Anharmonic Computations Meet Experiments (IR, Raman, Neutron

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Anharmonic Computations Meet Experiments (IR, Raman, Neutron Diffraction) for Explaining the Behavior of 1,3,5-tribromo-2,4,6-trimethyl-benzene Jean J. Meinnel, Camille Latouche, Ghanemi Soumia , Abdou Boucekkine, Vincenzo Barone, Alain Moréac, and Ali Boudjada J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b12467 • Publication Date (Web): 02 Feb 2016 Downloaded from http://pubs.acs.org on February 5, 2016

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The Journal of Physical Chemistry

Anharmonic Computations Meet Experiments (IR, Raman, Neutron Diffraction) for Explaining the Behavior of 1,3,5-tribromo-2,4,6-trimethyl-benzene Jean Meinnel,*a Camille Latouche,bc Soumia Ghanemi,ad Abdou Boucekkine,*a Vincenzo Barone,*b Alain Moréac,e and Ali Boudjada,d a

Institut des Sciences Chimiques de Rennes, UMR 6226 CNRS-Université de 35042 Rennes, France b Scuola normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy c Institut des Matériaux Jean Rouxel (IMN), Université de Nantes, CNRS, 2 Houssinière, BP 32229, 44322 Nantes Cedex 03, France d Laboratoire de Cristallographie, Département de Physique, Université Constantine, 25000 Constantine, Algeria e Institut de Sciences Physiques de Rennes, UMR CNRS 6626, Université de Avenue du Général Leclerc, 35042, Rennes, France.

Rennes 1,

rue de la MentouriRennes 1,

Abstract In the present paper we first show the experimental Raman, Infra-Red and Neutron INS spectra of tribromomesitylene (TBM) measured in the range 50-3200 cm-1 using crystalline powders at 6 or 4 K. Then, the bonds lengths and angles determined by neutron diffraction using a TBM single crystal at 14K are compared to the computed ones at different levels of theory. Anharmonic computations were then performed on the relaxed structure using the VPT2 approach, and for the lowest normal modes, the HROA model have led to a remarkable agreement for the assignment of the experimental signatures. A particularity appears for frequencies below 150 cm-1 and in particular those concerning the energy levels of “hindered rotation” of the three methyl groups, they must be calculated for onedimensional symmetrical tops independent of the frame vibrations. This fact is consistent with the structure established by neutron diffraction: the protons of the methyl groups undergoing huge “libration” motions, are widely spread in space. The values of the transitions between the librational levels determined by inelastic neutron scattering indicate that the hindering potentials are mainly due to intermolecular interactions different for each methyl group in the triclinic cell.

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Introduction Molecular rotors such as NH3, CH3, CH4 etc … experience a local potential which could be evaluated by tunneling spectroscopy. In the past years, researchers have started this type of investigation on the so-called tri-halogeno mesitylene molecules.1 In this paper we focus our attention on the structural and spectroscopic properties of the symmetrical (C3h) 1,3,5-tribromo-2,4,6-trimethylbenzene (tribromomesitylene or TBM) (Figure 1) in the solid state. Below 300 K it crystallizes in the triclinic system, our goal was to establish if the asymmetrical environment is able to perturb the molecular threefold symmetry and in particular what are the consequences on the spectroscopic properties. TBM is a derivative member of the restricted group of molecules M6 for which the barrier hindering the methyl rotation has a six-fold symmetry among which we may quote several substituted benzenes: toluene (Tol), parafluorotoluene (pFT), paraxylene (pX), 2,6difluorotoluene (26dFT), the 1,3,5-trimethylbenzene (mesitylene or Mes) and others which have been investigated in the past.2–8 The presence of three symmetrical tops (the three methyl groups) raises the question of their independence with the framework and also of their eventual coupling. Our previous studies of the fully hydrogenated TBM by inelastic neutron scattering (INS) spectroscopy in the range 0.01 to 100 cm-1 had established that the three methyl groups of TBM are independent and are tunneling at different energies,1 , so the question is to investigate if this non respect of the threefold symmetry is also encountered for other physical properties.

Figure 1. The 1,3,5-tribromo-2,4,6-trimethylbenzene (TBM) molecule. Despite its relative small size, deep investigations of the rotational motion and the effect of the bromine have not been addressed yet. In this paper we present the Raman, IR and INS spectra observed in the range 20 to 3200 cm-1. In order to complete this investigation, quantum calculations will be performed to show that proper use of the secondorder Vibrational Perturbation Theory (VPT2) permits an assignment of the vibration modes without ambiguity.9–16 The necessity to separate the hindered rotation of the

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methyl groups from the vibrations of the frame will be examined in details. Finally, an investigation of the potential barrier nature of the methyl groups of TBM will be also carried out.

Computational details Computations have been performed using methods rooted into Density Functional Theory (DFT) and have been carried out with a development version of the Gaussian suite of programs.17 The B3LYP functional has been employed18,19 in conjunction with the m-aug-cc-pVTZ basis set on H and C atoms, where d functions on hydrogens have been removed,20,21 and the Def2TZVP basis set used for Br atoms.22 Semi-empirical dispersion contributions by means of the D3 correction of Grimme, leading to B3LYP-D3 model, have been taken into account.23 Hereafter, we denote this level as I. Full geometry optimizations have been performed checking the nature of the obtained structures by diagonalization of their Hessians. Computations have been performed enforcing the C3h symmetry. In several papers devoted on IR and Raman spectroscopies and reported by some of us, it has been shown that using the so-called anharmonic level to compute vibrations is much more accurate than the use of an ad-hoc scale factor and so for a relative weak computational cost.9–16,24 Furthermore, only full account of both mechanical and electrical anharmonicity allows to assign the whole IR and Raman spectra (including overtones and combination bands).11,13 So cubic and semidiagonal quartic force constants have been computed by finite differences of analytical Hessians at the B3LYP-D3 to obtain anharmonic frequencies with the GVPT2 model taking into the proper account possible Fermi and DarlingDennison resonances, and the symmetry of the molecule.11,12,16,24 For the lowest normal modes, anharmonic vibrations have been obtained using the so-called Hindered Rotor (HR) treatment25,26 which gives access to HROA model.27,28 Some extra computations have also been performed using another hybrid functional, namely the MPW1PW9129–31 and have been associated to the LANL2DZ+polarization on all atoms basis set.32–35 Hereafter, we denote this level of computation as II.

Structural comparison between experiment and computation TBM was synthesized in the laboratory by direct bromination of a commercial dibromomesitylene in a solution of acetic acid at 70° in presence of a mixture of nitric and sulfuric acids. The obtained TBM was recrystallized by precipitation of a solution in chloroform at 40°C followed by sublimation under vacuum. The purity was better than 99.8 %. A single crystal neutron diffraction study of TBM at 14K has already been published.36 A striking result clearly appears on Figure 2: the probability density to find a


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nucleus of a carbon or a bromine atom is nearly concentrated at a point while that to find a proton of a methyl group is largely spread over the space.

Figure 2. Mean experimental bond lengths and angles within the hypothesis of a strict C3h symmetry. Projection on the (100) plane.

the carbon linked to a bromine atom, while it is 115.8(1)° facing the carbon linked to a methyl group. Each methyl group number p (p = 2, 4, 6) has an eclipsed bond Cmp-Hpa located into the molecular plane, the mean length of the intra-cyclic Cp-Cp+1 bonds facing an eclipsed Cmp-Hp bond is equal to 1.393 Å which is slightly smaller than the Cp-Cp-1 bond facing the two staggered Cmp-Hp bonds equal to 1.401 Å. The agreement with the computational level II is satisfactory although the computed distances are generally overestimating the experimental ones by ca 0.01 Å. Moreover, at the computational level (I), the agreement between experimental and computed data appears as excellent; particularly one should notice that the computed C-C bonds are now almost identical to the observed ones issuing from the neutron diffraction (ND) measurements. However, the mean computed C-Br bond length equal to 1.925 Å is slightly longer than the experimental one, i.e. 1.897(4) Å, but almost within the measured standard deviation. It is also worth noting that the measured bond angles values are perfectly reproduced using either level I or II of theory.

In Table 1 are collected the relevant observed and computed parametric data (see computational details vide infra). From an experimental point of view, the planar molecular ring retains the C3h symmetry within the accuracy of the instrument: the mean endo-cyclic angle is 124.2(1)° facing Table 1. Selected parametric data of TMB observed by neutron diffraction with a single crystal at 14 K and computed at different levels of theory.

Bond

14 K (ND)

C1-C2

1.3913(7)

C3-C4

1.3953(7)

C5-C6

Mean (ND)

Angle

14 K (ND)

C1-C2-C3

115.72(4)

C3-C4-C5

115.70(4)

1.3922(7)

C5-C6-C1

115.84(4)

C2-C3

1.4005(7)

C2-C3-C4

124.32(4)

C4-C5

1.3996(7)

C4-C5-C6

124.21(4)

C6-C1

1.4034(7)

C6-C1-C2

124.19(4)

C1-Br1

1.8940(7)

Br1-C1-C6

116.76(4)

C3-Br3

1.8952(7)

Br3-C3-C2

116.59(4)

C5-Br5

1.9006(7)

Br5-C5-C4

116.48(4)

C2-Cm2

1.4998(7)

Br1-C1-C2

119.05(4)

C4-Cm4

1.4961(7)

Br3-C3-C4

119.09(4)

C6-Cm6

1.4959(7)

Br5-C5-C6

119.30(4)

Cm2-H21

1.064(2)

Cm2-C2-C1

123.20(4)

Cm4-H41

1.074(2)

Cm4-C4-C3

123.47(4)

Cm6-H61

1.077(2)

Cm6-C6-C5

123.13(4)

1.393(2)

1.401 (2)

1.897(4)

1.497(2)

1.070(6)

I

1.395

1.401

1.925

1.501

1.082

II

1.404

1.409

1.916

1.505

1.091


Mean (ND)

I

II

115.8(1)

116.0

116.2

124.2(1)

124.0

123.8

116.6(2)

117.0

116.9

119.2(2)

119.1

119.2

123.3(2)

123.3

123.3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cm2-H22

1.082(2)

Cm2-C2-C3

121.08(4)

Cm4-H42

1.087(2)

Cm4-C4-C5

120.83(4)

Cm6-H62

1.080(2)

Cm6-C6-C1

121.04(4)

Cm2-H23

1.086(2)

C2-Cm2-H21

112.2(1)

Cm4-H43

1.084(2)

C4-Cm4-H41

111.9(1)

Cm6-H63

1.080(2)

C6-Cm6-H61

112.1(1)

1.083(3)

1.083(3)

1.090

1.090

1.096

1.096

From ND it appears that although each methyl group is symmetrically located between two equivalent bromine atoms in the isolated molecule, it has nevertheless a preferred orientation with one eclipsed C-H bond lying in the molecular plane, the extra-cyclic angles Φg and Φd around the rotation axis Cp-Cmp of the methyl n° p differ by ΔΦp = 2.3° (Figure 2). On the contrary, in the study of the dibromomesitylene structure by ND at 14 K it was found that the angles around C2-Cm2 symmetrically surrounded by two C-Br bonds differ by only ΔΦ2 = 0.8° while the proton probability density of the methyl group presents six maxima widely spread.37 These results show the influence of the molecular environment on the methyl groups conformations: a triclinic environment is able to generate a non-negligible anisotropic hindering potential which surpasses the symmetrical internal potential existing in the isolated molecule. It is also possible to evaluate separately the contribution I”p of the protons of each methyl group Mep to the diffracted intensity. If I’p is the intensity scattered by all atoms excluding the three protons of the methyl number p, using the fraction I”p = Ie – I’p of the diffracted intensity it can be drawn a difference-Fourier map of the protons probability density (PPD) of the methyl group Mep. Figure 3 gives the map of a section in the protons cloud of the methyl Me2, it shows that the proton density is largely spread into three crescentshaped blocks.

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121.0(2)

120.7

120.5

112.1(2)

111.7

112.5

PPD are found along the circle C of radius equal to 1.02 Å and the width at half height is around 46°. Similar results are found for the two other methyl groups Me4 and Me6. These results led us to propose to go beyond the BornOppenheimer approximation for locating hydrogen nuclei and to treat each methyl group as a quantum top independent of the frame to which it is linked. The contours of PPD are equidistant in 100.00 units. These experimental values obtained by neutron diffraction are compared to the values of the ΨΨ* calculated as solutions of the Schrödinger equation of a uni-dimensional rotor having the mass of 3 protons and rotating on the circle C (Figure 3).36

Infrared and Raman investigations The infra-red absorption spectrum was measured from 500 cm-1 to 4000 cm-1 using a Fourier transform spectrograph Bruker Equinox 55 with the KBr pellet technique at 295 K (Figure 4a). The resolution was approximately 2.5 cm-1. The IR range of 100-400 cm-1 at 4 K was investigated using an IFS125 MR spectrograph on the AILES line at SOLEIL. The resolution was around 1 cm-1 (Figure 4b). The Raman spectra (Figure 5) were obtained at 4 K or 6K with the excitation wavelength 747.77 nm of a laser titane-sapphire using a triple grating spectrometer HORIBA Jobin-Yvon. The resolution was then 1.5 cm-1. Information given by the optical spectra are complemented by inelastic neutron scattering spectra (INS) (Figure 6) particularly in the region of low wavenumbers below 400 cm-1 because they exhibit a good resolution around 2 to 4 cm-1 and are not submitted to optical selection rules.

Figure 3. Cut of the proton probability density in the plane containing the maxima of probability for the three H atoms in Me2 In this map are drawn iso-intensity curves that are distorted ellipsoids fitted into each other. The largest intensities of the


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Figure 4. Infrared spectra: 1a) at 295 K from 500 to 1600 cm-1, 1b) at 4 K from 100 to 400 cm-1.

Figure 6- Raman (upper) and inelastic neutron scattering spectra (lower) for wavenumbers smaller than 400 cm-1 According to the structural results, we computed the harmonic ωh and the anharmonic ωa normal modes of TBM, at the level I of theory. All calculations have been performed for molecules in vacuum to be directly compared to the experimental data. As one can see in Table 2, the harmonic computations barely reproduce the experimental signatures. However, after inclusion of anharmonic features, the computed vibrations are in a good agreement with the experimental ones (without the use of any scaling factor). Especially, it is often critical to obtain C-H stretchings matching nicely with the observed ones. For instance, the vibrations observed in Raman at 3022 cm-1 and 2982 cm-1 have been respectively computed at 3025 cm-1 and 2981 cm1. The agreement between experimental and computed data is excellent even for low wavenumber vibrations, such as the observed one at around 155 cm-1 (depending of the method) or the one around 570 cm-1, the computed ones being respectively equal to 154 cm-1 and at 569 cm-1. As a matter of fact, it appears that the average error of the computed vibrations with respect to the experimental ones is around 2 % (except for very low normal modes) giving confidence in the used model. Figure 5- Raman spectra obtained at 4 K using a triple grating spectrometer

Table 2 – Experimental and computed normal modes of TBM. Experimental data for Raman, I.R and INS are respectively in columns 4, 5 and 6 and the computed ones (level I) are in column 2 (harmonic) and column 3 (anharmonic). 0 n° 1a 2a

1 rep 1 2

2 ωh 3168 3168

3 ωa 3025 2981

4 ωR 3022 2982

5 ω ir 0 3023


6 ωn 3024

7 Sym A’ E’


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2b 3 4a 4b 5a 6a 6b 7a 7b 8 9a 9b 10 11a 11b 12 13a 13b 14a 14b 15 16 17 18 19a 19b 20a 20b 21 22a 22b 23 24a 24b 25 26a 26b

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

3092

2941

3092

2941

3049

2933

3048

2910

1572

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2951 2953

0

A” 2952

E”

2929 2924 2920

A’ 2931

2930

1533

1547

1543

1544

E’

1494

1447

1448

1456

1437

A’

1494

1448

1446

-

-

E”

1494

1447

1446

1450

1437

A”

1488

1444

1438

1437

1424

E’

1425

1390

1401

?

1423

1387

1385

1375

1375

E’

1381

1350

1374

1352

1362

E’

1326 1269 1070 1059

1294 1241 1052 1039

1306 1240 1062 1029

0 0 0

1314

A’ A’ A’ A’

1061

1034

1029

0

-

E”

1043

1019

1017

1018

1015

E’

1057

1020

1017

1018

1015

A”

971

955

957

953

952

E’

751

670

670

0

652

641

0

647

649

E’

600

590

585

0

585

A’

600

576

571

0

-

E”


E’

A’

1067

A”

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27


36a 36b

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

37

55

49

49

?

0

42

A”

38a 38b

56 57

120

120

?

?

42

E”

28a 28b 29a 29b 30 31a 31b 32 33 34a 34b 35

578

569

571

0

570

A’

381

373

381

387

378

E’

340

327

307

301

343? 337 0

338 0

340 332 295

296

294

297

300

295

E’

232 185

229 170

233 0

0 200

202

A’ A”

154

154

156

153

154

E’

116

116

127

127

?

0

45-55 68-59 59-50

Rot

Rotational barriers of the methyl groups In the first part of the paper, it has been shown that DFT calculations are able to determine with precision the conformation of the TBM molecules. So, starting with the molecular conformation found at the equilibrium geometry we may determine the height of the rotation barrier for one of the TBM methyl groups, the result being the same for the two others because the threefold symmetry of TBM. The calculations were performed using level I. If one takes the methyl group n°2 for example that is constrained to rotate around its symmetry axis, i.e. the bond C2-Cm2, the potential barrier hindering the methyl rotation is determined by constraining one local dihedral angle like γ21 = C2-Cm2-H21 at fixed values relatively to the plane of the ring and optimizing all other internal coordinates to minimize the total energy. In a first approximation the difference between the energies calculated for γ21 = 0° and 90° was taken as a threefold barrier V3 equal to 42 cm-1. But this value is about two to five times smaller than those found experimentally by INS measurements in a pure crystal i.e. 200, 184 and 111 cm-1 for the three methyl groups Me4, Me6 and Me2 respectively. These values were deduced from the assignment of the features observed in the regions 45-75 and 130-170 cm-1 of the INS spectrum of Fig. 6 to transitions between excited states of the methyl rotors. In fact, despite the apparent agreement for the molecular conformation, namely the DFT

E” A’

one for an isolated molecule and the crystal one, we must not forget that external contributions are not taken in account, namely the interactions of the stacked molecules in the crystal. This concerns also the interactions of the methyl group protons with the atoms of the neighboring molecules. Thus, it can be concluded that intermolecular interactions in the crystal are responsible for the high values of the observed rotation barriers, since an isolated molecule exhibits only a small barrier. On the contrary, these intermolecular interactions seem to have a negligible effect on the vibrations of the methyl groups, as demonstrated by our investigation using anharmonic computations. These findings imply, of course, that the single-term Fourier expansion, which fits well the torsional potential for the isolated molecule, is no longer sufficient for describing its behavior in the crystal.

Conclusion This paper presents the assignment of the Raman, IR and INS spectra of the TBM molecule in the crystal state, to its internal normal modes of vibration. First, the main features of the molecular structure and conformation obtained by ND at 14 K are presented; in the triclinic cell the molecule has a quasi-perfect C3h symmetry, each methyl group having one C-H bond lying in the plane of the benzene ring. As expected, the optimised B3LYP-D3 geometry is in excellent agreement with the ND structure. The broad spreading of the proton



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probability density of each methyl group found by the ND brings us to question about the reliability of the BornOppenheimer approximation for the calculation of the normal modes involving methyl groups. Nevertheless, the diffusion lines or absorption bands observed in the Raman, IR and INS spectra could be unambiguously assigned to the calculated in plane and out of plane vibrations, thanks to the B3LYP-D3 computations. If a satisfying sequence of wavenumbers is readily obtained employing the simple harmonic model, in particular for the in plane modes for which the motions of the bromine atoms are involved, on the contrary the stretching frequencies of the methyl C-H bonds and some out-of-plane skeleton modes are overestimated by more than 6 %. Full anharmonic computation using the GVPT2 model, have been carried out, taking into account the hindered rotor treatment extended to the anharmonic oscillator (HRAO) level. Excluding four out of plane normal modes the agreement between the anharmonic calculation and experiment is now excellent, the relative deviation being less than 1% without any use of scaling factors. The broad spreading of the proton cloud in each methyl group is related to this quantum rotor which has several magnetic states. This fact had already been confirmed by the INS studies of the tunnelling of the methyl protons. The magnitude V3 of the barrier hindering the proton exchange is slightly different for each methyl group, is around 100-200 cm-1; it has a main three-fold component. This experimental barrier is much larger than that calculated by DFT for an isolated molecule proving that its origin comes mainly from intermolecular interactions.

Acknowledgements

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The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement No. ERC-2012AdG-320951-DREAMS. The authors gratefully thank the high-performance computer facilities of the DREAMS center (http://dreamshpc.sns.it) for providing computer resources. The support of the COST CMTS-Action CM1002 “Convergent Distributed Environment for Computational Spectroscopy (CODECS)” is also acknowledged. The authors are also grateful to GENCI-IDRIS and GENCICINES for an allocation of computing time (Grant 2013/2014-080649).

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References (1)

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Meinnel, J.; Carlile, C. J.; Knight, K. S.; Godard, J. Assignment of Tunnelling Lines by Single Crystal Neutron Spectroscopy. Phys. B 1996, 226, 238–240. Rudolph, H. D.; Seiler, H. Mikrowellenspektrum, Hinderungspotential Der Internen Rotation Und Dipolmoment Des Para-Fluortoluols. Zeitschrift für

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Table of Entry Only Anharmonic computations performed on the relaxed structure of tribromomesitylene (TBM) using the VPT2 approach and for the lowest normal modes the HROA model, have led to a remarkable agreement for the assignment of the experimental signatures. The role of the molecular environment on the methyl rotation barriers of TBM in a crystal is also brought to light.


Anharmonic Computations Meet Experiments (IR, Raman, Neutron

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