Anharmonic Calculations Research Articles

Infrared action spectroscopy of doubly charged PAHs and their contribution to the aromatic infrared bands

The so-called aromatic infrared bands (AIBs) are attributed to emission of polycyclic aromatic hydrocarbons (PAHs). The observed variations toward different regions in space are believed to be caused by contributions of different classes of PAH molecules, that is to say with respect to their size, structure, and charge state. Laboratory spectra of members of these classes are needed to compare them to observations and to benchmark quantum-chemically computed spectra of these species. In this paper we present the experimental infrared (IR) spectra of three different PAH dications, naphthalene2+, anthracene2+, and phenanthrene2+, in the vibrational fingerprint region 500–1700 cm−1. The dications were produced by electron impact ionization of the vapours with 70 eV electrons, and they remained stable against dissociation and Coulomb explosion. The vibrational spectra were obtained by IR predissociation of the PAH2+ complexed with neon in a 22-pole cryogenic ion trap setup coupled to a free-electron infrared laser at the Free-Electron Lasers for Infrared eXperiments (FELIX) Laboratory. We performed anharmonic density-functional theory calculations for both singly and doubly charged states of the three molecules. The experimental band positions showed excellent agreement with the calculated band positions of the singlet electronic ground state for all three doubly charged species, indicating its higher stability over the triplet state. The presence of several strong combination bands and additional weaker features in the recorded spectra, especially in the 10–15 μm region of the mid-IR spectrum, required anharmonic calculations to understand their effects on the total integrated intensity for the different charge states. These measurements, in tandem with theoretical calculations, will help in the identification of this specific class of doubly-charged PAHs as carriers of AIBs.

Rotational spectroscopy of imidazole: Accurate spectroscopic information for three vibrationally excited states and the heavy-atom isotopologues up to 295 GHz

We report our analysis of the pure rotational spectra of low-lying vibrationally excited states and heavy-atom rare isotopologues of imidazole. To facilitate searches for imidazole in the interstellar medium, we previously described the analysis of the rotational spectrum of the imidazole main isotopologue across the 2–295 GHz range, and we extend this analysis here. Structure optimisation and anharmonic frequency calculations were performed to aid the spectral analysis. Three vibrationally excited states of imidazole were assigned in our room-temperature spectra, with energies up to approximately 670 cm−1 above the vibronic ground state. The vibrational states could act as temperature probes in warmer star-forming regions. The 13C and 15N heavy-atom isotopologues were assigned, which allowed for the structure of imidazole in the gas phase to be determined. Structural comparisons are drawn between the related heterocyclic molecules hydantoin and imidazolidine. An experimental gas-phase structure of the former is also determined in this work. The potential detection of the isotopologues could help deduce formation pathways towards imidazole and other nitrogen-containing cyclic compounds in interstellar space.

Cryogenic Messenger-IR Ion Spectroscopy Study of Phenol & Aniline Molecular Ions and of the common Fragment Ion [C5H6][rad]+ formed by EI-MS

Molecular ions of phenol and aniline as well as the fragment ion at m/z 66 formed by electron ionization are examined with cryogenic messenger-IR ion spectroscopy and theory. According to the recorded IR spectra aromatic ground state molecular ions of phenol and aniline are clearly identified. Similar to earlier reports our new set of spectroscopic and computational results supports the assumption that tautomeric molecular ions of phenol and aniline are only short-lived intermediates in the reaction path to the ultimate CO loss reaction product of phenol as well as the HNC loss product of aniline. Even the present cryogenic messenger-IR ion spectroscopy approach failed to collect spectroscopic evidence of the intermediate presence of these elusive tautomers of phenol and aniline molecular ions. However, our study clearly shows that the electron ionization mass spectrometry dissociation product ion of phenol and aniline at m/z 66 is the cyclopentadiene radical cation [C5H6]+ for the presence of which convincing spectroscopic evidence could be collected proving the structure assignment and identification. All messenger-IR ion spectroscopy experiments were conducted on a cryogenic 22-pole ion trap with the use of neon atoms for tagging. The MS instrument was coupled to a free electron laser delivering wavelength tunable IR radiation for spectroscopy. Harmonic and anharmonic force field calculations complement the experiments and support band assignments of the recorded IR spectra and general data interpretation.

The simplest sulfur-nitrogen hydrogen bond: Matrix isolation spectroscopy of H2S·NH3

Hydrogen bonding in SH⋯N systems has received little attention compared to other hydrogen bond motifs. To characterise SH⋯N bonding, infrared spectra of the most fundamental SH⋯N system—the H2S·NH3 complex—were recorded in solid argon. These experiments were complemented by high level ab initio and density functional theory calculations. The H2S symmetric stretch was observed to shift by −155.3 cm−1 when mixed with NH3, while the NH3 umbrella mode was found to shift by +31.8 cm−1. These, as well as deuterium and 15N isotopologue studies indicated the formation of a complex. The structure of the H2S·NH3 complex was determined to be almost identical to that of the H2O·NH3 complex, with a nearly linear SH⋯N bond. A binding energy of 8.6 kJ mol−1 (720 cm−1) was calculated at the CCSD(T) level of theory extrapolated to the complete basis set limit. Anharmonic frequency calculations at the DSD-PBEP86-D3BJ/aug-cc-pV(D+d)Z level of theory produced frequencies with a RMSD of 13 cm−1 for the complex, relative to the experimental values. Comparison with previous work showed that the SH⋯N bond is weaker in H2S·NH3 than the OH⋯N bond in the H2O·NH3 system.

A Spectroscopic View on Cosmic PAH Emission

ConspectusPolycyclic aromatic hydrocarbon molecules (PAHs) are ubiquitously present at high abundances in the Universe. They are detected through their infrared (IR) fluorescence UV pumped by nearby massive stars. Hence, their infrared emission is used to determine the star formation rate in galaxies, one of the key indicators for understanding the evolution of galaxies. Together with fullerenes, PAHs are the largest molecules found in space. They significantly partake in a variety of physical and chemical processes in space, influencing star and planet formation as well as galaxy evolution.Since the IR features from PAHs originate from chemical bonds involving only nearest neighbor atoms, they have only a weak dependence on the size and structure of the molecule, and it is therefore not possible to identify the individual PAH molecules that make up the cosmic PAH family. This strongly hampers the interpretation of their astronomical fingerprints. Despite the lack of identification, constraints can be set on the characteristics of the cosmic PAH family thanks to a joint effort of astronomers, physicists, and chemists.This Account presents the spectroscopic properties of the cosmic PAH emission as well as the intrinsic spectroscopic properties of PAHs and astronomical modeling of the PAH evolution required for the interpretation of the cosmic PAH characteristics. We discuss the observed spectral signatures tracing PAH properties such as charge, size, and structure and highlight the related challenges. We discuss the recent success of anharmonic calculations of PAH infrared absorption and emission spectra and outline the path forward. Finally, we illustrate the importance of models on PAH processing for the interpretation of the astronomical data in terms of the charge balance and PAH destruction.Throughout this Account, we emphasize that huge progress is on the horizon on the astronomical front. Indeed, the world is eagerly awaiting the launch of the James Webb Space Telescope (JWST). With its incredible improvement in spatial resolution, combined with its complete spectral coverage of the PAH infrared emission bands at medium spectral resolution and superb sensitivity, the JWST will revolutionize PAH research. Previous observations could only present spectra averaged over regions with vastly different properties, thus greatly confusing their interpretation. The amazing spatial resolution of JWST will disentangle these different regions. This will allow us to quantify precisely how PAHs are modified by the physical conditions of their host environment and thus trace how PAHs evolve across space. However, this will only be achieved when the necessary (and still missing) fundamental properties of PAHs, outlined in this Account, are known. We strongly encourage you to join this effort.

Anomalous High-Temperature Superconductivity in YH6.

Pressure-stabilized hydrides are a new rapidly growing class of high-temperature superconductors, which is believed to be described within the conventional phonon-mediated mechanism of coupling. Here, the synthesis of one of the best-known high-TC superconductors-yttrium hexahydride -YH6 is reported, which displays a superconducting transition at ≈224K at 166GPa. The extrapolated upper critical magnetic field Bc2 (0)of YH6 is surprisingly high: 116-158T, which is 2-2.5 times larger than the calculated value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coefficient 0.4 supports the phonon-assisted superconductivity. Current-voltage measurements show that the critical current IC and its density JC may exceed 1.75A and 3500A mm-2 at 4K, respectively, which is higher than that of the commercial superconductors, such as NbTi and YBCO. The results of superconducting density functional theory (SCDFT) and anharmonic calculations, together with anomalously high critical magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal-Eliashberg and Bardeen-Cooper-Schrieffer theories, and presence of an additional mechanism of superconductivity.

Van der Waals driven anharmonic melting of the 3D charge density wave in VSe2

Understanding of charge-density wave (CDW) phases is a main challenge in condensed matter due to their presence in high-Tc superconductors or transition metal dichalcogenides (TMDs). Among TMDs, the origin of the CDW in VSe2 remains highly debated. Here, by means of inelastic x-ray scattering and first-principles calculations, we show that the CDW transition is driven by the collapse at 110 K of an acoustic mode at qCDW = (2.25 0 0.7) r.l.u. The softening starts below 225 K and expands over a wide region of the Brillouin zone, identifying the electron-phonon interaction as the driving force of the CDW. This is supported by our calculations that determine a large momentum-dependence of the electron-phonon matrix-elements that peak at the CDW wave vector. Our first-principles anharmonic calculations reproduce the temperature dependence of the soft mode and the TCDW onset only when considering the out-of-plane van der Waals interactions, which reveal crucial for the melting of the CDW phase.

Fourier transform infrared (FTIR) spectroscopy of formaldoxime (CH2NOH) in the 450–3800 cm−1 region and its [formula omitted] band

The Fourier transform infrared (FTIR) spectrum of formaldoxime (CH2NOH) was recorded in the 700–3800 cm−1 region at the Australian Synchrotron with an unapodized resolution of 0.5 cm−1 to identify its fundamental and overtone bands and to measure their relative infrared (IR) intensities in this region. The high-resolution FTIR spectrum of the ν9 band of CH2NOH was also recorded with an unapodized resolution of 0.00096 cm−1 in the 450–600 cm−1 region for a rovibrational analysis. In the analysis of the A/B-hybrid type ν9 band, a total of 2011 infrared transitions (1655b-type and 356 a-type transitions) were fitted using the Watson's A-reduced and S-reduced Hamiltonians in the Ir representation with a root-mean-square (rms) deviation of 0.000096 cm−1 and 0.000305 cm−1 respectively. From this rovibrational analysis, the v9 = 1 state rotational constants (A, B and C) and five quartic terms (ΔJ, ΔJK, ΔK, δJ, δK) were improved from previous work and three sextic terms (ΦJK, ΦKJ, ΦK) were derived for the first time. The band center of the ν9 band of CH2NOH was found to be 530.0187764(63) cm−1 and 530.018762(18) cm−1 in the A-reduced and S-reduced Hamiltonians respectively. All five quartic and three sextic (ΦJK, ΦKJ, ΦK) centrifugal distortion terms of the ground state of CH2NOH were also improved with higher accuracy. They were obtained through the fitting of 3020 ground state combination differences (GSCDs) derived from the IR transitions of the ν9, ν12 and ν10 bands of CH2NOH, together with 23 previously reported microwave frequencies. The rms deviation of this GSCD fit was 0.000498 cm−1 and 0.000519 cm−1 in the A-reduced and S-reduced Hamiltonians respectively. Additionally, rotational constants and higher order centrifugal distortion terms of the ground and v9 = 1 states were computed from theoretical anharmonic calculations at two different levels of theory, B3LYP and MP2 with the cc-pVTZ basis set, for comparison with the experimental results. The calculated and experimental rovibrational constants of CH2NOH for both ground and v9 = 1 states were in good agreement.

IR photofragmentation of the phenyl cation: spectroscopy and fragmentation pathways.

We present the gas-phase infrared spectra of the phenyl cation, phenylium, in its perprotio (C6H5+) and perdeutero (C6D5+) forms, in the 260-1925 cm-1 (5.2-38 μm) spectral range, and investigate the observed photofragmentation. The spectral and fragmentation data were obtained using Infrared Multiple Photon Dissociation (IRMPD) spectroscopy within a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer (FTICR MS) located inside the cavity of the free electron laser FELICE (Free Electron Laser for Intra-Cavity Experiments). The 1A1 singlet nature of the phenylium ion is ascertained by comparison of the observed IR spectrum with DFT calculations, using both harmonic and anharmonic frequency calculations. To investigate the observed loss of predominantly [2C,nH] (n = 2-4) fragments, we explored the potential energy surface (PES) to unravel possible isomerization and fragmentation reaction pathways. The lowest energy pathways toward fragmentation include direct H elimination, and a combination of facile ring-opening mechanisms (≤2.4 eV), followed by elimination of H or CCH2. Energetically, all H-loss channels found are more easily accessible than CCH2-loss. Calculations of the vibrational density of states for the various intermediates show that at high internal energies, ring opening is thermodynamically the most advantageous, eliminating direct H-loss as a competing process. The observed loss of primarily [2C,2H] can be explained through entropy calculations that show favored loss of [2C,2H] at higher internal energies.

Exploration of chromophores for a VCD couplet in a spectrally transparent infrared region for biomolecules.

Interactions of two chromophores such as carbonyl groups yield a strong VCD couplet that reflects the molecular structures. The use of VCD couplets for biomacromolecular structural studies has been hampered by severe signal overlap caused by numerous functional groups that originally exist in biomacromolecules. Nitrile, isonitrile, alkyne, and azido groups show characteristic IR absorption in the 2300-2000 cm-1 region, where biomolecules do not strongly absorb. We herein examined the usefulness of these functional groups as chromophores to observe a strong VCD couplet that can be readily interpreted using theoretical calculations. Studies on a chiral binaphthyl scaffold possessing two identical chromophores showed that nitrile and isonitrile groups generate moderately-strong but complex VCD signals due to anharmonic contributions. The nature of their anharmonic VCD patterns is discussed by comparison with the VCD spectrum of a mono-chromophoric molecule and by anharmonic DFT calculations. On the other hand, through studies on diazido binaphthyl and diazido monosaccharide, we demonstrated that the azido group is more promising for structural analysis of larger molecules due to its simple, strong VCD couplet whose spectral patterns are readily predicted by harmonic DFT calculations.

Vibrationally resolved coupled-cluster x-ray absorption spectra from vibrational configuration interaction anharmonic calculations.

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the adaptive density-guided approach scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules.

A Rather Universal Vibrational Resonance in 1:1 Hydrates of Carbonyl Compounds.

When the lower frequency OH stretching fundamental of a water molecule is shifted to the 3500 cm-1 spectral range by the solvation of a carbonyl compound, in this case a ketone, its infrared intensity is shared with a dark state. It is shown by chemical and isotope substitution for more than a dozen systems that the location of this resonance is remarkably substitution-independent. Harmonic and anharmonic model calculations support its assignment to a combination of the water bending overtone and in-plane water libration. This previously unrecognized intramolecular-intermolecular coupling in single solvent water has a strength of 7-10 cm-1. It may have been sporadically observed before in a few other carbonyl compounds such as amides, without any previous exploration of its potential universality. The resulting generic picosecond energy redistribution channel for aqueous solutions may represent a slow counterpart and doorway model of what happens on a subpicosecond time scale when the hydrogen bonds become stronger, such as in carboxylic acid dimers or protonated water clusters.

Cyclohexane Vibrations: High-Resolution Spectra and Anharmonic Local Mode Calculations.

High-resolution infrared absorption spectra of cyclohexane have been recorded from 1100 to 4000 cm-1 at room temperature and 241 K. Cyclohexane is an oblate symmetric top with D3d symmetry. A rotational analysis was obtained for the ν27 (eu) and ν14 (a2u) CH2 scissor modes at 1452.9 and 1456.4 cm-1, respectively. Several combination modes were also assigned and rotationally analyzed. The C-H stretching modes are perturbed by overtone and combination modes of the CH2 scissor vibrations, and an anharmonic local mode calculation was needed to interpret the spectra. The four main strong allowed C-H stretching modes appear as two a2u eu pairs near at 2862 and 2933 cm-1. The Fermi-resonance local mode model coupling terms give physical insight into the effects that organize the cyclohexane vibrational energy levels. The unstrained cyclohexane molecule is a useful paradigm for six-membered rings in larger chemical and biological systems.

Vibrational spectroscopic signatures of hydrogen bond induced NH stretch-bend Fermi-resonance in amines: The methylamine clusters and other N-H⋯N hydrogen-bonded complexes.

The appearance of multiple bands in the N-H stretching region of the infrared spectra of the neutral methylamine dimer and trimer is a sign of NH bend-stretch anharmonic coupling. Ab initio anharmonic calculations were carried out in a step-wise manner to reveal the origin of various bands observed in the spectrum of the methylamine dimer. A seven-dimensional potential energy surface involving symmetric and asymmetric stretching and bending vibrations of both the hydrogen bond donor and the acceptor along intermolecular-translational modes was constructed using the discrete variable representation approach. The resulting spectrum of the dimer shows five bands that can be attributed to the symmetric stretching (νsym D), asymmetric stretchin (νasym D), and bending overtone (2νbend D) of the donor moiety. These appear along with the combination band arising out of bending vibrations of the donor and acceptor (νbend D + νbend A) and with the combination of the intermolecular translational mode over the donor bending overtone (νtrans + 2νbend D). The spectrum of the trimer essentially consists of all the features seen in the dimer with marginal changes in band positions. The analysis of the experimental spectra based on the two-state deperturbation model and ab initio anharmonic calculations yield a matrix element of about 40 cm-1 for the N-H bend-stretch Fermi resonance coupling. In general, the IR spectra of the hydrogen-bonded amino group depict three sets of bands that arise due to bend-stretch Fermi resonance coupling.

Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations.

The accuracy and convergence of a series of commonly used split-valence electronic basis sets are systematically investigated for the anharmonic molecular vibrational spectroscopic calculations using the second-order perturbative corrected vibrational self-consistent field theory. A series of 18 split-valence basis sets with increasing flexibility is assessed in conjunction with MP2 and density functional theory (DFT)-based dispersion-corrected B3LYP potentials and applied to a set of molecular systems with different electronic and vibrational characteristics. The computed fundamental transitions and intensities are compared with the experimental values to assess the accuracy of different basis sets. Comparisons with high levels of Dunning basis sets, aug-cc-pVQZ along with def2-TZVPP and aug-pc-2 type basis sets, are also tested to check the convergence. A full statistical error analysis has been performed, assessing the success and failure of each basis set in terms of both accuracy and precision. The general statement "the bigger the basis, the better the results" is not strictly followed for bigger basis sets that are nearly converged to the adiabatic ab initio limit. It is found that the basis set hierarchy holds good for minimal basis sets up to polarized double-ζ basis sets. Beyond that, the improvements in comparison to experimental results or with very high end aug-cc-pVQZ and others are found rather slow. Finally, a prescription regarding the choice of a basis set for a suitable balance between accuracy and the computational time is given, which can be further used to investigate specific normal modes and large molecules as a blackbox.

Rotational spectroscopy and precise molecular structure of 1,2-dichlorobenzene

Supersonic expansion rotational spectroscopy at 4–18 GHz with rectangular pulse and chirp excitation was used to measure spectra of twelve isotopic species of 1,2-dichlorobenzene at conditions of completely resolved double chlorine hyperfine structure by using a newly constructed slit expansion nozzle. Four species: 37Cl13 and the three singly substituted 13C species have been assigned for the first time. Spectroscopic constants for six isotopic species with single deuterium substitution were considerably improved by using chemically synthesised samples. Hyperfine constants in the field gradient principal axes system were determined and used as a test of self-consistency of the analysis. Additional room-temperature measurements up to 275 GHz allowed assignment of rotational transitions in first excited states of the three lowest normal modes. The determined values of vibrational changes in rotational constants, inertial defects, and quartic and sextic centrifugal distortion constants, allowed calibration of harmonic and anharmonic force field calculations, resulting in determination, among others, of precise semi-experimental equilibrium, reSE, geometry of 1,2-dichlorobenzene. It is found that r(C-C) and ∠(C-C-C) in the phenyl ring of 1,2-dichlorobenzene show very small changes relative to benzene.

Efficient anharmonic lattice dynamics calculations of thermal transport in crystalline and disordered solids

Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic lattice dynamics provides a powerful framework for the description of heat transport at the nanoscale. One of the advantages of this method is that it naturally includes quantum effects due to atoms vibrations, which are needed to compute the thermal properties of semiconductors widely used in nanotechnology, like silicon and carbon, even at room temperature. While the heat transport picture substantially differs between amorphous and crystalline semiconductors from a microscopic standpoint, a unified approach to simulate both crystals and glasses has been devised. Here, we introduce a unified workflow, which implements both the Boltzmann Transport equation and the quasi-harmonic Green-Kubo methods. We discuss how the theory can be optimized to exploit modern parallel architectures, and how it is implemented in κALDo: a versatile and scalable open-source software to compute phonon transport in solids. This approach is applied to crystalline and partially disordered silicon-based systems, including bulk silicon and clathrates, and on silicon–germanium alloy clathrates with largely reduced thermal conductivity.

Theory of the thickness dependence of the charge density wave transition in 1 T-TiTe2

Most metallic transition metal dichalcogenides undergo charge density wave (CDW) instabilities with similar or identical ordering vectors in bulk and in single layer, albeit with different critical temperatures. Metallic 1 T-TiTe2 is a remarkable exception as it shows no evidence of charge density wave formation in bulk, but it displays a stable 2 × 2 reconstruction in single-layer form. The mechanism for this 3D-2D crossover of the transition is still unclear, although strain from the substrate and the exchange interaction have been pointed out as possible formation mechanisms. Here, by performing non-perturbative anharmonic calculations with gradient corrected and hybrid functionals, we explain the thickness behaviour of the transition in 1 T-TiTe. We demonstrate that the CDW in single-layer TiTe2 occurs from the interplay of non-perturbative anharmonicity and an exchange enhancement of the electron-phonon interaction, larger in the single layer than in the bulk. Finally, we study the electronic and structural properties of the single-layer CDW phase and provide a complete description of its electronic structure, phonon dispersion as well as infrared and Raman active phonon modes.

Dual Basis Approach for Ab Initio Anharmonic Calculations of Vibrational Spectroscopy: Application to Microsolvated Biomolecules.

A dual electronic basis set approach is introduced for more efficient but accurate calculations of the anharmonic vibrational spectra in the framework of the vibrational self-consistent field (VSCF) theory. In this approach, an accurate basis set is used to compute the vibrational spectra at the harmonic level. The results are used to scale the potential surface from a more modest but much more efficient basis set. The scaling is such that at the harmonic level the new, scaled potential agrees with one of the accurate basis sets. The approach is tested in the application of the microsolvated, protected amino acid Ac-Phe-OMe, using the scaled anharmonic hybrid potential in the VSCF and VSCF-PT2 algorithms. The hybrid potential method yields results that are in good accord with the experiment and very close to those obtained in calculations with the high-level, very costly potential from the large basis set. At the same time, the hybrid potential calculations are considerably less expensive. The results of the hybrid calculations are much more accurate than those computed from the potential surface corresponding to the modest basis set. The results are very encouraging for using the hybrid potential method for inexpensive yet sufficiently accurate anharmonic calculations for the spectra of large biomolecules.

Torsional States and Tunneling Probability in HOSOH, DOSOD, and DOSOH Molecules Analyzed at the CBS Limit.

Torsional vibrations of a sulfoxylic acid molecule (HOSOH) and its two deuterated isotopologues were analyzed for the first time. Harmonic and anharmonic calculations of the vibrational frequencies of the trans- and cis-conformers were performed. More rigorous consideration of the torsional vibrations was made based on 2D potential energy and kinematic coefficient surface calculations. These calculations were made at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory, and then the results were extrapolated to the complete basis set limit. The 2D surface of the zero-point vibrational energy of a sulfoxylic acid molecule was calculated at the MP2/cc-pVTZ level of theory in anharmonic approximation and taken into account. The energies of the torsional states were found by numerical solution of the vibrational Schrödinger equation of the restricted dimensionality using the Fourier method. 2D surfaces of the dipole moment components were calculated too. Using all these data, the torsional IR spectra of the trans- and cis-conformers of the HOSOH, DOSOD, and DOSOH molecules were also modeled at different temperatures.