The ExoMol project (www.exomol.com) provides comprehensive spectroscopic data (line lists) for the study of atmospheres of exoplanets and other hot bodies.  These line lists serve as input for models of radiative transport through hot atmospheres and are useful for a variety of terrestrial applications. 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, k-coefficients and pressure broadening parameters. Currently containing 80 molecules and 190 isotopologues totaling over 700 billion transitions, the database covers infrared, visible and UV wavelengths. The field of the HR spectroscopy of exoplanets is growing extremely fast and urgently demands molecular data of high precision. Failure to detect molecules in atmospheres of exoplanets is often attributed to the lack of the underlying quality of
the line positions.  These developments have led us to begin a systematic attempt to improve the accuracy of the line positions for the line lists contained in the database. Our new ExoMolHD project aims to provide comprehensive line lists to facilitate their use in characterization of exoplanets using high resolution Doppler shift spectroscopy. Progress on this objective will be presented.