pubs.acs.org/JPCL
Adsorption of Aromatic and Anti-Aromatic Systems on Graphene through π-π Stacking
€rk,† Felix Hanke,† Carlos-Andres Palma,‡ Paolo Samori,‡ Marco Cecchini,‡ and Jonas Bjo Mats Persson*,† †
Surface Science Research Centre and Department of Chemistry, University of Liverpool, Liverpool L69 3BX, enierie Supramol eculaires - CNRS 7006, University de Strasbourg, United Kingdom, and ‡Institut de Science et Ing 8 Allee Gaspard Monge, 67000 Strasbourg, France
ABSTRACT The adsorption of neutral (poly)-aromatic, antiaromatic, and more generally π-conjugated systems on graphene is studied as a prototypical case of π-π stacking. To account for dispersive interactions, we compare the recent van der Waals density functional (vdw-DF) with three semiempirical corrections to density functional theory and two empirical force fields. The adsorption energies of the molecules binding to graphene predicted by the vdw-DF were found to be in excellent agreement with temperature desorption experiments reported in literature, whereas the results of the remaining functionals and force fields only preserve the correct trends. The comparison of the dispersive versus electrostatic contributions to the total binding energies in the aromatic and antiaromatic systems suggests that π-π interactions can be regarded as being prevalently dispersive in nature at large separations, whereas close to the equilibrium bonding distance, it is a complex interplay between dispersive and electrostatic Coulombic interactions. Moreover our results surprisingly indicate that the magnitude of π-π interactions normalized both per number of total atoms and carbon atoms increases significantly with the relative number of hydrogen atoms in the studied systems. SECTION Surfaces, Interfaces, Catalysis
lmost 80 years after the first derivation of the -C6/R6 nature of dispersive molecular forces by Fritz London,1 the efficient and accurate modeling of noncovalent interactions in large molecular systems remains an outstanding challenge. Their full quantification is at the very heart of subjects such as supramolecular engineering2 and medicinal chemistry.3 In these disciplines, the general concept of π-π stacking is used to describe the face-to-face stacking of aromatic systems involved in noncovalent interactions.3-5 π-π stacking is particularly relevant in polycyclic aromatic hydrocarbons (PAHs), making them interesting for technological applications, such as (opto)-electronics, photovoltaics, and so on.6 By exploring the adsorption behavior of 12 polycyclic aromatic and 4 antiaromatic hydrocarbons on graphene, this Letter demonstrates how recent approaches to the dispersion problem can be used to address fundamental questions on the chemical and physical nature of interactions, such as the influence of π-conjugation, electrostatics, and dispersion as well as additivity in π-π stacking. Recently, many developments toward modeling dispersive interactions using density functional theory (DFT)7-17 and molecular force fields18,19 have been reported. One approach relies on pair potentials of the form Vij (R) = -C6,ij fd,ij (R)/R6 between two atoms i and j at a distance R, either as terms in a molecular force field or as a correction to DFT. The choice of the interaction coefficients C6,ij relies on single-atom references,
such as atomic polarizability data,11-15 and effective atomic volumes14 or self-consistency within thermodynamical and crystallographic data.15,18-20 The damping function fd,ij(R) is required to prevent divergence of the energy. An alternative and nonempirical approach to the dispersion problem relies on the development of a fully nonlocal density functional to fix the shortcomings of semilocal DFT. The most widely used formulation7-10 is based on the revised PBE functional (revPBE),21 in which the correlation term is replaced by a correction based on the adiabatic connection formula. Such a van der Waals density functional (vdW-DF) was originally derived for layered structures8 and later extended to general geometries.16 Ab initio approaches are also available,22-24 but remain computationally too expensive for large molecular systems. To achieve a comprehensive understanding, we compute the adsorption of 12 polyaromatic and 3 antiaromatic hydrocarbons on graphene calculated with the vdW-DF theory,9,16,25 four empirical corrections to DFT,12-15,26 and two empirical force fields.18,19 This serves as a benchmark for the performance of different approaches to computing the dispersion interaction.
A
r 2010 American Chemical Society
Received Date: October 1, 2010 Accepted Date: November 11, 2010 Published on Web Date: November 18, 2010
3407
DOI: 10.1021/jz101360k |J. Phys. Chem. Lett. 2010, 1, 3407–3412
pubs.acs.org/JPCL
aromatic compounds to graphene Ebind ¼ NC ECC þ NH ðECH - ECC Þ
where ECC is the fitted adsorption energy per graphene-like carbon and ECH is the fitted energy per benzene-like carbon and its adjoining hydrogen atom; graphene-like carbons are carbon atoms of the adsorbate featuring three covalent bonds with adjacent carbons, whereas benzene-like carbons are carbon atoms covalently linked to two carbons and one hydrogen. The fitted parameters ECC and ECH as well as the MAE for the difference methods are summarized in Table 1. As reported in Figure 2, all models produce linear trends, and the calculated data are well-fitted by a line with a positive slope, meaning that ECH > ECC. For the empirical models, however, this result does not imply that benzene-like carbons have a higher binding affinity than graphene-like carbons because the positive slope is due to the presence of hydrogens, which are missing in the latter. By contrast, the vdW-DF and the Tkatchenko-Scheffler (TS) correction include information on the local chemical environment of atoms, either through the nonlocal density functional or via a Hirshfeld charge decomposition. Interestingly, the slope of their linear fits in Figure 2 is larger compared with the empirical models. This gives an indication that carbon atoms in a PAH with adjoining hydrogen atoms (benzene-like) are indeed chemically distinguishable from those without (graphene-like), with the former binding stronger to the substrate. Moreover, the linear trend of the vdW-DF results strongly indicates that additivity of interactions, which is a basic assumption in the force-field approach,30 is valid for describing the binding energy of PAHs on graphene. Altogether, these results suggest that a force-field approach considering two types of sp2-hybridized carbon atoms instead of one would be beneficial for treating the adsorption of PAHs on graphene more accurately than currently available models. To investigate further the influence of the chemical environment on the interactions between planar π-conjugated systems, we consider four antiaromatic molecules with NH = NC. Figure 3 compares the normalized binding energy of three antiaromatic systems with that of benzene. All density functional results show that a small antiaromatic molecule ([4]annulene) adsorbs significantly stronger than benzene, a trend that subsides for the larger two molecules ([8]- and [12]-annulene). This indicates that aromaticity does not play a primary role in the adsorption on graphene. This result suggests that advanced materials design with enhanced stacking properties would benefit from the use of admolecules exposing benzene-like carbons rather than graphene-like carbons. Therefore, high stacking capacities can be foreseen for multiarm rigid and planar molecules based on dendritic or hyperbranched polymers featuring both aromatic and nonaromatic moieties with NC ≈ NH. To gain additional insight into the π-π stacking interactions, we singled out the contributions to the binding energy predicted by the vdW-DF model for a series of aromatic and nonaromatic compounds as follows32 Etot ½n ¼ Ees ½n þ Ec, nl ½n þ Ekin ½n þ Ex, GGA ½n þ Ec, LDA ½n
Figure 1. Lateral configuration of the AB stacking for hexabenzocoronene (C42H18) on a graphene sheet. The indexes g and b refer to the graphene-like and benzene-like local atomic configurations found in a PAH adsorption on graphene. The total number of carbon atoms of type g and b determines the adsorption energy according to eq 1.
For all molecules considered in this study, it was assumed that the weak adsorption of a PAH on graphene does not perturb the intramolecular geometry of either the PAH or the graphene. Similar to the geometry of the stacking in graphite and in bilayer graphene, the lowest-energy configuration for benzene adsorption was found to be the AB-type stacking, which was then used for the case of aromatic hydrocarbons adsorbed on graphene. This geometry is illustrated for the case of hexabenzocoronene on graphene27,28 in Figure 1. For the antiaromatic molecules, all high-symmetry adsorption sites were computed, and the most stable one was used. In Figure 2, we compare the adsorption energies on graphene for 12 polyaromatic hydrocarbons as a function of the ratio of hydrogen to carbon atoms, NH/NC, using the different methods described above. The experimental data for the binding energy of benzene, naphtalene, coronene, and ovalene on graphite in Figure 2 were obtained from temperatureprogrammed desorption (TPD) experiments performed in ultrahigh vacuum.29 The binding energy of graphene in Figure 2 was obtained in ref 29 indirectly by extrapolation from the experimental binding energies of smaller aromatic systems adsorbed on graphene using the MM3 force field.30 Our results indicate that the first-principles vdW-DF gives the best agreement with TPD data with a lowest mean absolute error (MAE) of 6.1 meV/atom; see Table 1. Also, the WuYang (WY) scheme correlates well with experimental data (MAE of 7.7 meV/atom) but is not able to capture the exfoliation energy of graphite (52 ( 5 meV/atom) extrapolated from the experimental TPD data; note that the data from the Ortmann-Bechstedt-Schmidt (OBS) scheme could not be fitted to Figure 2 because of the large MAE. The computed data are linear in the ratio NH/NC, so that we can write down a straightforward ansatz for the binding energy of the
r 2010 American Chemical Society
ð1Þ
ð2Þ
3408
DOI: 10.1021/jz101360k |J. Phys. Chem. Lett. 2010, 1, 3407–3412
pubs.acs.org/JPCL
Figure 2. Binding energy per carbon atom for aromatic hydrocarbons adsorbed on graphene (Ebind). The gray error bars show data from temperature-programmed desorption (TPD) experiments for C6H6, C10H8, C24H12, and C42H14 and the binding energy of the graphene dimer from extrapolation of the TPD data.29 The vdW-DF binding energies of benzene, naphtalene, and graphene agree well with a previous vdW-DF study31 for these systems. Table 1. Values for the Energies E CC and E CH from the Linear Fits in Figure 2 of the Manuscript, Together with the Mean P Absolute Errors (MAE = i |E fit,i - E exp,i |/N exp ) from the 29a Experimental Data by Zacharia et. al ECC
ECH
MAE
vdW-DF
49.2
80.1
6.1
Wu-Yang
66.0
82.1
7.7
CHARMM
55.5
70.9
9.5
Grimme
52.6
68.0
11.4
MMFF TS
52.9 74.9
65.5 95.8
12.7 16.2
OBS
78.1
127.9
39.2
energy. The total interaction energy, Eint, along with the dispersive Ec,nl and electrostatic (Coulomb) Ees contributions are plotted in Figure 4 as a function of the separation between adsorbate and graphene layer. This energy decomposition shows that the attractive part of the adsorption energy is a complex combination of dispersive and electrostatic interactions around equilibrium distances. For distances >4.5 Å, the energy decomposition unveils that the (attractive) interaction is totally dispersive. In other words, the initial complex formation between the adsorbate and the substrate appears to be purely governed by dispersion forces, which effectively drive the former in close proximity to the latter, whereas the actual binding is finalized by short-range attractive electrostatic forces that further stabilize the interaction, even in the absence of formal charges. The repulsive part of Etot comes from the Pauli repulsion, which is manifested in the kinetic energy. (See Figure S1 of the Supporting Information for the complete energy decomposition.) In summary, the adsorption behavior of polyaromatic and antiaromatic hydrocarbons on graphene have been investigated
a
Experimentally extrapolated binding energy of bilayer graphene was not included in the calculation of the MAEs. All values are in units of meV/atom.
where Ees is the electrostatic Coulomb energy, Ec,nl is the nonlocal correlation energy, Ekin is the kinetic energy, Ex,GGA is the GGA exchange energy, and Ec,LDA is the LDA correlation
r 2010 American Chemical Society
3409
DOI: 10.1021/jz101360k |J. Phys. Chem. Lett. 2010, 1, 3407–3412
pubs.acs.org/JPCL
that eq 1 will be routinely used in the stage of molecular design of novel polyaromatic systems to fine-tune their adsorption propensity on graphene. Within currently available theories, we found that π-π interactions in the adsorption of neutral molecules on graphene are a complex combination of dispersive and electrostatic interactions. We conclude that purely dispersive forces drive the docking of the adsorbates on graphene, whereas short-range electrostatic interactions ultimately stabilize the complex.
Figure 3. Binding energy per carbon atom for three planarized cyclic antiaromatics. Note that all of these molecules have a hydrogen-to-carbon ratio of 1, and the dashed horizontal lines indicate the binding energy for benzene (ECH).
METHODS DFTcalculations were performed with the pseudo-potentialbased VASP package25 for calculations with the revPBE functional21 (related to the vdW-DF) and using the all-electron code FHI-aims26 for the results requiring PBE,33 related to TS,14 Grimme,12 WY,13 and OBS15. The DFT calculations use a supercell approach, with integration settings converged to
