Article

# In Situ Calculation of the Rotation Barriers of the Methyl Groups of Tribromomesitylene Crystals: Theory Meets Experiment

Anissa Amar<fnref n="1" />, Soria Zeroual<fnref n="2" />, Xavier Rocquefelte<fnref n="3" /> and Abdou Boucekkine<fnref n="3" />,*

**Abstract:** The computation of the rotation barriers of the methyl groups (Me) of tribromomesitylene (TBM) crystals has been carried out. Experimentally, the barriers of the three Me groups of TBM are found to be high and different. These groups do not experience the same hindering environment in the crystal state. For an isolated TBM molecule, the three barriers are equal and very low. We found that a cluster of 21 TBM molecules permits the reproduction of the crystal symmetry and structure of the bulk, with a central molecule surrounded by six molecules in the same plane and seven other molecules in two planes above and below. DFT computations including dispersion corrections have been carried out using the ONIOM procedure. The Me groups of the central TBM molecule were rotated step by step to determine the conformations of lowest and highest energy for each Me, thus allowing estimation of the rotation barriers as the difference between these energies. In doing so, we found the following barrier values, namely 105, 173, and 205 cm⁻<fnref n="1" />, whereas the experimental values were 111, 180 and 200 cm⁻<fnref n="1" />.

**Keywords:** methyl rotation barriers; tribromomesitylene; ONIOM calculations; DFT

<figure><img src="image_1.png" /></figure>

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**Citation:** Amar, A.; Zeroual, S.; Rocquefelte, X.; Boucekkine, A. In Situ Calculation of the Rotation Barriers of the Methyl Groups of Tribromomesitylene Crystals: Theory Meets Experiment. *Crystals* **2024**, *14*, 563. https://doi.org/10.3390/cryst14060563

Academic Editors: Antonio Frontera and Thomas M. Klapötke

Received: 19 April 2024

Revised: 2 June 2024

Accepted: 14 June 2024

Published: 18 June 2024

<figure><img src="image_2.png" /></figure>

**Copyright:** © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

A methyl (Me) group can act as a free rotor, as is the case for toluene in the gas phase [1]. However, molecules in crystals of pure materials that have a quasi-free methyl rotor are rare. It is expected that the hindering potential of the Me group is largely enhanced when molecules go from the gas phase or are isolated in a cage to a crystal, due to packing effects. In order to study the hindering potential experienced by the methyl rotors, methyl proton tunneling of halogeno-methyl benzenes in the solid state has been extensively studied experimentally and theoretically for a long time, particularly by Professor Jean J. Meinnel and his coworkers [2–8]. In a recent paper, they investigated the methyl rotation barriers in 1,3-dibromo-2,4,6-trimethyl-benzene [9]. The authors showed that the Me group located between the two bromines experiences a weak hindering V6 potential, contrary to the two other methyl groups that experience a high V3 potential. They provided an explanation for these behaviors.

In this paper, we theoretically investigate the structural properties of the 1,3,5-tribromo-2,4,6-trimethylbenzene molecule (tribromomesitylene or TBM) (Scheme 1) in its solid state. Our goal is to study how the packing environment in the crystal affects the rotation barriers of the methyl (Me) groups. An isolated TBM molecule is highly symmetrical, C₃h being its highest symmetry group. In an isolated molecule, the rotation barriers of the three Me groups are equal due to the molecule's symmetry. These barriers are expected to be low, around 40–50 cm⁻<fnref n="1" /> [6,7] the potential, exhibiting a six-fold symmetry, making a methyl group of TBM almost like a free rotor system. However, in the crystal, the hindering environment for the three Me groups is not the same, resulting in different barriers. In fact, Inelastic Neutron Scattering (INS) experiments to study the tunneling of the methyl

<footnote n="1">¹ Physics and Quantum Chemistry Laboratory, Mouloud Mammeri University, Tizi-Ouzou 15000, Algeria; anissa.amar@ummto.dz</footnote>

<footnote n="2">² LEVRES Laboratory, University of El Oued, El Oued 39000, Algeria; soria-zeroual@univ-eloued.dz</footnote>

<footnote n="3">³ Univ. Rennes, ISCR, UMR CNRS 6226, F-35042 Rennes, France; xavier.rocquefelte@univ-rennes.fr</footnote>

<footnote>* Correspondence: abdou.boucekkine@univ-rennes.fr</footnote>
protons reveals that these barriers are high, distinct, and within the range of 100–200 cm⁻¹, with a three-fold symmetry [8].

<figure><img src="image_3.png" /><figcaption>**Scheme 1.** Schematic representation of a TBM molecule with atoms numbers.</figcaption></figure>

Our aim is to compute the methyl rotation barriers in situ, specifically for a TBM molecule in the crystal form. As far as we know, this is the first time that such a computational study has been conducted.

**2. Materials and Methods**

To do so, we plan to carry out DFT calculations considering a cluster that mimics the bulk rather than performing periodic calculations. The rotation barrier for a Me group can be estimated by determining the potential energy of the rotation of this group around its axis. Comparing the rotation barriers computed for an isolated molecule and a molecule in the crystal will allow us to quantify the impact of packing on this property.

The DFT computations should include dispersion corrections in order to take into account the intermolecular interactions in the crystal, which are mainly responsible for its stability. Thus, two functionals, including empirical dispersion, have been considered, namely ωB97XD [10] and B3PW91 [11,12]. The latter functional was supplemented with the GD3BJ dispersion correction [13]. Due to the extensive computations to be carried out (vide infra), it was not possible and not necessary to check more functionals.

Moreover, similar results were obtained with the two considered functionals (see Figure S1 in the Supporting Information, SI). Therefore, we continued all our calculations using B3PW91-GD3BJ.

Moreover, the cluster of TBM molecules being considered should accurately replicate the symmetry and structure of the crystal, as well as the intermolecular distances between the TBM molecules. To minimize the computational time, this cluster should be as small as possible, while still accounting for all the packing effects on a given TBM embedded in the crystal.

**3. Computations and Results**

Thus, we carried out geometry optimizations of different clusters of TBM molecules, keeping in mind the crystal structure [14], and found that a cluster containing 21 molecules reproduces the symmetry of the bulk exactly. In this cluster, a central TBM molecule, namely the target molecule for the future conformational study, is surrounded by twenty molecules: six in the same plane and seven in each planes above and below the central plane (Figure 1). This cluster contains 441 atoms (189 H, 189 C, and 63 Br).
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Representation of the optimized cluster of TBM obtained using the ONIOM approach (B3PW91-GD3BJ/6-311 + G(d,p): B3PW91-GD3BJ/6-31G(d)).</figcaption></figure>

In order to reduce computational time, keeping in mind the future rotation barriers to be evaluated, we employed the ONIOM method [15], as implemented in the Gaussian 16 program [16]. This method divides the system into two parts, each computed at different levels of theory: a high level (of accuracy) for the targeted central TBM molecule and a low level for the rest of the cluster (20 molecules). We decided to use the same DFT functional for the high and low level systems. To accurately compute the energy of the central molecule we used the extended 6-311 + G(d,p) basis set, while the smaller 6-31G(d) basis set was used for the rest of the cluster. The Me groups of the central molecule were rotated to estimate the rotation barriers. The use of an extended basis set for the central molecule ensured accurate computation of the rotation barriers [6]. It must be kept in mind that the Me rotation induces a deformation of the ring due to hyperconjugation [17], so the full geometry optimization of the TBM target molecule must be carried out at each step of the rotation.

In our calculations, the number of basic functions for the cluster was 5103 (11,277 primitive Gaussians). Thousands of hours of CPU time, on a high-performance computer, were needed for these calculations and for each Me conformation.

The rotation barriers for each methyl group have been estimated as follows.

The methyl group under consideration was constrained to rotate around its symmetry axis, which is the C(phenyl)-C(methyl) bond. The potential barrier hindering the rotation of the methyl group was determined by fixing the dihedral angle of a hydrogen atom in the Me group and minimizing the total energy of the system, allowing for the optimization of all other internal coordinates of the target molecule. This calculation was repeated for different fixed dihedral angles, with increments of 30°, for the hydrogen atom being considered.

First, it is worth considering the rotation barriers of the Me groups in an isolated TBM molecule. Figure 2 displays the potential energy curve for the Me rotation in this case, calculated at the same level of calculation as the target molecule in the crystal, i.e., B3PW91-GD3BJ/6-311 + g(d,p) (vide supra). As can be seen, the computed rotation barrier is low, specifically 49 cm⁻¹. This barrier is the same for all three Me groups.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** The potential energy plot for the Me rotation in an isolated TBM molecule at the B3PW91-GD3BJ/6-311 + g(d,p) level. The arrow indicates the sense of rotation of the methyl group.</figcaption></figure>

Going back to the entire cluster containing 21 molecules, we conducted a full geometry optimization using the ONIOM method (vide supra). The command line used in the Gaussian16 program is as follows: oniom(B3PW91/6-311 + g(d,p): B3PW91/6-31G(d)) int = superfinegrid empiricaldispersion = GD3BJ. As mentioned earlier, the central TBM molecule is the high-level (H) system while the other 20 molecules constitute the low-level (L) system.

The optimized structure of the cluster, although respecting the symmetry of the crystal, exhibits intermolecular distances that are too small compared to the measured ones, as shown in Table 1 (the optimized Cartesian coordinates are given in the Supporting Information). The computed intermolecular distances between the central benzene of the target molecule and the centers of the other surrounding molecules in the same plane are approximately 0.38 Å lower than the X-ray structure, and the distances between the three considered molecular planes are also underestimated. This discrepancy is due to the empirical correction for dispersion used, which leads to an overestimation of the attraction between the TBM molecules and, consequently, causes the cluster to contract. Under these conditions, much higher rotational barriers than the measured ones are obtained, i.e., 530 cm⁻¹, 480 cm⁻¹, and 470 cm⁻¹, with the hindering effect of the environment on the Me rotation barriers being overestimated.

<table><caption>**Table 1.** Intermolecular distances between the central benzene of the target molecule and the surrounding ones in the same plane (d1–d6, Scheme 2) and the central benzene in the above (d7) and below (d8) planes after a full geometry optimization of the cluster.</caption><thead><tr><th>Distances (Å)</th><th>Optimized</th><th>X-ray [14]</th></tr></thead><tbody><tr><td>d1</td><td>8.629</td><td>9.066</td></tr><tr><td>d2</td><td>8.667</td><td>9.049</td></tr><tr><td>d3</td><td>8.673</td><td>9.083</td></tr><tr><td>d4</td><td>8.708</td><td>9.066</td></tr><tr><td>d5</td><td>8.691</td><td>9.049</td></tr><tr><td>d6</td><td>8.710</td><td>9.082</td></tr><tr><td>d7</td><td>3.562</td><td>3.935</td></tr><tr><td>d8</td><td>3.625</td><td>3.941</td></tr></tbody></table>

After this failure, we decided to optimize, at the same level of theory, only the geometry of the central molecule, while keeping the coordinates of the surrounding molecules fixed, as they are in the X-ray structure [14]. As we shall see below, this second approach was
successful. The as-obtained optimized geometrical parameters are given in Table 2 (the Cartesian coordinates are given in the Supporting Information). Our approach is not new. It is known that when computing local properties in a crystal, derived from tiny energy differences such as magnetic coupling constants, it is necessary to describe the crystal structure very accurately. Slight differences between optimized and X-ray coordinates could lead to significant deviations between the computed and observed properties. Generally, the X-ray structure, when available, is used for such computations.

<figure><img src="image_6.png" /><figcaption>**Scheme 2.** Representation of the atomic configuration of the central plane containing the target TBM molecule and its 6 neighboring molecules. The intermolecular distances were defined with respect to the barycenter of each benzene ring.</figcaption></figure>

At the very beginning, it is worth noting that the crystal packing does not affect the bond distances and angles of a TBM molecule, as shown in Table 2. Notably, the bond lengths and bond angles, computed at the same level of theory, i.e., B3PW91-GD3BJ/6-311 + G(d,p), are the same for an isolated molecule and the targeted molecule in the crystal. As expected, the conformation of the methyl groups could change due to the packing effect in the crystal. As we can see from Table 2, for example, the value of the H<sub>9</sub>-Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub> dihedral angle, which is 0° for the isolated molecule, becomes 18.86° under the packing effect. Similarly, the H<sub>14</sub>-Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub> dihedral angle, which is -120.79° in the isolated molecule, takes the value of -101.45° in the crystal.

Table 3 provides the distances between the centers of the benzene rings that are in the same plane, as well as the distance between two neighboring planes. The computed distances accurately match the expected values, keeping in mind that only the central TBM molecule has been optimized.
<table><caption>**Table 2.** Comparison between the X-ray [14] and computed geometrical parameters of the isolated molecule and target TBM molecule within the cluster at the ONIOM/B3PW91-GD3BJ level (numbering of atoms in Scheme 1).</caption><thead><tr><th rowspan="2">Bond</th><th colspan="3">B3PW91</th><th colspan="3">B3PW91</th><th colspan="3">B3PW91</th></tr><tr><th>X-ray</th><th>Isolated Molecule</th><th>Molecule in the Cluster</th><th>Angle</th><th>X-ray</th><th>Isolated Molecule</th><th>Molecule in the Cluster</th><th>Dihedral Angle</th><th>X-ray</th><th>Isolated Molecule</th><th>Molecule in the Cluster</th></tr></thead><tbody><tr><td>C<sub>1</sub>-C<sub>2</sub></td><td>1.391</td><td>1.397</td><td>1.408</td><td>C<sub>1</sub>-C<sub>2</sub>-C<sub>3</sub></td><td>115.65</td><td>115.986</td><td>115.513</td><td>C<sub>1</sub>-C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub></td><td>-0.63</td><td>0.00</td><td>-1.67</td></tr><tr><td>C<sub>3</sub>-C<sub>4</sub></td><td>1.401</td><td>1.397</td><td>1.406</td><td>C<sub>3</sub>-C<sub>4</sub>-C<sub>5</sub></td><td>115.80</td><td>115.983</td><td>115.575</td><td>C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub>-C<sub>5</sub></td><td>0.54</td><td>0.00</td><td>0.93</td></tr><tr><td>C<sub>5</sub>-C<sub>6</sub></td><td>1.406</td><td>1.397</td><td>1.389</td><td>C<sub>5</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>114.47</td><td>115.986</td><td>115.493</td><td>C<sub>3</sub>-C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub></td><td>-0.05</td><td>0.00</td><td>0.52</td></tr><tr><td>C<sub>2</sub>-C<sub>3</sub></td><td>1.382</td><td>1.402</td><td>1.388</td><td>C<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub></td><td>124.48</td><td>124.015</td><td>124.402</td><td>C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>-0.28</td><td>0.00</td><td>-1.04</td></tr><tr><td>C<sub>4</sub>-C<sub>5</sub></td><td>1.391</td><td>1.402</td><td>1.387</td><td>C<sub>4</sub>-C<sub>5</sub>-C<sub>6</sub></td><td>124.48</td><td>124.016</td><td>124.976</td><td>C<sub>5</sub>-C<sub>6</sub>-C<sub>1</sub>-C<sub>2</sub></td><td>0.16</td><td>0.00</td><td>0.19</td></tr><tr><td>C<sub>6</sub>-C<sub>1</sub></td><td>1.406</td><td>1.402</td><td>1.405</td><td>C<sub>6</sub>-C<sub>1</sub>-C<sub>2</sub></td><td>125.08</td><td>124.014</td><td>124.015</td><td>C<sub>6</sub>-C<sub>1</sub>-C<sub>2</sub>-C<sub>3</sub></td><td>0.26</td><td>0.00</td><td>1.06</td></tr><tr><td>C<sub>1</sub>-Br<sub>1</sub></td><td>1.909</td><td>1.914</td><td>1.924</td><td>Br<sub>1</sub>-C<sub>1</sub>-C<sub>6</sub></td><td>117.45</td><td>116.942</td><td>119.395</td><td>Br<sub>1</sub>-C<sub>1</sub>-C<sub>2</sub>-C<sub>3</sub></td><td>-178.90</td><td>180.0</td><td>179.17</td></tr><tr><td>C<sub>3</sub>-Br<sub>3</sub></td><td>1.909</td><td>1.914</td><td>1.930</td><td>Br<sub>3</sub>-C<sub>3</sub>-C<sub>2</sub></td><td>118.65</td><td>116.943</td><td>119.010</td><td>Br<sub>2</sub>-C<sub>3</sub>-C<sub>4</sub>-C<sub>5</sub></td><td>179.56</td><td>180.0</td><td>177.17</td></tr><tr><td>C<sub>5</sub>-Br<sub>5</sub></td><td>1.905</td><td>1.914</td><td>1.932</td><td>Br<sub>5</sub>-C<sub>5</sub>-C<sub>4</sub></td><td>118.65</td><td>116.942</td><td>118.147</td><td>Br<sub>3</sub>-C<sub>5</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>179.03</td><td>180.0</td><td>179.58</td></tr><tr><td>C<sub>2</sub>-Cm<sub>2</sub></td><td>1.494</td><td>1.498</td><td>1.474</td><td>Br<sub>1</sub>-C<sub>1</sub>-C<sub>2</sub></td><td>117.45</td><td>119.044</td><td>116.563</td><td>Cm<sub>2</sub>-C<sub>2</sub>-C<sub>1</sub>-C<sub>6</sub></td><td>179.61</td><td>180.00</td><td>179.84</td></tr><tr><td>C<sub>4</sub>-Cm<sub>4</sub></td><td>1.504</td><td>1.498</td><td>1.487</td><td>Br<sub>3</sub>-C<sub>3</sub>-C<sub>4</sub></td><td>116.85</td><td>119.041</td><td>116.571</td><td>H<sub>7</sub>-Cm<sub>2</sub>-C<sub>2</sub>-C<sub>1</sub></td><td>0.07</td><td>0.00</td><td>-0.52</td></tr><tr><td>C<sub>6</sub>-Cm<sub>6</sub></td><td>1.485</td><td>1.498</td><td>1.498</td><td>Br<sub>5</sub>-C<sub>5</sub>-C<sub>6</sub></td><td>116.85</td><td>119.043</td><td>116.776</td><td>H<sub>13</sub>-Cm<sub>2</sub>-C<sub>2</sub>-C<sub>1</sub></td><td>-119.95</td><td>-120.79</td><td>-120.77</td></tr><tr><td>Cm<sub>2</sub>-H<sub>7</sub></td><td>1.064</td><td>1.087</td><td>1.088</td><td>Cm<sub>2</sub>-C<sub>2</sub>-C<sub>1</sub></td><td>123.20</td><td>123.266</td><td>123.196</td><td>H<sub>10</sub>-Cm<sub>2</sub>-C<sub>2</sub>-C<sub>1</sub></td><td>120.03</td><td>120.79</td><td>120.00</td></tr><tr><td>Cm<sub>4</sub>-H<sub>9</sub></td><td>1.074</td><td>1.087</td><td>1.097</td><td>Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub></td><td>123.47</td><td>123.268</td><td>122.652</td><td>Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub>-C<sub>2</sub></td><td>179.84</td><td>180.00</td><td>-179.81</td></tr><tr><td>Cm<sub>6</sub>-H<sub>8</sub></td><td>1.077</td><td>1.087</td><td>1.098</td><td>Cm<sub>6</sub>-C<sub>6</sub>-C<sub>5</sub></td><td>123.13</td><td>123.268</td><td>121.641</td><td>H<sub>9</sub>-Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub></td><td>18.73</td><td>0.00</td><td>18.86</td></tr><tr><td>Cm<sub>2</sub>-H<sub>10</sub></td><td>1.082</td><td>1.093</td><td>1.097</td><td>Cm<sub>2</sub>-C<sub>2</sub>-C<sub>3</sub></td><td>121.28</td><td>120.748</td><td>121.289</td><td>H<sub>14</sub>-Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub></td><td>-101.42</td><td>-120.79</td><td>-101.45</td></tr><tr><td>Cm<sub>4</sub>-H<sub>12</sub></td><td>1.087</td><td>1.093</td><td>1.101</td><td>Cm<sub>4</sub>-C<sub>4</sub>-C<sub>5</sub></td><td>122.35</td><td>120.749</td><td>121.767</td><td>H<sub>11</sub>-Cm<sub>4</sub>-C<sub>4</sub>-C<sub>3</sub></td><td>138.63</td><td>120.79</td><td>138.22</td></tr><tr><td>Cm<sub>6</sub>-H<sub>11</sub></td><td>1.080</td><td>1.093</td><td>1.08</td><td>Cm<sub>6</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>122.75</td><td>120.746</td><td>122.853</td><td>Cm<sub>6</sub>-C<sub>6</sub>-C<sub>1</sub>-C<sub>2</sub></td><td>179.75</td><td>180.00</td><td>179.83</td></tr><tr><td>Cm<sub>2</sub>-H<sub>13</sub></td><td>1.086</td><td>1.093</td><td>1.100</td><td>C<sub>2</sub>-Cm<sub>2</sub>-H<sub>7</sub></td><td>109.39</td><td>111.513</td><td>112.732</td><td>H<sub>8</sub>-Cm<sub>6</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>-13.97</td><td>0.00</td><td>-1.036</td></tr><tr><td>Cm<sub>4</sub>-H<sub>14</sub></td><td>1.084</td><td>1.093</td><td>1.099</td><td>C<sub>4</sub>-Cm<sub>4</sub>-H<sub>9</sub></td><td>109.58</td><td>111.511</td><td>112.151</td><td>H<sub>15</sub>-Cm<sub>6</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>-134.0</td><td>-120.79</td><td>-120.86</td></tr><tr><td>Cm<sub>6</sub>-H<sub>15</sub></td><td>1.089</td><td>1.093</td><td>1.085</td><td>C<sub>6</sub>-Cm<sub>6</sub>-H<sub>8</sub></td><td>109.46</td><td>111.512</td><td>111.496</td><td>H<sub>12</sub>-Cm<sub>6</sub>-C<sub>6</sub>-C<sub>1</sub></td><td>105.90</td><td>120.79</td><td>120.17</td></tr></tbody></table>

<table><caption>**Table 3.** ONIOM/B3PW91-GD3BJ-calculated distances between the centers of the benzene rings compared to X-ray diffraction values (numbering of the distances in Scheme 2).</caption><thead><tr><th>Distances (Å)</th><th>X-ray [14]</th><th>Calculated</th></tr></thead><tbody><tr><td>d1</td><td>9.066</td><td>9.055</td></tr><tr><td>d2</td><td>9.049</td><td>9.043</td></tr><tr><td>d3</td><td>9.083</td><td>9.087</td></tr><tr><td>d4</td><td>9.066</td><td>9.052</td></tr><tr><td>d5</td><td>9.049</td><td>9.036</td></tr><tr><td>d6</td><td>9.082</td><td>9.096</td></tr><tr><td>d1</td><td>10.905</td><td>10.935</td></tr><tr><td>d2</td><td>11.355</td><td>11.337</td></tr><tr><td>d3</td><td>10.348</td><td>10.319</td></tr><tr><td>d4</td><td>8.708</td><td>8.731</td></tr><tr><td>d5</td><td>8.187</td><td>8.163</td></tr><tr><td>d6</td><td>9.395</td><td>9.379</td></tr><tr><td><sup>1</sup>d7</td><td>3.935</td><td>3.936</td></tr><tr><td>d1</td><td>10.947</td><td>10.892</td></tr><tr><td>d2</td><td>11.347</td><td>11.345</td></tr><tr><td>d3</td><td>10.328</td><td>10.358</td></tr><tr><td>d4</td><td>8.733</td><td>8.704</td></tr><tr><td>d5</td><td>8.166</td><td>8.167</td></tr><tr><td>d6</td><td>9.391</td><td>9.387</td></tr><tr><td><sup>2</sup>d8</td><td>3.941</td><td>3.936</td></tr></tbody></table>

<footnote n="1"><sup>1</sup>d7: distance between targeted molecule and the central molecule of the plane above. <sup>2</sup>d8: distance between targeted molecule and the central molecule of the plane below.</footnote>
The close agreement between the structure of the studied TBM cluster and the actual crystal gives us confidence that the computation of the rotation barriers of the methyl groups is reliable.

The rotation barriers for each methyl group of the target molecule in the cluster have been estimated using the same method as for the isolated molecule. The total energy was determined for different dihedral angles of the methyl hydrogen atom representing different conformations of the methyl group. The difference between the conformation of the highest energy obtained for the target molecule and the ground state energy (i.e., the energy of the fully optimized target molecule) allows for estimating the rotation barrier. These energies are given in Table 4. It is worth noting that the lack of rotational symmetry for the methyl groups in the crystal does not permit us to plot potential energy curves like the one for the isolated molecule (Figure 2).

<table><caption>**Table 4.** Lowest and highest conformation energies and related dihedral angles for the three Me groups of the central TBM molecule.</caption><thead><tr><th></th><th>Dihedral Angle (°)<br>Lowest Energy (au)</th><th>Dihedral Angle (°)<br>Highest Energy (au)</th><th>Barrier (cm<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Me (1)</td><td>0°<br>-8070.78204</td><td>90°<br>-8070.78156</td><td>105</td></tr><tr><td>Me (2)</td><td>180°<br>-8070.78204</td><td>150°<br>-8070.78111</td><td>205</td></tr><tr><td>Me (3)</td><td>-162°<br>-8070.78204</td><td>-132°<br>-8070.78125</td><td>173</td></tr></tbody></table>

The rotation barriers for a TBM molecule in the cluster are high (Figure 3), i.e., 205, 173, and 105 cm⁻¹, compared to the isolated TBM (49 cm⁻¹), highlighting the role of the intermolecular hindering potential of the stacked molecules in the crystal. These values are close to those found experimentally by the late Prof. Jean J. Meinnel and coworkers, using INS measurements of proton tunneling in a pure crystal [8], i.e., 200, 184, and 111 cm⁻¹ for the three methyl groups, respectively.

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Representation of the methyl conformations of the higher energies. The related computed rotation barriers are given.</figcaption></figure>

4. Conclusions

A computational approach has been developed to evaluate the rotation barriers of methyl (Me) groups in tribromomesitylene (TBM) crystals. This was achieved by performing molecular calculations, specifically on a TBM molecule, rather than using periodic calculations. DFT computations, which include empirical dispersion, have been successfully employed for this purpose. First, it has been demonstrated that a cluster of 21 TBM
molecules accurately reproduces the symmetry and structural parameters of the bulk ma-
terial. In this cluster, six molecules surround a central molecule in the same plane while
seven are in each plane (above and below). The methyl groups of the central molecule
were been rotated, permitting us to compute the energies of the different conformations for
each Me group. The barriers, computed as the difference between the highest and lowest
conformation energies, are found close to the INS experimental values of 111, 180, and
200 cm⁻¹ with values of 105, 175, and 205 cm⁻¹, respectively. The methodology developed
here can advantageously be used to evaluate rotation barriers, and even other molecular
properties, when a cluster of molecules can accurately mimic the full molecular crystal.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/cryst14060563/s1, Figure S1: methyl rotation potential curves.

**Author Contributions:** Conceptualization, methodology, writing—original draft preparation, supervision, A.B.; methodology, software, validation, A.A. and X.R.; investigation, data curation, A.A. and S.Z.; writing—review and editing, A.A., A.B., S.Z. and X.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

**Acknowledgments:** This paper is a tribute to Jean J. Meinnel who investigated methyl rotation barriers for several decades, until his death at 92 years old, and encouraged us to take interest in it.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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