Polycyclic Aromatic Hydrocarbons - American Chemical Society

Article pubs.acs.org/JPCA

Polycyclic Aromatic Hydrocarbons: Trends for Bonding Hydrogen Jakob Arendt Rasmussen* Interdisciplinary Nanoscience Center (iNANO) and Department of Physics and Astronomy, Ny Munkegade, Building 1520, Aarhus University, DK-8000 Aarhus C, Denmark ABSTRACT: Hydrogenation of carbonaceous materials is important within carbon-based electronics, hydrogen storage, and the catalytic formation of molecular hydrogen in space. This study presents a systematic investigation at the density functional theory level of the hydrogenation of all small closed-shell polycyclic aromatic hydrocarbons comprising up to four carbon hexagons plus pentacene, hexacene, and heptacene. Binding energies span from 0.43 to 2.70 eV. Two-fold coordinated carbon atoms are preferred as binding sites with binding energies from 1.06 to 2.70 eV. Analyzing the binding sites yields three different motifs each with a clear structural and electronic fingerprint explaining the ordering of the binding sites.

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INTRODUCTION Polycyclic aromatic hydrocarbons (PAH) have attracted much attention within different fields such as astrophysics and surface science.1−4 Proposed as catalyst in the formation of molecular hydrogen2,5,6 in space and as potential carrier for hydrogen storage,7 the interaction between hydrogen and PAHs was extensively investigated both theoretically and experimentally. Findings include that PAH cations are reactive toward both atomic and molecular hydrogen, depending on the stoichiometry of the molecule.8 Also, the reactivity between anions and H9 and between neutral naphthalene and H has been investigated.10 These findings should be compared to the correlation found between the presence of PAHs and the emission of H2 in the interstellar medium.2 This has led to numerous theoretical studies of the hydrogenation of PAHs: Superhydrogenation of coronene, that has recently been observed,11 and H2 evolution on coronene6 suggesting several routes to H2 formation; the possibility of hydrogen tunneling onto pyrene;12 hydrogenation of, hydrogen diffusion on, and H2 formation on pyrene;13 hydrogenation of small PAHs and assessment of the results with higher levels of theory.14 The usage of PAHs as model systems for graphene in a cluster model has also been exploited15 and challenged at the coupled cluster level of theory16 and thereby relating the chemistry of PAHs to that of graphene.17−19 Despite the many studies on the interactions between hydrogen and PAHs, several issues remain unexplained. The specific details that makes one position more reactive toward hydrogenation than another are still not on firm ground beyond the general agreement that 2-fold coordinated (i.e., coordinating two carbon atoms and one hydrogen) edge sites are preferred.5,6,10,13−15 This calls for a systematic investigation in order to uncover the trends that can reveal the physics behind the bonding of hydrogen to PAHs. The aim of this article is to investigate the bonding of hydrogen to PAHs with special emphasis on binding to the edge carbon atoms. This is done systematically for all PAHs © 2013 American Chemical Society

comprising up to four carbon hexagons plus pentacene (five hexagons), hexacene (six hexagons), and heptacene (seven hexagons). If we consider a series of linear PAHs, hydrogen will preferably bind to the 2-fold coordinated carbon atoms along the side of the molecule, and the longer the molecule, the better the binding. From these results, we introduce three structural motifs describing the different binding sites. For the 2-fold coordinated carbon atoms, the preferred sites are those that maximize the number of next-nearest neighbors. The survey is extended to include all the small PAHs verifying the distinct behavior of the motifs. A detailed qualitative understanding is achieved using the recently proposed π-band model.13 Finally, the results are successfully challenged by a set of larger sample molecules. The article is organized as follows: After going through the calculational details, the results are presented and discussed. We first discuss a series of small linear PAHs, then small PAHs of a more general geometry. Finally, we consider a set of larger PAHs before concluding.

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METHODS All systems under consideration have been treated at two levels of theory: first-principles density functional theory20,21 (DFT) calculations and the simple tight binding (TB) π-band model.13 DFT. Density functional calculations were conducted with the real-space grid implementation of the PAW method,22 GPAW,23,24 using the PBE exchange-correlation functional.25 The calculations were managed within the atomic simulation environment.26 The utilized basis set is a real space grid with grid spacing of 0.2 Å in a nonperiodic, orthorhombic supercell with approximately 3−4 Å vacuum around the molecules in the molecular plane and 6.5 Å perpendicular to the molecular plane. Structures were relaxed until forces were below Received: January 9, 2013 Revised: April 17, 2013 Published: April 26, 2013 4279

dx.doi.org/10.1021/jp400287h | J. Phys. Chem. A 2013, 117, 4279−4285

The Journal of Physical Chemistry A

Article

Table 1. DFT Binding Energies and TB π-Band Centers for the Small Linear PAHs

0.05 eV/Å. All calculations were spin polarized. The choice of PBE is motivated by a comparison between PBE and the hybrid functional PBE0 in a previous study.13 The more accurate PBE0 hybrid functional27 showed quantitative agreement with PBE, and we therefore consider PBE sufficient for this work. The lack of long-range-correlation in PBE is expected to be of minor importance as only binding energies where the covalent bond will dominate is considered. Had transition states been investigated, it should be tested whether long-range-correlation corrected functionals would contribute significantly to the energies. Binding energies are defined as Eb = (EPAH + EH) − EPAH−H so that a positive binding energy imply a stable binding. Tight Binding π-Band Model. The tight binding π-band center (εIπ) of site I is an electronic descriptor defined as επI ≡

∑ fn εn |⟨ψn|pzI ⟩|2 n

molecule benzene naphtalene

anthracene

tetracene

(1) pentacene

where n is a orbital index, ψn the orbital, εn the eigen energy, and f n the occupation. pIz is the 2pz-orbital of carbon atom I. This makes the π-band center the energetic average of the occupied projected density of states (PDOS) at carbon atom I. It is a simplified expression for the position dependent parts of the binding energy. Positions with a high weight in the HOMO-end of the occupied PDOS will have a high π-band center, which implies a high binding energy. The model relies on a set of assumptions, one of them being that the strength of the isolated covalent bond and the rehybridization of the lower carbon states from sp2 to sp3 is independent of the binding position. Though derived in a tight binding framework, the πband centers can also be calculated within, e.g., DFT. For more details, see ref 13.

hexacene

heptacene

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RESULTS AND DISCUSSION Small Linear PAHs. We start by investigating the binding of hydrogen to linear PAHs. These are shown in Figure 1 where also the binding sites are enumerated. The binding energies of H relative to atomic H are given in Table 1. The values range from 0.43 to 2.70 eV. In correspondence with previous results,5,6,10,13−15 a clear preference toward binding hydrogen

a

site

Eb (eV)

επ

1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8

1.13 1.26 1.45 0.43 1.45 1.63 0.51 1.93 1.59 1.72 0.69 2.15 a 1.70 1.79 0.86 2.29 0.53 2.40 1.78 1.85 0.98 2.38 0.68 2.56 0.54 1.85 1.89 1.07 2.45 0.82 2.66 0.64 2.70

−1.33 −1.33 −1.28 −1.63 −1.32 −1.27 −1.63 −1.21 −1.32 −1.27 −1.62 −1.20 −1.63 −1.32 −1.27 −1.62 −1.20 −1.63 −1.19 −1.32 −1.27 −1.62 −1.20 −1.62 −1.19 −1.62 −1.32 −1.27 −1.62 −1.20 −1.62 −1.19 −1.62 −1.19

Not possible to converge DFT calculation.

on the 2-fold coordinated carbon atoms is seen where we observe binding energies from 1.13 to 2.70 eV. Unlike previous studies focusing on the difference between edge and nonedge adsorption, we will now investigate in greater detail the binding of hydrogen to the 2-fold coordinated carbon atoms. The 2-fold coordinated binding sites can be divided in three groups depending on the position of the site within the linear PAH. The resulting groups are the terminal, near-terminal, and interior sites, which together account for all the 2-fold coordinated binding sites. In Figure 2, we depict the binding energies of the 2-fold coordinated binding sites against the size of the molecules. The three groups of binding sites show a clear trend in the behavior of the binding energies: the larger the molecule, the better the binding with a convex behavior within this data range. The almost linear correlation within the groups between the binding energies and the number of hexagons evidence that each group provides a unique binding environment and that further structural modifications of the molecules only causes minor quantitative perturbations to the binding. We offer the explanation that the increasing binding with PAH length is due to a better stabilization of the extra electron on a larger molecule (note that the product after adding hydrogen is a

Figure 1. Set of small linear PAHs. Numbers mark the symmetry inequivalent sites for H binding. 4280



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hydrogen that span from 1.06 to 1.83 eV. The three groups presented above each have their own structural motif defined by two nearest neighbors and the number of next-nearest neighbors (i.e., 2, 3, or 4). These motifs can be seen in Figure 4a where they have been named A, B, and C. Assigning motif A, B, or C to each of the 2-fold coordinated binding sites and grouping the binding energies accordingly yields the histogram shown in Figure 4b. This plot includes all 2-fold coordinated binding sites from the molecules in Figures 1 and 3. Motif A shows binding energies from 1.06 to 1.85 eV, motif B from 1.36 to 1.89 eV, and motif C from 1.81 to 2.70 eV. Although motifs A and B are clearly different, the binding energies tend to overlap, which is contrary to motif C, which has binding energies that are more separated from the others. This means that, at this level (DFT), the distinction between motifs A and B is generally smaller when gauged by the H chemisorption energy than when the measure is the more distinct structural properties of the sites (number of neighbors, number of next-nearest neighbors, etc., i.e., the molecular geometry). It turns out that at a lower level of theory, nearestneighbor tight-binding, the distinction between A and B is more pronounced, and we therefore find it instructive to maintain. The binding energies cannot directly be calculated within the nearest-neighbor tight-binding framework, but we can use an electronic descriptor proposed by us in a previous study of H-binding to pyrene: the tight binding π-band center model.13 In that work, the π-band centers were shown to have good correlation with binding energies as found by DFT. πband centers for all sites included in Figures 1 and 3 are tabulated in Tables 1 and 2. In Figure 4c, it is shown that the three groups are electronically distinct (as measured by επ) and that this distinction to some extent is maintained in the reactivity; see Figure 4b. We will now explain why motif C is preferred over motif A by analyzing the origin of the π-band center for the two motifs in an arbitrarily long linear PAH. Such a molecule can be seen as two aligned interacting chains with interactions between every second carbon atom. In Figure 5a is seen the two isolated chains of length N. Figure 5b shows the linear PAH with interactions between the two chains. The molecule is now being built within a molecular orbital theory picture with states on the isolated chains as basis states. Only the π-system is considered, rendering the system with one state per atom. The electronic structure of a finite chain is well-known29 and can be derived analytically within the nearest neighbor tight binding approximation, which makes it perfect as a choice of basis set. Identifying that motif A is situated at the end of the molecule, we consider the terminal site of the finite chain (site 1 in Figure 5a). At a terminal site of a finite chain, the projected density of states (PDOS) has a well-known semielliptical form (see left part of Figure 5c). The interaction between two states in a molecular orbital picture will cause a splitting. So the semielliptic PDOS for the chain (Figure 5a) will split up in two peaks for the molecule in Figure 5b. This is seen in the right part of Figure 5c, which is a calculation of the PDOS for motif A (site 1) in the molecule shown in Figure 5b. This PDOS shows the expected two peaks but more importantly a low weight at the fermi level. The π-band center is the weighted average of the shaded part of this figure and is shown with the red line.13 The previous analysis should be compared to a similar model for motif C. We choose a site somewhere in the middle of the chain, e.g., site i in Figure 5a. In that case, the PDOS is also

Figure 2. Linear PAHs: number of hexagons vs DFT binding energies. Three different types of sites are identified, with each type showing an increasing behavior of the binding energy as a function of the length of the molecule. Only 2-fold coordinated sites are included in the plot.

radical species). It has been documented that for linear PAH spontaneous symmetry breaking might occur creating edge localized spin states with antiferromagnetic spin ordering.28 For the systems under consideration, this is not important as the transition happens for molecules with more than seven hexagons (which is the upper limit in this study). Elongating the molecules beyond pentacene will yield an increasing amount of interior binding sites that can be grouped together. Choosing only these three groups (and not an open amount, scaling with the size of the largest molecule) allows us to condense the characteristics of the groups to the local binding environment. Furthermore, increasing the number of types of binding sites for these linear PAHs will only be relevant for the linear PAHs and not for a more general PAH. Having set the framework it is now possible to extend the study to include PAHs of a more general structure. Small PAHs. We now consider the extension of the structures to include all closed-shell (nonradical) PAHs with up to four hexagons. The new structures are shown in Figure 3. The binding energies for hydrogen binding to the small nonlinear PAHs have been calculated and are tabulated in Table 2. The binding energies range from 0.47 to 1.83 eV. Again, as for the linear PAHs, there is a preference for the 2fold coordinated binding sites, which have binding energies for

Figure 3. Set of small nonlinear PAHs. Numbers mark the symmetry inequivalent sites for H binding. 4281



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Table 2. DFT Binding Energies and TB π-Band Centers for the Small Nonlinear PAHs molecule

site

Eb (eV)

επ

benzo[a]anthracene

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 1 2 3 4 5

1.40 1.57 0.49 1.83 0.75 0.83 1.42 1.30 1.26 1.36 0.64 1.55 1.51 0.63 1.81 0.47 1.58 1.38 1.23 1.41 0.81 1.47 0.62 1.63 1.08 0.61

−1.32 −1.28 −1.62 −1.23 −1.59 −1.59 −1.29 −1.32 −1.33 −1.28 −1.62 −1.28 −1.28 −1.62 −1.22 −1.63 −1.27 −1.32 −1.33 −1.29 −1.59 −1.28 −1.62 −1.26 −1.34 −1.58

triphenylene

pyrene

molecule phenanthrene

benzo[c]phenanthrene

chrysene

site

Eb (eV)

επ

1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9

1.27 1.42 0.71 1.22 1.37 0.54 1.44 1.47 1.57 0.98 1.06 0.68 1.60 1.71 0.84 1.39 1.44 1.43 1.49 0.53 1.40 1.23 1.27 1.46 0.65 0.86

−1.32 −1.29 −1.59 −1.33 −1.28 −1.62 −1.28 −1.33 −1.29 −1.60 −1.55 −1.62 −1.28 −1.28 −1.62 −1.28 −1.33 −1.29 −1.27 −1.62 −1.28 −1.33 −1.32 −1.29 −1.59 −1.59

where the nature of the zigzag edge gives the possibility to have noninteracting states localized at the edge.30 In essence, this yields the calculated PDOS shown in the right part of Figure 5d. The large peak at the Fermi level for motif C pulls the πband center up toward the Fermi level as compared to the πband center for motif A, and this explains the preference for hydrogenation of sites characterized by motif C. The behavior of motif B is somewhat in between that of motifs A and C. This analysis is of course dependent upon choosing a site that will end up being 2-fold coordinated. Choosing a site that will end up being three-fold coordinated will instead introduce a splitting between the states at the Fermi level and therefore yield a low density of states there. Therefore, 3-fold coordinated sites will have no peak at the Fermi level but maintain the peaks at the band edges yielding a very low π-band center. The π-band center being ultimately a measure for the binding energy, we now have a rationale for the different reactivities of the three motifs. The motifs have been derived from a trend study of the linear PAHs, which have explicit zigzag character. A set of molecules with armchair geometry would not contain the most stable C sites, making the chosen set of linear PAHs the most general, and there is plenty of armchair in the full set of small PAHs (e.g., phenanthrene, chrysene, and pyrene) confirming the trends. Performing a prescreening of sites in terms of an electronic descriptor is desirable over using a geometric descriptor due to the generality of the formulation. Having explained the behavior of the π-band centers for the different motifs for the linear PAHs, we will now extend the analysis to PAHs with a more general structure. Figure 4 already testifies that the electronic structure correlates well with the geometric structure

Figure 4. Correlation between geometry, electronic structure, and energetics for all the small PAHs shown in Figures 1 and 3. Data are grouped in colors according to the three types of sites identified in Figure 2.

well-known having a cusp at each of the band edges (see left part of Figure 5d). The states at the band edges are delocalized over the entire chain. These two most distinct features of the PDOS at site i in the chain can be expected to cause new distinct features, i.e., cause a splitting by analogy to the situation in Figure 5c for the molecule. This is the two peaks at each end of the spectrum seen in the right part of Figure 5d. However, the chain states between the two peaks are also abundant and cause further states to form, e.g., a distinct resonance at the Fermi level. This has a parallel in zigzag graphene nanoribbons 4282



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Figure 7. Set of larger PAHs.

Table 3. It is clear that the larger sample molecules fit perfectly into the correlation, no exceptions present. The figure Figure 5. (a) Two isolated N atom chains. (b) A long linear PAH of 2N atoms. Left part of panel c shows the tight binding PDOS of a terminal site in the chain (e.g., site 1 in panel a). The interaction at terminal sites induce a splitting, which is seen in the right part of panel c showing the tight binding PDOS of motif A (site 1 in panel a) with two distinct peaks. Left part of panel d shows the tight binding PDOS of an interior site in a chain (e.g., site i in panel b). The PDOS shows the expected two peaks at the edges of the spectrum. The interaction between the two chains will induce a splitting of each of the two states into a total of four states. The states at the Fermi level (the shaded part in the left part of panel d) will upon interaction between two chains localize as nonbonding states at the Fermi level in a zigzag graphene nanoribbon fashion. This amounts to a total of five peaks, which is seen in the right part of panel d showing the tight binding PDOS of motif C (site i in panel b) with five peaks. In the left parts of panels c and d, the π-band centers (the average of the shaded part of the figures) are depicted as red lines. The large peak at the Fermi level for motif C rises the π-band center as compared to motif A.

Table 3. DFT Binding Energies and TB π-Band Centers for the Larger PAHs Shown in Figure 7 molecule

site

Eb (eV)

επ

dibenzo[a,j]anthracene

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6

1.25 1.30 1.42 0.79 0.76 1.77 1.72 0.60 1.49 1.51 0.62 1.36 0.64 0.67 1.39 0.75 0.75 0.66 0.85 1.41 1.44 1.55 0.55 1.88 0.73 0.70 0.76 1.79 0.67 1.49

−1.33 −1.32 −1.29 −1.59 −1.59 −1.25 −1.22 −1.62 −1.28 −1.28 −1.62 −1.28 −1.61 −1.58 −1.28 −1.58 −1.57 −1.58 −1.61 −1.28 −1.28 −1.28 −1.62 −1.21 −1.58 −1.58 −1.57 −1.21 −1.62 −1.28

coronene

for the set of small PAHs in Figures 1 and 3. Figure 6 brings further evidence by explicitly correlating the electronic structure with the DFT binding energies and including data for the set of larger PAHs shown in Figure 7. Hydrogen binding energies and π-band centers for the molecules in Figure 7 are tabulated in

ovalene

circumcoronene

furthermore emphasizes the reason for including only 2-fold coordinated carbon atoms above. The data points appear to be divided into two separate parts, especially along the π-band center axis: the 2-fold and 3-fold coordinated binding sites. Energetically, there is a small overlap between the binding energies of these two groups. For screening purposes, this has no effect as one is certain to get the most stable sites, which is also clear from Figure 6. The dispersion in Figure 6 is due to the approximations within the π-band center model, e.g., assuming that the isolated strength of the C−H bond is

Figure 6. Correlation between π-band centers and DFT binding energies. A clear growing behavior is seen with only minor deviations from the expected linear correlation. Crosses depict all data points from Tables 1 and 2. 4283



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π-band model as it does not accommodate spin at the tight binding level. However, one of the recognized consequences of the appearance of an antiferromagnetic groundstate is an increased reactivity, 28 and the model is therefore expected to behave nicely.

position invariant but perhaps more important the neglection of structural contributions. Bonfanti et al.14 showed that the reorganization energy, the cost to deform the molecule prior to binding, unintuitively is largest for the best binding positions proving that first the rehybridization energy of the binding carbon atom from sp2 to sp3 is not position invariant as assumed in this model; second that binding occurs despite the unfavorable reorganization energy. The consequence is that the electronic contributions have to be even larger for the good adsorption sites than expected; this underlines the sense in using an electronic descriptor as a screening parameter. The correlation in Figure 6 demonstrates the π-band model as a detailed screening tool, giving the most stable binding sites for a wide range of molecules at a very modest computational cost (επ is calculated before adsorption via tight-binding or DFT, i.e., only one calculation). Other alternatives exist: One simpler method would be the number of next-nearest neighbors, i.e., the three motifs in Figure 4. The performance of that measure is tested in Figure 8a. The figure is less detailed

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CONCLUSIONS In the present work, we have performed a systematic investigation of the binding of hydrogen on small PAHs at the DFT level of theory. In general, hydrogen binding to 2-fold coordinated carbon atoms are preferred over 3-fold coordinated, but there appears to be a preference for zigzag-edge type binding sites. Specifically, this is seen for the series of small linear PAHs where the relatively small molecule heptacene gives large binding energies of up to 2.7 eV along the side of the molecule. Furthermore, we see enhanced binding when increasing the molecular size. The results were interpreted in terms of the π-band model, and a simple structural model, three motifs, for the best binding sites was outlined. The model is simple and is robust when tested on a set of larger molecules. For this large set of molecules, the tight binding π-band center model correlates very well with the DFT binding energies and is therefore a valuable tool for screening. In conclusion, we have shown that the binding of hydrogen to PAHs is guided by the local environment of the binding site together with a small size-dependent component. The edge always appears to be the most favorable place to bind with a preference for zigzag edge-type binding sites, and the larger the molecule, the better.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

Figure 8. (a) Correlation between the number of next-nearest neighbors and DFT binding energies. (b) Correlation between the hypercoordination and DFT binding energies. A larger deviation is seen for the latter. A particular erroneous data point for dibenzo[a,j]anthracene is marked by an arrow. The legend is identical to that of Figure 6.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author thanks Bjørk Hammer and Henrik Høgh Kristoffersen for fruitful discussions and thorough reading. This work was supported by the Danish Strategic Research Council and the Danish Center for Scientific Computing.

than Figure 6, but the trend is maintained and the qualitative conclusion (i.e., choosing binding sites for higher level treatment) from the two plots are the same. A related model by Bonfanti et al.14 should be mentioned. They introduce the hypercoordination defined as the number of next-nearest neighbors that are 2-fold coordinated and argue that it is a measure of the reactivity for a given site. In Figure 8b, the hypercoordination of all the binding sites of the molecules in Figures 1 and 3 is plotted against the DFT binding energies. While maximizing the hypercoordination predicts the most stable binding sites, it also predicts some very unfavorable sites, and the model therefore has a much larger deviation. The biggest problem though is site 6 in dibenzo[a,j]anthracene (Figure 7); the most stable binding site (by DFT) in that molecule but with a hypercoordination of 0 that will cause it to be disregarded in a screening (marked by an arrow in Figure 8). The π-band model predicts it to be second-best (green triangle in Figure 6). Finally, the question appears whether the issue of symmetry breaking in larger zigzag-type systems will affect the presented model. The transition to an antiferromagnetic system will imply a slight stabilization of the initial state thereby decreasing the binding energy. This effect is not captured in the

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Polycyclic Aromatic Hydrocarbons - American Chemical Society

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