A new method for the precise semiempirical determination of the basic parameters (structural parameters and parameters of the intramolecular potential energy surface, PES) of a molecule on the basis of highly accurate experimental data from the microwave and submillimeter-wave regions is suggested. The options and advantages of this method in comparison with the other methods of molecular PES determination are discussed using a diatomic molecule as an appropriate illustration. The HCl molecule is exploited as a suitable example. It is shown with this example that the use of a very limited number (ten for H35Cl and five for D35Cl) of submillimeter-wave line positions allows one to determine the values of the equilibrium rotational parameter, harmonic frequency, and anharmonic coefficients of the third, fourth, and fifth order with accuracy of 0.01%, 0.01%, 0.01%, 2.1%, and 10.1%, respectively, in comparison with the analogous results obtained from extensive infrared studies.

The infrared spectrum of mono-silane was measured at varied experimental conditions with a Bruker Fourier transform infrared spectrometer IFS125HR and analyzed for the first time in the 2600-2950 cm-1 region of the octad where 16 strongly interacting triply excited bending bands are located. The 3505 transitions belonging to fourteen sub-bands of the octad (with the exception of unappeared 3 4 ( 1 ) and 3 2 ( 2 ) ) were assigned (max = 20) and theoretically analyzed in the frame of the effective Hamiltonian model. The obtained set of 139 fitted parameters reproduces the initial 3505 experimental line positions with the rms = 7.3 x 10 -4 cm-4. A list of assigned experimental transitions is presented as the Supplementary data 2 to this paper.

High resolution spectra of the H232S hydrogen sulfide are re–analysed in the region of its first decade. Thanks to the improvement of the experimental conditions (in particular, an increase in both the instrumental resolution and the effective absorption path length by 1.5 times), on the one hand, and of the use of a more correct Hamiltonian model (which additionally takes into account the interactions of the bands under study with the ν1+4ν2 and 4ν2+ν3 bands), on the other hand, the information obtained as a result of the analysis of experimental data has been significantly expanded and improved compared to the previous status. In particular, (1) the total number of assigned lines has been increased by approximately 15 percent, (2) the maximum values of quantum numbers Jmax and Kamax for the assigned lines have been increased for the studied bands in average by 20–25 percent, (3) the number of obtained ”experimental“ energy levels of the upper vibrational states (especially for the (121) and (022) vibrational states) has been significantly increased, (4) despite the increase in the number of initial vibrational–rotational energies and quantum numbers Jmax and Kamax, the value of the standard deviation drms has improved 2.7 times for the obtained upper vibrational–rotational energies.

A highly accurate rotational-vibrational analysis of Fourier transform infrared spectra of the 12CD4 molecule is presented. The high resolution infrared spectra were measured with a IFS125 HR Fourier transform interferometer from Bruker at an optical resolution of 0.003 cm(-1) and analyzed in the 1750-2400 cm(-1) region. Here the 2 nu(2), nu(2)+nu(4), 2 nu(4), nu(1) and nu(3) bands (altogether, nine sub-bands of different symmetry) of the pentad are located. The number of 1213/1993/1576/77/1582 transitions with the J(max) = 23/23/23/14/32 were assigned to the 2 nu(2), nu(2)+nu(4), 2 nu(4), nu(1) and nu(3) bands of 12CD4. The obtained experimental data were used for the determination of the upper ro-vibrational energy values. To provide more correct values of the upper energies, more than 7800 highly accurate "hot" transitions from the dyad region were additionally processed. In general, 4088 upper ro-vibrational energies of the pentad (for comparison, 2525 upper ro-vibrational energies with the value of J(max)=20 are known in the modern literature up to now) were determined, which were used then in the weighted fit procedure with a goal to determine the spectroscopic parameters (band centers, rotational, centrifugal distortion, tetrahedral splitting and resonance interaction parameters) of the effective Hamiltonian. The obtained drms value is 5.5x10(-4) cm(-1) which is almost one hundred times better than the reproduction of the same set of experimental data by the parameters known in the earlier literature.

We have started a measurement campaign of numerous methanol isotopologs in low-lying torsional states in order to provide extensive line lists for radio astronomical observations from an adequate spectroscopic model and to investigate how the intricate vibrationtorsion-rotation interactions manifest themselves in the spectra of different isotopic species. After CD3OH and CD3OD, we turn our focus to CH3OD, which is an important species for studying deuteration in prestellar cores and envelopes that enshroud protostars. Notably, deuteration is frequently viewed as a diagnostic tool for star formation. The measurements used in this study were obtained in two spectroscopic laboratories and cover large fractions of the 34 GHz-1.35 THz range. As done in previous studies, we employed a torsion-rotation Hamiltonian model for our analysis that is based on the rho-axis method. The resulting model describes the ground and first excited torsional states of CH3OD well up to quantum numbers J <= 51 and K-a <= 18. We derived a line list for radio astronomical observations from this model that is accurate up to at least 1.35 THz and should be sufficient for all types of radio astronomical searches for this methanol isotopolog in these two lowest torsional states. This line list was applied to a reinvestigation of CH3OD in data from the Protostellar Interferometric Line Survey of IRAS 16293-2422 obtained with the Atacama Large Millimeter/submillimeter Array. The new accurately determined value for the column density of CH3OD implies that the deuteration in methanol differs in its two functional groups by a factor of similar to 7.5.

A set of new relations between different spectroscopic parameters of the high symmetry XY4 spherical top molecules is derived on the basis of the general isotopic substitution theory, and a comprehensive high accurate analysis of the five stretching bands (the bands ν1+ν3(F2), 2ν3(F2), 2ν3(E), 2ν3(A1), and 2ν1(A1); the three latter ones are forbidden in absorption) of the tetradecad of the SiH4 molecule is made. The high resolution spectra of MSiH4 (M=28,29,30) in their natural abundance were recorded with a Bruker IFS125 HR Fourier transform infrared spectrometer at the Technische Universität Braunschweig, Germany with an optical resolution of 0.003 cm−1 and theoretically analyzed (in this case, for the first time both for all five bands of the 29SiH4 and 30SiH4 species, and for 2ν3(E), 2ν1(A1) bands of the 28SiH4 one). The number of 2713 transitions of the 28SiH4 species (which is more than fourteen times higher compared to analogous studies carried out earlier) belonging to all five ro-vibrational bands of the tetradecad (which are 272, 1897, 15, 369, and 160 transitions of the ν1+ν3(F2), 2ν1(A1), 2ν3(A1), 2ν3(F2), and 2ν3(E) bands) were assigned with the values of quantum number Jmin/Jmax = 5/22, 1/24, 14/20, 4/24, and 6/23, respectively. The analysis of the obtained experimental data was made on the basis of the Hamiltonian model which takes into account all effects and resonance interactions which are possible in such molecular system. The weighted fit of the 2713 transitions led to a set of 40 rotational, centrifugal distortion, tetrahedral splitting, and resonance interaction parameters which reproduce the initial experimental data with an accuracy of drms=4.11×10−4 cm−1. An analogous analysis was made for the two other isotopologues, 29SiH4 and 30SiH4, of silane. In this case, the initial values of the most important spectroscopic parameters of both species were theoretically estimated on the basis of results of the isotopic substitution theory. As the result of the analysis, two sets of the 12 spectroscopic parameters were obtained from the weighted fits for the 29SiH4 and 30SiH4 molecules which reproduce the 461 and 375 initial ro-vibrational transitions with the drms of 3.91×10−4 and 4.9710−4 cm−1.

We report here the analytical description of vibrational wave functions being most important for applications in quantum mechanics, molecular and chemical physics as applied to the high symmetry XY4 (Td) molecules. A general method is discussed and, for the first time, all vibrational functions of such molecule type are presented in an analytical and symmetrized form for all polyads up to the polyad number N=4. To illustrate the relevant application of the derived results, an accurate prediction of all vibrational band centers up to 8000 cm−1 is made for five stable isotopologues MGeH4 (M=76,74,73,72,70) of the germane molecule.

The new improved effective dipole moment model is derived for molecules of the axial C3v symmetry. The obtained result is, on the one hand, of the same order of efficiency but much simpler and clearer in applications in comparison with previous models derived on the basis of the irreducible tensorial sets theory and, on the other hand, mathematically more correct in comparison with concepts like the Herman–Walles function. Symmetric ro–vibrational bands of the mentioned molecule types are considered in the present study with taking into account the fourth order centrifugal corrections to the main effective dipole moment operator both for”allowed“ and ”forbidden“ transitions.

A set of new relations between different spectroscopic parameters of the high symmetry XY4 spherical top molecules is derived on the basis of the general isotopic substitution theory, and a comprehensive high accurate analysis of the five stretching bands (the bands ν1+ν3(F2), 2ν3(F2), 2ν3(E), 2ν3(A1), and 2ν1(A1); the three latter ones are forbidden in absorption) of the tetradecad of the SiH4 molecule is made. The high resolution spectra of MSiH4(M=28,29,30) in their natural abundance were recorded with a Bruker IFS125 HR Fourier transform infrared spectrometer at the Technische Universität Braunschweig, Germany with an optical resolution of 0.003 cm-1 and theoretically analyzed (in this case, for the first time both for all five bands of the 29SiH4 and 30SiH4 species, and for 2ν3(E), 2ν1(A1) bands of the 28SiH4 one). The number of 2713 transitions of the 28SiH4 species (which is more than fourteen times higher compared to analogous studies carried out earlier) belonging to all five ro-vibrational bands of the tetradecad (which are 272, 1897, 15, 369, and 160 transitions of the ν1+ν3(F2), 2ν1(A1), 2ν3(A1), 2ν3(F2), and 2ν3(E) bands) were assigned with the values of quantum number Jmin/Jmax = 5/22, 1/24, 14/20, 4/24, and 6/23, respectively. The analysis of the obtained experimental data was made on the basis of the Hamiltonian model which takes into account all effects and resonance interactions which are possible in such molecular system. The weighted fit of the 2713 transitions led to a set of 40 rotational, centrifugal distortion, tetrahedral splitting, and resonance interaction parameters which reproduce the initial experimental data with an accuracy of drms=4.11×10-4 cm-1. An analogous analysis was made for the two other isotopologues, 29SiH4 and 30SiH4, of silane. In this case, the initial values of the most important spectroscopic parameters of both species were theoretically estimated on the basis of results of the isotopic substitution theory. As the result of the analysis, two sets of the 12 spectroscopic parameters were obtained from the weighted fits for the 29SiH4 and 30SiH4 molecules which reproduce the 461 and 375 initial ro-vibrational transitions with the drms of 3.91×10-4 and 4.9710-4 cm-1.

A highly accurate ro-vibrational analysis of FTIR spectra (line positions of 13CD4 and line strengths of both the 12CD4 and 13CD4 species) is presented. The high-resolution infrared spectra of both molecules were measured with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.003 cm−1 and analyzed in the regions of 800–1400 cm−1 where the ν2/ν4 dyad is located. The number of 901 transitions with Jmax=23 were assigned to the ν4 and ν2 bands of 13CD4 (this number is about 5.3 times higher in comparison with the number of known assigned transitions for 13CD4). The weighted fit of experimental line positions was made using the Hamiltonian model which takes into account the resonance interactions between the (0001,F2) and (0100,E) vibrational states. As a result, set of 18 fitted parameters of the (0001,F2)/(0100,E) vibrational states of 13CD4 was determined which reproduce the initial 901 experimental ro–vibrational line positions with the drms=2.59×10−4 cm−1, which is close to the experimental uncertainty of the recorded spectra and about 1330 times better in comparison with the reproduction of the same line position values by the use of parameters from Loëte et al. (1983). The analysis of 1557 experimental lines of the dyad of 12CD4 and 131 lines of the dyad of 13CD4 was fulfilled with the Hartmann–Tran profile to simulate the measured line shape and to determine experimental line intensities. Sets of 6/1 varied effective dipole moment parameters of 12CD4/13CD4 are determined which reproduce the initial 1557/131 line strengths with the drms=4.80% and 4.21%. Lists of the assigned line positions and strengths in the studied region are presented as the Supplementary data to this paper.

We report here the analytical description of one of the important problems in the study of XY4 (Td) molecules, namely, description of vibrational tetrahedral sub-level structures and resonance interactions caused by the high symmetry of a molecule. The results obtained are applied to description of the vibrational energy spectrum of the CH4 and GeH4 molecules.

A highly accurate ro-vibrational analysis of FTIR spectra (line positions of (CD4)-C-13 and line strengths of both the (CD4)-C-12 and (CD4)-C-13 species) is presented. The high-resolution infrared spectra of both molecules were measured with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.003 cm(-1) and analyzed in the regions of 800-1400 cm(-1) where the v(2)/v(4) dyad is located. The number of 901 transitions with J(max) = 23 were assigned to the v(4) and v(2) bands of (CD4)-C-13 (this number is about 5.3 times higher in comparison with the number of known assigned transitions for (CD4)-C-13). The weighted fit of experimental line positions was made using the Hamiltonian model which takes into account the resonance interactions between the (0001, F-2) and (0100, E) vibrational states. As a result, set of 18 fitted parameters of the (0001, F2)/(0100, E) vibrational states of (CD4)-C-13 was determined which reproduce the initial 901 experimental ro-vibrational line positions with the d(rms) = 2.59 x 10(-4) cm(-1), which is close to the experimental uncertainty of the recorded spectra and about 1330 times better in comparison with the reproduction of the same line position values by the use of parameters from Loete et al. (1983). The analysis of 1557 experimental lines of the dyad of (CD4)-C-12 and 131 lines of the dyad of (CD4)-C-13 was fulfilled with the Hartmann-Tran profile to simulate the measured line shape and to determine experimental line intensities. Sets of 6/1 varied effective dipole moment parameters of (CD4)-C-12/(CD4)-C-13 are determined which reproduce the initial 1557/131 line strengths with the d(rms) = 4.80% and 4.21%. Lists of the assigned line positions and strengths in the studied region are presented as the Supplementary data to this paper.

Highly resolved spectra of the 16O35Cl16O isotopologue of chlorine dioxide were recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer in the region of the ν3 band. The analysis was made in the frame of the spin-rotational effective Hamiltonian (in A-reduction and Ir-representation) taking into account spin-rotational coupling operators up to the sixth order and the corresponding reduction of the Hamiltonian. The mathematical description of the ro-vibrational spectra was implemented to the specially created computer program ROVDES. Under the present experimental conditions, we were able to assign more than 5200 spin-rotational transitions to the ν3 band. This number is 2.4 times higher compared to the previous studies available from the literature. The vibrational ground state parameters were improved, and the 2220 upper spin-rotation-vibration energy levels were determined and used as initial data in the inverse spectroscopic problem with the derived effective spin-rotational Hamiltonian. A total of 37 fitted parameters were determined (22 rotational and centrifugal parameters and 15 parameters of spin-rotation coupling). The appearance of strong Coriolis resonance interactions between the (001) and (100) vibrational states in the sets of (001)[N,Ka = 9], (001)[N,Ka = 17], (001)[N,Ka = 18] and (001)[N,Ka = 19] spin-rotation-vibration levels was experimentally observed for the first time and explained. The drms = 1.4 × 10-4 cm-1 reproduction of the initial "experimental" upper ro-vibrational energy values was achieved which is considerably better compared to the use of parameters from a previous study ([J. Ortigoso et al., J. Mol. Spectrosc., 1992, 155, 25-43]).

The effective dipole moment model for molecules of axial C3v symmetry is derived on the basis of the symmetry properties of a molecule which, on the one hand, is of the same order of efficiency (but much simpler and clearer in applications) as the analogous models derived on the basis of the irreducible tensorial sets theory, and, on the other hand, mathematically more correct in comparison with concepts like the Herman–Walles function used in the models. As an application of the general results obtained, we discuss high-resolution infrared spectra of CH335Cl, recorded with the Zürich prototype ZP2001 (Bruker IFS125 HR) Fourier transform infrared spectrometer at a resolution of 0.001 cm−1 and analyzed in the region of 880–1190 cm−1 (ν6 bending fundamental centered at ν0 = 1018.070790 cm−1). Absolute strengths of more than 2800 transitions (2081 lines) were obtained from the fit of their shapes both with Voigt and Hartmann–Tran profiles, and parameters of the effective dipole moment of the ν6 band were determined by the computer code SYMTOMLIST (SYMmetric TOp Molecules: LIne STrengths), created on the basis of a derived theoretical model. As the first step of the analysis of the experimental data, assignments of the recorded lines were made. A total of 5124 transitions with Jmax = 68, Kmax = 21 were assigned to the ν6 band. The weighted fit of 2077 upper energy values obtained from the experimentally recorded transitions was made with a Hamiltonian which takes into account different types of ro–vibrational effects in doubly degenerate vibrational states of the C3v-symmetric molecule. As the result, a set of 25 fitted parameters was obtained which reproduces the initial 2077 upper “experimental” ro–vibrational energy values with a root mean square deviation drms=4.7×10−5 cm−1. At the second step of the analysis, the computer code SYMTOMLIST was used for determination of the parameters of the derived effective dipole moment model. Six effective dipole moment parameters were obtained from the weighted fit procedure which reproduces absolute experimental strengths of the 2804 initial experimental transitions with a relative drms=3.4%.

Solar-type prestellar cores and protostars display large amounts of deuterated organic molecules. Recent findings on CHD$_2$OH and CD$_3$OH toward IRAS 16293-2422 suggest that even fully deuterated methanol, CD$_3$OD, may be detectable as well. However, searches for CD$_3$OD are hampered in particular by the lack of intensity information from a spectroscopic model. The objective of the present investigation is to develop a spectroscopic model of CD$_3$OD in low-lying torsional states that is sufficiently accurate to facilitate searches for this isotopolog in space. We carried out a new measurement campaign for CD$_3$OD involving two spectroscopic laboratories that covers the 34 GHz-1.1 THz range. A torsion-rotation Hamiltonian model based on the rho-axis method was employed for our analysis. Our resulting model describes the ground and first excited torsional states of CD$_3$OD well up to quantum numbers $J \leq 51$ and $K_a \leq 23$. We derived a line list for radio-astronomical observations from this model that is accurate up to at least 1.1 THz and should be sufficient for all types of radio-astronomical searches for this methanol isotopolog. This line list was used to search for CD$_3$OD in data from the Protostellar Interferometric Line Survey of IRAS 16293$-$2422 obtained with the Atacama Large Millimeter/submillimeter Array. While we found several emission features that can be attributed largely to CD$_3$OD, their number is still not sufficiently high enough to establish a clear detection. Nevertheless, the estimate of 2$\times 10^{15}$ cm$^{-2}$ derived for the CD$_3$OD column density may be viewed as an upper limit that can be compared to column densities of CD$_3$OH, CH$_3$OD, and CH$_3$OH. The comparison indicates that the CD$_3$OD column density toward IRAS 16293-2422 is in line with the enhanced D/H ratios observed for multiply deuterated complex organic molecules.

The high resolution spectrum of the v1 + v3 band of the 35ClO2 free radical was recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer and theoretically analysed with an improved theoretical basis including the reduced effective spin-rotation Hamiltonian (which takes into account sixth order operators describing spin-rotational interactions) and a newly created computer code ROVDES for the ro-vibrational spectra of open-shell free radicals. About 2600 spin-ro-vibrational transitions with the values Nmax = 59 and Kmax a = 17 (being about 2.4 times higher in comparison with the number of assigned transitions known in the literature) were assigned to the v1 + v3 band of 35ClO2 and 1049 spin-ro-vibra tional energies (produced only from unblended non-saturated and not very weak experimental lines) of the (101) upper vibrational state were obtained. A set of 30 varied parameters of the effective spin-rota tion-vibration Hamiltonian of the (101) vibrational state (vibrational energy, 17 rotational and centrifugal distortion parameters and 12 are spin-rotational ones) was determined from the weighted fit of parameters of the effective spin-rotational Hamiltonian in A-reduction and Ir-representation. The obtained set of parameters reproduces the initial 1049 "experimental" upper state energies with the drms = 2.5 x 10-4 cm-1 which is close to the experimental uncertainty of the recorded spectra and is almost 70 times higher in comparison with the analogous reproduction of the same initial upper energies with the use of parameters from (J.Mol.Spectrosc., 158, 347 -356(1993)).(c) 2022 Elsevier B.V. All rights reserved.

We report here the analytical description of one of the important problems in the study of XY4 (Td) molecules, namely, description of vibrational tetrahedral sub-level structures and resonance interactions caused by the high symmetry of a molecule. The results obtained are applied to description of the vibrational energy spectrum of the CH4 and GeH4 molecules.

The high resolution infrared spectra of CD4 were measured with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.003 cm( -1) and analyzed in the region of 80 0-140 0 cm( -1) where the nu(2)/nu(4) dyad is located. The number of 3633 and 1927 transitions with J(max) = 31 and J(max)= 28 were assigned to the nu(4 )and nu(2) bands of CD4 (which is more than three times higher in comparison with the number of assigned transitions known in the literature). The subsequent weighted fit of experimentally assigned transitions was made with the Hamiltonian model which takes into account the resonance interactions between the upper (0 0 01 , F (2)) and the (0100 , E) vibrational states. As a result, a set of 52 fitted parameters (10 parameters of the ground vibrational state, 19 parameters of the (0 0 01 , F- 2) vibrational state, 9 parameters of the (0100 , E) vibrational state, and 14 resonance interaction parameters) was obtained which reproduces the positions of the initial 5560 experimental rovibrational transitions with the d(rms )= 1 . 83 x 10 (-4) cm(-1) which is close to the experimental uncertainty of the recorded spectra and is about 615 times better in comparison with the reproduction of the same 5560 transition values by the use of parameters from (J. Mol. Spectrosc., 99 , 63 - 86(1983) ). A list of assigned transitions in the studied region is presented as the Supplementary material to this paper. (C) 2022 Elsevier Ltd. All rights reserved.

Исследован ИК спектр высокого разрешения фундаментальной полосы ν 6 молекулы 13 CHF 3 , расположенной в районе 450-750 cm -1 . Анализ спектра выполнялся на основе метода комбинационных разностей основного состояния. В результате анализа было проинтерпретировано около 5500 переходов, на основе которых определено 2607 экспериментальных значений энергий колебательно-вращательных уровней в состоянии v_6=1. Полученные результаты превосходят известную в литературе информацию как по объему полученной экспериментальной информации, так и по числу извлеченных из экспериментальных данных высоковозбужденных колебательно-вращательных уровней энергии. На основе извлеченных из спектра данных были определены спектроскопические параметры исследуемого состояния, которые воспроизводят исходные данные с погрешностью 4.4·10 -5 cm -1 . Ключевые слова: трифторметан, колебательно-вращательный спектр, спектроскопические параметры.