There are different ways to analyze rovibrational structure of molecules having several large amplitude motions of different type, like internal rotation and inversion or ring-puckering. In my research group we have developed and used methods starting from potential surfaces for large amplitude motions but also applied purely effective Hamiltonians, where tunneling splittings were key parameters. Whatever is the method the following problems must be solved when addressing a rovibrational problem with large amplitude vibrations: 1) a definition of the permutation-inversion molecular symmetry group, 2) a choice of the internal coordinates and their transformation in the symmetry group, 3) derivation of the Hamiltonian in chosen coordinates, 4) calculation of the Hamiltonian matrix elements in a symmetrized basis set. These points will be discussed. The advantage of methods which start from the geometry and potential surface for large amplitude vibrations give much clearer picture of internal dynamics of molecules but generally the fit to experimental data is much poorer. The fitting procedure is strongly non-linear and the iteration procedure much longer. The effective Hamiltonians the fit is generally much better since almost all optimized parameters are linear but the parameters have no clear physical meaning. This method is very useful in the assignment of experimental spectra. Results of the application of both method to methylamine and hydrazine will be presented.

Last year we presented a new hybrid-model fitting program for methylamine-like molecules, based on an effective Hamiltonian in which the ammonia-like inversion motion is treated using a tunneling formalism, while the internal-rotation motion is treated using an explicit kinetic energy operator and potential energy function. This new hybrid program was successfully applied to 2-methylmalonaldehyde, for which we refit the already published ground state v_t = 0 data. This fitI. Kleiner and J. T. Hougen, J Phys Chem A. 119, 10664-76 (2015) which was of almost the same quality as that obtained using an all-tunneling formalism, removed one of the major puzzles in the isotope-dependence of the internal-rotation tunneling parameters found in the all-tunneling fit. This year we are trying to illustrate a second advantage of the new hybrid formalism, which allows one to carry out global fits of data from two or more torsional states in methylamine-like molecules. We are, in fact, trying to simultaneously fit the v_t = 0 and v_t = 1 microwave and infrared date on methylamine itself. This data is also in the literature, but the all-tunneling Hamiltonians used could only fit each of the two torsional states separately. At the time of writing this abstract, we have preliminary fits of about 1200 methylamine transitions to 25 or 30 torsion-inversion-rotation parameters, but these hybrid-program fits are not yet at the same level as the all-tunneling-program fits in the literature. We hope to report significant further progress on this work in June.

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I. Kleiner and J. T. Hougen, J Phys Chem A. 119, 10664-76 (2015),

The first excited torsional band of methylamine, ν₁₅, has been reassigned in a high resolution spectrum in the region from 40 to 360 cm⁻¹. Over 12400 transitions with a resolution of 0.00125 cm⁻¹ with K from 0 up to 16 and J from 0 up to 40 have been assigned for all six symmetry species. A global fit of the infrared, pure rotational and microwave data has been carried out and the band centre was determined at 264.5825(60) cm⁻¹. The combined data were fit to a single state model based on the group theoretical formalism of Hougen and Ohashi resulted in the total standard deviation of 0.004 cm⁻¹ for the infrared spectrum and 0.40 MHz for microwave spectrum. From the same spectrum the upper state combination differences produced data for the rotational structure of the ground state which could be fitted with the standard deviation of 0.0003 cm⁻¹. The fit to ground state rotational transitions in the MHz region gave the standard deviation of 0.21 MHz. Although the precision of the energies calculated for the excited torsional state is not fully satisfactory it allows us to assign several thousands of lines in the hot bands ν₁₅-2ν₁₅, ν₁₅-3ν₁₅ and ν₁₅-4ν₁₅ , which are quite intense in the spectrum recorded at room temperature.

Torsional splitting has been observed in the ν₈ and ν₂₁ IR bands of propane near 870.4 and 921.4 cm⁻¹, respectively, recorded at the AILES Beamline at the SOLEIL synchrotron.A. Perrin et al., J. Mol. Spectrosc. 315 (2015), 55-62; A. Perrin et al., ISMS15, presentation TG04.ver 4000 individual transitions of the ν₈ band were assigned and analyzed with an expanded version of the effective rotational Hamiltonian for molecules with two symmetric internal rotors (ERHAM).P. Groner, J. Chem. Phys. 107 (1997) 4483–4498; P. Groner, J. Mol. Spectrosc. 278 (2012) 52–67. least-squares fit approximated a large portion of the assigned transitions with a model of an isolated ν₈ state with acceptable precision. However, this model was unable to reproduce many systematic deviations and local resonances. A torsional analysis of existing experimental data and ab initio predictions allows the conclusion that Fermi resonance between ν₈ and the torsional combination state 2ν₁₄+2ν₂₇ most likely caused the failure of the isolated state model. Additional modifications to ERHAM that include Fermi resonance with another state support the conclusion that most of the observed torsional splitting in ν₈ is caused by the 2ν₁₄+2ν₂₇ state. The continuing detailed analysis is expected to yield more definitive results by the time of this meeting.

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Footnotes:

A. Perrin et al., J. Mol. Spectrosc. 315 (2015), 55-62; A. Perrin et al., ISMS15, presentation TG04.O P. Groner, J. Chem. Phys. 107 (1997) 4483–4498; P. Groner, J. Mol. Spectrosc. 278 (2012) 52–67.A

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward.

At this symposium in 2013, we reported our preliminary results on modeling the spectrum of ammonia 2ν₂ and ν₄ states (see Paper TB09 in 2013). This presentation reports the final results on our extensive experimental measurements and data analysis for the 2ν₂ and ν₄ inversion-rotation and vibrational transitions. We measured 159 new transition frequencies with microwave precision and assigned 1680 new ones from existing Fourier Transform spectra recorded in Synchrotron SOLEIL. The newly assigned data significantly expand the range of assigned quantum numbers. Combined with all the previously published high-resolution data, the 2ν₂ and ν₄ states are reproduced to 1.3σ using a global model. We will discuss the types of transitions included in our global analysis, and fit statistics for date sets from individual experimental work.

A new study of the millimeter wave spectrum of nitromethane CH₃NO₂ is reported. The new measurements covering the frequency range from 49 GHz to 236 GHz have been carried out using spectrometer in IRA NASU (Ukraine). The transitions belonging to the m ≤ 8 torsional states have been analyzed using the RAM36 programV. Ilyushin, Z. Kisiel, L. Pszczółkowski, H. Mäder, J. T. Hougen J. Mol. Spectrosc. 259 (2010) 26-38. which has been modified for this study to take into account the quadrupole hyperfine structure due to presence of the nitrogen atom. The dataset consisting of 5838 microwave line frequencies and including transitions with J up to 50 was fit using a model consisting of 93 parameters and weighted root-mean-square deviation of 0.89 has been achieved. In the talk the details of this new study will be discussed.

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V. Ilyushin, Z. Kisiel, L. Pszczółkowski, H. Mäder, J. T. Hougen J. Mol. Spectrosc. 259 (2010) 26-38.,

Recently we reanalyzed the microwave absorption spectra of the trans-ethyl methyl ether molecule, state by state, in the ground vibrational, O-methyl torsional, C-methyl torsional and skeletal torsional states with the use of an IAM-like tunneling matrix formalism based on an extended permutation-inversion (PI) group idea, whose results appeared in Journal of Molecular Spectroscopy recently. Since a single rho-axis does not exist in trans-ethyl methyl ether that has two methyl-tops and the IAM formalism is not available as in the case of the one methyl-top molecule, we adopted instead an IAM-like (in other word, partial IAM) formalism. We will show the outline of the present formalism and the results of the spectral analyses briefly. We also would like to review the IAM formalism for the one top molecules based on the extended PI group, and show the result of the application to the spectral analysis.
If possible, we would like to compare the IAM and IAM-like formalisms based on the extended PI group with the ERHAM formalism developed by Groner, especially, in the form of Hamiltonian matrix elements, and discuss about similarity and difference.

The solution of a C_3V internal rotation problem for the torsional manifold of an isolated vibrational state such as the ground state is well established. However, once an interacting small amplitude vibrational state is involved the path to a solution becomes far less clear and there is little guidance in the literature on how to proceed. The fundamental challenge is that the torsional problem and the internal axis system are unique to each torsional manifold of a specific vibrational state. In an asymmetric top molecule vibrational angular momentum can be rotated away, but this sort of rotation changes the angle between the internal rotation axis and the principle axis when there is an internal rotor. This means that there is an angle between the internal axis systems of each torsional manifold of a vibrational state. The net result is that the coupling between the two states must account for the difference in internal axis angle and will have some significant consequences to the selection rules and interactions. Two cases will be discussed, methanol and ethyl cyanide.

The interest in laboratory spectroscopy of ethane stems from the desire to understand the methane cycle in the atmospheres of planets and their moons and from the importance of ethane as a trace species in the terrestrial atmosphere. Solar decomposition of methane in the upper part of these atmospheres followed by a series of reactions leads to a variety of hydrocarbon compounds among which ethane is often the second most abundant species. Because of its high abundance, ethane spectra have been measured by Voyager and Cassini in the regions around 30, 12, 7, and 3 μm. Therefore, a complete knowledge of line parameters of ethane is crucial for spectroscopic remote sensing of planetary atmospheres. Experimental characterization of torsion-vibration states of ethane lying below 1400 cm⁻¹ have been made previously N. Moazzen-Ahmadi and J. Norooz Oliaee, J. Quant. Spectrosc. Radiat. Transfer, submitted. but extension of the Hamiltonian model for treatment of the strongly perturbed ν₈ fundamental and the complex band system of ethane in the 3 micron region requires careful examination of the operators for many new torsionally mediated vibration-rotation interactions. Following the procedures outlined by Hougen J.T. Hougen, Can. J. Phys., 42, 1920 (1964) J. T. Hougen, Can. J. Phys., 43, 935 (1965) we have re-examined the transformation properties of the total angular momentum, the translational and vibrational coordinates and momenta of ethane, and for vibration-torsion-rotation interaction terms constructed by taking products of these basic operators. It is found that for certain choices of phase, the doubly degenerate vibrational coordinates with and symmetry can be made to transform under the group elements in such a way as to yield real matrix elements for the torsion-vibration-rotation couplings whereas other choices of phase may require complex algebra. In this talk, I will discuss the construction of a very general torsion-vibration-rotation Hamiltonian for ethane, as well as the prospect for using such a Hamiltonian to obtain a global frequency analysis (based in large part on an extension of earlier programs and ethane fits^a from our laboratory) of all the vibrational bands of ethane at or below the 3-micron region.

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Footnotes:

N. Moazzen-Ahmadi and J. Norooz Oliaee, J. Quant. Spectrosc. Radiat. Transfer, submitted., J.T. Hougen, Can. J. Phys., 42, 1920 (1964)^, J. T. Hougen, Can. J. Phys., 43, 935 (1965),

ERHAM has been used to analyze rotational spectra of many molecules with torsional splitting caused by one or two internal rotors.P. Groner, J. Mol. Spectrosc. 278 (2012) 52–67.he gauche form of dimethyl ether-d₁ whose equilibrium structure has C₁ symmetry is an example of a molecule for which ERHAM could not model additional small splittings resolvable for many transitions, whereas the spectrum of the symmetric (anti, trans) form with a C_s equilibrium structure could be analyzed successfully with ERHAM.C. Richard et al. A&A 552 (2013), A117. more recent example where ERHAM failed is pinacolone CH₃−CO−C(CH₃)₃.Y. Zhao et al., J. Mol. Spectrosc. 318 (2015) 91–100, with references to all other programs mentioned in the abstract.n this case, the barriers to internal rotation of the methyl groups within the −C(CH₃)₃ unit are too high to produce observable internal rotation splittings, but the splittings due to the CH₃−CO methyl group could not be modeled correctly with ERHAM nor with any other available program (XIAM, BELGI-C_s, BELGI-C₁, RAM36). In the paper, it was speculated that BELGI-C_s-2tops might be able to the job, but arguments against this possibility have also been put forward. The correlation between irreducible representations of groups and their subgroups according to WatsonJ. K. G. Watson, Can. J. Physics 43 (1965) 1996-2007.an be used not only to determine the total number of substates (components) to be expected but also to help decide which particular program has a chance for a successful analysis. As it turns out, the number of components of split lines depends on the molecular symmetry at equilibrium in relation to the highest possible symmetry for a given molecular symmetry group. Therefore, for pinacolone, the vibrational ground state is split into 10 torsional substates.

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Footnotes:

P. Groner, J. Mol. Spectrosc. 278 (2012) 52–67.T C. Richard et al. A&A 552 (2013), A117.A Y. Zhao et al., J. Mol. Spectrosc. 318 (2015) 91–100, with references to all other programs mentioned in the abstract.I J. K. G. Watson, Can. J. Physics 43 (1965) 1996-2007.c