Large Amplitude Torsions in Nitrotoluene Isomers
Studied by Rotational Spectroscopy and Quantum
Chemistry Calculations

Anthony Roucou, Manuel Goubet, Isabelle Kleiner, Sabath Bteich, Arnaud
Cuisset

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Anthony Roucou, Manuel Goubet, Isabelle Kleiner, Sabath Bteich, Arnaud Cuisset. Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations. ChemPhysChem, 2020, 21 (22), pp.2523-2538. 10.1002/cphc.202000591. hal-04568655

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"Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations"

Roucou, Anthony ; Goubet, Manuel ; Kleiner, Isabelle ; Bteich, Sabath ; Cuisset, Arnaud

ABSTRACT

Rotational spectra of ortho-nitrotoluene (2-NT) and para-nitrotoluene (4-NT) have been recorded at low and room temperatures using a supersonic jet Fourier Transform microwave (MW) spectrometer and a millimeter-wave frequency multiplier chain, respectively. Supported by quantum chemistry calculations, the spectral analysis of pure rotation lines in the vibrational ground state has allowed to characterise the rotational energy, the hyperfine structure due to the 14N nucleus and the internal rotation splittings arising from the methyl group. For 2-NT, an anisotropic internal rotation of coupled ## CH3 and ## NO2 torsional motions was identified by quantum chemistry calculations and discussed from the results of the MW analysis. The study of the internal rotation splittings in the spectra of three NT isomers allowed to characterise the internal rotation potentials of the methyl group and to compare them with other mono-substituted toluene derivatives in order to study the isomeric influence on the internal rotation barrier.

CITE THIS VERSION

Roucou, Anthony ; Goubet, Manuel ; Kleiner, Isabelle ; Bteich, Sabath ; Cuisset, Arnaud. Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations. In: ChemPhysChem, Vol. 22, no.22, p. 1 (2020) http://hdl.handle.net/2078.1/237918 -- DOI : 10.1002/cphc.202000591

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# Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations

Anthony Roucou,*[a, b] Manuel Goubet,[c] Isabelle Kleiner,[d] Sabath Bteich,[a] and Arnaud Cuisset*[a]

Rotational spectra of ortho-nitrotoluene (2-NT) and para-nitrotoluene (4-NT) have been recorded at low and room temperatures using a supersonic jet Fourier Transform microwave (MW) spectrometer and a millimeter-wave frequency multiplier chain, respectively. Supported by quantum chemistry calculations, the spectral analysis of pure rotation lines in the vibrational ground state has allowed to characterise the rotational energy, the hyperfine structure due to the ¹⁴N nucleus and the internal rotation splittings arising from the methyl group. For 2-

NT, an anisotropic internal rotation of coupled –CH₃ and –NO₂ torsional motions was identified by quantum chemistry calculations and discussed from the results of the MW analysis. The study of the internal rotation splittings in the spectra of three NT isomers allowed to characterise the internal rotation potentials of the methyl group and to compare them with other mono-substituted toluene derivatives in order to study the isomeric influence on the internal rotation barrier.

## 1. Introduction

In recent years, intensive research has been conducted to develop a compact, selective and low-cost explosive vapour sensor with subppm detection limits capable of replacing canine detection, but with no success so far. Although high-resolution rovibrational spectroscopy proved to be a powerful tool for the detection, identification and quantification of gaseous molecular species of atmospheric and astrophysical interest, the optical methods used present a lack of sensitivity or selectivity for detection of low volatility explosive vapours at room temperature. Indeed, the energetic compounds have very low saturation vapour pressures at room temperature, for example: Trinitrotoluene (TNT) is one of the most volatile industrially manufactured explosives with a vapour pressure of only 1.3 mPa at 300 K.[1] The volatility of most other explosives such as cyclo-1,3,5-trimethylene-2,4,6-trinitramine (RDX) or pentaerythritol tetranitrate (PETN) are significantly lower by several orders of magnitude. In 2004, D. S. Moore published a

review related to instrumentation for detecting traces of gas-phase explosives.[2] Several techniques have been considered but each of them has specific disadvantages for an unambiguous detection of explosive vapors: (i) the ultra-sensitive photothermal deflection,[3] intracavity (Cavity RingDown Spectroscopy)[4] and photoacoustic infrared (IR) spectroscopy probing intense vibrational transitions[5] allowed to measure the gas-phase IR signatures of TNT and RDX but their selectivity does not allow to unambiguously discriminate the compounds of the same family or the isomers (with widths of vibrational bands 100 to 1000 times wider than that of rotational lines), (ii) Raman spectroscopy has also been used to detect residual explosives in signature samples,[6] but its ability to detect very small solid samples does not allow measurements in the gas phase due to a lack of sensitivity, and (iii) promising results have been obtained in the UV/visible domain by laser photo-fragmentation[7] or by single-photon ionization[8] but they do not exclude the possibility to fragment the parent molecule. Despite the low vapour pressure of industrially manufactured explosives, more volatile chemical markers are added or naturally present in many explosives[9] and usually used for the detection in the atmosphere by specifically trained dogs. Two types of explosive markers can be considered: those that can detect the presence of a bomb and those that allow the authorities to identify the explosive after a bomb explosion. The explosives taggants initially mentioned in the ICAO convention of 1991[10] are the 2,3-dimethyl-2,3-dinitrobutane (DMNB) which is only used in the US, the Ethylene glycol dinitrate (EGDNT) which is used to mark Semtex and the more volatile ortho-mononitrotoluene (2-NT) and para-mononitrotoluene (4-NT) which are used to mark TNT.[11, 12] Those two last markers are the objects of the present study. A first gas phase spectroscopic study at room temperature has been performed in the far infrared (FIR) region for the three NT isomers where the vibrational cross-sections have been measured and assigned at low resolution (Δν = 0.5 cm⁻¹).[13] The results have

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<footnote>[a] Dr. A. Roucou, Dr. S. Bteich, Prof. A. Cuisset
Université du Littoral Côte d'Opale, UR 4493, LPCA, Laboratoire de Physico-Chimie de l'Atmosphère, F-59140 Dunkerque, France</footnote>

<footnote>E-mail: anthony.roucou@univ-littoral.fr
arnaud.cuisset@univ-littoral.fr</footnote>

<footnote>[b] Dr. A. Roucou
Institut de la Matière Condensée et des Nanosciences (IMCN), Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium</footnote>

<footnote>[c] Dr. M. Goubet
Univ. Lille, CNRS, UMR8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille, France</footnote>

<footnote>[d] Prof. I. Kleiner
Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), CNRS UMR 7583, Université Paris-Est Créteil & Université de Paris, Institut Pierre Simon Laplace (IPSL), 61 avenue du Général de Gaulle, F-94010 Créteil cedex, France</footnote>

<footnote>Supporting information for this article is available on the WWW under
https://doi.org/cphc.202000591</footnote>
<figure><img src="image_7.png" /></figure>

highlighted the selectivity of gas phase THz/FIR spectroscopy for identification of nitro-aromatic compounds and its ability to discriminate the different isomers of mono-nitrotoluene but it was not possible to resolve at room temperature the rotational structure of the rovibrational FIR bands, even at the maximal resolution of the FTIR instrument (10⁻³ cm⁻¹)[¹⁴] Indeed, the density of rovibrational lines is so high that it prevented their individual observation at room temperature, which is mostly explained by low rotational constants, numerous hot bands involving the lowest energy modes and splittings due to large amplitude motions. Considering this study, the resolution of the rovibrational structure of FIR fundamental bands at very low temperature could be studied, but it is out of reach for a majority of semi-volatile molecules yet.[¹⁵, ¹⁶] The opportunity to probe pure rotational transitions of explosive taggans in the microwave (MW) and millimeter-wave (mm-wave) frequency ranges using electronic sources with exceptional spectral purities has been firstly considered for the meta-mononitrotoluene (3-NT) isomer. In this study, a high complexity was encountered from the experimental and theoretical point of view.[¹⁷] From an experimental point of view, the mm-wave experimental instrument has been pushed to its limit of sensitivity and resolution resulting in a weak rotational spectrum with low signal-to-noise ratio (S/N) due to weak room temperature vapour pressure (P<sub>vap.</sub>(293K) = 8.55 Pa[¹⁸]) and a high density of lines with many blended lines. Concerning the spectroscopic analysis, a specific effective Hamiltonian taking into account the nuclear quadrupole coupling (NQC) for the hyperfine structure observed in MW frequency range and the large amplitude motion of the methyl group presenting a very low internal rotation barrier (V₃ = 6.7659(24) cm⁻¹) were required to reproduce the spectra at the experimental accuracy. As a consequence, a similar approach has been used in this study to measure and analyze the MW and mm-wave spectra of the two TNT markers, 2-NT (P<sub>vap.</sub>(293K) = 12.7 Pa[¹⁸]) and 4-NT (P

vap. (293K) = 3.79 Pa[¹⁸]), to reach a full knowledge of the rotational energy description of the nitrotoluene isomers supported by quantum chemistry calculations, to study the influence of the isomeric form on the internal rotation and NQC and, finally to produce a set of reliable ground state molecular constants and a rotational line list for future in situ detection.

## 2. Results and Discussion

### 2.1. Spectra analysis

#### 2.1.1. 4-Nitrotoluene

The analysis of 4-NT follows strictly the steps of the 3-NT analysis.[¹⁷] Based on quantum chemistry calculations described in computational methods section and presented in details in Table S1 of supporting information I, the jet-cooled MW spectrum (see section 5.1) has been firstly measured and analysed up to J'' = 12 and K''_a = 6 taking into account both the coupling with internal rotation of the methyl group, the NQC and the spin statistics. The A1/A2 and B1/B2 species were preliminary assigned using the SPFIT/SPCAT Pickett's programs[¹⁹] (semi-rigid rotor model in the l' representation of A-reduced Watson's Hamiltonian) and completed with the E1/E2 species arising from internal rotation coupling using llyushin's code RAM36hf.[²⁰⁻²³] This code especially developed for the analysis of internal rotation splittings of G₁₂ point group molecules including high order internal rotation coupling terms for low internal rotation barriers and NQC terms has been firstly used on nitromethane.[²³] According to the permanent dipole vector orientation (see Figure 1), only *a*-type transitions have been observed with a total of 304 individual transitions (83 A1/A2, 74 B1/B2, 78 E1 and 69 E2 species) assigned to 226 blended

<figure><img src="image_8.png" /><figcaption>**Figure 1.** 4-NT geometry optimized at the MP2/cc-pVQZ level of theory in the principal axis orientation. The atoms have been labelled for the spin statistics analysis. All of them are in the (a,b) plane except the hydrogens of the methyl group.</figcaption></figure>

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lines with a RMS deviation of 1.97 kHz (1.82 kHz for A1/A2, 2.00 kHz for B1/B2, 1.91 kHz for E1 and 2.16 kHz for E2 species). The E1 and E2 species have been assigned with splittings varying up to 270 MHz. As shown in Figure 2, the hyperfine structures where not all fully resolved.

In order to predict the mm-wave spectra (see section 5.2) by extrapolation, the rotational constants obtained from the fit of the MW lines have been used as initial set of constants for an updated version of RAM36hf adapted for high rotational quantum number values ($J_{max}$ = 180). A code has been written to convert the input/output files of RAM36hf in a usable format

for the ASCP/SVIEW graphical interface of the AABS Package.[24,25] As shown in zoomed parts of Figure 3, several characteristic features from the ground vibrational state (ν = 0) may be assigned despite the congestion of the blended lines arising from the internal rotation splittings and the presence of numerous hot band transitions. A total of 3188 transitions (1111 A1/A2, 869 B1/B2, 558 E1 and 650 E2 and species) corresponding to 990 blended lines were fitted up to $J'' = 163$ and $K_a'' = 41$ in a global fit including the MW lines with a total RMS deviation of 105 kHz (96.0 kHz for A1/A2, 101.3 kHz for B1/B2, 116.7 kHz for E1 and 114.4 kHz for E2 species) with a special treatment of

<figure><img src="image_11.png" /><figcaption>**Figure 2.** Experimental microwave spectrum of 4-NT for two $^3$R-type transitions: (a) 9<sub>1,9</sub>–8<sub>1,8</sub> (300 co-added scans) and (b) 10<sub>0,10</sub>–9<sub>0,9</sub> (200 co-added scans). Doppler doublets have been assigned in the $F'→F''$ format for hyperfine NQC transitions and the internal rotation splitting are identified for the A/B species (in red) and E species (in blue).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Part of the 70–230 GHz experimental mm-wave spectrum of 4-NT compared to the simulated spectrum obtained from the fit (see section 4.1): (a) is the 165 GHz–215 GHz experimental spectrum (black); (b) is the global simulated spectrum for the $ν = 0$ ground state (orange). Some characteristics patterns of 4-NT are presented in (c), (d) and (e) with the individual frequencies calculated from the fit of A/B and E species in red and blue, respectively. All intense saturated spurious patterns in (a) are artefacts of saturated noise due to the sensitivity limit of the spectrometer pushed on its maximum.</figcaption></figure>

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blends. Internal rotation splittings have been observed up to several GHz. The molecular constants resulting from the analysis of 4-NT spectra are presented and compared with quantum chemistry calculations in Table 1. The association of mm-wave transitions to MW transitions in the fit provides a better determination of all the molecular constants, in particular the accuracy of $\Delta_J$, $\Delta_{JK}$, $\delta_J$ are improved by several orders of magnitude and $\Delta_K$ and $\delta_K$ have been fitted. Concerning the internal rotation parameters, the accuracy of $V_6$ is improved by

one order of magnitude and the higher order internal rotation coupling parameter $F_{bc}$ is determined. The fitted constants match very well with the calculated values, especially the rotational constants with relative differences lower than 2.3%. NQC and internal rotation barriers are specifically discussed in sections 2.2 and 2.3, respectively.

<table><caption>**Table 1.** Ground state torsion-rotation constants of the 4-NT obtained from the MW and mm-wave fits of A1/A2, B1/B2, E1 and E2 species with RAM36hf compared with quantum chemistry calculations. Numbers in parentheses represent one standard deviation in units of the least significant digit.</caption><thead><tr><th></th><th>Unit</th><th>RAM36hf<br>MW</th><th>RAM36hf<br>MW/mm-wave</th><th>Calc.<sup>a</sup></th><th>Operator<sup>b</sup></th></tr></thead><tbody><tr><td>A</td><td>MHz</td><td>3985.927(10)<sup>c</sup></td><td>3985.9141(85)<sup>c</sup></td><td>3894.435</td><td>p<sup>2</sup><sub>a</sub></td></tr><tr><td>B</td><td>MHz</td><td>815.376511(82)<sup>c</sup></td><td>815.376644(42)<sup>c</sup></td><td>814.113</td><td>p<sup>2</sup><sub>b</sub></td></tr><tr><td>C</td><td>MHz</td><td>677.377020(70)<sup>c</sup></td><td>677.376918(41)<sup>c</sup></td><td>676.603</td><td>p<sup>2</sup><sub>c</sub></td></tr><tr><td>Δ<sub>J</sub></td><td>kHz</td><td>0.01188(12)</td><td>0.0125519(17)</td><td>0.012357</td><td>-p<sup>4</sup></td></tr><tr><td>Δ<sub>JK</sub></td><td>kHz</td><td>0.01295(91)</td><td>0.010011(52)</td><td>0.009828</td><td>-p<sup>2</sup>P<sup>2</sup><sub>a</sub></td></tr><tr><td>Δ<sub>K</sub></td><td>kHz</td><td>0.321574<sup>f</sup></td><td>0.329(11)</td><td>0.321574</td><td>-p<sup>4</sup><sub>a</sub></td></tr><tr><td>δ<sub>J</sub></td><td>kHz</td><td>0.203(15)</td><td>0.00239320(70)</td><td>0.002411</td><td>-2p<sup>2</sup>(P<sup>2</sup><sub>b</sub> - P<sup>2</sup><sub>c</sub>)</td></tr><tr><td>δ<sub>K</sub></td><td>kHz</td><td>-0.00542<sup>f</sup></td><td>0.05078(18)</td><td>-0.00542</td><td>-{P<sup>2</sup><sub>a</sub>, (P<sup>2</sup><sub>b</sub> - P<sup>2</sup><sub>c</sub>)}</td></tr><tr><td>χ<sub>aa</sub></td><td>MHz</td><td>-1.1732(56)</td><td>-1.1724(62)</td><td>-1.3557</td><td>2P<sup>2</sup><sub>a</sub>(f(I, J, F)/J(J + 1))</td></tr><tr><td>χ<sub>bb</sub></td><td>MHz</td><td>0.258(18)<sup>d</sup></td><td>0.262(19)<sup>d</sup></td><td>0.0387</td><td>2P<sup>2</sup><sub>b</sub>(f(I, J, F)/J(J + 1))</td></tr><tr><td>χ<sub>cc</sub></td><td>MHz</td><td>0.915(12)</td><td>0.910(13)</td><td>1.317</td><td>2P<sup>2</sup><sub>c</sub>(f(I, J, F)/J(J + 1))</td></tr><tr><td>F</td><td>cm<sup>-1</sup></td><td>5.528<sup>f</sup></td><td>5.528<sup>f</sup></td><td>5.528</td><td>p<sup>2</sup><sub>a</sub></td></tr><tr><td>ρ</td><td>unitless</td><td>0.0239077(20)<sup>e</sup></td><td>0.0241437(17)<sup>e</sup></td><td>0.024061</td><td>p<sub>a</sub>P<sub>a</sub></td></tr><tr><td>V<sub>6</sub></td><td>cm<sup>-1</sup></td><td>12.5(22)</td><td>12.22(18)</td><td>11.283</td><td>(1/2)(1 - cos(6α))</td></tr><tr><td>F<sub>J</sub></td><td>kHz</td><td>-1.147(18)</td><td>-1.146(17)</td><td></td><td>p<sup>2</sup><sub>a</sub>P<sup>2</sup></td></tr><tr><td>ρ<sub>J</sub></td><td>kHz</td><td>0.1586(44)</td><td>0.1644(18)</td><td></td><td>p<sub>a</sub>P<sub>a</sub>P<sup>2</sup></td></tr><tr><td>F<sub>bc</sub></td><td>kHz</td><td></td><td>0.335(52)</td><td></td><td>(P<sup>2</sup><sub>b</sub> - P<sup>2</sup><sub>c</sub>)p<sup>2</sup><sub>a</sub></td></tr><tr><td>δ<sup>g</sup></td><td>rad</td><td>0</td><td>0</td><td>0</td><td></td></tr><tr><td>I<sup>h</sup><sub>as</sub></td><td>amu.Å<sup>2</sup></td><td>3.12438483(20)</td><td>3.12438457(17)</td><td>3.122</td><td></td></tr><tr><td>Δ<sup>l</sup>''<sup>h</sup></td><td>amu.Å<sup>2</sup></td><td>-0.51913(30)</td><td>-0.51933(26)</td><td>-3.606</td><td></td></tr><tr><td>J''</td><td></td><td>12</td><td>12/163</td><td></td><td></td></tr><tr><td>K''<sub>a</sub></td><td></td><td>6</td><td>6/41</td><td></td><td></td></tr><tr><td>N<sup>l</sup><sub>a</sub></td><td></td><td>304</td><td>304/3188</td><td></td><td></td></tr><tr><td>RMS<sup>l</sup></td><td>kHz</td><td>1.97</td><td>1.95/117.84</td><td></td><td></td></tr><tr><td>WRMS<sup>l</sup></td><td>Unitless</td><td>0.98</td><td>0.97/1.18</td><td></td><td></td></tr></tbody></table>

<sup>a</sup> A, B and C in the ground state have been calculated at the “hybrid” level extrapolated at the CBS limit (see section computational methods for details). The centrifugal distortion constants $\Delta_J$, $\Delta_{JK}$, $\Delta_{KJ}$, $\delta_J$ and $\delta_K$ have been calculated at the MP2/CBS level. The NQC constants $\chi_{aa}$, $\chi_{bb}$ and $\chi_{cc}$ have been calculated at the B98/cc-pVQZ level. The internal rotation constants F and $\rho$ have been estimated from A, B, C at the “hybrid” level and direction cosines $\lambda_a$ and $I_a$ estimated from the MP2/cc-pVQZ equilibrium structure. The $-\text{CH}_3$ internal rotation barrier $V_6$ have been calculated (ZPE corrected) at the MP2/CBS level. In all cases, the choice of the method is discussed in Ref. [17].

<sup>b</sup> $P_{aa}$, $P_{bb}$, $P_{cc}$ are the components of the overall rotation angular momentum, $\rho_a$, is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle $\alpha$ and $f(I, J, F)$ is the Casimir function. {u, v} is the anti-commutator equal to: $uv + vu$. The product of the parameter and operator from a given row yields the term actually used in the vibration-rotation-torsion Hamiltonian, except for F, $\rho$, and A, which occur in the Hamiltonian in the form $F(p_{\alpha} - \rho p_{\alpha})^2 + AP_{\alpha}^2$. Like the internal axis of $CH_3$ is colinear with the a-axis, the RAM and PAM constants are equivalent.

<sup>c</sup> Recalculated from $A - \frac{B+C}{2}$, $\frac{B+C}{2}$ and $\frac{B-C}{2}$, note that these constants defined in RAM are the same in PAM because the internal rotation axis i is coaxial with the a axis.

<sup>d</sup> Recalculated from $\chi_{aa} + \chi_{bb} + \chi_{cc} = 0$ ($z = a, x = b, y = c$), the standard deviation of $\chi_{bb}$ is calculated from the standard deviation of $\chi_{aa}$ and $\chi_{cc}$.

<sup>e</sup> Recalculated from the fit of $-2\rho F$.

<sup>f</sup> Fixed to the calculated value.

<sup>g</sup> The $\langle i, a \rangle$ defined as the Euler angle $\delta$ which is the angle between the internal rotation axis i and the principal axis z = a.

<sup>h</sup> $I_a$ is the inertia moment related to the $-\text{CH}_3$ internal top derived from $F = h^2/2rl_a$ in RAM36hf (see Eq. 2). $\Delta l'' = l_c - l_b - l_a$ is the inertia defect related to the rotation of the molecular frame.

<sup>i</sup> Number of fitted a-type transitions.

<sup>j</sup> RMS and WRMS are the standard and the unitless standard deviations of the fit defined as: and with N the numbers of fitted lines and $\Delta_J$, the experimental error.

<figure><img src="image_15.png" /></figure>
<figure><img src="image_16.png" /></figure>

### 2.1.2. 2-Nitrotoluene

With the support of the quantum chemistry calculations presented in detail in supporting information (table S2), the jet-cooled MW spectrum (see section experimental methods) have been analysed up to $J' = 9$ and $K_a'' = 5$ taking into account both the internal rotation of the methyl group and the NQC effects. The A species were preliminary assigned identically to the 4-NT analysis, using the SPFIT/SPCAT Pickett's programs[19] (semi-rigid rotor model in the I' representation of A-reduced Watson's Hamiltonian). Then, the E species arising from internal rotation coupling of -CH₃ were assigned using the BELGI-C₅-hyperfine code, which is a slightly modified version of the BELGI-C₁-hyperfine code allowing to treat internal rotation effects with hyperfine structure for molecules with a planar frame.[26,27] Note that no c-type transitions were observed, which would have been consistent with a permanent dipole lying in the (a,b) plane in a C₁ structure (see Figure 4). In addition to the

internal rotation splittings due to the -CH₃ group, additional splittings, likely due to the large amplitude motion (LAM) of the -NO₂ group have been observed in the 2-NT spectrum: 48 hyperfine components corresponding to 16 rotational transitions have been identified (see Table S3 of supplementary information II). Due to their limited number, these lines resulting from the -NO₂ torsion splitting were not included in the fit. Moreover, these splittings were very small (of about a few kHz to a few dozen of kHz, see Figure 5) and they were not always resolved.

The observed splittings for internal rotation coupling, NQC and Doppler doublets are small and very close, typically tens of kHz (see Figure 5), which leads to many overlapped signals. As a consequence, it was not possible to reach the experimental accuracy of 2 kHz for isolated lines, but a reasonable fit have been obtained considering 282 blended lines assigned to 390 transitions up to $J' = 10$ and $K_a'' = 5$, including 197 A species and 193 E species with a RMS deviation of 3.4 kHz. The

<figure><img src="image_17.png" /><figcaption>**Figure 4.** 2-NT geometry in the principal axis orientation optimized at the MP2/cc-pVQZ level of theory, (a) is a representation in the (ab) plane and (b) is tilted to show the out-of-plane -NO₂.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 5.** Experimental MW rotational lines of 2-NT for two *R*-type transitions: (a) 5<sub>23</sub>→4<sub>22</sub> (200 coadded scans) and (b) 7<sub>34</sub>→6<sub>33</sub> (500 co-added scans). Doppler doublets have been assigned in the *F'*→*F''* format for hyperfine transitions. The internal rotation splittings corresponding to the -CH3 internal rotation are identified in red for the A species and in blue for the E species. Additional splitting identified in green can be associated to the -NO₂ internal rotation.</figcaption></figure>

<figure><img src="image_19.png" /></figure>
<figure><img src="image_20.png" /></figure>

complete set of molecular costants resulting from the analysis
of 2-NT spectrum with the BELGI-C<sub>s</sub>-hyperfine are presented in
the supplementary Table S3 of supplementary information I.
They are compared with quantum chemistry calculations in
Table 2 after transformation from the Rho Axis Method (RAM)
to the Principal Axis Method (PAM). Thirteen parameters were
floated, the three rotational constants (A, B, C), four centrifugal
distortion constants (Δ<sub>j</sub>, Δ<sub>jk</sub>, Δ<sub>K</sub>, δ<sub>K</sub>), the potential barrier height
V<sub>3</sub>, two higher order parameters c<sub>1</sub> and k<sub>2</sub> (see Table S3), the D<sub>ab</sub>
parameter and two NQC terms, χ<sub>aa</sub> and χ<sub>cc</sub>. The χ<sub>ab</sub> NQC term
was kept fixed to a value estimated from ab initio calculations
and the other non-diagonal NQC terms were set to zero. Other
parameters, such as the quartic centrifugal distortion term δ<sub>j</sub> or
higher order torsion-rotational parameters, were not well
determined and they did not improve the fit, so we set their
values to zero. While the RMS deviation is close to the
experimental accuracy for the fit using the BELGI-C<sub>s</sub>-hyperfine
code, we noticed that the rotational constants and the NQC
constants differ from their values obtained from quantum
chemical calculations. On the contrary, the floated torsional
parameters V<sub>3</sub>, the derived inertia moment I<sub>ia</sub> of the –CH<sub>3</sub> group
and the δ Euler angle are rather good agreement with those
calculations, showing that the assigned splittings correspond to
the –CH<sub>3</sub> internal rotation. Another fit was performed using the
XIAM program<sup>[28,29]</sup> with the same line assignments. As shown in
Table 2, the XIAM fit gives a RMS deviation of 3.5 kHz similar to
the one obtained with the BELGI-C<sub>s</sub>-hyperfine code. But with
XIAM, the rotational and NQC parameters are in rather good

agreement with the calculated values, while the values of the *F*
internal rotation constant and *ρ* derived by XIAM are very
different (see discussion section 2.3 which explains why the two
fits complement each other).

Concerning the 2-NT room temperature mm-wave spec-
trum, the semi-rigid asymmetric rotor description of SPFIT/
SPCAT Pickett's programs[19] was sufficient to carry out an
analysis without considering any of the LAMs, internal rotation
of –CH₃ or –NO₂ torsion. Indeed with such high barriers
hindering these LAM motions, the line splittings are not
resolved at the mm-wave spectrometer resolution. A total of
10746 transitions of A species corresponding to 7504 blended
lines have been assigned up to J" = 187 and K"a = 84 using
combination differences and the ASCP/SVIEW graphical inter-
face of the AABS Package.[24,25] The global fit including only the
MW and mm-wave A species allows to reproduce the spectra in
the vibrational ground state with a very good unitless RMS of
1.03. The Figure 6 shows the good agreement between
observed and simulated spectra in different parts of the mm-
wave spectra. The molecular constants resulting from the mm-
wave analysis of 2-NT using the SPFIT/SPCAT code are
presented in Table 2. We can see that the mm-wave analysis
allowed to improve the description of the semi-rigid rotor
model including the determination of the two quartic constants
kept fixed in the MW fit and all the sextic constants accurately
determined.

<figure><img src="image_21.png" /><figcaption>**Figure 6.** Part of the 70–330 GHz experimental mm-wave spectrum of 2-NT compared to the simulated spectrum obtained from the fit (see section 4.2): (a) is the 165 GHz–215 GHz experimental spectrum (black); (b) is the global simulated spectrum for the $v=0$ ground state (orange). Some characteristics patterns of 2-NT are presented in (c), (d) and (e) with the individual frequencies calculated from the fit (red).</figcaption></figure>

<figure><img src="image_22.png" /></figure>
<figure><img src="image_23.png" /></figure>

<table><caption>**Table 2.** Ground state torsion-rotation constants of the 2-NT obtained from the MW fit of A and E species (with BELGI-Cs-hyperfine and XIAM) and semi-rigid rotor constants obtained from the mm-wave/MW global fit of the A species (with SPFIT/SPCAT) are compared with quantum chemistry calculations. The numbers in parentheses represent one standard deviation in units of the least significant digit.</caption><thead><tr><th></th><th>Unit</th><th>BELGI-Cs-hyperfine<br>MW<br>(A and E species)</th><th>XIAM<br>MW<br>(A and E species)</th><th>SPFIT/SPCAT<br>MW/mm-wave<br>(A species)</th><th>Calc.<sup>a</sup></th><th>Operator<sup>b</sup></th></tr></thead><tbody><tr><td>A</td><td>MHz</td><td>2205.4(137)<sup>c</sup></td><td>2265.16372(68)<sup>d</sup></td><td>2265.168753(101)</td><td>2268.664</td><td>p<sup>2</sup><sub>a</sub></td></tr><tr><td>B</td><td>MHz</td><td>1220.4(145)<sup>c</sup></td><td>1247.2475(57)<sup>d</sup></td><td>1247.2185033(268)</td><td>1240.220</td><td>p<sup>2</sup><sub>b</sub></td></tr><tr><td>C</td><td>MHz</td><td>829.32(45)<sup>c</sup></td><td>834.2319(56)<sup>d</sup></td><td>834.2641880(166)</td><td>841.059</td><td>p<sup>2</sup><sub>c</sub></td></tr><tr><td>Δ<sub>J</sub></td><td>kHz</td><td></td><td>0.06105(41)</td><td>0.06012280(211)</td><td>0.05899</td><td>-p<sup>4</sup></td></tr><tr><td>Δ<sub>JK</sub></td><td>kHz</td><td></td><td>-0.0461(41)</td><td>-0.0347652(184)</td><td>-0.0239</td><td>-p<sup>2</sup>p<sup>2</sup><sub>a</sub></td></tr><tr><td>Δ<sub>K</sub></td><td>kHz</td><td></td><td>0.17906<sup>f</sup></td><td>0.185629(143)</td><td>0.17906</td><td>-p<sup>4</sup><sub>a</sub></td></tr><tr><td>δ<sub>J</sub></td><td>kHz</td><td></td><td>0.01148<sup>f</sup></td><td>0.01147527(99)</td><td>0.01148</td><td>-2p<sup>2</sup>(p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>)</td></tr><tr><td>δ<sub>K</sub></td><td>kHz</td><td></td><td>0.2009(41)</td><td>0.1926039(218)</td><td>0.18765</td><td>-{p<sup>2</sup><sub>a</sub>, (p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>)}</td></tr><tr><td>Φ<sub>J</sub></td><td>mHz</td><td></td><td></td><td>-0.010579(78)</td><td></td><td>p<sup>6</sup></td></tr><tr><td>Φ<sub>JK</sub></td><td>mHz</td><td></td><td></td><td>0.07526(100)</td><td></td><td>p<sup>4</sup>p<sup>2</sup><sub>a</sub></td></tr><tr><td>Φ<sub>KJ</sub></td><td>mHz</td><td></td><td></td><td>-0.5100(38)</td><td></td><td>p<sup>2</sup>p<sup>4</sup><sub>a</sub></td></tr><tr><td>Φ<sub>K</sub></td><td>mHz</td><td></td><td></td><td>1.0309(299)</td><td></td><td>p<sup>6</sup><sub>a</sub></td></tr><tr><td>φ<sub>J</sub></td><td>mHz</td><td></td><td></td><td>-0.010187(38)</td><td></td><td>2p<sup>4</sup>(p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>)</td></tr><tr><td>φ<sub>JK</sub></td><td>mHz</td><td></td><td></td><td>-0.07722(57)</td><td></td><td>p<sup>2</sup>[p<sup>2</sup><sub>a</sub>(p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>) + (p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>)p<sup>2</sup><sub>a</sub>]</td></tr><tr><td>φ<sub>K</sub></td><td>kHz</td><td></td><td></td><td>1.1609(42)</td><td></td><td>[p<sup>4</sup><sub>a</sub>(p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>) + (p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>)p<sup>4</sup><sub>a</sub>]</td></tr><tr><td>χ<sub>aa</sub></td><td>MHz</td><td>-1.077(21)<sup>e</sup></td><td>-1.1518(32)<sup>e</sup></td><td>-1.15068(256)</td><td>-1.3381</td><td>2p<sup>2</sup><sub>a</sub>(f(I, J, F)/J(J + 1))</td></tr><tr><td>χ<sub>bb</sub></td><td>MHz</td><td>0.340(25)<sup>e</sup></td><td>0.4151(49)<sup>e</sup></td><td>0.41417(58)</td><td>0.1788</td><td>2p<sup>2</sup><sub>a</sub>(f(I, J, F)/J(J + 1))</td></tr><tr><td>χ<sub>cc</sub></td><td>MHz</td><td>0.7367(38)<sup>e</sup></td><td>0.7367(16)<sup>e</sup></td><td>0.73651(316)</td><td>1.1593</td><td>2p<sup>2</sup><sub>c</sub>(f(I, J, F)/J(J + 1))</td></tr><tr><td>F</td><td>cm<sup>-1</sup></td><td>5.464<sup>f</sup></td><td>0.711<sup>g</sup></td><td></td><td>5.464</td><td>p<sup>2</sup><sub>α</sub></td></tr><tr><td>ρ</td><td>unitless</td><td>0.01000<sup>f</sup></td><td>0.08386<sup>g</sup></td><td></td><td>0.01085</td><td>p<sup>2</sup>p<sup>2</sup></td></tr><tr><td>V<sub>3</sub></td><td>cm<sup>-1</sup></td><td>686.3(34)</td><td>672(48)</td><td></td><td>645</td><td>(1/2)(1 - cos(3α))</td></tr><tr><td>Dpi2-</td><td>MHz</td><td></td><td>0.00078(7)<sup>h</sup></td><td></td><td></td><td>(p<sub>α</sub> - ρP<sub>r</sub>)<sup>2</sup>(p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>) + (p<sup>2</sup><sub>b</sub> - p<sup>2</sup><sub>c</sub>)(p<sub>α</sub> - ρP<sub>r</sub>)<sup>2</sup></td></tr><tr><td>δ<sup>i</sup></td><td>rad</td><td>0.9251(113)</td><td>0.9678(277)</td><td></td><td>1.0655</td><td></td></tr><tr><td>I<sub>α</sub><sup>j</sup></td><td>amu.Å<sup>2</sup></td><td>3.115034(47)</td><td>25.8(18)</td><td></td><td>3.122</td><td></td></tr><tr><td>Δl''<sup>i</sup></td><td>amu.Å<sup>2</sup></td><td>-33.9(60)</td><td>-22.5031(22)</td><td>-22.5354788(66)</td><td>-29.372</td><td></td></tr><tr><td>J''</td><td></td><td>9</td><td>9</td><td>9/187</td><td></td><td></td></tr><tr><td>K''<sub>a</sub></td><td></td><td>5</td><td>5</td><td>5/84</td><td></td><td></td></tr><tr><td>N''<sub>a</sub><sup>k</sup></td><td></td><td>300</td><td>300</td><td>300/10746</td><td></td><td></td></tr><tr><td>N''<sub>b</sub></td><td></td><td>90</td><td>90</td><td>90/0</td><td></td><td></td></tr><tr><td>RMS<sup>l</sup></td><td>kHz</td><td>3.4</td><td>3.5</td><td>3.7/82.8</td><td></td><td></td></tr><tr><td>WRMS<sup>l</sup></td><td>unitless</td><td>1.7</td><td>1.7</td><td>1.9/1.03</td><td></td><td></td></tr></tbody></table>

<sup>a</sup> A, B and C in the ground state have been calculated at the "hybrid" level extrapolated at the CBS limit. The centrifugal distortion constants Δ<sub>J</sub>, Δ<sub>JK</sub>, Δ<sub>K</sub>, δ<sub>J</sub> and δ<sub>K</sub> have been calculated at the MP2/CBS level. The NQC constants χ<sub>aa</sub>, χ<sub>bb</sub> and χ<sub>cc</sub> have been calculated at the B98/cc-pVQZ level. The internal rotation constants F and ρ have been estimated from A, B, C at the "hybrid" level and direction cosines λ<sub>g</sub> and l<sub>α</sub> estimated from the MP2/cc-pVQZ equilibrium structure. The -CH<sub>3</sub> internal rotation barrier V<sub>3</sub> is obtained from the 2D-PES along the two torsional angles (CH<sub>3</sub> and NO<sub>2</sub>) calculated at the MP2/cc-pVTZ in the adiabatic path (see section 2.3 for more details).

<sup>b</sup> P<sub>α</sub>, P<sub>J</sub>, P<sub>c</sub> are the components of the overall rotation angular momentum, p<sub>α</sub> is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle α, P<sub>r</sub> is the angular momentum vector along the ρ axis (only used in XIAM) and f(I, J, F) is the Casimir function. {u, v} is the anti-commutator equal to: uv + vu. The product of the parameter and operator from a given row yields the term actually used in the vibration-rotation-torsion Hamiltonian, except for F, ρ, and A, which occur in the Hamiltonian in the form F(p<sub>α</sub> - ρp<sub>a</sub>)<sup>2</sup> + AP<sub>α</sub><sup>2</sup>.

<sup>c</sup> Recalculated from RAM to PAM using the D<sub>ab</sub> operator (off-diagonal element of the inertial tensor in RAM system) fitted with the BELGI-Cs-hyperfine code.[26]

<sup>d</sup> Recalculated from the fitted constants B<sub>J</sub> = B<sub>g</sub>/2, B<sub>K</sub> = B<sub>z</sub> - B<sub>g</sub>/2 and B<sub>-</sub> = B<sub>g</sub>/2 in XIAM in the I<sup>2</sup> representation (z=a, x=b, y=c).

<sup>e</sup> χ<sub>aa</sub> and χ<sub>cc</sub> have been fitted and χ<sub>bb</sub> calculated from χ<sub>aa</sub> + χ<sub>bb</sub> + χ<sub>cc</sub> = 0. The BELGI-Cs-hyperfine NQC constants have been converted in PAM with a calculated non diagonal χ<sub>ab</sub> kept fixed in RAM. The XIAM constants are recalculated from χ<sub>zz</sub> and χ<sub>-</sub> = χ<sub>αα</sub> - χ<sub>αγ</sub>/2 with χ<sub>xx</sub> + χ<sub>yy</sub> + χ<sub>zz</sub> = 0.

<sup>f</sup> Fixed values estimated from the calculated value.

<sup>g</sup> Derived from the fitted values of F<sub>0</sub> = 19.6(14) GHz, of the rotational constants (A, B, C) and of the δ = ∠(i, a) Euler angle (see Eq.(2)).

<sup>h</sup> Internal rotation overall-rotation distortion constant defined in XIAM.

<sup>i</sup> The ∠(i, a) defined as the Euler angle δ which is the angle between the internal rotation axis i and the principal axis z = a. In BELGI-Cs-hyperfine, δ is obtained from tan∠(i, a) = λ<sub>g</sub>/λ<sub>α</sub> = l<sub>g</sub>/l<sub>α</sub> tanθ<sub>RAM</sub> with tan(2θ<sub>RAM</sub>) = 2D<sub>ab</sub>/B<sub>RAM</sub>-A<sub>RAM</sub> obtained from the fit of D<sub>abr</sub> B and A in RAM.

<sup>j</sup> The inertia moment l<sub>α</sub> related to the -CH<sub>3</sub> internal top is calculated from F = h<sup>2</sup>/2rl<sub>α</sub> in BELGI-Cs-hyperfine (see Eq. (2)), and from F<sub>0</sub> = h<sup>2</sup>/8π<sup>2</sup>crl<sub>α</sub> = 0.654 (47) cm<sup>-1</sup> in XIAM. Δl'' = l<sub>c</sub> - l<sub>b</sub> - l<sub>α</sub> is the inertia defect related to the rotation of the molecular frame.

<sup>k</sup> Number of fitted a-type and b-type transitions are presented as N<sub>a</sub> and N<sub>b</sub>.

<sup>l</sup> RMS and WRMS are the standard and the unitless standard deviations of the fit defined as: $\sqrt{\frac{1}{N} \sum_{i} (f_{i}^{\text{obs.}} - f_{i}^{\text{calc.}})^{2}}$ and with N the numbers of fitted lines and Δ<sub>i</sub> the experimental error.

<figure><img src="image_24.png" /></figure>
<figure><img src="image_25.png" /></figure>

## 2.2. Nuclear quadrupole coupling

The two largest diagonal NQC constants, i.e. $\chi_{aa}$ and $\chi_{cc}$, were used in the fit of 2-NT and 4-NT and the third diagonal constant ($\chi_{bb}$) and its uncertainty were retrieved according to the traceless NQC tensor. Concerning the off-diagonal $\chi_{ij}$ ($j \neq i$) terms, none were added in the fits because only the most intense $\Delta F = \Delta J$ transitions were measured, which are insensitive to the off-diagonal constant. The calculated NQC tensor of 2-NT $\chi_{ij}$ has been diagonalized in the principal axes system of the $^{14}$N nucleus (i. j = x, y, z) in order to link the NQC constants to the molecular geometry and to the electronic structure ($\chi_{ij} = eQ_{ij}$ with e the electric charge of the proton, Q the quadrupole moment and $Q_{ij}$ the molecular electric field gradient). Concerning the NQC tensor of 4-NT and the fitted NQC of 2-NT, the matrices were already diagonal and only identification of the NQC in the principal axis of the molecule to the principal axis of the nucleus was needed. The electric field gradient orientation can be evaluated using the asymmetry parameter $\eta$.[30] If the bond to the quadrupolar nucleus is axially symmetric ($\eta = 0$), it follows that $\chi_{xx} = \chi_{yy} = -\chi_{zz}/2$ due to the traceless coupling tensor and any deviation from axial symmetry reflects itself in a non-zero asymmetry parameter $\eta$. Therefore, a non-zero value of $\eta$ would indicate significant deviations of the electric field gradient from the usually admitted cylindrical symmetry around the z-axis (coincident with the C–N bond here).

As can be seen from Table 3, most of the experimental and calculated (B98/cc-pVQZ) values of the relevant NQC constants for the three NT isomers poorly agree. Although DFT calculations of NQC constants for nitrogen containing molecules are usually accurate,[31] none of the most studied species contains a nitro group, for which difficulties were pointed out in an early study[32] and in the case of 3-NT.[17] Adding to this the rather complex treatment of an internal rotor, NQC results for the present species should be considered carefully. However, based on relative considerations only (i.e. considering that errors made are roughly the same for the three isomers), a strong isomeric dependence of the $\eta$ parameter is observed with the experimental values while the calculated values are roughly the same. Indeed, experimental $\eta$ increases as the methyl group

gets farther from the nitro group (0.28, 0.45 and 0.55 for 2-NT, 3-NT and 4-NT, respectively) and thus converging to the calculated values (around 0.9 for the three isomers). For any reason difficult to assess, the influence of the methyl group on the electric field gradient around the quadrupolar nucleus clearly depends on the relative position of the functional groups in the benzene ring and this effect is not taken into account by the calculations.

## 2.3. Interaction between –CH₃ and –NO₂ in 2-NT

### 2.3.1. Anisotropic behaviour with a back-and-forth movement

The interaction between –CH₃ and –NO₂ has to be considered in the 2-NT “ortho” isomer, which appears as a peculiar case because of the immediate proximity of the two functional groups. Indeed, the equilibrium structure with the two groups tilted out the benzene plane, the surprisingly low barrier to –NO₂ internal rotation and the discrepancies between the values determined for the rotational and torsional parameters from our XIAM or BELGI-C₅-hyperfine fits compared to quantum chemical calculations are pointing toward some interaction between the torsional modes of these two groups. For these reasons, an exploration of the two-dimensional potential energy surface (2D-PES) along the two torsional angles has been performed at the MP2/cc-pVTZ level by mean of a relaxed scan procedure along C₃–C₂–C₁–H₁ dihedral angle at a given (fixed) value of the C₂–C₃–N₁–O₂ dihedral angle with 5° steps. To reduce the calculation time, scans were set to cover a 120° rotation of –CH₃ and a 180° rotation of –NO₂ and were then symmetrically expand to plot the complete surface (360°×360°) as shown in Figure 7 bottom-left panel. As expected, a standard 3-fold potential is observed along the –CH₃ rotation (equivalent minima and maxima every 120°). We also retrieve the “twisted” equilibrium positioning: the reference H atom is neither in the plane of benzene nor perpendicular but at 45°, this highlights the steric hindrance between the two groups. The –NO₂ rotation is more surprising: two different sequences reproducible at 180° are observed. Indeed, as –NO₂ is also “twisted”,

<table><caption>**Table 3.** Fitted NQC constants $\chi_{ij}$ in the principal axes system (i, j=a, b, c) for the NT isomers (including 3-NT from Ref.[17]) resulting from their global fit including MW and mm-wave transitions. Diagonalized $\chi_{ij}$ in the principal axes system of the 14N nucleus (i, j=x; y; z) and asymmetry parameter $\eta$ have been calculated for each set of parameters with their differential uncertainties on the last digit. The NQC constants of 3-NT were determined in Ref. [17].</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Unit</th><th rowspan="2">Exp.</th><th colspan="2">2-NT</th><th colspan="2">3-NT</th><th colspan="2">4-NT</th></tr><tr><th>B98/cc-pVQZ</th><th>Exp.</th><th>B98/cc-pVQZ</th><th>Exp.</th><th>B98/cc-pVQZ</th></tr></thead><tbody><tr><td>χ<sub>aa</sub></td><td>MHz</td><td>-1.15068(256)</td><td>-1.3381</td><td>-1.0494(16)</td><td>-1.244</td><td>-1.1724(62)</td><td>-1.3557</td></tr><tr><td>χ<sub>bb</sub></td><td>MHz</td><td>0.41417(58)<sup>a</sup></td><td>0.1788</td><td>0.1986(91)<sup>a</sup></td><td>-0.082</td><td>0.262(19)<sup>a</sup></td><td>0.0387</td></tr><tr><td>χ<sub>cc</sub></td><td>MHz</td><td>0.73651(316)</td><td>1.1593</td><td>0.8507(20)</td><td>1.326</td><td>0.910(13)</td><td>1.317</td></tr><tr><td>χ<sub>ab</sub></td><td>MHz</td><td></td><td>0.1074</td><td>(-0.4106(31)</td><td>-0.388</td><td></td><td></td></tr><tr><td>χ<sub>ac</sub></td><td>MHz</td><td></td><td>-0.0164</td><td></td><td></td><td></td><td></td></tr><tr><td>χ<sub>bc</sub></td><td>MHz</td><td></td><td>-0.371</td><td></td><td></td><td></td><td></td></tr><tr><td>χ<sub>xx</sub></td><td>MHz</td><td>0.41417(58)</td><td>0.0610</td><td>0.3244(102)</td><td>0.036</td><td>0.262(19)</td><td>0.0387</td></tr><tr><td>χ<sub>yy</sub></td><td>MHz</td><td>0.73651(316)</td><td>1.2847</td><td>0.8507(20)</td><td>1.326</td><td>0.910(13)</td><td>1.317</td></tr><tr><td>χ<sub>zz</sub></td><td>MHz</td><td>-1.15068(256)</td><td>-1.3458</td><td>-1.17507(50)</td><td>-1.362</td><td>-1.1724(62)</td><td>-1.3557</td></tr><tr><td>η<sup>b</sup></td><td>unitless</td><td>0.2801(57)</td><td>0.909</td><td>0.4479(106)</td><td>0.947</td><td>0.5527(365)</td><td>0.943</td></tr></tbody></table>

<figure><img src="image_26.png" /></figure>

<footnote><sup>a</sup> Calculated according to $\chi_{aa} + \chi_{bb} + \chi_{cc} = 0$, standard deviation of $\chi_{bb}$ is calculated from the standard deviation of $\chi_{aa}$ and $\chi_{cc}$.</footnote>

<footnote><sup>b</sup> Asymmetry parameter $\eta = \frac{\chi_{xx} - \chi_{yy}}{\chi_{zz}}$.</footnote>
<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /><figcaption>**Figure 7.** 2-D PES along the two torsional angles (–CH₃ and –NO₂) calculated at the MP2/cc-pVTZ level. Bottom-left panel: surface map plot for a complete rotation of both torsional groups; calculations were performed to cover a 120° rotation of CH₃ and a 180° rotation of –NO₂ and then symmetrically expand to plot the complete surface. Top-right panel: top view in iso-surface format of an elementary area (120°–180°) of the surface between four equilibrium structures. Top-left panel: cuts of the PES for a 180° rotation of –NO₂ showing the adiabatic energy curve (in black) and the relaxed energy curve (in orange and green). Bottom-right panel: cuts of the PES for a 120° rotation of –CH₃ showing the adiabatic energy curve (in black) and the relaxed energy curve (in yellow).</figcaption></figure>

there is an equilibrium structure at 35° (and 215°) from the plane of benzene (denoted "eq") and its mirror image at 180–35=145° (and 325°) (denoted "mir"), strictly iso-energetic. However, this mirror image is only possible if the –CH₃ group rotates accordingly (going from 45° to 120–45=75°), once again highlighting the interaction between the two functional groups.

The top-right panel of Figure 7 shows a top view (iso-surface format) of an elementary area (120°×180°) of the surface between four equilibrium structures. We clearly see that the paths of least energy to go from one equilibrium position (bottom-left corner) to the other (top-left or bottom-right corners) involve the movement of the two groups, but in an anisotropic manner:

- The top-left panel of Figure 7 shows cuts of the PES for a 180° rotation of –NO₂: the adiabatic energy curve, i.e. the vertical line corresponding to –CH₃ kept fixed at 45° (in black), and the relaxed energy curve, i.e. following the minimum energy points with –CH₃ free to move (in orange

and green). The least energy (the latter) passes through the mirror image and therefore implies a non-negligible rotation of the –CH₃.

- The bottom-right panel of Figure 7 shows cuts of the PES for a 120° rotation of –CH₃: the adiabatic energy curve, i.e. the horizontal line corresponding to NO₂ kept fixed at 35 (in black), and the relaxed energy curve, i.e. following the minimum energy points with –NO₂ free to move (in yellow). In this case, the least energy (the latter) only implies a slight rotation of the –NO₂.

Figures 8a and 8b displays the relaxed energy curves, thus the least energy path, for a 180° rotation of –NO₂ and a 120° rotation of –CH₃; the dotted lines mark the variations of the angle of the –CH₃ and –NO₂ groups, respectively. The top panel shows the relevant molecular structures with in white the reference atoms considered for the measurement of dihedral angles compared to the plane of benzene. Denoting couples of angles as (CH₃, NO₂), the lowest energy path, starting from equilibrium (45°, 35°) towards the equivalent equilibrium (45°,

<figure><img src="image_29.png" /></figure>
<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /><figcaption>**Figure 8.** 2-NT lowest energy paths according to the –NO₂ (8a) and –CH3 (8b) LAMs and associated molecular structures. (a) Relaxed energy curve for a 180° rotation of –NO₂. The dotted lines separate the corresponding values of the angle of the –CH₃ group. The top panel shows the relevant molecular structures with in white the reference atoms considered for the measurement of dihedral angles compared to the plane of benzene. (b) Relaxed energy curve for a 120° rotation of –CH₃. The dotted lines separate the corresponding values of the angle of the –NO₂ group. The top panel shows the relevant molecular structures with in white the reference atoms considered for the measurement of dihedral angles compared to the plane of benzene.</figcaption></figure>

215°), goes through three remarkable states which may be described for the –NO₂ rotation (Figure 8a) as: (i) a “perpendicular” transition state (60°, 90°) = 604 cm⁻¹, (ii) an iso-energetic mirror image of the equilibrium (75°, 145°) and (iii) an “in plane” transition state (60°, 180°) = 233 cm⁻¹. While –NO₂ twists towards the perpendicular position, it leaves room for the methyl to take its symmetrical position. Then, after a 90° rotation, the opposite oxygen atom pushes the methyl towards

its mirror image such that it will have rotated by 35°. By continuing to twist to the equivalent position (+180°), –NO₂ pushes the methyl in an opposite rotation to bring it back to the initial position (45°) passing by the “in plane” transition state. The 180° rotation of –NO₂ is therefore accompanied by a back-and-forth movement of the methyl over an amplitude up to 35°.

<figure><img src="image_32.png" /></figure>
<figure><img src="image_33.png" /></figure>

Figure 8b displays the least energy path for a 120° rotation of –CH₃. In this case, the situation is more simple since, starting from equilibrium (45, 35) towards the equivalent position (165°, 35°), the path of least energy does not pass through a mirror image. The –CH₃ rotation over 120° is accompanied by a smaller back-and-forth movement of the nitro group, with an amplitude of 15°, inducing a rotation barrier of 553 cm⁻¹, slightly lower compared to the adiabatic path: 645 cm⁻¹. It is quite interesting to note that the experimental values for the barrier height hindering the –CH₃ internal rotation (V₃=672(48) cm⁻¹, and V₃=686.3(34) cm⁻¹ deduced from the fits of the XIAM code and the BELGI-Cs-hyperfine code, respectively) are in very good agreement (6% for BELGI-Cs-hyperfine and 4% for XIAM) with the *ab initio* barrier height calculated with the adiabatic path.

### 2.3.2. Discussion on the molecular parameters

The BELGI-Cs-hyperfine and XIAM fits have provided rotational constants with significant differences: 2.7%, 2.2%, 0.6% differences for A, B and C, respectively, if we compare the XIAM constants with respect to those of BELGI-Cs-hyperfine. Nevertheless, both fits and quantum chemical calculations provide a strong negative inertial defect $\Delta l^{[33]}$ induced by the out of plane tilted –NO₂ group. With a deviation of 1.5% for A, 1.6% for B, and 0.8% for C, the rotational constants obtained from the XIAM fit agree well with the A₀, B₀, C₀ constants calculated at the "hybrid" level (see section computational methods). In comparison, the rotational constants obtained from the BELGI-Cs-hyperfine code do not match so well (–2.9%, –1.6% and –1.4% for A, B and C, respectively). These differences are due to the fact that the XIAM and BELGI-Cs-hyperfine are based on two different models (see section methods to analyse the LAMs). As a consequence, different sets of parameters are used in XIAM and BELGI. Then, the conversion of some RAM parameters to PAM parameters is not unique and introduces some errors when trying to compare the parameters with each other. In the XIAM code, we note in Table 2 the very unusual values of the internal rotation parameter *F* of 0.711 cm⁻¹, corresponding to an extremely high value for the moment of the inertia of the –CH₃ top *l*<sub>α</sub> = 25.8(18) amu.Å² (instead of the "more classical" calculated value of 3.12 amu.Å² for a –CH₃), as well as the rather large value of the *ρ* parameter of 0.08386 which is around 8 times larger than the calculated value and that was used in the BELGI-Cs-hyperfine fit. Both *F* and *ρ* are non fitted parameters. They are derived in XIAM from Eq. (2) and from the Euler angle between the principal axis *a* and the internal axis of the top, (δ = ∠(*i*, *a*) = 0.9678(277) rad., see Table 2). Therefore, the *l*<sub>α</sub> XIAM value correspond to a "dummy" heavier internal top reflecting the influence of the –NO₂ internal rotation. On the other hand, in the BELGI-Cs-hyperfine code, we do not fit directly any angle. Instead, we float the *D*<sub>ab</sub> parameter which is related to the off-diagonal terms in the inertia tensor. The value for the δ = 0.9251(113) angle is obtained by diagonalizing this inertia tensor. Moreover, in the present study, with experimental data originating only from the ground torsional state *v*<sub>t</sub> = 0, the internal rotation parameters are highly correlated and we

have to fix the values of *F* and *ρ* to their calculated values. Finally, none of the codes used in this study take into account explicitly the coupling of a methyl internal rotation and the back-and-forth LAM motions of the –NO₂ group. With the 2-NT molecule, we are facing a rather complex case of coupled LAMs due to existence of two relatively high barrier of similar magnitude (672 cm⁻¹ for the three-fold potential V₃ of the CH₃ and 604 cm⁻¹ for the two-fold potential V₂ of the –NO₂).

## 2.4. Influence of the isomery on the methyl group internal rotation

Table 4 reports the –CH₃ internal rotation barrier constants V₃ and/or V₆ in mono-substituted toluene derivatives with various substituents in ortho (o-), meta (m-) and para (p-) positions determined experimentally in the literature by different spectroscopic techniques. For the ortho isomers, all the –CH₃ internal rotation barriers are rather high with V₃ constants of several hundreds of wavenumbers. The different V₃ values are consistent with a steric hindrance increasing more or less the barrier according to the close neighbouring functional group. Moreover, we can notice that only MW experiments have been performed for these ortho isomers allowing the sole determination of the V₃ constant and no higher order term such as V₆ is available. This can be explained by two reasons: (i) internal rotation splittings of rotational transitions in the excited torsional states are required to determine these higher order terms but the jet-cooled conditions prevent their observation and (ii) the internal rotation splittings are usually very small for high internal rotation barriers and are only resolved by Fabry-Pérot Fourier-transform microwave (FP-FTMW) experiments. For the meta and para isomers, the V₃ and/or V₆ barrier constants are very low and never exceed few tens of wavenumbers. Notably, few spectroscopic studies (mainly meta isomers analyses) determined both V₃ and V₆ in their description of the internal rotation potential. Only our 3-NT study combining jet cooled FP-FTMW and room temperature mm-wave data in Ref. [17] was able to determine both terms with a high degree of accuracy. Finally, most of the para isomers belong to the C₂ᵥ symmetry group, so the V₆ constants are solely fitted. The V₆ term in toluene reflects the difference in potential energy for a C-H bond of the methyl group lying in the ring plane or lying in a plane perpendicular to the ring plane.[34] Similar values for V₆ are found for p-chlorotoluene, p-fluorotoluene and p-toluidine. Interestingly the value for the V₆ term in 4-NT is almost 2.5 times bigger than for those species, showing that the methyl group barrier is sensitive to the existence of a –NO₂ resonance group located at the other part of the molecule versus a local symmetry effect at the methyl site itself. A V₃ potential appears when the C₂ᵥ symmetry is broken by a non symmetric substituent. One example is the para-tolualdehyde study where information on the broken C₂ᵥ symmetry by the aldehyde functional group at the top of the ring being transmitted to the methyl-group site at the bottom of the ring can be obtained by quantifying the influence of the aldehyde group on the internal rotation barrier seen by the methyl group.[34]

<figure><img src="image_34.png" /></figure>
<figure><img src="image_35.png" /></figure>

<table><caption>**Table 4.** V₃ and V₆ constants of mono-substituted toluene derivatives (ortho, meta and para isomers).</caption><thead><tr><th>Molecule</th><th>Substituent</th><th>V<sub>3</sub>°/cm<sup>-1</sup></th><th>V<sub>6</sub>°/cm<sup>-1</sup></th><th>Type of spectroscopy</th><th>Ref.</th></tr></thead><tbody><tr><td>o-chlorotoluene</td><td>-Cl</td><td>466.2(15)</td><td>-</td><td>MW</td><td>[56]</td></tr><tr><td>o-fluorotoluene</td><td>-F</td><td>227.28(2)</td><td>-</td><td>MW</td><td>[57]</td></tr><tr><td>o-toluidine</td><td>-NH<sub>2</sub></td><td>531(7)</td><td>-</td><td>MW</td><td>[58]</td></tr><tr><td><b>o-nitrotoluene</b></td><td><b>-NO<sub>2</sub></b></td><td><b>686.3(34)/672(48)<sup>a</sup></b></td><td>-</td><td><b>MW/mm-wave</b></td><td><b>This work</b></td></tr><tr><td>o-xylene</td><td>-CH<sub>3</sub></td><td>521(17)</td><td>-</td><td>MW</td><td>[59]</td></tr><tr><td>o-Tolunitrile</td><td>-CN</td><td>187.699(3)</td><td>-</td><td>MW</td><td>[29]</td></tr><tr><td>o-cresol (trans)</td><td>-OH</td><td>369.95(11)</td><td>-</td><td>MW</td><td>[60]</td></tr><tr><td>o-cresol (cis)</td><td>-OH</td><td>661.4(38)</td><td>-</td><td>MW</td><td>[60]</td></tr><tr><td>o-cresol-OD (trans)</td><td>-OD</td><td>371.046(40)</td><td>-</td><td>MW</td><td>[60]</td></tr><tr><td>o-cresol-OD (cis)</td><td>-OD</td><td>669.10(50)</td><td>-</td><td>MW</td><td>[60]</td></tr><tr><td>o-methylanisole</td><td>-OCH<sub>3</sub></td><td>444.48(42)</td><td>-</td><td>MW</td><td>[61]</td></tr><tr><td>m-chlorotoluene</td><td>-Cl</td><td>2.452/3.2398(50)<sup>d</sup></td><td>17.197(36)/-10.991<sup>d</sup></td><td>MW</td><td>[62]</td></tr><tr><td>m-fluorotoluene</td><td>-F</td><td>20.20(45)</td><td>-7.70(41)</td><td>electronic</td><td>[63]</td></tr><tr><td>m-toluidine</td><td>-NH<sub>2</sub></td><td>1.97(5)</td><td>-</td><td>MW</td><td>[58]</td></tr><tr><td><b>m-nitrotoluene</b></td><td><b>-NO<sub>2</sub></b></td><td><b>6.7659(24)</b></td><td><b>0.02333(22)</b></td><td><b>MW/mm-wave</b></td><td><b>Previous work<sup>[17]</sup></b></td></tr><tr><td>m-xylene</td><td>-CH<sub>3</sub></td><td>4.49(14)</td><td>-</td><td>MW</td><td>[64]</td></tr><tr><td>m-tolunitrile</td><td>-CN</td><td>14.1960(3)</td><td>-11<sup>e</sup></td><td>MW</td><td>[65]</td></tr><tr><td>m-cresol (trans)</td><td>-OH</td><td>3.2(2)</td><td>-13.88(15)</td><td>MW</td><td>[66]</td></tr><tr><td>m-cresol (cis)</td><td>-OH</td><td>22.44(7)</td><td>-11.2(8)</td><td>MW</td><td>[66]</td></tr><tr><td>m-cresol-OD (trans)</td><td>-OD</td><td>3.188(180)</td><td>-</td><td>electronic</td><td>[67]</td></tr><tr><td>m-cresol-OD (cis)</td><td>-OD</td><td>21.341(52)</td><td>-</td><td>electronic</td><td>[67]</td></tr><tr><td>m-tolualdehyde (cis)</td><td>-CHO</td><td>35.925(3)</td><td>-</td><td>MW</td><td>[68]</td></tr><tr><td>m-tolualdehyde (trans)</td><td>-CHO</td><td>4.64(3)</td><td>-</td><td>MW</td><td>[68]</td></tr><tr><td>m-methylanisole (cis)</td><td>-OCH<sub>3</sub></td><td>55.7693(90)</td><td>-</td><td>MW</td><td>[69]</td></tr><tr><td>m-methylanisole (trans)</td><td>-OCH<sub>3</sub></td><td>36.6342(84)</td><td>-</td><td>MW</td><td>[69]</td></tr><tr><td>toluene</td><td>-</td><td>none<sup>b</sup></td><td>4.83783988(48)</td><td>MW/mm-wave</td><td>[21]</td></tr><tr><td>p-chlorotoluene</td><td>-Cl</td><td>none<sup>b</sup></td><td>4.873(13)</td><td>MW</td><td>[70]</td></tr><tr><td>p-fluorotoluene</td><td>-F</td><td>none<sup>b</sup></td><td>4.8298(63)</td><td>MW</td><td>[71]</td></tr><tr><td>p-toluidine</td><td>-NH<sub>2</sub></td><td>none<sup>b</sup></td><td>±5.6<sup>e</sup></td><td>electronic</td><td>[72]</td></tr><tr><td><b>p-nitrotoluene</b></td><td><b>-NO<sub>2</sub></b></td><td><b>none<sup>b</sup></b></td><td><b>12.22(18)</b></td><td><b>MW/mm-wave</b></td><td><b>This work</b></td></tr><tr><td>p-xylene</td><td>-CH<sub>3</sub></td><td>none<sup>b</sup></td><td>10<sup>e</sup></td><td>electronic</td><td>[73]</td></tr><tr><td>p-tolunitrile</td><td>-CN</td><td>none<sup>b</sup></td><td>-10<sup>e</sup></td><td>electronic</td><td>[74]</td></tr><tr><td>p-cresol</td><td>-OH</td><td>18.39(3)</td><td>-7.3(6)</td><td>MW</td><td>[75]</td></tr><tr><td>p-tolualdehyde</td><td>-CHO</td><td>28.111(1)</td><td>-4.768(7)</td><td>MW</td><td>[34]</td></tr><tr><td>p-methylanisole</td><td>-OCH<sub>3</sub></td><td>49.6370(1)</td><td>-</td><td>MW</td><td>[76]</td></tr></tbody></table>

### 3. Conclusions

The rotational spectra of two TNT explosive taggants, the 2-NT and 4-NT, have been measured and analyzed by jet-FTMW and mm-wave room temperature rotational spectroscopies. Combined with quantum chemistry calculations, the MW study allowed to describe the lowest rotational energy levels of the molecules taking into account both the internal rotation coupling of the -CH₃ group and the NQC involved by the ¹⁴N nucleus in the -NO₂ group. In the mm-wave spectral domain, an important congestion of the rotational lines is mainly due to the presence of hot bands involving the low-lying vibrational modes populated at room temperature: most of the lines are blended, hyperfine structures and 2-NT internal rotation splittings are not resolved. Concerning the analysis of the MW and mm-wave spectra of 4-NT, larger internal rotation splittings have been observed with a low internal rotation barrier (V₆ = 12.22(18) cm⁻¹), the spin statistics has been calculated to reproduce the line intensities and the NQC have also

been analysed from the MW transitions. The analysis of 2-NT MW line splittings was particularly complicated and challenging due to the coupling of the neighboring -CH₃ and -NO₂ torsional motions characterized by two barriers with closed amplitudes (~680 cm⁻¹). Quantum chemistry calculations performed in this study have revealed an unexpected anisotropic behaviour with a back-and-forth movement of the methyl/nitro double torsion. The two different adiabatic internal rotation models BELGI-Cs-hyperfine and XIAM reproduce the splitting due to NQC and -CH₃ internal rotation close to the experimental accuracy but not those due to -NO₂ internal rotation observed only in 16 MW lines. Nevertheless, with such rather high internal rotation barriers, it was not necessary to take into account these internal rotation effects at the resolution of the frequency multiplication chain in order to reproduce the most intense mm-wave lines of the 2-NT vibrational ground state spectrum. From a fundamental point of view, the NT rotational analyses produced in this study and in Ref. [17] associated with other high-resolution spectroscopic studies explain

<figure><img src="image_36.png" /></figure>

<footnote>a the two values correspond to the barrier fitted with BELGI-Cs-hyperfine/XIAM code.</footnote>

<footnote>b because of the C₂v symmetry of the molecule.</footnote>

<footnote>c "-" if no value is explicitly given for V₃ or V₆.</footnote>

<footnote>d two fits have been performed in Ref.[62]: one with V₃ fixed to MP2/6-311++G(2d,2p) calculation, the other with V₆ fixed to the same level.</footnote>

<footnote>e values found in the literature without uncertainties.</footnote>
<figure><img src="image_37.png" /></figure>

the isomeric influence on the internal rotation barriers in the
mono-substituted toluene derivatives.

For future work it will be important to extend the multi-
dimensional coupling of LAMs in theoretical effective Hamil-
tonians models by taking into consideration a C₁ frame coupled
with two non equivalent LAMs in a gearing back-and-forth
motion. In the 2-NT mm-wave spectrum, it could allow to
analyse torsional splittings potentially resolved for higher tor-
sional levels (with v_t ≥ 1) in order to decrease the correlations
between various parameters in the Hamiltonian and to permit
the determination of higher order terms (V₆, V₉...) of the
potential hindering the internal rotation. From a more applied
point of view, mm-wave rotational lines list, produced for the
three NT isomers and provided in electronic supplementary
information II (see Tables S1, S2, S4 and S5), are crucial for a
future monitoring of these explosive taggants in realistic
conditions. As an example, the transition frequencies of the
strongest lines may be used for an unambiguous recognition of
the NT even in a vapor mixture with the different isomers (see
Figure S3 in supplementary information I). However, taking into
account the experimental difficulties to measure at room
temperature the rotational signatures of these weakly volatile
taggants, the ability to perform field measurements of NT vapor
traces requires important improvements of the mm-wave
spectrometers in terms of sensitivity. Nevertheless, recent
technological breakdowns based on intra-cavity techniques[35,36]
push the detection limits while preserving the incomparable
selectivity of the high-resolution mm-wave rotational spectro-
scopy.

Experimental and theoretical methods

Jet-cooled FP-FTMW spectroscopy

The 2-NT (liquid at 293K) and 4-NT (solid at 293K) have been purchased from Aldrich Chemistry with high level of purity (of ≥ 99%). The NT spectra have been measured in the MW region (2-20 GHz) using the FP-FTMW technique coupled to a pulsed supersonic jet.[37,38] A heated nozzle[39] allowed to mix the NT vapour with the carrier gas (neon) at a backing pressure of about 0.2 MPa. Temperatures ranging from 373 K to 393 K were found to optimize the S/N ratio depending on the amplitude of recorded lines. The mixture was introduced into the FP cavity through a series 9 General Valve pin hole nozzle (0.8 mm) at a repetition rate of 1.5 Hz. Jet-cooled molecules (T<sub>rot</sub> of a few K) were polarized within the supersonic expansion by a 2 µs pulse. The free-induction decay (FID) signal is recorded using heterodyne detection at 30 MHz, and is digitized at a repetition rate of 120 MHz on a 14 bit resolution electronic card. FID signals were accumulated between 50 and 1000 times, depending on the line intensity. After Fourier trans- formation of the average FID, rotational lines of the amplitude spectrum were observed as Doppler doublets due to the coaxial arrangement of the jet and the FP cavity. Each resonance frequency was measured as the average frequency of the two Doppler components. The spectral resolution is depending on the number of recorded points. The frequency grid was set to 1.8 kHz, which was found sufficient since the Doppler linewidths should be of several kHz. According to this value, the experimental accuracy of the MW measured lines was estimated to 2 kHz.

Room temperature mm-wave spectroscopy

The room temperature absorption spectra of NT isomers have been measured in the mm-wave region (70-330 GHz and 70-230 GHz for the 2-NT and 4-NT, respectively) using a frequency multiplication chain.[40] A continuous flow of 8 µbar of the sample, maintained by a roughing pumping, was passed through a 125 cm-long and 56 mm-diameter double path stainless steel absorption cell equipped with Teflon windows and probed by the radiation generated by a frequency multiplier chain (Virginia Diodes, Inc). Two off-axis parabolic mirrors are used to collimate the radiation into the cell and then to refocus it into a liquid helium cooled InSb bolometer. Compared to the previous single pass cell configuration detailed in Ref. [17] the double pass configuration developped by adding a rooftop mirror and a grid in Ref. [41] allowed to improve the S/N ratio of the molecular transitions. The spectra have been recorded in 2F frequency modulation by using a frequency modulation of 10 kHz, a modulation depth of 33 kHz, a time constant of 50 ms for the 140-330 GHz region recorded with the InSb bolometer and 200 ms for the 70-110 GHz range recorded with a Schottky diode. Frequency steps have been adjusted from 100 kHz to 150 kHz following the frequency dependence of the Doppler linewidth in the 70-330 GHz scanned range. A post treatment of the mm-wave spectra have been successfully applied with a low-pass FFT filter subtraction to simulate and remove the strong baseline variations arising from stationary waves between the source, the cell and the detector.[17] The obtained spectra are very dense, weak and complicated by the presence of rotational transitions in many low-lying vibrational states populated at room temperature and by the congestion of the lines which are mostly blended. The mm-wave line accuracy has been estimated to 80 kHz and 100 kHz for the 2-NT and 4-NT, respectively, according to the average S/N ratio of the measured lines.[42]

Computational methods

Geometries and symmetries

All geometries were fully optimized at the MP2 and B98 levels with a tight convergence criterion using Gaussian 16 rev B.01 software[43] on the computing cluster of PhLAM laboratory. The frozen-core approximation was used throughout. Extrapolations to complete basis set (CBS) for energies (including Zero Point Energy (ZPE) corrections) and rotational constants were performed using Dun-ning and coworkers formula[44] and correlation consistent basis set cc-pVXZ (X = D, T, Q).[45] Vibrational frequencies and ground state (ν = 0) rotational constants were calculated at the anharmonic level (VPT2 calculations as implemented in the Gaussian software)[46] with a tight SCF convergence criterion and the ultrafine integral grid option. Anharmonic corrections have been extrapolated from DFT (B98 functional) to the MP2 level following a method suggested by Barone et al.[47] and recently successful in the case of various systems,[48] including internal rotors[17,49] (denoted "hybrid" here-after, see Refs for details).

The geometry of 2-NT and 4-NT optimized at the MP2/cc-VQZ level of theory is presented in Figs. 1 and 4, respectively. A strong permanent dipole moment is expected for the two molecules with μ ≃ 4.8 D in the (a,b) plane for 2-NT (μ<sub>a</sub> ≃ 4.7 D and μ<sub>b</sub> ≃ 0.8 D) and μ ≃ 5.8 D along the a-axis for 4-NT. They are both prolate tops with a strong asymmetry for 2-NT (κ = −0.44) and a slight asymmetry for 4-NT (κ = −0.91). Concerning 2-NT, the equilibrium structure shows a G<sub>3</sub> permutation inversion (PI) symmetry with a C<sub>1</sub> frame and a C<sub>3v</sub> top for the methyl group. [50] This can be explained by a steric repulsion between the −CH<sub>3</sub> and −NO<sub>2</sub> which twists the −NO<sub>2</sub> out of the plane of the benzene ring (see Figure 4 (b)). For 4-

<figure><img src="image_38.png" /></figure>
<figure><img src="image_39.png" /></figure>

NT, the equilibrium structure calculated at the MP2/cc-pVQZ level of theory shows a G₁₂ PI symmetry with a C₂ᵥ molecular frame and a C₃ᵥ top for the methyl group. [20] In opposite to 2-NT and 3-NT, the G₁₂ symmetry of 4-NT leads to equivalent atoms and thus to a nuclear spin statistics which affect the intensity of the lines according to the (A1/A2, B1/B2, E1, E2) species of the G₁₂ PI group. The degeneracy has been determined considering four equivalent hydrogens with a nuclear spin of I=1/2 (permutations (H₄ ↔ H₅) and (H₆ ↔ H₇)), four equivalent carbons with I=0 (permutations (C1 ↔ C2) and (C3 ↔ C4)) and two equivalent oxygens with I=0 (permutations (O1 ↔ O2)) (see Figure 4 for the labels). For each equivalent atom, (2I + 1)(I + 1) symmetric and (2I + 1)I antisymmetric nuclear spin eigenfunctions have been identified using the G₁₂ PI group[20] and the total nuclear spin eigenfunction Ψₙₛ has been determined from the total (C1 ↔ C2)(C3 ↔ C4)(H₄ ↔ H₅)(H₆ ↔ H₇)(O1 ↔ O2) permutations. Finally, the statistical weight have been determined to (5, 3, 3, 5) from the Pauli principle application to Ψₜₜ = Ψₑℓ Ψᵥ vib Ψₜₜ Ψₙₛ which correspond to a symmetric total eigenfunction.

Internal rotation couplings

In order to have an initial prediction of the frequency splitting
arising from the internal rotation coupling of –CH₃, it was necessary
to estimate the main torsional parameters V(α), F and ρ. These
parameters correspond to the barrier height, the internal rotation
constant and a coupling constant between rotation and torsion,
respectively.[51] Firstly, the potential function V(α) can be expressed
as a Fourier series in terms of the torsional angle α and of the
number of equivalent positions n of the methyl group torsion:[51]

$$
V(\alpha) = \frac{1}{2} V_n \left(1 - \cos(n\alpha)\right) + \frac{1}{2} V_{2n} \left(1 - \cos(2n\alpha)\right) + \dots, \quad (1)
$$

The first term in Eq. 1 includes the barrier height V<sub>n</sub>, with n = 3 for 2-NT and n = 6 for 4-NT. The barrier height values were estimated at the MP2 level by optimizing the transition state of the methyl group rotation (QST2 method as implemented in Gaussian16), then extrapolated at the CBS limit and ZPE corrected from harmonic frequency calculations at equilibrium and transition state optimized geometries. A barrier of V<sub>3</sub> = 501 cm<sup>-1</sup> has been calculated for 2-NT and V<sub>6</sub> = 11.3 cm<sup>-1</sup> for the 4-NT. Then, the internal rotation constant F and the ρ<sub>g</sub> components (with g = a, b, c) of the ρ vector have been calculated from the principal moments of inertia of the molecule I<sub>g</sub>, the moment of inertia of the internal top I<sub>i</sub>, and the direction cosines λ<sub>g</sub> of the internal rotation axis i in the principal axis system (i.e. λ<sub>g</sub> = cos(θ<sub>i</sub>, g))) derived from the MP2/cc-pVQZ equilibrium structure with the expressions: [51]

$$
\rho_g = \lambda_g \frac{l_g}{l_g} \qquad F = \frac{n^2}{2rl_g} \qquad r = 1 - \sum_g \frac{\lambda_g^2 l_g}{l_g} \qquad (2)
$$

Additional calculations at the MP2/cc-pVTZ level have been
performed to calculate the internal rotation barrier height of the
–NO₂ group for the three isomers (transition state energy from
QST2 method). As for 3-NT, [17] the –NO₂ group of 4-NT can be
considered as rigid compared to the molecular frame with V₂=
1692 cm⁻¹ (ZPE corrected). For 2-NT, an unexpected value of V₂=
443 cm⁻¹ has been calculated, leading to a lower barrier than the 2-
NT –CH₃ internal rotation barrier. Considering the short distance
between –NO₂ and –CH₃ (close neighbors in the benzene ring), an
interaction between the two groups might be expected. Therefore,
the 2D-PES of total electronic energy has been calculated at the
MP2/cc-pVTZ level for a complete rotation of –CH₃ and –NO₂ with

steps of 5. As suggested by the equilibrium structure showing tilts
of the two functional groups out of the plane of benzene (see
Figure 4), a clear interaction between the two groups is evidenced
by the PES calculation (see section 2.3 for complete discussion).

Nuclear quadrupole coupling

Concerning the NQC of the electric field gradient tensor induced by the coupling with the ¹⁴N nuclear spin (I = 1) of 2-NT and 4-NT, large differences have been observed between MP2 and B98 results. This difference was also observed in the study of 3-NT with a nitrogen in NO₂ which behaves as if it is quadruply bonded to a dummy atom (equivalent to the two oxygen atoms) of lower electro-negativity.[17,52,53] Based on additional calculations at the B2PLYP, B3PW91 and MP2(full) levels of theory with specific basis-set, it was established for 3-NT in Ref. [17] that MP2 and MP2(full) failed in predicting correctly NQC constants, independently from the size of basis set. Considering that the Density Functional Theory (DFT) methods B2PLYP, B98 and B3PW91[31] can provide reliable results with relative uncertainties of few %, the hyperfine constants calculated at the B98/cc-pVQZ level of theory have been used for the analysis of the hyperfine splittings in MW spectra of 2-NT and 4-NT, as in the case of 3-NT.

Methods to analyse the LAMs

In the frame of the various methods which describe the LAMs
effects, effective rotation torsional Hamiltonian are set up in either
the PAM or in the RAM. The RAM allows us to eliminate at the zero
order certain coupling terms in the kinetic energy between the
internal angular momentum p<sub>α</sub> and the global rotational momen-
tum P, and to simplify the diagonalization of the Hamiltonian.<sup>[26,51]</sup>
This approach is used in the BELGI series of codes,<sup>[26,27,54,55]</sup> as well as
in the RAM36hf code<sup>[20,21]</sup> of which a version will be used in the 2-
NT and 4-NT spectra analyses, respectively. The molecular parame-
ters obtained by those two approaches can be transformed into the
PAM by an angle called θ<sub>RAM</sub>.<sup>[54]</sup> A first estimation of θ<sub>RAM</sub> can thus
be obtained from the ab initio equilibrium structure. In other codes
such as XIAM<sup>[28,29]</sup> (used also in the 2-NT study), the internal rotation
operator is also set up in the RAM but the eigenvalues and
molecular parameters are transformed back from the PAM via a
rotation about the Euler angles δ and γ' which have been firstly
estimated from the optimized equilibrium structure. The difference
between the XIAM code and the BELGI/RAM36 codes lies in the fact
that XIAM treats the A and E species of each torsional v<sub>t</sub> state set by
itself, with different sets of parameters for each v<sub>t</sub> state ("local
methods"), whereas BELGI/RAM36 treat all the torsional manifold v<sub>t</sub>
states from a given vibrational state together, and diagonalize the
matrix of the torsional-rotational Hamiltonian containing thus all
the interactions between the torsional states ("global methods").<sup>[26]</sup>

Acknowledgements

We thank Vadim Ilyushin from the Institute of Radio Astronomy of
NASU (Ukraine) for the modification of its RAM36hf code to extend
the energy level calculations from *J* = 100 to *J* = 180 for the mm-
wave spectral analysis of 4-NT and H. V. Lam Nguyen from the
Université Paris-Est Créteil & Université de Paris for her recom-
mendations and tests in the XIAM fit of 2-NT. Marc Fourmentin
from the Université du Littoral Côte d'Opale (LPCA) for the design
of the cover feature. We thank the PhD financial supports of A.
Roucou, i.e. the region Hauts-de-France and the French Délégation

<figure><img src="image_40.png" /></figure>
<figure><img src="image_41.png" /></figure>

Générale pour l'Armement (DGA), and the PhD financial supports of S. Bteich, i.e. the region Hauts-de-France and the Laboratory of Excellence CaPPA (Chemical and Physical Properties of the Atmosphere) funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissements d'Avenir) under Contract No. ANR-11-LABX-005-01. A. Roucou was funded by the "Groupe de Recherche GdR SPECMO" to visit I. Kleiner in LISA, Créteil. The mm-wave spectrometer has been supported by the French "Délégation Générale pour l'Armement" (Projet de Recherche Exploratoire et Innovation No. 06.34.037).

## Conflict of Interest

The authors declare no conflict of interest.

**Keywords:** Explosive taggart • Large amplitude torsions • Molecular dynamics • Nitrotoluene isomers • Rotational spectroscopy

[1] H. Östmark, S. Wallin, H. G. Ang, *Propellants Explos. Pyrotech.* **2012**, *37*, 12–23.

[2] D. S. Moore, *Rev. Sci. Instrum.* **2004**, *75*, 2499–2512.

[3] A. R. Krause, C. Van Neste, L. Senesac, T. Thundat, E. Finot, *J. Appl. Phys.* **2008**, *103*, 094906.

[4] M. Snels, T. Venezia, L. Belfiore, *Chem. Phys. Lett.* **2010**, *489*, 134–140.

[5] R. Prasad, R. Prasad, G. Bhar, S. Thakur, *Spectrochim. Acta Part A* **2002**, *58*, 3093–3102.

[6] A. G. Mercado, J. A. Janni, B. Gilbert, *SPIE Proc.* **1995**, *2511*, 142–152.

[7] D. Wu, J. P. Singh, F. Y. Yueh, D. L. Monts, *Appl. Optics* **1996**, *35*, 3998–4003.

[8] C. Mullen, A. Irwin, B. V. Pond, D. L. Huestis, M. J. Coggiola, H. Oser, *Anal. Chem.* **2006**, *78*, 3807–3814.

[9] H. Diez y Riega, R. Gunawidjaja, H. Eilers, *J. Photochem. Photobiol. A* **2013**, *268*, 50–57.

[10] Convention on the marking of plastic explosives for the purpose of detection, signed at montreal, on 1 march 1991 (monral convention 1991).

[11] Y. Chen, H. Liu, Y. Deng, D. B. Veksler, M. S. Shur, X.-C. Zhang, D. Schauki, M. J. Fitch, R. Osiander, C. Dodson, et al. *P. Soc. Photo.-Opt. Ins.* **2004**, *5411*, 1–9.

[12] S. Letzel, T. Göen, M. Bader, J. Angerer, T. Kraus, *Occup. Environ. Med.* **2003**, *60*, 483–488.

[13] A. Cuisset, S. Gruet, O. Pirali, T. Chamaillé, G. Mouret, *Spectroc. Acta A* **2014**, *132*, 838–845.

[14] A. Cuisset, I. Smirnova, R. Bocquet, F. Hindle, G. Mouret, C. Yang, O. Pirali, P. Roy, A. Predoi-Cross, B. E. Billinghurst, *AIP Proceedings* **2010**, *1214*, 85–87.

[15] M. Cirtog, P. Asselin, P. Soulard, B. Tremblay, B. Madebéne, M. E. Alikhani, R. Georges, A. Moudens, M. Goubet, T. R. Huet, O. Pirali, P. Roy, *J. Phys. Chem. A* **2011**, *115*, 2523–2532.

[16] P. Asselin, J. Bruckhuisen, A. Roucou, M. Goubet, M.-A. Martin-Drumel, A. Jabri, Y. Belkhodja, P. Soulard, R. Georges, A. Cuisset, *J. Chem. Phys.* **2019**, *151*, 194302.

[17] A. Roucou, I. Kleiner, M. Goubet, S. Bteich, G. Mouret, R. Bocquet, F. Hindle, W. L. Meerts, A. Cuisset, *ChemPhysChem* **2018**, *18*, 1056–1067.

[18] J. A. Widegren, T. J. Bruno, *J. Chem. Eng. Data* **2009**, *55*, 159–164.

[19] M. H. Pickett, *J. Mol. Spectrosc.* **1991**, *148*, 371–377.

[20] V. V. Ilyushin, Z. Kisiel, L. Pszczółkowski, H. Mäder, J. T. Hougen, *J. Mol. Spectrosc.* **2010**, *259*, 26–38.

[21] V. V. Ilyushin, E. A. Alekseev, Z. Kisiel, L. Pszczółkowski, *J. Mol. Spectrosc.* **2017**, *339*, 31–39.

[22] A. Belloche, A. A. Meshcheryakov, R. T. Garrod, V. V. Ilyushin, E. A. Alekseev, R. A. Motiyenko, L. Margulés, H. S. P. Müller, K. M. Menten, *Astron. Astrophys.* **2017**, *601*, A49.

[23] V. V. Ilyushin, *J. Mol. Spectrosc.* **2018**, *345*, 64–69.

[24] Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski, *J. Chem. Phys.* **1998**, *109*, 10263–10272.

[25] Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski, *J. Mol. Spectrosc.* **2000**, *199*, 5–12.

[26] I. Kleiner, *J. Mol. Spectrosc.* **2010**, *260*, 1–18.

[27] R. Kannengießer, W. Stahl, H. V. L. Nguyen, I. Kleiner, *J. Phys. Chem. A* **2016**, *120*, 3992–3997.

[28] H. Hartwig, H. Dreizler, *Z. Naturforsch. A* **1996**, *51*, 923–932.

[29] N. Hansen, H. M'ader, T. Bruhn, *Mol. Phys.* **1999**, *97*, 587–595.

[30] E. L. Hahn, T. P. Das, *Nuclear quadrupole resonance spectroscopy*. New York, Academic Press, **1958**.

[31] W. C. Bailey, *Chem. Phys.* **2000**, *252*, 57–66.

[32] M. H. Palmer, *Z. Naturforsch. A* **1996**, *51a*, 451–459.

[33] A. Jabri, D. Fontanari, A. Roucou, C. Bray, F. Hindle, G. Dhont, G. Mouret, R. Bocquet, A. Cuisset, *J. Chem. Phys.* **2019**, *150*, 104303.

[34] H. Saal, J.-U. Grabow, A. R. Hight Walker, J. T. Hougen, I. Kleiner, W. Caminati, *J. Mol. Spectrosc.* **2018**, *351*, 55–61.

[35] F. Hindle, R. Bocquet, A. Pienkina, A. Cuisset, G. Mouret, *Optica* **2019**, *6*, 1449.

[36] M. A. Koshelev, I. I. Leonov, E. A. Serov, A. I. Chernova, A. A. Balashov, G. M. Bubnov, A. F. Andriyanov, A. P. Shkaev, V. V. Parshin, A. F. Krupnov, M. Y. Tretyakov, *IEEE T. THZ Sci. Techn.* **2018**, *8*, 773–783.

[37] M. Tudorie, L. H. Coudert, T. R. Huet, D. Jegouso, G. Sedes, *J. Chem. Phys.* **2011**, *134*, 074314.

[38] S. Kassi, D. Petitprez, G. Wlodarczak, *J. Mol. Struct.* **2000**, *517*, 375–386.

[39] S. Kassi, D. Petitprez, G. Wlodarczak *J. Mol. Spectrosc.* **2004**, *228*, 293–297.

[40] G. Mouret, M. Guinet, A. Cuisset, L. Croize, S. Eliet, R. Bocquet, F. Hindle, *IEEE Sens. J.* **2013**, *13*, 133–138.

[41] A. Roucou, D. Fontanari, G. Dhont, A. Jabri, C. Bray, G. Mouret, R. Bocquet, A. Cuisset, *ChemPhysChem* **2018**, *19*, 1–8.

[42] M.-A. Martin-Drumel, F. Hindle, G. Mouret, A. Cuisset, J. Cernicharo, *Astrophys. J.* **2015**, *799*, 115.

[43] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseeman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidì, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, D. J. Fox, Gaussian 16 Revision B.01, **2016**. Gaussian Inc. Wallingford CT.

[44] D. E. Woon, T. H. Dunning Jr, *J. Chem. Phys.* **1994**, *101*, 8877–8893.

[45] R. A. Kendall, T. H. Dunning Jr, R. J. Harrison, *J. Chem. Phys.* **1992**, *96*, 6796–6806.

[46] V. Barone, *J. Chem. Phys.* **2005**, *122*, 014108.

[47] M. Bicyzko, P. Paneck, G. Scalmani, J. Bloino, V. Barone, *J. Chem. Theory Comput.* **2010**, *6*, 2115–2125.

[48] S. Grimme, M. Steinmetz, *Phys. Chem. Chem. Phys.* **2013**, *15*, 16031–16042.

[49] S. Bteich, M. Goubet, R. A. Motiyenko, L. Margules, T. R. Huet, *J. Mol. Spectrosc.* **2018**, *348*, 124–129.

[50] P. Bunker, *Molecular Symmetry and Spectroscopy*. Elsevier, **2012**.

[51] C. C. Lin, J. D. Swalen, *Rev. Mod. Phys.* **1959**, *31*, 841.

[52] A. P. Cox, S. Waring, K. Morgenstern, *Nature Phys.* **1971**, *22*, 22–23.

[53] J.-U. Grabow, *Handbook of high-resolution spectroscopy*, Vol. 2. John Wiley & Sons, Ltd, **2011**.

[54] J. T. Hougen, I. Kleiner, M. Godefroid, *J. Mol. Spectrosc.* **1994**, *163*, 559–586.

[55] I. Kleiner, J. T. Hougen, *J. Chem. Phys.* **2003**, *119*, 5505–5509.

[56] D. Gerhard, A. Hellweg, I. Merke, W. Stahl, M. Baudelet, D. Petitprez, G. Wlodarczak, *J. Mol. Spectrosc.* **2003**, *220*, 234–241.

[57] S. Jacobsen, U. Andresen, H. Mader, *Struct. Chem.* **2003**, *14*, 217–225.

[58] R. G. Bird, D. W. Pratt, *J. Mol. Spectrosc.* **2011**, *266*, 81–85.

[59] H. D. Rudolph, K. Walzer, I. Krutzik, *J. Mol. Spectrosc.* **1973**, *47*, 314–339.

[60] A. Welzel, A. Hellweg, I. Merke, W. Stahl, *J. Mol. Spectrosc.* **2002**, *215*, 58–65.

[61] L. Ferres, H. Mouhib, W. Stahl, H. V. L. Nguyen, *ChemPhysChem* **2017**, *18*, 1855–1859.

<figure><img src="image_42.png" /></figure>
<figure><img src="image_43.png" /></figure>

[62] K. P. Rajappan Nair, S. Herbers, A. Lesarri, J.-U. Grabow, *J. Mol. Spectrosc.* **2019**, *361*, 1–7.

[63] L. D. Stewart, J. R. Gascooke, W. D. Lawrance, *J. Chem. Phys.* **2019**, *150*, 174303.

[64] C. Thomsen, H. Dreizler, *Z. Naturforsch. A* **2001**, *56*, 635–640.

[65] T. Bruhn, H. Mäder, *J. Mol. Spectrosc.* **2000**, *200*, 151–161.

[66] A. Hellweg, C. Haettig, I. Merke, W. Stahl, *J. Chem. Phys.* **2006**, *124*, 204305.

[67] G. Myszkiewicz, W. L. Meerts, C. Ratzer, M. Schmitt, *Phys. Chem. Chem. Phys.* **2005**, *7*, 2142–2150.

[68] A. J. Shirar, D. S. Wilcox, K. M. Hotopp, G. L. Storck, I. Kleiner, B. C. Dian, *J. Phys. Chem. A* **2010**, *114*, 12187–12194.

[69] L. Ferres, W. Stahl, H. V. L. Nguyen, *J. Chem. Phys.* **2018**, *148*, 124304.

[70] G. E. Herberich, *Z. Naturforsch. A* **1967**, *22*, 761–764.

[71] J. Rottstegge, H. Hartwig, H. Dreizler, *J. Mol. Struct.* **1999**, *478*, 37–47.

[72] X.-Q. Tan and D. W. Pratt, *J. Chem. Phys.* **1994**, *100*, 7061–7067.

[73] P. J. Breen, J. A. Warren, E. R. Bernstein, J. I. Seeman, *J. Chem. Phys.* **1987**, *87*, 1917–1926.

[74] M. Fujii, M. Yamauchi, K. Takazawa, M. Ito, *Spectrosc. Acta A* **1994**, *50*, 1421–1433.

[75] A. Hellweg, C. Hättig, *J. Chem. Phys.* **2007**, *127*, 024307.

[76] L. Ferres, W. Stahl, I. Kleiner, H. V. L. Nguyen, *J. Mol. Spectrosc.* **2018**, *343*, 44–49.

Manuscript received: July 10, 2020

Revised manuscript received: August 27, 2020

Accepted manuscript online: August 28, 2020

Version of record online: ■■, ■■

<figure><img src="image_44.png" /></figure>
ARTICLES

**Anisotropic internal rotation coupling revealed in an explosive taggant:** The complete study of large amplitude torsions in nitrotoluene isomers by mean of high resolution microwave and mm-wave spectroscopy allowed to provide rotational line lists crucial for explosive taggants detection in gas phase. Quantum chemistry calculations performed on 2-NT has revealed an anisotropic back-and-forth internal rotation of –CH₃ and –NO₂.

<figure><img src="image_45.png" /></figure>

Dr. A. Roucou*, Dr. M. Goubet, Prof. I. Kleiner, Dr. S. Bteich, Prof. A. Cuisset*

1 – 17

**Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations**

<figure><img src="image_46.png" /></figure>