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Institute of Organic Chemistry and Biochemistry (IOCB), Academy of Sciences of the Czech Republic and Center for Biomolecules and Complex Molecular Systems, Flemingovo nam. 2, 166 10 Prague, Czech Republic ‡ Department of Physical Chemistry, Faculty of Science, Regional Centre of Advanced Technologies and Materials (RCPTM), Palacky University Olomouc, tr. 17. listopadu 12, 771 46 Olomouc, Czech Republic § Department of Chemistry, Pohang University of Science and Technology (POSTECH), San 31, Hyojadong, Namgu, Pohang 790-784, Korea ABSTRACT: The adsorption of Ag, Au, and Pd atoms on benzene, coronene, and graphene has been studied using post HartreeÀFock wave function theory (CCSD(T), MP2) and density functional theory (M06-2X, DFT-D3, PBE, vdW-DF) methods. The CCSD(T) benchmark binding energies for benzeneÀM (M = Pd, Au, Ag) complexes are 19.7, 4.2, and 2.3 kcal/mol, respectively. We found that the nature of binding of the three metals is diﬀerent: While silver binds predominantly through dispersion interactions, the binding of palladium has a covalent character, and the binding of gold involves a subtle combination of charge transfer and dispersion interactions as well as relativistic eﬀects. We demonstrate that the CCSD(T) benchmark binding energies for benzeneÀM complexes can be reproduced in plane-wave density functional theory calculations by including a fraction of the exact exchange and a nonempirical van der Waals correction (EE+vdW). Applying the EE+vdW method, we obtained binding energies for the grapheneÀM (M = Pd, Au, Ag) complexes of 17.4, 5.6, and 4.3 kcal/mol, respectively. The trends in binding energies found for the benzeneÀM complexes correspond to those in coronene and graphene complexes. DFT methods that use empirical corrections to account for the eﬀects of vdW interactions signiﬁcantly overestimate binding energies in some of the studied systems.
ARTICLE Figure 1. 2. It was anticipated that the results obtained would make it possible to develop general guidelines for the eﬃcient and accurate modeling of extended systems involving vdW interaction. calculations were also performed using the relativistic Pol-DK36 basis sets and the otherwise-equivalent nonrelativistic Pol basis sets.1021/ct200625h |J. Au. This comparison was performed to identify a DFT method that can be used to accurately model the interactions of transitionmetal atoms with graphene. as calculated using the M06-2X method. With the exception of the 1s2 electrons of the carbon atoms. π-stacking.22À24 When used in conjunction with an extended basis set. and (h) the ‘hollow’ site above the center of the aromatic ring. Moreover. starting from geometries in which the metal was adsorbed at the (t) position. the coroneneÀAg complex (green). coroneneÀM. Geometries of the complexes were optimized at the M06-2X level.35 These basis sets contain diﬀuse and polarization functions. the interaction energy is deﬁned as the diﬀerence between the energy of a complex and the sum of the energies of its components. we sought to investigate the performance of the second-order MøllerÀPlesset (MP2). and other noncovalent interactions. we initially studied two smaller systems as models of the graphene surface: benzene and coronene. which are important when studying noncovalent interactions. In the case of coronene. which are important in heavy transition metals (especially gold) and their complexes. Ag) complexes were investigated. SYSTEMS INVESTIGATED BenzeneÀM.26 and M06-2X27À29 methods.39À41 Throughout this paper. Since the number of quantum chemical methods that can be used to study inﬁnite graphene sheets is rather limited. 7. and palladium. Relativistic eﬀects.1 kcal/mol)21 and is therefore used to ‘benchmark’ the performance of less computationally expensive WFT and DFT techniques that account for dispersion interactions in some way. the MP2 method25 was also used. MP2 calculations were performed using the VDZP and VTZP contractions as well as with a combination denoted VDZP/VTZP (VDZP for benzene and VTZP for the metal).21 In general. Chem.21 The aim of the study reported herein was to investigate the interaction of graphene with three diﬀerent transition metals: gold. the coroneneÀPd complex (blue). and grapheneÀM (M = Pd. (b) a ‘bridge’ site above the midpoint of a CÀC bond. We then planned to use this method to study binding in coroneneÀM complexes. 3743–3755 . it is negative when the components are attracted to one another. the use of DFT techniques that do not account for dispersion energy causes binding energies to be underestimated.38 This was done because comparisons of the relativistic and nonrelativistic stabilization energies can provide helpful insights into the nature of the bonding between an aromatic system and a metal atom. 3.25 DFTD3. Our second aim was to compare the performance of DFT methods utilizing a plane-wave basis set to that of CCSD(T) in the benzeneÀM model systems. All relativistic MP2 and CCSD(T) calculations were performed with ANORCC basis sets. To compare the relativistic and nonrelativistic CCSD(T) binding energies.Journal of Chemical Theory and Computation energy.34. All ﬁnal optimized geometries have been bonded on the coronene in (t) position.doi. Our ﬁrst aim was to identify a computational method that is less computationally demanding than CCSD(T) and uses a local basis set but yields good agreement with the CCSD(T) benchmark data.22À24. all of the electrons in benzene and coronene were correlated. Ag) complexes are comparatively small. accurate calculations on these two groups of complexes would provide insights into the nature of the binding of the three diﬀerent adatoms to carbon surfaces. while the M06-2X functional achieves the same objective by incorporating modiﬁed parameters into its exchangeÀcorrelation functional.33 in all wave function methods. silver. Another advantage of these basis sets is that they are available with various degrees of contraction. All benchmark CCSD(T) calculations on the benzeneÀM complexes were performed with the VTZP contraction. The DFT-D3 method models the eﬀects of dispersion forces using an additional empirical term that is proportional to RÀ6. Theory Comput. Figure also shows the charge distribution in the bonds of the free coronene molecule (black).37 both of which are suitable for calculating molecular electronic properties and the interaction energies of noncovalent complexes. showing the three potential sites for the adsorption of metal atoms. this method provides stabilization energies for various types of noncovalent complexes with chemical or even higher accuracy ((1 or (0.30 Because of the high computational demands of CCSD(T). Speciﬁcally. CALCULATIONS Benchmarking calculations on the benzeneÀM complexes were carried out at the spin-adapted CCSD(T) level with a restricted closed-/open-shell HartreeÀFock (HF) reference function. halogen bonding.31 were modeled using the scalar one-component DouglasÀKrollÀHess approximation32. Because the benzeneÀM (M = Pd. the analogous positions above the central benzenoid ring were considered (Figure 1). The (n À 1)p6 (n À 1)d10 shells of palladium and (n À 1)p6 (n À 1)d10 ns1 shells of silver and gold were correlated. Au. The metal atoms were modeled as being adsorbed at one of three diﬀerent positions: (t) a ‘top’ site directly above a C atom. The binding energy is deﬁned as the absolute value of the interaction energy and is 3744 dx. it is well-known that dispersion energy is an important component of the overall stabilization energy in various types of noncovalent complexes such as those held together by hydrogen bonding. they can be studied using even very accurate and computationally expensive wave function theory (WFT) methods based on the coupled cluster technique with iterative evaluation of the contributions of single and double electron excitations and perturbative evaluation of the contributions of triple excitations (CCSD(T)). Coronene molecule. 2011.org/10. and the coroneneÀ Au complex (red).
7. MP2..553 7.46. The structural parameters of benzene and graphene were relaxed by minimizing the forces acting on the atoms using a conjugate gradient algorithm.304481 60 α DK rel. The total energy was then calculated using the expression: Enl ¼ EDFT À EPBE À EPBE þ ðEPBE þ ELDA À Enl Þ tot tot c x x c c ð2Þ We refer to this method as PBE+vdW. i. slope. which was evaluated in VASP using one-electron x KohnÀSham orbitals.47 The GGA of PerdewÀBurkeÀErnzerhof (PBE)48 was used to parametrize the exchangeÀcorrelation functional. we replaced one-quarter of EPBE with the exact HartreeÀFock x exchange.990 7. EHF. 2011. DK Relativistic and Nonrelativistic Values of the IP. The resulting total energy is denoted as EE+vdW. without spinÀorbit coupling (except one test calculation for benzeneÀ Au complex.. The DFT-D3 calculations were performed using Turbomole 6. Pd (MP2) Pd (CCSD(T)) Pd (expt) Ag (MP2) Ag (CCSD(T)) Ag (expt) Au (MP2) Au (CCSD(T)) Au (expt) a EA (eV) DK rel. Because of its electron affinity. The EPBE terms are x written out explicitly to emphasize the point that the PBE exchange energy inside the parentheses could in principle be replaced by that calculated using some other semilocal formulation.880 1.781 8.48 who showed that this hybrid matches the LDA in value.1. This construction minimizes electrostatic interactions between repeated images. the revised PerdewÀBurkeÀErnzerhof (revPBE) was suggested in the original formulation of the vdW-DF method by Dion et al. The graphene sheet was modeled using a 4 Â 4 supercell.55 to describe the exchange energy.0.4658 2. were included by means of the vdW density functional (vdWDF)49 for PBE-optimized geometries.63 In this paper. Isolated Systems.108 7. 0.e. Au is a much stronger electron acceptor than Ag and Pd.44 Å. followed by Au and Pd.043 1.51.562157 1. We used the JuNoLo program to evaluate the vdW term.57623 9. we propose a diﬀerent approach. Long range vdW (dispersion) interactions. 3743–3755 3745 . and their geometries were assumed to be frozen in all subsequent WFT and DFT calculations.44 and the M06-2X calculations were performed using Gaussian 09.43 The DFT-D3/TPSS/def2-QZVP26 and M06-2X/lanl2dz27À29 methods were also used to evaluate the interaction energies of the studied complexes. Consequently. it was expected that charge-transfer stabilization would be most important in the gold complexes. these effects are much smaller in the other metals considered.0658 These calculations were been performed using the aug-cc-pVTZ and aug-cc-pVTZ-DK basis sets.372 8. and second derivative and is therefore readily embedded into the DFT scheme. nonrel.191 62 52. while the M06-2X method accounts for dispersion using a reparameterized exchangeÀcorrelation functional. Spin polarization was taken into account in all calculations.1. which are absent in standard DFT. The periodically repeating benzene molecules were separated by at least 8 Å of vacuum in the plane containing the benzene ring and 18 Å of vacuum in the perpendicular direction. and the shortest distance between metal atoms was 10 Å. 4.308664 36. The core of the vdW-DF method is a fully nonlocal expression for the correlation energy Enl. Chem. EA. All calculations were carried out using scalar relativistic approximation.22553 61 59 7. r 0 Þnðr 0 Þ ð1Þ Here.e.072 0.250 2. n(r) is the electron density obtained from a standard DFT calculation and the kernel Φ(r. The repeated sheets were separated from each other by 18 Å of vacuum.doi. Relativistic effects significantly increase the electron affinity and the ionization potential of the gold atom and decrease its dipole polarizability. and CCSD(T) energies were calculated using the MOLCAS 7. Benzene and coronene are electron donors. All calculated WFT interaction energies were corrected for the basis set superposition error (BSSE) using the counterpoise correction. with PBE electron densities serving as inputs. A Γ-centered 5 Â 5 Â 1 k-point mesh was found to provide converged total energies and was consequently used for Brillouin zone integration. Notice that EHF does not match the local density x exchange in the constant density limit and so one should not simply exchange EPBE for EHF. in the spirit of the hybrid screened exchange functionals.109 1.137 9.Journal of Chemical Theory and Computation therefore always positive.248 2.064 1.013 6. We chose to use the PBE exchange functional. and Dipole Polarizability (α) for Metal Atomsa IP (eV) DK rel.1. while the metal atoms are electron acceptors. The structures of benzene and coronene were optimized at the MP2/cc-pVTZ level.336956 7. which is discussed later in the text).279 1. with the exception of the M06-2X calculations on the coroneneÀM complexes.1021/ct200625h |J. The DK relativistic and nonrelativistic CCSD(T) and MP2 one-electron properties of all three metal atoms are presented in Table 1.54. Theory Comput.248 0.45 Plane-wave DFT calculations for an inﬁnite graphene surface were performed using the Vienna Ab initio Simulation Package (VASP) which makes use of the projector augmented wave (PAW) construction for the pseudopotential. WFT and DFT Calculations on Benzene(Coronene)ÀM Complexes. each supercell contained 32 carbon atoms. i. Ag has the greatest polarizability. The DFT-D3 method uses an empirical correction term to describe the dispersion energy. it was expected that the dispersion interaction would be strongest in the dx. 8.581 nonrel.49 and other exchange functionals have also been considered. 24. 4. The energy cutoﬀ for the plane-wave expansion of the eigenfunctions was set to 500 eV.615 7. making them applicable to large molecular systems. which takes the following form: c Z nl Ec ¼ dr 3 dr 03 nðrÞΦðr. for which the change in the geometry of the coronene induced by adatom adsorption was studied by full reoptimization of the complex.342 9. Both of the DFT techniques are substantially less computationally demanding than CCSD(T).2 program package.521 0. r0 ) is a function that depends on r À r0 and the magnitudes and gradients of the electron densities at the points r and r0 . since it was the functional used to calculate the input electron densities.50 The vdW-DF method uses standard semilocal GGA functionals ARTICLE Table 1.42 RHF/ROHF. Consequently.org/10. using the calculated CÀC bond length of 1.. A rationale for mixing one-quarter x x of EHF with the approximate local density exchange was provided x by Perdew et al. RESULTS AND DISCUSSION 4.
benzene(coronene)ÀAg complexes and would become progressively smaller in the corresponding Au and Pd species. 2. MP2.2 kcal/mol. both were more stable than that in which the gold atom occupied the ‘hollow’ site (h) above the center of the ring. respectively) are smaller than the corresponding values for the benzeneÀAu complexes by about 30% for (h) and 50% for the (t) and (b) positions. BenzeneÀM Complexes. respectively.2. The DK-MP2/ANO-RCCVDZP method yielded similar binding energies to CCSD(T) for all positions.5 Å larger in the Ag species than in their Au counterparts for the (b) and (t) positions. the DFT-D3 energies were in worse agreement with the benchmark data than those obtained with M06-2X.Journal of Chemical Theory and Computation ARTICLE Figure 2. MP2. Figure 4.doi. Relativistic WFT (BSSE corrected RHF/ROHF. and 1. MP2. the species generated by adsorption above the ‘hollow’ (h) was the most favorable but was only 25% more stable than the least favorable. As was the case with the Au species. (b). For the (t) and (b) positions. the equilibrium distances between the metal atom and the ring were more than 0. Relativistic WFT (BSSE corrected RHF/ROHF. and 3. 3743–3755 .3. DK-MP2/ANO-RCC-VDZP provided binding energies that mirrored the benchmark results fairly 3746 dx. CCSD(T)/ANO-RCC-VTZP) binding energies for the (t).1. The benchmark binding energies for the (h).org/10. (b) and (t) positions (2. Figures 5À7) overestimated the binding energies. but MP2 calculations using the larger VTDZP and VTZP basis sets (cf. Figures 2À10 and Table 2 show the characteristics of all complexes investigated in this work. Figure 3. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀAg complex with the metal adsorbed at the (t) position. Relativistic WFT (BSSE corrected RHF/ROHF. The M06-2X results were also qualitatively inconsistent with the CCSD(T) benchmarks in that they predict the complex with the gold atom in the (h) site to be the most stable. which was generated by adsorption over a carbon atom (t). 2011. 4. Chem. Relativistic WFT (BSSE corrected RHF/ROHF. Theory Comput. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀAg complex with the metal adsorbed at the (b) position. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀAu complex with the metal adsorbed at the (t) position. MP2.1.2.0. The benzeneÀAu complex with the Au atom positioned over a carbon atom (t) was energetically similar but slightly more stable than that in which the metal atom was positioned over a CÀC bond (b). but M06-2X strongly overestimates the stabilization for the (h) position. 4. Figure 5. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀAg complex with the metal adsorbed at the (h) position. Similar trends were observed with all of the computational methods examined. Additionally. The situation changes somewhat on switching from Au to Ag. the calculated CCSD(T) energies for all three Ag adsorption positions were similar. The same relative order was given by all methods investigated. Speciﬁcally. The benchmark (DK rel.1021/ct200625h |J. M06-2X and DFT-D3 systematically overestimated the binding energies by 40À100%. 7.9 kcal/mol. and (h) positions were 4.
both DFT-D3 and M06-2X strongly overestimated the stabilization for all three positions. 3743–3755 . closely. (t). MP2. 18. Relativistic WFT (BSSE corrected RHF/ROHF. and (h) positions were 19. MP2. Chem. are preferred to (h). The (b) and (t) positions. Of the computational methods tested. The benchmark binding energies for the (b). whereas the Pd binding energies encroach on ranges more commonly associated with covalent bonds. As in both of the preceding cases. Figures 8À10).doi. the interaction between the metal and the arene is partially covalent. These results clearly demonstrate that the interactions of Pd atoms with benzene diﬀer signiﬁcantly from those of Au and Ag atoms.Journal of Chemical Theory and Computation ARTICLE Figure 6. Figure 8. The binding energies of Pd are much higher than those of Au and Ag.org/10. although the (t) and (b) sites are slightly underbound. Figures 2À4). These higher binding energies were associated with considerably shorter internuclear distances between the Pd and C atoms than was the case in the Au and Ag complexes. DK-MP2/ANO-RCC-VDZP was the method whose energies were in best agreement with the benchmark values.1021/ct200625h |J. and the corresponding internuclear distances are much shorter. respectively. DK-MP2/ANO-RCC-VDZP provided the best 3747 dx. Figure 7. with the other MP2 methods once again signiﬁcantly overestimating the binding energies for all three positions (cf. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀPd complex with the metal adsorbed at the (b) position. The binding energies for Pd were an order of magnitude higher. All three binding sites yield broadly similar binding energies for the adsorption of Au and Ag. Theory Comput.7. Neither of the DFT methods examined provided reliable binding energies. suggesting that in this case. but the (b) and (t) positions are clearly favored over the (h) site in the case of Pd adsorption. MP2. DFT-D3 also signiﬁcantly overestimates the binding energies (by 35% or more). Figure 9. but M06-2X provides binding energies that agree quite well with the benchmark values. which is similar to the length of covalent CÀPd bonds. which are similar in energy. 2011. The Au and Ag binding energies are in the range typically associated with noncovalent interactions. adsorption of Pd in the (t) position resulted in an internuclear distance of only 2. 7. and 12.1 Å. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀPd complex with the metal adsorbed at the (t) position. MP2. The low binding energies for Au and Ag are indicative of noncovalent binding.8 kcal/mol. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀAu complex with the metal adsorbed at the (b) position. Relativistic WFT (BSSE-corrected RHF/ROHF. Relativistic WFT (BSSE-corrected RHF/ROHF. while MP2 with triple-ζ basis set overestimated the binding energies (cf. Relativistic WFT (BSSE corrected RHF/ROHF.8. and all methods examined yielded the same order of energies. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀAu complex with the metal adsorbed at the (h) position.
such comparisons indicate that the stabilization of the benzeneÀ Ag complex is almost entirely due to the London dispersion energy.1 kcal/ mol for the (t). The nature of the metalÀarene binding in all three complexes differs. 4. agreement with the benchmark CCSD(T) energies and can thus reasonably be expected to provide accurate results when applied to larger model systems. as indicated by the differences in the binding energies calculated using different levels of theory. 3.7. Indeed.0.4 kcal/mol. and CCSD(T)) and DFT (DFT-D3 and M06-2X) potential energy curves for the benzeneÀPd complex with the metal adsorbed at the (h) position. Compared to Ag.5 Å) distances between the benzene ring and the metal atom in the gold complexes. there is relatively little charge transfer from benzene to the Ag atom. i. For example. The lower polarizability of Au implies that dispersion interactions will be less important in its complexes.64À66 3748 dx. Mulliken population analyses indicated that the magnitude of the charge transfer in the benzeneÀAu complexes was approximately twice that in the benzeneÀAg complexes. has been presented in previous works.. (b). However. and (h) positions of the benzeneÀAg complex.3. and 2. relativistic effects are only important in the Au complexes. 5. 7.9 kcal/mol. relativistic eﬀects change the nature of binding in the benzeneÀAu complexes.1. It is worth noting that for Au+ and Ag+ ionÀarene complexes. which means that there is very little overlap of the orbitals of the metal and the arene. MP2 and DFT-D3 appear to be superior to M06-2X. Because of the low electron aﬃnity of Ag and the large separation of the metal atom and the arene. Our results strongly contradict the ﬁndings of previous studies in which DFT methods were used. However. while benzene is an electron donor. respectively. here. a diﬀerent picture emerges. 3743–3755 . giving a benchmark Pd:Au:Ag ratio of 9:2:1. and the higher electron aﬃnity is likely to increase the importance of charge-transfer interactions. 2011. Chem. One of the most reliable ways of obtaining information on the nature of the bonding is to compare the electronic structure of the bound species to that of the isolated atom. and (h) positions. it is still rather computationally demanding. and 2.7. the formation of new bonding and antibonding orbitals from the doubly occupied 5d0 orbital of Au and the benzene pz orbitals was observed.6 vs 1. and 3.1021/ct200625h |J. DFT/BPW91/ TZP calculations52 on benzeneÀM (M = Ag and Au) complexes provided binding energies for the (h). The CCSD(T) benchmark calculations indicate that the binding energy of Pd to benzene is nine times greater than that of Ag and that of Au is two times greater. respectively.3. MP2. the corresponding nonrelativistic binding energies are significantly smaller (2.1. determined using the MP2/ANO-RCC-VDZP method) revealed that Ag carries a negative charge of À0. these in turn affect the benzeneÀAu binding energies. respectively. we also determined the relativistic vs nonrelativistic binding energies for the (t).org/10. which are significantly reduced by the omission of relativistic effects.11 and À0. Au is signiﬁcantly less polarizable and has a higher electron aﬃnity (Table 1). Of the faster DFT techniques. while the MP2 method is less expensive than CCSD(T). as discussed below.5 kcal/mol. which highlights the importance of charge transfer. 2. Relativistic WFT (BSSE-corrected RHF/ROHF. i. when considering the relative magnitudes of the binding energies for the three elements. This indicates that the stabilization of all benzeneÀM complexes originates from correlation effects. This is consistent with the high polarizability of Ag and the relatively large distance between the Ag nucleus and the benzene ring.05 e in all of the structures examined. It should be noted that better agreement for double-ζ basis set (than for triple-ζ basis set) arises from compensation of errors.0. In the case of Ag. but the M06-2X results (3:1:1) strongly disfavor Pd. (b) and (t) positions of 5. The omission of the correlation energy causes the binding energies to be strongly underestimated. since it gave absolute binding energies that better matched the benchmark values. This enhanced charge transfer is attributable to relativistic eﬀects because their omission halves the electron aﬃnity of the gold atom (Table 1).9. and 3. For the sake of comparison. respectively. Figures 2À10 show that the HF energy curves for all atoms and all adsorption positions are universally repulsive. The calculated ionization potential and electron affinity of Au change dramatically when relativistic effects are included. Nature of the Bonding in BenzeneÀM Complexes. the bonding becomes mainly electrostatic. and 5. While charge transfer plays a key role for gold atoms in the (b) and (t) positions. M06-2X is preferable to DFT-D3. 2. while correlation effects are important in the binding of all three of the investigated metals.doi.1. (b).39À41 The dramatic increase in stability for complexes of Au is due to relativistic eﬀects. and 5.7. the dispersion energy provides a larger contribution to the binding energy.3. the orbitals of the complex are almost identical to those of its separated constituents. for Au.1. it acts as an electron acceptor. Speciﬁcally. for comparing the binding energies of diﬀerent metals. The stabilization of the benzeneÀAu complex by charge-transfer interactions is demonstrated by the fact that their binding energies are more than twice as large as those for the corresponding benzeneÀAg complexes and by the considerably shorter (by more than 0. and binding energies are almost an order of magnitude higher. no binding occurs. These ﬁndings are clearly incompatible with the benchmark data reported herein. Thus. Theory Comput. which were 2..3 kcal/mol. with the Au atom carrying negative charges of À0. The relativistic CCSD(T)/Pol-DK binding energies are 3. 2. respectively).e.12 e for the (t) and (b) positions. respectively.Journal of Chemical Theory and Computation ARTICLE Figure 10. since they suggest that the binding energies for Au are smaller than those for Ag. and 2. it is less pronounced in the (h) position. 5. However. This is probably due to the neglect of relativistic eﬀects at the DFT/BPW91/TZP level of theory.2. These shorter distances reﬂect a greater overlap between the orbitals of the two systems. for Ag. Analysis of the charge transfer in the Ag complexes (Mulliken charges. The MP2 (10:2:1) and DFT-D3 ratios (7:2:1) matched the benchmark values fairly closely. This conclusion is supported by the calculated one-electron properties shown in Table 1. This interaction model. which increase the metal’s electron aﬃnity and thus favor the transfer of charge from the ligand to the metal.e.
05 PBE+vdW À2.74 À4.6 3. A dative bond of this kind would account for the high binding energies observed for the benzeneÀPd complex.09 À3.11 À2.07 À6.9 3.6 2.69 À8.2 2.41 À7. Pd) Complexes Calculated at the Various DFT with Dispersion Correction and DK Relativistic and Nonrelativistic WFT Levels benzeneÀPd (t) (b) (h) (t) benzeneÀAg (b) (h) (t) benzeneÀAu (b) (h) DFT-D3/TPSS/def2-QZVP ΔE R ΔE R ΔE R ΔE R ΔE R ΔE R ΔE R ΔE R ΔE R ΔE R a À28.6 3.1 3. CCSD(T)/Pol EE + vdW + spinÀorbit coupling (soc) À5.29 À1.8 2.4 3.41 À2.5 3.45 À12.18 À29.2 2.3 2.12 À1.2 3.1 2.34 À2.1 3.29 À1.73 À2.org/10.0 3.3 2.6 3. In the ground state.08 À30.83 À3.2 3.Journal of Chemical Theory and Computation ARTICLE Table 2. The metalÀligand bonding in the benzeneÀPd complexes diﬀers signiﬁcantly from that in the Ag and Au complexes due to the diﬀerent electronic structure of Pd.4 3. and the ﬁrst virtual orbital is the 5s.97 À27.7 2.8 2.7 3.2 2.37 À5.0 2. CCSD(T)/Pol-DK nonrel.23 À2.5 3.09 À3.2 3.19 À1.17 À2.1a 2.2 2.32 À4.46 À5.10 À2.17 EE+vdW À2. 7.6 3.5 2.0 3.6 3.2 2.5 2.1.9 2.4 2.4 3.07 À15.7 3.24 À2.6 3.83 À12. CCSD(T)/ANO-RCC-VTZP DK rel. DFT-D3/def2-QZVP. Therefore. Detailed analyses indicated a signiﬁcant loss of electron density from the Pd valence d-orbitals (relative to the situation in the free atom) and a simultaneous signiﬁcant increase in electron density in the virtual 5s orbital.01 À13.2 2.6 2.9 2.36 À18.10 À1.51 À5. leading to an increase in the electron density of the benzene ring and a decrease in that of the Pd atom.01 À19.7 2.3 2.67 À3.3 1. binding energies calculated using the MP2 method were used as reference values for the coronene complex.5 2.9 3.17 À17. since this level of theory provided absolute and relative binding energies that were reasonably close to the benchmark CCSD(T) values for all of the benzeneÀmetal 3749 dx. Chem. The size of the coronene complexes meant that it would have been impractical to perform CCSD(T) calculations on them to obtain benchmark binding energies.7 3. and all its carbon atoms bind exclusively to other carbon atoms.10 À21.7 3.0 2.37 À19.79 À4.79 À2.10 À15.6 2.1 2. indicating that it was acting as an electron donor.01 À2. 3743–3755 . as discussed in the preceding section. the Pd atom carried a small positive charge. Au. and Pd atoms to coronene using the MP2/ANO-RCC-VDZP.3 3. We investigated the binding of Ag.41 À4.16 À10. In all of the benzeneÀPd complexes examined in this work. Au.3 3. and M06-2X/lanl2dz methods. Extrapolated Interaction Energies ΔE [kcal/mol] and Optimal Bond Lengths R (in terms of the shortest distance between the metal atom and the benzene plane) [Å] for BenzeneÀM (M = Ag.8 2.01 À1.3 3.56 À5. 4.0 3.09 À1.doi.97 À12.1 3.04 À À À À À19. MP2/ANO-RCC-VDZP DK rel.34 À3.33 À2.05 À18.39 À4.7 kcal/mol.22 M06-2X/lanl2dz DK rel. the valence d-orbitals of palladium are fully occupied. Coronene is a more complex model of graphene than benzene.64 À7.29 GGA PBE À1. The central aromatic ring of coronene (Figure 1) is surrounded only by other aromatic rings.7 3.18 À18.5 3. This is consistent with the formation of a socalled dative bond. CoroneneÀX Complexes.0 3.7 2.11 À À À À À27.2 2. 2011.9 3.8 2.63 3.9 3.1021/ct200625h |J.1 2.07 À21.5 1.15 À22.6 3.4.18 À2.3 2.39 À2.18 À2. MP2/ANO-RCC-VTZP DK rel.7 2.99 À4.19 À2.5 3.10 À4.0 3.36 À6.3 3.21 À3.1 1.10 À3.13 À À À À À26.44 À5.70 À5.3 3.97 À4.28 À5.11 À28. Theory Comput. This polar complex is then stabilized by back donation of charge from the carbon atom to the valence 5s orbital of Pd.3 2.07 À4.17 À6.24 À2.1 2.63 À3.3 3. in which charge is transferred from Pd to benzene.3 2.16 À3.1 2.66 À8.5 2.8 2.39 À1.22 À3.
12 À14. DFT-D3.7 3.0 ∼3.99 0. (b). the relative strength of binding to Pd. MP2. the diﬀerence between the binding energies for Pd and Ag was smaller than that observed with the corresponding benzene complexes.075 À13.80 À7. In the case of adsorption of an Ag adatom. the diﬀerences between the distances in the benzene and coronene complexes were small.063 coroneneÀAg (b) (h) (t) coroneneÀAu (b) (h) complexes discussed in the preceding section. All three methods considered (i.12 À0. M06-2X.e.8 2. While the extent of charge transfer in the silver complexes of benzene and coronene was very similar.007 À7. However.09 0. As with the benzene complexes. However. At the MP2 level. Silver atoms bind exclusively via dispersion forces.068 À7.47 0. Au. and M06-2X binding energies and equilibrium distances for all of the coronene complexes considered are summarized in Table 3..052 À4.19 À0. No signiﬁcant diﬀerence in distance was observed in the Pd complexes. In all cases. the magnitude of the charge transfer in the coroneneÀAu complexes was approximately 40% smaller than that in the corresponding benzene complexes. the internuclear distances between the metal and the plane containing the arene increased on going from benzene to coronene. but the overlap population of the AuÀC bond remains negative (À0.001).325. The MP2 charges.7 1.051 À6.21 À7. and M062X) indicate that the adsorption of Pd is signiﬁcantly more favorable than that of Au or Ag.Journal of Chemical Theory and Computation ARTICLE Table 3.1021/ct200625h |J.09 À4. The situation with the gold complexes is more complicated.06 À0. however. it was found that the binding energies for Au and Ag increased on going from benzene to coronene. but those for the Ag complex were overestimated by about 60%. 2011.06 À0.6 1. However. were greater than the M06-2X charges and can be compared to those calculated for the benzene complexes.12 À0. Figure 1 shows the (t). although binding in the (h) position was slightly stronger in the coronene complex than in the corresponding benzene species. and Ag remained as it had been in the case of benzene. 3750 dx.2 3. This is the cause of the greater carbonÀAg distances in coronene complexes of silver. and so the distances between the Au atom and the plane containing the arene are somewhat greater in the coronene complexes. and 0. 2:1:1).067 À3.325. although the diﬀerence is relatively modest.17 À0.051 À26. the exchange repulsion is greater in the coronene complexes of Au than in the benzene species.13 À0. 7. DFT-D3.9 ∼3. DFT-D3.82 À0. Both the DFT-D3 and M06-2X calculations exhibited trends similar to those observed in the MP2 data. 4:2:1. For the Au complexes.028 À7.45 0. 0.052 DFT-D3 À5.009 À6.1 2. Chem. As with the Ag complexes. and (h) positions for adsorption on coronene and also the M06-2X overlap populations in the CÀC bonds that are aﬀected by adsorption.3 2.032 À24. The M06-2X method was used to optimize the geometries of the coroneneÀM complexes and to estimate the changes in the electronic structure of the coronene following adatom adsorption.doi.09 À0. while the polarizability of coronene is greater than that of benzene. but the extent to which this is the case depends on the method used (MP2.045 À26. This is not the case in the corresponding Au complexes. a “covalent” bond is formed between the carbon atoms and Pd by the overlap of the d-orbitals of Pd with the π orbitals of the coronene.84 À6. there is no signiﬁcant change in the overlap populations relative to those in the isolated coronene. It is apparent that the binding energies for the coronene complexes diﬀer from their benzene counterparts.1 ∼3.0 2. which were used as reference values. because both the dispersion energy and the charge transfer are important in their stabilization.3 2.027 À7. The DFT-D3 interaction energies for the gold complexes were very similar close to those obtained at the MP2 level. DK rel.9 2.7 2. and the relative stabilities of all of the coroneneÀmetal complexes considered were well reproduced. Both gold and silver atoms in the coronene complexes carry partial negative charges.3 3.370).92 À0. 4:1:1.08 À14.067 À6. and M06-2X Extrapolated Interaction Energies ΔE [kcal/mol] and Metal Atom Charges [e] for CoroneneÀM (M = Ag.0 3.3 2.46 0.2 3.010 À6.16 M06-2X À6.org/10. It appears that the nature of the metalÀarene bond in the coroneneÀPd complexes is very similar to that in the benzeneÀPd complexes. 3743–3755 . going from benzene to coronene reduced the binding energy of Pd by around 10%. DFT-D3. in which all the CÀC bonds in coronene are weakened relative to those in the isolated molecule (having electron populations of 0.7 3.0 2.8 3. the DFT-D3 binding energies for the Ag and Pd complexes exceeded the MP2 values by 50% or more. this is outweighed by the fact that the coronene complexes have a greater number of carbon atoms and therefore experience more exchange repulsion than their benzene counterparts.9 2.014).7 2.073 À17.3 3. by around 50% in the case of Au and around 100% in the case of Ag. it is possible to obtain insights into the bonding and charge transfer in coroneneÀmetal complexes by analyzing the Mulliken charges on the adatoms. indicating that both function as electron acceptors. the corresponding internuclear distances decreased.0 3. Pd) Complexes with an Optimized Bond Length R [Å] coroneneÀPd (t) (b) (h) (t) MP2 ΔE R charge ΔE R ΔE R charge À17.11 0. 9 2. and the total overlap between Ag and the nearest C is also negligible (À0. for the Ag complexes. The M06-2X binding energies for the Pd and Au complexes agreed well with the MP2 values.99 À12. MP2.027 À5. Conversely. Theory Comput.0 3. as did the relative binding energies for adsorption at diﬀerent positions around the ring.12 À0.83 À0. The MP2. Au. in both cases.14 À6.
BenzeneÀM Complexes. Figures 11À13 and Table 2 show the binding energies calculated using the plane-wave approach. and (h) positions are 5. The overlap populations between the Pd and C atoms are comparable to those between carbon atoms in the vicinity of the adsorption site. Compared to the CCSD(T) benchmark results. whereas Pd binds covalently. and (h) positions. Figure 12. Periodic plane-wave DFT/PBE. The CÀC bonds in coronene are weakened due to their relatively strong interaction with the Au adatom. Chem. which is also used in studies of adsorption on graphene. which determines the nonlocal vdW contribution (see eq 1). and DFT/EE+vdW potential curves for the benzeneÀAu complex with the metal adsorbed at the (t). overestimates the binding energy by more than 100% in all cases examined (data not shown) and yields unreasonably short bond distances as well. (b). Periodic plane-wave DFT/PBE. The inclusion of dispersion forces affords greatly improved agreement with the benchmark values. occurring primarily via dispersion forces. (b). the PBE+vdW equilibrium energies and distances are higher than those given by the PBE calculation. i. 7.1.8. and (h) positions. 3751 dx. the (t) position is preferred to the (b) position. but the calculated energetic diﬀerences are reduced when the nonlocal vdW term is incorporated into the calculations. 4. These numbers clearly show that the binding of Ag to coronene (and to some extent. demonstrating that the adsorption of Pd signiﬁcantly weakens the covalent CÀC bonds in the vicinity of the site of adsorption and results in the formation of a partly covalent bond between the Pd and C atoms.7 kcal/mol.. 2011. On examining the PBE+vdW energy curves. As suggested by the WFT methods.1021/ct200625h |J.2.214 and 0. This means that both the values of binding energies and the diﬀerences between the binding energies for the (t). The binding energy for Au in the (t) position as calculated using the EE+ vdW+soc method is 5. Periodic Plane-Wave DFT Calculations. Even more dramatic changes occur upon the adsorption of Pd. Inspection of the interaction energy curves in Figure 12 indicates that the vdW term is actually repulsive.4 kcal/mol. although the binding energies for these two spots are very similar and are both signiﬁcantly greater than that for the hollow (h) position. DFT/PBE+vdW. DFT/PBE+vdW. The benzeneÀAu complex has a total spin moment of 1 μB due to the single valence electron of the Au atom.e. and (h) positions are within 1 kcal of the benchmark CCSD(T) values. The main differences between the investigated elements can be seen even in the results of the simple PBE/GGA calculations. 0. It should be noted that the LDA approximation. whereas the benzeneÀAg complex is underbound. The inclusion of one-quarter of exact exchange in the calculation further reduces the binding energies and yields the best agreement with the benchmark CCSD(T) calculations. as discussed in more detail below. also that of Au) is noncovalent. 4. and (h) positions. It was found that soc has a slight eﬀect on the total PBE energy but has little impact on the charge density distribution within the complex. and DFT/EE+vdW potential curves for the benzeneÀPd complex with the metal adsorbed at the (t). The EE+vdW binding energies for the (t). The PdÀC bond is signiﬁcantly populated (0.214. we tested the inﬂuence of spinÀorbit coupling (soc) on the interaction energy for the (t) position. (b). respectively. the benzeneÀPd and ÀAu complexes are significantly overbound. Periodic plane-wave DFT/PBE. and the overlap populations of the CÀC bonds are signiﬁcantly reduced (0.243) relative to those in the free coronene. DFT/PBE+vdW. 3743–3755 . The relative order of energies is the same for all methods investigated. (b). and DFT/EE + vdW potential curves for the benzeneÀAg complex with the metal adsorbed at the (t). Theory Comput. 4.2.doi.1.org/10.154). The spin moment does not change substantially as a function of the distance between the Au atom and the benzene ring. (b). and 3. Figure 13. indicating that there is negligible charge transfer between the Au atom and the C atoms of the benzene ring. As gold is known to display signiﬁcant relativistic eﬀects.Journal of Chemical Theory and Computation ARTICLE Figure 11. although this method is rather unsatisfactory in quantitative terms. it is apparent that this disagreement is primarily due to the neglect of dispersion forces.
and (h) positions. the DFT binding energies were slightly lower than the reference values). and (h) positions.3 kcal/mol. Using PBE alone. and (h) positions were thus reduced to 17.e. the calculated binding energies for the (t). and 2. In contrast to the situation with the Ag complex. 7..5. Here. giving binding energies of 21. the geometry of the graphene was allowed to 3752 dx. 18. respectively.e.1021/ct200625h |J. Ag. Periodic plane-wave DFT/PBE and DFT/PBE+vdW potential curves for the grapheneÀAg complex with the metal adsorbed at the (t). Periodic plane-wave DFT/PBE. 27. and (h) positions. these binding energies are slightly greater than the benchmark values. the kernel Φ(r. identical binding energies of 2. respectively. and Au atoms on graphene have been published very recently.5 kcal/mol. Theory Comput.2. These values are signiﬁcantly higher than the benchmark CCSD(T) values.0 kcal/mol.53 Our calculations differ from those reported in that publication. The potential curves for the benzeneÀAg complex are shown in Figure 11 and clearly illustrate the importance of the vdW dispersion term. and DFT/EE+vdW potential curves for the grapheneÀAu complex with the metal adsorbed at the (t). By including the vdW term. the covalent interaction between the metal and the arene means the binding energy is large. while the binding energy of 2. which is consistent with a negligible electrostatic interaction between the Ag atom and the carbon atoms of the benzene ring. Obviously.53 Figures 14À16 and Table 4 summarize the calculated interaction energies for the grapheneÀM complexes. and 13.0 kcal/mol for the (t). which was found to be the preferred site in the CCSD(T) calculations. Incorporating a fraction of the exact exchange energy further reduced the calculated binding energy. especially for the hollow position. it is predicted to be 26. they were further improved upon by adding a fraction of the exact exchange. On examining the binding energy of the grapheneÀAu complex. While this may be surprising at ﬁrst sight. however. It should be noted that such repulsive corrections are impossible in the various empirical DFT+D2 (or D3)26 approaches. While these values are already in very good agreement with the benchmark values.7. Figure 15. GrapheneÀM Complexes.Journal of Chemical Theory and Computation ARTICLE Figure 14.49 Thus. DFT/PBE+vdW. the inclusion of the vdW term substantially reduces the predicted binding energies. (b). this made the hollow (h) position the preferred site for adsorption. the PBE+vdW calculation corrects the overbinding predicted by PBE alone. The binding energy calculated using the GGA/PBE approximation alone is very weak (∼1.6 kcal/mol). it should be noted that PBE+vdW interaction energies for Cu. (b).8.3. and (ii) our calculations used carbon atoms that were fixed in place (i. A diﬀerent situation obtains for the benzeneÀPd complex.6 kcal/mol. which stands in stark contrast to the situation in the benzeneÀAu complex. The role of geometrical relaxation of the graphene surface is thoroughly discussed by Amft et al. The EE+vdW binding energies for the (t). (b). We therefore used this method to obtain DFT benchmark energies for the interactions of metal atoms with a graphene sheet. respectively. as was the case for the benzeneÀAu complex. and 19. The main advantage of calculations that use periodic plane-wave basis sets is that they can be applied to the study of extended systems. The spin moment remains constant at 1 μB for all internuclear distances. they provide a nonzero and positive (in terms of the deﬁnition of binding energy used in this paper) contribution to the binding energy. Chem. as predicted by CCSD(T). In this context. Our studies on benzeneÀM complexes demonstrated that the PBE functional can yield binding energies that agree very well with reference CCSD(T) values when augmented with a nonlocal vdW correction and onequarter of the exact exchange (EE+vdW). r0 ) used to describe the interactions between electron densities (eq 1) becomes repulsive at small distances. using the PBE method. 2. (b).3. 21. The EE+vdW binding energies for the (t).2.2 kcal/mol for the most favorable (t) position reported in previous works.. 2011. and 1. it is apparent the bonding is dominated by vdW term.13 The diﬀerence in the GGA binding energies can be attributed to the fact that in those previous works.3. because D2 and D3 terms are always attractive. and 10. no geometrical relaxation of the graphene sheet was allowed) in order to facilitate comparisons of the bonding of metals adsorbed on graphene with that in benzene and coronene complexes. respectively. 1. since (i) we included the contribution of the exact HF exchange in order to obtain more reliable interaction energies. 3743–3755 . (b). (b) and (h) positions were 2.org/10. demonstrating that methods for improving on the treatment of long-range correlation eﬀects (the vdW term) should be used in conjunction with methods that treat midrange exchange properly. which is consistent with the GGA values of 2.3. and (h) positions were 1.6 kcal/mol for the hollow position (h) was slightly lower. As before.4.12. these values are unrealistically low.7 kcal/mol were obtained for the (t) and (b) positions. the inclusion of one-quarter of the exact exchange yielded DFT results that were very close to the benchmark value (although in this case. i.doi. As was the case for the benzeneÀAu complex.
the incorporation of a fraction of the exact exchange energy slightly reduced the calculated binding energies. The EE+vdW binding energies for the (t). and (h) positions. (b).9. and 15. respectively.8.2 R 2.07 3. respectively. was optimized).9. Chem.07. and 6. and the calculated binding energies for the adsorption of gold atoms on graphene are somewhat lower than those for the coroneneÀAu complex.67 The incorporation of exact exchange reduces the distances between the metal atom and the graphene sheet. These results clearly show that the LDA is inadequate for modeling the interactions of graphene with gold atoms or surfaces. Au.49 the authors suggested to replace the PBE exchange energy by its revPBE counterpart to obtain more accurate binding energies. for the grapheneÀM (M = Pd.35 3. 10. and (h) positions in grapheneÀAu complex. Finally.6 À1.4. and 5. respectively.42 EE+vdW ΔE À17. the energetic diﬀerences between the three adsorption sites examined were negligible.1. In this case. Pd) Complexes with an Optimized Bond Length R [Å] grapheneÀPd (t) (b) (h) (t) PBE ΔE À22. 3743–3755 .9. 18.0 kcal/mol. The adsorption of Pd at the (b) position results in the formation of a partial covalent bond with neighboring carbon atoms. The PBE+vdW method gives rather uniform binding energies of 6. respectively.9 À12. and DFT/EE+vdW potential curves for the grapheneÀPd complex with the metal adsorbed at the (t)..07 2. whereas the MP2 results for coronene predict that the above-bond position (b) is the most stable. Periodic plane-wave DFT/PBE. the pure GGA predicts only very weak bonding of ∼0.6. Adsorbed silver atoms can thus easily slide over a graphene surface.3. The EE+vdW binding energies for the (t). which are 3.33 grapheneÀAg (b) (h) (t) grapheneÀAu (b) (h) relax (i.6 À0. and (h) positions were 17. discussed in the previous paragraph. and (h) positions. Table 4.3 À19. The PBE+vdW energies are 20.6 kcal/mol and agree very well with those for the coroneneÀPd complex. The same applies also for grapheneÀPd complexes (see the following paragraph). 12. as was demonstrated by means of an overlap population analysis in the preceding section. For the sake of completeness.3 À4. respectively.3 kcal/mol for the (t).4 À6. and 3.18 3.6 À0. are approximately two-times lower than the corresponding benchmark energies for coroneneÀAu complexes. These values and the diﬀerences between them are in good agreement with the MP2 values calculated for the coroneneÀAu complex.4 kcal/mol. examination of the energy proﬁles for the grapheneÀ Ag complex reveals that silver atoms bind a little more strongly to graphene than to benzene. On the other hand. LDA calculations gave binding energies of 12. The interaction energies for the top (t) and bond (b) positions are slightly lowered in comparison with benzene. respectively (data not shown).0 À4.35 3. The elongation of bonding distances with respect to benzene complex is consistent with the elongation of the metalÀcarbon bond observed in the coroneneÀAu complex. The small diﬀerences of the electronic structure between graphene and coronene.72 3.2 À6. DFT/PBE+vdW.14 3.2 R 2. indicating unphysical overbinding by the LDA method.35 3. Au) complexes.8.35 3.14.18 3.73 3.33 Å for the (t).4 À15.63 PBE+vdW ΔE À20. and 12. 6.11 2.30 3.8 À21.1021/ct200625h |J. 15.6 À1. The energies of the grapheneÀPd complex shown in Figure 16 continue the trend observed on going from benzene to coronene.20 2.5. which would appear to support the hypothesis that gold binds only very weakly to graphene surfaces. and 8.doi.0 À0.22 2. (b). and 3.21 2. 3.2 kcal/mol for the (t).2 kcal/mol.5 Å.Journal of Chemical Theory and Computation ARTICLE Figure 16. These energies are twice as high as the benchmark values calculated for the coroneneÀAu complex.17 2. 5. It should also be noted that our test calculations using the B3LYP hybrid functional (data not shown) predicted no binding at all for gold in the (t) position on graphene.41 3.org/10. and (h) positions. (b). respectively.72 3. The revPBE+vdW binding energies of 3.39 3.39 3. Because of the interaction between the silver atom and the graphene sheet is dominated by dispersion forces.3 À4.4. This is largely due to the underestimation of the charge-transfer contribution in the pure PBE GGA calculation.3.3 À4.6.2 À5. whereas the energy of the hollow (h) site is higher. the barriers to their diﬀusion 3753 dx. which is becoming more and more popular.3 À6. and (h) positions were 12. (b).2.3 À4. the electronic structures of coronene and graphite are certainly not suﬃciently dissimilar to account for this discrepancy.5 À5. It should be noted that the preferred (t) position of gold on graphene surface agrees with recent experimental data. 3. (b).e. at large equilibrium distances of around 3. (b). 7. primarily because of stronger vdW (dispersion) interactions. and 10. The only diﬀerence is that the (t) position is predicted to be the most stable for graphene.9 kcal/mol for the (t). The distance between the metal atom and the plane containing the arene increases consistently on going from benzene to coronene to graphene. which is highlighted when one compares the results for the graphene and benzene complexes.1 À18. and (h) positions. imply that the revPBE+vdW binding energies are signiﬁcantly underestimated and that the revPBE+vdW method cannot be recommended for such type of calculations. In the original paper by Dion et al. Theory Comput.6 À1.6 À5. We tested this scheme. (b). The carbonÀmetal bonding distances are longer than those in the benzeneÀAu complex because of the greater exchange repulsion between the Au atom and the carbon atoms in the graphene sheet.54 3.6 kcal/mol. As was the case with the benzeneÀM complexes.02 3.6 À4. (b).36 3.6 R 2. and (h) positions were 5. 2011. Interaction Energies ΔE [kcal/mol] for GrapheneÀM (M = Ag.3 À15. the revPBE+vdW binding energies for the (t).
M. B. J. wave function-based CCSD(T) and MP2 with a local basis set and the density functional-based EE+vdW method. R.2 kcal/mol for the (t).. G.3. Nano Res. L. K.. Au. H. B. and 4. Chem. X. M€lhaupt. 7. they are repulsive and serve to correct the overbinding predicted by the PBE method. J. M. while that for EE+vdW is 9:3:2.00/03.7. Shi. A. J. Pd) indicate that Pd is bound most strongly.05/2. it forms a (partial) covalent bond with the arene. Nano Lett. respectively.3. these two methods both yield similar ratios for the binding energy of Pd relative to Au and Ag. B. The values obtained for the benzene complexes agree with the benchmark CCSD(T) energies to within chemical accuracy *E-mail: michal... W. the inclusion of an exact exchange correction has little impact on the calculated interaction energies. 8262.. Phys. Steurer. with a plane-wave basis set) indicates that the calculated graphene binding energies reported in this paper can be used as reliable benchmark values and that EE+vdW is a useful and practical method for accurate computational studies of extended systems. changing them by less than 0. T. 7. On the other hand.. Zhang. S. in Pd complexes. Ag) complexes were 19. F. CONCLUSIONS WFT and DFT calculations performed for the benzeneÀM and coroneneÀM complexes (M = Ag. (4) Li. awarded to P. While silver binds primarily via dispersion forces in both cases. J. 114. This implies that using empirical corrections to simulate dispersion interactions can be counterproductive when studying grapheneÀmetal systems.. S. B. and (h) positions. (2) Baby. R. ARTICLE (∼1 kcal/mol). Qi. Theory Comput. Aravind. and 2. L. 71..7. Sens.cz. since corrections of this kind will always favor binding. W. B. Ji.. Wang. 3833... Avouris.53 The interaction energies for the grapheneÀAg complex calculated using the PBE+vdW method were 4.4. Rakhi. J. the binding of gold is primarily attributable to charge-transfer interactions between the electron donor (benzene or coronene) and the electron acceptor (the gold atom). but surprisingly. 2011. Au.2. Ji. 4. pavel.. 3743–3755 .1 kcal/mol for all positions. G. On comparing the results for coronene and graphene. In accord with the negligible electrostatic interaction between silver and graphene. Y. Chem. Chem. and 4. it also demonstrates that coronene complexes are useful model systems for modeling adsorption on graphene with chemical accuracy. G. J.. The support of Praemium Academiae. the PBE+vdW values can eﬀectively be regarded as the benchmark in this case. 5. Zhang. 4. 2010. the revPBE+vdW underbinds studied complexes. Bull.. Wang. A. 2009.1. (5) Li.3 kcal/mol. Xu. The nature of the adsorption of these three elements is diﬀerent. J. and (h) positions.cas. the ratio for MP2 is 9:5:2.. reduced on going from benzene to coronene.3. Y. J. L....1.. Bannwarth. P. Y. Z40550506 of the Institute of Organic Chemistry and Biochemistry. Mater. Z. Youth and Sports of the Czech Republic and by grant No..1. 4. Relativistic eﬀects are important in the binding of gold. S. Fan. 2011. Y. Res. Our results agree very well with PBE+vdW values published by Amft et al.. which is most pronounced at the hollow site. Q. These numbers indicate that the nature of the binding of the metal atoms does not change dramatically on going from benzene to coronene and that the values obtained at the benchmark CCSD(T) level can thus be used to characterize the adsorption of metals on a carbon surface. It was also supported by the operational program Research and Development for Innovations of European Regional Development Fund (CZ.0.1 kcal/mol. J. Ag) complexes were 18. (6) Scheuermann. the binding energies calculated for the benzeneÀM and grapheneÀM (M = Pd.-Y. 3. The CCSD(T) benchmark binding energies for the benzeneÀM (M = Pd. respectively. the MP2 binding energies for the coroneneÀM (M = Pd. Soc. Au.5. ) These authors contributed equally to this work.Journal of Chemical Theory and Computation relate primarily to the buckling of the graphene sheet. Au.1021/ct200625h |J. Academy of Sciences of the Czech Republic. M.4 kcal/mol for the (t). respectively.. Fan. ’ AUTHOR INFORMATION Corresponding Author Author Contributions 5. P208/10/ 1742 from the Grant Agency of the Czech Republic. 45. it was demonstrated that the vdW corrections are purely attractive only in Ag complexes.org/10.doi. R. 1413.. By comparing the pure GGA binding energies to those calculated using the nonlocal vdW correlation.otyepka@upol. T. Am.. 2010.. referred here as EE+vdW. Bai. PBE+vdW performs well. Burghard. P.. Engel. Moreover. ’ ACKNOWLEDGMENT This work was a part of research project no. The diﬀerence in binding energy between the strongest and weakest complexes is.hobza@uochb. Arockiadoss. Moreover. however. Comparison between the reference CCSD(T) and planewave DFT calculations demonstrates that neither LDA nor GGA provide reliable binding energies. 4. it is apparent that MP2 and EE+vdW strongly favor the adsorption of Pd over Au or Ag. followed by Au and Ag. Y. The good agreement obtained with two rather diﬀerent computational methods (speciﬁcally. (3) Hong. Krupke. Y. ’ REFERENCES (1) Sundaram. Kern. respectively)53 and also with the MP2 values calculated for the coroneneÀAg complex. The most accurate plane-wave DFT method identiﬁed was PBE+vdW with an exact exchange correction. Academy of Sciences of the Czech Republic. u 3754 dx. M. 1822.00/20. Zhang. Ag) complexes were 17.cz. R. G. in terms of both overall trends and absolute values.0058) and the Operational Program Education for Competitiveness of European Social Fund (CZ. and their neglect leads to dramatic underestimation of the binding energy. Z. LC512 and MSM6198959216 from the Ministry of Education. and 4. The binding of Pd is quite diﬀerent again. L. Moreover. calculations using this method accurately reproduced the trends in binding energy observed on switching from benzene to coronene or graphene as well as the corresponding absolute reference values. 5. 11. Chiu.5... in 2007 is also acknowledged. L. Rumi. (b). 429. 131. As such. Steiner. Ramaprabhu. X. C 2010. 2. Z. J.6. Using this method. Zhang.7.. The two methods also predict similar behavior for the binding energy on switching from benzene to coronene or graphene.0017). 145. B 2010. F. Gu..1. (Ag: 4. S. X. It was also supported by the Korea Science and Engineering Foundation (World Class University program R32-2008-000-10180-0). 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