Potential Vibrational Modes Tied to Diffuse Interstellar Bands

Heger (1922) observed that absorption lines at 5780 and 5797 Å were superposed upon the spectra of binary stars, and lacked the requisite oscillatory Doppler shifting. The source(s) of these lines lie mainly within interstellar clouds along the sightline (see also Hartmann, 1904, regarding interstellar calcium). A century later several hundred diffuse interstellar bands (DIBs) are known (e.g., Bondar, 2012; Fan et al., 2019). PAHs remain a leading hypothesis as a principal carrier (e.g., Bondar, 2020), and for several DIBs C${}_{60}^{+}$ is debated (e.g., Campbell et al., 2015; Galazutdinov et al., 2017, 2021; Schlarmann et al., 2021; Nie et al., 2022; Majaess et al., 2025). Indeed, heterofullerenes and (endo/exo)hedral inclusions are likewise being explored as DIB carriers (e.g., Kroto, 1987; Omont, 2016).

Here, the objective is to explore whether vibrational transitions may be identified by delineating energy differences between correlated DIB pairs (e.g., Jenniskens & Desert, 1993; Moutou et al., 1999; Bondar, 2020). For example, Jenniskens & Desert (1993) suggested the energy separation between DIBs 5797 and 6269 Å could be indicative of a PAH C$=$C vibration (7.7 $\mu m$). Moutou et al. (1999) underscored that the gap between the correlated 6196 and 6614 Å DIBs is tied to an aromatic vibration (9.8 $\mu m$). Bondar (2020, their Table 4) relays that the energy offset between DIBs 5545 and 6614 Å may be linked to a PAH or aliphatic C$-$H vibration (3.3 $\mu m$). DIBs associated with a given molecule may represent a vibronic progression (e.g., McCall et al., 2010, and discussion therein).

The Fan et al. (2019) APO catalog was examined, and the analysis was subsequently limited to DIB pairs exhibiting higher Pearson correlated equivalent widths ($r-\sigma_{r}\geq 0.8$, $EW/\sigma_{EW}\geq 5$), possessing $\geq 12$ sightlines, and whose energy difference falls within $500-4000$ cm^-1. The Pearson correlation, equivalent width, and their uncertainties are described by $r$, $\sigma_{r}$, $EW$, and $\sigma_{EW}$. The sightline to VI Cyg 12 was excluded owing to its circumstellar shell and color-excess beyond the field (e.g., Maryeva et al., 2016; Xing et al., 2024).

The final sample hosts $\simeq 10^{3}$ DIB pairs. Wavenumbers linked to the energy spacing between DIB pairs were compiled into a histogram (23 cm^-1 bin width). Vibrations were identified by relying on Colthup et al. (1990), the ChemCompute+GAMESS quantum chemistry framework (Perri & Weber, 2014; Barca et al., 2020), and the NASA Ames PAH IR spectroscopic database (Boersma et al., 2014; Bauschlicher et al., 2018; Mattioda et al., 2020). Tentatively, the peaks in Fig. 1 can be assigned to various chemical bonds (e.g., C$\equiv$C, C$\equiv$N, S$-$H, C$-$O, C$=$O, Si$-$H). For example, the potential aromatic out of plane (oop) bending C$-$H vibration may represent the line near 745 cm^-1, which is the most prominent maximum,¹¹1Linearly binned wavelength (rather than wavenumber) would reveal a maximum toward small $\lambda$. with an underestimated uncertainty (formal) being half the bin width (i.e., $745\pm 12$ cm^-1). Peaks in its vicinity could represent differing aromatic substitution patterns. The prominence of $\simeq 745$ cm^-1 (13.4 $\mu m$) in concert with $\simeq 697$ cm^-1 (14.8 $\mu m$) may be indicative of mono-substitution. The feature near 606 cm^-1 (16.5 $\mu m$) was identified by Moutou et al. (2000) as linked to PAHs (see also Bondar, 2020, and their DIB family). Aromatics are likewise relayed by the in-ring C$\mathbf{{}^{\underline{...}}}$C line perhaps appearing near 1573 cm^-1, and C$-$H line beyond $\simeq 3000$ cm^-1, while shortward of the latter are aliphatic C$-$H. Furthermore, overdensities near 5.25 (FWHM$\approx 0.12$ $\mu m$) and 5.7 $\mu m$ (FWHM$\approx 0.17$ $\mu m$) can be conducive to PAH emission from overtones, combinations, etc. (Boersma et al., 2009, and references therein). The two longer wavelength C$\mathbf{{}^{\underline{...}}}$C may be tied to fullerenes, and a degeneracy could likewise extend to the putative 10.8 $\mu m$ and oop C$-$H features. The diversity of vibrational transitions reaffirms prior analyses indicating numerous molecules give rise to DIBs (e.g., on the basis of correlated equivalent widths, common correlations relative to reddening, and spectral line morphology, Cami et al., 1997; Smith et al., 2021, 2022; Ebenbichler et al., 2024).

Crucially, artifacts may exist owing to noise (e.g., N$-$H), and a balance was sought where sufficient statistics were achieved in concert with a reasonable selection of the correlation threshold, sightline number, and binning. Consequently, a histogram for DIB pairs displaying low correlations was constructed (i.e., $|r\pm\sigma_{r}|\leq 0.5$, Fig. 2) as one possible means of assessing the veracity of the maxima. The maxima were expectedly sensitive to the criteria selected (e.g., $r-\sigma_{r}\geq 0.8$). The dominant $\simeq 745$ cm^-1 line that characterized higher correlated DIB pairs (Fig. 1) vanishes, and the underlying substructure at smaller wavenumbers is likewise absent. A subset of vibrational modes potentially remain with less significance owing to the lower correlation criterion, with only one exceeding 3$\sigma$. The red dotted lines in Fig. 2 stem from the bin centers of Fig. 1. Sample sizes for Figs. 1 and 2 are 1143 and 854 DIB pairs, accordingly.

Yet ultimately, the preliminary vibrations designated in Fig. 1 require further benchmarking and independent vetting. Adjustments shall likewise proceed as a consensus is achieved over time, since vibrational modes can overlap, their wavelengths can shift owing to other constituents within the molecule, and broadening and degeneracies occur (e.g., Zapata Trujillo et al., 2023).

In this brief exploratory note, DIB energy differences (e.g., Fig. 1) may unveil the building blocks inherent to the broader host molecules. For example, aromatics (e.g., hydrocarbons and potentially heterocycles) and fullerenes could represent a subset of DIB carriers (Fig. 1), as noted previously by others. Subsequent key steps moving forward include continuing to isolate DIB families (i.e., same carrier) on a multi-dimensional basis of equivalent widths, optical and near-infrared reddening, line profiles, etc. (e.g., Ebenbichler et al., 2024). Such ongoing research is required to mitigate the noise in Fig. 1, which partly arises from correlated DIB pairs linked to separate carriers whose abundances are commensurate. A critical aspect is to correctly unveil the DIB tied to the origin band, which may represent the transition to the ground vibration of the first excited electronic state.²²2Slight offsets between observed vibrational wavenumbers implied by DIB pairs relative to those in compilations are expected if the latter are linked to the ground electronic state. Concurrently, the APO catalog can be expanded by extracting additional EWs from high-quality GOSSS and X-shooter spectra (Ma´ız Apellániz et al., 2013; Verro et al., 2022), while simultaneously characterizing the number and properties of dust clouds along the sightline by utilizing new Gaia DR3 parallax and $\lambda\simeq 330-1050$ nm spectroscopic observations (Gaia Collaboration et al., 2023; Xing et al., 2024). The latter may provide the desirable rationale behind outliers amongst Pearson correlation determinations (e.g., circumstellar shell for VI Cyg 12, Xing et al., 2024, their Fig. 1). Moreover, viewing a DIB through multiple clouds along the sightline can be preferable when establishing broad correlations, thereby mitigating anomalies endemic to any one cloud.

Future work likewise includes awaiting temporally costly extensive vibrational coupled cluster calculations for an expansive set of neutral and cation species, and undertaking analyses of linearly binned wavelength histograms and unidentified infrared emission lines (UIEs).³³3Kwok (2022) favors mixed aromatic/aliphatic organic nanoparticles (MAONs) for UIEs rather than canonical PAHs. DIBs and UIEs should share a subsample of molecules,⁴⁴4e.g., Bondar (2020), and for C${}_{60}^{+}$ see Foing & Ehrenfreund (1994, DIBs) and Sadjadi et al. (2022, UIEs). however, differences are expected (e.g., $\lambda$ linked to neutral versus ion species, intensity shifts, separate molecules) owing to disparate ambient temperatures, densities, neutral and ion population ratios, radiation field, etc. (broader discussions in Peeters 2002 and Bondar, 2020, and references therein).