S Zeroual

Jean Meinnel
email: jean.meinnel@cegetel.net

A Lapinski

S Parker

A Boudjada

A Boucekkine

Vibrational spectroscopy and DFT calculations 1, 3-dibromo-2,4,6trimethylbenzene. (Anharmonicity, Coupling and Methyl group tunneling)

Keywords: Raman spectroscopy, IR spectroscopy, Inelastic neutron scattering, DFT calculations, 1,3-dibromo-2,4,6-trimethylbenzene

The Raman, IR and INS spectra of 1,3-dibromo-2,4,6-trimethylbenzene (DBMH) were recorded in the 80-3200 cm -1 range. The molecular conformation and vibrational spectra of DBMH were computed at the MPW1PW91/LANL2DZ level. Except for the methyl 2 environment, the agreement between the DFT calculations and the neutron diffraction structure is almost perfect (deviations < 0.01 Å for bond lengths, < 0.2° for angles). The frequencies of the internal modes of vibration were calculated with the harmonic and anharmonic approximations; the later method yields results that are in remarkable agreement with the spectroscopic data, resulting in a confident assignment of the vibrational bands. Thus, no scaling is necessary. The coupling, in phase or antiphase, of the motions of symmetrical C-Br and C-Me bonds is highlighted. Our DFT calculations suggest that the torsion of methyl groups 4 and 6 is hindered in deep wells, whereas methyl group 2 is a quasi-free rotor. The failure of the calculations to determine the frequencies of the methyl torsional modes is explained as follows: DFT does not consider the methyl spins and assumes localization of the protons, whereas the methyl groups must be treated as quantum rotors.

1-Introduction

A tremendous amount of work has been devoted to the spectroscopy of polysubstituted benzenes.

Among those relative to penta-and hexa-substituted compounds, two extensive papers were published in 1985: one paper compared eleven polymethyl-benzenes (pMeB) [1] and the second described six chloromethyl-benzenes C 6 (CH 3 ,Cl) 6 (ClMeB) [2]. In these studies, the experimental spectra were assigned using normal coordinate calculations to determine a common multi-parameter force field. Because the molecular conformations were not accurately known the authors assumed that the aromatic ring in all molecules was a regular hexagon, that the bond angles were 120°, and the bond lengths were 1.396 Å for the carbon-carbon aromatic bond, 1.509 Å for the methyl carbonaromatic carbon bond, 1.083 Å for the aromatic carbon-hydrogen bond and 1.096 Å for the methylcarbon hydrogen bond. For the pMeB species, the Raman and infra-red measurements were performed with samples in the gaseous phase at approximately 550 K. A 46-parameter valence force field had been proposed, and the average error between the 736 observed and calculated wavenumbers was 6.4 cm -1 . This agreement suggests that the use of an excessive number of off-diagonal constants (interactions terms) allows us to compensate for the large errors done in the geometrical parameters. According to the authors in these previous studies: "there is a great stability of the internal methyl modes, in a limit of ± 5 cm -1 they are located at: 2930 cm -1 for the C-H stretching, 1445 cm -1 for the asymmetric C-H bending, 1380 cm -1 for the C-H symmetric bending, 1000 and 1060 cm -1 for the C-H rocking". For the "torsion mode" of the methyl groups, no experimental data were available. The authors assumed without proof that these groups are "free" rotors", which is rather rare for a methyl group in solid state molecules. On the contrary this finding is well established for one of the three methyl groups of dibromomesitylene that was studied in this paper.

The parent ClMB molecules were studied as crystals from room temperature to liquid nitrogen temperature. It was also assumed that in these molecules the benzene rings are perfect hexagons.

Because the CH 3 group vibrations have been observed at similar frequencies to those in the pMeB molecules these groups were assumed to be not affected by the skeleton vibrations. Thus by considering the methyl group to be a point mass the authors were able to independently study the remaining 30 vibrations of the carbon-chlorine skeleton as those of a cyclic C 6 (X,Cl) 6 system.

Then, the authors used an optimized multi-parameter valence force field to reproduce the 121 assigned frequencies in seven different molecules. The potential energy was determined using nine principal force constants corresponding to nine different types of deformations (bond lengths and angles). To incorporate the interactions between the substituent vibrations and the deformations of the benzene ring, 37 near neighbor interaction coefficients were considered. In fact, using these new interaction parameters partially corrects the errors introduced when using a regular hexagon for the benzene ring in these asymmetrically substituted molecules. Finally the calculated frequencies reproduce the observed frequencies with an average error of only 10.9 cm -1 .

In parallel to these empirical molecular mechanic calculations, quantum chemistry programs were established that were able to provide a molecular conformation in good agreement with the Xray determination. In the late 1970s, the analytical second-derivative techniques were introduced at the Hartree-Fock (HF) level resulting in the sequence of the fundamental frequencies. However, when compared to the experimental frequencies, the computed HF frequencies were consistently 7-15 % too high. This overestimation of the frequencies may largely be attributed to the HF method itself because this method neglects electron correlation, basis set truncation and anharmonicity.

Because the overestimation is fairly uniform, a proposed solution involves the application of a single scaling factor to the theoretical harmonic frequencies to provide better agreement with the experimental data. For example in 1981, Pople et al. [3] proposed a scaling factor of 0.89 for a set of 38 molecules (477 HF/3-21G harmonic frequencies). The need for this type of correction diminishes when using density functional methods because these methods include -more or less empirically-a significant part of the total electron correlation. In 1996, Scott and Radom [4] improved the global scaling technique in their scaled quantum mechanical force field (SQMFF) procedure. They have shown that all DFT calculations, in particular those using B3-PW91/6-31G(d) or B-LYP/6-311G(df,p), were much more successful than those based on HF or MP2. At the same time, Pulay et al. [5,6] proposed an alternative approach to the SQMFF method that involves a direct scaling of the primitive valence force constants. In a study of 60 molecules (1500 vibrational frequencies), these authors obtained an average error of less than 8.5 cm -1 in the scaled frequencies. This result corresponds to an average percentage error smaller than 1 %. Notably when one hydrogen atom is implied, the scaling factors proposed for the stretching ( C-H, N-H, O-H) andbending (X-C-H, X-O-H, X-X-H, H-N-H) vibrations are in the range of 0.87 -0.95, whereas the scaling factor for C-Cl stretching is 1.04. The agreement between theory and experiment was further improved using larger basis sets in the DFT computations. Thus, the majority of Raman and IR experimental spectra are now assigned using DFT calculations. In addition to the data provided by these two spectroscopic techniques, inelastic neutron scattering (INS) furnishes new information because of the absence of selection rules and the predominance of scattering due to hydrogen atoms. An example of a study of symmetrical molecules is a paper describing sym-C 6 F 3 H 3 and C 6 F 6 [7], in which the results of DFT calculations (using five different basis sets) were used to assign the lines observed in Raman, IR and INS spectra. The INS spectrum of C 6 F 6 directly exhibits seven bands of the nine vibrations that are inactive in the Raman and IR spectra. The overall RMS for the agreement between calculation and experiment is better than 20 cm -1 , demonstrating the high quality of the theoretical predictions.

Currently, each year, several new publications are presented describing studies of substituted benzenes using a combination of Raman and IR spectroscopies and DFT or HF theoretical calculations. Curiously, no systematic spectroscopic studies of mesitylene (or 1,3,5-trimethylbenzene) derivatives have been undertaken whereas extensive studies of the protons tunneling in methyl groups have been published [8]. For the trichloro-tribromo-and triiodo-mesitylene (TCM, TBM, TIM) species, INS on powder samples [9] and on single crystals [10,11] has been used to establish that the three methyl groups in each molecule have a different tunneling gap, which is contrary to what is expected for a molecule with true C 3h symmetry. For TIM, for example, three excitations were observed at 15, 24 and 89 eV [8,9]. This difference in tunneling gaps is due to the difference in the intermolecular interactions exerted on the methyl groups located in non equivalent sites in the triclinic crystal cell. Neutron diffraction studies of the molecular conformations have shown additional consequences: not only the proton probability density but also the orientation differs for each methyl group [12,13,14]. These deviations from the ideal symmetry have visible consequences in the Raman and IR spectra at low temperatures (< 50 K): the inactive modes for C 3h symmetry become visible whereas the previously degenerate modes E" and E" are split [15]. The influence of intra and intermolecular symmetry on the tunneling properties of the methyl groups is still more spectacular in the case of the fully hydrogenated dibromomesitylene (C 9 Br 2 H 10 or DBMH) [16]. In this compound, the methyl group surrounded by two bromine atoms behaves as a quasi-free rotor, and its tunneling gap as using INS is large (387 eV or 3.1 cm -1 ). Furthermore, several torsional modes have been observed in the range 1.7 -4 meV (14-32 cm -1 ) using INS [16,17] and also Raman diffusion [18]. In contrast, the rotation of the two other methyl groups located between one bromine atom and one hydrogen atom is highly hindered, and the tunneling gap is less than 1 eV [17]. Therefore, we have undertaken a detailed study of the vibrational modes of DBMH with the intention to detect other spectroscopic consequences of the presence of two types of methyl groups.

Molecular conformation of dibromomesitylene DBMH.

The structure of DBMH has already been determined using neutron diffraction on a single crystal.

Table 1 lists the values of the bond lengths and angles obtained using neutron diffraction at 120 and 14 K that have been published [19]. These values must be compared with the results of DFT calculations obtained under different symmetry conditions.

Molecular conformation of DBMH determined using neutron diffraction at 14 K and 120 K.

The thermal differential analysis indicated that DBMH exists in two different crystal phases with an order-disorder transition at 292 ± 0.3 K.. The structure of the low temperature ordered phase was solved by Hernandez et al. using neutron diffraction with a single crystal [19]. The crystal is monoclinic and assigned to the space group P2 1 /n with 4 molecules in the unit cell. The molecules form molecular columns parallel to the a axis. In these columns, the arrangement is "anti-dipolar".

The structure determination was performed with a great accuracy, the goodness factor R being 0.032 at 120 K and 0.026 at 14 K. The experimental bond lengths and angles are listed in Table 1 and depicted in Fig. 1b.

Table 1

Figures 1a, 1b, 1c

The hexagonal ring in DBMH is distorted. There are large differences between the six intracyclicangles, these angles vary from 115.8° for C 1 -C 2 -C 3 to 123.6° for C 2 -C 3 -C 4 . Thus, using a mean value of 120° as was used in [1,2] should be a very crude hypothesis. Fig. 1b relative to the molecular conformation determined at 14 K suggests that the C 2v symmetry prediction is fulfilled to a good degree of accuracy. There is a plane of symmetry P perp perpendicular to the benzene ring bisecting carbon atoms C m2 , C 2 , C 5 and hydrogen atom H 5 . The proton probability densities (PPD) relative to Me 4 and Me 6 are well localized with three peaks (Fig. 2), corresponding to three well localized protons. In contrast, the PPD in Me 2 is delocalized on a ring with six broad maxima from the refinement (Fig. 1b and2) or from the map of a Fourier difference performed in the plane of the nuclei of the three hydrogen atoms of the methyl group (Fig. 2). The extra-cyclic angles C 1 C 2 C m2 and C 3 C 2 C m2 are equal to 122.0° in the limit of 0.1°, which is contrary to those observed for Me 4 and Me 6 , for which the extra-cyclic angles are 120.2° on one side and 122.7° on the other side (Table 1 and Fig. 1b). The small departure from symmetry observed at 120 K between the angles Br 1 C 1 C 2 and Br 3 C 3 C 2 was not observed at 14 K. One important result is that if the thermal librational scattering (TLS) is considered during the neutron diffraction (ND) refinement, the benzene ring is determined to be planar with an accuracy greater than 0.005 Å. Therefore, it can be concluded from the ND results that in the solid state, the DBMH molecule retains two planes of symmetry: the ring plane (P ring ) and one plane (P perp ) perpendicular to P ring . The intersection between these two planes is the axis of symmetry C 2 .

DFT calculations of the molecular conformation

All of the computations were performed using the Gaussian 2009 program package [START_REF] Frisch | Gaussian 03[END_REF]. The DFT calculation that yielded the equilibrium conformation is referred to as "Cal 1 P ring " in Table 1 and Fig. 1a. This conformation was obtained using the MPW1PW91 functional with the LANL2DZ basis set augmented with polarization functions on all atoms except for the hydrogen atoms. At equilibrium the benzene ring is a plane of symmetry. There is a remarkable agreement between the calculated values and the experimental data for the molecular region containing Me 4 , H 5 and Me 6 and good agreement for the angles around C 4 , C 5 and C 6 with a tolerance of 0.1°. The calculated bond distances are slightly larger than the experimental distances by only 2 to 4x10 -3 Å. Importantly, in the equilibrium conformation, the two methyl groups Me 4 and Me 6 have one CH bond located in the ring plane P ring that points towards the atom H 5 . This finding is in perfect agreement with the C 2v symmetry observed for the molecule using neutron diffraction. These orientations of Me 4 and Me 6 groups correspond to very stable orientations: the barrier hindering the rotation of these groups has been calculated to be 490 cm -1 . In contrast, the configuration calculated for the environment of the third methyl group, Me 2 , is not consistent with the C 2v symmetry. At equilibrium, the calculated structure corresponds to a methyl group with three punctual protons and one CH bond in the plane of the aromatic ring. It is clear from Fig. 1a that the left and right sides of the molecule around Me 2 are not symmetric; this lack of symmetry occurs because the trigonal symmetry of the methyl group is not compatible with the C 2v symmetry of its environment which consists of two equivalent pairs of carbon-bromine atoms C 1 -Br 1 and C 3 -Br 3 . The DFT optimized geometry has only C s symmetry, with the aromatic ring as the symmetry plane P ring . It is possible to estimate the height of the barrier hindering the Me 2 "rotation" using this DFT computation. The calculated barrier of 53 cm -1 is ten times smaller than that of the two other methyl groups. This small value partially explains why the DFT computations could lead to the actual conformation of this group. The true source of discrepancy is the strict application of the Born-Oppenheimer approximation to protons and not considering the spin of the methyl groups: proton spins are central to the phenomenon of "proton rotational tunneling" and thus to spatial delocalization [10] and to the existence of NMR. Another molecular conformation was obtained using the DFT computation "Cal 2 P perp " involving the same functional and basis set, but constraining the plane P perp containing C m2 and H 5 to be perpendicular to the initial ring plane P ring as a symmetry plane (Fig. 1c). In a normal projection onto P ring , the "left" and "right" sides of the molecule are now symmetrical. The agreement between the experimental results and those obtained using Cal 2 is better than 0.005 Å for the bond lengths and better than 0.3° for all of the angles; therefore, Cal 2 provides a better representation of the molecular geometry than Cal 1 does for the environment around Me 2 . To obtain this new orientation of Me 2 , it is necessary to admit the loss of planarity of the aromatic ring; however, these deviations are very small: 8.10 -3 Å for atom C 2 , 15x10 -3 Å for atom C m2 and -3x10 -3 Å for the Br atoms. The extra-cyclic angles around the C 2 -C m2 bond are now equivalent and equal to 122.9°. But, a new problem has been introduced.

There are now two possibilities for the displacement of the atom C m2 relative to the plane P ring : i.e. above or below the plane? To summarize, the two calculations Cal 1 and Cal 2 provide molecular conformations that, with the exception of the Me 2 group, are not significantly different from the experimental geometry. The energy of formation found by Cal 2 is less favorable than that found by Cal 1 by only 200 cm -1 , it concerns almost exclusively Me 2 environment. This explains that only the modes implying mainly Me 2 could be altered by the choice of the equilibrium structure.

Spectroscopic measurements, experimental details

The commercially purchased DBMH (Sigma-Aldrich, F) was purified by crystallization using a solution in chloroform and pumping the solvent. This step was followed by a vacuum sublimation.

Small single crystals were obtained by slowly crystallizing the purified compound from a solution of methanol. 2, Fig. 3a, 3b, 3c and6b.

Raman spectra: Table

The Raman spectra of DBMH were measured using a Horiba Jobin-Yvon HR 800 Raman spectrometer. The excitation source was a He-Ne laser operating on the 632.817 nm line. The spectra were recorded at 288 K in the 80 -4000 cm -1 region with a resolution of 3 cm -1 . It was possible to use single crystals with dimensions as small as 20x20x100 m 3 . Thus, we obtained two types of Raman polarized spectra. In the first orientation (Fig. 3b), the polarization vector E of the incident laser beam was approximately in the bc crystallographic plane, i.e., it was oriented at an angle smaller than 20° relative to the DBMH ring plane. In the second orientation (Fig. 3c), the electric field E was oriented approximately along the crystallographic axis a, i.e., it was oriented at an angle approximately 18° relative to a line perpendicular to the ring plane. Thus, in the case of similar Raman activities, the intensity of an in-plane vibration band is larger in the spectrum shown in Fig. 3b, while an out-of-plane vibration band is stronger in the spectrum shown in Fig. 3c. Table 2 lists the Raman band positions observed at 288 K (column 3) and the relative experimental intensities of these spectral features (column 16) in comparison with the calculated intensities (column 15). The spectrum recorded in the 2800 -3200 cm -1 range is shown in Fig. 6b.

2. Infra-red spectra at room temperature: Table 2, Fig. 4a, 4b & 6c.

The infra-red absorption spectra were measured from 400 to 4000 cm -1 , using a Fourier transform spectrograph (Bruker Equinox 55) and using the KBr pellet technique. The resolution was approximately 2.5 cm -1 . The IR range of 100 -400 cm -1 was investigated using another Fourier transform spectrograph (IFS 125 MR) with synchrotron radiation on the AILES line at SOLEIL. The sample was a pellet of compressed pure DBMH that was 1mm thick. The resolution was better than 1 cm -1 . The frequencies of the IR absorption lines observed experimentally in the range (Fig. 4b) are given in Table 2, column 4. The calculated relative intensities of these features are listed in column 17, and those observed experimentally are in column 18. The spectrum recorded in the 2800 -3200 cm -1 region is depicted in Fig. 6c.

Inelastic neutron scattering spectra

The INS spectra were obtained using the TOSCA-II inelastic spectrometer of the ISIS pulsed neutron source at Rutherford Appleton Laboratory (Chilton, Didcot, U.K.). TOSCA-II is a crystal-analyzer inverse-geometry spectrometer. The incident neutron beam spans a broad energy range that covers the energy transfer region from 4 to 500 meV (30 -4000 cm -1 ). The final energy of the scattered neutrons (approximately 3.35 meV) was selected by two sets of pyrolytic graphite crystals placed nearly at 43° and 138° relative to the incident beam. Because of this fixed geometry, the wave-vector transfer Q is roughly proportional to the square root of the incoming neutron energy. The energy resolution in the accessible energy range allows a resolution better than 3 cm -1 for Q smaller than 700 cm -1 . The samples were pellets approximately 1 mm thick, resulting in a surface area of 3x4 cm 2 , packed in an aluminum pocket. Approximately 2 g of DBMH was used, and the samples were frozen below 30 K in an "orange" helium cryostat. The frequencies of the maxima of the scattered neutrons are given in Table 2, column 5, and illustrated by Fig. 5.

Calculations of the frequencies of the normal modes of vibration

4.1. Comparison of "harmonic", "harmonic scaled" and "anharmonic" frequencies calculated by DFT, the ring plane P ring being a plane of symmetry Table 2 lists the results of three DFT calculations of the normal modes of vibration that were performed using the Gaussian 2010 [START_REF] Frisch | Gaussian 03[END_REF] program package. These results were obtained using the MPW1PW91 functional with the LANL2DZ basis set augmented with polarization functions. The equilibrium molecular geometry is that presented in section 2.2, the ring plane P ring being a plane of symmetry. The DBMH molecule containing 21 atoms has 57 optical modes of vibration. Relatively to the plane of symmetry, the 57 modes of vibration may be divided into two types: 36 are of symmetry A" (in-plane), and 21 are of symmetry A" (out-of-plane) (see column 2, Table 2). The calculated modes are numbered from the largest frequency to the smallest within each fundamental frequency. The frequencies may be compared with the experimental results from the Raman spectroscopy at 288 K (column 3) or, if the Raman intensities are too small, to the IR data (column 4) or to the INS data (column 5). The  h wave numbers (column 10) correspond to the frequencies that were calculated by assuming the harmonic approximation without any scaling. These  h frequencies are larger than the experimental frequencies by 14 to 72 cm -1 in the range of 600 -1700 cm -1 (i.e. 2 to 4 %), by 160 to 230 cm -1 in the range of 2800 -3250 cm -1 (i.e. 6 to 8 %), while between 150 and 600 cm -1 there are fluctuations amounting to ± 3 %. The five smallest calculated frequencies should be treated separately because they must contain the three methyl groups "torsions" and are very sensitive to the type of calculation. These DFT computations also predict the quantitative specificities of the IR and Raman lines. In fact, the Gaussian program calculates the Raman activity S i for each normal mode n° i of an isolated molecule. We calculated the Raman activity in parallel to the  h frequencies assuming the harmonic approximation (see column 14 Table 2). The result was then converted to Raman intensity using the following relationship derived from the intensity theory of Raman scattering [START_REF] Long | Raman Spectroscopy[END_REF][START_REF] Shen | [END_REF]23]

I i = C ( 0 - i ) 4 S i /  i [1 -exp(-h c  Ri / kT)]
where  0 is the laser excitation frequency in cm -1 (in our experiments  0 = 15802 cm -1 )  i is the vibrational frequency of the i-th normal mode in cm -1 , h and k are the Planck and Boltzmann constants, T is the temperature in Kelvin and C is a suitably constant chosen that serves as a common normalization factor for all peak intensities. For these spectra, we chose a relative intensity of 100 for excitation n° 41 calculated at  h = 560 cm -1 and observed at  i = 563 cm -1 , because it is for this band that the intensity calculated in the range 200-1600 cm -1 is the highest. The relative intensities calculated for the Raman spectra are found in Table 2, column 15, and are represented in Fig. 3a. These intensities must be compared to those observed in the spectra: (column 16). However, because the Raman spectra were obtained with oriented crystals, it is possible to independently estimate those intensities arising from "in-plane" vibrations (Fig. 3b) and those arising from vibrations perpendicular to the molecular plane (Fig. 3c). Nevertheless, this estimation must be performed with caution because the spectra were obtained near room temperature, which means that the lines are broadened and only peak maximum intensities may be estimated.

To obtain a better agreement between theory and experiment, it is customary to scale down the calculated harmonic frequencies [4,5,6]. Recently, empirical scaling factors have been proposed after DFT calculations on benzenic compounds: 0.957 for tolunitrile [24], 0.960 for p-chlorobenzoic acid [25] and 0.958 and 0.983 for halogenoanilines above and below 1700 cm -1 , respectively [26,27,28]. Column 9b lists the values of the ratio  R /  h between our Raman experimental and calculated values. These values vary from 0.935 to 1.013. As a result, we multiplied frequencies  h by the "often used" scaling factors of 0.958 for frequencies larger than 1800 cm -1 and 0.983 for the other frequencies, thus obtaining the  hsc frequencies listed in column 8. The new differences between theory and experiment ( hsc - R ) (column 9) are smaller than the preceding differences ( h - R ) by a factor 2 to 3 for frequencies larger than 700 cm -1 . Only the frequencies calculated for the C-H stretching vibrations remain too large, by 40 to 95 cm -1 , and could be better estimated using a scaling factor of approximately 0.94. It is essential to determine whether the discrepancies between theory and experiment are mainly due to the neglect of the anharmonicity of the potential energy in the calculations. Thus, we computed the "anharmonic frequencies" ( anh ) using the automated code implemented in Gaussian by Barone [29]. Starting from the optimized geometry, the program computes the third and semi-diagonal fourth derivatives of the formation energy and then evaluates the  anh frequencies of the fundamental bands using second order perturbation theory (keyword: freq(anharmonic)). This calculation also provides the frequencies of the overtones ( o anh ) and those of the combination bands ( c anh ). The  anh frequencies of DBMH are listed in column 6 of Table 2, and the deviations from the experimental values,  anh - R are given in column 7. It appears that the agreement is remarkable in the entire range of 130 -1500 cm -1 , this agreement is even better than that observed for the scaled frequencies; the deviations are smaller than 15 cm -1 for 39 of the 41 modes.

The agreement is also greatly improved for the C-H stretching modes ( anh ) and is now overestimated by less than 3% (compared to the previous 8%) for the "harmonic" frequencies  h . These results for DBMH, a poly-methylated molecule, confirm the ability of the analytical secondorder perturbation treatment to consider the anharmonicity during the calculation of the internal modes of vibration. Similar results have also been observed in studies of azabenzenes [29,30,31], pyrrole and furan [32], uracil [33] or, more recently, monofluoroanilines [26]. The anharmonic frequencies  anh obtained for DBMH are in very good agreement with the experimental values, and this agreement is even better than that observed for  hsc , whose values were obtained semiempirically using the scaled quantum mechanical method. Thus, for the assignment of each type of motion to a specific frequency, we will only compare  R (or  IR ) and  anh .

Calculations of the frequencies of the normal modes of vibration assuming that the plane of symmetry is the plane P perp perpendicular to the benzene ring: Table 2 columns 12-13

In the case of DBMH, it must be remembered that the model used in the DFT calculations does not perfectly represent the environment of the methyl group Me 2 . Section 2.2 discussed another calculation that was performed when the molecule is constrained to have a symmetry plane P perp normal to the ring plane. This conformation is illustrated in Fig. 1c and takes into account the symmetry around the Br 1 and Br 2 atoms and the Me 2 substituent. It corresponds approximately to the neutron diffraction structure although it partially breaks the planarity of the benzene ring. However, for DFT calculations, this conformation corresponds to an unstable equilibrium in energy and is located on a saddle point. It is of interest to determine whether this conformation still provides valuable vibrational frequencies. Consequently, a fourth set of data was calculated using the harmonic approximation which is presented as  hp in column 12. The vibrations of the new symmetries A" and A" correspond to symmetrical (Sym ) and antisymmetrical (AntiSym) motions, respectively for the bonds that are equivalent by symmetry such as C 1 -Br 1 and C 3 -Br 3 for example .

The calculated frequencies are listed in Table 2, column 12. All of the differences ( h - hp ) are smaller than 4 cm -1 (column 13), with the exception of the lowest frequencies that are in direct connection with the Me 2 torsion. Thus, the majority of the overestimation of the unscaled harmonic frequencies is effectively caused by the anharmonicity of the atomic motions, particularly those of the hydrogen atoms. The two geometric models, that are slightly "imperfect" relatively to the neutron scattering structure, are practically equivalent for the DFT calculations, except for mode n° 57, which is relative to the torsion of the Me 2 group (see below).

Table 2

A distinction between the internal vibration modes and the lattice modes

For a DBMH crystal below 292 K, there are four molecules in the monoclinic P2 1 2 1 2 1 cell, thus, 6 Z "Iattice modes" are predicted, where Z is the number of molecules in the unit cell. Consequently, 21 new optical modes are expected. Generally, the intensity of the lattice modes in the Raman spectra is smaller than that of the internal modes. In a previous study conducted at approximately 4 K [18], almost all of these lattice modes occured at frequencies smaller than 100 cm -1 . The widths of the bands grew quickly as the temperature increases, so that the peaks are very flat at 288 K and difficult to detect. In Fig. 5, five peaks with maximum scattering of neutrons are detected below 135 cm -1 at a temperature of approximately 10 K. In these experiments, the scattering due to hydrogen atoms is the most intense phenomenon. This region has been studied in previous experiments examining the proton tunneling of the methyl groups [16,17]. Thus, if peaks at 61, 79, 91 cm -1 originate in transitions 1 A -2 A , O E -2 E and O A -2A between torsional levels of Me 2 , only the peaks at 117 (124 in R), 135 and 156 (157 in R) may be assigned to internal modes.

5.Vibrational spectra and their assignments

Labelling of the internal coordinates used to describe the vibrations.

The labeling used to describe the vibrations is that proposed by Decius and alt. [START_REF] Wilson | Molecular Vibrations[END_REF]. When the atomic displacements occur in the symmetry plane (i.p.), the variations in the lengths or angles (Fig. 1b) are labeled as follows: t n = stretching of a C n -C n+1 bond into the ring (n=1-6), s p = stretching of a C p -C mp bond for a methyl substituent n° p (p = 2, 4, 6), s i = stretching of a C i -Br i bond for a bromine substituent n° i (i = 1 or 3), s 5 = stretching of the C 5 -H 5 bond,  n = C n-1 -C n -C n+1 ring angle breathing, and  n = in-plane bending of a C n -X n bond, knowing that  nd = X n -C n -C n+1 and  ng = C n-1 -C n -X n are outer ring angles, and in consequence  n = nd - ng and  n = 360° -( nd + ng ). A positive  n =  nd +  ng angle corresponds to a clockwise motion. The following labels apply for a motion within a methyl group n° p: r pa = stretching of the C mp -H pa bond (in the ring plane), r pb and r pc correspond to the two staggered C-H bonds, and  p = "i.p." torsion of the axis of this methyl group Me p . For example,  4 corresponds to symmetrical rotations of planes C 4 -C m4 H 4b and C 4 -C m4 -H 4c around the C 4 -C m4 bond relative to the ring plane.  pa denotes the C p -C mp -H pa variation with  p =  pa +  pb +  pc.

whereas  pa denotes the H pb -C mp -H pc angle variation with  p =  pa +  pb +  pc .

The out-of-plane (o.p.) motions are labeled as follows:  n = out-of-plane bending of a C n -X n bond, it is also named wagging [2],  i = out -of-plane benzene ring torsion of a C i -C i+1 bond and  p = sum of out-of-plane torsion of the methyl C-H bonds around the C p -C mp bond. For deformations inside the methyl groups, r" mp = C mp -H pi for the o-p methyl group stretching (i = a, b or c) when the atom C mp and H pi move out of the ring plane P ring , " p = sum of angles for the C p -H pi -H pi+1 variations, " p = sum of angles for the variations C p -C mp -H i . Two remarks must be added. First, if during a large wagging  n the substituent X n moves up then the carbon C n is moving down relative to the atoms C n-1 and C n+1 in the ring, this generates small ring torsions  i-1 and  i ; secondly, for a ring torsion  i there is also a displacement of the bond C i -X i in the same direction than C i , this will be noted  i and is distinct from a  i for the PED calculations.

Calculation of the potential energy distribution (PED) for each mode.

To understand the molecular dynamics, it is useful to visualize the individual deformations of the bonds and angles. A first approach was obtained based on the information presented in Fig. 7, 8 and 9. These figures were drawn using the Molekel 98 package to visualize the deformations that are characteristics of each frequency  h . This qualitative approach was completed using a quantitative estimation of the potential energy distribution, the PED. The PED was obtained using the key-word freq(internal) in the Gaussian package. Table 3 provides the contribution to the PED for each mode due to the principal in-plane deformations. Table 4 lists the PED for the out-of-plane deformations.

The two approaches are not strictly equivalent because a large displacement of a light hydrogen atom has a smaller relative contribution to the PED than a displacement of a Br atom or a Me group does.

These tables list the main deformations, for equivalent atoms, the + sign indicates motions in-phase, and thesign indicates opposite motions. The numbers indicate the percentage of each contribution to the PED.

Table 3

A criterion for validity: the calculation-experiment agreement for the most intense frequencies:

A first test to confirm the ability of the DFT calculations to accurately predict the experimental data is to examine the sequence of the intense lines in the IR and Raman spectra that are presented in Table 2 (columns 15-18) and in Figs. 3 and4. The criterion for the comparison requires the relative intensity to be larger than 50 for the experiment and greater than 30 for the calculations (reference 100 for band n° 41 observed at 560 cm -1 in the Raman spectra). The experimental and calculated frequencies will be compared and indicated in the following order: in first the frequency observed,  R , and then, inside parentheses, ( anh ) the "anharmonic" frequency calculated using DFT. The intense bands observed in the Raman spectra are located at: 157 (153), 252 (248), 561 (560), 590 (586), 1306 (1313), 1387 (1392) and 2923 (2977) cm -1 . The intense bands in the I.R. spectra are observed at:190 (166), 228 (222), 253 (248), 296 (288), 636 (637), 852 (854), 960 (962), 1043 (1041), 1375 (1378), 1456 (1460) and 2920 (2977) cm -1 . The inelastic neutron scattering spectrum (Fig. 5) confirms the presence of essentially all of the modes calculated below 1000 cm -1 , particularly several weak peaks that were difficult to detect in the IR or Raman spectra. For example, column 5 of Table 2, one may note the high intensity for the scattered lines at 193, 365, 542, 853 and 1031 cm -1 . The agreement between the calculated and observed frequencies is remarkable. The success of the first inspection encouraged us to pursue a detailed assignment of the bands observed experimentally.

Regarding the labels: in-plane or out-of-plane mode, "methyl" or "skeleton" vibrations, symmetric or anti-symmetric modes

Because there are 21 atoms in the DBMH molecule, 57 normal modes of vibration are expected. In our calculations the plane P ring is a plane of symmetry for the equilibrium conformation. Thus, there are 36 vibration frequencies with symmetry A" for which the motions of the Br, C, and H a atoms occur within the plane P ring . These vibrations are illustrated in Figs. 7 and8. For the 21 other vibrations which have symmetry A", these atoms are moving normally to P ring as shown in Fig. 9. Of the 57 modes of vibration, 27 modes must correspond to the stretching of the C m -H bonds (r mp , r" mp ) or to deformations of the C ring -C methyl -H i entities (,  pp ,  p ,  p , " p , " p ). These modes will be entitled "methyl modes of vibrations". The criterion to validate this label is that the contribution of the methyl deformations to the PED is larger than 60 %. As mentioned in the introduction section, the methyl groups linked to an aromatic ring are characterized by specific modes concentrated in narrow bands, appearing around 3000 cm -1 , 1445 cm -1 , 1380 cm -1 , 1060 cm -1 and 1000 cm -1 and below 150 cm -1 . The 30 other modes must therefore mainly involve the aromatic ring and its substituents and may be labeled as "skeleton vibrations". These vibrations are located throughout the region below 1700 cm -1 . A rapid examination of Table 2 shows that 24 frequencies are smaller than 1000 cm -1 and may correspond to 21 skeleton modes and the three methyl torsion modes. Thus, only 9 "skeleton modes" are expected in the range of 1000 -1700 cm -1 . The pictures in Fig. 7 reveal the importance of the pseudo-symmetry relative to P perp perpendicular to P ring . DFT calculations done with the conformation of Fig. 1c are given Table 2, column 12b. If the atoms that are located symmetrically relative to this plane have in-phase displacements, the vibrations are of symmetry species A", if they are moving in opposite directions they have the symmetry species A". In the text, we will refer to vibrations as Sym or Antisym, respectively.

Assignment of specific in-plane vibrations to normal modes of species A'.

To describe the spectral assignments, the characteristic number of the vibration in order of decreasing observed frequency is given in first, it is followed by the experimental frequency  R (or  IR ) and by the calculated frequency  anh written within parentheses The Sym "skeleton modes" of species A" correspond to the eleven pictures in the upper part of Fig. 7, whereas the ten Antisym modes are shown in the lower part of the figure. The "methyl modes" are represented in Fig. 8. 2 and3

In plane skeleton modes implying large radial displacements (Tables

, Figs. 7)

Mode n° 49, R = 253 (248) cm -1, involves Sym stretches of the C 1 -Br 1 and C 3 -Br 3 bonds (22%) with a Sym variation of the opposite  angles (9%) it is associated with Sym bendings of C 4 -C m4 andC 6 -C m6 ( 4 - 6 ) (20%) All of these motions are in perfect agreement with the presence of a mirror of symmetry, which is the plane P perp . Mode n° 47,  IR = 295 (288) cm -1 , consists in AntiSym motions of the same atoms: stretches (18%) and bending (15%), of C-Br bonds which are associated with AntiSym breathing vibrations involving angles - 4 + 6 opposite to methyl groups 4 and 6) (24%). These two modes, n os 49 and 47, illustrate the splitting of the "C-Br stretching vibration" as a result of a coupling between the motions of the C 1 -Br 1 and C 3 -Br 3 bonds. The Sym mode n° 41 ,  R = 561 (560) cm -1 , is mainly due to ring breathing: two Sym angles enlargements ( 1 + 3 ) (20%), two angle reductions (- 2 - 5 ) (28%). Mode n° 40,  R = 590 (586) cm -1 , is also a Sym mode, it is mainly due to Sym C-C m stretching vibrations (14%) plus reduction of the corresponding angles ( 4 +  5 +  6 ) (44%), Mode n° 38,  IR = 636 (637) cm -1 , has contributions similar to those of n° 40 but arranged in an AntiSym manner. Sym mode n° 35,  R = 940 (947) cm -1 , involves: Sym stretching vibrations of the C-C m bonds (11%), cycle angles variations (15%) and Sym. tilting vibrations (52%) of the Me 4 and Me 6 groups. These deformations are similar in nature and intensity to the "methyl" rocking vibrations indicating strong interactions between the ring and methyl group motions in this frequency range. For AntiSym mode n° 34,  IR = 962 (960) cm -1 , almost one half of the contributions are attributed to AntiSym pairs of C-Br and C-C m stretching vibrations: (16%) and the corresponding angles variations (21%), and the other half is a result of the Me 2 tilting vibration (34%). Note that for these two modes, n°s 34 and 35, the methyl groups have a contribution to the PED as large as that of the "skeleton" motions. The Sym mode n° 27,  IR = 1047 (1043) cm -1 , can be described as the trigonal ring-breathing mode or the "star of David" vibration, it implies dilatations of three ring angles (25%) accompanied by contractions of the three others (23%).

Sym mode n° 24 ,  R = 1305 (1314+1322) cm -1 , is also a trigonal breathing mode consisting of stretching motions of the three C p -C mp bonds (15%) associated with alternate ring angles breathing (12%) while methyl umbrella deformations contribute 39%. Sym mode n° 20,  R = 1387 (1392) cm - 1 , is due to Sym stretching motion C p -C mp bonds (13%)but again contributions from the umbrella bending motions of Me 2 and Me 6 (65%) are larger than those of the skeleton indicating strong interactions in this frequency region. For Sym mode n° 1,  IR 3014 cm -1 (3085), almost all the PED is due to stretching of the C 5 H 5 bond. 2 and3

In plane skeleton modes implying large tangential displacements (Tables

, Figs. 7)

Among the remaining i.p. skeleton modes only four have relative intensities in the calculated Raman spectra that are larger than 20%: n os 53, 46, 11 and 12, which is in agreement with the experimental results. N° 53 ,  R = 157 cm -1 (153), primarily consists of the Sym scissoring motion of the two C-Br bonds (52%) with a slight stretching contribution(14%). N° 50,  R = (229 cm -1 (222), also involves the two C i -Br i bonds, but the bending motion in this mode is AntiSym (33%) with a small stretching character (s 1s 3 ) (17%). N° 46 is observed at 323 cm -1 (315), it involves the Sym bending (36%) of the pair C 4 -Me 4 and C 6 -Me 6 plus a Me 4 and Me 6 tilting motion (23%) N° 44 is observed at 374 cm -1 (360), this mode consists of the AntiSym bending motion of the C-C m bonds (32%) and in-plane tilting motions of Me groups (24%) . Mode n° 42 is observed 541 cm -1 (542), it is an AntiSym bending motion involving an in-phase oscillation of the C-Br and C-C m bonds ( n  n ~ 50%) accompanied by in-plane tilting of the methyl group (34%). The AntiSym bending mode n° 26 (1217 cm -1 (1235) includes contributions from the bending vibration of the C 5 -H 5 bond (28%)and tilting of the three methyl groups (34%).The mode n° 25, ,  R = 1306 cm -1 (1314) ,corresponds to a trigonal deformation of the benzene ring caused by C a -C a stretching motions (33%) and large tilting motions of the methyl groups (42%). This mode is also referred to as the Kekule mode. The Sym stretching mode n° 21 may be a part of the broad band observed at 1387 cm -1 ., this "skeleton" mode has very significant contributions from methyl groups. The AntiSym mode n° 19,  R = 1392 (1397) cm -1 , may correspond to the peak in the IR spectrum at 1392 cm -1 . It consists of C-Br and C-C m and C 5 -H 5 motions (30%), and to a larger extent, umbrella deformations of the methyl groups (52%). Mode n° 12,  R = 1562 cm -1 (1588), corresponds to deformations of the C-C bonds in the benzene ring (32%), the vibrations are roughly parallel to the direction of the C 2 axis. These vibrations are accompanied by a large narrowing of the  2 and  5 angles (15%) and enlargements of the           angles  (15%). AntiSym mode n° 11 has been detected at 1587 cm -1 (1629) with I R = 15 (28). The deformations in the ring are perpendicular to P perp and the  2 and  5 angles remain constant. All of these excitations are also detected in the INS spectrum (Fig. 5).

Assignment of the in-plane "methyl groups" modes of vibration

We previously proposed that the criteria for this labeling requires small contributions from the s, t,  and/or  deformations but large contributions from the H-C-H () and C-C-H () bonds motions (> 30%) and from in-plane torsions () of the C-C m bonds, i.e., more than 60% contribution to the PED from the methyl groups. In our experiments at 288 K, we observed a broadening of the lines so that the resolution was generally not sufficient to assign individual frequencies for Me 4 and Me 6 and individual intensities into these broad lines.

The calculated rocking modes of CH 3 are: N° 33 ,  IR = 1013 cm -1 , n° 32, R = 1028 cm -1 , n° 29  R = 1024 cm -1 . The contribution of  pp torsions to the total PED is almost equal to that of internal methyl deformations (. Small bands are observed at 1015 and 1032 cm -1 in the Raman spectra (Fig. 3) but it would be necessary to obtain spectra at much lower temperatures to propose a secure detailed assignment.

In-plane bending modes (or umbrella modes): For mode n° 23,  R = 1380 cm -1 (1378), the deformations of the Me 4 and Me 6 groups are in phase but out of phase relative to those of Me 2 , For n° 22, R = 1387cm -1 (1384), the deformations of Me 4 and Me 6 are in phase while Me 2 is at rest. For mode n° 20, IR = 1387 cm -1 (1393), the deformations of Me 2 and Me 6 are in phase and out of phase to the small deformations of Me 4 . The total intensity for these modes is distributed into a broad Raman band at 1387 cm -1 and must be associated with modes n°s 19 and 20.

In-plane bending (or scissor) modes of CH 3 : In the IR spectra the sum of the relative intensities for n° 16 and that of the neighboring out-of-plane modes n os 17-18 is I IR = 45 in agreement with 30 calculated. For mode n° 16, R = 1435 cm -1 (1438), the torsions  2 ,  4 and  6 are calculated in phase while only the clippings for Me2 and Me6 are in phase. For mode n° 14, R = 1456 cm -1 (1462), the main contributions to the PED is calculated for Me 4 . For n° 13, R = 1456 cm -1 (1460), Me 4 is almost at rest, while Me 2 and Me 6 are moving in opposition.

Symmetric in-plane stretching (or breathing) modes of CH 3 : N os 10, 9 and 8 correspond to the broad and intense Raman line at  R = 2923 cm -1 (2977). For n° 10, groups Me 4 (48%) and Me 6 (42%) exhibit breathing motions that are out-of-phase (o.p.) For n° 9, these vibrations are in-phase (i.p.), and for n° 8, only Me 2 vibrates (88%).

Asymmetric in-plane stretching modes of CH 3 : For these modes, in each methyl group the in-plane bonds C pm -H pa move in opposite direction to the staggered C pm -H pb and C pm -H pc bonds. Modes n os 3 and 4 correspond to  R ~ 2978 cm -1 (3041) with I R = 12 (36). N° 2 corresponds to motions only within Me 2 . This mode was calculated to be at 3066 cm -1 with a weak intensity, experimentally it appears as a bump in the IR spectra at 2985 cm -1 . 2 and3, Figs. 3, 4 and5)

Out of plane modes (Tables

In a Raman spectrum from a powdered sample of DBMH, it is more difficult to assign the o.p. modes than it is to assign the i.p. modes because the former have weaker intensities. Thus, we collected the Raman spectra shown in Fig. 3c using a small single crystal excited by a laser beam that was polarized approximately along the b axis of the crystal. Consequently, in this spectrum, the intensities of the i.p. vibrations are reduced and those of the o.p. modes are relatively enhanced which helps with the assignment. Nine normal modes of vibration of species A" were calculated and observed in the range of 1000-3050 cm -1 . For each of them the contribution of the CH 3 groups to the PED is larger than 60%, so they are labelled "methyl o-p modes". They are represented in the lower part of Fig. 9. Six A" modes located in the range of 200-1000 cm -1 were assigned as skeleton modes.

For the six remaining modes, the torsion (hindered rotation) of the methyl groups plays a major part.

"Methyl groups" o. p. modes with frequencies higher than 1000 cm -1

Table 4. Fig. 6 and9 At 288 K, a broad band is observed at R = 2956 cm -1 in the Raman spectra and at 2954 cm -1 in the IR spectrum. This band is located between two packets of i.p. modes already assigned: n°s 3 and 4 observed at  R = 2978 cm -1 (3041) and n os 8, 9,10observed at 2923 cm -1 (2977). Thus, this band may be assigned to modes n°s 5, 6 and 7 calculated at  anh = 3015 cm -1 . For each mode, the internal motions involve stretchings of the two staggered C m -H mb and C m -H mc bonds, into a specific Me group. The modes n°s 15, 17 and 18 at  R = 1435 cm -1 (1440) are caused by the o.p. tilting motion and a type of clipping (",") within the methyl groups in almost equal proportions. The mode n° 15 involves only Me 2 ( 2 = 47%). Mode n° 18 implies out-of-phase vibrations of Me 4 and Me 6 ( 4 + 6 = 48%) whereas those vibrations are in-phase for mode n° 17 ( 4 + 6 = 49%). Modes n os 28 and 30 ( R = 1045 cm -1 (1035) are characteristic of the o.p. rocking motions of the methyl groups. Mode n° 28 concerns in phase o.p. vibrations involving Me 4 and Me 6 . The vibrations are out-of-phase for mode n° 30 whereas for mode n° 31,  R = 1032 cm -1 (1028) only Me 2 is excited.

"Skeleton out-of-plane" modes

Table 4 gives a detailed panorama of the motions for each mode which are shown in the upper part of Fig. 8. These motions are complex and then difficult to describe in detail. Thus, we will indicate only the main contributions to the PED. For example, Sym mode n° 36,  R = 853 cm -1 (854), is composed almost entirely of the o-p bending  5 (55%) of the C 5 H 5 bond. Sym mode n° 37 seen by neutrons at  n = 698 cm -1 (708) is the trigonal puckering of the ring it consists mainly of alternate torsions  i up and down of the C-C in the ring (31%). AntiSym mode n° 39,  R = 588 cm -1 (583), consists of 20% of ring torsions, 21% of o.p. bending motions and 38% of methyl groups torsions.

No° 43, R = 517 cm -1 (526), appears as a Sym butterfly flapping around the C 2 axis, it consists of 16 % of ring torsions, 36% of o.p. bending motions. No° 45,  R = 339 cm -1 (332), appears as an AntiSym motion. The PED contains 16% of ring torsion, 33% of o.p. bending motions and 36% of torsions of the methyl groups around their axes. No° 48,  R = 276 cm -1 (269), involves nearly the same motion as n° 45, but the ring oscillates now around an axis perpendicular to the C 2 axis.

Methyl torsion modes and/or o.p. bending modes?

Mode n°51 ( IR = 190 cm -1 ,  anh =166,  h = 188) is a type of breathing motion in which all atomic substituents move in the opposite direction of that of the ring carbon atoms, ( i = 19%). This mode results in an intense neutron scattering at 193 cm -1 and a medium I.R. absorption at 190 cm -1 , but it is inactive in Raman spectroscopy. Interestingly, there is also an important contribution to the PED (56%) due to torsions around the axis of the Me 4 and Me 6 groups. These torsion phenomena occur for all the modes with frequencies smaller than 200 cm -1 . For mode n°52, R = 124 cm -1 (135), the calculations indicate in-phase librations of Me 4 and Me 6 groups, the largest contribution to the PED coming from Me 6 (57%). For mode n°54, R = 124 cm -1 (136), the librations of the Me 2 and Me 6 groups are out of phase and the largest contribution to the PED is coming from Me 4 (63%). The assignment of a Raman frequency  R for n°55 is difficult because its frequency cannot be known using the anharmonic approach (anh = -145). Using the harmonic approximation, this mode was assigned as a Me 2 libration (  = 82%). Mode n° 56, R = 88 cm -1 (66), corresponds to AntiSym C-Br bending (-1 +3) (26%) associated with a libration of Me 2 (23%). The anharmonic DFT calculations did not result in a real frequency for mode n° 57 (anh = -56). Using the harmonic approximation (h = 71), the contributions to the PED are attributed to Sym C-Br bending vibrations (1 +3) (16 %) with a larger contribution from the torsional motion of the Me 2 group (53 %). These results confirm the particular behavior of the "symmetrical" methyl group Me 2 . So it is now necessary to discuss the validity of these conclusions knowing the inadequacy of the DFT models to represent the molecular geometry around Me 2 .

Remarks about the methyl groups torsion modes.

In section 2.1, we summarized the results of the structural studies involving neutron diffraction at 120 and 14 K. For the methyl groups Me 4 and Me 6 , a "normal" conformation with three well defined maxima was observed with the protons probability density (PPD) [17]. In contrast, for Me 2 , the PPD is widely spread over a torus. For Me 4 and Me 6 , the DFT calculations generated an equilibrium conformation that is in agreement with the experimental results: for each methyl group, there is a preferred orientation with one C-H bond pointing towards the hydrogen H 5 (Table 1, Fig. 1a and1c).

Starting from these configurations, DFT calculations then provided values equal to 158 and 167 cm -1 using the harmonic approximation and equal to 135 and 136 cm -1 using the anharmonic approximation for the torsion mode of these groups. The calculated frequency does not vary significantly with the plane of symmetry (P ring or P perp ) retained for the model molecule studied (Table 3). The intensity calculated for these excitations is very low in I.R., INS and Raman. In fact, based on inelastic neutron scattering experiment using a reduced fixed window [17], it was possible to estimate the hindering potentials V 3 of these methyl groups to be approximately 590 cm -1 plus a small out of phase component V 6 = 90 cm -1 . Using this potential, the "libration" transition 0 A -1 A (almost equal to 0 E -1 E ) is approximately 145 cm -1 ; this value is compatible with the preceding predictions relative to the Raman line at 136 cm -1 . The problem is different for the Me 2 group. A high-resolution inelastic neutron scattering study of the DBMH crystal [16] revealed that this group is a quasi-free rotor, which is contrary to the crude idea that the "big" bromine atoms will hamper the space around Me 2 and, thus, hinder its "rotation". Below 40 K, the INS spectra exhibit excitations at 14.7 and 24.6 cm -1 that were assigned to transitions between levels of same symmetry 0 A -1 A and 0 E -1 E In the Raman spectra [18], scattered lines exist at 15.2 and 23.7 cm -1 . The fact that the intensities of these transitions are a function of time after freezing is another consequence of the quantum behavior of the rotor Me 2 . Specifically this phenomenon is a consequence of the progressive departure of a part of the population with spin ½ into level 0 E to more stable O A level (spin 3/2) via spin conversion. In section 2.2, it was indicated that the DFT calculations could not reproduce the Me 2 experimental conformation because, at equilibrium, the methyl group must always present only three PPD maxima as in Fig. 1b. These calculations were performed strictly using the Born-Oppenheimer approximation to the hydrogen nuclei without considering their spin states.

Consequently, the energy states of the methyl groups in small hindering potentials must always be studied as solutions of the Schrodinger equation of a uni-axial quantum rotor.

Conclusion

6.

1. An experimental study of the Raman and infra-red spectra of the fully hydrogenated 1,3dibromo-2,4,6-trimethylbenzene (DBMH) at 288 K was presented. These spectra cover the range 80 -3500 cm -1 with a resolution of approximately 3 cm -1 . Additionally, INS spectra were recorded in the same frequency range below 30 K. In parallel, quantum chemistry calculations of the molecular conformation and of the internal modes of vibration were performed. They consisted of DFT calculations using the MPW1PW91 functional with the LANL2DZ basis set augmented with polarization functions. The molecular equilibrium conformation that was calculated theoretically is very close to that obtained using neutron diffraction at 120 and 14 K with the exception of the Me 2 environment. The DFT calculations fail to produce the exact molecular conformation because they cannot consider the fact that Me 2 is a symmetrical "quantum rotor" with spin states. Nevertheless, these calculations provide an acceptable value for the rotation hindering barrier because they take into account the energy related to the spatial part of the Hamiltonian.

6.2.

Using the geometry with P ring as a symmetry plane as the equilibrium molecular geometry, a first calculation of the internal modes frequencies was performed assuming the harmonic approximation. The use of scaling factors of 0.983 for frequencies smaller than 1800 cm -1 and another factor equal to 0.958 for higher frequencies results in an agreement better than 1.5%.

Furthermore, the values of the calculated intensities are qualitatively in agreement with those of the experimental peaks.

6.3.

Another DFT calculation was performed using the same starting equilibrium conformation, but taking into account the anharmonicity of the motions. The agreement between calculation and experiment is now excellent for all of the frequencies below 1800 cm -1 , and the calculations overestimate the C-H stretching modes in the range 2900-3200 cm -1 by less than 1.5 %. It is not necessary to use arbitrary scaling factors.

6.4.

The contribution of internal vibrations to normal vibration potential energy (PED) was obtained within the harmonic approximation. Rocking, bending and stretching modes that are specific to internal methyl groups deformations during the vibration were localized and the calculations resulted in small differences in the frequencies of the Me 2 vibrations and those of Me 4

and Me 6 . The specific excitations of the methyl torsion modes cannot be seriously calculated using DFT because this type of calculation neglects the spins of the methyl groups. Our previous INS studies [16,17] demonstrated the necessity to take into account the quantum behavior of the methyl groups, particularly Me 2 , which is subjected to a small hindering potential because of the symmetry of its environment.

Figures captions

Fig.

1 .

 1 Fig. 1. Bond angles in the DBMH molecule: 1a-Optimized conformation using DFT computation; 1b-Obtained from neutron diffraction at 120 K; 1c-Conformation obtained from DFT calculations with the constraint that the plane perpendicular to the ring plane is a symmetry plane.

Fig. 2 .

 2 Fig. 2. Proton probability density for methyl groups Me 2 , Me 4 and Me 6 obtained using neutron diffraction on a single crystal of DBMH at 120 K [18]. Each probability density graph is a cut in a plane perpendicular to the C i -C mi bond and containing the maxima of the PPD (i= 2, 4 or 6).

Fig. 3 .

 3 Fig. 3. DBMH Raman spectra: 3a-Calculated using DFT with the optimized conformation; 3b and 3c: Experimental spectra obtained at 288 K using excitation from an He-Ne laser line at 6328 Å, for 3b-the electric field E of the excitation beam was nearly in the molecular plane, for 3c-E was nearly normal to the molecular plane.

Fig. 4 .

 4 Fig.4. DBMH infra-red absorption spectra: 4a-Calculated using DFT with the optimized conformation, 4b-In the range 500 -1800 cm -1 , spectrum obtained using a Varian Fourier transform spectrometer; In the range100 -400 cm -1 spectrum obtained on the AILES line using synchrotron radiation at SOLEIL and a Bruker Fourier transform spectrometer.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Inelastic neutron scattering spectra which were obtained below 30 K using the TOSCA spectrometer at ISIS

Fig. 7 .

 7 Fig. 7. Illustration of the atomic displacements for the twenty one "skeleton" in-plane vibrational modes (from DFT calculations): the first number at the top of each small figure corresponds to the frequency of an experimental observation (Raman or IR), the second (in parentheses) corresponds to the numbering from the highest frequency to the lowest, and the third number is the calculated anharmonic frequency.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Illustration of the atomic displacements for the fifteen in plane vibrational modes of "methyl groups" (from DFT calculations)

Table 1 .

 1 Bond lengths and angles in DBMH. Column n° 2: neutron diffraction at 14 K, col. n° 3:

	Tables
	neutron diffraction at 120 K, col. n°s 4 and 6: DFT calculations with the MPW1PW91 functional and
	the LANL2DZ basis set augmented with polarization functions (the plane of symmetry is the
	benzenic ring plane for n° 4 and the plane perpendicular to the ring for n° 6), col. n° 5: basis set
	without polarization functions.
	1	2	3	4	5	6
	Distances	Expe	Expe	Cal1	Cal2	Cal3
	Angles	14 K	120 K	Pring	Pperp	Pperp
	C1-C2	1.4025(19)	1.403	1.4061	1.4055	1.4058
	C2-C3	1.4038(15)	1.399	1.4050	1.4108	1.4058
	C3-C4	1.3962(14)	1.392	1.4030	1.4055	1.4012
	C4-C5	1.3943(19)	1.391	1.3960	1.4030	1.3964
	C5-C6	1.3939(15)	1.391	1.3968	1.4030	1.3964
	C1-C6	1.3967(14)	1.392	1.3995	1.4055	1.4013
	C1-Br1	1.9037(19)	1.898	1.9154	1.9645	1.9173
	C2-Cm2	1.4993(15)	1.497	1.5020	1.5068	1.5024
	C3-Br3	1.9060(30)	1.904	1.9183	1.9645	1.9170
	C4-Cm4	1.5008(16)	1.498	1.5024	1.5067	1.5022
	C5-H5	1.0911(16)	1.091	1.0864	1.0855	1.0864
	C6-Cm6	1.5000(20)	1.501	1.5019	1.5067	1.5022

Table 2 .

 2 DBMH normal modes of vibration: Comparison of the experimental Raman (3), IR (4) and INS (5) bands with the theoretical anharmonic  anh(6), harmonic scaled  hsc(8) and harmonic  h(10) frequencies, Raman scattering activities(14), Raman intensities: calculated(15) and observed(16), IR absorption: calculated(17) and observed(18)

			Experimental frequencies				Calculated frequencies				Raman activity and	IR
				cm -1						cm -1					intensities		absorption
	1	2	3	4	5	6	7	8	9	9b	10	11	12	12b	13	14	15	16	17	18
	N°	Sym Pring	R Raman	IR IR	N INS	anh cm -1	col.6 -col.3	hsc cm -1	col.8 -col.3	Ra/h cm -1	h cm -1	col.10 -col.3	hp cm -1	Sym Pperp	col.12 -col.10	Activity Å 4 /amu	Ical rel.	IR exp rel.	Acal. km/mol	IIR exp.
	1	A'	3014	3012		3085	71	3088	74	0,935	3223	209	3223	A'	0	94	33	17	10	9
					3000
	2	A'	2987	2985		3066	79	3080	95	0,928	3215	230	3201	A"	-14	27	11	14	5	3
	3	A'	2978	2976		3041	63	3051	71	0,935	3185	207	3184	A'	-1	70			19
																	36	12		15
	4	A'	2978	2976		3041	63	3050	72	0,935	3184	206	3184	A"	0	29			9
	5	A"	2956	2954	2970	3015	59	3030	74	0,935	3163	207	3172	A'	9	52			6
	6	A"	2956	2954		3014	58	3026	70	0,936	3159	203	3159	A'	0	33	63	26	11	18
	7	A"	2956	2954		3015	59	3026	70	0,936	3159	203	3159	A"	0	90			4
	8	A'	2924	2920		2977	53	2961	38	0,946	3091	168	3087	A'	-4	157			8
					2925												193	97		20
	9	A'	2924	2920		2977	53	2963	40	0,948	3082	159	3082	A'	0	344			16

Acknowledgements

-This work benefited from the "Polish-French Polonium 2009-2010 program". S. Zeroual received financial support for her thesis work from the "PROFAS-Boursiers Franco-Algériens" program, and she thanks the "Laboratoire Sciences Chimiques de Rennes" for its hospitality. Thanks to Pr. R. Swietlik, Dr P. Roy, Dr. O Hernandez and Dr. M. Fourmigué for their helpful advices. The data from neutron diffraction or inelastic scattering have been collected thanks to LLB, ILL and ISIS.

53 159 14 (s1 +s3) -52(  - 3 ) -6  -   8 (t1+t2) --

Remark-the meaning of the symbols used is defined in the text (section 5.1) Table 4. The predominant components of the PED matrix (relative phases and % contributions) for the out-of-plane modes of vibration of DBMH Remark-the meaning of the symbols used is defined in the text (section 5.1)


Lionel Mercury

Kirill I Shmulovich

Experimental superheating and cavitation of water and solutions at spinodal-like negative pressures

The superheated liquids are metastable with respect to their vapour, what means they can exist under arid conditions whatever the temperature: capillary liquid extracted from arid soils (desert shrubs, Mars sub-surface, …), solutions in the deep Earth crust, or water involved in rapid disequilibrium events (terrestrial or submarine geysers). The superheating state changes the solvent properties of liquids, and so modifies phase transitions (solid-liquid, liquidvapor) P-T-X conditions. The synthetic fluid inclusion (SFI) enables to fabricate micro-volumes of hand-made liquid dispersed inside quartz, which readily superheat. Volumes of SFI are intermediate between macro-systems, in which superheating is restricted to around -30-35 MPa with very short lifetime, and nanosystems, wherein confinement effects predominate and in which the host size is similar to the one of the critical nucleus of vapour phase (huge nucleation barrier). This volume-to-metastability relationship is still to be defined quantitatively, and we are targeting to combine thermometric classical measurements with spectrometric characterizations, enabling to establish the threshold between micro-and nano-systems precisely. Meanwhile, the experiments performed so far illustrate the diversity of contexts and situations that could be impacted by superheating issues.

INTRODUCTION

Liquid water presents a remarkable ability to stay liquid against evaporative demand by becoming superheated with respect to water vapor. Water can be readily superheated by increasing the temperature higher than 100°C at constant 1 atm pressure, or by decreasing its internal pressure, it becomes superheated even at low temperature (Fig. 1a). Meanwhile, the driving force is toward evaporation and so the liquid is prone to nucleate bubbles at any time, except if some reasons, notably the trapping in a host solid, make the nucleation probability to decrease and the lifetime to lengthen (Fig 1b). It is why superheating is a feature closely interwoven with capillarity and confinement, in which cases the closeness of the solid walls make the infilling liquid to behave differently than the bulk.

A. B.

Fig. 1. A. Phase diagram of pure water in P-T space, calculated with the IAPWS-95 equation of state [START_REF] Wagner | The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use[END_REF]. Kinetic spinodal is drawn after [START_REF] Kiselev | Curvature effect on the physical boundary of metastable states in liquids[END_REF]. B. Qualitative relationship between space volume allowed to liquid and lifetime of its superheating (potential) state (after [START_REF] Skripov | Thermophysical properties of liquids in the metastable (superheated) state[END_REF]).

As a consequence, the conditions of occurrence and the features of superheated water are relevant to understand the dynamics of liquid water in arid (deserts) and hyper-arid (Mars surface) settings, and its possible volume and influence as a function of the environment. Experimentally, the most efficient way to produce superheated liquid is to carry out an isochoric cooling on a liquid trapped in a strictly closed container with rigid walls. With water, as the isochores are very steep (around 20 bars per degree) and the saturation curve is very flat, a slight cooling below liquid-vapor equilibrium puts the occluded liquid under significant superheating degree, even down to negative pressures (Fig. 1a). Negative pressure or tension, is allowed for condensed matter that thus undergo internal stretching or tensile stress without losing the cohesion of its structure (e.g., [START_REF] Imre | Thermodynamics of negative pressures in liquids J. Non-Equilib[END_REF]). Capillary water, common in non-saturated soils, has got superheated properties without its limited lifetime because the capillary channel/pore has the size of the nucleating bubble, meaning that the boiling restoring equilibrium cannot start.

Metastable superheated liquid

Stable bulk liquid

Unstable liquid

In this sense, capillary water is a superheated water "de-metastabilized" or "re-stabilized" by geometrical constraints defined by the so-called Young-Laplace equation. At the liquid-air interfaces, capillary water is at equilibrium with dryer atmosphere than the bulk (Kelvin law), which is the driving force to "capillarization". Actually, lower vapor pressure than the saturation value drives a liquid-vapor system to either evaporation or capillarity. Water located in restricted volume ("confined water") has also peculiar properties due to the additional thermodynamic term afforded by the surface fields from the close walls (disjoining pressure effect). In many respect, confined water has got similar properties than the capillary or superheated water. Interestingly, confinement experimentally exhibits metastable behaviors (e.g., [START_REF] Restagno | Metastability and nucleation in capillary condensation[END_REF][START_REF] Morishige | Tensile effect on a confined phase[END_REF]).

The present contribution reports experimental data obtained with synthetic fluid inclusions on the extreme tensile strengths (negative pressure) that pure water and aqueous solutions can attain and on the lifetime over which they can sustain them. It has also the ambition to enlist the possible consequences of superheating (and so capillarity, and/or confinement) in terms of macroscopic behaviors. Putting the liquid under extreme conditions of tension gives pathway to measure directly how the superheating properties, even moderate, may drive specific behavior in the corresponding natural settings.

EXPERIMENTAL SECTION

Synthetic Fluid Inclusions (SFI) are made in internally-heated pressure vessels (IHPV, or "gas bombs"). The hydrothermal syntheses were performed at 750 MPa in the 530-700°C range, during 8 to 13 days. For each run, the IHPV is loaded with 3 or 4 Pt-capsules filled with quartz (2x2x12 mm, with the longest dimension parallel to the quartz c-axis), the selected liquid (pure water or aqueous solutions at the chosen concentration) and amorphous silica. Sealed capsules were placed on a Ta or Mo holder wherein the temperature is controlled by two Pt-Pt 13% Rh thermocouples (certified to ± 1°), and pressure measured by manganin gauges after calibration at the mercury melting point. Once the required synthesis time elapsed, the power supply is turned off and temperature decreases to 100°C in one minute, while pressure is decreased by intensifier to 300 MPa. In a second step, the IHPV is allowed to cool down on its own to room temperature and is finally opened to recover the capsules and quartz samples the healing of which trapped the liquid.

The microthermometric procedure consists of progressive heating on a "Linkam" stage of one sample, in general containing initially the biphasic liquid+vapour assemblage (L+V).

Fig. 2. Classic microthermometric path from the ambient conditions (see text). Nucleation can appear instantaneously (Tn commonly measured by inclusionists, sparky point) or after a delay (starry points) if the temperature is stopped before reaching the instantaneous Tn.

The first step corresponds to the displacement along the saturation line, with a progressive change of temperature, liquid density and bubble pressure (A to B path, Fig. 2). At a particular density, the trapped liquid invades the whole inclusion space: there is no more vapour and the inclusion is said to be homogenized (B point, Fig. 2). The temperature at which this filling appears is then the homogenization temperature, noted Th. Just before Th, vapour bubble is so small that it can move along the minor thermal gradients within the inclusion, which results in the appearance of a mobile shadow.

Further heating drives the P-T conditions in the inclusion along the isochore inside the stable domain of liquid (B to C path, Fig. 2). Special care must be taken because overheating above Th may lead to the decrepitation of the inclusion, especially at overheating greater than 30°C (but 10°C can be sufficient; see also [START_REF] Bodnar | Synthetic fluid inclusions. VI. Quantitative evaluation of the decrepitation behavior of fluid inclusions in quartz at one atmosphere confining pressure[END_REF]): this depends also on (at least) the shape of the inclusion, its thickness and the distance to neighboring inclusions. One decrepitation event can be detected when a further Th measurement on the same inclusion increases by more than 1°C with respect to antecedent measurements. The second step is the progressive cooling of the sample, which follows the isochoric path as long as the inclusion remains homogeneously filled with liquid (C to D path without nucleation at B, Fig. 2). The temperature of the bubble appearance is called the nucleation temperature (Tn) and is always located within the tensile domain: nucleation in fluid inclusions often disobeys the saturation conditions. The bubbling at Tn produces either one-two big bubbles or a large amount of intermediate-sized bubbles which explode violently.

SUPERHEATING LIMITS AND LIFETIME 3.1 Measurements and interpretation

The basic measurements are then of two types: first the (Th -Tn) gap at which instantaneous nucleation occurs, and the time needed for a nucleation to occur for any temperature set between Th and Tn (Fig. 3). The present dataset is reported in figure 3, and lists hundreds of inclusions measured in more than 40 samples. (Th -Tn) gap are strongly liquid-and temperature-dependent, varying the most for CsCl electrolytic solutions at low T (scattering over 80°C) and denser pure water (scattering over 70°C). The smallest gaps are encountered with dilute NaOH solutions whatever the temperature, and for each type of solutions, the gap is narrowing with increasing temperature. This last feature fits well the expected behavior considering the narrowing of the saturation to spinodal gap with temperature (Fig. 1). A close discussion of the different trends is outside the scope of this paper, some aspects are developed elsewhere [START_REF] Shmulovich | Experimental superheating of water and aqueous solutions[END_REF].

Fig. 3: Measurements classically performed on liquids trapped in SFI by microthermometry: temperature gap to observe instantaneous nucleation, and lifetime of superheated state.

The conversion of micro-thermometric measurements into internal pressure of superheated liquids requires using an equation of state (EoS). Basically, measuring Th enables to define the density of the trapped liquid at homogenization (Dh). Assuming a perfectly isochoric cooling, the couple (Tn,Dh) can be readily turn into (Tn,Pn), with Pn stands for the internal pressure inside liquid just before nucleation (Fig. 4).

Fig. 4: P-T phase diagram, including the (Th,Tn) measurements of different datasets turned into (P,T) data points (see text) using the IAPWS-95 equation of state for water [START_REF] Wagner | The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use[END_REF].

Two questions are actually embedded in such procedure: i) applicability of EoS to superheating state, and ii) having the EoS characteristic of the measured solutions. About the first issue, pure water EoS can be readily used for dilute solutions, in which most of the molar content is made of water molecules (Fig. 4). However, studying the saline solutions require to extrapolate the available EoS, not always internally-consistent, toward the metastable state (e.g., [START_REF] Thiéry | Explosive properties of water in volcanic and hydrothermal systems[END_REF]). As a consequence, interpretation are certainly correct in terms of global trends, but cannot be considered as Pure water kinetic spinodal [START_REF] Kiselev | Curvature effect on the physical boundary of metastable states in liquids[END_REF] quantitatively precise for the time being. About the second issue, the general feeling is toward admitting the continuity of behavior from stability to metastability, meaning that superheated water is no more than a "particular" state of otherwise-bulk liquid (e.g. [START_REF] Skripov | Metastable states[END_REF][START_REF] Mercury | Thermodynamic properties of solutions in metastable systems under negative or positive pressures[END_REF][START_REF] Mercury | Infrared imaging of bulk water and water-solid interfaces under stable and metastable conditions[END_REF][13]), but, here again, some doubts still need to be lifted. A current experiment tries to quantify the internal stress in fluid inclusions, by recording direct signals of the pressure change directly inside the inclusion, shunting any use of EoS. To do this, an aqueous solution of Na 2 WO 4 has been trapped in inclusion, because the Raman peak of this anion is pressure-dependent. Running classic micro-thermometry path into a Raman spectrometer resulted in a continuous Raman shift that demonstrates an increasing tension inside the trapped solution. This experiment solved the challenge on the measurement itself (the shift is lower than the absolute precision of the spectrometer) and provided direct evidence on the internal tension of the occluded liquid: extrapolating the positive pressure behavior (Fig. 5B), the tension comes to -432 bars. However, this experiment has not fully answered the question, since these Raman measurements cannot be compared to EoS calculations, not existing for Na 2 WO 4 . Complementary experiments are under way.

A. B. Fig. 5: A. Spectroscopic pressure measured by the Raman shifts of the tungstate dissolved in tensile solutions trapped in SFI. B. Calibration at positive pressure.

Lifetime and cavitation

In terms of lifetime, the measurements have been fitted by the Classical Nucleation Theory (CNT) which considers the work of creating LV surface compared to the work brought about by the higher stability of the vapor embryo. Interestingly, the CNT equation for homogeneous nucleation (the source of work in the system is the thermal fluctuations) does not fit the data, but that for the heterogeneous nucleation on a hydrophobic (and pure quartz is) surface does (Fig. 6). Fig. 6: Lifetime of superheated pure water SFI in quartz (50x20 µm; [START_REF] Mekki | Metastable systems under pressure[END_REF]), plotted against the distance to temperature of instantaneous nucleation (Fig. 2). The heterogeneous CNT equation is from [START_REF] Blander | Bubble nucleation in liquids[END_REF], compared to the usual homogeneous CNT one (e.g., [START_REF] Debenedetti | Metastable liquids. Concepts and principles[END_REF]).

These are preliminary results since the data are only acquired over 3 days for restricted distance to instantaneous nucleation (T max = 6°C). Interestingly, the extrapolation of the fitted trend indicates that a very long metastable lifetime is possible even for significant superheating state (T  18°, possibly corresponding to a tension down to -500 bars). The present target is to confirm the validity of the heterogeneous CNT equation toward extrapolation, by performing longer experiments increasing the range of distance to equilibrium.

Predicted by CNT (heterogeneous nucleation)

Predicted by CNT (homogeneous nucleation)

 Measurements lifetime = 1 Million years

One interesting feature should be additionally addressed: the role of the host volume to stabilize the superheating as evoked in figure 1. This question is beyond a simple academic interest and corresponds to understand the size threshold below which the confinement effect would suppress the nucleation event, allowing to safely produce highly superheated liquid.

A first clue comes from an open question in the physics of metastability [START_REF] Caupin | Cavitation in water: a review[END_REF]: among the different techniques available to produce superheating, only the SFI enables to reach high level of metastability (Fig. 7A). A key difference between SFI and all other technique is the way the liquid volume occupy the experimental cell. In case of dynamic/capillary techniques there is only one experimental water volume, so that the first nucleation event makes all the volume to boil.

In case of inclusions samples, liquid is dispersed as numerous micrometric cavities in the same solid fragment, and the vapour nucleates at P,T conditions peculiar to each inclusion. That means the geometrical confinement, even over hundreds of micrometers (which make a pretty large volume), should help in pushing the superheating state at larger value in inclusions than in the other experimental cells without walls.

A. B. A second clue is afforded by the common relationship between the (Th -Tn) metastability gap and the host volume (e.g., [START_REF] Shmulovich | Experimental superheating of water and aqueous solutions[END_REF], see their figure 8a,b). However, as apparent in figure 7B, this relationship is common but has exceptions or limits (see also figure 8b in [START_REF] Shmulovich | Experimental superheating of water and aqueous solutions[END_REF]), demonstrating that other factors are embedded in this size factor, for instance the internal shape of the inclusions that reveals its degree of equilibrium ("negative quartz shape") [START_REF] Shmulovich | Experimental superheating of water and aqueous solutions[END_REF]. Even Th itself can vary (over 1-3°C) with the size of inclusion due to surface tension effects [START_REF] Fall | The effect of fluid inclusion size on determination of homogenization temperature and density of liquid-rich aqueous inclusions[END_REF]. In another direction, the size of the inclusion and the internal faceting of the space void, partly control the properties of the SFI, notably the modes of their non-elastic deformation (stretching, leakage, decrepitation) [START_REF] Bodnar | Synthetic fluid inclusions. VI. Quantitative evaluation of the decrepitation behavior of fluid inclusions in quartz at one atmosphere confining pressure[END_REF].

Here again, complementary experiments are needed to decipher how the size of inclusions combine with other critical factors to control the behavior of inclusions, notably the extent of metastability and the deformability.

EXPECTED BEHAVIOUR OF SUPERHEATED (CAPILLARY & CONFINED) WATER 4.1 Geochemistry of phase transitions

Capillary liquids have the same properties of superheated water, and most probably confined water as well. Superheated water is known to be a very good solvent for organics compounds as pesticides, making it the "ultimate green solvent for separation science" (e.g., [START_REF] Smith | Superheated water: the ultimate green solvent for separation science[END_REF][START_REF] Chienthavorn | Modified superheated water extraction of pesticides from spiked sediment and soil[END_REF]). This experimental observation can be easily illustrated extrapolating the solubility line of different metals sulfides in aqueous solution beyond the saturation LV line, down to the spinodal (Fig. 8A). Additionally, the diagram shows that the cavitation which restores the equilibrium changes the saturation conditions and contributes to precipitate the excess dissolved mass. Interestingly, a recent study showed the ice nucleation just following the bubble cavitation in superheated water [25]. B. Fig. 8: A. Solubility line, empirically extrapolated at negative pressures, illustrating the solvent effect of superheated (capillary/confined) liquid (after [START_REF] Shmulovich | Experimental superheating of water and aqueous solutions[END_REF]). B. Gases solubility as a function of the internal tension in superheated/capillary water (modified from [START_REF] Mercury | The effect of the negative pressure of capillary water on atmospheric noble gas solubility in groundwater and palaeotemperature reconstruction[END_REF]).

In the second part of the figure, it appears that the gases are more soluble in superheated/capillary water than in bulk water. Actually, this in-gassing effect could be of significant importance to understand the global carbon cycle: the immobile water trapped under tension in the capillary clusters of all the arid and semi-arid soils of Earth are pumping in more atmospheric CO 2 than expected without considering the capillary role on dissolution. These findings are mitigated by the small volume of capillary water at dry conditions that limits the total mass that can be actually stored in soils.

Geochemistry and geomechanics

The liquid under tension when trapped in solids exerts traction on the host solid, and so contributes to the geomechanical balance at the pore scale [START_REF] Bouzid | In-pore tensile stress by drying-induced capillary bridges inside porous materials[END_REF]. Drying experiments performed in micrometric round pore showed that a first precipitation of cubic salt allowed the arising of capillary bridge at the salt-pore contacts that generated a deformation of the host (Fig. 9A).

A.

B. Fig. 9: A. Cubic NaCl precipitation in round pore (radius = 5 µm), secondary precipitation of concave-curved NaCl at the prior salt-pore contacts, and resulting deformation. B. Raman shift inside the quartz matrix around an inclusion filled with 5m CsCl, and put at (Th-Tn) = 90°C (unpublished results; Collab. CEMTHI, P. Simon).

Another experiment is presently running, searching to record the constraints implied in the surrounding solid by the tension inside a highly superheated electrolytic aqueous solution (Fig. 9B). Interestingly, part of the surrounding quartz is under slight tension (darkest part, to the left of the inclusion), while another part is under compression (dark/light grey, to the right of the inclusion). These two compartments are easily distinguished by two lines making a 120° angle between, classic in crystalline quartz. The current interpretation is that the in-inclusion tension pulls up the right compartment that moves as a wedge and so is put under overpressure, while the other rigid compartment does not move and undergo the tensile elastic deformation. This first experiment demonstrates the complexity of the stress field all around an inclusion, active as long as the liquid tension is effective, and evidences the compensation effects due to the heterogeneity on the matrix itself.

Explosivity

A superheated liquid is metastable with respect to its vapour and then able to nucleate at any moment (Fig. 10A). During the 18 th century, Rev. Dayton already reported on the easiness to superheat a liquid and the associated explosive danger [START_REF] Dayton | An experience to prove, that water, when agitated by fire, is infinitely more elastic than air in the same circumstances[END_REF]. Nowadays, this is a well-known class of industrial spills accidents, connected to the Boiling Liquid Expanding Vapour Explosion (BLEVE) type (for instance, [START_REF] Reid | Superheated liquids[END_REF]). As thermodynamically demonstrated [START_REF] Thiéry | Explosive properties of water in volcanic and hydrothermal systems[END_REF], the superheating state of the mother liquid does not increase so much the energy release at the LV phase transition, but dramatically increases the rate of this transition. The power of one explosion is the product of the energy release by the time of release, it comes to the superheating boiling can be qualified as explosive because it is a rapid-phase transition whose rapidity is depending on the superheating "level" [START_REF] Reid | Superheated liquids[END_REF].

A. B. Fig. 10: A The cavitation event produces a sound wave that can be recorded to characterize the intensity of the prior metastability and estimate the mass that cavitates (Fig. 10B). Additionally, several sensors can be used to detect the exact location of cavitation which is not so valuable when working with transparent material like quartz SFI, but could become interesting if using this system to record cavitation event in heterogeneous porous systems. Interestingly, the boiling of large bubbles in porous soils was evoked as a potentially important factor to the transport in porous media (e.g., [START_REF] Mcmanus | Dilation-induced pore fluid cavitation in sands[END_REF][START_REF] Or | Cavitation during desaturation of porous media under tension[END_REF]). Actually, this boiling occurs in water immobilized against gravity due to the capillary forces. The boiling breaking out this capillary suction makes the water body able to flow again according to the gravitational field. This de-metastabilization event can also be expected to move an initially continuously water body into a sum of dispersed flowing/not-flowing water clusters, shaping a discontinuous water content in soils. CONCLUSION Superheated water is a special state which appears for different reasons (decreasing vapor pressure, increasing temperature) and can be useful for different purposes. First, the properties of superheated water are of interest for those situations during which this special metastable state arises. Second, these properties also fit the capillary properties, because capillarity is no more than a superheated state without metastability. However, an open question is the role the superheating plays in the confinement of liquid in geometrical restricted pore spaces. But again, the superheated properties could fit well with the confinement behavior. On another point of view, this study outlines the shortage of knowledge about the consequences in natural settings to contain liquid water with superheated properties (whatever its actual form: confined, capillary, or strictly superheated). In particular, the phase transitions (gas/solid-solution interactions, liquid-vapor explosive boiling) are drastically changed that could impact significantly our understanding of the mass transfer in the corresponding pore networks. All the results showed here need to be extended and generalized, and relativized to the surface area of the liquid-solid interface, and also to the volume of liquid involved and available for the reaction. A completely overlooked aspect is the retention/flow duality and more generally the consequences of the superheating on the transport functions of the infilling pores liquid.

Fig. 7 :

 7 Fig. 7: A. Extreme tensile strength obtained with different static and dynamic methods [17-21]. Black dots are Berthelot tubes and SFI. B. Relationship in CsCl-filled samples (1 and 5m CsCl) between (Th-Tn) and the volume of the inclusions (1D simplification) (dotted lines are only guides for eyes).

  . Intense and brutal boiling in 5m NaCl: Th = 221°C; Th-Tn = 51°C (also at http://www.iem.ac.ru/staff/kiril). B. Soundwave accompanying the trapped liquid cavitation recorded by an acoustic emission sensor (Euro Physical Acoustics).

ACKNOWLEDGMENTS

This work has received support from the French Agency for Research (Agence Nationale de la Recherche, ANR) through the grant CONGE BLAN-61001 and ANR-10-LABX-100-01.