Rovibrational Interaction Research Articles

Hunting for Sulfur-containing Molecules in Space: A Spectroscopic Characterization of Cyclopropenethione Based on High-level Ab Initio Calculations

Cyclopropenethione falls into the class of complex organic molecules but has not yet been observed in the interstellar medium or any circumstellar disks. However, its existence is very likely, and thus this study provides high-level ab initio predictions, which may serve as reference data for future observations or experimental work. Rovibrational configuration interaction theory based on multidimensional potential energy surfaces being obtained from explicitly correlated coupled-cluster calculations has been used to predict the fundamental vibrational modes, the microwave spectrum, and low-lying rovibrational transitions. Rotational constants as well as quartic and sextic centrifugal distortion constants were obtained from vibrational perturbation theory.

Thioformyl cyanide, HC(S)CN, revisited: accurate rovibrational simulations for a molecule observed in interstellar clouds

Thioformyl cyanide, HC(S)CN, and its deuterated isotopologue have been studied by high-level ab initio methods. Based on multidimensional potential energy surfaces including up to four-mode coupling terms and obtained from explicitly correlated coupled-cluster calculations, their geometrical parameters, vibrational transitions, rovibrational spectrum and spectroscopic constants have been studied in detail. The latter two properties, being obtained from vibrational configuration interaction theory (VCI) and vibrational perturbation theory (VPT), have been compared with available experimental data. The rotational and rovibrational spectra have been studied by rovibrational configuration interaction theory (RVCI) and colour coding has been used to obtain detailed insight into the rotational fine structure.

Elucidation of rotational-interaction coupling and collision-induced effects in rovibrational transitions of β-N2O isotopologue at 7.8 µm mid-infrared region by cavity ring-down spectroscopy

High-sensitive cavity ring-down spectroscopy (CRDS) coupled with a cw-quantum cascade laser operating at 7.8 μm mid-infrared (MIR) region has been employed to investigate the rovibrational interaction coupling for various MIR rotational transitions of the P-and R-branches in the ν1 fundamental vibrational band (1000 ← 0000) of the β-site-specific isotopologue of nitrous oxide (β-N2O) i.e., 15N14N16O. The coupled rotational interaction was experimentally quantified from the high-resolution CRDS data and a data-driven approach was taken for the approximation of the Herman-Wallis series. Moreover, J-dependent pressure-broadened absorptions and their collision lifetimes in response to foreign-perturbing gas molecules were investigated to understand the collision-induced rotational quantum effect in β-N2O molecule. This study reveals an experimental elucidation of the fundamental infrared physics underlying rovibrational interaction and its coupling to the vibrational and rotational degrees of freedom for a non-centrosymmetric linear polyatomic molecule possessing a permanent dipole moment. Moreover, the experimentally probed interference-free spectral lines of β-N2O molecule attributing different spectroscopic signatures in the MIR region may drive new applications in environmental monitoring, biological and biomedical diagnostics in the future.

A theoretical study of propynal under interstellar conditions and beyond, covering low-frequency infrared spectra, spectroscopic constants, and hot bands

ABSTRACTFrom an astrochemical point of view, propynal is a complex organic molecule. Moreover, it is a potential candidate for the formation of prebiotic propanal and propenal. Therefore, this molecule is of particular interest for astrochemical investigations. As it has been detected in the interstellar medium, it is of high relevance in this field of research. Although experimental data are available for the vibrational fundamental bands and rotational constants, experimental data for vibrational overtones and combination bands are scarce and fairly old. Additionally, high-level ab initio calculations are also not reported. In this work, we provide accurate quantum chemical calculations as well as a detailed analysis of vibrational and rovibrational properties for this molecule. The low-frequency spectrum up to $350\, \,\,\text{cm}^{-1}$ has been studied for temperatures between 10 and $300\, \text{K}$. For the same temperature range, partition functions are provided. Furthermore, the impact of hot bands up to room temperature has been investigated. A comparison of our results with experimental data is provided for the rotational constants, geometrical parameters, and a rovibrational spectrum. The underlying potential energy surface within these calculations is based on explicitly correlated coupled-cluster theory and includes up to four-mode coupling terms within an n-mode expansion. The vibrational and rovibrational calculations rely on vibrational and rovibrational configuration interaction theories, respectively.

Convergence of series expansions in rovibrational configuration interaction (RVCI) calculations.

Rotational and rovibrational spectra are a key in astrophysical studies, atmospheric science, pollution monitoring, and other fields of active research. The ab initio calculation of such spectra is fairly sensitive with respect to a multitude of parameters and all of them must be carefully monitored in order to yield reliable results. Besides the most obvious ones, i.e., the quality of the multidimensional potential energy surface and the vibrational wavefunctions, it is the representation of the μ-tensor within the Watson Hamiltonian, which has a significant impact on the desired line lists or simulated spectra. Within this work, we studied the dependence of high-resolution rovibrational spectra with respect to the truncation order of the μ-tensor within the rotational contribution and the Coriolis coupling operator of the Watson operator. Moreover, the dependence of the infrared intensities of the rovibrational transitions on an n-mode expansion of the dipole moment surface has been investigated as well. Benchmark calculations are provided for thioformaldehyde, which has already served as a test molecule in other studies and whose rovibrational spectrum was found to be fairly sensitive. All calculations rely on rovibrational configuration interaction theory and the discussed high-order terms of the μ-tensor are a newly implemented feature, whose theoretical basics are briefly discussed.

Determination of spectroscopic constants from rovibrational configuration interaction calculations

Rotational constants and centrifugal distortion constants of a molecule are the essence of its rotational or rovibrational spectrum (e.g., from microwave, millimeter wave, and infrared experiments). These parameters condense the spectroscopic characteristics of a molecule and, thus, are a valuable resource in terms of presenting and communicating spectroscopic observations. While spectroscopic parameters are obtained from experimental spectra by fitting an effective rovibrational Hamiltonian to transition frequencies, the ab initio calculation of these parameters is usually done within vibrational perturbation theory. In the present work, we investigate an approach related to the experimental fitting procedure, but relying solely on ab initio data obtained from variational calculations, i.e., we perform a nonlinear least squares fit of Watson's A- and S-reduced rotation-vibration Hamiltonian to rovibrational state energies (resp. transition frequencies) from rotational-vibrational configuration interaction calculations. We include up to sextic centrifugal distortion constants. By relying on an educated guess of spectroscopic parameters from vibrational configuration interaction and vibrational perturbation theory, the fitting procedure is very efficient. We observe excellent agreement with experimentally derived parameters.

Herman-Wallis factor for a molecule of type HCN

We suggest a novel theoretical approach to calculate Herman-Wallis factors in rovibrational spectra of non-centrosymmetric linear molecules possessing a permanent dipole. A fresh glance allowed to extend the theory recently formulated in [K.V. Kazakov and A.A. Vigasin, Phys. Rev. A, 104, 042805 (2021)]. Our obtained expressions for the first Herman-Wallis correction factors result in evaluation of the rovibrational interaction impact on the line intensities belonging to fundamental modes ν1,ν2, and ν3 for H12C14N, H13C14N, H12C15N, D12C14N, D13C14N, and D12C15N. As an auxiliary outcome, the sum rule for the Coriolis constants is generally derived in detail.

Theory of rovibrational line intensities in allowed and collision-induced absorption spectra of linear molecules

A theoretical approach is developed for the Herman-Wallis factors describing the variation of the line intensities caused by rovibrational interaction in a linear molecule. In the case of ${\ensuremath{\nu}}_{2}$ and ${\ensuremath{\nu}}_{3}$ fundamentals and the ${\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{3}/2{\ensuremath{\nu}}_{2}+{\ensuremath{\nu}}_{3}$ resonance combination band in a ${\mathrm{CO}}_{2}$ molecule, our theory is capable of generating reliable numerical estimates for the linear Herman-Wallis coefficients without recourse to complicated algebra. On the assumption of nearly free rotating monomers, an analog of the Herman-Wallis factors is introduced for the dipole-forbidden ${\ensuremath{\nu}}_{2}+{\ensuremath{\nu}}_{3}$ band, which manifests itself in ${\mathrm{CO}}_{2}$ collision-induced absorption (CIA). The rovibrational perturbation is appropriate to explain a pronounced crossflow of intensity among rovibrational branches in a virtually rotationally unresolved CIA envelope.

High-Level Rovibrational Calculations on Ketenimine.

From an astrochemical point of view ketenimine (CH2CNH) is a complex organic molecule (COM) and therefore likely to be a building block for biologically relevant molecules. Since it has been detected in the star-forming region Sagittarius B2(N), it is of high relevance in this field. Although experimental data are available for certain bands, for some energy ranges such as above 1200 cm−1 reliable data virtually do not exist. In addition, high-level ab initio calculations are neither reported for ketenimine nor for one of its deuterated isotopologues. In this paper, we provide for the first time data from accurate quantum chemical calculations and a thorough analysis of the full rovibrational spectrum. Based on high-level potential energy surfaces obtained from explicitly correlated coupled-cluster calculations including up to 4-mode coupling terms, the (ro)vibrational spectrum of ketenimine has been studied in detail by variational calculations relying on rovibrational configuration interaction (RVCI) theory. Strong Fermi resonances were found for all isotopologues. Rovibrational infrared intensities have been obtained from dipole moment surfaces determined from the distinguishable cluster approximation. A comparison of the spectra of the CH2CNH molecule with experimental data validates our results, but also reveals new insight about the system, which shows very strong Coriolis coupling effects.

Evaluation of the substitution structures of two partially fluorinated cyclopentanes C5H3F7 and C5H2F8

The pure rotational spectra of the title compounds have been recorded and analyzed. For both species the spectra from all of the singly substituted carbon-13 isotopologues were observed in natural abundance. Ground state rotational constants together with the results of quantum chemical calculations have been used to investigate the ground state structures of each molecule. The substitution structures show carbon-carbon bond lengths which are clearly wrong. As a rationale for this finding it is proposed that the presence of very low frequency normal modes cause an isotopologue-dependent rovibrational interaction and, hence, differences between the ground state geometries of the parent isotopologues and those of the singly substituted carbon-13 rings. These differences preclude satisfactory substitution structural analyses.

Calculation of Spectroscopic Parameters of Diatomic Molecules with an Open Electron Shell

The spectroscopic parameters of the BeH and CH molecules with an open electron shell are calculated in the basis of the Slater functions. An analytical expression for the total electron energy of molecules with an open electron shell is obtained. The total electron energy of the BeH and CH molecules was calculated by the Hartree–Fock–Roothaan (HFR) method for seven internuclear distances, including the equilibrium internuclear distance. A table of total energy values is constructed depending on the internuclear distance R. The total energy of a diatomic molecule is approximated as a third-degree polynomial in R. Applying the least squares method to energy values from the above-mentioned table, an analytical formula for the total energy of the BeH and CH molecules is obtained as a function of R. The analytical formula for E(R) has allowed the spectroscopic parameters ωe (harmonic vibrational frequency), ωexe (anharmonicity constant), Be (rotational constant), and αe (rovibrational interaction constant) to be calculated.

Pure rotation spectrum of CF4 in the v3 = 1 state using THz synchrotron radiation

Spherical-top tetrahedral species like CH4, SiH4, CF4, …possess no permanent dipole moment. Therefore, probing their pure rotation spectrum is very challenging since only a very weak dipole moment can be induced by centrifugal distortion and/or rovibrational interaction. If some Q branch lines have been recorded thanks to microwave techniques, R branch lines in the THz region have been poorly explored until recently. In previous studies, we have reported the pure rotation THz spectrum of cold and hot band lines of methane recorded at the SOLEIL Synchrotron facility. Here, we present the first recorded THz spectrum of the R branch of CF4, a powerful greenhouse gas, in its v3=1 state. This Fourier transform spectrum covers the R(20) to R(37) line clusters, in the 20–37cm−1 spectral range. It was recorded thanks to a 150m multiple path cell at room temperature. We could estimate the vibration-induced dipole moment value and also include the recorded line positions in a global fit of many CF4 transitions.

Accurate sub-millimetre rest frequencies for HOCO+ and DOCO+ ions

HOCO$^+$ is a polar molecule that represents a useful proxy for its parent molecule CO$_2$, which is not directly observable in the cold interstellar medium. This cation has been detected towards several lines of sight, including massive star forming regions, protostars, and cold cores. Despite the obvious astrochemical relevance, protonated CO$_2$ and its deuterated variant, DOCO$^+$, still lack an accurate spectroscopic characterisation. The aim of this work is to extend the study of the ground-state pure rotational spectra of HOCO$^+$ and DOCO$^+$ well into the sub-millimetre region. Ground-state transitions have been recorded in the laboratory using a frequency-modulation absorption spectrometer equipped with a free-space glow-discharge cell. The ions were produced in a low-density, magnetically-confined plasma generated in a suitable gas mixture. The ground-state spectra of HOCO$^+$ and DOCO$^+$ have been investigated in the 213-967 GHz frequency range, with the detection of 94 new rotational transitions. Additionally, 46 line positions taken from the literature have been accurately remeasured. The newly-measured lines have significantly enlarged the available data sets for HOCO$^+$ and DOCO$^+$, thus enabling the determination of highly accurate rotational and centrifugal distortion parameters. Our analysis showed that all HOCO$^+$ lines with Ka $\geq$ 3 are perturbed by a ro-vibrational interaction that couples the ground state with the v$_ 5$ = 1 vibrationally-excited state. This resonance has been explicitly treated in the analysis in order to obtain molecular constants with clear physical meaning. The improved sets of spectroscopic parameters provide enhanced lists of very accurate, sub-millimetre rest-frequencies of HOCO$^+$ and DOCO$^+$ for astrophysical applications. These new data challenges a recent tentative identification of DOCO$^+$ toward a pre-stellar core.

Structural and spectroscopic characterization of methyl isocyanate, methyl cyanate, methyl fulminate, and acetonitrile N-oxide using highly correlated ab initio methods

Various astrophysical relevant molecules obeying the empirical formula C2H3NO are characterized using explicitly correlated coupled cluster methods (CCSD(T)-F12). Rotational and rovibrational parameters are provided for four isomers: methyl isocyanate (CH3NCO), methyl cyanate (CH3OCN), methyl fulminate (CH3ONC), and acetonitrile N-oxide (CH3CNO). A CH3CON transition state is inspected. A variational procedure is employed to explore the far infrared region because some species present non-rigidity. Second order perturbation theory is used for the determination of anharmonic frequencies, rovibrational constants, and to predict Fermi resonances. Three species, methyl cyanate, methyl fulminate, and CH3CON, show a unique methyl torsion hindered by energy barriers. In methyl isocyanate, the methyl group barrier is so low that the internal top can be considered a free rotor. On the other hand, acetonitrile N-oxide presents a linear skeleton, C3v symmetry, and free internal rotation. Its equilibrium geometry depends strongly on electron correlation. The remaining isomers present a bend skeleton. Divergences between theoretical rotational constants and previous parameters fitted from observed lines for methyl isocyanate are discussed on the basis of the relevant rovibrational interaction and the quasi-linearity of the molecular skeleton.

Far-infrared spectra of dimethyl-ether and its 13C enriched isotopologues: The fundamental band of the C–O–C in plane bending mode, ν7

We recorded the ν7 fundamental band of dimethyl-ether around 400cm−1 for the normal and 13C-enriched isotopologues using the Fourier transform spectrometer at the SOLEIL Synchrotron facility. For all three species P, Q and R branch-transitions up to J=20 and Ka=5 were assigned and the band origins and rotational parameters of Watson’s A-reduced Hamiltonian have been determined by the least-squares fitting procedure. The line splitting due to the torsional tunneling is observed for low J transitions, which is attributed to the ro-vibrational interaction with the excited torsional states.

Experimental values of the rotational and vibrational constants of deuterated silyl fluoride

ABSTRACTAccurate experimental values of the αA and αB rotation–vibration interaction, and ωi, xij and gij vibrational constants have been extracted from the most recent high-resolution Fourier transform infrared and millimetre-wave measurements in the spectra of the prolate symmetric top SiD3F, between 400 and 2000 cm−1. From the experimental values of the ground state rotational and rovibrational interaction parameters, accurate equilibrium rotational constants have been derived: Ae = 1.432326 (12) cm−1 and Be = 0.4112012 (45) cm−1 for silyl fluoride. The effective ground state structure has also been determined from the observed moments of inertia of SiD3F: r0(Si-D) = 1.4755 (29) Å; r0(Si-F) = 1.5931 (26) Å; θ0(DSiD) = 110.47 (32)° and θ0(DSiF) = 108.45 (56)°. A merge of equilibrium moments of 28SiH3F and 28SiD3F yielded an experimental equilibrium structure of silyl fluoride. This geometry has been found in good agreement with semi-experimental median values, as well as with the recent semi-experimental ab initio equilibrium structure obtained using all data available of the various isotopic species of silyl fluoride.

Line position analysis of the ν2 band of SO2F2 using the C2vTop Data System

A new high-resolution infrared spectrum of the ν2 band of SO2F2 centered at 849.46cm−1 has been recorded with a resolution of 0.00102cm−1 at the AILES beamline of SOLEIL Synchrotron facility. More than 1600 lines up to Jmax=41 have been assigned and fitted in line position using a tensorial formalism adapted to the case of XY2Z2 asymmetric molecules developed as an extension of the usual one used for spherical tops (Rotger et al., 2002). The analysis has been performed in the O(3)⊃Td⊃C2v group chain, thanks to the C2vTDS program suite (Wenger et al., 2005). This approach allows a systematic development of rovibrational interaction to study any polyad of SO2F2 and makes easier global analysis. Compared to a previous study (Merke et al., 2006), the present fit uses less effective Hamiltonian parameters but we assigned lines up to a lower J value.

Experimental values of the rotational and vibrational constants and equilibrium structure of nitrogen trifluoride

Several accurate experimental values of the rovibrational interaction constants αC and αB, the harmonic wave-number parameters ωij, and the anharmonicity xij and gij constants have been extracted from the most recent high-resolution Fourier transform infrared (FTIR), centimeter-wave (CMW) and millimeter-wave (MMW) measurements in the spectra of the oblate symmetric top molecule 14NF3. The data used are those of the four fundamental, the overtone, the combination and the hot bands identified and analyzed in the range between 400cm−1 and 2000cm−1. Combining the recent experimental values of the constants αC and αB, with the accurate experimental ground state rotational constants C0 and B0, new equilibrium rotational constants have been evaluated: Ce=0.1968006 (26)cm−1 and Be=0.358981442 (43)cm−1 for the pyramidal molecule NF3, from which the following equilibrium structure is obtained: re(F-N)=1.36757 (58)Å; θe(FNF)=101.8513 (10)°. This experimental equilibrium geometry is in excellent agreement with the recent structure determined by ab initio calculations at the CCSD(T)/aug-cc-pVQZ level of theory.

Experimental rovibrational constants and equilibrium structure of phosphorus trifluoride

Thanks to recent high-resolution Fourier transform infrared (FTIR) and pure rotational (RF/CM/MMW) measurements, several experimental values of the rotation–vibration parameters of the oblate molecule PF3 have been extracted, contributing thus to the knowledge of the molecular potential of phosphorus trifluoride. The data used are those of the fundamental, overtone and combination bands studied in the 300–1500cm−1 range. The new values are in good agreement with ones determined at low resolution, but significantly more accurate. The agreement is excellent with the available values determined by ab initio HF-SCF calculations employing the TZP/TZ2P triple-zeta basis. From the recent experimental rovibrational interaction constants αC and αB, new accurate equilibrium rotational constants Ce and Be have been derived for the symmetric top molecule PF3, which were used to derive the equilibrium geometry of this molecule: re(F–P)=1.560986 (43)Å; θe(FPF)=97.566657 (64)°.

Hidden physics in molecular rovibrational spectrum

An algebraic method for rotational energies (AMr) is proposed to unearth the rotational spectrum {ɛJ} and the rovibrational interaction energies ευJint that are hidden in the rovibrational energies EυJ. The applications to the excited electronic state a3Σu+ of 7Li2 and the ground state X1Σ+ of NaF molecules show that: (1) the rotational energies ɛJ of the lighter 7Li2 molecule have better accuracies than the widely used rigid rotor rotational energies εJrr particularly for the lowest two rotational states, while the rigid rotor model produces satisfied rotational energies for the heavier NaF molecule and (2) the attractive rovibrational interaction energies ευJint stabilize a molecular rovibrational system.