The ExoMol database ( www.exomol.com ) provides molecular data for spectroscopic studies of hot atmospheres. While the data are intended for studies of exoplanets and other astronomical bodies, the dataset is widely applicable. The basic form of the database is extensive line lists; these are supplemented with partition functions, state lifetimes, cooling functions, Landé g-factors, temperature-dependent cross sections, opacities, pressure broadening parameters, k -coefficients and dipoles. This paper presents the latest release of the database which has been expanded to consider 80 molecules and 190 isotopologues totaling over 700 billion transitions. While the spectroscopic data are concentrated at infrared and visible wavelengths, ultraviolet transitions are being increasingly considered in response to requests from observers. The core of the database comes from the ExoMol project which primarily uses theoretical methods, albeit usually fine-tuned to reproduce laboratory spectra, to generate very extensive line lists for studies of hot bodies. The data have recently been supplemented by line lists derived from direct laboratory observations, albeit usually with the use of ab initio transition intensities. A major push in the new release is towards accurate characterisation of transition frequencies for use in high resolution studies of exoplanets and other bodies.

A new hot line list for the main isotopologue of CO2, 12C16O2 is presented. The line list consists of almost 2.5 billion transitions between 3.5 million rotation-vibration states of CO2 in its ground electronic state, covering the wavenumber range 0–20 000 cm−1 (λ > 0.5 µm) with the upper and lower energy thresholds of 36 000 cm−1 and 16 000 cm−1, respectively. The ro-vibrational energies and wavefunctions are computed variationally using the accurate empirical potential energy surface Ames-2. The ro-vibrational transition probabilities in the form of Einstein coefficients are computed using an accurate ab initio dipole moment surface with variational program TROVE. A new implementation of TROVE which uses an exact nuclear-motion kinetic energy operator is employed. Comparisons with the existing hot line lists are presented. The line list should be useful for atmospheric retrievals of exoplanets and cool stars. The UCL-4000 line list is available from the CDS and ExoMol data bases.

In this article, a numerical implementation of the exact kinetic energy operator (KEO) for triatomic molecules (symmetric of XY 2type and asymmetric of YXZ-type) is presented. The implementation is based on the valence coordinates with the bisecting (XY 2type 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.

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In the present work, we report a detailed description of the symmetry properties of the eight-atomic molecule ethane, with the aim of facilitating the variational calculations of rotation-vibration spectra of ethane and related molecules. Ethane consists of two methyl groups CH 3 where the internal rotation (torsion) of one CH 3 group relative to the other is of large amplitude and involves tunneling between multiple minima of the potential energy function. The molecular symmetry group of ethane is the 36-element group G 36 , but the construction of symmetrized basis functions is most conveniently done in terms of the 72-element extended molecular symmetry group G 36 (EM). This group can subsequently be used in the construction of block-diagonal matrix representations of the ro-vibrational Hamiltonian for ethane. The derived transformation matrices associated with G 36 (EM) have been implemented in the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). TROVE variational calculations will be used as a practical example of a G 36 (EM) symmetry adaptation for large systems with a non-rigid, torsional degree of freedom. We present the derivation of irreducible transformation matrices for all 36 (72) operations of G 36 (M) (G 36 (EM)) and also describe algorithms for a numerical construction of these matrices based on a set of four (five) generators. The methodology presented is illustrated on the construction of the symmetry-adapted representations both of the potential energy function of ethane and of the rotation, torsion and vibration basis set functions.