Approaching the free rotor limit: extremely low methyl torsional barrier observed in the microwave spectrum of 2,4-dimethylfluorobenzene

Abstract

The microwave spectrum of 2,4-dimethylfluorobenzene was recorded using a molecular jet Fourier transform microwave spectrometer in the frequency range from 2.0 to 26.5 GHz. The spectral assignment and modeling were challenging due to the large tunnelling splittings resulting from the very low barrier to internal rotation of the p-methyl group that approaches the free rotor limit. Internal rotation splittings arising from two inequivalent o- and p-methyl groups were observed, analysed and modelled using the modified version of the XIAM code and the BELGI-C_s-2Tops code, giving a root-mean-square deviation of 549.1 kHz and 4.5 kHz, respectively, for a data set of 885 rotational lines. The torsional barriers of the o- and p-methyl groups were determined to be 227.039(51) cm⁻¹ and 3.23(40) cm⁻¹, respectively. The V₃ barrier observed for the p-methyl group is lower than in any other para-methyl substituted toluene derivatives with coupled internal rotations, becoming the lowest value ever observed to date. The barrier to internal rotation of the o-methyl group next to a fluorine atom is consistently around 220 cm⁻¹, as confirmed by comparing it to barriers observed in other toluene derivatives. The experimental rotational constants were compared to those obtained by quantum chemical calculations.

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1 Introduction

Internal rotation of methyl groups is one of the most extensively studied Large Amplitude Motions (LAMs) in high resolution microwave spectroscopy. The analysis and modelling of this LAM have been always challenging, but become particularly difficult if the barrier hindering the methyl torsion is low, resulting in large splittings of rotational transitions. The lower the barrier, the more difficult the analysis, especially when the barrier approaches the free rotor limit (V₃ < 10 cm⁻¹).¹ Despite efforts dedicated to study the effects of methyl internal rotations hindered by low barriers, the number of investigations remains small, and they mainly concern methyl-substituted aromatic molecules.² The first aromatic molecule known to experience an extremely low-barrier is toluene^3–8 with a pure V₆ potential of 4.9 cm⁻¹. In some toluene derivatives featuring one methyl internal rotation with pure V₆ potential due to symmetry, the methyl torsion is hindered with a barrier height of less than 13 cm⁻¹, such as in p-fluorotoluene (4.8 cm⁻¹),⁹p-nitrotoluene (12.5 cm⁻¹),¹⁰ and p-chlorotoluene (4.8 cm⁻¹).¹¹ In many cases, a combination of V₃/V₆ is observed, i.e., 14.2/−11 cm⁻¹ for m-tolunitrile,¹² 18.4/−7.3 cm⁻¹ for p-cresol,¹³ 3.2/−13.9 cm⁻¹ for the anti-conformer of m-cresol,¹⁴ 7.9/−24.7 cm⁻¹ for p-toluic acid,¹⁵ and 6.8/0.023 cm⁻¹ for 3-nitrotoluene.¹⁶ In other cases, a pure V₃ term is sufficient to model the microwave spectrum, i.e., for the anti-conformer of m-methylbenzaldehyde (4.6 cm⁻¹),¹⁷ 3-methylphenylacetylene (11.4 cm⁻¹),¹⁸ 3-fluorotoluene (17.2 cm⁻¹),¹⁹ and the syn and anti-conformers of m-toluic acid (17.9 cm⁻¹ and 9.6 cm⁻¹, respectively).²⁰ The lowest V₃ barrier approaching the free rotor limit was obtained for m-toluidine with only 2.0 cm⁻¹.²¹

The low barrier problem becomes even more problematic if the molecules possess more than one methyl rotor, often coupled to each other. Only a few toluene derivatives featuring two methyl tops hindered by low barriers have been investigated. They are m-xylene (4.5 cm⁻¹),²² 3,5-dimethylbenzaldehyde (syn-m: 53.0 cm⁻¹ and anti-m: 25.3 cm⁻¹)²³ and 3,5-dimethylanisole (syn-m: 58.6 cm⁻¹ and anti-m: 36.1 cm⁻¹).²⁴ A few other six-membered rings exhibit two internal rotations hindered by different torsional barriers, an intermediate one and a very low one, such as the three isomers of dimethylanisole (2,5-,²⁴ 2,3-²⁵ and 2,4-dimethylanisole²⁶) and syn-2,5-dimethylbenzaldehyde.²³ In the case of syn-2,5-dimethylbenzaldehyde, Tudorie et al. reported an extremely low barrier of 5.4 cm⁻¹ for the m-methyl group and an intermediate barrier of 565.7 cm⁻¹ for the o-methyl group.

We have recently initiated a systematic investigation of the dimethylfluorobenzene family with the aim of studying the LAMs of two methyl groups. Our focus is on the sensitivity of the methyl torsional barrier to the steric and electrostatic surrounding. Studies on the microwave spectra of the 2,6-, 3,4- and 2,3-isomers^27–29 have shown the influence of steric effects, where the barrier to internal rotation of a methyl group adjacent to a fluorine atom is always around 220 cm⁻¹ and that of a methyl group adjacent to another methyl group is around 500 cm⁻¹. For the 2,3-isomer, the torsional barrier observed for the 2-methyl group cannot be explained by steric effects alone, and electrostatic effects within the conjugated double bond must be considered as well. To gain a deeper comprehension about the interplay between steric and electrostatic effects, we continued with 2,4-dimethylfluorobenzene (24DMFB) where the methyl group in the para position experiences no steric hindrance from surrounding and its torsional barrier of less than 4.0 cm⁻¹ approaches the free rotor limit.

2. Quantum chemical calculations

2.1. Geometry optimisations

All quantum chemical calculations were carried out with the Gaussian 16³⁰ package. The geometry optimisations were performed at the B3LYP-D3BJ/6-311++G(d,p), MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels of theory first. These three levels have been benchmarked for the 2,6, 3,4- and 2,3-isomers^27–29 to be the most suitable known levels that predict reliable rotational constants close to the experimental values and also yield accurate molecular structure parameters for many aromatic molecules containing methyl groups such as 5-methyl furfural,³¹ 2-acetyl-5-methylthiophene,³² 2,5-dimethylfuran³³ and 4-methyl-5-vinylthiazole.³⁴ The predicted dipole moment components and rotational constants are given in Table 1. Ground state rotational constants and quartic centrifugal distortion constants were obtained from anharmonic frequency calculations. The geometry of 24DMFB optimised at the B3LYP-D3BJ/6-311++G(d,p) level is illustrated in Fig. 1. The atomic Cartesian coordinates are given in Table S1 in the ESI.†

Table 1 Equilibrium rotational constants (A_e, B_e, C_e), vibrational ground state rotational constants (A₀, B₀, C₀), centrifugal distortion constants and dipole moment components calculated at the B3LYP-D3BJ/6-311++G(d,p), MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels of theory

Par.	Unit	B3LYP-D3BJ/6-311++G(d,p)	MP2/6-311++G(d,p)	MP2/6-31G(d,p)
A e	MHz	3001.7	2989.7	3013.0
B e	MHz	1282.4	1276.7	1279.2
C e	MHz	908.6	904.7	908.0
A 0	MHz	2976.1	2960.6	2986.6
B 0	MHz	1275.9	1270.5	1273.0
C 0	MHz	902.9	898.8	902.5
Δ J	kHz	0.02555	0.02553	0.02504
Δ JK	kHz	0.14677	0.06376	0.06551
Δ K	kHz	0.36802	0.45835	0.44972
δ J	kHz	0.00774	0.00776	0.00758
δ K	kHz	−0.31064	0.05164	0.04028
|μa|	D	1.7	1.6	1.4
|μb|	D	0.8	0.8	0.6
|μc|	D	0.0	0.0	0.0

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Fig. 1 Optimised molecular structure of 24DMFB obtained at the B3LYP-D3BJ/6-311++G(d,p) level of theory in the principal axes of inertia.

A large number of method-basis set combinations were used to optimise the structures of the 2,6-,²⁷ 2,3-²⁹ and 3,4-isomers.²⁸ Benchmark calculations are increasingly used to provide equilibrium rotational constants that facilitate the assignments of microwave spectra. Based on our previous results on the three investigated DMFB isomers, we continued our benchmarking efforts with calculations using the density functional methods B3LYP-D3,^35–37 B3LYP-D3BJ,³⁸ CAM-B3LYP-D3BJ,³⁹ PBE0,⁴⁰ ωB97X-D,⁴¹ MN15⁴² and M06-2X.⁴³ MP2⁴⁴ and coupled cluster CCSD⁴⁵ were used as ab initio methods. All methods except CCSD were combined with several Dunning⁴⁶ and Pople⁴⁷ basis sets. The obtained rotational constants are collected in Table S2 in the ESI.†

2.2. Methyl internal rotations

The LAMs of 24DMFB are complex since the molecule possesses two inequivalent internal rotors, the methyl groups in the ortho and para positions. To study these LAMs, the barriers to internal rotation were calculated at the three levels of theory used for geometry optimisations by varying the dihedral angles α₁ = ∠(C₃, C₂, C₇, H₁₂) and α₂ = ∠(C₅, C₄, C₈, H₁₅), corresponding to torsions about the C₂–C₇ and C₄–C₈ bonds, respectively. All other geometry parameters were reoptimised. The resulting potential energy points were parameterised with one-dimensional (1D) Fourier expansions. The obtained potential energy curves are presented in Fig. 2 and 3. The corresponding 1D Fourier coefficients used to plot the curves are given in Table S3 in the ESI.† For the o-methyl group, we found a three-fold V₃ potential with small V₆ contribution, i.e., 203.4 cm⁻¹ for B3LYP-D3BJ/6-311++G(d,p), 235.4 cm⁻¹ for MP2/6-311++G(d,p) and 202.6 cm⁻¹ for MP2/6-31G(d,p). For the p-methyl group, the ab initio predicted energy curves feature the characteristics of a six-fold potential, as shown in Fig. 3 and can be also recognised in Table S3 (ESI†) from the dominant V₆ terms. At the MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels, the predicted V₃/V₆ ratios are 7.7/27.7 cm⁻¹ and 8.5/22.7 cm⁻¹, respectively. Several studies on similar toluene derivatives have shown that energy potentials calculated using the MP2 method for such steric-hindrance-free methyl groups often involve a V₆ term which dominates the V₃ one.^15,48,49 At the B3LYP-D3BJ/6-311++G(d,p) level of theory, a V₃ larger than V₆ value with a V₃/V₆ ratio of 12.1/4.5 cm⁻¹ was obtained, but both values are very small.

Fig. 2 The potential energy curves of 24DMFB obtained by rotating the o-methyl group about the C₂–C₇ bond (for atom numbering, see Fig. 1). The dihedral angle α₁ = ∠(C₃, C₂, C₇, H₁₂) was varied on a 10° grid. Calculations were performed at the B3LYP-D3BJ/6-311++G(d,p) (red curve), MP2/6-311++G(d,p) (blue curve) and MP2/6-31G(d,p) (green curve) levels of theory. The predicted torsional barriers are 203.4 cm⁻¹, 235.4 cm⁻¹ and 202.6 cm⁻¹, respectively.

Fig. 3 The potential energy curves of 24DMFB obtained by rotating the p-methyl group about the C₄–C₈ bond (for atom numbering, see Fig. 1). The dihedral angle α₂ = ∠(C₅, C₄, C₈, H₁₅) was varied on a 2° grid. Calculations were performed at the B3LYP-D3BJ/6-311++G(d,p) (red curve), MP2/6-311++G(d,p) (blue curve) and MP2/6-31G(d,p) (green curve) levels of theory. To reproduce the obtained energy points, V₃/V₆ combinations of 12.1/4.5 cm⁻¹, 7.7/27.7 cm⁻¹ and 8.5/22.7 cm⁻¹, respectively, are needed.

2.3. Potential energy surfaces

To study the coupling between the two methyl groups, one with a very low and one with an intermediate barrier, two-dimensional potential energy surfaces (2D-PES) depending on the dihedral angles α₁ and α₂ were calculated at the B3LYP- D3BJ/6-311++G(d,p) and MP2/6-311++G(d,p) levels of theory. The two dihedral angles were varied in 10° steps, while all other geometry parameters were reoptimised. The calculated energies were parameterised using a 2D-Fourier expansion accounting for the C₃ symmetry of the o- and p-methyl groups. The Fourier coefficients are given in Table S4 in the ESI.† The resulting 2D-PES are plotted in Fig. 4. The 2D-PES calculated at the MP2/6-3G(d,p) level is very similar to that obtained at the MP2/6-311++G(d,p) level and is given in Fig. S1 in the ESI.† At the B3LYP-D3BJ/6-311++G(d,p) level of theory, the minimum regions feature stretched oblate shapes that indicate a significant coupling between the two tops. Calculations at the MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels show clearly double minimum ranges. That the o- and p-methyl rotations strongly influence each other is reflected in addition by the strong coupling terms cos(3α₁)cos(3α₂) and sin(3α₁)sin(3α₂), as well as the large V₆ contribution predicted for the p-methyl group (see Table S4 in the ESI†).

Fig. 4 Two-dimensional potential energy surfaces of 24DMFB calculated at the B3LYP-D3BJ/6-311++G(d,p) and MP2/6-311++G(d,p) levels of theory depending on the dihedral angles α₁ = ∠(C₃,C₂,C₇,H₁₂) and α₂ = ∠(C₅,C₄,C₈,H₁₅). α₁ and α₂ were varied in steps of 10° while all other geometry parameters were reoptimised. The numbers in the colour code indicate the energy (in percent) relative to the global minimum (0%) and maximum (100%) with the absolute values E_min(B3LYP-D3BJ) = −410.265769 Hartree (0%), E_max(B3LYP-D3BJ) = −410.264764 Hartree (100%), E_min(MP2) = −409.063791 Hartree (0%) and E_max(MP2) = −409.062557 Hartree (100%).

3. Experimental section

3.1. Measurements

The rotational spectrum of 24DMFB was recorded in the frequency range from 2.0 to 26.5 GHz using a pulsed molecular jet Fourier transform spectrometer with a coaxially oriented beam-resonator arrangement (COBRA).⁵⁰ The liquid sample of 24DMFB with a purity of 98% was purchased from TCI Europe, Zwijndrecht, Belgium, and measured without further purification. Some drops of the sample were put on a 6 cm piece of a pipe cleaner and inserted in a steel tube placed upstream the nozzle. Helium was used as carrier gas and the He-24DMFB mixture was expanded into the cavity with a backing pressure of about 2 bar. For 24DMFB, a survey scan in the frequency range from 9.6 to 14.0 GHz was recorded by overlapping spectra with a step width of 0.25 MHz. A portion of the scan from 11 715 MHz to 11 845 MHz is shown in Fig. 5. All signals observed in the survey scan were remeasured at higher resolution with an experimental line half-width of 2 kHz,⁵¹ appearing as doublets due to the Doppler effect caused by the COBRA set up. The estimated measurement accuracy is about 4 kHz. Additional measurements outside the survey were carried out after the spectrum had been assigned. Typical high resolution spectra of the five torsional species of the 9₀₉ ← 8₀₈ transition are given in Fig. 6.

Fig. 5 A part of the survey spectrum of 24DMFB in the frequency range from 11 715 MHz to 11 845 MHz recorded by overlapping spectra with 50 co-added free induction decays (FIDs) per each spectrum and a 0.25 MHz step width. The arbitrary intensity is given in a logarithmic scale. All lines are labelled with their torsional species in parentheses and rotational quantum numbers .

Fig. 6 Typical high resolution spectra of the a-type transition 9₀₉ ← 8₀₈ of 24DMFB with its five torsional components (00), (10), (01), (11) and (12). The frequencies are in MHz. The brackets indicate Doppler doublets. The (01) and (11) components are captured in two overlapping spectra which are distinguished by different colours. The polarisation frequencies of 17 280.85, 17 296.0, 17 298.2 and 17 299.1 MHz are marked as red ticks. For each spectrum, 85, 35, 60 and 30 FIDs were co-added, respectively. The intensities are normalised.

3.2. Spectral assignments and fits

At the beginning, the rigid-rotor spectrum of 24DMFB was predicted with the program XIAM⁵² using the equilibrium rotational constants A_e, B_e and C_e calculated at the B3LYP-D3BJ/6-311++G(d,p) level of theory recommended for the DMFB family.^27–29 Strong a-type, weaker b-type and no c-type transitions were expected based on the dipole moment components given in Table 1. Intense a-type transitions with low K_a values were assigned first. Thereafter, we assigned and included in the rigid-rotor fit further a-type lines with larger K_a values, as well as some b-type transitions.

Due to internal rotations of the two inequivalent methyl groups at the ortho and para positions of the phenyl ring, each rotational transition splits into five torsional species (00), (10), (01), (11), and (12). To consider these LAMs, we first examined the internal rotation of the o-methyl group whose barrier height is calculated to be intermediate. We predicted the (10) torsional species frequencies using the rotational constants of the rigid-rotor fit as well as the values for V_3,1 and the angle ∠(i₁,a) between the internal rotor axis and the principal a-axis obtained at the B3LYP-D3BJ/6-311++G(d,p) level of theory. The assignment of the (10) species lines was straightforward, and we were able to establish a XIAM fit that only includes the (00) and (10) species with a root-mean-square deviation (rms) within the measurement accuracy.

The one-top fit was then expanded into a two-top fit to account for the torsional splittings arising from the p-methyl rotor. The assignments of the (01), (11) and (12) species were much more challenging because of the very low barrier to internal rotation, which causes large, difficult to quantify splittings between these species in the microwave spectrum. To guide the assignment, we searched first for the (01) components of a-type transitions with K_a = 0 and 1 using the XIAM prediction. After fitting the frequencies of these lines, more (01) lines could be found but the XIAM prediction started to fail after a certain number of lines had been included in the fit. To check the correctness of the assignment, we initially used combination difference loops (Ritz cycles)⁵³ which sum to about 4 kHz. The loop ladders are shown in Fig. 7. Subsequently, each torsional species was separately fitted using the SFLAMS program⁵⁴ where odd power parameters were included in the H_op Hamiltonian:

Fig. 7 Schematic illustration of almost all recorded (00), (10) (01), (11) and (12) torsional components of 24DMFB. Solid lines connecting the circles represent transitions that were checked by combinations difference loops. Almost all loops sum within 2 kHz, but there are also some loops which sum to about 10 kHz. From the average of all loop sums, the estimated measurement accuracy is 4 kHz. Some weak b-type transitions could not be measured. Consequently, some loops are not closed. Transitions involving in such loops are indicated as dashed lines.

We first fitted the K_a = 0 and 1 lines of the (01) species that are loop-checked separately. With the prediction from this separate fit, further lines could be found and both the XIAM fit and the SFLAMS fit were extended. Molecular parameters obtained from the XIAM fit including the (00), (10) and (01) species were used to guide the assignment of the first (11) and (12) torsional lines. After several attempts, we were able to assign a sufficient number of lines that could be checked by combination difference loops and fitted by the SFLAMS program with a standard deviation within the measurement accuracy. Predictions from the SFLAMS fits later guided further assignments. No c-type lines were expected in the microwave spectrum of 24DMFB since the c-dipole moment component is zero due to the C_s symmetry of the molecular frame, but some c- and x-type transitions were still observed for the (10), (01), (11) and (12) species. These types of transitions are forbidden for the (00) species by the rigid-rotor selection rules.⁵⁵ For the other species, they are allowed by the perturbations arising from the methyl internal rotations. The K_a and K_c quantum numbers lost physical meaning for these transitions, as they only indicate the order of energy. The molecular parameters of the five SFLAMS fits are given in Table 2. Finally, a global fit consisting of 885 torsional lines was carried out using the modified version of the program XIAM^54,56 that can include two more higher-order parameters D_c3K and D_c3−, yielding a standard deviation of 549.1 kHz. This rather large deviation is not a rare observation when XIAM has to deal with very low barrier internal rotation. We observed such large values for 2-methylthiazole,⁴⁸ 4,5-dimethylthiazole⁴⁹ and 2,4-dimethylthiazole.⁵⁷ Finally, we applied the BELGI-C_s-2Tops program⁵⁸ on the same data set which succeeded to decrease the rms deviation to 4.5 kHz, satisfactorily close to the measurement accuracy using more higher order parameters. The molecular parameters in the principal axis system obtained with XIAM and BELGI-C_s-2Tops are given in Table 3; the complete list of fitted frequencies with their residuals is available in Table S5 in the ESI.† The BELGI-C_s-2Tops parameters obtained in the “quasi-PAM” system are summarized in Table 4. Note that only a limited number of BELGI molecular parameters can be converted into the principal axis system shown in Table 3.

Table 2 Molecular parameters of the (00), (10), (01), (11) and (12) species fits of 24DMFB as obtained with the program SFLAMS

Par.^a	Unit	Fit (00)	Fit (10)	Fit (01)	Fit (11)	Fit (12)
a All parameters refer to the principal axis system. Watson's A reduction in I^r representation was used. b Number of lines. c Root-mean-square deviation of the fit.
A	MHz	3051.91814(12)	3050.73760(11)	3035.60202(19)	3034.42121(20)	3034.23252(20)
B	MHz	1284.460569(47)	1284.188752(46)	1284.366566(64)	1284.096990(54)	1284.102121(54)
C	MHz	909.093172(34)	909.096395(33)	909.114959(49)	909.120662(36)	909.116213(36)
Δ J	kHz	0.02347(22)	0.02264(21)	0.01785(37)	0.01623(24)	0.01670(24)
Δ JK	kHz	0.11479(75)	0.07318(74)	0.5234(12)	0.4891(11)	0.4750(11)
Δ K	kHz	0.7384(36)	0.7379(38)	18.6894(95)	18.6372(96)	18.783(11)
δ J	kHz	0.00874(13)	0.00762(13)	0.00862(21)	0.00696(15)	0.00739(15)
δ K	kHz	0.002243(64)	0.001594(67)	0.00482(11)	0.004174(87)	0.004064(84)
q	MHz		53.65721(23)	5409.01107(60)	5350.70931(62)	5455.31239(50)
q J	kHz		−2.2031(33)	−4.7020(77)	−2.4461(73)	−6.5910(72)
q K	kHz		−3.437(12)	−575.871(56)	−571.995(56)	−583.601(48)
q JK	kHz			−0.02224(25)	−0.02219(24)	−0.02493(24)
q KK	kHz			−0.4602(19)	−0.4589(19)	−0.4601(18)
r	MHz		24.6679(39)	519.16058(50)	542.20062(49)	493.71397(48)
r J	kHz			−0.3370(60)	−0.9640(58)	0.4213(57)
r K	kHz			−118.50(13)	−131.32(12)	−108.76(12)
N		186	200	151	172	176
rms^c	kHz	1.8	2.3	4.6	4.7	4.8

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Table 3 Molecular parameters of 24DMFB in the principal axis system obtained using the XIAM_mod and BELGI-C_s-2Tops programs

Par.^a	Unit	XIAMmod	BELGI	Calc.^b
a All molecular parameters refer to the principal axis system. b Calculated at the B3LYP-D3BJ/6-311++G(d,p) level of theory. The rotational constants refer to the equilibrium structure. Centrifugal distortion constants are obtained from anharmonic frequency calculations. c The Vcc parameter multiplies cos(3α1)cos(3α2). d Derived parameters in XIAMmod. e Fixed to values from the XIAMmod fit. f Fixed due to symmetry. g Number of lines. h Root-mean-square deviation of the fit.
A	MHz	2997.983(16)	2927.5(72)	3001.7
B	MHz	1283.7868(33)	1277.53(83)	1282.4
C	MHz	909.0878(26)	909.3679(33)	908.6
Δ K	kHz	−1.72(44)		0.36802
V 3,1	cm^−1	227.039(51)	233.92(41)	203.4
V 3,2	cm^−1	3.23(40)	16.860(58)	12.1
V cc	cm^−1	−12.9(1.8)^c	−6.529(43)	−6.03^c
ρ 1	Unitless	0.01404^d	0.012953(57)
ρ 2	Unitless	0.01841^d	0.018843(22)
F 1	GHz	161.6173^d	161.6173^e
F 2	GHz	162.4878^d	162.4878^e
D π^2K,1	MHz	0.841(59)
D π^2K,2	MHz	0.477(56)
D π^2−,2	MHz	−0.264(72)
D c3J,2	MHz	1.02(15)
D c3K,2	MHz	39.1(67)
D c3−,2	MHz	10.8(33)
∠(i1,a)	°	132.616(37)	132.97(36)	133.6
∠(i1,b)	°	42.616(37)	42.97(37)	43.6
∠(i1,c)	°	90.0^f	90.0^f	90.0
∠(i2,a)	°	12.8652(11)	12.29(99)	13.1
∠(i2,b)	°	77.1348(11)	77.708(35)	76.9
∠(i2,c)	°	90.0^f	90.0^f	90.0
N		885	885
rms^h	kHz	549.1	4.5

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Table 4 Molecular parameters of 24DMFB in the “quasi-PAM” system obtained by the program BELGI-C_s-2Tops

Operator^a	Par.^b	Unit	Value
a Operator which the parameters multiply in the program. {A, B} is the anti-commutator AB + BA. α1 and α2 correspond to the o- and p-methyl groups, respectively. b All parameters refer to the quasi-PAM system. c Fixed to values from the XIAMmod fit. d Number of lines. e Root-mean-square deviation of the fit.
P z ^2	A	MHz	3007.7(72)
P x ^2	B	MHz	1282.88(83)
P y ^2	C	MHz	909.3679(33)
−P^4	Δ J	kHz	0.0104595(82)
−P^2Pz^2	Δ JK	kHz	−0.21511(64)
−Pz^2	Δ K	kHz	−0.3614(38)
(1/2)(1 − cos 3α1)	V 3,1	cm^−1	233.92(41)
P 1 ^2	f 1	GHz	161.6173^c
P x p 1	r 1	GHz	−1.7591(84)
P x p 1 P ^2	r 1J	kHz	−8.01(40)
(1/2){Pz^2, Px}p1	r 1K	MHz	−0.1331(73)
P z p 1	q 1	GHz	−3.856(20)
P z p 1 P ^2	q 1J	kHz	−2.67(83)
P z ^3 p 1	q 1K	MHz	−0.208(18)
P 1 ^2 P z ^2	f 1K	MHz	7.63(70)
P 1 ^2 P x ^2	B 1	MHz	0.494(74)
(1/2)(1 − cos 3α1)P^2	V 3,1J	GHz	0.0099(11)
(1/2)(1 − cos 3α1)Pz^2	V 3,1K	GHz	0.248(20)
(1/2)(1 − cos 3α1){Px^2 − Py^2}	V 3,1BC	GHz	0.0107(11)
(1/2)(1 − cos 3α2)	V 3,2	cm^−1	16.860(58)
P 2 ^2	f 2	GHz	162.4878^c
P x p 2	r 2	GHz	−0.58045(18)
P z p 2	q 2	GHz	6.1314(71)
p 2 ^2 P z ^2	f 2K	MHz	2.81(12)
(1/2)(1 − cos 3α2)P^2	V 3,2J	MHz	−0.4611(34)
(1/2)(1 − cos 3α2)Pz^2	V 3,2K	MHz	−15.59(94)
(1/2)(1 − cos 3α2){Pz, Px}	V 3,2AB	MHz	5.70(14)
(1/2)(1 − cos 3α2){Px^2 − Py^2}	V 3,2BC	MHz	−0.3290(55)
P 2 ^2 P x ^2	B 2	MHz	0.0478(16)
(1 − cos 3α1)(1 − cos 3α2)Pz^2	V 12CK	GHz	−0.0498(11)
(1 − cos 3α1)(1 − cos 3α2)	V 12C	cm^−1	−6.529(43)
p 1 p 2	F 12	cm^−1	−0.10538(74)
	N		885
	rms^e	kHz	4.5

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4. Results and discussion

The microwave spectrum of 24DMFB was analysed and 885 rotational lines were fitted using the XIAM_mod and BELGI-C_s-2Tops programs. The assignment was checked by a combination of separately fitting the torsional species and Ritz cycles. The XIAM_mod fit given in Table 3 reaches an rms deviation of 549.1 kHz. The BELGI-C_s-2Tops program decreases the deviation to 4.5 kHz, satisfactorily close to the measurement accuracy of 4 kHz, using additional higher order parameters as given in Table 4.

4.1. Rotational constant benchmarking

The benchmark calculations given in Table S2 in the ESI† have shown that all levels of theory used to perform geometry optimisations of 24DMFB yielded equilibrium rotational constants that are in good agreement with the experimental values obtained using the XIAM_mod programs with deviations being less than 1.8% in all cases. The rotational constants calculated at the B3LYP-D3BJ/6-311++G(d,p), MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels of theory used to benchmark the 2,6-, 3,4- and 2,3-isomers of DMFB^27–29 all performed very well with deviations less than 0.7%, especially B3LYP-D3BJ with deviations less than 0.1%. Therefore, we continue to recommend the B3LYP-D3BJ/6-311++G(d,p) level for microwave spectral assignment of related molecules. The ωB97X-D method in combination with the 6-31+G(d,p), 6-31++G(d,p) and aug-cc-pVDZ basis sets also provided satisfactory results.

4.2. Barriers to methyl internal rotation

The torsional barriers of the o- and p-methyl groups are determined to be 227.039(51) cm⁻¹ and 3.23(40) cm⁻¹, respectively, using the XIAM_mod program. The value of 233.92(41) cm⁻¹ for the methyl group at the ortho position obtained with the BELGI-C_s-2Tops program is in the same order of magnitude. For the p-methyl group, the BELGI value of 16.860(58) cm⁻¹ is much larger. This is probably connected to the different V_cc values obtained with the two programs. We also note that the A rotational constant obtained with BELGI differs significantly from that of XIAM_mod, while the difference is negligible for the C constant. This can be explained by the different approaches used in each program and the large correlation between the rotational constants and the D_ab parameter floated in the BELGI code. Therefore, the XIAM values for the rotational constants are more physically meaningful despite the large rms deviation of the fit and they are taken as reference values for comparison with theoretical ones. For the o-methyl group, the barrier heights predicted at the B3LYP-D3BJ/6-311++G(d,p), MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels are 203.4 cm⁻¹, 235.4 cm⁻¹ and 202.6 cm⁻¹, respectively, which are in the same order of magnitude as the value obtained using the XIAM_mod and BELGI codes. Unlike the o-methyl group, for the p-methyl top there are large deviations between the calculated values and the XIAM_mod value because of the different V₆ contributions predicted at different levels. For the MP2/6-311++G(d,p) and MP2/6-31G(d,p) levels of theory, the V₆ contribution dominates the V₃ term, while it is the inverse for the B3LYP-D3BJ/6-311++G(d,p) level. However, we cannot confirm this experimentally since the V₆ term could not be determined using the experimental data set due to the lack of transitions from excited vibrational states. The V₆ term can be, in principle, fixed to the predicted value. However, when we fixed the V₆ term to the predicted value in the BELGI fit, we obtained almost the same value for the resultant semi-experimental V₃ term as when V₆ was fixed to zero, and with a similar rms deviation. This is not surprising since in the absence of experimental data from torsional excited states, it is impossible to get a reliable value of V₆.

The torsional barrier of 227.039(51) cm⁻¹ obtained for the o-methyl group is very close to the value found for 26DMFB (2)²⁷ and for 23DMFB (3)²⁹ as illustrated in Fig. 8. The value is also close to that obtained for 2-fluorotoluene (227.3 cm⁻¹),⁵⁹ 2,3,4-trifluorotoluene (216.3 cm⁻¹),⁶⁰ 2,4,5-trifluorotoluene (190.7 cm⁻¹),⁶⁰ 2,3-difluorotoluene (210.5 cm⁻¹),⁶¹ 2,4-difluorotoluene (234.2 cm⁻¹)⁶² and 2,5-difluorotoluene (215.7 cm⁻¹),⁶³ confirming the conclusion given in our previous studies on 23DMFB²⁹ and 26DMFB²⁷ that the barrier to internal rotation of a methyl group adjacent to a fluorine atom is always around 220 cm⁻¹. If we compare the torsional barrier of the p-methyl group to the value of the p-methyl group in 3,4-dimethylfluorobenzene (molecule 4 in Fig. 8),²⁸ a large difference is expected and also observed since the two para methyl groups experience different steric surroundings. The steric-hindrance-free environment leads to an extremely low barrier of the p-methyl group in 24DMFB while an intermediate barrier of 490 cm⁻¹ was found in the case of 34DMFB due to the steric hindrance between the two neighbouring methyl groups. We also compare the very low barrier of the para methyl top in 24DMFB to those obtained for other steric-hindrance-free para-methyl substituted toluene derivatives available in the literature. The value of 3 cm⁻¹ observed for 24DMFB is lower than that of 2,4-dimethylanisole (5, 47.6 cm⁻¹),²⁶p-methyl anisole (6, 49.6 cm⁻¹),⁶⁴p-tolualdehyde (7, 28.1 cm⁻¹),⁶⁵p-cresol (8, 18.4 cm⁻¹),¹³ and p-toluic acid (9, 7.9 cm⁻¹).¹⁵ The V₃ value of the p-methyl group in 24DMFB is even lower than the pure V₆ potential of about 4.9 cm⁻¹ obtained for toluene (10),^3–8p-fluorotoluene (11)⁹ and p-chlorotoluene (12).¹¹ 24DMFB is thus the dimethyl substituted toluene derivative with the lowest barrier height ever determined, i.e. lower than the lowest barrier know so far of m-methyl group of syn-2,5-dimethylbenzaldehyde (5.4 cm⁻¹).²³

Fig. 8 Comparison of the barriers to methyl internal rotation in toluene derivatives: (1) 2,4-dimethylfluorobenzene (this work), (2) 2,6-dimethylfluorobenzene,²⁷ (3) 2,3-dimethylfluorobenzene,²⁹ (4) 3,4-dimethylfluorobenzene,²⁸ (5) 2,4-dimethylanisole,²⁶ (6) p-methyl anisole,⁶⁴ (7) p-tolualdehyde,⁶⁵ (8) p-cresol,¹³ (9) p-toluic acid,¹⁵ (10) toluene,^3–8 (11) p-fluorotoluene⁹ and (12) p-chlorotoluene.¹¹

Despite the same position of the methyl groups in these different molecules and the same steric-hindrance-free surrounding, the barrier values are different from one system to another. This is mediated by the electronic environment and the electronic exchanges through the π-conjugated system depending on the substituents attached to the phenyl group. The coupling between the internal rotations also influences the observed torsional barriers, as shown by the significant V_cc term of the XIAM and BELGI fits as well as calculated by the 2D-PES.

5. Conclusions

The microwave spectrum of 24DMFB was recorded in the frequency range from 2.0 to 26.5 GHz. Torsional splittings were observed due to the internal rotations of two inequivalent methyl groups at the ortho and para positions. The complex splitting patterns were analysed and fitted using the XIAM_mod and BELG-C_s-2Tops programs, giving rms deviations of 549.1 kHz and 4.5 kHz, respectively. Combination difference loops and separate fittings of the five torsional components were used to check the assignment and predict new lines. The experimental torsional barriers were determined to be 227.039(51) cm⁻¹ and 3.23(40) cm⁻¹ for the o- and p-methyl groups, respectively. The 2D-PES visualised a significant coupling between the methyl groups, which is also reflected by a large V_cc contribution in the fit. The barrier found for the o-methyl group was compared to those obtained for other ortho-substituted toluene derivatives, confirming that the barrier to internal rotation of a methyl group adjacent to a fluorine atom is always around 220 cm⁻¹. The V₃ barrier of the p-methyl group is the lowest value ever observed to date, surpassing all other para-methyl substituted toluene derivatives.

Author contributions

The manuscript was written with the contributions of all authors. All authors approved the final version of the manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by the Agence Nationale de la Recherche ANR (project ID ANR-18-CE29-0011) and by the European Union (ERC, 101040480-LACRIDO). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union. Neither the European Union nor the granting authority can be held responsible for them.

References

1. H. V. L. Nguyen and I. Kleiner, Phys. Sci. Rev., 2022, 7, 679.
2. H. V. L. Nguyen, W. Caminati and J.-U. Grabow, Molecules, 2022, 27, 3948.
3. H. D. Rudolph, H. Dreizler, A. Jaeschke and P. Wendung, Z. Naturforsch., 1967, 22a, 940.
4. W. A. Kreiner, H. D. Rudolph and B. T. Tan, J. Mol. Spectrosc., 1973, 48, 86.
5. V. Amir-Ebrahimi, A. Choplin, J. Demaison and G. Roussy, J. Mol. Spectrosc., 1981, 89, 42.
6. Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski and H. Mäder, J. Mol. Spectrosc., 2004, 227, 109.
7. V. V. Ilyushin, Z. Kisiel, L. Pszczólkowski, H. Mäder and J. T. Hougen, J. Mol. Spectrosc., 2010, 259, 26.
8. V. V. Ilyushin, E. A. Alekseev, Z. Kisiel and L. Pszczółkowski, J. Mol. Spectrosc., 2017, 339, 31.
9. J. Rottstegge, H. Hartwig and H. Dreizler, J. Mol. Struct., 1999, 478, 37.
10. A. Roucou, M. Goubet, I. Kleiner, S. Bteich and A. Cuisset, ChemPhysChem, 2020, 21, 2523.
11. V. A. Shubert, D. Schmitz and M. Schnell, Mol. Phys., 2013, 111, 2189.
12. T. Bruhn and H. Mäder, J. Mol. Spectrosc., 2000, 200, 151.
13. A. Hellweg and C. Hättig, J. Chem. Phys., 2007, 127, 024307.
14. A. Hellweg, C. Hättig, I. Merke and W. Stahl, J. Chem. Phys., 2006, 124, 204305.
15. E. G. Schnitzler, N. A. Seifert, I. Kusuma and W. Jäger, J. Phys. Chem. A, 2017, 121, 8625.
16. A. Roucou, I. Kleiner, M. Goubet, S. Bteich, G. Mouret, R. Bocquet, F. Hindle, W. L. Meerts and A. Cuisset, Chem. Phys. Chem., 2018, 19, 1056.
17. A. J. Shirar, D. S. Wilcox, K. M. Hotopp, G. L. Storck, I. Kleiner and B. C. Dian, J. Phys. Chem. A, 2010, 114, 12187.
18. D. A. Obenchain, P. Pinacho, S. Zinn and M. Schnell, J. Mol. Struct., 2020, 1213, 128109.
19. K. P. R. Nair, S. Herbers, H. V. L. Nguyen and J.-U. Grabow, Spectrochim. Acta, Part A, 2020, 242, 118709.
20. W. Jäger, Microwave study of atmospheric oxidation and product m-toluic acid and its monohydrate, https://hdl.handle.net/2142/97117.
21. R. G. Bird and D. W. Pratt, J. Mol. Spectrosc., 2011, 266, 81.
22. C. Thomsen and H. Dreizler, Z. Naturforsch., 2001, 56a, 635.
23. M. Tudorie, I. Kleiner, M. Jahn, J.-U. Grabow, M. Goubet and O. Pirali, J. Phys. Chem. A, 2013, 117, 13636.
24. L. Ferres, Quantum Chemical and Microwave Spectroscopic Investigations on Phenyl Ring Containing Molecules, PhD dissertation, RWTH Aachen University, Aachen, Germany, 2019.
25. L. Ferres, K.-N. Truong, W. Stahl and H. V. L. Nguyen, Chem. Phys. Chem., 2018, 19, 1781.
26. L. Ferres, W. Stahl and H. V. L. Nguyen, J. Chem. Phys., 2019, 151, 104310.
27. S. Khemissi and H. V. L. Nguyen, ChemPhysChem, 2020, 21, 1682.
28. J. Mélan, S. Khemissi and H. V. L. Nguyen, Spectrochim. Acta A, 2021, 253, 8.
29. S. Khemissi, A. Pérez Salvador and H. V. L. Nguyen, J. Phys. Chem. A, 2021, 125, 8542.
30. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, 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. Egidi, 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 and D. J. Fox, Gaussian 16, Revision B.01, Inc., Wallingford CT, 2016.
31. R. Hakiri, N. Derbel, H. V. L. Nguyen and H. Mouhib, Phys. Chem. Chem. Phys., 2018, 20, 25577.
32. C. Dindić and H. V. L. Nguyen, Phys. Chem. Chem. Phys., 2022, 25, 509.
33. V. Van, J. Bruckhuisen, W. Stahl, V. Ilyushin and H. V. L. Nguyen, J. Mol. Spectrosc., 2018, 343, 121.
34. S. Khemissi, M. Schwell, I. Kleiner and H. V. L. Nguyen, Mol. Phys., 2022, 120, e2052372.
35. A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
36. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785.
37. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 15104.
38. S. Grimme, S. Ehrlich and L. Goerigk, J. Comput. Chem., 2011, 32, 1456.
39. T. Yanai, D. P. Tew and N. C. Handy, Chem. Phys. Lett., 2004, 393, 51.
40. C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158.
41. J.-D. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys., 2008, 10, 6615.
42. H. S. Yu, X. He, S. L. Li and D. G. Truhlar, Chem. Sci., 2016, 7, 5032.
43. Y. Zhao and D. G. Truhlar, Theor. Chem. Acc., 2008, 120, 215.
44. C. Møller and M. S. Plesset, Phys. Rev., 1934, 46, 618.
45. R. J. Bartlett and M. Musiał, Rev. Mod. Phys., 2007, 79, 291.
46. T. H. Dunning, J. Chem. Phys., 1989, 90, 1007.
47. M. J. Frisch, J. A. Pople and J. S. Binkley, J. Chem. Phys., 1984, 80, 3265.
48. T. Nguyen, V. Van, C. Gutlé, W. Stahl, M. Schwell, I. Kleiner and H. V. L. Nguyen, J. Chem. Phys., 2020, 152, 134306.
49. V. Van, T. Nguyen, W. Stahl, H. V. L. Nguyen and I. Kleiner, J. Mol. Struct., 2020, 1207, 127787.
50. J.-U. Grabow, W. Stahl and H. Dreizler, Rev. Sci. Instrum., 1996, 67, 4072.
51. J.-U. Grabow and W. Stahl, Z. Naturforsch., 1990, 45a, 1043.
52. H. Hartwig and H. Dreizler, Z. Naturforsch., 1996, 51a, 923.
53. Y. Zhao, H. V. L. Nguyen, W. Stahl and J. T. Hougen, J. Mol. Spectrosc., 2015, 318, 91.
54. S. Herbers, S. M. Fritz, P. Mishra, H. V. L. Nguyen and T. S. Zwier, J. Chem. Phys., 2020, 152, 074301.
55. J. T. Hougen, I. Kleiner and M. Godefroid, J. Mol. Spectrosc., 1994, 163, 559.
56. S. Herbers and H. V. L. Nguyen, J. Mol. Spectrosc., 2020, 370, 111289.
57. S. Khemissi, V. Van, M. Schwell, I. Kleiner and H. V. L. Nguyen, J. Phys. Chem. A, 2023, 127, 5779.
58. M. Tudorie, I. Kleiner, J. T. Hougen, S. Melandri, L. W. Sutikdja and W. Stahl, J. Mol. Spectrosc., 2011, 269, 211.
59. S. Jacobsen, U. Andresen and H. Mäder, Struct. Chem., 2003, 14, 217.
60. K. P. R. Nair, S. Herbers, D. A. Obenchain and J.-U. Grabow, Can. J. Phys., 2020, 98, 543.
61. K. P. R. Nair, S. Herbers, J.-U. Grabow and A. Lesarri, J. Mol. Spectrosc., 2018, 349, 37.
62. K. P. R. Nair, S. Herbers, D. A. Obenchain, J.-U. Grabow and A. Lesarri, J. Mol. Spectrosc., 2018, 344, 21.
63. K. P. R. Nair, D. Wachsmuth, J.-U. Grabow and A. Lesarri, J. Mol. Spectrosc., 2017, 337, 46.
64. L. Ferres, W. Stahl, I. Kleiner and H. V. L. Nguyen, J. Mol. Spectrosc., 2018, 343, 44.
65. H. Saal, J.-U. Grabow, A. R. Hight Walker, J. T. Hougen, I. Kleiner and W. Caminati, J. Mol. Spectrosc., 2018, 351, 55.

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Footnote

† Electronic supplementary information (ESI) available: Nuclear Cartesian coordinates, basis set variation, Fourier coefficients of the potential curves and the 2D-PES, potential energy surface depending on the dihedral angles α₁ and α₂ calculated at the MP2/6-311++G(d,p) level of theory, and frequency list. See DOI: https://doi.org/10.1039/d3cp04748b

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