2023ApJ...944...33V

We aim to compare variations in the full-UV dust extinction curve (912-3000 Å), with the H I/H₂/total H content along diffuse Milky Way sightlines, to investigate possible connections between ISM conditions and dust properties. We combine an existing sample of 75 UV extinction curves based on IUE and FUSE data, with atomic and molecular column densities measured through UV absorption. The H₂ column density data are based on existing Lyman-Werner absorption band models from earlier work on the extinction curves. Literature values for the H I column density were compiled, and improved for 23 stars by fitting a Lyα profile to archived spectra. We discover a strong correlation between the H₂ column and the far-UV extinction, and the underlying cause is a linear relationship between H₂ and the strength of the far-UV rise feature. This extinction does not scale with H I, and the total H column scales best with $A\left(V\right)$ instead. The carrier of the far-UV rise therefore coincides with molecular gas, and further connections are shown by comparing the UV extinction features to the molecular fraction. Variations in the gas-to-extinction ratio $N({\rm{H}})/A\left(V\right)$ correlate with the UV-to-optical extinction ratio, and we speculate this could be due to coagulation or shattering effects. Based on the H₂ temperature, the strongest far-UV rise strengths are found to appear in colder and denser sightlines.