The ExoMol project: Software for computing large molecular line lists

The use of variational nuclear motion programs to compute line lists of transition frequencies and intensities is now a standard procedure. The ExoMol project has used this technique to generate line lists for studies of hot bodies such as the atmospheres of exoplanets and cool stars. The resulting line list can be huge: many contain 10 billion or more transitions. This software update considers changes made to our programs during the course of the project to allow for such calculations. This update considers three programs: Duo which computed vibronic spectra for diatomics, DVR3D which computes rotation-vibration spectra for triatomics, and TROVE which computes rotation-vibration spectra for general polyatomic systems. Important updates in functionality include the calculation of quasibound (resonance) states and Landé g-factors by Duo and the calculation of resonance states by DVR3D. Significant algorithmic improvements are reported for both DVR3D and TROVE. All three programs are publically available from ccpforge.cse.rl.ac.uk. Future developments are also considered

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

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

Molecular line shape parameters for exoplanetary atmospheric applications

We describe the recent updates to the ExoMol database regarding the molecular spectral line shapes. ExoMol provides comprehensive molecular line lists with a special emphasis on the applications involving characterization of hot atmospheres such as those found in exoplanets and cool stars. Among important requirements of such applications are (i) the broadening parameters for hydrogen and helium dominating atmospheres and (ii) very broad ranges of temperature and pressures. The current status of the available line shape data in the literature, demands from the exoplanetary community and their specific needs are discussed

A hyperfine-resolved spectroscopic model for vanadium monoxide (51V16O)

Vanadium monoxide ((Formula presented.) V (Formula presented.) O) is believed to play an important role in the atmospheres of hot-Jupiters, but high-resolution studies have so far failed to detect it, at least in part because of the inaccuracy of available lists. It is likely that the large hyperfine splittings in the spectra of VO, arising from the large nuclear spin (Formula presented.) of the (Formula presented.) V atom, has contributed to the non-detections with the current hyperfine-unresolved VOMYT line list. To aid in the production of a new line list, a fully hyperfine-resolved spectroscopic model has been constructed which includes 15 low-lying electronic states (6 quartets and 9 doublets) of VO with the inclusion of hyperfine couplings based on use of the new, hyperfine-resolved version of the diatomic variational nuclear motion programme Duo. The new spectroscopic model is refined against empirical Marvel energies derived from experimental transitions, and hyperfine couplings are fit for the 3 electronic states for which hyperfine effects have been resolved in lab spectra. This model is used to assign some previously identified perturbations

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

Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣∣ν1,ν2,νℓ33;J,k,m⟩ , tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3 , which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v (M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h (AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h (AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications

Communication: Tunnelling splitting in the phosphine molecule

Splitting due to tunnelling via the potential energy barrier has played a significant role in the study of molecular spectra since the early days of spectroscopy. The observation of the ammonia doublet led to attempts to find a phosphine analogous, but these have so far failed due to its considerably higher barrier. Full dimensional, variational nuclear motion calculations are used to predict splittings as a function of excitation energy. Simulated spectra suggest that such splittings should be observable in the near infrared via overtones of the ν2 bending mode starting with 4ν2

Communication: Tunnelling splitting in the phosphine molecule

Splitting due to tunnelling via the potential energy barrier has played a significant role in the study of molecular spectra since the early days of spectroscopy. The observation of the ammonia doublet led to attempts to find a phosphine analogous, but these have so far failed due to its considerably higher barrier. Full dimensional, variational nuclear motion calculations are used to predict splittings as a function of excitation energy. Simulated spectra suggest that such splittings should be observable in the near infrared via overtones of the ν2 bending mode starting with 4ν2

ExoMol line lists - III. An improved hot rotation-vibration line list for HCN and HNC

A revised rotation-vibration line list for the combined hydrogen cyanide (HCN)/hydrogen isocyanide (HNC) system is presented. The line list uses ab initio transition intensities calculated previously and extensive data sets of recently measured experimental energy levels. The resulting line list has significantly more accurate wavelengths than previous ones for these systems. An improved value for the separation between HCN and HNC is adopted, leading to an approximately 25 per cent lower predicted thermal population of HNC as a function of temperature in the key 2000 to 3000 K region. Temperature-dependent partition functions and equilibrium constants are presented. The line lists are validated by comparison with laboratory spectra and are presented in full as supplementary data to the article and at www.exomol.com