The structure of coronene cluster ions inferred from H 2 uptake in the gas phase †

Mass spectra of helium nanodroplets doped with H2 and coronene feature anomalies in the ion abundance that reveal anomalies in the energetics of adsorption sites. The coronene monomer ion strongly adsorbs up to n = 38 H2 molecules indicating a commensurate solvation shell that preserves the D6h symmetry of the substrate. No such feature is seen in the abundance of the coronene dimer through tetramer complexed with H2; this observation rules out a vertical columnar structure. Instead we see evidence for a columnar structure in which adjacent coronenes are displaced in parallel, forming terraces that offer additional strong adsorption sites. The experimental value for the number of adsorption sites per terrace, approximately six, barely depends on the number of coronene molecules. The displacement estimated from this number exceeds the value reported in several theoretical studies of the bare, neutral coronene dimer.


Introduction
5][6] The highly symmetrical, planar coronene molecule (C 24 H 12 , D 6h symmetry) is a strong candidate for many unidentified interstellar bands. 7[10] The interaction between coronene molecules has been investigated to model the interaction between graphene sheets; [11][12][13] clusters of coronene and other PAHs serve as realistic models of carbon grains in interstellar space. 14The Bravais lattice of bulk coronene is monoclinic.In the conventional gamma-herringbone structure coronene molecules are stacked parallel but displaced; columns of molecules are separated from each other by molecules that are tilted by 851. 15(Another recently discovered stable polymorph, 16 the beta-herringbone structure, can be grown in the presence of a magnetic field.)In this phase adjacent molecules are either parallel but displaced, or nearly perpendicular to each other in a T-shaped configuration.9][20][21][22][23][24][25][26] Molecules in clusters slightly larger than the dimer are still stacked in a parallel arrangement; 12,20,27 handshake and multicolumnar structures start appearing at m E 8. 20,26,[28][29][30] However, the exact ground state structure of the coronene dimer is still a matter of debate.The perfectly superimposed stack (or sandwich) does not form a local minimum. 20,21,23,25sing an empirical potential for the repulsion-dispersion interaction, Rapacioli et al. found that the twisted sandwich (TS) represents the most stable structure at À0.98 eV. 20][33][34][35] Here we study adsorption of molecular hydrogen on positively charged coronene and its clusters.Neutral complexes of hydrogen and coronene are synthesized by passing helium nanodroplets through vapors of C 24 H 12 (abbreviated Cor from now on) and H 2 ; the doped droplets are then ionized by electron impact.Mass spectra predominantly show ions with the composition (H 2 ) n HCor m + and a weaker series of unprotonated (H 2 ) n Cor m Guided by previous experimental data 36 for He n Cor + and theoretical work involving complexes of coronene with hydrogen, 37 helium, [38][39][40] and heavier noble gases 41,42 we attribute the anomaly at n = 38 to an abrupt drop in the adsorption energy once all hollow adsorption sites are occupied, completing a solvation shell.As shown in Fig. 1, each face of coronene offers 1 central (c) hollow site, 6 inner (i) hollow sites that surround the c site, and 12 outer (o) hollow sites formed by H-C-C-C-H atoms at the border of the molecule, i.e. a total of 38 hollow sites.The distance between adjacent centers of the carbon rings is only 0.246 nm, less than the minimum in the pair potential between H 2 -H 2 or, for that matter, He-He or Ne-Ne.In a complete commensurate solvation shell these particles would thus be displaced radially outwards as observed in several theoretical studies. 37,38,40,41Quantum mechanical delocalization would exacerbate the outward trend but the D 6h symmetry of the substrate would likely be preserved.Interestingly, adsorption of H 2 on dimers, trimers, and tetramers of coronene reveal an approximately constant shift of the anomaly by Dn = 11.4AE 0.6 per added coronene.We attribute this shift to a parallel-displaced structure of the coronene cluster because a displacement opens additional hollow adsorption sites.A cluster with sandwich (or twisted sandwich) structure, i.e. a vertical stack of coronenes, would not offer any additional strong adsorption sites, only more weakly bound peripheral sites on the mantle of the stack.The observed shift Dn thus provides a benchmark for quantum chemical studies of (H 2 ) n HCor m + or (H 2 ) n Cor m + because the larger the displacement the larger the number of additional strong adsorption sites.4][25][26] Note, however, that adsorption of H 2 may enhance and stabilize the displacement because of the large adsorption energy of H 2 on coronene.

Experiment
Helium nanodroplets were produced by expanding helium (Messer, purity 99.9999%) at a stagnation pressure of 21 bar through a 5 mm nozzle, cooled by a closed-cycle refrigerator to 9.6 K, into vacuum.At these conditions the droplets contain an estimated average number of 4 Â 10 5 helium atoms. 43The expanding beam was skimmed by a 0.8 mm conical skimmer located 8 mm downstream from the nozzle and traversed a differentially pumped pick-up cell filled with coronene vapor produced by heating coronene powder (Sigma-Aldrich, specified purity 97%) to about 135 1C.It then passed through another cell filled with H 2 (estimated partial pressure 3.9 Â 10 À5 mbar).
The beam of the doped helium droplets was collimated and crossed by an electron beam with a nominal energy of 70 eV.Cations were accelerated into the extraction region of a reflectron time-of-flight mass spectrometer (Tofwerk AG, model HTOF) with an effective mass resolution m/Dm = 3000 (Dm = full-width-at-halfmaximum).Further experimental details have been published elsewhere. 44ass spectra were evaluated by means of a custom-designed software designed to extract the abundance of specific ions after deconvoluting possible overlapping contributions to particular mass peaks by different ions and isotopologues. 45For example, the mass difference between isotopically pure HCor + (i.e.H 12 C 24 H 12 + ) and pure coronene containing one 13 C isotope is only 0.0045 u, 22 times smaller than the instrumental peak width Dm.The software automatically fits mass peaks, subtracts background signals, and explicitly considers isotopic patterns of all ions that are expected to contribute to a given peak.The procedure and significance of accounting for isotope patterns is illustrated in Fig. S1 (ESI †)., probably arising from a benzo[ghi]perylene impurity in the coronene sample. 32,46he most intense ion series that follows Cor m + is due to (H 2 ) n HCor m + (the notation reflects the fact that the proton affinity of coronene, 8.927 eV, is more than twice that of H 2 ). 48he series exhibits abrupt drops in abundance; their positions are obtained from a nonlinear least square fit (see below for details) and marked by vertical lines.(and similar ion pairs) remain unresolved, their contributions are disentangled by the analysis software which considers the complete pattern of isotopologues. 45Fig. S1 (ESI †) illustrates the procedure; it also shows expanded sections of the mass spectrum.The prominent ion series below 300 u is due to He n

+
. An asterisk at 456.3 u marks a region in which this series is nearly isobaric with the series of protonated coronene ions.The amplitudes of these mass peaks add, giving rise to a volcano-shaped envelope.
The ion abundances of several ion series, extracted from mass spectra, are displayed in Fig. 3. Data for ions that suffer Close inspection of the data (see the insets in Fig. 3a and b) reveals another abrupt drop in the abundance of (H 2 ) n Cor + and (H 2 ) n (Cor) 2 + ; results of the fitted step functions are included in Fig. 4 and labelled ''minor step.''The corresponding protonated ion series feature similar but even weaker steps.

Discussion
The most striking feature of the mass spectra of coronenehydrogen complexes is an abrupt drop in the ion abundance of (H 2 ) n H(Cor) m + (as well as the unprotonated ion series) at n E 38 for the coronene monomer that shifts approximately linearly as m increases.Increments range from Dn = 10 to 13; the average increment is 11.4 AE 0.6.In the following we present a structural model that accounts for this and other results.0][51] Even so, we expect that the classical structures discussed here will have some bearing on the spatial probability distribution of the actual quantum mechanical system.3][54] Pickup of dopants and growth of neutral clusters in a superfluid helium nanodroplet is statistical, resulting in broad, featureless size distributions.Highly metastable configurations such as helium sandwiched between coronene molecules may be formed as well. 55However, a large amount of excess energy is released when dopants solvated inside the helium droplet are ionized, leading to extensive dissociation and annealing of the resulting ions. 56he interaction of H 2 with coronene has been the subject of several theoretical studies 8,9,37,58-61 but only one (classical) study considers H 2 adsorption on cationic coronene which features enhanced adsorption energies, 59 and only one (quantum mechanical) study considers adsorption of more than six H 2 molecules. 37Therefore our discussion will also resort to theoretical work involving adsorption of other quantum gases on coronene.
The energetically most favorable adsorption site of H 2 on neutral coronene is above the central carbon ring (site c, see Fig. 1) with the H 2 axis normal to the coronene plane and an adsorption energy of D e = 49 meV. 60Adsorption on top of one of the six inner (i) hexagonal rings is about 10% weaker than at c. 8,58 The total energy for adsorbing more than one H 2 is approximately additive provided the molecules do not occupy adjacent hexagonal rings in which case their interaction would be strongly repulsive. 8(H 2 ) 6 Cor with its alternating occupation of i-sites on both sides of the molecular plane (symmetry C 3v ) seems to be particularly stable, 8 providing a possible rationale for the enhanced abundance of (H 2 ) 6 HCor + , see Fig. 3a.However, we note that a theoretical study by Rodriguez-Cantano et al. that includes quantum effects finds enhanced stability for Ar 6 Cor and Kr 6 Cor but not Ne 6 Cor. 42he trio of anomalies in the abundance of (H 2 ) n HCor + at n = 32, 36, and 38 is reminiscent of a trio of anomalies in the abundance of He n Cor + at n = 38, 41 and 44, 36 reproduced in Fig. 3d.7][38][39][40] Particles at i-and o-sites are pushed radially outwards because their size exceeds the separation (0.246 nm) between the centers of adjacent carbon rings.For helium, 3 or 6 additional atoms can be accommodated at or close to o-sites resulting in anomalies at n = 41 and 44. 36,40H 2 , however, is larger than He; a monolayer on graphite accommodates 23% fewer H 2 than He. 62,63Therefore, rather than accommodating particles beyond n = 38, vacancies at o-sites will help to reduce the repulsive energy in the crowded commensurate (H 2 ) 38 HCor + , leading to abundance anomalies at (H 2 ) 36 HCor + and (H 2 ) 32 HCor + .The exact structure of these species remains to be determined.
Calvo and Yurtsever have reported path-integral molecular dynamics (PIMD) simulations of neutral coronene complexed with para-H 2 and ortho-D 2 at 2 K. 37 From spatial distributions they calculate an upper bound of n = 42 molecules for para-H 2 and 43 molecules for ortho-D 2 in the first solvation shell, in reasonable agreement with our value of n = 38.
Our key observation is the approximately constant shift of the step in the ion abundance with increasing number m of coronene molecules (Fig. 4), and the absence of anomalies at or near n = 38 for m 4 1.These observations rule out a columnar cluster structure with zero displacement which would still offer 38 strongly bound aromatic adsorption sites at the top and bottom of the stack plus additional sites in the mantle region.The PIMD simulation of hydrogen adsorption on the neutral coronene monomer 37 shows that peripheral sites are less tightly bound and more delocalized than aromatic sites.Interaction with and localization at positively charged coronene would be enhanced 40,59 but the differences between aromatic and mantle sites would likely remain.Therefore adsorption at vertical columnar coronene clusters would be expected to produce an abrupt drop in the abundance near n = 38, possibly followed by another one when all mantle sites are filled.The weaker steps in the ion abundance of (H 2 ) n Cor m + (m = 1, 2)  shown in the insets of Fig. 3 may in fact be due to closure of shells that include the mantle region.On the other hand, a non-vertical columnar structure offers additional aromatic adsorption sites on newly formed terraces as indicated in Fig. S2 (ESI †).A dimer would feature two identical terraces, one on each coronene.The larger the displacement between the monomers the larger the number of additional adsorption sites (t) on the terrace.Because of the short-range character of the coronene-coronene interaction 20 we expect, supported by calculations, 18 that the displacement between adjacent coronenes does not change with cluster size m.In other words, each terrace would feature the same number of t-sites, approximately six, and the total number of strong adsorption sites would increase linearly with the number of coronene molecules, as seen in Fig. 4.
The average shift in the steps observed in the ion abundances equals 11.4 AE 0.6 (the statistical error should be taken with a grain of salt; individual shifts range from 10 to 13).Thus each terrace offers 5 to 7 t-sites.A visual inspection of the structures computed for (neutral or cationic) He 38 Cor 38,40 suggests that a displacement by about 0.25 to 0.30 nm would offer that many sites on each terrace (about 4 o and 2 i-sites).4][25][26] For comparison, the displacement between adjacent planes in hexagonal graphite is 0.143 nm, parallel to the long axis of the aromatic rings. 12owever, the coronene dimer structures are floppy; an ab-initio calculation by Janowski et al. computes an energy barrier of only 6 meV for planar sliding between one energy minimum and another symmetrically equivalent minimum. 25 direct comparison of displacements computed for neutral dimers and our experimental estimate is complicated by the fact that our value refers to charged systems.Theoretical treatment of cationic dimers will be challenging, last but not least because of charge delocalization. 27Furthermore, H 2 adsorption will tend to increase displacements due to the non-negligible adsorption energy.Kocman et al. 60 and Gould et al. 61 compute adsorption energies of 49 meV for the H 2 -coronene complex.However, the quantum nature of H 2 may reduce these energies by more than 50%. 64In their PIMD study Calvo and Yurtsever find an average adsorption energy of only 11 meV for (H 2 ) 38 Cor. 37or a comparison between experiment and theory the vibrational temperature will be of relevance.We have no direct way to determine or control the temperature of the ions but the evaporative model pioneered by Klots (in the classical regime) suggests that, for an experimental, mass spectrometric time scale of roughly 10 À4 s, the thermal energy k B T equals approximately D/23.5 where D is the activation energy for the most facile dissociation reaction. 52,53An average adsorption energy of 11 meV thus translates to a vibrational temperature of 5 K.
Finally we note that the abundance distributions of (H 2 ) n HCor 2 + and He n Cor 2 + are strikingly different while those of (H 2 ) n HCor + and He n Cor + are rather similar, see Fig. 3.He n Cor 2 + shows no anomaly beyond an intriguing (and as yet unexplained) abrupt drop at n = 20.One possible, heuristic explanation would be the existence of several geometrical isomers that differ in the amount and direction of the displacement between the two coronene molecules.Perhaps the lower adsorption energy of helium provides for less stabilization of a distinct coronene dimer structure.Detailed quantum chemical calculations that include the anisotropy of H 2 and the effect of the net charge will be required to elucidate details of (H 2 ) n HCor m + and (H 2 ) n Cor m + cluster ions.

Conclusions
In summary, the mass spectra of helium droplets doped with coronene and H 2 feature anomalies in the ion abundance that have been traced to particularly stable structures.For the coronene monomer ion features are akin to those in He n Cor + although the larger size of H 2 will favor vacancies in an otherwise highly symmetric, commensurate solvation shell of D 6h symmetry.For cluster ions containing up to m = 4 coronene molecules a shift of a stepwise decrease in the ion abundance indicates the existence of terraces that offer approximately six additional adsorption sites per terrace.This value provides a benchmark for theoretical studies.

Fig. 2
Fig. 2 displays a mass spectrum of helium nanodroplets doped with coronene and hydrogen.Prominent mass peaks are due to bare coronene cluster ions, Cor m + , m = 1 through 5.They are preceded by mass peaks due to Cor mÀ1 C 22 H 12 +

Fig. 1
Fig. 1 Approximate location of the central (c), inner (i) and outer (o) adsorption sites on one face of (H 2 ) 38 Cor + .

Fig. 2
Fig. 2 Electron ionization mass spectrum of helium nanodroplets doped with coronene (C 24 H 12 , mass 300.09 u for the most abundant isotope) and molecular hydrogen.The most prominent mass peaks are due to Cor m + with m = 1, 2, 3, 4, 5.They are followed by a series of (H 2 ) n HCor m + ions; abrupt drops in their ion yields are marked by vertical lines.Peaks at 24 u below the Cor m + peaks are due to an impurity in the coronene sample.

Fig. 3
Fig. 3 Abundance distributions of protonated (H 2 ) n HCor m + (full dots) and unprotonated (H 2 ) n Cor m + (open dots) for m = 1 and 2 (panels a and b, respectively); distributions of (H 2 ) n HCor 3 + and (H 2 ) n HCor 4 + are displayed in c.Local anomalies and step functions fitted to the data (red lines) are indicated.The insets in panels a and b reveal another weaker step at larger n-values.Abundance distributions of He n Cor + and He n Cor 2 + are displayed in d.

Fig. 4
Fig. 4 The position s of step functions identified in the abundance distributions shown in Fig. 3 versus the number of coronene molecules m.The slope of the straight line equals 11.4 AE 0.6 for major steps (m = 1 to 4).