The systematic analysis of the correlations between diffuse interstellar bands (DIBs) is extended to weak DIBs through the comprehensive catalogue of the Apache Peak Observatory (APO) of 559 DIBs in 25 lines of sight with diverse interstellar properties. The main results are the following: 1) An extension of the number of DIBs identified to be related to C2, that is, those that need very shielded interstellar regions for their carriers to survive UV photo-dissociation. Based on the correlations with the reference C2 and ζ DIBs, anticorrelations with UV-favoured (σ) DIBs, and the strength ratios in shielded and unshielded sight lines, we propose 12 new C2 candidates and 34 possible “C2-related” DIBs (mostly at λ <5950 Å) in addition to the ~20 known confirmed C2 DIBs. With these additions, the census of C2 DIBs might approach completion. 2) We discovered that the intensities of a large set of poorly studied DIBs are strongly enhanced in one or two of the sight lines of HD 175156 and HD 148579. This tentative class, denoted χ for the time being, extends over the whole wavelength range of visible DIBs. It might include up to 50–100 members, half at λ > 6000 Å, and a number of C2 DIBs. These possible enhancements might reflect specific formation processes of their carriers that are yet to be identified in the interstellar medium of these two sight lines. The possible matches of the wavelength of five very broad DIBs, including three χ DIBs, with the strong bands that were recently measured by action spectroscopy might favour some long carbon chains and rings as carriers of some DIBs. These correlations and findings justify further theoretical and laboratory efforts for improving our understanding of the complex physics, spectroscopy, and chemistry of the various carbon chains and rings, and their possible formation and destruction in the diffuse interstellar medium.
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