One of the current “frontiers” in the spectroscopy of molecules with large amplitude motion is the extension of the analysis of excited vibrational states to move beyond the isolated state model to a more global treatment including several coupled vibrational modes. Before that, of course, one needs to explore the isolated states themselves, and there are still states even for small molecules like methanol, methyl mercaptan and methylamine whose structures have not yet been characterized in detail. In this task, the use of Loomis-Wood plots and Excel spreadsheets has proved to be very helpful, in conjunction with solid bases of ground-state energy term values provided by the pioneering work of the microwave and THz community. The Excel difference table approach relies on systematic trends in the J-dependence of the spectral sub-bands, and can be a sensitive pointer to perturbations arising from level-crossing resonances between interacting modes. The vibrational modes can also exhibit anharmonic resonances with the ground-state torsional manifold as it rises up through the vibrational regions. Isotopic substitution can then serve as a useful tool for tuning the resonances with two degrees of freedom, one along the energy axis by altering the relative energies of the coupled states, and a second along the K-axis by changing the value of the ρ parameter which governs the periodic K-dependence of the torsional energies. Examples will be presented of this “isotopic tuning” for isotopologues of methanol, along with discussion of features of the Excel spreadsheet approach. We will also illustrate how isotopic shifts may give insight into sub-band vibrational assignments from comparison of the torsion-vibration manifolds of the lower modes of normal CH₃OH and its O-18 relative.

The presently available tools of rotational spectroscopy do not provide a meaningful way to treat small organic radicals with methyl groups. This in turn prevents astrochemical detection of these species as it is not possible to accurately predict rotational spectra complicated by both spin-rotation coupling and methyl torsions. This work presents a new program capable of treating these interactions in C_s molecules as well as a new operator to account for spin-torion interactions. The program, written in Julia, utilizes BELGI's two stage diagonalization process to address the torsions in the first stage with the spin-rotation and spin-torsion terms being added into the second diagonalization stage. SPCAT and PGOPHER were used to test just the spin-rotation implementation while BELGI was used to test the torsional-rotation implementation. This preliminary testing of the new program has shown initial agreement with the existing programs. The current status of the program and the next stages in its implementation will be discussed.

In simple cases of methyl group internal rotation, the barrier to internal rotation is equal to the V₃ coefficient in the standard equation of the potential function. In the past few years, methyl internal rotation potentials have been reported with significant V₆ contributions, of which p-toluic acid is just one example.E.G. Schnitzler, et al., J. Phys. Chem. A 121 (2017) 8625or |V₆| << |V₃|, the barrier is still |V₃|. However, if 0 < |V₃/V₆| < 4, there are now two different barriers because there are two different potential minima (or maxima), and none of the barriers is equal to |V₃| or |V₆|. Their difference is exactly |V₃| but, for V₃ > 0 and V₆ < 0 , the lower barrier is equal to −V₆(1+V₃/(4 V₆))². It is therefore incorrect to say that |V₃| or |V₆| is the barrier. Of course, corresponding effects are also present in systems with two or more internal rotors. However, in 2-D systems, additional minima and/or maxima may occur when potential interaction terms become significant, e.g. when V₃₃ and/or V′₃₃ have magnitudes similar to V₃ in a molecule like acetone (molecular symmetry group G₃₆ = [33]C_2v). A number of examples for 1-D and 2-D systems are given and some consequences for the spectroscopy are discussed.

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E.G. Schnitzler, et al., J. Phys. Chem. A 121 (2017) 8625F

Doubly deuterated methanol CD₂HOH is a non-rigid molecule displaying internal rotation of its asymmetrical CD₂H methyl group. Like the isotopic species of methanol with a symmetrical CH₃ or CD₃ group, it displays a strong rotation-torsion Coriolis coupling. Unlike these species, it also displays a dependence of its generalized inertia tensor on the angle of internal rotation. Its complicated rotation-torsion spectrum was investigated in the microwave,Liu and Quade, J. Mol. Spectrosc. 146 (1991) 252; Su, Liu, and Quade, J. Mol. Spectrosc. 149 (1991) 557; Quade, Liu, Mukhopadhyay, and Su, J. Mol. Spectrosc. 192 (1998) 378; Su and Quade, J. Chem. Phys. 90 (1989) 1396ubmillimeter-wave,^b,c terahertz,^b and FIR^b,c,d domains. Although more than 3000 transitions have been assigned so far, no global analysis, like the one performed for the analogous species CH₂DOH,^e has been carried out. In this talk, new assignments in the terahertz and FIR spectra of CD₂HOH will be reported. Parallel and perpendicular transitions, characterized by a higher K-value than in our previous investigation,^b could be identified up to J=35 for the three lowest lying torsional states. Using the theoretical approach developed for CH₂DOH,^e a global analysis of the available high-resolution data could also be carried out and parameters describing the hindering potential and the generalized inertia tensor^f were determined. So far, this global analysis has been restricted to transitions with K ≤ 9 as rotation-torsion levels with K > 9 are affected by a yet non-identified rotation-torsion couplings and cannot be properly modeled.

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Liu and Quade, J. Mol. Spectrosc. 146 (1991) 252; Su, Liu, and Quade, J. Mol. Spectrosc. 149 (1991) 557; Quade, Liu, Mukhopadhyay, and Su, J. Mol. Spectrosc. 192 (1998) 378; Su and Quade, J. Chem. Phys. 90 (1989) 1396s

We presentThis work was done under support of the Deutsche Forschungsgemeinschaft and Volkswagen foundation. The assistance of Science and Technology Center in Ukraine is acknowledged (STCU partner project P756).he results of our new study of the torsion-rotation spectra of the two deuterated isotopologues of methanol: CD₃OH and CH₃OD. The new microwave measurements were carried out from the millimeter wave range (starting at 34 GHz) to the THz range (up to 1.1 THz) using spectrometers in Kharkiv and Köln. The new measurements in the FIR range were carried out in Braunschweig for CD₃OH from 20 to 900 cm⁻¹. In this work we significantly extend the rotational quantum number coverage for both isotopologues (from J_up = 26 [1] to J_up = 55 for CD₃OH and from J_up =21 [2] to J_up =40 for CH₃OD). The analysis is done using the rho axis method and the RAM36 program code. Our preliminary fits show that for both isotopologs the v_t = 2 torsional state is significantly affected by intervibrational interactions with non-torsional vibrational modes which propagate down through intertorsional interactions. At the same time, for CD₃OH we were able to get a fit within experimental error for v_t = 0, 1 states. For CH₃OD analysis is in progress now. In the talk the details of this new study will be discussed. [1] A. Predoi-Cross, Li-Hong Xu, M.S. Walsh, R.M. Lees, M. Winnewisser, and H. Lichau J. Mol. Spectrosc.188, 94–101 (1998). [2] Y.-B. Duan, I. Ozier, S. Tsunekawa, and K. Takagi, J. Mol. Spectrosc. 218 (2003) 95–107.

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This work was done under support of the Deutsche Forschungsgemeinschaft and Volkswagen foundation. The assistance of Science and Technology Center in Ukraine is acknowledged (STCU partner project P756).t

We used our hybrid programI. Kleiner and J. T. Hougen, J. Mol. Spectrosc., 368, 111255 (2020)o fit an extended dataset consisting of almost 30000 rotational-torsionial-wagging transitions in the MW and FIR of v_t = 0, 1 and 2 of CH₃NH₂. The program can fit rotational levels in molecules with one CH₃ internal-rotation large-amplitude motion, one NH₂ inversion large-amplitude motion. Our data set contains around 3000 MW and 26848 FIR transitions, which are fit to a weighted standard deviation of 1.75 using 102 parameters. Most of the FIR transitions are taken from recent measurements of the v_t = 1-0 band centered near 265 cm-1I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc. 342 (2017) 25-30 and the ground torsional state transitions are from Motiyenko et al.R.A. Motiyenko, V.V. Ilyushin, B.J. Drouin, S. Yu, L. Margulès, Astron.Astrophys. 563 (2014) A1 Around new 340 and 176 microwave transitions were also assigned in the v_t = 1-1 and v_t = 2-2 states respectivelly. We hope to be able to fit all this data simultaneously with the far-infrared data from v_t = 2-1, 2-0 and 2-2Part of this work has been funded by the Programme National de Physique Chimie du Milieu Interstellaire (PCMI) and French ANR Labex CaPPA through the PIA under Contract No. ANR-11-LABX-0005-01

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I. Kleiner and J. T. Hougen, J. Mol. Spectrosc., 368, 111255 (2020)t I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc. 342 (2017) 25-30, R.A. Motiyenko, V.V. Ilyushin, B.J. Drouin, S. Yu, L. Margulès, Astron.Astrophys. 563 (2014) A1. Part of this work has been funded by the Programme National de Physique Chimie du Milieu Interstellaire (PCMI) and French ANR Labex CaPPA through the PIA under Contract No. ANR-11-LABX-0005-01.

Li-Hong Xu, Jon Hougen, Isabelle Kleiner, Jens-Uwe Grabow et al. beautifully analyzed ro-vibrational levels in the ground state of acetaldehyde taking CH₃-torsion rotation interaction into consideration L.-H. Xu, J. T. Hougen et al., J. Mol. Spectrosc. 214, 175 (2002).I. Kleiner, J. T. Hougen, J.-W. Grabow et al., J. Mol. Spectrosc. 179, 41 (1996).. For the lowest electronic excited state S₁ (nπ^∗) state, the ro-vibrational level structure is much more complicated because of the out-of-plane distorsion in the CHO moiety (tunnel splitting due to double minimum potential) in addition to the profound level structure of CH₃ torsion M. Baba, I. Hanazaki, and U. Nagashima, J. Chem. Phys. 82, 3938 (1985).M. Baba, U. Nagashima, and I. Hanazaki, J. Chem. Phys. 83, 3514 (1985).. We observed and analyzed rotationally resolved ultrahigh-resolution spectra for the S₁ ← S₀ transition of jet-cooled aectaldehyde, of which the resolution was much higher than those reported previously E. C. Lim, R. H. Judge, D. C. Moule et al., J. Mol. Spectrosc. 190, 78 (1998).I.-C. Chen et al., J. Chem. Phys. 115, 5089 (2001).. The effective rotational constant A_eff was found to be drastically different between the levels of below and above the barrier to CH₃ rotation. We well explained this fact by considering the mechanism of Coriolis interaction and estimating the interaction strength by a model calculation.

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L.-H. Xu, J. T. Hougen et al., J. Mol. Spectrosc. 214, 175 (2002).

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M. Baba, I. Hanazaki, and U. Nagashima, J. Chem. Phys. 82, 3938 (1985).

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E. C. Lim, R. H. Judge, D. C. Moule et al., J. Mol. Spectrosc. 190, 78 (1998).

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2-methylmalonaldehyde (2-MMA) has two large amplitude strongly coupled large amplitude vibrations (LAVs), internal rotation of the methyl group and proton tunneling between two equivalent oxygen atoms, which results in a multiple splitting of the ground vibrational state. Since the symmetry group of 2-MMA is G₁₂ isomorphic to a point group C_6v, each vibrational level of LAV is split into nondegenerate (A₁, A₂, B₁, B₂) and degenerate (E₁, E₂) substates. In the present paper a four-dimensional model for 2-MMA is discussed where the out-of-plane vibrations are treated together with LAVs. In the standard approach the out-of-plane vibrations are handled as non-degenerate. In the non-rigid picture both out-of plane vibrations can be treated as a degenerate mode strongly coupled to LAVs and are also split into nondegenerate and degenerate substates. This effect is shown numerically using a simple harmonic model for out-of-plane degenerate mode. The results show that the out-of-plane vibrations are split into several components and their vibrational excitation should create a system of several transitions belonging to different species of the G₁₂ symmetry group.

As a large amplitude motion, the internal rotation of a methyl group, methyl torsion, is traditionally treated as being separate from the remaining small amplitude vibrations.[1] However, recent studies have shown that this is not the case in toluene,[2] several substituted toluenes[3,4] and N-methylpyrrole,[5] where methyl torsion interacts with vibrations involving out-of-plane wagging of the methyl group. Likewise, interaction between silyl torsion and the out-of-plane silyl wagging mode has been observed in phenylsilane.[6] The origin of this interaction is discussed from a kinetic energy perspective in a curvilinear framework. The model considered consists of three vibrational motions when an XH₃ group is attached to a planar frame: the in-plane and out-of-plane wagging motions of the XH₃ group and XH₃ group internal rotation. Tilting of the XH₃ group relative to the frame is included. When the “equilibrium position” of the XH₃ group at each torsional angle involves it being tilted relative to the planar frame, the XH₃ wag vibrations kinetically couple with the torsional motion, with the coupling terms being linearly dependent on the magnitude of the respective XH₃ tilt angles. The coupling only vanishes when the tilt angle is zero. XH₃ tilt also leads to the -XH₃ group precessing relative to the frame during the torsional motion. Quantum chemistry calculations on a range of methylated molecules show the ubiquitous nature of in-plane and out-of-plane methyl group tilt, and hence the pervasive nature of the interaction between methyl torsion and in-plane and out-of-plane wag vibrations of the methyl group. 1. D. G. Lister, J. N. Macdonald and N. L. Owen, Internal rotation and inversion: an introduction to large amplitude motions in molecules. (Academic Press, London, 1978). 2. J. R. Gascooke, E. A. Virgo and W. D. Lawrance, J. Chem. Phys. 142, 024315 (2015). 3. J. R. Gascooke, L. D. Stewart, P. G. Sibley and W. D. Lawrance, J. Chem. Phys. 149, 074301 (2018). 4. L. D. Stewart, J. R. Gascooke and W. D. Lawrance, J. Chem. Phys. 150, 174303 (2019). 5. J. R. Gascooke and W. D. Lawrance, unpublished results. 6. M. Griggs, J. R. Gascooke and W. D. Lawrance, unpublished results.

We determined the electronic nature, the dipole moments and the torsional barriers in the ground and electronically lowest excited singlet state of substituted indoles using rotationally resolved laser induced fluorescence Stark spectroscopy. The electronic origin bands of 1-, 3- and 5-methylindole have been investigated before via high resolution spectroscopy and the perturbation by the hindered internal rotation of the methyl group was discussed in detail by the groups of Pratt and Meerts [1,2]. In general each spectrum consists of two overlapping subbands due to the 0a₁ ← 0a₁ and 1e ← 1e torsional transitions. In 6-methylindole the difference of the torsional level splitting between the 0a₁ and 1e levels in the ground and excited state is large enough, to have the two origins of the subbands shifted more than 90 GHz, i.e. completely separated. Both resulting spectra were evaluated via evolutionary algorithms and compared to the results of ab initio calculations. The rotational constants, the orientation of the transition dipole moment, the size and orientation of the permanent dipole moment, the torsional barrier heights and the orientation of the internal rotor axis in the ground and electronically excited states along with the fluorescence lifetime could be determined. Finally a comparison with the torsional barriers of other methylindoles is given in this presentation.
[1] T. M. Korter and D. W. Pratt, J. Phys. Chem. B 105, 4010 (2001)
[2] K. Remmers, E. Jalviste, I. Mistrík, G. Berden, and W. L. Meerts, J. Chem. Phys. 108, 8436 (1998)

We study large amplitude motions of methyl group in 9-methylanthracene (9MA) by high-resolution spectroscopy. 9MA molecules are delivered in a supersonic beam and are excited by a single mode Ti:Sapphire laser. The frequency of the laser is controlled with reference to an Er doped fiber optical frequency comb. The figure is the observed rovibronic spectra of S₁(0a₁′) ← S₀(0a₁′) and S₁(1e") ← S₀(1e") transitions. Although the two transitions are overlapped, the rotational lines are well resolved. Now we try to assign the rotational lines and to analyze interactions in the vibronic excited states. r0pt Figure