Artur Aleksanyan

Etienne Brasselet
email: etienne.brasselet@ubordeaux.fr

Self-eclipsing: alignment-free vortex coronagraphy

We report on a self-induced strategy to achieve highcontrast optical imaging, without the need for any manmade optical masks, which relies on the self-induced spin-to-orbital angular momentum conversion phenomenon. This is experimentally demonstrated by realizing a laboratory demonstration of self-eclipsing of a light source following the generation of a self-adapted vectorial optical vortex transmission mask. The proposed concept, namely the realization of an alignment-free optical vortex coronagraph, may inspire the development of future generations of smart astronomical imaging instruments. In searching and understanding extrasolar planets, starting from the pioneering observation by Mayor and Queloz [1], the de velopment of high contrast optical imaging techniques, such as coronagraphs, is a primary topic of modern observational astro physics [2]. In addition to the continued development of adap tive optics and detectors with better performance, there is a constant need to realize optical phase and/or amplitude masks with ever increasing complexity. This is especially true in the context of future large telescopes and space missions that re quire the development of instruments with demanding speci fications and whose technological solutions remain so far under study.

Among possible options that have been developed since the era of stellar coronagraph initiated by Lyot in the 1930s [3], optical vortex coronagraphs have emerged in the 2000s [4,5], whose vectorial version has been found to be promising enough to equip several large telescopes worldwide [START_REF] Absil | Proc. SPIE[END_REF]. A vec torial vortex coronagraph basically relies on a space variant anisotropic phase mask characterized by a birefringent phase retardation Δ π and a spatial distribution of the optical axis orientation angle of the form ψ mϕ, with ϕ being the polar angle in the plane of the mask with a m ≥ 1 integer, which leads to the generation of optical vortices with topological charge 2m. After a few years of on sky harvest using vectorial vortex coronagraphs of fundamental order m 1 [START_REF] Absil | Proc. SPIE[END_REF], astrono mers now work toward the implementation of high charge vec torial vortex coronagraphs, namely m ≥ 2 [START_REF] Delacroix | Proc. SPIE[END_REF]. In practice, the case m 2 appears as a good compromise between an enhanced pointing stability and a small inner working angle. Such high order masks have been already realized using liquid crystal poly mer technology and tested on high contrast imaging testbeds [START_REF] Mawet | Proc. SPIE[END_REF], and since then, the technology has been improved [START_REF] Nersisyan | [END_REF]10]. Still, large spectral bandwidth coronagraphs remain an important issue deserving continuous development, in particular using various vectorial approaches, such as the polymer liquid crystal technol ogy [11,12] and the subwavelength gratings technology [13]. Exploring new avenues to achieve a smart stellar light rejection is the context of the present work, which considers the case of vectorial vortex coronagraph with m 1.

Recently, a nature assisted approach to realize high resolution liquid crystal vectorial vortex coronagraph of order m 1 made of self engineered topological defects has been proposed [14]. However, although the latter attempt is en dowed with good coronagraphic performances compared to that of the state of the art artificial strategies [START_REF] Absil | Proc. SPIE[END_REF], they remain endowed with major drawbacks toward practical implementa tion. First, the created phase masks randomly appear, and uncontrollable residual drifts may occur due to the liquid crystalline nature of the used materials, which prevents imple mentation in large telescopes. Second, the spatial extent of the appropriately structured birefringent material is usually lim ited to a few tens of microns. Solving these issues while preserving self engineered features would generate the potential to foster novel generation of smart astronomical imaging instruments.

In this context, here we propose and experimentally report on the laboratory demonstration of the self eclipsing of a bright source that leaves a faint nearby companion almost unaffected. Namely, the bright source creates its own vectorial optical vortex transmission mask inside an isotropic absorptive medium via a photoelastic phenomenon driven by thermal radial gradients. Remarkably, since the latter effect is reversible, our alignment free vortex mask has real time self adaptation capabilities; hence it is naturally resilient to low frequency pointing noise.

For the purpose of demonstration, we use a simple slab of absorptive glass (from Thorlabs) as the photoactive singular optical element, with thickness L 1.89 mm and optical den sity 1, while light sources are prepared from a continuous wave diode pumped solid state laser with wavelength 532 nm. According to Ref. [15], a light beam passing through such a slab generates a vectorial vortex mask with m 1, whose birefringent phase retardation depends on the distance r to the beam axis, Δr. In the limit of small absorption (that is, a z independent heat deposition in the bulk of the medium) and under the cylindrical beam approximation, an analytical profile for Δr can be obtained assuming a Gaussian heat source, namely [16] Δr Δ ∞ F r∕w 0 ;

(1)

with

F x 1 exp 2x 2 1 2x 2 ; ( 2
)
where Δ ∞ is the asymptotic value at large r, and w 0 is the waist radius of the incident laser beam with an intensity profile I r I 0 exp 2r 2 2 0 . Since the incident beam is prepared by focusing the output field of an uniformly illuminated iris of radius R 1 1 mm by a lens with focal length f 1 500 mm, see Fig. 1(a), the numerical aperture is NA 0.002. Moreover, we note that the cylindrical beam approximation implies L ≪ z 0 where z 0 πw 2 0 ∕λ is the Rayleigh distance of the Gaussian beam. In our case, the beam profile in the focal plane of the lens f 1 is not a Gaussian spot but an Airy spot with an intensity profile I r 4I 0jJ 1 kR 1 r∕f 1 ∕kR 1 r∕f 1 j 2 , where k 2π∕λ and J 1 is the first order Bessel function of the first kind. In fact, an Airy pattern can be locally described to a good approximation by an effective Gaussian profile with a waist radius w eff ≃ 0.7r 0 , where r 0 0.61λ∕NA ≃ 160 μm is the first zero of the intensity profile, which is obtained by perform ing a fit over the range 0 ≤ r∕r 0 ≤ 1.25. Thus, one obtains z 0 ≃ 7 cm, which validates the approximation L ≪ z 0 .

The creation of a self adapted vortex mask with m 1 is experimentally assessed by probing the glass slab with a spatially extended collimated laser beam at 633 nm wavelength, as shown in Fig. 1(a). The incident polarization state is set as cir cular and the intensity profile of the orthogonally polarized component of the output field is recorded by a camera via imaging with a microscope objective, see Fig. 2(a). The ob tained intensity profile between crossed circular polarizers is ex pressed as I r∕I ∞ sin 2 Δr∕2∕ sin 2 Δ ∞ ∕2, where I ∞ is the asymptotic value at large r. In practice, the power of the generated vortex beam is only a small fraction of the output light field; indeed, we measured the latter fraction to be on the order of 0.1%. Therefore, the above expression of the re duced intensity radial profile can be safely approximated by the universal profile I r∕I ∞ F 2 r∕w 0 . A satisfying agreement is obtained between the experimental data, see markers in Fig. 2(b), and the expression given by Eq. ( 1), see solid curve in Fig. 2(b), a good match being found for w 0 75 μm that should be compared with the effective Gaussian waist w eff ≃ 110 μm. Such a discrepancy could be attributed to the Gaussian heat source assumption, but it is more likely because our experimental conditions (10% power transmis sion) go beyond the approximation of a z independent bulk heat deposition [16]. Alternatively, the expected spatial distri bution of the optical axis orientation angle ψ ϕ is also retrieved experimentally from the reduced Stokes parameters s 1 and s 2 [START_REF] Born | Principles of Optics[END_REF] following ψ 1∕2 arctans 2 ∕s 1 σπ∕4, where σ 1 refers to the helicity of the incident circularly polarized probe beam, see Figs. 2(c) and 2(d). The above measurements are made under pump incident power P 192 mW, which is large enough to ensure a satisfying signal to noise ratio after polarization filtering and gives Δ ∞ ∼ 0.06 for the pump wave length in the present case. We note that these results are inde pendent of the polarization state of the pump light, as expected form the thermal origin of the photoelastic effect in iso tropic media.

Next, we explore the coronagraphic capabilities of such self adapted vortex masks. This is conducted using the exper imental arrangement sketched in Fig. 1(b), which refers to the typical setup for the laboratory demonstration of a corona graph, where the starlight is mimicked by an on axis incident quasi plane wave clipped by the input pupil of the telescope defined by the iris I 1 . Here, the starlight generates its own vec torial vortex mask, which leads to a self eclipsing phenomenon in the exit pupil plane located at a distance f 2 1 f 2 ∕f 1 from the output of the telescope made of two lenses of focal lengths f 1 and f 2 , see Fig. 1(b). We note that since the self generated vector vortex mask is far from ideally efficient (see 0.1% vortex generation purity mentioned above), the practical validation of the proposed concept implies the use of crossed circular polarizers observations, see Fig. 1(b).

The recorded image of the self eclipse is shown in Fig. 3(a). The corresponding radial intensity profile is com pared to the prediction of the model given under the approxi mation of paraxial wave propagation. Namely, I exit pupil jF -1 τr; ϕF E input pupil j 2 , where F (F -1 ) refers to the (inverse) Fourier transform and E input pupil ∝ circr∕R 1 refers to the uniformly illuminated circular input pupil plane, with circr∕ρ 0 for r > ρ and 1 for r < ρ. In addition, the complex amplitude transmittance of the self adapted vortex mask is, up to a constant factor [14], τr; ϕ sinΔr∕2 exp2iϕ iΔr∕2:

(3)

As shown in Fig. 3(b), we obtain a satisfying match between the measured (thick red solid curve) and calculated (thin black solid curve) data, where we used the experimentally determined value, w 0 75 μm, for the simulations. For comparison, we have added on the latter figure the expected radial intensity profile associated with an ideally uniform vortex mask de scribed by a complex transmittance τ ideal ϕ exp2iϕ giving I ∕I max 0 if r < R 2 and I ∕I max R 2 ∕r 2 if r > R 2 [5] (thin black dotted curve) with R 2 f 2 ∕f 1 R 1 . Such a com parison enables appreciation that the non uniform birefringent phase retardation profile inherent to the photoelastic effect must be taken into account for a proper quantitative descrip tion of the self eclipsing phenomenon.

By placing a so called Lyot stop [namely, the iris I 2 , see Fig. 1(b)] in the exit pupil plane, one can selectively reject the on axis starlight while the less intense off axis light from a "planet" is expected to be unaltered by the self adapted vortex mask created by the star. Practically, this is made by using a Lyot stop with radius R 0 2 0.75R 2 , an incident star beam power 10 times larger than the incident planet beam power and an angular separation of ≃2α diff between the star and planet light sources, where α diff 0.61λ∕R 1 is the diffraction limit associated with the circular entrance pupil aperture of radius R 1 . This gives a power rejection rate, defined as the ratio between the power out side and inside the Lyot stop, of ≃40. Next, the coronagraphic capabilities are tested by reimaging the star and planet on the camera by the lens L 2 , see Fig. 1(b). The experimental results are displayed in Figs. 4(a) and 4(b). The former figure corre sponds to the situation just after the illumination is switched on, namely the vortex mask is not activated, which refers to the OFF state of the coronagraph. In contrast, the latter figure corresponds to the steady state situation when the self adapted vortex mask is formed and stationary, which thus refers to the ON state of the coronagraph. As expected, self eclipsing enables the achievement of high contrast imaging, which is quantified by comparing the values of the ratio ζ I max star ∕I max planet when the self coronagraph is OFF and ON, where I max star and I max planet refer to the local intensity maxima associated with the star and planet, see black crosses shown in Figs. 4(a) and 4(b). We found ζ OFF ≃ 10 and ζ ON ≃ 0.1, which corresponds to a peak to peak contrast improvement by a factor ≃100 that is a decent value when compared with reported values using standard corona graphs [START_REF] Absil | Proc. SPIE[END_REF]11,[START_REF] Delacroix | [END_REF].

In the present situation, the characteristic time to reach the steady state regime is of the order of a few seconds. This is Here the incident power of the star source is ≃50 mW, which is 10 times larger than that of the secondary source. Scale bar applies for all four panels with I max being the maximal intensity value of each panel. illustrated in Fig. 5(a) where the dynamics of the self induced vortex mask observed between crossed circular polarizers is shown at different times t, the laser being switched on at t 0, for on axis illumination with incident power P ≃ 50 mW according to the setup shown in Fig. 1(a). The relax ation takes place over similar time scale, as shown in Fig. 5(b). Note that Fig. 5 emphasizes large scale material structuring (here a couple of millimeters), which is another advantage of the proposed mechanism associated with the nonlocal nature of the photoelastic effect. Moreover, since the photoelastic ef fect is a reversible phenomenon, the proposed alignment free approach to vectorial vortex coronagraphy is thus endowed with real time self adaptation capabilities. In other words, such a self coronagraph is naturally resilient to low frequency time dependent pointing, which offers a novel strategy to long term observations without source tracking. One may argue that the low level photon flux associated with on sky astronomical ap plications cannot trigger a photoelastic effect, enabling the generation of a self adapted vortex mask. However, one may realistically consider the implementation of a source tracking feedback mechanism ensuring local heating of a slab of an iso tropic material transparent to the observation wavelength. For instance, by laser heating at a wavelength associated with an absorption band or by electrical heating using localized trans parent electrode coated on the slab, which would have the ad vantage to not compromise the throughput of the instrument. Another aspect that is worth mentioning is the chromaticity; indeed, stellar coronagraphs are ideally required to operate over large bandwidth. In the present case, the reported effect corre sponds to a space variant stress induced birefringent phase retardation that scales as ∝ 1∕λ (neglecting the dispersion of the induced optical anisotropy), which implies wavelength dependent performances.

In conclusion, we have explored an original high contrast imaging strategy where the light source that should be rejected creates its own, self adapted, vortex mask. In other words, we unveiled a self eclipsing phenomenon. The effect relies on a self induced spin to orbital angular momentum conversion phenomenon driven by the photoelastic effect in absorptive iso tropic media. Although we are aware that there is a practical gap toward a direct implementation of such an alignment free coronagraph for astronomical observations without the assis tance of a feedback phenomenon enabling the local heating of the sample, we believe that the proposed concept may stimu late the development of smart alternatives to mainstream high contrast imaging instruments.

  OCIS codes: (350.5340) Photothermal effects; (050.4865) Optical vortices.

Fig. 1 .

 1 Fig. 1. (a) Setup for creating the self adapted vectorial vortex mask of order m 1. I 1 , iris with radius R 1 1 mm; L 1 , lens with focal length f 1 500 mm; BS, beam splitter; CP, circular polarizer; F , notch filter at 532 nm wavelength that blocks the pump beam while fully transmitting the probe beam; CA, circular analyzer for the mea surement of Δr; LA, linear analyzer for the measurement of ψϕ; Obj, microscope objective (×4, NA 0.1); and Cam, camera. (b) Setup for the demonstration of alignment free optical vortex co ronagraphy. The two beams labeled "star" and "planet" have an angular separation α, with the starlight propagation direction aligned with the telescope axis. I 2 , iris with radius R 0 2 0.75f 2 ∕f 1 R 1 and L 2 , lens with focal length f 2 300 mm.

Fig. 2 .

 2 Fig. 2. (a) Typical experimental image of the self adapted vortex mask observed between crossed circular polarizers for an incident pump beam power P ≃ 190 mW. (b) Markers: measurement of the reduced radial intensity profile of the self generated vortex beam I ∕I ∞ from the data shown in panel (a), in spatial units of w 0 . Solid curve: theoretical dependence given by the function F 2 , see Eq. (2). (c) Typical experimental map of the spatial distribution of the light induced optical axis orientation angle ψ. (d) Markers: measured ψϕ from the radial average between the two dashed circles shown in panel (c). Solid curve: theoretical dependence expected from a vectorial vortex mask with charge m 1.

Fig. 3 .

 3 Fig. 3. (a) Self eclipsing of the starlight observed by placing the camera at the exit pupil plane for an incident power P ≃ 50 mW. (b) Thick solid red curve: azimuth average radial intensity profile of the data shown in panel (a). Thin solid black curve: calculated in tensity profile based on the self adapted vortex mask model used here. Thin dotted black curve: calculated intensity profile for a vectorial vortex mask with ideally uniform birefringent phase retardation.

Fig. 4 .

 4 Fig. 4. Laboratory demonstration of alignment free optical vortex coronagraphy of a star/planet binary source with 2α diff angular sepa ration, using a 12 bit camera. Panels (a) and (b) refer to experimental data when the coronagraph is OFF (a) and ON (b).Here the incident power of the star source is ≃50 mW, which is 10 times larger than that of the secondary source. Scale bar applies for all four panels with I max being the maximal intensity value of each panel.

Funding.

  Agence Nationale de la Recherche (ANR) (ANR 10 IDEX 03 02, ANR 15 CE30 0018).

Fig. 5 .

 5 Fig. 5. (a) Excitation and (b) relaxation dynamics of the self adapted vectorial vortex mask monitored by imaging the sample between crossed circular polarizers following the setup shown in Fig. 1(a) under pump incident power P ≃ 50 mW.

Acknowledgment. This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Programme IdEx Bordeaux LAPHIA and HYPERPHORB project.


R Lozada Garcia

N Nieuwjaer

C Desfrançois

F Lecomte

S D Leite

B Manil

M Broquier

G Grégoire

Vibronic spectra of protonated hydroxypyridines: contributions of prefulvenic and planar structures

Various hydroxypyridine derivatives are endogenous or synthetic photosensitizers which could contribute to solar radiation damages. The study of their excited states could lead to a better understanding of their action mechanisms. We present here the ultraviolet (UV) spectra of the protonated 2-, 3-and 4-hydroxypyridine. These spectra were obtained with an experimental device coupling an electrospray ion source with a cold quadrupole ion trap and a time of flight mass spectrometer. They display well resolved vibrational structures, with a clear influence of the position of the OH group. These results are interpreted with excited states calculations at the coupled cluster CC2 level.

-Introduction

 The deactivation of excited DNA molecules may involve local, « monomer-like » processes, 2 which reinforces the importance of understanding the photochemistry of model molecules that mimic the molecular subunits comprising larger biologically relevant compounds. 2-, 3-and 4-hydroxypyridines are such model systems. Indeed, 2hydroxypyridine exhibits two stable tautomeric forms: the enol form and the keto one called 2-

pyridone. These two tautomers are related by H atom transfer between N and O sites of the molecule and they are nitrogen heterocycles with the same H-bonding sites as uracil and thymine.

These similarities make the mixed 2-pyridone 2-hydroxypyridine dimer a relevant model compound for tautomeric DNA-base pair analogues. [START_REF] Switzer | Enzymatic recognition of the base pair between isocytidine and isoguanosine[END_REF] As a consequence, gas phase spectroscopy of the neutral 2-hydroxypyridine in molecular beams has been extensively documented over the last decades. [START_REF] Lee | Resonantly-enhanced Two-photon Ionization and Mass-Analysed Threshold Ionization (MATI) Spectroscopy of 2-Hydroxypyridine[END_REF][START_REF] Sakota | Dispersed fluorescence spectroscopy of 2-hydroxypyridine and its cyclically hydrogen-bonded water clusters in the gas phase : an examination of occurrence of excited-state proton transfer[END_REF][START_REF] Nimlos | Spectroscopy, structure, and proton dynamics of 2hydroxypyridine and its clusters with water and ammonia[END_REF][START_REF] Matsuda | IR-UV Double-Resonance Spectroscopic Study of 2-Hydroxypyridine and Its Hydrogen-Bonded Clusters in Supersonic Jets[END_REF][START_REF] Meuwly | Energetics, dynamics and infrared spectra of the DNA basepair analogue 2-pyridone 2-hydroxypyridine[END_REF] Concerning 3-hydroxypyridine, its cation has been identified as a minimum phototoxic chromophore sufficient to effect skin cell sensitization [START_REF] Wondrak | Proteins of the Extracellular Matrix Are Sensitizers of Photo-oxidative Stress in Human Skin Cells[END_REF] and 3-hydroxypyridine derivatives, comprising a wide range of skin biomolecules, are capable of skin photo-oxidative damage. [START_REF] Wondrak | 3-Hydroxypyridine Chromophores Are Endogenous Sensitizers of Photooxidative Stress in Human Skin Cells[END_REF] This molecule is then more than a model system, and the study of its excited states could lead to a better understanding of its action mechanisms.

Chart 1: Structures of the three investigated protonated hydroxypyridines HPH + We present here a systematic study of the influence of the position of the hydroxyl group in protonated hydroxypyridine molecules (see chart 1). Production and spectroscopic studies of protonated aromatic amino acids [START_REF] Talbot | Photodissociation Spectroscopy of Trapped Protonated Tryptophan[END_REF][START_REF] Boyarkin | Electronic Spectroscopy of Cold Protonated Tryptophan and Tyrosine[END_REF][START_REF] Stearns | Conformation-Specific Spectroscopy and Photodissociation of Cold, Protonated Tyrosine and Phenylalanine[END_REF][START_REF] Nolting | Protonation effect on the electronic spectrum of tryptophan in the gas phase[END_REF] and of the protonated DNA/RNA bases [START_REF] Berdakin | Excited States of Protonated DNA/RNA bases[END_REF][START_REF] Pedersen | Structures of Protonated Thymine and Uracil and Their Monohydrated Gas-Phase Ions from Ultraviolet Action Spectroscopy and Theory[END_REF][START_REF] Nielsen | Physical Chemistry in Action : Photophysics of Ionic Biochromophores[END_REF] and their homodimers [START_REF] Féraud | Excited States of Proton-bound Base Homo-dimers : Pyrimidines[END_REF] have merged recently and have been made possible by the coupling of an electrospray source with a cold ion trap. [START_REF] Wang | Investigations of Protonated and Deprotonated Water Clusters Using a Low-Temperature 22-Pole Ion Trap[END_REF] Well-resolved vibronic spectroscopy can thus be recorded and assigned through comparison with ab initio quantum mechanics calculations. Studying model systems gives insight into the photochemistry of protonated nitrogen heterocycles that in turn aids in understanding biologically relevant photochemistry. The simplest protonated aromatic molecule, benzene, and aromatic nitrogen heterocycle, pyridine, have been characterized at medium resolution only very recently. [START_REF] Esteves-López | Excited State of protonated benzene and toluene[END_REF][START_REF] Hansen | Ultraviolet photodissociation action spectroscopy of the N-pyridinium cation[END_REF] The electronic spectrum of protonated benzene is structure-less, which is in agreement with the large geometrical changes and the fast dynamic toward internal conversion predicted by ab-initio calculations. [START_REF] Rode | Computational Study on the Photophysics of Protonated Benzene[END_REF] Concerning protonated pyridine, the spectra recorded in the photon energy range 37000 -45000 cm -1 reveal a broad electronic band exhibiting vibronic resolved structure. The excited state structure is buckled in a prefulvenic geometry. This behavior is a familiar feature of many small aromatics [START_REF] Rosenberg | Excited State Aromaticity and Antiaromaticity : Opportunities for Photophysical and Photochemical Rationalizations[END_REF][START_REF] Palmer | An MC-SCF study of the S1 and S2 photochemical reactions of benzene[END_REF][START_REF] Sobolewski | Ab initio investigation of potential-energy surfaces involved in the photophysics of benzene and pyrazine[END_REF] and is also observed for neutral pyridine. [START_REF] Chachisvilis | Femtosecond Dynamics of Pyridine in the Condensed Phase : Valence Isomerization by Conical Intersections[END_REF][START_REF] Zhong | Femtosecond dynamics of valence-bond isomers of azines : transition states and conical intersections[END_REF][START_REF] Sobolewski | Photophysically relevant potential energy functions of low-lying singlet states of benzene, pyridine and pyrazine : an ab initio study[END_REF][START_REF] Grove | Photo-rearrangement of N-substituted pyridinium and metaalkoxypyridinium ions[END_REF] Very recently, Broquier et al. have undertaken the investigation of protonated ortho, meta and para aminopyridine molecules [START_REF] Broquier | Twisted Intramolecular Charge Transfer in Protonated Amino Pyridine[END_REF][START_REF] Soorkia | Multiscale excited state lifetimes of protonated dimethyl aminopyridines[END_REF] and have shown that although protonated aminopyridines are rather simple aromatic molecules, their deactivation mechanisms are indeed quite complex. In the present study, the spectroscopy of the protonated 2-, 3-and 4hydroxypyridine (HPH + ) is investigated across the photon energy range 33 500 -41 000 cm -1 using an experimental device coupling an electrospray ion source with a cold quadrupolar ion trap and a time of flight mass spectrometer. We present the vibrationally resolved electronic spectra of cold HPH + along with dissociation kinetics through one-and two-color photofragmentation spectroscopy. Ultraviolet-ultraviolet hole-burning (UV-UV HB) spectroscopy was also used to discriminate conformational isomers in the case of the protonated meta 3-hydroxypyridine.

-Experimental and computational methods

2-, 3-and 4-hydroxypyridine were purchased from Sigma Aldrich and directly dissolved in water/methanol mixtures (50/50 by volume) at 100 µM and together with few droplets of acetic acid. The electronic spectra were obtained via photo-fragmentation spectroscopy in a cryogenic cold quadrupole ion trap QIT (Paul trap from Jordan TOF Products, Inc.) installed at the CLUPS facility in Orsay. The setup is similar to the one developed by X. B. Wang et al. [START_REF] Wang | Development of a Low-Temperature Photoelectron Spectroscopy Instrument Using an Electrospray Ion Source and a Cryogenically Controlled Ion Trap[END_REF] and has already been described elsewhere. [START_REF] Féraud | Excited State Dynamics of Protonated Phenylalanine and Tyrosine : Photo-Induced Reactions Following Electronic Excitation[END_REF][START_REF] Broquier | A comprehensive study of cold protonated tyramine: UV photodissociation experiments and ab initio calculations[END_REF] The protonated species are produced from an Electrospray Ion Source (ESI). They pass through a 10 Hz pulsed octopole ion guide that produces ion packets with a duration time between 500 ns and 1 s, and are then trapped in the QIT which is mounted on a cold head of a compressed helium cryostat that maintains the temperature around 10-15 K. A mass gate located before the entrance of the trap allows for mass-selecting the parent ion. The photodissociation laser is triggered after few tens of millisecond when thermalization of the ions through collisions with helium buffer gas is reached, and all ionic fragments and parent molecules are then extracted and accelerated for mass-analysis in a linear time-of-flight mass spectrometer. The photodissociation laser is either a picosecond Optical Parametric Amplifier (OPA), with a spectral resolution of 8 cm -1 , or a nanosecond dye laser (Quantel TDL 90), which resolution is about 0.2 cm -1 .

For the fragmentation kinetics measurements, the fragmentation time is recorded by changing the delay between the laser and the extraction pulse ejecting the ions from the ion trap to the time-offlight. The time resolution, on the order of 80 ns, is limited by the rise time of the high voltage pulser.

UV-UV hole burning (HB) spectroscopy (using two dye lasers) has been performed in order to reveal the possible distinct isomers that are present in the trap after the low temperature cooling process.

We have used the tickle method initially proposed by Kang et al., [START_REF] Kang | New Method for Double-Resonance Spectroscopy in a Cold Quadrupole Ion Trap and Its Application to UV-UV Hole-Burning Spectroscopy of Protonated Adenine Dimer[END_REF] which consists of applying on one cap of the QIT an auxiliary RF whose frequency is tuned to selectively eject a given ionic fragment. By doing that, the chosen ionic fragment of a first UV laser (burn), set on a given vibronic band, is ejected from the trap, which allows recording the signal induced by a second UV laser (probe) scan, over the whole spectral range, without background signal. The tickle RF voltage is kept below 1 V and sent for 10 ms after the excitation from the burn laser. In order to increase the HB signal-to-noise ratio, we run the burn laser at 5 Hz while keeping the probe at 10 Hz and perform the experiment using the modified active baseline subtraction methods (ABS). [START_REF] Zwier | The Spectroscopy of Solvation in Hydrogen-bonded Aromatic Clusters[END_REF][START_REF] Sen | How do Pseudoenantiomers Structurally Differ in the Gas Phase? An IR/UV Spectroscopy Study of Jet-Cooled Hydroquinine and Hydroquinidine[END_REF]

Computational methods

Ab initio calculations have been performed with the TURBOMOLE program package (v6.2) 41 making use of the resolution-of-the-identity (RI) approximation for the evaluation of the electron-repulsion integrals. [START_REF] Weigend | RI-MP2 : First Derivatives and Global Consistency[END_REF] The equilibrium geometries of protonated 2-, 3-and 4-hydroxypyridines in their ground electronic (S0) and excited states have been determined at the CC2 level with the correlationconsistent polarized valence double- aug-cc-pVDZ basis set augmented with diffuse functions. [START_REF] Dunning | Gaussian Basis Sets for Use in Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen[END_REF] The vibrational modes of the ground and the first excited states have been calculated at the same level, and the Franck-Condon analysis has been performed using PGOPHER software. [START_REF] Western | PGOPHER, a Program for Simulating Rotational Structure[END_REF]

Isomers

Hydroxypyridines are protonated at the pyridinic nitrogen and can adopt two conformations according to the position of the oxygen lone pair as compared to the position of the proton. The conformer with the lone pair oriented towards the proton will be denoted syn, and the conformer with a rotation of  around the C-O bond will be denoted anti. For protonated 2-hydroxypyridine, the anti conformer is likely to be unstable due to the repulsion between the proton bound to nitrogen and the hydroxyl hydrogen. For the protonated 4-hydroxypyridine, the two isomers are identical due to the NCO symmetry axis. Only in the case of protonated 3-hydroxypyridine, the two isomers can coexist and are energetically close. As compared to the neutral molecule, the protonated hydroxypyridine can hardly display tautomerization because the keto form would correspond to a positively charge doubly hydrogenated nitrogen atom with a sp 3 tetrahedral molecular orbital structure calculated 1.7 eV higher than the initial sp 2 hybridization.

-Results

Protonated 2-Hydroxypyridine : 2-HPH +

Figure 1a shows the vibrationally-resolved UV photofragmentation spectrum obtained with the ps OPA laser on a large spectral domain, from 34 500 cm -1 up to 2000 cm -1 above. The UV excitation of 2-HPH + (m/z 96) results in the dissociation into m/z 78 ions, which corresponds to the loss of H2O. This fragment, which is also the main dissociation channel in CID, is produced immediately with a kinetics of formation shorter than the time resolution of the experiment defined by the rising time of 80 ns of the extraction pulse from the QIT.

The vibronic spectrum of 2-HPH + is composed of intense and sharp bands, the first one being observed at 35 435 ± 5 cm -1 , while low intensity transitions are barely seen in the red of this intense band. The higher resolution spectrum obtained with the dye laser is reported in Fig. 1b and confirms that the first weak vibronic band is indeed recorded at 34 806 ± 5 cm -1 , i.e. about -630 cm -1 from the intense band. These weak transitions cannot be assigned to hot bands because they are too far in the red from the intense band. In the low frequency region, there is a vibrational progression of +82 cm -1 built from the first transition at 34 806 cm -1 with at least 2 quanta with increasing intensity. This suggests a geometry distortion in the excited state along a low frequency mode, leading to a weak band origin. The low signal makes a firm assignment of all the observed transitions difficult.

We can nevertheless recover the same vibrational progression built from a band at 390 cm -1 above the first transition. In overall, the vibronic spectrum of 2-HPH + indeed closely resembles to the one recorded for protonated 2-aminopyridine. [START_REF] Broquier | Twisted Intramolecular Charge Transfer in Protonated Amino Pyridine[END_REF] As it will discussed below, these two sets of intense and weak transitions will be assigned to two distinct minima in the excited state of 2-HPH + , as observed for protonated 2-aminopyridine. The band origin of 2-HPH + is red-shifted by more than 1300 cm -1 as compared to neutral 2-hydroxypyridine.

Protonated 3-Hydroxypyridine : 3-HPH +

The vibrationally resolved vibronic spectrum of 3-HPH + , shown in Figure 2a, is obtained with the OPA laser from 33 500 cm -1 up to 3000 cm -1 above. The UV-induced fragmentation produces mainly two fragment ions that are also observed through CID: m/z 68, which is the main fragment and corresponds to the loss of CO, and m/z 78, which is ten times less intense and corresponds to the loss of H2O, as observed for 2-HPH + . A fragmentation kinetics of 210 µs for the two fragmentation channels has been measured and is consistent with a dissociation in the ground state following internal conversion. As for 2-HPH + , the vibronic spectrum is composed of a set of intense transitions starting a 34 357 ± 5 cm -1 along with low intensity bands further in the red. The higher resolution spectrum recorded with the dye laser (Fig. 2b) allows asserting the position of the first weak transition at 33 814 cm -1 , i.e. about 540 cm -1 in the red of the intense band. Here again, these weak bands are too red-shifted to be assigned to progression from hot bands and the overall vibronic spectrum closely resembles the one record for 2-HPH + with two sets of intense and weak vibronic transitions. For 3-HPH + , two low-lying energy isomers (syn and anti) can be populated at low temperature.

Ultraviolet-ultraviolet hole-burning spectroscopy was used to discriminate these conformational isomers. The very low intensity of the vibronic spectrum in the red of the first intense transition precludes to record any UV-UV HB signal in that spectral region. We thus turn to the region where intense transitions are detected. The burn laser was first set on the band at 34 357 cm -1 (Fig. 3a).

Most of the vibronic transitions are detected in the HB spectrum except a first one at 34 686 cm -1 .

A second HB spectrum (Fig. 3b) is thus obtained by fixing the burn laser at this frequency. The two HB spectra allow recovering the entire vibronic spectrum of 3-HPH + , which clearly reveals that only two conformers contribute to the experimental spectrum, at least in that spectral region. It should be noted that the burn laser seems to induce some hole-filling signals as reflected by few and weak positive HB bands for the two burn wavelengths.

Protonated 4-Hydroxypyridine : 4-HPH +

In that case, the fragmentation leads to three fragments: the main fragment is m/z 68 (CO loss) along with m/z 78 (H20 loss) and a weak signal at m/z 69 (HCN loss). The fragmentation kinetics is in the order of 2.5 ms which is much longer than for 2-and 3-HPH + . As for the other molecules, such long fragmentation kinetics strongly suggests that dissociation occurs in the ground electronic state after internal conversion. The photofragmentation spectrum of 4-HPH + recorded with the ps OPA laser (Fig. 4a) is quite noisy and much less structured than the ones for 2-and 3-HPH + . With the dye laser, only a couple of sharp transitions are observed before an intense one followed by the onset of a broad continuum starting from roughly 40 350 cm -1 . The first transition is located at 39 660 cm - 1 and should be assigned to the band origin. This 00 0 transition is significantly blue shifted as compared to those of protonated 2-and 3-hydroxypyridines. A first vibrational band is found 120 cm -1 above the origin transition while the most intense band appears 637 cm -1 higher in energy. As for the two other isomers, an intense vibronic transition is detected about 600 cm -1 above the first weak transition of the excitation spectrum but the overall vibronic spectrum is clearly different.

-Discussion

Vertical and adiabatic excited state calculations

Ab initio coupled-cluster (CC2 / aug-cc-pVDZ) calculations have been performed for the three HPH + molecules. As expected, the syn conformer is more stable than the anti conformer by 4.15 kcal/mol and 0.95 kcal/mol for the 2-and 3-HPH + , respectively. While the former one is thus not expected to be populated at low temperature, 3-HPH + should adopt both conformations. Since the calculated electronic properties are similar and share the same trends for the syn and anti structures of 3-HPH + , we will discuss only the results of the syn conformer. For all molecules, the ground state equilibrium structure is planar, all HPH + molecules thus belong to the Cs point group. The vertical excited state energies of 2-3-and 4-HPH + are reported in Table 1 along with the corresponding frontier molecular orbital representation. The first low lying excited states are all of * character and no nN* is present since the lone pair of the pyridinic nitrogen is involved in bonding with the proton. The NH* state is calculated more than 2 eV above the * state, which bears the oscillator strength for UV excitation, so that it is not involved in the deactivation process in HPH + . In 4-HPH + , the first and second * states are almost degenerated and strongly mixed, with several orbitals involved in the frontier MO decomposition of the states. In these planar ground state structures, the lone pair of the hydroxyl group (pz orbital) is in the same plane as the  orbitals of the pyridine ring and contributes to the  * transition. Geometry optimizations of the first * state have been performed for the three HPH + molecules without symmetry constraint. In all cases, the optimization has converged to a planar * state preserving the Cs symmetry. However, these Cs structures are saddle points of the potential energy surface (PES) with one imaginary frequency of roughly -50/-80 cm -1 depending on the molecules.

The associated mode corresponds to out-of-plane butterfly motion of the pyridinic ring. With such a low negative frequency in the * state, we cannot assert from the calculations whether or not the Cs structure is a saddle point or a true secondary minimum of the * PES.

In order to escape from the planar Cs geometry in S1, the structures have been distorted along the calculated negative frequency mode. For 2-and 3-HPH + , this has led to slightly non planar geometries in a boat-like, prefulvenic structure, the N1H and C4H groups pointing above the aromatic ring (See Fig. 5). These optimized structures are true minima of the PES without imaginary frequency. These two adiabatic structures closely resemble the N-pyridinium excited state structure calculated at the DFT/CAM-B3LYP/aug-cc-pVDZ by Hansen et al. [START_REF] Hansen | Ultraviolet photodissociation action spectroscopy of the N-pyridinium cation[END_REF] , although the nitrogen pyramidalization is less pronounced in the present case. In pyridinium, the barrier height to planarity is calculated at 2000 cm -1 , while in 2-and 3-HPH + , CC2/aug-cc-pVDZ calculations predict a very small barrier of about 100 cm -1 (see Table 2).

Such small energy difference, which more or less matches the amplitude of the negative frequency of the Cs structure, is certainly within the error of the CC2 method and the relative energy of the two structures in the excited state should be taken with great care. Experimentally, for 2-and 3-HPH + , the first intense transition is blue-shifted by about 600 cm -1 as compared to the weak band origin. As it will be discussed below, the Franck-Condon analysis allows deciphering the contribution of two minima of the * PES in the experimental vibronic spectra of 2-and 3-HPH + .

For 4-HPH + , geometry optimization following distortion along the butterfly mode has led to a conical intersection with the ground state 0.

Franck-Condon analysis

The electronic spectrum of 4-HPH + will not be discussed in this section because only a very few active vibronic bands are observed which precludes the assignment of the structure in the * PES.

The vibronic spectra of 2-and 3-HPH + exhibit two sets of sharp transitions with quite different intensities. The excited state calculations have revealed the presence of two close lying structures in the * PES, an adiabatic prefulvenic structure and a second one of planar Cs geometry as in the electronic ground state. This is exactly what was found in protonated 2-aminopyiridine [START_REF] Broquier | Twisted Intramolecular Charge Transfer in Protonated Amino Pyridine[END_REF] . Its electronic spectrum has been assigned to the combination of two vibronic progressions of these two PES minima that have rather different Franck-Condon (FC) activities. Intense transitions were calculated for the Cs structure that correspond to the band origin (BO) along with the in-plane mode (a') of the pyridinic ring, while the red-shifted low intensity bands are assigned to the adiabatic minimum with progression of out-of-plane modes. In 2-and 3-HPH + , the simulated vibronic spectra of the adiabatic minima have been calculated and their overall intensity are ten-fold weaker than those for the Cs structures. For 3-HPH + , the presence of the two conformers and the impossibility to perform the hole-burning spectroscopy in the low frequency region makes the assignment highly hypothetical. Comparison between the calculated and experimental spectra are thus reported in Fig. 6 for 2-HPH + . The calculated band origin has a very weak intensity. A progression of the butterfly mode 1 (a") calculated at 90 cm -1 built from the BO with a maximum at 3-4 quanta closely matches the experimental low frequency progression of 82 cm -1 experimentally observed for 2-HPH + . The same 1 progression built from the Franck-Condon active modes 4, 5, 7, 13 and 15 is calculated.

If the intensities of the calculated 00 0 and 1 progression are scaled to the corresponding experimental bands, it is clear from these simulations that the intense experimental transitions from 630 cm -1 above the BO cannot be attributed to the adiabatic minimum. In Figure 7, the experimental vibronic spectrum of 2-HPH + is compared to the Franck-Condon simulations of the Cs structure (Fig. 7a) with its origin set at the most intense vibronic band (35 435 cm -1 ) of the experimental spectrum. It is noteworthy that the calculated and experimental band origins (Table 2) of the Cs structure only differ by less than 100 cm -1 . Besides, their calculated transition intensities are one order of magnitude larger than the ones of the prefulvenic structure.

Selection rules of the Cs point group impose that only totally symmetric a' vibrational modes are active along with even quanta of out-of-plane a" modes. This is exactly reproduced in the simulated FC spectrum. The in-plane active modes of the Cs structure are calculated at 402, 503, 547, 804 and 958 cm -1 and correspond to COH bending, 6a-b, mode 1 and 12b according to the Wilson notation, respectively (see Fig. 7). Only the first a" mode (1 = 162 cm -1 ) with two quanta has non negligible intensity in the calculated FC spectrum. While these active modes nicely match some of the intense experimental vibronic transitions, others are obviously missing in this simulation, in particular, the two first transitions found at +76 and + 183 cm -1 from the 35 435 cm -1 band. The absence of the active low frequency modes of the Cs structure suggests that the missing bands might come from vibronic coupling between the prefulvenic and Cs minima. Figure 8 shows a schematic diabatic representation of the double-well potential (harmonic approximation) with Q(1) as the butterfly bending mode coordinate relevant for this spectroscopic study. Vibronic transitions from the Cs ground state structure to the Cs excited state structure have large intensities for the in-plane (a') modes, while Franck-Condon active transitions to the prefulvenic excited state structure involve a progression of the butterfly 1 mode. We have used the screwer module in Turbomole to distort the 2-HPH + molecule along the normal mode 1 as a function of the temperature. Within the harmonic oscillator approximation, the energy of a vibrational normal mode i (Ei) is given by Ei =1/2 i 2 * Qi 2 , where i and Qi are the wavenumber and normal coordinate of mode i, respectively. If one substitutes E by kbT, (kb for Boltzmann constant and T the temperature), the coordinates can be distorted along the butterfly mode (1= 90 cm -1 for 2-HPH + ) with a temperature step of 125 K. In the right panel of Fig. 8, the corresponding distorted structures of 2-HPH + are reported, and it can be readily checked that with 3 or 4 quanta in 1, the prefulvenic structure has almost recovered the planarity. Indeed, the calculated FC spectrum of the prefulvenic structure (Fig. 6) reveals that the largest transitions are those with 3 quanta in v1, which scales the prefulvenic to planar coordinate displacement in the excited state. Qualitatively, a vibronic coupling between the prefulvenic and planar (Cs) minima should involve vibrations of the prefulvenic state that recover the planar symmetry (butterfly mode) and match the general selection rules of the Cs point group, i.e. totally symmetric a' modes. The simulated FC spectrum of Fig. 7b has been calculated as combination bands of 4 quanta in the butterfly mode and all the inplane bending and stretching modes (a') of the adiabatic structure. Most of the missing transitions in the simulated spectrum of the Cs structure, in particular the two intense transition at + 76 cm -1 and + 183 cm -1 from the BO of the Cs structure, can now be assigned to the contribution of combination bands of the prefulvenic structure with in-plane (a') modes and 4 quanta of the butterfly mode needed to recover the planarity. This diabatic harmonic formalism used to simulate the experimental spectrum is certainly a crude approximation of the true adiabatic potential energy surface of the excited state. Nevertheless, it provides a very good qualitative and satisfying quantitative agreement with the experimental spectrum.

The same procedure has been applied to 3-HPH + to assign the intense vibronic bands of the experimental spectrum. As already pointed out, two conformers account for all the intense vibronic transitions. The band origins of the syn and anti conformers in the planar Cs structure have been assigned through the hole-burning spectroscopy and compared to the calculated ones. The syn conformer has its BO at 34 357 cm -1 , 329 cm -1 to the red of the BO of the anti conformer. Both the absolute and relative adiabatic transition energies are very well reproduced by the calculation, in particular the splitting between the two conformers predicted at 357 cm -1 , i. e. within 30 cm -1 of the experimental one (see Table 2). The UV-UV hole-burning spectrum of the anti conformer (Fig. 3b) covers a limited spectral range of 500 cm-1 where only the first two in-plane active modes (a') of the Cs structure are detected at 388 and 500 cm-1 along with combination bands involving 4 quanta of the mode 1 of the adiabatic minimum. In the Cs structure, the frequencies of in plane modes (breathing vibration of the cycle) are not quite different for three HPH+, even less for the syn/anti conformers of 3HPH + . Nevertheless, as for 2-HPH + , the intense vibronic bands assigned to the syn conformer in Figure 3a can be reproduced with the active in-plane a' modes of the Cs minimum along with combination of 4 quanta of the butterfly motion with in-plane a' modes of the prefulvenic minimum structure (Fig. SI1).

-Conclusions

We have investigated the photofragmentation processes in protonated hydroxypyridine through a combined experimental and theoretical study. Although protonated ortho, meta and para hydroxypyridine appear as simple model molecules that mimic the molecular subunits comprising larger biologically relevant compounds, the understanding of their vibronic spectroscopy is more complex than expected. These three molecules show well resolved electronic excitation spectra, with a strong influence of the position of the hydroxyl group. In particular, the band origin of 4-HPH + is significantly blue-shifted in comparison with 2-and 3-HPH + . UV-UV hole burning spectroscopy for the 3-HPH + clearly reveals the presence of two syn-and anti-conformers at low temperature. For all molecules, the weak intensity of the band origin along with the progression on low frequency modes reveals a geometry change in the excited state, as predicted by the prefulvenic structure found through excited-state optimized geometry calculated at the CC2 / aug-cc-pVDZ. Besides, the intense vibronic transitions are assigned to the planar Cs structure that corresponds to tenfold larger intensities. For both adiabatic and Cs structures, the calculated band origins including ZPE corrections are in good agreement with the experimental data within an absolute error of about 500 cm -1 . Finally, a strong vibronic interaction between the prefulvenic and planar structures in the excited state seems to account for the experimental spectra.

Figure 1 .

 1 Figure 1. Photofragmentation spectrum of protonated 2-HPH + recorded on the m/z 78 ionic fragment. (a) on the left, the spectrum is obtained over a large spectral range with the ps OPA laser (8 cm -1 resolution). (b) on the right, low frequency region obtained with the dye laser (0.2 cm -1 resolution).

Figure 2 .

 2 Figure 2. Photofragmentation spectrum of protonated 3-HPH + recorded on the m/z 68 ionic fragment.(a) on the left, the spectrum is obtained over a large spectral range with the ps OPA laser (8 cm -1 resolution). (b) on the right, low frequency region obtained with the dye laser (0.2 cm -1 resolution).

Figure 3 .

 3 Figure 3. UV-UV hole-burning spectra of 3-HPH + obtained at two burn laser frequencies (indicated by an arrow) of (a) 34 357 cm -1 and (b) 34 686 cm -1 . For each plot (same vertical scale), the top trace (black line) is the UV photo-induced (PID) signal while the bottom trace (red line) is the UV-UV hole-burning (HB) signal.

Figure 4 .

 4 Figure 4. Photofragmentation spectrum of protonated 4-HPH + averaged on the three ionic fragments at m/z = 78, 69 and 68. (a) on the left, the spectrum is obtained over a large spectral range with the ps OPA laser (8 cm -1 resolution). (b) on the right, low frequency region obtained with the dye laser (0.2 cm -1 resolution).

  3 eV below the energy of the Cs structure. At this point, the pyramidalization at the protonated nitrogen is large with the adjacent CH group pointing almost perpendicular to the pyridine cycle. The access, through a very small barrier, from the Franck-Condon region (Cs structure) to the conical intersection in 4-HPH + is consistent with the absence of a vibrational progression in the vibronic spectrum of 4-HPH + .

Figure 5 .

 5 Figure 5. * excited state optimized prefulvenic structures of 2-and 3-HPH + . For 4-HPH + , the geometry optimization leads to a conical intersection with the ground state, point where the optimization is stopped.

Figure 6 .

 6 Figure 6. Comparison of the experimental (top) and Franck-Condon simulated spectrum of the prefulvenic structure of 2-HPH + .

Figure 7 .

 7 Figure 7. Comparison of the 2-HPH + experimental (top) and calculated Franck-Condon spectra of (a) Cs structure and (b) the prefuvenic structure obtained as a combination of 4 quanta of the butterfly mode 1 with the in-plane (a') modes.All spectra are plotted as a function of excess energy (cm -1 ) from the band origin of the prefulvenic structure. The inplane (a') modes are reported for the Cs structure.

Figure 8 .

 8 Figure 8. (left) Schematic diabatic representation of the double-well potential with Q(1) as the butterfly bending mode coordinate that connects the planar (Cs) and prefulvenic minima in S1. (Right) distorted structures of 2-HPH + as a function of butterfly mode v1 progression.

Table 1 .

 1 Electronic configurations and vertical transition energies (eV) of 2-3-and 4-HPH + (CC2/aug-cc-pVDZ) syn conformers. In bold, * transition bearing the oscillator strength for UV excitation.

		2-HPH + (Cs)		3-HPH + (Cs)		4-HPH + (Cs)
		Configuration Energy Configuration	Energy	Configuration	Energy
	S1	* (A') (4a"-5a")	4.82	* (A') (4a"-5a")	4.59	* (A') (3a"-6a") + (4a"-5a")	5.43
	S2	 (A') (4a"-6a")	6.27	 (A') (4a"-6a")	5.75	 (A') (3a"-5a")	5.58
	S3	 (A') (3a"-5a")	7.19	 (A') (3a"-5a")	6.72	 (A') (4a"-5a") + (3a"-6a")	6.59
	S4	NH* (A") (4a"-27a')	7.28	NH* (A") (4a"-22a')	7.07	* (A') (4a"-6a")	7.39

Table 2 .

 2 Experimental

	molecules	Symmetry	00 0 calc	00 0 exp	(calc-exp)
	2-HPH + Syn	prefulvenic Cs	35 427 35 522	34 806 35 435	621 86
	3-HPH + Syn	prefulvenic Cs	34 059 34 124	33 814 34357	245 -233
	3-HPH + Anti	prefulvenic Cs	34 337 34 481	-34686	-204
	4-HPH +	prefulvenic Cs	IC 40 523	39 660 40 297	226

and calculated * energy transition of 2-, 3-and 4-HPH + . Calculated energy transitions (CC2/augcc-pVDZ) corrected by the difference in zero point energy (ZPE) between the ground and excited states. All values are in cm -1 .

Acknowledgments

We acknowledge the use of the computing facility clusters GMPCS of the LUMAT federation (FRLUMAT 2764) and MAGI of the University Paris 13.

Supplementary Materials: