Excited states of anions are few and far between, but they are applicable in many areas of chemistry and materials science ranging from solar energy harvesting to astrochemical observation [1
]. The reactivity and transience of anions creates difficulty for laboratory study but makes them excellent candidates for quantum chemical analysis. Fermi and Teller first probed the properties of anions via quantum mechanics finding that the binding energy of excess electrons is dependent upon the dipole moment of the corresponding neutral [6
]. The dipole moment should be greater than 1.625 D in order to possess a first dipole bound state, but, practically, it should be at least greater than 2.00 D as studies have since indicated [7
]. Additionally, dipole moments above this value will have a higher likelihood of exhibiting dipole bound states implying a proportional relationship between the dipole moment and the electron binding energy (eBE) [7
were the first experimental examples of organic anions documented with dipole bound excited states [9
]. Excitations into these states involve promotion of a valence electron into a highly diffuse, Rydberg-like orbital and transpire in the visible and near-infrared region of the electromagnetic spectrum [22
]. These properties led Sarre to examine the A
dipole bound excitation of CH
at 8037.78 Å for its coincidence with an astronomical absorption peak at 8037.8 ± 15 Å [23
]. The similarity of the two excitation energies led him to the currently unrefuted hypothesis that dipole bound anions are possible carriers for some of the diffuse interstellar bands (DIBs).
The DIB absorption lines have been observed towards innumerable interstellar sightlines with surprising consistency in the signal, have been recorded for more than century, and occur in the visible and near-infrared regions [23
]. In fact, the highest concentration of DIB features are in wavelengths longer than green. The rotational substructure of the peaks has led to the conclusion that these features are molecular in origin, but few of the peaks appear to be related. Unfortunately, only four of the hundreds of peaks have been currently attributed to specific molecular carriers [27
]. Electronic transitions of C
, conclusively observed in 2015, are linked closely to four of the DIBs [27
] that reside in the near-infrared range. The rest of the DIBs remain unresolved.
Anions typically have lower energy excited states than cations and neutrals due to the weak association of the additional electron. This causes the eBE to be lower than the ionization potential of an uncharged molecule [22
]. Incident energy above the eBE in the anion would most likely remove the excess electron instead of exciting it for absorption. Similarly, anions will only have one or two excited states, if any at all, implying that any spectrum containing them will require numerous different species to fill the census of peaks [29
]. Consequently, anion wavelengths and absorption characteristics are longer and solitary making them tantalizing candidates for being carriers of the DIBs as has been proposed for CH
Anions appear in varied astrophysical environments including the interstellar medium (ISM), planetary nebulae, and molecular clouds. Even so, they have only been on the roster of astronomically-known molecules for less than two decades even though they were proposed well before the turn of the last century [31
]. Polycyclic aromatic hydrocarbons (PAHs) are also predicted to be distributed throughout space, as well, but the first detection of one of these is even more recent. While buckyballs (C
) have been known for the past decade [46
], benzontrile, simply a cyano-functionalized benzene, was first observed towards TMC-1 via rotational spectroscopy less than two years ago [47
], confirming the long-held belief that PAHs are likely omnipresent in the ISM. Additionally, Saturn’s moon Titan has produced evidence, initially during the Voyager
mission, that its atmosphere contains a variety of hydrocarbons, which are building blocks for PAHs [48
], in addition to a wealth of nitrogen chemistry. More than 25 years later, the Cassini
mission found heavy anions in Titan’s atmosphere ranging from 10–200 amu. The smaller masses are likely atomic anions and small molecules such as CN
, but the larger species could be nitrogen-containing PAH anions [55
]. PAH anions may be additional candidates for application to the carriers of various astronomical spectral features including the DIBs. In fact, excited states of the cation forms have been shown to take place in energetic regions close to the DIBs [61
To explore the nature of dipole bound anions, proper quantum chemical treatment of such charged molecules requires a sufficient choice of basis set. Adding additional diffuse functions to standard correlation consistent basis sets can effectively describe dipole bound anion states, but this is a computationally expensive approach at the t-aug-cc-pVDZ (tapVDZ) level and beyond [17
]. Adding just four hydrogen such as s-type diffuse functions (+4s) on a dummy atom either at the center of charge (COC) or center of mass (COM) to aug-cc-pVDZ (apVDZ) can make the computation less expensive. Dipole bound excited state energies for closed-shell, deprotonated anions of quinoline are practically identical for tapVDZ and aug-cc-pVDZ+4s (apVDZ+4s), but the latter reduces the basis set by 48%, thus reducing the computational cost and time [63
]. In addition, adding more, dummy-atom-centered diffuse functions further increases the accuracy of describing dipole bound excited states. The aug-cc-pVDZ+6s6p2d (apVDZ+6s6p2d) basis set with these additional, hydrogen-like functions provides the limit at which more basis functions stop changing the effective excitation energy for rovibronic analysis of c-C
]. Consequently, dipole bound excited states with just the +4s functions added on to the apVDZ basis set are not likely sufficient for quantitatively computing dipole bound excited state energies, but the +6s6p2d functions give indication of being such. Differently, valence excited states, by their very nature, do not require such extensively diffuse orbitals. Additional diffuse functions are not subsequently needed to study valence excited states of singly deprotonated PAH anions, but they are often included since the valence and dipole excited states are computed during the same run [65
The present work builds upon previous studies [63
] to provide further analysis for computing the electronically excited states of singly deprotonated PAH anions functionalized with a single cyano group. The cyano-functionalized PAH stabilities, eBEs, and electronically excited states are explored herein in a manner similar to previous studies with smaller molecules [62
] but where the +6s6p2d orbitals may be required [67
]. The cyano group is chosen for its behavior as an exceptionally strong electron withdrawing group which should increase the dipole moment even more than that predicted is with PANHs [63
] and for its obvious relevance to the discovery of benzonitrile [47
]. Extending the rings increases the likelihood of more excited states, as previously shown with related PANH and PAH anions [63
]. Thus, the additional cyano group should affect photophysical properties more so than simple inclusion of nitrogen heteroatoms in the PAH structure and open the door for new photophysics of anions in various astrophysical environments or for other applications of anions.
2. Computational Details
Benzene, naphthalene, and anthracene are singly deprotonated and functionalized with a cyano group to create closed-shell anions and corresponding open-shell neutrals. There are multiple positions for the cyano group, and each is explored in this work. The methods utilized here are similar to approaches done previously for other closed-shell anions [63
]. Geometry optimizations of the neutral radical and closed-shell anions utilize B3LYP/apVDZ [68
] within Gaussian16 [69
]. These optimizations provide the relative energies, dipole moments of the neutral radicals, and geometries for both the closed-shell anions and the corresponding neutral radicals. Additionally, the relative energies of the neutral radicals and anions are compared between B3LYP, MP2 [70
] for benzonitrile in order to assess the performance of the various methods. Previous work shows B3LYP provides sufficient optimized structures for larger molecular systems especially for subsequent excited state analysis [63
Vertical excited states of the anion and radical geometries utilize both CFOUR [73
] and MOLPRO [74
] with equation of motion coupled cluster theory at the singles and doubles level (EOM-CCSD) [75
]. The basis set is augmented with six s-type, six p-type, and two d-type basis functions as past studies have shown is necessary [64
]. Furthermore, two additional s
-type diffuse functions are added onto the apVDZ+6s6p2d basis set (the apVDZ+8s6p2d basis set) for the benzene and naphthalene class in order to determine if a higher number of diffuse functions are needed to properly characterize the anion. In either case, the diffuse functions can be localized as ghost atoms at either the center of charge (COC) or center of mass (COM). Similar to the cyanoamide anions [67
], the dummy atom placement for the COC is determined at the positive end of the radical dipole moment whether the actual geometry utilized is that for the optimized neutral radical or anion geometry.
The COM excitations have the dummy atom’s additional diffuse orbitals placed at the COM, which is also the origin coordinate. Past work on cyanoamide anions shows that a lower energy wavefunction is produced by placing diffuse orbitals on the COC and is less likely not to destabilize occupied molecular orbitals as seen with the NCNC
]. As with previous work [67
], the vertically excited states computed from the optimized anion geometry are interpreted here to be absorption behavior since the closed-shell anion is being excited. Excitations from the radical geometry can be viewed as emission (with opposite sign of the energy) from the dipole bound excited state since the radical and dipole bound geometries should be synonymous. The DIBs represent absorption leading most of the present discussion toward that end, but emission spectra are also reported.
The eBEs are computed to determine the maximum amount of energy that can produce an excited state before the electron dissociates. They are computed using EOM-CCSD with the ionization potential formalism (EOMIP) [81
] with the apVDZ basis set in the CFOUR program [73
]. Additional diffuse functions are not needed since the electrons in the radical are valence by construction. As a benchmark, the experimental eBE value for CH
is 1.543 eV, and the computed value using EOMIP-CCSD/apVDZ is 1.524 eV, a difference of only 0.02 eV [9
Once a deprotonated, closed-shell cyano-functionalized PAH anion contains three rings, it will exhibit at least one electronically excited valence state. This is similar to inclusion of nitrogen heteroatoms in related PANH anions where similar behavior was also observed for three rings [63
]. However, pure PAH anions require at least four rings [66
], unless, as this present work demonstrates, they are functionalized. The electron-withdrawing nature of the cyano group destabilizes the ring structure similarly to the N heteroatom. This produces closer gaps between the HOMO and LUMO allowing for valence excited states. Such behavior is most notable in the 1-cyanonaphthalene anion 4 isomer which is producing both dipole bound and
valence excited states. The oscillator strengths for all of the dipole bound states are in the same ∼ f
value range. Once the number of rings is three (and likely larger), the oscillator strengths of the valence excited states are of the same magnitude as their dipole bound relatives.
Every neutral radical explored in this paper has a dipole moment large enough to theoretically keep a electron bound in a dipole bound state of the corresponding closed-shell anion. Hence, all of the anions explored here should produce dipole bound excited states. This is presently shown and quantitatively given. The most meaningful data really are the relative differences between the dipole bound excited state energy and the eBE. Hence, the present work provides quantitative predictions for such relative energies. Furthermore, the excited states computed with the apVDZ+6s6p2d COC centered functions do not differ by more than 1.0 meV from the slightly larger apVDZ+8s6p2d basis even for dipole moments of corresponding neutral radicals of greater than 4.00 D. As a result, the accuracy for the EOM-CCSD/apVDZ+6s6p2d COC approach utilized here is in the range of approximately 1.0 meV relative to the eBE.
Deprotonation of PAHs will be most stable when the resulting lone pair is adjacent to the functional group unless symmetry distributions of the orbital space are present like in anion 6 of 1-cyanoanthracene. The radicals, however, will be most stable in the opposite trend where the singly-occupied orbital is farthest away from the functional group. The resonance of the lone pair in the anion with the orbitals of the cyano group are constructive, but the single electron cannot fully create such a positive interaction. Even so, the relative energies between all isomers of a set are fairly small, implying that only extremely low-temperature regions, such as the ISM, will delineate deprotonated PAH isomers to any observable extent.
Furthermore, Sarre’s dipole bound excited state anion hypothesis for the DIBs has been extended here to the titular molecules. The dipole bound and exhibited valence excited states of these various PAH anions all fall within the densest DIB field between 450 and 900 nm [83
]. Additionally, the substructures of the valence and dipole bound excitation peaks will differ since the valence states will largely retain the structure of the anion, but the dipole bound states will necessarily have the radical geometry. As a result, the valence and the dipole bound excited states of these closed-shell, deprotonated, functionalized PAH anions will appear to be caused by different molecules to some extent. However, further, experimental studies are needed to say conclusively whether these anions are carriers of the DIBs, but the present theoretical data support such a possible correlation.