Alejandro Gutiérrez-Quintanilla
email: alejandro.gutierrez-quintanilla@u-psud.fr

Michèle Chevalier

Claudine Crépin

Double deuterated acetylacetone in neon matrices: infrared spectroscopy, photoreactivity and tunneling process

The effect of deuteration of acetylacetone (C5O2H8) is explored by means of IR spectroscopy of its single and double deuterated isotopologues trapped in neon matrices. The whole vibrational spectra of chelated enols are very sensitive to the H-D exchange of the hydrogen atom involved in the internal hydrogen bond. UV excitation of double deuterated acetylacetone isolated in neon matrices induces the formation of four open enol isomers which can be divided in two groups of two conformers, depending on their formation kinetics. Within each group, one conformer is more stable than the other: a slow conformer interconversion due to a tunneling process is observed in the dark at low temperature. Moreover, IR laser irradiation at the OD stretching overtone frequency is used to induce interconversion either from the most stable to the less stable conformer or the opposite, depending on the excitation wavelength. The interconversion process is of great help to assign conformers which are definitively identified by comparison between experimental and calculated IR spectra. Kinetic constants of the tunneling process at play are theoretically estimated and agree perfectly with experiments, including previous experiments with the totally hydrogenated acetylacetone [Lozada García et al.

I. Introduction

Acetylacetone (C5H8O2) is the simplest molecule of the β-diketones family. For many years, this compound has served as prototype in the investigations of three important physico-chemical processes: intramolecular proton transfer, [1][2][3][4] keto-enolic tautomerism [5][6][7][8] and photo-induced isomerization. [9][10][11][12][13][14] Surprisingly very few studies are related with the effect of the exchange of an H atom by another (D or F for example) 1,3,4 although this change, deuteration in particular, could give information on the various physico-chemical properties of the molecule. The enolic form is stabilized by an internal hydrogen bond (Fig. 1) so only a small amount of the β-diketone form (keto) is present in the gas phase. 5,15 The keto-enol tautomerism can be strongly affected by the environment 16 but the prevailing form of the isolated molecule is chelated enol which symmetry has been a controversial topic: is it C2v or Cs? 17 Many experimental and theoretical works support the Cs symmetry. 8,[18][19][20] Theoretically, eight stable enolic isomers are found: the chelated enol form -depicted in Fig. 1 -and seven open conformers * . 10,11,21 They are obtained by rotations around three bonds, two CC bonds and one CO bond as shown in Fig. 1, and are denoted XYZ, where letters X, Y and Z stand for C or T depending on the cis or trans positions of the groups around the C-C, C=C and C-O bonds, respectively. The chelated enol (CCC) is the most stable form and the only one observed in the gas phase. In cryogenic matrices, it is also the most stable but several open conformers can be produced by UV irradiation. 9,10,14,22,23 The highly stabilizing hydrogen bond interaction in the CCC form prevents isomerization in the electronic ground state and an electronic excitation is required to access to the open forms. It has been suggested, from experiments and theoretical calculations, that this occurs through the excitation of the molecule to the S2 level via a π-π* transition. Non-radiative processes like * "conformer" is used here to refer to enolic rotational isomers internal conversion (IC) and intersystem crossing (ISC) between S2/S1/T2/T1 states lead the system to the T1 state, where fragmentation (in gas phase) or isomerization (in cryogenic matrix) can occur. 11,14,[24][25][26] Photo-isomerization in matrices was probed in previous works by electronic and vibrational spectroscopy. Different kinds of matrices were used in order to test the influence of the environment in this photophysical process, among them: N2, Ne, Ar, Xe and hydrogen hosts (normal hydrogen n-H2, normal deuterium n-D2 and para-hydrogen p-H2). 9,10,12,14,23 The stabilization of different open conformers depends on the host. Previous studies in our group showed that in Ne and p-H2 matrices, only the CTC, TCC and TTC conformers, in which the OH group is in the cis conformation, were observed after 266 nm laser irradiation. 14 In n-H2 and n-D2, TCT (OH in trans conformation) was also detected. This conformer was also observed in Ar, Xe and N2 matrices. 10,12 Furthermore, CTT was stabilized in N2 and Xe. 12,23 Consequently, it was proposed that CTT and TCT conformers were not observed in p-H2 and Ne because of a fast tunneling process of the hydrogen in the OH group converting CTT and TCT into CTC and TCC respectively. 14 It is known from previous studies on small organic compounds (including acetylacetone) that interchange between two rotational conformers could be induced by irradiation with infrared laser matching its wavelength to the absorption of corresponding bond in the molecule. 23,27,28 IR irradiation did not affect the CCC conformer but selective IR irradiation on the OH stretching fundamentals induced changes in the CTC/CTT and TCC/TCT pairs of conformers. 12 The interconversion was matrix dependent: not observed in Ne and Ar matrices, observed only in the CTC/CTT pair in Xe and observed in both pairs in N2.

The present paper is focused on the role played by the hydrogen atom from the OH group in the stabilization of non-chelated enolic conformers, with an experimental approach. For this purpose, we study double deuterated acetylacetone, an isotopologue of the original fully hydrogenated molecule. The structural picture of acetylacetone in its chelated enol form is presented in Fig 1 . As it can be seen this molecule has two CH3 groups and hydrogens in OH and CH groups. It is known that OH and CH hydrogens are much more labile and could be easily exchanged with deuterons in the presence of e.g. D2O. The double deuteration concerns these most labile hydrogen atoms, labeled in white color in Fig. 1. In this study we present investigation of the deuteration influence to the vibrational spectra as well as to the structure and stability of the isomers. The double deuterated acetylacetone has been previously studied in pure solid, liquid and gas phases through FT-IR spectroscopy. [29][30][31][32] All these works report studies on the chelated enol form (CCC), and none of them on the open enol conformers. In the present work, UV and IR induced isomerization is investigated in solid neon using FT-IR spectroscopy for detailed characterization of possible isomers. Infrared absorption bands are assigned to the particular conformer based on the calculated spectra of the conformers. After the presentation of the experimental and theoretical methods used in the study (part II), the results are described and discussed in part III. Geometries, energetic and vibrational frequencies from calculations are briefly described. The deuterated isotopologues, including double and mono deuterated acetylacetone, in freshly deposited samples are then characterized. UV absorption spectra of conformers of acetylacetone isolated in neon matrices are also reported.

Photo-isomerization induced by UV or IR laser irradiation is described and analyzed. Various conformers are obtained. Some of them are metastable in the matrix, as shown by the timeevolution of their bands without any irradiation. The vibrational structure of five conformers of double deuterated acetylacetone (XYZ=CCC, CTC, CTT, TCC and TCT) is thus clearly documented as well as the interconversion between them. The tunneling process at play in the interconversion is discussed at the end of part III. Part IV summarizes the main conclusions of the work.

The following notations will be used: AcAcH8, AcAcD2 and AcAcD1 to name fully hydrogenated, double deuterated and monodeuterated acetylacetone, respectively. There are two AcAcD1, distinguished by the notations AcAcD1(CD) and AcAcD1(OD), depending on the position of deuterium atom. Specific conformers of the corresponding species will be noted XYZ(H8), XYZ(D2), XYZ(D1) (or XYZ(CD) and XYZ(OD)) with X, Y and Z standing for C or T.

II. Methods

II. 1.Experimental

Acetylacetone (99.5%) was purchased at Fluka, Na2SO4 (>99.5%) at Merck, D2O (99.9%) and NaCl (>99%) at Sigma-Aldrich. Double deuterated acetylacetone (AcAcD2) was prepared mostly following synthesis steps published in Dea Kin-Kin doctoral thesis. 33 Briefly, synthesis consists in refluxing a mixture of acetylacetone and deuterated water (D2O) for approximately 4 hours at 80 o C, using a desiccant at the open part of the system to minimize the entry of atmospheric water. After reaching equilibrium at room temperature, organic and aqueous phases are separated by a decantation process, adding sodium chloride (NaCl) and cooling the sample to improve the separation. We add a small quantity of sodium sulfate (Na2SO4) to eliminate possible water impurities in the final product and decant this mixture at the end. During the deuteration procedure, exchange yields of 90 % were reached for non-methyl hydrogens. The deuteration ratio was determined from infrared absorption band intensity ratio of hydrogenated and deuterated species assuming similar absorption coefficients. Products include both single and double deuterated species, with a yield of AcAcD2 above 65%. IR bands coming from AcAcH8, AcAcD2 and AcAcD1 were used to estimate these ratios.

Matrix samples were obtained by direct deposition of a gas mixture containing deuterated acetylacetone and neon (Messer 5.0) in a ratio of 1-1.5:1000 onto a CsI substrate, cooled between 7 and 8 K inside a closed cycle He cryostat (APD Cryogenics Inc.). Deposition times varied from 30 to 40 min, and the deposition rate was around 10 mmol h -1 .

Infrared spectra were acquired using standard FT-IR spectrometer (Nicolet Nexus 870) and liquid nitrogen-cooled MCT detector. All the spectra were recorded in the transmission mode with a 0.5 cm -1 resolution. The IR beam path was purged with dry air.

Ultraviolet absorption spectra were acquired using a 0.6 m Jobin Yvon grating monochromator and a CCD camera (Andor DH720). We used a deuterium lamp as light source and sapphire as deposition window for these studies.

UV and IR induced isomerization experiments were performed using an Optical Parametric Oscillator (OPO) nanosecond laser from Continuum, pumped by the 355 nm line of a tripled Nd:YAG laser, 10 Hz repetition rate, wavelength range from 192 nm to 2700 nm. The pulse energies were in the range of 1-6 mJ. Laser bandwidths for UV and IR wavelengths were around 7 cm -1 in both cases. Irradiation times varied typically from several minutes to several hours. Laser irradiation was stopped during measurements of FT-IR spectra.

II.2. Calculations

Geometry optimizations were performed for all isomers (keto and eight enol forms) of deuterated acetylacetone followed by frequency calculations. In all the steps we used DFT level of theory with B3LYP functional 34,35 and 6-311++g(3df,3pd) basis set. A very tight convergence criteria and an ultrafine optimization grid were also used. Vibrational frequencies were obtained by means of both harmonic and anharmonic approaches. For the presented harmonic spectra a scaling factor of 0.981 was used. This value was optimized to fit the theoretical results to the experimental values taking into account the interaction between the host and the molecule.

Rotational barriers between cis and trans positions of OH/OD in open enol conformers of acetylacetone were obtained through relaxed scans, using CCOH/CCOD, respectively, dihedral angle as variable parameter, with 10 and 15 degrees steps. Frequency calculations were performed for initial, final and transition states (TS) in order to account for the Zero Point Energy corrections (ZPE). Each TS structure was optimized through a Berny optimization algorithm, and confirmed through an Internal Reaction Coordinate (IRC) calculation. Calculations related to the barrier were done at the MP2 level of theory using the same basis set as mentioned before. All calculations were performed using the Gaussian 09 package. [START_REF] Frisch | Gaussian 09, Revision D.01[END_REF] Chemcraft software was used as graphical program for the visualization of the results. 37

III. Results and Discussion

III. 1. Theoretical results

Calculations show that the geometries of deuterated isomers are very similar to those of the related non-deuterated isomers. 14 All enolic conformers have a planar structure (carbonated skeleton and CCOD dihedral). The geometry of CCC(D2) (see Fig. 1) is fully described in the Electronic Supplementary Information (ESI), Table S1. The stability order for the open enol conformers in deuterated isotopologues is the same as in the case of non-deuterated acetylacetone:

CCC > CTC > CTT > TCC > TCT > TTC > CCT > TTT Energies relative to the CCC conformer for AcAcD2 (CCC(D2)) are reported in Fig. 2. They differ from those of AcAcH8 by no more than 0.2 kJ/mol in the different isotopologues, corresponding to the deuteration effect on the Zero Point Energy (ZPE) contribution, not large enough to perturb the order of stability. On the other hand, one can remark that the keto isomer is the most stable after the chelated enol. Calculated vibrational frequencies and intensities for the keto isomer and conformers were computed in order to identify the IR absorption bands of each of them and to obtain the aforementioned ZPE values. The whole set of theoretical data is reported in the ESI (Tables S2,S3 and S4). The most distinct feature in the case of AcAcD2 conformers is the presence of OD stretching modes near 2790-2760 cm -1 for the open conformers, whilst the same mode for the CCC form is 500 cm -1 down shifted. This frequency range is especially important to check the formation of open conformers under laser irradiation.

III. 2. FT-IR Vibrational spectroscopy of as-deposited samples

As previously noticed, our samples contain deuterated and non-deuterated acetylacetone.

Figure 3 shows in the left panels the spectra of AcAcH8 (a) and of the deuterated species (b) in neon matrices at 7.6 K. The latter spectrum (b) is obtained after subtraction of the bands of AcAcH8 from the spectrum of the as-deposited sample. The calculated spectrum of CCC(D2) in the harmonic approximation is displayed in panel (c) for comparison. Calculated frequency is scaled by the factor 0.981 for the better comparison with the experimental data. Frequencies obtained in the anharmonic approximation are reported in Table I, together with the scaled harmonic frequencies. The agreement between the theoretical spectrum (c) and the experimental one (b) for the most intense bands is very good, and we conclude that AcAcD2 in its chelated enol form is the main structure observed in the experimental spectrum (b).

Nevertheless, there are several bands which do not correspond to CCC(D2) (see Fig. 3, right panel: zoom of 1340 -1460 cm -1 region). When comparing experimental and theoretical spectra for double deuterated and monodeuterated conformers, we found that these bands correspond to the CCC forms of the monodeuterated species AcAcD1 i.e. of AcAcD1(CD) and AcAcD1(OD).

In addition, similarly to the case of the non-deuterated molecule, we observe the keto tautomer in the deposited samples, assigning to it two weak vibrational bands at 1717.2 and 1185.4 cm -1 .

Theoretical calculations suggest that these frequencies are very close from one isotopologue to another (see ESI, Tables S2,S3, S4). The amount of keto tautomer is very low (approximately 1%), just as with the AcAcH8 isotopologue. This result shows that the keto-enol equilibrium is not significantly perturbed by deuteration. andc) Calculated spectrum of CCC(D2) (harmonic frequency calculation with a 0.981 scaling factor). Right: Zoom on the 1340-1470 cm -1 region: experimental spectrum (top) and theoretical spectra (bottom, AcAcD2 red line and AcAcD1 -same amount of both isotopologues -grey dotted line). k denotes keto band, * denotes bands assigned to AcAcD2 in the zoomed region, the other bands are assigned to AcAcD1 (see Fig. 5). The theoretical spectrum is shown using a convolution with a Lorentzian profile of 2 cm -1 bandwidth.

III. 2. a. AcAcD2, CCC conformer

In order to distinguish the bands from AcAcD2 to those from monodeuterated isotopologues, we made subtraction between two spectra of samples with different AcAcD2/AcAcD1 ratios (i.e. different deuteration yields of synthesis). The list of bands assigned to double deuterated CCC and the calculated bands of CCC(D2) are reported in Table I. The agreement is good for both calculations even if the scaling factor underestimates the effect of the anharmonicity for the highest frequencies. Only the OD stretching mode which is the most anharmonic and the most perturbed by the H bond, is not very well reproduced.

In previous studies of deuterated acetylacetone in the gas phase, the authors suggest the presence of this stretching band around 2025 cm -1 . 29,32,[START_REF] Howard | [END_REF] A closer look at this frequency region was required to find a possible assignment for it: a weak and broad band around 2000 cm -1 could correspond to νOD (see Fig. 4). The large red shift of νOD is due to the internal hydrogen bond. In fact, it induces an inversion in the energy ordering of CD and OD stretching modes, observed experimentally and theoretically (see Fig. 4 and Table I). It is known that for most molecules the position of the OH/OD stretching mode allows easy the discrimination between non-deuterated and deuterated isotopologues. However in AcAcH8, despite its high intensity, the OH band is difficult to observe experimentally because it spreads over hundreds of wavenumbers due to the high delocalization of the hydrogen atom in the hydrogen bond, as suggested by the previous works in the gas phase at room temperature. 29,32 It is expected that the bandwidth should decrease significantly in the low temperature matrices, [START_REF] Howard | [END_REF] however it remains very large even at lowest temperature, as proton delocalization is still high even in the cryogenic matrices. This fact makes the observation of the band very difficult and its maximum position can't be determined accurately. In particular, the OH stretching band of AcAcH8 was not clearly observed in neon matrices at 4 K. 14 One can see in Fig. 3 that most of the bands of AcAcD2 are narrower than those of AcAcH8. The decrease of the bandwidth for OH normal modes upon a H-D exchange was expected. [START_REF] Mielke | Isotope Effects In Chemistry and Biology[END_REF] In both molecules, the stretching and especially the bending of the OH/OD group contribute to several normal modes: it could explain in part, the global broadening of bands in CCC(H8) compared to CCC(D2). Table II reports FWHM of the main assigned lines of CCC(D2) and CCC(H8) in Ne, with a short description of the modes in order to directly compare both isotopologues. The OH/OD stretching modes are not included in Table II because, as it was written above, OH-CCC(H8) was not observed. Thus as we observe the OD-CCC(D2) band (Fig. 4), it should be narrower than the OH-CCC(H8) band.

III. 2. b. Monodeuterated isotopologues (CCC(OD) and CCC(CD))

AcAcD1 is always present in the samples as CCC forms of AcAcD1(OD) and AcAcD1(CD). We were able to obtain the spectrum of AcAcD1 in Ne (Fig. 5 a) by subtracting spectra of samples with different deuteration ratios and to assign few bands of the monodeuterated isotopologues. It appears that the ratio between isotopomers AcAcD1(OD) and AcAcD1(CD) is roughly the same in all the samples, close to 50/50 (a precise measurement is not possible). The band assignment to a particular isotopomer is complicated because AcAcD1(OD) and AcAcD1(CD) have many modes with very similar frequencies. Nevertheless, we were able to identify some bands for each isotopologue using the theoretical spectra (Fig. 5 b andc). These bands suggest that similarly to AcAcD2 and AcAcH8, those corresponding to AcAcD1(OD) are narrower than those of AcAcD1(CD). Additional bands can be tentatively assigned to each isotopologue following this remark. The experimental frequencies compared to calculations are reported in Table III.

Considering that AcAcD2 and AcAcD1(OD) in one hand, and AcAcH8 and AcAcD1(CD) in the other hand have similar bandwidths we conclude that the  hydrogen (olefinic hydrogen) does not have a wide impact in the band broadening.

III. 3. UV irradiation and open conformers

UV irradiation of matrix samples doped with acetylacetone induces the photo-isomerization of the enolic form and the production of open enol conformers. In our previous studies with AcAcH8 isolated in neon matrices, we showed that the produced open conformers can be separated in two groups: a first one, reduced to CTC, growing from CCC upon irradiation at 266 nm and disappearing in a prolonged irradiation, and a second group, including mainly TCC with a very weak amount of TTC, growing slower upon the same irradiation. 14 In order to precise the efficiency of the UV irradiation on the various conformers of acetylacetone, we recorded first the UV absorption spectra of acetylacetone isolated in solid neon. These spectra helped in the choice of the excitation wavelengths to induce photoisomerization. UV spectra are described in the next part, followed by the results on the first and the second groups of conformers.

III.3.a. UV absorption spectra of acetylacetone in solid neon

The UV absorption of AcAcH8 (CCC form) in neon matrices is shown in Fig. 6, left panel -black solid line. Electronic absorption spectra of acetylacetone in different matrices were already published, but the spectrum in solid neon was lacking. [START_REF] Coussan | [END_REF] The CCC absorption band is slightly red shifted from the gas phase 41 with a maximum of absorption at 265 nm in Ne (262.7 nm in the gas phase). The maximum of the band was also found around 265 nm in N2 and was red shifted in Ar and Xe (maximum around 270 nm). 12 All these results indicate a weak effect of the matrix on the electronic structure of acetylacetone. We benefit from our previous study of photo-isomerization of AcAcH8 in Ne 14 to use the best experimental conditions to get samples with almost only one conformer trapped and we obtain the spectra of CTC and TCC displayed in Fig. 6, left panel (red dot and blue dash lines respectively). In the spectra shown in Fig. 6, the CCC conformer spectrum was subtracted from the open enol conformer spectra for better clarity, and spectra were normalized.

The three conformers have broad absorption bands. The UV absorption spectra of CTC and TCC are very close (maxima around 240 nm and 237 nm respectively). The IR spectra of the same samples in the frequency range of free OH stretching modes are displayed in the right panel of Fig. 6 to confirm the assignments: CCC-black solid (no free OH), CTC -red dot and TCC -blue dash.

Theoretical calculations on the electronic states of AcAcH8 (CR-EOMCCSD(T) method) [START_REF] Coussan | [END_REF] reported a difference of only 7nm in the electronic absorption of CTC and TCC, whereas a blue shift of 19 nm was calculated between CTC and CCC: these estimations are in good agreement with the present results in Ne.

The UV absorption spectra of deuterated acetylacetone should be very similar to those of AcAcH8, because of the small perturbation due to deuteration. This assumption was confirmed by recording the absorption spectrum of AcAcD2/Ne after deposition to get the electronic absorption spectrum of the CCC form. We use then the clear results obtained with AcAcH8 to choose the UV wavelengths for the photo-isomerization experiments.

III. 3. b. First group of deuterated conformers

In order to obtain mostly the first group, we irradiated the deposited sample in the red part of the CCC absorption, at 280 nm, far from the maximum of absorption of the other conformers and especially that of CTC (see Fig. 6). In Fig. 7 we can observe the simultaneous decrease of CCC with the increase of the two different groups of conformers. These groups differ by their kinetics, in the same way as in AcAcH8/Ne experiments. 14 When CCC is almost depleted, the first group is predominant. Its spectrum is reproduced in Fig. 8. The second group will be discussed in the next section. experiments were performed with different AcAcD1/AcAcD2 ratios. AcAcD1 bands can be easily observed in some spectra whereas the IR spectrum of Fig. 8, panel a, corresponds to a sample with a negligible amount of AcAcD1. On the other hand, some bands in the spectrum exhibit a doublet structure which comes from site effects. Such doublets are also observed in nondeuterated conformers trapped in solid neon. The presence of different sites is confirmed with annealing effects. The site structure is more pronounced in the spectra of modes involving significantly OD motion, e.g. OD stretching modes and OD in-plane bending modes (group of doublets near 950 cm -1 ).

Surprisingly, when leaving the sample in the dark, we observe an evolution in the spectrum of open conformers: some bands increase while others decrease. The corresponding difference spectrum is displayed in Fig. 8, panel b. This change is attributed to an interconversion between CTT and CTC. The process is very slow, with a kinetic rate estimated at 10 -7 s -1 from experimental measurements. This result gives an important information about conformers stability but also a confirmation of the attribution of the lines of the most stable conformer (CTC with the lowest energy, see Fig. 2). One can notice that the spontaneous CTT CTC interconversion depends on the site where CTT(D2) is trapped, as can be seen in Fig. 8, panel b. In order to confirm and complete the previous assignment, we performed IR laser irradiation experiments with the laser frequency in the range of the OD stretching first overtone. The vibrational excitation of the fundamental OH mode in open conformers of AcAcH8 was found to promote isomerization between XYC and XYT conformers (X and Y being C or T). 23 The region of the first OD overtones was not recorded in the IR absorption spectra. We found and assigned them by scanning the OPO laser frequency in the region predicted by the anharmonic calculations. The CTC ↔ CTT interconversion is effectively observed when the laser is in resonance with the first overtone. The effect of IR irradiation at 5235 cm -1 is displayed in Fig. 8, panel c. In this case, CTC bands are depleted while those of CTT increase in intensity. An irradiation at 5280 cm -1 produces the CTT → CTC interconversion, making the process reversible. Combining the information from all the experiments and theoretical calculations, we conclude that the conformers produced in the first group are CTC(D2) and CTT(D2). Experimental frequencies and calculated values for CTC(D2) and CTT(D2) conformers are summarized in Table V. One can notice that there is no obvious narrowing of the CTC bands from AcAcH8 to AcAcD2, even on the OH/OD stretching bands (bandwidths of 1.7 cm -1 in AcAcH8 and 1.5 cm -1 in AcAcD2).

The large bandwidth difference observed only between the chelated enols allows to conclude that highest influence of deuteration is on intramolecular hydrogen bond properties. The first group of open conformers was reduced to CTC in the case of AcAcH8 trapped in Ne. A fast CTT→CTC interconversion was assumed to explain the absence of CTT, in comparison with the behavior of irradiated AcAcH8 in other matrices where CTT was observed. This assumption is confirmed by the deuteration effect: the tunneling process at play in the CTT→ CTC interconversion is slower in the case of AcAcD2, allowing the detection of CTT in solid neon.

III. 3. c. Second group of deuterated conformers

After depletion of the CCC conformer upon irradiation at 280 nm, samples were irradiated at 260 nm to enhance the production of the second group of conformers. At 260nm, the absorption of the second group is lower than that of the first one while the CCC can still absorb and react.

The second group is the only one growing under 260 nm irradiation. The spectrum of the second group is shown in Fig. 9, panel a. Two strong bands are observed in the OD stretching region. One decreases while the other increases in the dark (Fig. 9, panel b).

Consequently, we assign them to two conformers prone to interconversion process, similarly to the CTT/CTC pair. Kinetics of this process is slow: the kinetic constant is estimated around 10 -6 s - 1 , which is one order of magnitude larger than for the CTT/CTC pair. We also performed IR laser irradiation in the range of OD stretching overtones, similarly to the experiments with the first group, and we observed the same behavior, i.e. the reversible conversion of one species to the other (Fig. 9, panel c). Overtones measurements are reported in Table IV.

Combining the information coming from all the experimental and theoretical data, we conclude that the second group is formed by TCC(D2) and TCT(D2). The theoretical spectra of these two conformers are reported in Fig. 9, panel d for comparison. Experimental frequencies and calculated values for conformers assigned to the second group are summarized in Table VI.

Importantly, the TCT conformer is clearly detected in AcAcD2/Ne samples while it was not observed in AcAcH8/Ne samples. As in the case of the first group, there is a slow quantum tunneling of the deuterium, compared to the measurement time scale, whereas the tunneling of hydrogen was too fast in AcAcH8 to be observed. In the present experiments, there is no evidence of the TTC conformer which was detected in a very low amount in AcAcH8/Ne. As the bands were very weak, if TTC(D2) exists, its bands cannot be clearly distinguished from bands coming from the different conformers of AcAcD1. So, no conclusion can be stated for TTC(D2).

In addition to the experiments previously discussed, we performed a supplementary irradiation at 250 nm after the irradiation at 260 nm in order to excite more efficiently the second group itself. This last irradiation induces a change inside the second group: TCT bands increase and TCC bands decrease. We do not see any increase of the bands associated with other conformers. It suggests that the TCT/TCC production ratio depends on the energy of the system in the excited S2 state and/or on the initial geometry of acetylacetone in this state. Consequently, the measured TCT/TCC ratio in Ne depends on the UV irradiation wavelength just after UV irradiation and then evolves in time. Because of the fast TCT→TCC conversion in the case of AcAcH8, this kind of process cannot be explored with the fully hydrogenated isotopologue. On the other hand, TCT was also observed in more perturbative matrices (Ar, Xe, N2, n-H2 and n-D2)

where it can be stabilized by interactions with the host. In these latter cases, matrix effects must play a role in the observed molecular processes.

III. 3. d. Monodeuterated conformers

III. 3. e. Tunneling process

CTT→CTC and TCT→TCC interconversion processes are assumed to be due to proton tunneling because of the significant deuteration effect we observed. The tunnel effect is very important at low temperatures and it has been found in several small organic molecules and complexes. 42,43 We performed relaxed scan (and Internal Reaction Coordinate) calculations in order to estimate the rotational barriers for the processes under study. Theoretical value 2x10 -1 2x10 -7 1 3x10 -6 ‡ ZPE included VII).

The experimental kinetic constants k related to the tunneling rates are estimated for each pair from the evolution after 68 h of the intensities of some characteristic bands assigned to each conformer. We can compare them with the theoretical values obtained within the WKB semiclassical approximation. [START_REF] Bell | The Tunnel Effect in Chemistry[END_REF] This methodology has been successfully used in the description of other systems, but gives only an order of magnitude of the kinetic rate. [START_REF] Tsuge | [END_REF]46 In this approach, k is expressed as:

𝑘 𝑊𝐵𝐾 = 𝜔 0 × 𝑃(𝜀) (1)
Where ω0 is the frequency of the torsional mode (in Hz) and P(ε) is the permeability of the barrier obtained through: 44

𝑃(𝜀) = 1 1+𝑒 2𝜃(𝜀) (2)
with θ(ε) evaluated by the following integral:

𝜃(𝜀) = 1 ћ ∫ √2𝜇[𝑉(𝑥) -𝜀]𝑑𝑥 𝑥 2 𝑥 1 (3)
where μ is the reduced mass of the particle and ε its kinetic energy evaluated as the difference of the Zero Point Energies between the transition state (TS) and the initial state (XYT).

Integration limits x1 and x2 are defined by the turning points where V(x)-ε = 0.

The calculated values are reported in Table VII together with the estimated experimental values.

A difference of six orders of magnitude in the values of the theoretical rates between non deuterated and deuterated isotopologues is found in each pair. The barriers are quite similar and the major difference comes from the reduced masses and ZPE values in the two isotopologues. The orders of magnitude of k obtained for the non-deuterated molecules highlight a fast tunneling process, in the timescale of seconds, and fully explain the absence of XYT(H8) conformers in the FT-IR spectra recorded more than few seconds after the laser irradiation. 14 Deuteration totally changes the XYT lifetimes. Theoretical values for deuterated pairs describe very well the slow process observed. We obtain a very good agreement for both pairs of conformers, despite the WKB approximation and the fact that the matrix is not taken into account. It seems that the effect of the neon matrix in this process is negligible. Generally, the presence of the matrix slows down the isomerization, but it depends both on the host and the guest. [START_REF] Tsuge | [END_REF]47 Theoretical estimations open in fact a puzzling matrix effect: whereas tunneling rate constants are larger for TCT→TCC than for CTT→CTC, TCT is found easier stabilized by a cryogenic lattice than CTT (TCT is observed in Ar, n-H2 and n-D2 and not CTT). This could be related to the fact that in the TCT/TCC pair, the OH group stays in the vicinity of methyl groups, while it is only the case in the less stable CTT conformer of the CTT/CTC pair (see Fig. 2): the geometries of two methyl groups are slightly modified in the TCT→TCC process, while only one is involved in the CTT→CTC tunneling and the global modification of the molecule can be more perturbed by the matrix in the former case than in the latter.

IV. Conclusions

Deuteration effects on the molecular properties of acetylacetone are explored by the study of the double deuterated acetylacetone (AcAcD2) trapped in neon matrices with a focus on vibrational spectroscopy and photochemistry.

The IR spectrum of the chelated enol form exhibits well-defined and narrow bands. It allows the assignment of most of the vibrational modes, whereas the previous spectroscopic data were obtained in the gas phase at room temperature and many bands were thermally broadened.

The agreement with the gas phase and the theoretical calculations is very good, underlining the weakness of the perturbation induced by the neon environment. The IR spectra of the monodeuterated isotopologues are also obtained.

The comparison between the spectroscopic results of AcAcH8, AcAcD2 and AcAcD1 trapped in solid neon highlights the effect of the strong internal hydrogen bond in the -OH isotopologues: almost all the vibrational bands are broadened, and not only those which are the most involved in the H-bond. Because of the narrowing of bands in AcAcD2, we were able to detect its OD stretching mode around 2000 cm -1 whereas the corresponding OH stretching mode was always too large to be detected.

Excitation of AcAcD2 to S2 state induces the isomerization of the enol form in solid neon. As for AcAcH8, we distinguish two groups of conformers in the photo-isomerization process.

Nevertheless, there are two major differences. The first is the number of conformers. We observed the CTT/CTC and the TCT/TCC pairs. Only the corresponding XYC conformers were detected in AcAcH8/Ne samples 14 , suggesting that in AcAcH8 the XYT conformers disappeared as soon as they are produced by an efficient XYT→XYC interconversion. The second difference, related to the first one, is the slow XYT→XYC interconversion observed when AcAcD2/Ne samples stay in the dark. The slowing down of this process with deuteration is in agreement with the assumption of a quantum tunneling in the -OH(D) part of the molecule and the measured lifetimes are in very good agreement with calculations. These measurements also underline the weak interaction between the guest and the Ne matrix for this process. The study will be extended to other deuterated isotopologues in order to get a deeper insight on the deuteration effect and, in particular, to analyze the consequences of the deuteration of the methyl groups whose torsion is entangled with the proton transfer in the chelated enol conformer. 48 Similar studies in halogenated analogs of acetylacetone are also under way.

Figure 1 :

 1 Figure 1: CCC enol conformer of acetylacetone. Hydrogen atoms exchanged with deuterium are marked in white. Each colored arrow defines one of the possible rotations in order to produce a new conformer.

Figure 2 :

 2 Figure 2: Schemes and relative energies (kJ/mol) of open enol conformers and keto isomer compared to the CCC conformer, in AcAcD2. Zero Point Energy is included in each reported value.

Figure 3 :

 3 Figure 3: Left: a) As deposited acetylacetone (AcAcH8) in Ne, b) As deposited deuterated acetylacetone in Ne (after subtraction of residual AcAcH8 bands),and c) Calculated spectrum of CCC(D2) (harmonic frequency calculation with a 0.981 scaling factor). Right: Zoom on the 1340-1470 cm -1 region: experimental spectrum (top) and theoretical spectra (bottom, AcAcD2 red line and AcAcD1 -same amount of both isotopologues -grey dotted line). k denotes keto band, * denotes bands assigned to AcAcD2 in the zoomed region, the other bands are assigned to AcAcD1 (see Fig.5). The theoretical spectrum is shown using a convolution with a Lorentzian profile of 2 cm -1 bandwidth.

Figure 4 :

 4 Figure 4: 1860-2320 cm -1 region in deposited deuterated acetylacetone spectrum. OD and CD stretching bands for AcAcD2 isotopologue are assigned.

Figure 5 :

 5 Figure 5: a) IR spectrum of monodeuterated isotopologues (obtained after removing AcAcD2 and AcAcH8 from the original spectrum); IR theoretical spectra -Lorentzian bandwidths of 2 cm -1 -in the scaled harmonic approximation of CCC forms of b) AcAcD1(OD) and c) AcAcD1(CD) isotopologues. Zoom (x3) below 1200 cm -1 for a better comparison. Assignment is shown with dashed colored lines for some of the most important bands.

  A similar behavior is expected with AcAcD2 isolated in neon matrices. With the OPO laser as the UV irradiation source, it is possible to excite acetylacetone in a broad range of UV wavelengths. We observe different behaviors according to the different wavelengths used in the 250-280 nm range, but in any case, new bands are growing while the CCC conformer is disappearing. The spectra are complex but these bands can be classified in two groups of open conformers. A clear assignment was possible in each group based on two additional processes: (i) the relative intensities of the new bands change in time without irradiation, meaning that the spectra contained the signature of stable and meta-stable conformers; (ii) IR laser irradiation performed after UV irradiation affects differently the produced conformers.

Figure 6 :

 6 Figure 6: Left: Electronic absorption spectra of acetylacetone (AcAcH8). CCC (black solid line), first group (CTC) (red dots) and second group (mainly TCC) (blue dash) of conformers; Right: IR spectra corresponding to each group. The open conformer spectra are obtained combining different weighted spectra in order to get separated spectra for each conformer.

Figure 7 :

 7 Figure7: Evolution of acetylacetone IR spectrum under 280 nm laser irradiation (from the rear to the front). Left: OD stretching region of non-chelated conformers (zoom 14x). Right: C=O and C=C stretching region. The first group of conformers is mainly produced but a small amount of second group is also observed in the spectra.

Figure 8 ,

 8 Figure 8, panel a, shows the most relevant regions of the IR spectrum of the first group in a neon matrix. The bands coming from CCC and from the second group have been subtracted from the original spectrum. Theoretical spectra of CTC(D2) and CTT(D2) are also reported in Fig. 8 (top panel) for comparison. They allow the assignment of most of the intense bands to these two species. Bands in the 2660-2710 cm -1 region (Fig. 8, left) correspond to the OD stretching modes of the deuterated isotopologues. Their number should give an idea of the number of produced conformers. However, because of the mixture of double and mono deuterated isotopologues, these OD modes could belong to AcAcD2 and AcAcD1(OD) open conformers. In fact,

Figure 8 :

 8 Figure 8: a) IR spectra of the first group of conformers (bands from CCC and from the second group are subtracted from the original spectrum), b) Difference IR spectrum between the sample just after UV irradiation and 68 h later in the dark, c) Difference IR spectrum between after and before IR laser irradiation at 5235 cm -1 , obtained from a sample with a relatively high AcAcD1/AcAcD2 ratio; AcAcD1(OD) bands are marked with *, d) IR theoretical spectrum in the harmonic approximation (scaled by 0.981) of CTC(D2) (blue up) and CTT(D2) (red down) conformers (Lorentzian bandwidths of 2 cm -1 ); the positive/negative spectra are set in order to compare to panel b showing more stable (positive)/ less stable (negative) species. Zooms in the left and middle panels refer to the optical density of the right panel.

  Furthermore, after IR irradiation at 5235 cm -1 , CTT converts back to CTC once the IR laser is turned off, similarly to what happens after UV irradiation. The overtones of the three main OD stretching bands of Fig. 8, panel c are obtained and the values are reported in Table IV, in comparison with theoretical estimations calculated within the anharmonic approach. These experiments proved that the three OD bands (Fig. 8 a, left panel) belong to AcAcD2 open conformers -one to CTC(D2) and two to CTT(D2) -, and not to the monodeuterated isotopologue.

Figure 9 :

 9 Figure 9: a) IR spectra of the second group of isomers (negative bands come from non-compensated subtraction of first group and H8 isomers), b) Difference IR spectrum between the sample just after UV irradiation and 72 h after in the dark, c) Difference IR spectrum after and before IR laser irradiation at 5280 cm -1 , obtained from a sample with a relatively high AcAcD1/AcAcD2 ratio; AcAcD1(OD) bands are marked with *, d) IR theoretical spectrum in the harmonic approximation (scaled by 0.981) of TCC(D2) (blue up) and TCT(D2) (red down) conformers. Zooms in the left and middle panels refer to the optical density of the right panel.

Figure 10 :

 10 Figure 10: Calculated CTT → CTC and TCT → TCC (from the left to the right) theoretical barriers, through IRC method. The dashed line represents approximately the kinetic energy of the particle (deuterium atom), estimated as 𝛥𝑍𝑃𝐸 = 𝑍𝑃𝐸(𝑡𝑟𝑎𝑛𝑠) -𝑍𝑃𝐸(𝑇𝑆) (different for each pair -see TableVII).

  Additional laser irradiation of the open enol conformers in the first overtones of their OD stretching modes induces reversible XYT↔XYC interconversion. This process occurs in the ground state, similarly to the tunneling process. It allows a clear assignment of the IR spectra of the observed open conformers and the experimental measurement of the overtones frequencies.

Table I :

 I CCC(D2) conformer assignment. Experimental frequencies of the chelated enol form of AcAcD2 in a neon matrix, compared to experimental values obtain by Tayyari et al 32 in gas phase, calculated harmonic and anharmonic frequencies [B3LYP/6-311++G(3df,3pd)] (cm -1 ). Intensities (km/mol) obtained in the harmonic approximation.

	Assignment a	Experiment	Tayyari (Gas)	Theoretical harmonic*sf b anharmonic Intensity
	νaCH3 (CO side)	3034 c	3018	3083.2	3003.2	10
	νaCH3 (OD side)	3027 c		3078.3	2998.7	9
	νaCH3 (OD side)		2970	3031.5	2949.3	5
	νaCH3 (CO side)			3021.5	2954.3	6
	νsCH3 (OD side)	2951 c	2940	2980.5	2928.5	8
	νsCH3 (CO side)			2976.4	2951.5	3
	νCD	2304.5	2300	2328.7	2297.0	1
	νOD	2000 c	2027	2158.3	1857.1	259
	νa(C=C + C=O )	1641.8	1633	1631.7	1616.5	263
	νs(C=C + C=O ) + δOD	1544.2	1544	1530.6	1515.2	374
	δaCH3 (OD side)	1449.4	1448	1448.3	1436.7	87
	δaCH3 (CO side)	1429.3	1448	1436.9	1432.6	39
	δsCH3 (OD side)	1392.7		1391.5	1390.5	28
	δsCH3	1376.1	1365	1376.8	1368.0	11
	δsCH3 (CO side)	1354.0	1365	1358.5	1354.1	54
	sC-C-C=C-C ring breath	1279.5	1273	1278.4	1270.3	126
	δOD	1088.6	1082	1098.9	1076.0	52
	ρCH3 (OD side)	1029.5	1025	1027.5	1027.4	34
	CH3 (CO side)	1020.6		1027.2	1020.9	7
	ρCH3 (+ δOD)	993.9		990.2	991.5	10
	νC-CH3(CO side) + ρCH3	936.3	936	927.8	933.4	25
	Δ ring + ρCH3	874.9	880	874.9	881.8	17
	δCD	831.1		831.6	837.1	0.5
	γOD	706.1	707	735.5	740.9	38

a main characteristic motions; ν, stretching; δ, in plane bending; γ, out of plane bending; ρ, in plane rocking; , out of plane rocking; Δ, in plane ring deformation; s, symmetric; a, asymmetric b sf: scaling factor (0.981) c Broad bands

Table II :

 II Bandwidths in Ne for some bands of the CCC conformer of AcAcH8 8 and AcAcD2. Only bands where a measurement of FWHM was possible are shown. The assignment is set according to ref.8, and pairing modes was made taking into account the most relevant motions involved in each mode. Position and width are in cm -1 . nm: measurement was not possible.

	Assignment a	Position	AcAcH8	Width	Position	AcAcD2	Width
	νa(C=C + C=O )	1642.0 b	16	1641.8		2.5
	νs(C=C + C=O ) + δOH	1619.7 b	11	1544.2		5.7
	δaCH3 (OH side)	1465.1		4.6	1449.4		2.0
	aCH3	1435.8		6.6	1429.3		1.3
	δCH3	1428.1		4.3	1376.1		0.8
	δsCH3 (OH side)	1378.6		2.6	1392.7		1.6
	δsCH3 (CO side)	1362.9		1.5	1354.0		0.9
	δOH	1297.2		78	1088.6		2.3
	sC-C-C=C-C ring breath	1251.4		7.3	1279.5		2.9
	δCHolefinic	1171.5		3.3	831.1		nm
	ρCH3 (OH side)	1015.8		1.8	1029.5		1.3
	ρCH3 (CO side)	995.2 b		1.4	993.9		1.0
	γOH	947.9		5.5	706.1		nm
	Δ ring + ρCH3	910.6		6.3	874.9		1.3

a main characteristic motions; ν, stretching; δ, in plane bending; γ, out of plane bending; ρ, in plane rocking; Δ, in plane ring deformation; s, symmetric; a, asymmetric b bands with shoulders

Table III :

 III Experimental frequencies (cm -1 ) of the chelated enol form of AcAcD1(OD) and AcAcD1(CD) conformers in Ne, compared to calculated harmonic and anharmonic frequencies [B3LYP/6-311++G(3df,3pd)]. Experimental bandwidths [Δ (cm -1 )] and intensities obtained in the harmonic approximation (km/mol) are also reported. nm: measurement was not possible.

			CCC(OD)						CCC(CD)
	Assignment a	CCC-OD Exp.	Δ	Theo. harm.*sf b (Anharm.)	Int.	Assignment a	CCC-CD Exp.	Δ	(Anharm.) Theo. harm.*sf b	Int.
							ν CD	2306.8		2328.7 (2296.2)	0.8
	νa(C=C + CO )	1648.7	3.9	1641.9 (1625.5)	273	νa(C=C + CO )	1630.5	14	1634.0 (1608.6)	355
	νs(C=C + CO ) + δOD	1552.7	4.7	1536.7 (1517.1)	384	νs(C=C + CO ) + δOH	1616.8	18	1614.6 (1603.9)	283
	δaCH3(OD side) + δCH	1461.2	nm	1462.1 (1454.2)	32	δaCH3(OH side) + δOH	1451.2	nm	1451.5 (1446.9)	38
	δaCH3(CO side)	1431.2	nm	1436.9 (1427.8)	21	δaCH3(CO side) + δOH	1439.7	nm	1438.9 (1427.8)	20
							δOH+ νs (carbon skeleton)	1411.3	7.7	1410.1 (1397.8)	180
	δaCH3(OD side)	1404.5	nm	1407.7 (1399.8)	64	δsCH3 (OH side)	1380.7	nm	1384.1 (1365.8)	35
	δsCH3 (CO side)	1361.7	0.8	1364.6 (1361.4)	50	δsCH3 (CO side)	1356.6	3.0	1359.9 (1358.9)	45
	νs (carbon skeleton) + (δOD)	1261.4	8.5	1279.7 (1260.7)	119	νs (carbon skeleton) + δOH	1249.1	10.2	1244.3 (1232.1)	135
	δCH	1175.0	1.7	1175.6 (1170.2)	21
	δOD	1079.9	3.5	1091.4 (1039.3)	66
	CH3 (CO side)	1027.0	nm	1027.4 (1025.0)	7	CH3 (CO side)	1027.0	nm	1027.2 (1024.3)	8
	ρCH3 (OD side)	1013.0	0.8	1013.0 (1013.7)	16	ρCH3	1048.9	nm	1044.4 (1041.4)	6
	ρCH3 (CO side) + δOD	976.7	1.1	972.4	(978.9)	33	ρCH3	1001.6	1.8	999.7 (1001.4)	10
	Δ ring + ρCH3	925.2	0.8	920.6	(923.3)	4	Δ ring + ρCH3	938.2	2.4	929.8 (933.0)	14
	Δ ring + ρCH3(CO side)	884.1	1.5	884.7	(890.5)	20	Δ ring + ρCH3 (CO side)	893.9	nm	893.7 (907.3)	32
	γCH	777.5	nm
	γOD	706.1	nm	732.4	(734.1)	50	γOH	947.4	3.6	986.9 (986.2)	70

a main characteristic motions; ν, stretching; δ, in plane bending; γ, out of plane bending; ρ, in plane rocking; , out of plane rocking; Δ, in plane ring deformation; s, symmetric; a, asymmetric; b sf: scaling factor (0.981)

Table IV :

 IV Experimental and theoretical frequencies (cm -1 ) of the first overtones (OD modes) in AcAcD2 open enol conformers

		νanharmonic/cm -1	νanharmonic/cm -1
		(Theoretical)	(Experimental)
	CTC	5255	5235
	CTT	5279	5260 5280
	TCC	5230	5243
	TCT	5289	5280

Table V :

 V First group of conformers: experimental frequencies (cm -1 ) in Ne compared to theoretical frequencies (cm -1 ) [B3LYP/6-311++G(3df,3pd)]. Theoretical values in scaled harmonic approximation (and anharmonic approximation). Intensities (km/mol) obtained in the harmonic approximation.

	Assignments a	Experimental	CTC	Theoretical	CTT	Intensity
	νOD	2696.5 b 2686.8 b		2727.4 (2684.0)	53
	νOD	2674.3	2706.4 (2672.1)		29
	νa(C=C + CO )	1707.7	1701.6 (1701.4)		170
	νa(C=C + CO )	1698.8		1699.3 (1694.4)	171
	νs(C=C + CO )	1632.9		1617.7 (1603.3)	481
	νs(C=C + CO )	1610.0	1597.1 (1566.1)		545
	δaCH3 (OD side)	1433.1		1431.9 (1427.7)	41
	δaCH3 (OD side)	1431.4	1431.0 (1418.0)		80
	δsCH3 (OD side)	1382.8	1357.7 (1378.4)		49
	δsCH3 (OD side)	1376.7		1378.8 (1373.0)	46
	δsCH3 (CO side)	1359.8	1358.1 (1351.7)		30
	δsCH3 (CO side)	1359.8		1358.5 (1352.7)	34
	δsCH3 + ν(C-CH3) (OD side)	1304.1	1296.0 (1288.8)		122
	δsCH3 + ν(C-CH3) (OD side)	1292.5 b 1291.2 b		1285.0 (1275.3)	251
	ν(C-CH3 ) (CO side) + ν(C-O) +δCH3	1273.5	1265.4 (1249.6)		16
	ν(C-CH3 ) (CO side) + ν(C-O) +δCH3	1273.5		1265.7 (1258.9)	17
	ρCH3 (CO side)	1087.0	1085.2 (1079.6)		63
	ρCH3 (CO side)	1082.7		1079.8 (1078.2)	18
	ρCH3 (OD side)	1001.3	1002.6 (999.1)		30
	ρCH3 (OD side)	1001.3		1000.1 (994.6)	35
	ρCH3 (CO side) + δ OD	954.9 b 953.8 b	942.0 (934.5)		145
	ρCH3 (CO side) + δ OD	948.4 b 947.2 b		935.8 (936.6)	64
	δOD	909.4		898.7 (901.1)	113
	δOD + δCD	890.1 b 889.4 b	884.9 (886.1)		14

a main characteristic motions; ν, stretching; δ, in plane bending; ρ, in plane rocking; Δ, in plane ring deformation; s, symmetric; a, asymmetric b bands with doublets due to sites effects

Table VI :

 VI Second group of conformers: experimental frequencies (cm -1 ) in Ne compared to theoretical frequencies (cm -1 ) [B3LYP/6-311++G(3df,3pd)]. Theoretical values in scaled harmonic approximation (and anharmonic approximation). Intensities (km/mol) obtained in the harmonic approximation.

	Assignments a	Experimental	TCC	Theoretical	TCT	Intensity
	ν OD	2695.4		2737.3 (2689.2)	56
	ν OD	2679.8	2714.8 (2661.9)		52
	νa(C=C + CO )	1681.8	1683.9 (1686.3)		232
	νa(C=C + CO )	1678.0		1684.3 (1685.3)	175
	νs(C=C + CO ) + δOD	1664.1		1650.3 (1646.3)	363
	νs(C=C + CO ) + δOD	1635.4	1617.2 (1614.0)		397
	δaCH3(OD side)	1447.5	1451.2 (1451.2)		36
	δaCH3(CO side)	1427.2		1434.3 (1424.2)	22
	δsCH3(OD side)	1396.1	1394.2 (1407.8)		33
	δsCH3(OD side)	1389.2		1391.0 (1401.2)	23
	δsCH3 (CO side)	1369.4		1367.7 (1360.3)	48
	δsCH3(CO side)	1354.1	1351.5 (1342.4)		67
	ν (carbon skeleton) + δsCH3	1328.6	1328.0 (1319.2)		101
	ν (carbon skeleton) + δsCH3	1320.2		1314.3 (1303.9)	126
	νs C-CH3 + ρCH3 (CO side)	1224.1	1211.0 (1202.8)		68
	νs C-CH3 + ρCH3 (CO side)	1222.6		1208.8 (1200.4)	118
	ρCH3(OD side) + δOD	1098.0	1095.5 (1093.3)		41
	ρCH3(OD side) + δOD	1097.1		1093.8 (1092.3)	36
	ρCH3 (CO side)	1000.8		992.9 (993.2)	44
	ρCH3 (OD side)	994.1	991.7 (990.3)		55
	ρCH3 (CO side)	977.0	970.9 (970.3)		18
	δ CD + δ OD	936.2	921.3 (903.8)		40
	δ OD	919.0		903.5 (908.7)	25
	δ CD	847.6		845.2 (853.1)	47
	a main characteristic motions; ν, stretching; δ, in plane bending; ρ, in plane rocking; Δ, in plane ring
	deformation; s, symmetric; a, asymmetric

  The theoretical heights of the barriers, ZPE included, for both pairs of conformers and both isotopologues (AcAcH8 and AcAcD2) are reported in TableVII. ΔZPE is the difference in ZPE energies obtained for the transition state and the trans conformer XYT (CTT or TCT); 𝜔 0 is the calculated OH/OD rotation frequency (OH mode) at MP2 level.A first conclusion is that these barriers are too high compared to thermal energy (6.7 x 10 -2 kJ/mol at 8 K) to be overpassed thermally, confirming the tunneling assumption. As indicated by the values reported in Table VII, the differences in rotational barrier heights between both isotopologues are small, confirming also that the different heights do not govern the different behaviors of AcAcD2 and AcAcH8. The two barriers (IRC calculation) are drawn in Fig.10in the case of double deuterated isotopologues. They are found very similar (height and width), the barrier is slightly lower between TCT and TCC than between CTT and CTC.

Table VII :

 VII Theoretical rotational barrier (in kJ/mol and cm -1 ), ZPE difference (ΔZPE in kJ/mol) and frequency of the OH/OD rotational mode (Hz) at MP2 level for the pairs of observed conformers, experimental and calculated tunneling rates, k (s -1 ).

			CTT →CTC	TCT →TCC
			AcAcH8	AcAcD2	AcAcH8	AcAcD2
	Barrier height (kJ/mol) ‡	23.8	24.5	21.4	22.1
		[cm -1 ]	[1989.5]	[2048.0]	[1788.9]	[1847.4]
	ΔZPE	(kJ/mol)	2.8	2.1	2.5	1.8
	𝝎 𝟎	(Hz)	1.17x10 13	8.69 x10 12	1.09 x10 13	8.29 x10 12
				Tunneling rate constant (k)
	Experimental value	-	5x10 -7	-	3x10 -6

Acknowledgements

This work was supported by the RTRA Triangle de la Physique (2010-004-T NOSTADYNE and 2013-0436T REACMAQ). The authors are grateful to Dr. Justinas Ceponkus for fruitful discussions.


Florian Lemaitre

Lionel Lacassagne

A NEW RUN-BASED CONNECTED COMPONENT LABELING FOR EFFICIENTLY ANALYZING AND PROCESSING HOLES

Keywords: Connected component labeling and analysis, Euler number, adjacency tree, hole processing, hole filling

This article introduces a new connected component labeling and analysis algorithm for foreground and background labeling that computes the adjacency tree. The computation of features (bounding boxes, first statistical moments, Euler number) is done on-the-fly. The transitive closure enables an efficient hole processing that can be filled while their features are merged with the surrounding connected component without the need to rescan the image. A comparison with existing algorithms shows that this new algorithm can do all these computations faster than algorithms processing black and white components.

INTRODUCTION & STATE OF THE ART

Connected Component Labeling (CCL) is a fundamental algorithm in computer vision. It consists in assigning a unique number to each connected component of a binary image. Since Rosenfeld [START_REF] Rosenfeld | Sequential operator in digital pictures processing[END_REF], many algorithms have been developed to accelerate its execution time on CPU [START_REF] Cabaret | What is the world's fastest connected component labeling algorithm ?[END_REF][START_REF] He | The connected-component labeling problem: a review of state-ofthe-art algorithms[END_REF][START_REF] Bolelli | Spaghetti labeling: Directed acyclic graphs for block-based connected components labeling[END_REF], SIMD CPU [START_REF] Hennequin | Designing efficient SIMD algorithms for direct connected component labeling[END_REF], GPU [START_REF] Playne | A new algorithm for parallel connected-component labelling on GPUs[END_REF] or FPGA [START_REF] Klaiber | A single cycle parallel multi-slice connected components analysis hardware architecture[END_REF].

In the same time Connected Component Analysis (CCA) that consists in computing Connected Component (CC) features -like bounding-box to extract characters for OCR, or the first raw moments (S, Sx, Sy) for motion detection and tracking -has also risen [START_REF] Bailey | Single pass connected component analysis[END_REF][START_REF] Lacassagne | Light Speed Labeling for RISC architectures[END_REF][START_REF] Lacassagne | Light Speed Labeling: Efficient connected component labeling on RISC architectures[END_REF][START_REF] Tang | A linked list run-length-based single-pass connected component analysis for real-time embedded hardware[END_REF][START_REF] He | An efficient two-scan algorithm for computing basic shape features of objects in a binary image[END_REF]. Parallelized algorithms have been also designed [START_REF] Cabaret | Parallel Light Speed Labeling for connected component analysis on multicore processors[END_REF][START_REF] Hennequin | A new direct connected component labeling and analysis algorithm for GPUs[END_REF][START_REF] Bailey | Zig-zag based single-pass connected components analysis[END_REF]. The initial Union-Find algorithm [START_REF] Tarjan | Efficiency of good but not linear set union algorithm[END_REF] has been also analysed [START_REF] Tarjan | Worst-case analysis of set union algorithms[END_REF] and improved [START_REF] Galil | Data structures and algorithms for disjoint set union problems[END_REF] with decision tree [START_REF] Wu | Optimizing two-pass connected-component labeling algorithms[END_REF] and various path compression/modification algorithms [START_REF] Manne | A scalable parallel union-find algorithm for distributed memory computers[END_REF][START_REF] Patwary | Experiments on union-find algorithms for the disjoint-set data structure[END_REF]. Some other features -useful for pattern classification/recognition -are computed by another set of algorithms: the Euler number with Bit-Quads [START_REF] Gray | Local properties of binary images in two dimensions[END_REF], the adjacency (also known as homotopy or inclusion) tree [START_REF] Rosenfeld | Digital topology[END_REF] and more recently, foreground (FG) and background (BG) labeling (also known as B&W labeling) [START_REF] He | A new algorithm for labeling connected-components and calculating the euler number, connected-component number, and hole number[END_REF] and hole filling [START_REF] He | A new algorithm for labeling connected-components and calculating the euler number, connected-component number, and hole number[END_REF] with also improvements in the last decade: [START_REF] Yao | Bit-quadbased euler number computing[END_REF][START_REF] Del Rio | Computing the component-labeling and the adjacency tree of a binary digital image in near logarithmic-time[END_REF].

Section 2 provides a short description of LSL algorithm that is used for our new algorithm, Section 3 introduces our new algorithm, Section 4 presents a benchmark of existing algorithms and their analysis and Section 5 is the conclusion.

CLASSICAL LSL

We chose to base our new algorithm on LSL [START_REF] Lacassagne | Light Speed Labeling: Efficient connected component labeling on RISC architectures[END_REF] because it is runbased (segment processing) and thus is able to compute features very quickly compared to pixel-based algorithms.

The specificity of LSL is to combined segments with linerelative labeling to speed segment adjacency detection up. Like

1 1 1 1 1 1 1 ER i ER i-1 j X i X i-1 RLC i RLC i-1 j 0 1 2 3 4 5 6 7 8 9 j 0 0 1 2 3 e T 1 2 3 unification 0 0 1 2 3 e T 1 1 1 0 0 1 2 3 0 0 1 ERA i ERA i-1 er 0 1 2 3 4 5
Fig. 1: LSL tables for classic foreground labeling: the even relative labels corresponding to background components are equivalent to zero in ERA tables (they will be equivalent to other labels for the proposed foreground and background labeling). all direct CCA algorithms, it is split into two steps and performs a single image scan.

The first step assigns a temporary/provisional label to each connected component and computes its associated features. Equivalences between labels are built when needed. It is composed of a segment detection (Algorithm 1) and a segment Unification (Algorithm 2 modified for B&W labeling). From two consecutive input lines Xi-1, Xi, two relative labelings (ERi, ERi-1) are produced where FG runs (or segments) have odd numbers and BG runs have even numbers. The associated semi-open intervals are stored in tables RLC i-1, and RLC i. The table ERAi holds the translation between Relative and Absolute labels: ea = ERAi[er].

To find out which labels of the previous line are connected to the current segment (Unification), one has to read the value of relative labels from table ERi-1 at the positions given by RLC i, and translates them into absolute labels to update the equivalence table T . Features are also computed during this step and stored in table F .

The second step solves the equivalence table by computing the transitive closure (TC) of the graph associated to the label equivalence and merge the features together. Unlike for CCL algorithms, the third step that performs a second scan to replace temporary labels of each connected component with their final labels (Algorithm 4) is usually avoided (but can be done for visual verification).

In order to differentiate temporary root and final root, we define a (a ← Find(ea)) as the temporary root of the absolute label ea used in Algorithm 2, while r used in Algorithm 3 and Algorithm 4 is the final root of the connected component.

arXiv:2006.09299v1 [cs.CV] 16 Jun 2020

Algorithm 1: segment detection (LSL step 1a)

1 // prolog 2 RLC i [0] ← 0 3 er ← 0 4 x 1 ← 0 // previous value of X (x1 = Xi[j -1]) 5 for j = 0 to w -1 do 6 x 0 ← X i [j] // current value 7 RLC i [er + 1] ← j // will later be overwritten if f = 0 8 f ← x 0 ⊕ x 1 //

LSL AND HOLE PROCESSING

Our goal is to propose a new all-in-one algorithm that finds holes and processes them efficiently by computing the adjacency tree between foreground and background connected components. Then, filling holes only consists in modifying the adjacency tree and the equivalence table, without modifying pixels or labels in the image (the same approach can be used to apply arbitrary connected operators [START_REF] Salembier | Connected operators[END_REF]). We also want our algorithm to be able to compute statistical features on-the-fly, to relabel the whole image and to compute adjacency features like the Euler number -or just a subset.

In the following, a "component" means a Connected Component, either foreground or background.

Holes and adjacency tree

A component C1 is surrounded by another component C2 -written C1 C2 -if and only if all paths from C1 to the exterior of the image contain at least one pixel from C2. A hole is a background component that is surrounded by a foreground component.

The adjacency tree is encoded in a new table I. For a label e1 associated to a component C1, e2 = I[e1] is one of the temporary labels of the unique component C2 that is both adjacent to C1 and surrounding C1 (C1 C2). I[e1] = -1 if e1 = 0, or e1 is not a root label (T [e1] = e1). In short, the table I represents the adjacency tree whose edges are directed according to the surrounding relation.

We considered two methods to build the adjacency tree and the surrounding relation: detecting closing pixels [START_REF] He | A very fast algorithm for simultaneously performing connected-component labeling and euler number computing[END_REF], or looking at the adjacency at exterior pixels [START_REF] Del Rio | Computing the component-labeling and the adjacency tree of a binary digital image in near logarithmic-time[END_REF].

A closing pixel is a pixel neighboring both ends of a path (using 4-adjacency for BG and 8-adjacency for FG). Figure 2a shows the patterns of a closing pattern while it is being processed. The surrounding C1

C2 where C1 and C2 are adjacent can be detected during the Unification when C2 is unified with itself. If C2 is FG (8-adjacency), the pixel above the closing pixel is in C1. If C2 is BG (4-adjacency), the upper-left pixel is in C1.

The other method relies on the adjacency at exterior pixels. In our case, we consider the top most pixels of a component because those require the creation of a new label which is easy to detect. Every time a new label is created, the label directly above the current pixel is recorded in I as its initial adjacency and speculative surrounding. It is actually simpler to look for the label on the left that is necessarily from the same component as above (Figure 2b). When two labels a < b are unified, the initial adjacency I[b] is discarded . The order on labels implies that top pixels of a are higher than top pixels of b -or at least at the same height. It means that the higher initial adjacency and speculative surrounding is kept while the other is discarded. Once a component has been fully scanned, the only initial adjacency kept for this component is the one from the root label which is, by construction, the label of top most pixels, and thus on the exterior of the component. The remaining initial adjacency and speculative surrounding is thus necessarily a true surrounding.

We chose to use the initial adjacency method as it saves one extra branch and one extra Find within the Unification compared to the closing pixel method. Moreover, the update of I when an adjacency is discarded is actually not necessary as I is accessed only for root labels whose initial adjacencies are kept by construction. While the adjacency is a local property, the surrounding is not and thus is defined and correct only when the component has been fully scanned. Consequently, initial adjacency builds a speculative I that is correct only at the end of the image scan and that cannot be worked on beforehand.

New Black and White LSL

Our new algorithm -LSL BW -extends the unification and the transitive closure steps to support B&W labels and the adjacency tree (Algorithm 2 and Algorithm 3). B&W labels require to process both odd and even segments instead of just odd ones (in Algorithm 2 and 4). Consequently, ERAi table does not necessarily have zeros at even indices anymore. The first encoded segment is always a BG one, but might have 0 length if the first pixel is FG. Thus, the unification needs a prolog (Algorithm 2, lines 1 to 5) to skip the first segment if empty, and an epilog (Algorithm 2, lines 39 to 44) to attach the first segment and the last segment if it is BG to the exterior. The transitive closure need no modification to handle Black&White labels.

In addition, the correction of coordinate and indices are now dependant on the parity of the segment being processed (Algorithm 2, lines 13 and 18). Note that Algorithm 2 implements the algorithm using 8-adjacency for FG and 4-adjacency for BG. The line 11 should be modified to c8 ← p ⊕ 1 if one wants the complementary adjacency (4-FG, 8-BG).

The construction of the adjacency table requires only a few modifications to the algorithms to set the initial adjacency (Algorithm 2 line 37) and to convert temporary labels into final labels within the I table (Algorithm 3 line 11). Hole filling is done during the transitive closure (Algorithm 3, lines 3 to 5).

Like for classical LSL, the computed features for each FG and BG components are the bounding-box and the first statistical moments S, Sx, Sy.

Algorithm 2: B&W Unification (step 1b)

1 er s ← 0 // starting segment 2 if RLC i [1] = 0 then 3 ERA i [0] ← 0 4 er s ← 1 5 // White-
c 8 ← p // if current segment is 8-C, c8 = 1 12 f ← ComputeFeatures(i, j 0 , j 1 )
13 // fix extension in case of 8-connected component

14 j 0 ← max(j 0 -c 8 , 0) 15 j 1 ← min(j 1 + c 8 , w) 16 er 0 ← ER i-1 [j 0 ] 17 er 1 ← ER i-1 [j 1 -1] //
1 for i = 0 to h -1 do 2 j 0 ← RLC i [0]
// j0 is 0 3 // White-only would have have step = 2 and unconditionally store the BG label for even er // final label

7 j 1 ← RLC i [er + 1] 8 E i [j 0 , j 1 [ ← r 9 j 0 ← j 1

Example

Figure 3 shows how our algorithm builds the equivalence table T and the adjacency tree I on a simple, yet complete, example. It shows the input image with initial labels and their speculative surrounding (FG in gray and BG in white), as well as a graph representing both the equivalence table T and the adjacency tree I.

On the first three lines (i = 0, i = 1 and i = 2), five new labels are created 1 , 2 , 3 , 4 and 5 . Their initial adjacency is set as their speculative surrounding: 1 0 , 2 1 , 3 1 , 4 2 and 5 3 . At i = 3, two new labels are created with the following speculative surroundings: 6 4 and 7 5 . In addition, 3 ≡ 2 is detected. Consequently, the speculative surrounding of 3 is discarded in favor of 2 1 . At i = 4, as 5 ≡ 4 , the speculative surrounding 5 3 is discarded.

At i = 5, two new equivalences are detected: 2 ≡ 0 and 7 ≡ 6 . Consequently, the speculative surroundings of 2 and 7 are dropped. The component 0 2 3 has no more surrounding as 0 is the exterior of the image. While the algorithm is not capable to detect it, we can see that the surrounding 6 4 is no more speculative and is actually final.

At i = 6, the last equivalence 4 ≡ 1 is detected and the speculative surrounding 4 2 is discarded, and the surrounding 1 0 is kept. This leads to the final state before transitive closure where all remaining surroundings ( 64 and 1 0 ) are no more speculative and are actually true surroundings. When holes are filled, the adjacency edge 6 4 is replaced by an equivalence edge 6 ≡ 4 . Note that our algorithm actually fills hole during transitive closure and not beforehand.

BENCHMARK & PERFORMANCE ANALYSIS

We measured the performance of our algorithms using a protocol similar to [START_REF] Bolelli | Toward reliable experiments on the performance of connected components labeling algorithms[END_REF]. We tested randomly generated 2048×2048 images with varying density and granularity on a Skylake Gold 6126 Xeon @2.60GHz. Grana's [START_REF] Bolelli | Spaghetti labeling: Directed acyclic graphs for block-based connected components labeling[END_REF] and Diaz' [START_REF] Diaz Del Rio | Parallel connected-component-labeling based on homotopy trees[END_REF] works have been ran and measured on our machine. We also ran the CCA algorithms from [START_REF] Cabaret | What is the world's fastest connected component labeling algorithm ?[END_REF] on our machine and kept three of them: Rosenfeld+F as the reference, He HCS2+F and LSLST D +F as the fastest pixel-based and run-based algorithms at this time. The other ones have been estimated from their paper. To have comparable results across machines, we give all the results in cycles per pixel (cpp) that is the execution time multiplied by the clock frequency and divided by the number of pixels. Table 1 shows the minimal and maximal processing time of our new labeling algorithm. The first line corresponds to a base processing: foreground and background CC labeling and computing their adjacency tree. The next lines provide the extra times to do extra computations like Euler or Hole Filling and B&W Feature Computation. The extra times are the worst case we measured for doing this extra computation. One can then estimate the total processing time for all the computations they are interested in just by adding all the extra times.

i = 0 i = 1 i = 2 i = 3 i = 4 i = 5 i = 6 i = 0: i = 1: i = 2: 1 0 , 2 1 , 3 1 , 4 2 , 5 3 0 1
On this table, we can observe that the minimal extra time for all computations but relabeling is 0. This is a property of run-based algorithms: those computation times depend on the number of segments -which is 1 per line for empty images. Euler number computation and Hole filling are really inexpensive using our approach. On the opposite, relabeling is very expensive, almost doubling the total time, and should be avoided if not required.

Figure 4 shows the processing time of the labeling with hole filling and either relabeling or feature computation depending on both granularity and density. We can see that the processing time quickly decreases with higher granularity. Random images with g = 1 are highly artificial but are useful to stress the algorithms where they appear to be slowest. Our labeling is much faster at g = 4 with an average time of 5.3 cpp. This is interesting because natural images (like SIDBA database) usually have an average processing time close to the processing time of random images with granularity greater than In Table 2, each State-of-the-Art algorithm are compared to one configuration of our new algorithm that computes at least as much. The execution time of our algorithm is close to the best classical foreground CCL algorithm [START_REF] Bolelli | Spaghetti labeling: Directed acyclic graphs for block-based connected components labeling[END_REF] despite computing background labels and adjacency tree in addition. This is possible thanks to our lightweight adjacency-tree computation and the use of segments that allows a symmetric computation of BG and FG components.

Our work outperforms both existing B&W algorithms [START_REF] Diaz Del Rio | Parallel connected-component-labeling based on homotopy trees[END_REF][START_REF] He | An algorithm for connectedcomponent labeling, hole labeling and euler number computing[END_REF] or CCL algorithm with Euler number computation [START_REF] He | A very fast algorithm for simultaneously performing connected-component labeling and euler number computing[END_REF]. While we compute much more, Euler computation is faster than dedicated algorithms [START_REF] Yao | Bit-quadbased euler number computing[END_REF][START_REF] Yao | new run-based algorithm for euler number computing[END_REF]. Our run-based algorithm is faster than pixel-based CCA algorithms, like already observed in [START_REF] Cabaret | What is the world's fastest connected component labeling algorithm ?[END_REF] with classical LSL. Classical LSLST D +F -the base of our algorithm -remains obviously faster. The most noticeable difference is for the maximum processing time: our BW algorithm needs to process twice as much segments than classical LSL.

CONCLUSION

In this article, we have introduced a new connected component labeling and analysis algorithm that is able to do in one single pass of the image, both the Euler number computation but also a double foreground and background labeling with the adjacency tree computation. The modified transitive closure algorithm enables an efficient hole processing: holes can be filled and the surrounding connected components are updated on-the-fly. Our approach can easily be adapted to other connected operators like filtering out components based on their statistical features. Table 2: Performance comparison between State-of-the-Art algorithms ("Their") and this work ("Our"). The "compute" columns show what is computed by the algorithms. "min" and "max" columns show the minimum and maximum processing time in cpp measured for each algorithm.

As far as we know our algorithm is faster than B&W labeling algorithms and algorithms computing features related to hole processing.

Fig. 2 :

 2 Fig.2: Patterns demonstrating how surroundings are detected when the current pixel x is processed. Foreground is 8-adjacent and background is 4-adjacent.

43a←Algorithm 3 : 2 a 3 if 4 i 6 if a < e then 7 r ← T [a] 8 T 9 F

 32346789 Find(ERA i [ner i -44 T [a] ← 0 B&W Transitive closure (step 2) 1 for e = 0 to ne -1 do Hole filling and e = a then // If label is root ← I[e] // label of the surrounding component 5 if T [i] > 0 then a ← T [e] ← i [e] ← r // Transitive Closure [r] ← F [r] ∪ F [e] // Feature merge 10 else // e is a root 11 I[e] ← T [I[e]] // point adjacency to root Algorithm 4: B&W Relabeling (step 3)

4 for er = 0 to ner i -1 step 1 do 5 e// provisional label 6 r

 456 ← ERA i [er] ← T [e]

Fig. 3 :

 3 Fig. 3:Step by step example of our new B&W labeling focusing on equivalences building and adjacency setting.

Fig. 4 :

 4 Fig. 4: Processing time in cpp of hole filling with either feature computation or relabeling.

  only would have er s = 1 and step = 2 6 for er = er s to ner i -1 step 1 do

	7	// semi open interval segment extraction [j0, j1[
	8	j 0 ← RLC i [er ]
	9	j 1 ← RLC i [er + 1]
	10	p ← er mod 2	// parity of current segment
	11

Table 1 :

 1 Minimal and maximal processing time in cpp of our base B&W algorithm and extra computation for 2048×2048 random images.

			min	max
	B&W + Adjacency	2.80	15.3
	+Euler number	+ 0	+ 0.66
	+Hole Filling	+ 0	+ 0.74
	+Feature Computation + 0	+ 10.3
	+Relabeling	+ 0.59 + 13.2
	Relabeling	Features	g = 1	g = 2	g = 4

  : standard CCL algorithms transformed into 1-pass CCA algorithms (features only)

	Algorithm	Their compute min max compute min max Our
	Grana [4] Diaz [30]	WR BWAR 18.4 3.40 25.7 59.0	BWAR 3.41 28.9
	He BW [31] He combined [28]	BWER 9.00 79.7 BWAER 3.41 29.0 WER 16.6 48.0
	He run-based [32] He bit-quad [25]	E E	5.54 36.5 2.87 23.7	BWAE 2.80 15.9
	Rosenfeld+F * [2]	WF	4.68 48.0
	He HCS2+F * [2]	WF	4.33 38.6	BWAF 2.80 24.8
	LSLST D +F [2]	WF	2.69 14.4
	B : Black labeling (BG)	A: Adjacency tree	F: Feature Computation
	W: White labeling (FG)	E: Euler number	R: Relabel

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