Five carbon- and nitrogen-bearing species in a hot giant planet's atmosphere.

The atmospheres of gaseous giant exoplanets orbiting close to their parent stars (hot Jupiters) have been probed for nearly two decades1,2. They allow us to investigate the chemical and physical properties of planetary atmospheres under extreme irradiation conditions3. Previous observations of hot Jupiters as they transit in front of their host stars have revealed the frequent presence of water vapour4 and carbon monoxide5 in their atmospheres; this has been studied in terms of scaled solar composition6 under the usual assumption of chemical equilibrium. Both molecules as well as hydrogen cyanide were found in the atmosphere of HD 209458b5,7,8, a well studied hot Jupiter (with equilibrium temperature around 1,500 kelvin), whereas ammonia was tentatively detected there9 and subsequently refuted10. Here we report observations of HD 209458b that indicate the presence of water (H2O), carbon monoxide (CO), hydrogen cyanide (HCN), methane (CH4), ammonia (NH3) and acetylene (C2H2), with statistical significance of 5.3 to 9.9 standard deviations per molecule. Atmospheric models in radiative and chemical equilibrium that account for the detected species indicate a carbon-rich chemistry with a carbon-to-oxygen ratio close to or greater than 1, higher than the solar value (0.55). According to existing models relating the atmospheric chemistry to planet formation and migration scenarios3,11,12, this would suggest that HD 209458b formed far from its present location and subsequently migrated inwards11,13. Other hot Jupiters may also show a richer chemistry than has been previously found, which would bring into question the frequently made assumption that they have solar-like and oxygen-rich compositions.

MARVEL analysis of high-resolution rovibrational spectra of 13 C 16 O 2 .

A set of empirical rovibrational energy levels, obtained through the MARVEL (measured active rotational-vibrational energy levels) procedure, is presented for the 13 C 16 O 2 isotopologue of carbon dioxide. This procedure begins with the collection and analysis of experimental rovibrational transitions from the literature, allowing for a comprehensive review of the literature on the high-resolution spectroscopy of 13 C 16 O 2 , which is also presented. A total of 60 sources out of more than 750 checked provided 14,101 uniquely measured and assigned rovibrational transitions in the wavenumber range of 579-13,735 cm - 1 . This is followed by a weighted least-squares refinement yielding the energy levels of the states involved in the measured transitions. Altogether 6318 empirical rovibrational energies have been determined for 13 C 16 O 2 . Finally, estimates have been given for the uncertainties of the empirical energies, based on the experimental uncertainties of the transitions. The detailed analysis of the lines and the spectroscopic network built from them, as well as the uncertainty estimates, all serve to pinpoint possible errors in the experimental data, such as typos, misassignment of quantum numbers, and misidentifications. Errors found in the literature data were corrected before including them in the final MARVEL dataset and analysis.

MARVEL analysis of high-resolution rovibrational spectra of 16O12C18O.

Empirical rovibrational energy levels are presented for the third most abundant, asymmetric carbon dioxide isotopologue, 16O12C18O, based on a compiled dataset of experimental rovibrational transitions collected from the literature. The 52 literature sources utilized provide 19,438 measured lines with unique assignments in the wavenumber range of 2-12,676 cm-1. The MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol, which is built upon the theory of spectroscopic networks, validates the great majority of these transitions and outputs 8786 empirical rovibrational energy levels with an uncertainty estimation based on the experimental uncertainties of the transitions. Issues found in the literature data, such as misassignment of quantum numbers, typographical errors, and misidentifications, are fixed before including them in the final MARVEL dataset and analysis. Comparison of the empirical energy-level data of this study with those in the line lists CDSD-2019 and Ames-2021 shows good overall agreement, significantly better for CDSD-2019; some issues raised by these comparisons are discussed.

Predissociation dynamics of the hydroxyl radical (OH) based on a five-state spectroscopic model.

Multi-reference configuration interaction potential energy curves (PECs) and spin-orbit couplings for the X 2Π, A 2Σ+, 1 2Σ-, 1 4Σ-, and 1 4Π states of OH are computed and refined against empirical energy levels and transitions to produce a spectroscopic model. Predissociation lifetimes are determined by discretizing continuum states in the variational method nuclear motion calculation by restricting the calculation to a finite range of internuclear separations. Varying this range gives a series of avoided crossings between quasi-bound states associated with the A 2Σ+ and continuum states, from which predissociation lifetimes are extracted. 424 quasi-bound A 2Σ+ state rovibronic energy levels are analyzed, and 374 predissociation lifetimes are produced, offering good coverage of the predissociation region. Agreement with measured lifetimes is satisfactory, and a majority of computed results were within experimental uncertainty. A previously unreported A 2Σ+ state predissociation channel that goes via X 2Π is identified in the calculations. A Python package, binSLT, produced to calculate predissociation lifetimes, associated line broadening parameters, and lifetime uncertainties is made available. The PECs and other curves from this work will be used to produce a rovibronic ExoMol line list and temperature-dependent photodissociation cross sections for the hydroxyl radical.

Infrared Spectra of Small Radicals for Exoplanetary Spectroscopy: OH, NH, CN and CH: The State of Current Knowledge.

In this study, we present a current state-of-the-art review of middle-to-near IR emission spectra of four simple astrophysically relevant molecular radicals-OH, NH, CN and CH. The spectra of these radicals were measured by means of time-resolved Fourier transform infrared spectroscopy in the 700-7500 cm-1 spectral range and with 0.07-0.02 cm-1 spectral resolution. The radicals were generated in a glow discharge of gaseous mixtures in a specially designed discharge cell. The spectra of short-lived radicals published here are of great importance, especially for the detailed knowledge and study of the composition of exoplanetary atmospheres in selected new planets. Today, with the help of the James Webb telescope and upcoming studies with the help of Plato and Ariel satellites, when the investigated spectral area is extended into the infrared spectral range, it means that detailed knowledge of the infrared spectra of not only stable molecules but also the spectra of short-lived radicals or ions, is indispensable. This paper follows a simple structure. Each radical is described in a separate chapter, starting with historical and actual theoretical background, continued by our experimental results and concluded by spectral line lists with assigned notation.

A variational model for the hyperfine resolved spectrum of VO in its ground electronic state.

A variational model for the infra-red spectrum of vanadium monoxide (VO) is presented, which aims to accurately predict the hyperfine structure within the VO XΣ-4 electronic ground state. To give the correct electron spin splitting of the XΣ-4 state, electron spin dipolar interaction within the ground state and the spin-orbit coupling between XΣ-4 and two excited states, AΠ4 and 1Σ+2, are calculated ab initio alongside hyperfine interaction terms. Four hyperfine coupling terms are explicitly considered: Fermi-contact interaction, electron spin-nuclear spin dipolar interaction, nuclear spin-rotation interaction, and nuclear electric quadrupole interaction. These terms are included as part of a full variational solution of the nuclear-motion Schrödinger equation performed using program Duo, which is used to generate both hyperfine-resolved energy levels and spectra. To improve the accuracy of the model, ab initio curves are subject to small shifts. The energy levels generated by this model show good agreement with the recently derived empirical term values. This and other comparisons validate both our model and the recently developed hyperfine modules in Duo.

A method for calculating temperature-dependent photodissociation cross sections and rates.

The destruction of molecules by photodissociation plays a major role in many radiation-rich environments, including the evolution of the atmospheres of exoplanets, which often exist close to UV-rich stars. Most current photodissociation calculations and databases assume T = 0 K, which is inadequate for hot exoplanets and stars. A method is developed for computing photodissociation spectra of diatomic molecules as a function of temperature exploiting bound state variational nuclear motion program Duo and post-processing program ExoCross. Discrete transition intensities are spread out to represent a continuous photodissociation spectrum either by Gaussian smoothing or by averaging calculations over a range of different grid sizes. Our approach is tested on four different chemical species (HCl, HF, NaCl and BeH+), showing its ability to reproduce photodissociation cross sections and rates computed with other approaches and experiment. The temperature dependence of photodissociation cross sections and rates is studies showing strong temperature variation of the photodissociation cross sections.

Modelling the non-local thermodynamic equilibrium spectra of silylene (SiH2).

This paper sets out a robust methodology for modelling spectra of polyatomic molecules produced in reactive or dissociative environments, with vibrational populations outside local thermal equilibrium (LTE). The methodology is based on accurate, extensive ro-vibrational line lists containing transitions with high vibrational excitations and relies on the detailed ro-vibrational assignments. The developed methodology is applied to model non-LTE IR and visible spectra of silylene (SiH2) produced in a decomposition of disilane (Si2H6), a reaction of technological importance. Two approaches for non-LTE vibrational populations of the product SiH2 are introduced: a simplistic 1D approach based on the Harmonic approximation and a full 3D model incorporating accurate vibrational wavefunctions of SiH2 computed variationally with the TROVE (Theoretical ROVibrational Energy) program. We show how their non-LTE spectral signatures can be used to trace different reaction channels of molecular dissociations.

Rovibronic spectroscopy of PN from first principles.

We report an ab initio study on the rovibronic spectroscopy of the closed-shell diatomic molecule phosphorous mononitride, PN. The study considers the nine lowest electronic states, X 1Σ+, A 1Π, C 1Σ-, D 1Δ, E 1Σ-, a 3Σ+, b 3Π, d 3Δ and e 3Σ- using high level electronic structure theory and accurate nuclear motion calculations. The ab initio data cover 9 potential energy, 14 spin-orbit coupling, 7 electronic angular momentum coupling, 9 electric dipole moment and 8 transition dipole moment curves. The Duo nuclear motion program is used to solve the coupled nuclear motion Schrödinger equations for these nine electronic states and to simulate rovibronic absorption spectra of 31P14N for different temperatures, which are compared to available spectroscopic studies. Lifetimes for all states are calculated and compared to previous results from the literature. The calculated lifetime of the A1Π state shows good agreement with an experimental value from the literature, which is an important quality indicator for the ab initio A-X transition dipole moment.

Electric quadrupole transitions in carbon dioxide.

Recent advances in high sensitivity spectroscopy have made it possible, in combination with accurate theoretical predictions, to observe, for the first time, very weak electric quadrupole transitions in a polar polyatomic molecule of water. Here, we present accurate theoretical predictions of the complete quadrupole rovibrational spectrum of a non-polar molecule CO2, important in atmospheric and astrophysical applications. Our predictions are validated by recent cavity enhanced absorption spectroscopy measurements and are used to assign few weak features in the recent ExoMars Atmospheric Chemistry Suite mid-infrared spectroscopic observations of the Martian atmosphere. Predicted quadrupole transitions appear in some of the mid-infrared CO2 and water vapor transparency regions, making them important for detection and characterization of the minor absorbers in water- and CO2-rich environments, such as those present in the atmospheres of Earth, Venus, and Mars.

A spectroscopic model for the low-lying electronic states of NO.

The rovibronic structure of A2Σ+, B2Π, and C2Π states of nitric oxide (NO) is studied with the aim of producing comprehensive line lists for its near ultraviolet spectrum. Empirical energy levels for the three electronic states are determined using a combination of the empirical measured active rotation-vibration energy level (MARVEL) procedure and ab initio calculations, and the available experimental data are critically evaluated. Ab initio methods that deal simultaneously with the Rydberg-like A2Σ+ and C2Π and the valence B2Π state are tested. Methods of modeling the sharp avoided crossing between the B2Π and C2Π states are tested. A rovibronic Hamiltonian matrix is constructed using the variational nuclear motion program Duo whose eigenvalues are fitted to the MARVEL. The matrix also includes coupling terms obtained from the refinement of the ab initio potential energy and spin-orbit coupling curves. Calculated and observed energy levels agree well with each other, validating the applicability of our method and providing a useful model for this open shell system.

Theoretical rovibronic spectroscopy of the calcium monohydroxide radical (CaOH).

The rovibronic (rotation-vibration-electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the Ã2Π-X̃2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X̃2Σ+ and Ã2Π electronic states along with Ã-X̃ transition dipole moment surfaces (DMSs). For the ground X̃2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm-1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the Ã2Π state PESs and Ã-X̃ DMSs. Variational calculations consider both Renner-Teller and spin-orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the Ã2Π state, line list calculations up to J = 125.5, and an analysis of Renner-Teller splittings in the ν2 bending mode of CaOH are discussed.

Detection of electric-quadrupole transitions in water vapour near 5.4 and 2.5 µm.

Nowadays, the spectroscopic databases used for the modeling of Earth and planetary atmospheres provide only electric-dipole transitions for polyatomic molecules (H2O, CO2, N2O, CH4, O3…). Very recently, electric-quadrupole transitions have been detected in the high sensitivity cavity ring down spectrum (CRDS) of water vapour near 1.3 µm [A. Campargue et al., Phys. Rev. Res., 2020, 2, 023091, DOI: 10.1103/PhysRevResearch.2.023091]. This discovery paved the way to systematic searches of quadrupole transitions in water vapor and other polyatomic molecules. In the present work, on the basis of high accuracy ab initio predictions, H216O quadrupole lines are detected for the first time in the 5.4 µm and 2.5 µm regions where they are predicted to have their largest intensities (up to 10-26 cm per molecule). A total of twelve quadrupole lines are identified in two high sensitivity Fourier transform spectra recorded with a 1064 m path length. Ten lines in the 4030-4150 cm-1 region are assigned to the ν3 band while the lines near 1820 and 1926 cm-1 belong to the ν2 band. The derived line intensities which are largely above the dipole intensity cut-off of the standard spectroscopic databases, agree nicely with the theoretical predictions. We thus conclude that the calculated line list of quadrupole transitions, validated by the present measurements, should be incorporated in the spectroscopic databases.

Treating linear molecules in calculations of rotation-vibration spectra.

In this article, a numerical implementation of the exact kinetic energy operator (KEO) for triatomic molecules (symmetric of XY2-type and asymmetric of YXZ-type) is presented. The implementation is based on the valence coordinates with the bisecting (XY2-type molecules) and bond-vector (YXZ) embeddings and includes the treatment of the singularity at linear geometry. The KEO is represented in a sum-of-product form. The singularity caused by the undetermined angle at the linear configuration is resolved with the help of the associated Legendre and Laguerre polynomials used as parameterized bending basis functions in the finite basis set representation. The exact KEO implementation is combined with the variational solver theoretical rovibrational energies, equipped with a general automatic symmetry-adaptation procedure and efficient basis step contraction schemes, providing a powerful computational solver of triatomic molecules for accurate computations of highly excited ro-vibrational spectra. The advantages of different basis set choices are discussed. Examples of specific applications for computing hot spectra of linear molecules are given.

Spectroscopy of YO from first principles.

We report an ab initio study on the spectroscopy of the open-shell diatomic molecule yttrium oxide, YO. The study considers the six lowest doublet states, X2Σ+, A'2Δ, A2Π, B2Σ+, C2Π, D2Σ+, and a few higher-lying quartet states using high levels of electronic structure theory and accurate nuclear motion calculations. The coupled cluster singles, doubles, and perturbative triples, CCSD(T), and multireference configuration interaction (MRCI) methods are employed in conjunction with a relativistic pseudopotential on the yttrium atom and a series of correlation-consistent basis sets ranging in size from triple-ζ to quintuple-ζ quality. Core-valence correlation effects are taken into account and complete basis set limit extrapolation is performed for CCSD(T). Spin-orbit coupling is included through the use of both MRCI state-interaction with spin-orbit (SI-SO) approach and four-component relativistic equation-of-motion CCSD calculations. Using the ab initio data for bond lengths ranging from 1.0 to 2.5 Å, we compute 6 potential energy, 12 spin-orbit, 8 electronic angular momentum, 6 electric dipole moment and 12 transition dipole moment (4 parallel and 8 perpendicular) curves which provide a complete description of the spectroscopy of the system of six lowest doublet states. The Duo nuclear motion program is used to solve the coupled nuclear motion Schrödinger equation for these six electronic states. The spectra of 89Y16O simulated for different temperatures are compared with several available high resolution experimental studies; good agreement is found once minor adjustments are made to the electronic excitation energies.

The rotation-vibration spectrum of methyl fluoride from first principles.

Accurate ab initio calculations on the rotation-vibration spectrum of methyl fluoride (CH3F) are reported. A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) have been generated using high-level electronic structure methods. Notably, the PES was constructed from explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit and considered additional energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms beyond perturbative triples, scalar relativistic effects, and the diagonal Born-Oppenheimer correction. The PES and DMS are evaluated through robust variational nuclear motion computations of pure rotational and vibrational energy levels, the equilibrium geometry of CH3F, vibrational transition moments, absolute line intensities of the ν6 band, and the rotation-vibration spectrum up to J = 40. The computed results show excellent agreement with a range of experimental sources, in particular the six fundamentals are reproduced with a root-mean-square error of 0.69 cm-1. This work represents the most accurate theoretical treatment of the rovibrational spectrum of CH3F to date.

A variationally computed room temperature line list for AsH3.

Calculations are reported on the rotation-vibration energy levels of the arsine molecule with associated transition intensities. A potential energy surface (PES) obtained from ab initio electronic structure calculations is refined to experimental data, and the resulting energy levels display sub-wavenumber accuracy for all reliably known J = 0 term values under 6500 cm-1. After a small empirical adjustment of the band centres, our calculated (J = 1-6) rovibrational states reproduce 578 experimentally derived energies with a root-mean-square error of 0.122 cm-1. Absolute line intensities are computed using the refined PES and a new dipole moment surface (DMS) for transitions between states with energies up to 10 500 cm-1 and rotational quantum number J = 30. The computed DMS reproduces experimental line intensities to within 10% uncertainty for the ν1 and ν3 bands. Furthermore, our calculated absorption cross-sections display good agreement with the main absorption features recorded in the Pacific Northwest National Laboratory (PNNL) for the complete range of 600-6500 cm-1.

Variationally Computed IR Line List for the Methyl Radical CH3.

We present the first variational calculation of a hot-temperature ab initio line list for the CH3 radical. It is based on a high-level ab initio potential energy surface and dipole moment surface of CH3 in the ground electronic state. The ro-vibrational energy levels and Einstein A coefficients were calculated using the general-molecule variational approach implemented in the computer program TROVE. Vibrational energies and vibrational intensities are found to be in very good agreement with the available experimental data. The line list comprises 9 127 123 ro-vibrational states ( J ≤ 40) and 2 058 655 166 transitions, covering the wavenumber range up to 10 000 cm-1 and should be suitable for temperatures up to T = 1500 K.

Theoretical rotation-vibration spectroscopy of cis- and trans-diphosphene (P2H2) and the deuterated species P2HD.

Growing astronomical interest in phosphorous (P) chemistry is stimulating the search for new interstellar P-bearing molecules, a task requiring detailed knowledge of the microwave and infrared molecular spectrum. In this work, we present comprehensive rotation-vibration line lists of the cis- and trans-isomers of diphosphene (P2H2). The line lists have been generated using robust, first-principles methodologies based on newly computed, high-level ab initio potential energy and dipole moment surfaces. Transitions are considered between states with energies up to 8000 cm-1 and total angular momentum J ≤ 25. These are the first-ever line lists to be reported for P2H2, and they should significantly facilitate future spectroscopic characterization of this system. The deuterated species trans-P2HD and the effect of its dynamic dipole moment on the rovibrational spectrum are also discussed.

Climbing the Rotational Ladder to Chirality.

Molecular chirality is conventionally understood as space-inversion-symmetry breaking in the equilibrium structure of molecules. Less well known is that achiral molecules can be made chiral through extreme rotational excitation. Here, we theoretically demonstrate a clear strategy for generating rotationally induced chirality: An optical centrifuge rotationally excites the phosphine molecule (PH_{3}) into chiral cluster states that correspond to clockwise (R enantiomer) or anticlockwise (L enantiomer) rotation about axes almost coinciding with single P─H bonds. The application of a strong dc electric field during the centrifuge pulse favors the production of one rotating enantiomeric form over the other, creating dynamically chiral molecules with permanently oriented rotational angular momentum. This essential step toward characterizing rotationally induced chirality promises a fresh perspective on chirality as a fundamental aspect of nature.