor | Theory of communication[END_REF] introduced windowed Fourier transform to find the frequency distribution of sounds. Shuman et al. [START_REF] Shuman | A windowed graph Fourier transform[END_REF] extended this transform to the graph setting by defining the generalized translation and modulation operators. In this method, a function is localized around a point in spatial domain by a window function and then the Fourier transform of this localized function is computed. The windowed Fourier transform on graph enables us to do a "vertex-frequency" analysis. Specially, for analyzing highly complicated surfaces like human cerebral cortex, local analysis would be more reasonable to get useful morphometric information about the gyri and sulci in different scales.

The generalized translation operator T i from IR N to itself of a function f ∈ IR N is defined as:

(T i f )(n) := √ N N ∑ l=1 f (l)χ l (i)χ l (n), (2)
and the generalized modulation operator M k from IR N to itself of a function f ∈ IR N is defined as:

(M k f )(n) := √ N f (n)χ k (n). (3)
If g ∈ IR N is a window function, then the windowed graph Fourier atom is vs. k delivers local information about the function defined on the triangulation. We plan to extract some indices from these distributions to measure the amount of folding of a surface at different scales.

g i,k (n) := (M k T i g)(n) = N χ k (n) N ∑ l=1 ĝ(l)χ l (i)χ l (n), i, k = 1,
Given the mean curvature function on vertices of triangulation, the absolute value and variation of this function are increased in more folded regions. It increases the frequency powers [10, Theorem 2] and some higher frequencies appear in frequency distribution of this function (see Fig. 1(b)). Based on these observations, we propose two local indices of folding and explain why they can be potentially good representation of degree of folding.

1. Total Power (TP) of each vertex:

TP(i) = N ∑ k=1 Sf (i, k) 2 .
(

) 5
Thanks to Parseval's identity, Shuman et al. [10, proof of Theorem 2] showed that

N ∑ k=1 Sf (i, k) 2 = √ N ∥f (T i g)∥ 2 2 . ( 6
)
In the above formula, T i g translates the window g to vertex P i . So, based on the property of window g, f (T i g), the component-wise multiplication of vectors f and T i g, gives more weights to function value of vertices closer to P i . It means that for two vertices P i and P j , if the norm of f around P i is greater than the norm of f around P j , then TP(i) > TP(j). Since in more folded regions the norm of f (mean curvature) is increased, TP can be a good measure of folding. This measure, however, is blind to frequencies. In other words, TP does not discriminate general increase in frequency powers from local increase in higher frequency powers as they appear in frequency distributions of more folded regions. So we define a measure which gives more weights to higher frequencies.

2. Total Weighted Power (TWP) of each vertex:

TWP(i) = N ∑ k=1 ( λ k ∥Λ∥ 2 ) 2 Sf (i, k) 2 , ( 7
)
in which, the weights are the Laplacian eigenvalues that are normalized by norm-2 of Laplacian spectrum Λ = (λ 1 , λ 2 , . . . , λ N ) T . This normalization is used to remove the effect of size of the surface on weighting. In definition of TWP ( 7), both Laplacian eigenvalues and eigenvectors are involved. By investigating the above total weighted power of frequencies at vertex P i we have

N ∑ k=1 ( λ k ∥Λ∥ 2 ) 2 Sf (i, k) 2 = ( 1 ∥Λ∥ 2 ) 2 N ∑ k=1 λ 2 k |⟨f (T i g), √ N χ k ⟩| 2 (8) = ( √ N ∥Λ∥ 2 ) 2 ∥Lf (T i g)∥ 2 2 , (9)
where ( 8) and ( 9) are obtained by definition of generalized modulation operator M k and Parseval's identity respectively. Since Laplacian operator measures how much a function differs at a point from its average value at neighbor points, (Lf T i g)(P m ) measures the variation of localized f at vertex P m and so, TWP(i) sums up all of these variations of localized f around vertex P i . One important feature of this method is existence of a free parameter, called window size, which causes a locality tradeoff between frequency and spatial domains. Actually, by utilizing a wider window in spatial domain, the function f is localized in a larger neighborhood of each vertex and on the other hand, the more local frequency distribution of the function in that neighborhood is obtained. Based on the Heisenberg's Uncertainty Principle, it is not possible to have sharp localizations in spatial domain and in frequency domain at the same time. Using this property enables us to compute the GIs at different scales.

Results

The GIs defined above have been computed on a set of triangulated surfaces modelling left hemispheres of the cerebral cortex. We used 20 subjects for which a T1 anatomical Magnetic Resonance Image had been acquired at a spatial resolution of 1 × 1 × 1 mm 3 . Images were segmented using the Freesurfer software1 . The white matter segmentations were then meshed using the BrainVisa software2 , which resulted in triangular meshes with spherical topology and approximately 50,000 nodes depending on the subjects. Inter-subject matching between all subjects was also computed using HIP-HOP method [START_REF] Auzias | Model-driven harmonic parameterization of the cortical surface: HIP-HOP[END_REF] in order to be able to perform group statistics. For each surface, the mesh Laplace operator (1) was computed as well as its first 5000 eigenvectors. The window function g was set to ĝ(l) = exp(-τ λ l ) and is normalized to ∥g∥ 2 = 1 where the parameter τ > 0 determines the size of window -the lower τ the smaller (more local) window in the prefrontal cortex, some parts of the parietal lobe, the occipital lobe and the pole of the temporal lobe. The regions with the lowest values are also consistently the insula and the central sulcus. The central sulcus is a good example since it is a very deep fold but with a high regularity and straight shape where we expect a low measure of folding. The methods in [START_REF] Schaer | A surface-based approach to quantify local cortical gyrification[END_REF][START_REF] Toro | Brain size and folding of the human cerebral cortex[END_REF] give it a high gyrification index and we believe that it is a depth artefact as shown in Fig. 1(a), whereas both our GIs produce low values and are therefore able to differentiate depth from folding complexity.

In Fig. 2, subjects are ordered by increasing size (the volume of the white matter) from left to right. It is visible that the overall values of GIs are higher for the largest brain. Indeed, the normalized average values of TP and TWP are increasing with brain volume, as shown in Fig. 3. For subject s, the average of TP(i)'s and TWP(i)'s are calculated by

TP(s) = ∑ N i=1 TP(i, s) N , (10)
TWP(s) = ∑ N i=1 TWP(i, s) N . ( 11
)
Then all TP(s)'s and TWP(s)'s are normalized by their mean value ∑ 20 s=1 TP(s)/20 and ∑ 20 s=1 TWP(s)/20. By this normalization, both TPs and TWPs are shifted into the same range while their behaviors are preserved. This increasing relationship between the volume of the white matter and total gyrification is expected and has been studied (see e.g. [START_REF] Toro | Brain size and folding of the human cerebral cortex[END_REF][START_REF] Germanaud | Larger is twistier: spectral analysis of gyrification (SPANGY) applied to adult brain size polymorphism[END_REF]). Fig. 3 shows that TWP produces a larger effect than TP for this relationship and discriminates smaller brains from larger ones better than TP.

In Fig. 4, it is shown that the window size parameter τ can be used to control the scale of observations for the GIs. At τ = 20, the spatial scale is fine and high values are located mostly on the ridge of complex gyri, while low values are located on the walls of regular sulci. As the window size increases, a more regional effect becomes visible, with a very smooth and low variations map at value τ = 1000 , which gives a coarse scale global observation of the gyrification.

Finally, we computed the group average of both GIs with τ = 20, 200, 1000 using the cortical surface inter-subject matching presented in [START_REF] Auzias | Model-driven harmonic parameterization of the cortical surface: HIP-HOP[END_REF]. Results are depicted on an inflated cortical surface in Fig. 5. They show average patterns similar to those observable on individual subjects, which shows that the GI's spatial patterns are reproducible across subjects. Even on these group average maps, the scaling effect of the window size τ is visible, which shows that the inter-subject reproducibility still holds at fine scales to some extent.

Conclusion

In this work, we applied graph windowed Fourier transform on the mean curvature function of triangulated human cerebral cortex to assess the degree of folding. Based on the frequency distribution at each vertex of the triangulation, two gyrification indices have been proposed and we showed their relevance.

The proposed indices were computed for a group of cerebral cortices. The resulting maps suggest that the prefrontal cortex, some parts of the parietal lobe and the occipital lobe are consistently the most folded part of the brain. As expected, the insula and the central sulcus take the lowest values due to their high regularity compared to other regions. The relationship between average values of the indices and brain volume confirms that the larger brains are twistier. Moreover, changing the size of window function brings interesting information about the degree of folding in different scales.

For future works, we are going to apply this method on a large database to study the correlation between anatomical parameters and behavioral patterns on the quantity of gyrification of different regions of human cerebral cortex.

Fig. 1 .

 1 Fig. 1. (a) Cross-section of deep folds (red curve) and wavy folds (green curve) with equal areas in a neighborhood (black circle). By using the methods based on the ratio of areas, these deep and wavy folds have equal GIs! (b) Second row, right: a wavy rectangle; from left to right, it becomes more folded. The color map represents the mean curvature of this surface. First row: frequency distributions of two vertices located in less and more folded regions (blue and red points, respectively). Second row, left: proposed gyrification indices (TP and TWP) for the vertices lie on the middle longitudinal line of the wavy rectangle

Fig. 2 .

 2 Fig. 2. Gyrification indices, TP and TWP, for 3 subjects with different sizes (the volume of the white matter), lateral and medial views, with window size τ = 200

Fig. 3 .Fig. 4 .

 34 Fig. 3. Normalized average of gyrification indices TP and TWP vs. Volume of the white matter for each subject, window size τ = 200

Fig. 5 .

 5 Fig. 5. Average of gyrification indices, TP and TWP, of all 20 subjects derived from 3 different window sizes (τ ) on the inflated surface of the first subject

http://freesurfer.net/

http://brainvisa.info/

Acknowledgements

This work has been supported by the Labex Archimede (http://labex-archimede.univamu.fr). This work has been also partially supported by the Agence Nationale de la Recherche (ANR MoDeGy, ANR-12-JS03-001-01).