Methods applicable to the spectroscopic study of non-rigid organic molecular species with various large amplitude motions (torsions and inversions), are shown. Recent studies of ethylene glycol, C₃O₆H₆ isomers, and other species containing C, H, O, and N are employed as examples. Many organic molecules display non-rigidity. Vibrational modes (inversions and torsions) interconvert different conformers separated by relatively low barriers. Some conformers can be stabilized by the presence of hydrogen intermolecular bonds that can determine their geometry, symmetry, the shape of the potential energy surface and the internal dynamics. When a species displays three or more large amplitude motions, which cannot be separated because they interact strongly, the variational calculation of vibrational levels is complex and requires to search for ways reducing computational efforts. Especially tricky is the classification of the vibrational levels and their splittings.

The conformational analysis represents the first step toward a detailed characterization and understanding of the structure-function relationships of molecular systems. In this respect spectroscopic experiments on isolated bio- and organic-molecules allow detection of different binding schemes and three-dimensional (3D) conformations without perturbing effects of the environment. Detection of multiple 3D-geometries concomitantly present in an experimental mixture can be facilitated by “in situ” structural changes induced either by thermal variations, or the interaction with near-IR (NIR) to ultraviolet (UV) light. These sophisticated experiments need to be supported by accurate and reliable computational studies allowing to link the rich experimental data to the desired information on the structure and properties of complex molecular systems. Therefore a reliable computational approach should be able to provide a balanced description of all interactions allowing for extended mapping of the whole conformational space, including the accurate prediction of equilibrium structures, their relative positions on the potential energy surface (PES), free energies corresponding to the specific experimental conditions and the spectroscopic properties. Computations based on the second-order perturbation theory (VPT2) allow accounting for the anharmonicity of both wave function and properties. This results in a correct description of the intensity of non-fundamental transitions and more accurate band-shapes. Moreover, the same anharmonic force fields as employed in the determination of vibrational spectra allow considering vibrational corrections to molecular properties or thermodynamic functions. For flexible molecules, the large amplitude-motion (LAM) free approach, where all LAMs anharmonic constants are excluded, allows overcoming problems due to contaminating the overall VPT2 treatment and higher frequency vibrations. The most reliable structural, spectroscopic and energetic results can be obtained combining various computational methods ranging from density functional theory (DFT) to coupled-cluster (CC), with the latter representing also references for the benchmarking of different DFT methodologies.

2-Chloro-4-fluorotoluene was investigated using a combination of molecular jet Fourier transform microwave spectroscopy in the frequency range from 5 to 21 GHz and quantum chemistry. The molecule experiences an internal rotation of the methyl group, which causes a fine splitting of all rotational transitions into doublets with separation on the order of a few tens of kHz. In addition, hyperfine effects originating from the chlorine nuclear quadrupole moment coupling its spin to the end-over-end rotation of the molecule are observed. The torsional barrier was derived using both the rhoA. Belloche, A.A. Mescheheryakov, R.T. Garrod, V.V. Ilyushin, E.A. Alekseev, R.A. Motiyenko, I. Margules, H.S.P. Müller, K.M. Menten, Astron. Astrophys. 601, A49 (2017).nd the combined-axis-method,H. Hartwig, H. Dreizler, Z. Naturforsch. 51a 923 (1996).iving a value of 462.5(41) cm⁻¹. Accurate rotational constants and quadrupole coupling constants were determined for two ³⁵Cl and ³⁷Cl isotopologues and compared with Bailey’s semi-experimental quantum chemical predictions.W.C. Bailey, J. Mol. Spectrosc. 209 57 (2001).he gas phase molecular structure was deduced from the experimental rotational constants supplemented with those calculated by quantum chemistry at various levels of theory. The values of the methyl torsional barrier and chlorine nuclear quadrupole coupling constants were compared with the theoretical predictions and with those of other chlorotoluene derivatives.

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A. Belloche, A.A. Mescheheryakov, R.T. Garrod, V.V. Ilyushin, E.A. Alekseev, R.A. Motiyenko, I. Margules, H.S.P. Müller, K.M. Menten, Astron. Astrophys. 601, A49 (2017).a H. Hartwig, H. Dreizler, Z. Naturforsch. 51a 923 (1996).g W.C. Bailey, J. Mol. Spectrosc. 209 57 (2001).T

Water clusters provide an opportunity to explore the effects of nuclear quantum effects on the stability of hydrogen-bonded networks. Because of their well-defined size, such studies provide an opportunity to make detailed comparisons between experiment and calculation and explore experimental measurable consequences of nuclear quantum effects through explorations of changes in zero-point structures upon partial or full deuteration. Such studies are challenging due to the large number of relevant degrees of freedom, as the changes in the anharmonic frequencies of OH stretching vibrations upon hydrogen bond formation are comparable to the zero-point energy in the low-frequency intermolecular vibrations. This also makes these systems challenging for calculations by Diffusion Monte Carlo (DMC). Earlier studies indicated that ensemble sizes of upwards of 10⁶ walkers are needed to obtain reliable energies.Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.n this presentation, we will describe recent work in our group in developing a modified DMC approach in which guiding functions are used to improve the sampling of the high-frequency intramolecular vibrations (OH stretches and HOH bends). With this modification, the energies and wave functions can be obtained using ensembles that are more than an order of magnitude smaller compared to those used in earlier studies.Lee, V. G. M.; Vetterli, N. J.; Boyer, M. A. and McCoy, A. B., J. Phys. Chem. A (2020), 124, 6903-6912.ith this more efficient algorithm, we explore the effects of nuclear quantum effects on the relative energies of the low-energy prism and cage structures, as well as the relative energies of the partially deuterated (H₂O)₅(D₂O) and (H₂O)(D₂O)₅ clusters.

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Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.I Lee, V. G. M.; Vetterli, N. J.; Boyer, M. A. and McCoy, A. B., J. Phys. Chem. A (2020), 124, 6903-6912.W

Diffusion Monte Carlo (DMC) is a technique that can be used to obtain the ground state energy and ground state wave function given a potential energy surface (PES) that fully describes the system of interest. However, one complication with this technique is that in order to obtain accurate results for molecular systems that have couplings between the high and low frequency vibrations, large ensemble sizes are needed. Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.ne approach to combat these large ensemble sizes is to use a guiding function to describe the high-frequency vibrations. This approach has been applied to studies of neutral water clusters, protonated water clusters, and CH₅⁺, where a significant reduction in the ensemble sizes that were needed in the simulations was achieved. Lee, V. G. M. and McCoy, A.B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.Finney, J. M., DiRisio, R. J., McCoy, A.B., J. Phys. Chem. A (2020), 124, 45, 9567-9577. An extension of this idea has been used to obtain excited state information in the coordinates described by the guiding functions. In this work, I will describe the applications of this approach to systems with large coupling among the vibrational degrees of freedom. The use of a guiding function that describes the ground state wave function of the high-frequency vibrations allow us to use smaller ensemble sizes, while producing ground state energies and wave functions that are as accurate or more accurate than those obtained using traditional DMC approaches. By using an excited state guiding function in the degrees of freedom that are being excited, we can obtain the excited state energy and wave functions through fixed-node DMC. With these wave functions in hand, we can also obtain overlaps between the ground state and first excited state, allowing us to evaluate intensities. This approach provides accurate representations of the excited state energy and the intensity of the transition from the ground state as long as the guiding functions for the ground and excited states provide fairly accurate representations of the wave functions along the excited degree of freedom.

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Footnotes:

Mallory, J. D. and Mandelshtam, V. A., J. Phys. Chem. A (2015), 119, 6504-6515.O Lee, V. G. M. and McCoy, A.B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.

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The rotational spectrum of the thiophene–water (thiophene–w) complex was studied for the first-time using Fourier transform microwave (FTMW) spectroscopy from 7 to 20 GHz. Supported by density functional theory (DFT) calculations, transitions belonging to a single dominant conformer were observed in the spectrum. By comparing the experimentally derived spectroscopic parameters, which includes data for the singly substituted ¹⁸O isotopic species, with the results from quantum chemical calculations at the B2PLYP-D3(BJ)/def2-TZVP level of theory, we show that the observed pattern of transitions is consistent with a structure that is highly averaged over a large amplitude rocking motion of the water. This effective geometry, stabilized via a primary O–H...π hydrogen bond, has the oxygen atom of water sitting above the plane of the thiophene molecule centered on the ring’s σ_v plane of symmetry. The spectrum also reveals a tunneling splitting with a characteristic 3:1 intensity ratio that arises from a water-centered internal rotation about its C₂ axis which exchanges its hydrogen atoms with an estimated barrier of approximately 2.7 kJ/mol (B2PLYP-D3(BJ)/def2-TZVP). Based on symmetry-adapted perturbation theory (SAPT) calculations, electrostatic and dispersive interactions are shown to be the most stabilizing contributors behind the formation of thiophene–w.

We have proposed that the ro-vibrationally averaged structure of a linear molecule is observed as being "bent."T. Hirano, U. Nagashima, P. Jensen, J. Mol. Spectrosc. 343, 54 (2018); T. Hirano, U. Nagashima, M. Baba, J. Mol. Spectrosc. 369, 111252 (2020); and references therein.o provide more evidence for this assertion, we here chose a linear molecule (XeHXe)⁺. We expected: The Xe atoms at both ends are so heavy that they stand still during vibration, so that in the bending mode, the central H⁺ atom inevitably moves perpendicularly against the a principal axis to give a "bent" ro-vibrationally averaged structure. The potential energy surface was calculated at the valence-CCSD(T)_DK3/[ANO-R3(Xe),cc-pV5Z-DK(H)] level, and ro-vibrational properties were calculated from the DVR3D wavefunctions in Discrete Variable Representation. The central H⁺, which has +0.6 e charge, polarizes the Xe atoms by its reaction field, giving 136 kcal/mol of the heat of formation: (XeHXe)⁺ is a stable cation. The equilibrium structure for Xe1-H-Xe2 has r_e(Xe1-H) = r_e(H-Xe2) = 1.8694 Å and ∠(Xe1-H-Xe2) = 180^°, so that (XeHXe)⁺ is a linear molecule. The ro-vibrationally averaged structure has 〈r(Xe1-H)〉₀ = 1.8913 Å, 〈r(H-Xe2)〉₀ = 1.9017 Å, and 〈∠(Xe1-H-Xe2)〉₀ = 166.6^°, indicating a large amplitude bending motion. The harmonic vibrational frequencies ω₁ (antisymmetric stretch), ω₂ (bending), and ω₃ (symmetric stretch) are 824, 562, and 149 cm⁻¹, respectively. The corresponding term values ν₁, ν₂, and ν₃ are 847, 545, and 143 cm⁻¹, respectively, to be compared with the values in para-H₂ matrixM. Tsuge, J. Kalinowski, R.B. Gerber, Y-P. Lee, J. Phys. Chem. A 119, 2651 (2015)_1 = 847.0 cm^-1 and _3 = 125.1 cm^-1.The relation _1 > _1 is a typical feature for [(ultra)heavy-light-(ultra)heavy] system.In the antisymmetric stretch mode, the central H^+ moves back and forth between almost stand−still two Xe atoms just like a ball in catch−ball play, and hence the _1 value is not affected by matrix medium. On the other hand, the symmetric stretching mode should severely be affected by the mass of the matrix medium, as is reported,^b

1,1,1,3,3,3-hexafluoro-2-propanol (hexafluoroisopropanol, HFIP) is an important solvent widely used in organic syntheses and biomatter treatments and is also considered as a greenhouse gas pollutant. The rotational spectrum of the most stable conformer of the HFIP—water complex, i.e. trans-HFIP—water, was reported before.[1] In the current study, rotational spectra of HIFP with water were recorded using a broadband, chirped pulse Fourier transform microwave spectrometer. A less stable gauche-FIP-water complex was identified and its rotational spectrum assigned for the first time. Ab initio calculations including some multidimensional rigid potential energy surface (PES) scans of possible water rotational/wagging motions were carried out and were employed to characterize the large amplitude motions (LAM)s in the both HFIP-water conformers. Several deuterium Isotopic species were also studied to aid the analysis of the large amplitude motions. Furthermore, non-covalent interaction (NCI) analyses were carried out to characterized the hydrogen bonding interactions in HFIP—water. [1] Shahi, A.; Arunan, E., Microwave spectroscopic and theoretical investigations of the strongly hydrogen bonded hexafluoroisopropanol-water complex. Physical Chemistry Chemical Physics 2015, 17 (38), 24774-24782.

2,2,3,3,3-pentafluoropropanol (PFP) is an important solvent for organic syntheses. It is also considered to be a green-house gas pollutant because it is radiatively active in the mid-infrared region. Understanding properties of PFP and its hydrogen bonding interactions with water in the gas phase may help to develop more realistic estimate of its effects because of the abundance of water in the atmosphere. In the current study, we apply both rotational spectroscopy and ab initio calculations to characterize large amplitude motions in PFP and its water complex and also hydrogen bonding interactions between PFP with water. Their rotational spectra were recorded using a cavity-based and a chirped pulse Fourier transform microwave spectrometers. Two most stable PFP conformers, Pg+g+ and Ptg+ were identified. The rotational transitions of the latter exhibit tunneling splittings. Two PFP-H2O conformers were identified and both of them show tunneling splittings. Deuterated species of the water complex were also investigated to assist the identification of the tunneling paths, in addition to the theoretical calculations. The large amplitude motions responsible for these splittings will be discussed.

Organic hydroperoxides and their radical products are important contributors to atmospheric chemistry, especially in atmospheric oxidation processes. Through understanding the vibrational spectroscopy of these compounds, we gain insights into their abundance in the atmosphere. The vibrational spectra of tert-butyl Hydrogen Peroxide (TBHP) and its radical product QOOH have been studied both experimentally and theoretically.¹ Due to their floppy nature and many low frequency degrees of freedom, standard methods such as harmonic treatments and second order vibrational perturbation theory are insufficient to fully characterize vibrational spectra of these molecules. In this work, we introduce a reaction path model that is sufficient to explain the OH-stretching region of QOOH. Within this model, we perform an adiabatic separation of the OH-stretching and COOH-torsion modes and add a harmonic zero-point energy correction to account for the other vibrational degrees of freedom. In the process of developing this model, we first investigated the OH-stretching region of THBP.²⁻³ Through this study, we discovered a strong contribution to the overall intensity in the v_OH + n_tor combination feature coming from the torsional dependence of the transition dipole moment. At low levels of vibrational excitation, the intensity of this feature reflects the torsion-dependence of the dipole function, while at higher levels of OH excitation (v_OH = 4 or 5) the intensity in this combination feature can be captured through a Franck-Condon treatment of the intensity. The transition from a mechanical to electrical origin to the intensity in this feature is discussed. Extension to QOOH will also be discussed. ¹ M. D. Likar, J. E. Baggott, and F. F. Crim, J. Chem. Phys. 90, 6266–6274 (1989). ² A. S. Hansen, R. M. Huchmala, E. Vogt, M. Boyer, T. Bhagde, M. F. Vansco, C. V. Jensen, A. Kjaersgaard, H. G. Kjaergaard, A. B. McCoy, and M. I. Lester, J. Chem. Phys. Submitted. 2021 ³ E. Vogt, R. M. Huchmala, C. V. Jensen, M. Boyer, Jens Wallberg, A. S. Hansen, A. Kjaersgaard, H. G. Kjaergaard, M. I. Lester, and A. B. McCoy, J. Chem. Phys. Submitted. 2021