van der Waals Interactions Between Organic Adsorbates and ... · van der Waals Interactions Between Organic Adsorbates and at Organic/Inorganic Interfaces Alexandre Tkatchenko, Lorenz

MRS BULLETIN • VOLUME 35 • JUNE 2010 • www.mrs.org/bulletin 435

van der WaalsInteractionsBetween OrganicAdsorbates and atOrganic/InorganicInterfacesAlexandre Tkatchenko, Lorenz Romaner,

Oliver T. Hofmann, Egbert Zojer, Claudia Ambrosch-Draxl, and Matthias Scheffler

actions play a noticeable role even forchemisorption when strong chemicalbonds are formed between docking groupsof a molecule and the substrate (e.g., forself-assembled monolayers [SAMs] bondedto gold by thiolates).10 Here they can deci-sively influence the molecular tilting angle,molecular distortions, or isomerization.3Not surprisingly, the interface geometry iscrucial for its electronic properties, which,in turn, control the function of organicdevices. In particular, the interface dipole,and hence the alignment of the molecularelectronic states with respect to the Fermilevel of the electrode, are sensitive to theatomic positions.

Generally, the term “vdW forces” canrefer to different types of intermolecularinteractions, such as electrostatics (perma-nent multipole–permanent multipoleinteraction), induction (permanent multi-pole–induced multipole interaction), anddispersion (induced multipole–inducedmultipole interaction). Dispersion usuallyis the strongest attractive term for mole-cules physisorbed or weakly chemisorbedon surfaces. Hence, the term “dispersionenergy” is frequently used interchange-ably with “vdW energy,” and we followthis convention in this article. The disper-sion energy arises from the correlatedmotion of electrons and must be describedby many-electron quantum mechanics.Unfortunately, accurate quantum-chemicalcalculations are only feasible in the nearfuture for finite systems up to ∼100 lightatoms. Thus, for most systems of interestin interface modeling, fully first-principlescalculations of vdW forces are not realisticat present. However, for many situations,alternative approaches exist that havecomparable accuracy, and we will discussthese approaches in the next section, par-ticularly concentrating on Kohn-Shamdensity-functional theory (DFT). Ourmain focus is on methods that currentlyshow the most promise, contain fewempirical parameters, and have alreadybeen applied to the modeling of inter -faces. Next, the influence of vdW interac-tions for the geometry and electronicstructure of an organic/inorganic modelsystem—PTCDA on Ag(111)—will be discussed. Lastly, it will be shown thatvdW interactions also play a prominentrole in determining the structure and func-tion of real interfaces, such as SAMs onmetal surfaces.

Methods for Treating van der WaalsInteractions

Noncovalent vdW forces are crucial forthe formation, stability, and function of mol-ecules and materials. The vdW dispersionenergy arises from the correlated motion of

IntroductionBonding at organic/organic and

organic/inorganic interfaces results frominterplay of several interactions, mostnotably (covalent) hybridization of wavefunctions, electron transfer processes, vander Waals (vdW) interaction, and Paulirepulsion. Typically, one distinguishes dif-ferent bonding regimes: In the case of purephysisorption, the attraction between theadsorbate and the substrate is mainly dueto vdW forces, which are, hence, essentialfor a correct description. Standard systemscharacterized by vdW bonding are mole-cules adsorbed on the basal plane of

graphite.1,2 An intermediate bondingregime arises for π-conjugated moleculesadsorbed on metal surfaces where alsoelectron transfer processes and covalentbonding come into play.3–9 In this con -text, we will discuss the adsorption ofperylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) on Ag(111) asan example, as this is one of the best- characterized metal/organic interfacesboth in experiment and in theory.36 For thisand similar systems, vdW forces are foundto be crucial for obtaining reliable geome-tries and energies. Interestingly, vdW inter-

AbstractVan der Waals (vdW) interactions play a prominent role in the structure and function

of organic/organic and organic/inorganic interfaces. Their accurate determination fromfirst principles, however, is a notoriously difficult task. Recently, a surge of interest inmodeling vdW interactions has led to promising theoretical developments. This articlereviews the state-of-the-art of describing vdW interactions by density-functional theorywith respect to accuracy and practicability. The performance of the different methods isdemonstrated for simple systems, such as rare-gas dimers and small organicmolecules. The nature of binding at organic/inorganic interfaces is then exemplified forthe perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) molecule atsurfaces of coinage metals. This fundamental system is the best-characterized organicmolecule/metal interface in experiment and theory. We emphasize the crucialimportance of a balanced description of both geometry and electronic structure in orderto understand and model the properties of such systems. Finally, the relevance of vdWinteractions to the function of actual devices based on interfaces is discussed.

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Van der Waals Interactions Between Organic Adsorbates

436 MRS BULLETIN • VOLUME 35 • JUNE 2010 • www.mrs.org/bulletin

electrons and must be described by many-electron quantum mechanics. Based on elec-tronic structure, there are two primaryapproaches for calculating vdW interac-tions: the quantum-chemical wave functionmethods based on Hartree-Fock (HF) andmethods rooted in Kohn-Sham DFT. BothHF and Kohn-Sham DFT are based on anindependent-electron picture. HF theory is

self-interaction free (the electrostatic interac-tion of an electron with itself is exactly can-celed), and it provides a natural startingpoint for including electron correlation(quantum many-body effects) with compu-tationally expensive wave function–basedmethods. On the other hand, DFT, togetherwith standard exchange-correlation (xc)functionals (local density approximation

[LDA], Perdew-Burke-Ernzerhof [PBE]),contains spurious self-interaction but pro-vides a route to include electron correlationeffects in an effective way at a relatively lowcomputational cost. However, the electroncorrelation in DFT is usually of (semi-)localorigin (i.e., an electron only “sees” otherelectrons in its close vicinity). See Tables Iand II for brief descriptions of DFT-based

Table I. Brief Descriptions, Advantages, and Shortcomings of DFT-Based Electronic Structure Methods.

Method Description Advantages ShortcomingsDFT Density-functional theory. The

ground-state properties of an interacting many-electron system are uniquely determined by its electron density n[r].

In principle, DFT is exact. Typically, it is employed in the Kohn-Sham form with an approximate electron exchange-correlation (xc) functional.

Improvement toward “better” functionals is not systematic.

Nobel prize to W. Kohn for the development of DFT in 1998.

Existing approximations to the xc functional yield good accuracy for many applications.

LDA Local-density approximation to the exchange-correlation functional in DFT.

The xc energy at each spatial point only depends on the electron density at that point.

Exact for the homogeneous electron gas.

Lattice constants of solids predicted within 2% of experiment (underestimated).

Applicable to big systems (thousands of atoms).

Overestimates solid cohesive energies and bulk moduli by 10%–20%.

Large overestimation of intermolecularinteraction energies (30%). No vdW interactions.

Self-interaction error (an electron interacts with itself) results in an adequate description of electronic spectra and electron transfer.

GGA (e.g., PBE54

or revPBE25)Generalized-gradient approximation

to the xc functional in DFT.The xc energy also depends on

the density gradient at a point. The construction of GGAs is not unique.

PBE: Perdew-Burke-Ernzerhof functional.revPBE: revised PBE functional of

Zhang and Yang. Fits exact exchange energy of rare-gas atoms.

Partially corrects the LDA for inhomogeneous electron densities.

Molecular atomization energies are significantly improved.

Lattice constants of solids within 2% of experiment using PBE (overestimated).

Applicable to big systems (thousands of atoms).

Underestimates solid cohesive energies and bulk moduli by 10%–20%.

Large underestimation of intermolecular interaction energies (60%).

No vdW interactions.Self-interaction error still present.

DFT-D22 Corrects DFT by adding interatomic vdW C6R−6 interaction,with empirical C6 coefficients and cutoff at short distances.

Remarkable accuracy for intermolecular interactions (15%–20% error for energies and 0.1–0.2 Å for equilibrium distances).

Can be connected to different DFT xc functionals.

Same computational cost as the underlying DFT calculation.

Needs at least two empirical parameters for each atom in the periodic table.

Does not describe different possible hybridization states of an atom in a molecule.

Empirical connection between DFT and the vdW energy tail.

Not yet applied to solids.

DFT+vdW24 Corrects DFT by adding interatomic vdW C6[n]R−6

interactions, with C6[n] coefficientsand vdW radii obtained from the DFT electron density (n).

Remarkable accuracy for intermolecular interactions (8% error for energies and 0.1 Å for equilibrium distances).

Handles different hybridization states transparently.

Can be connected to different DFT xc functionals.

Same computational cost as the underlying DFT calculation.

Empirical connection between DFT and the vdW energy tail.

Not yet applied to solids.

Continued




Table I. Brief Descriptions, Advantages, and Shortcomings of DFT-Based Electronic Structure Methods. (Continued )

Method Description Advantages ShortcomingsvdW-DF20 Van der Waals density functional

by Langreth and Lundqvist.Non-local xc functional to treat

vdW interactions in DFT.It employs the revPBE functional for

exchange and the LDA for local correlation.

First-principles solution without empiricism.

Has been applied to molecules and solids.

Computational cost comparable with DFT-PBE.

Errors of 20%–30% for intermolecular energies and 0.3–0.4 Å for equilibrium distances.

Accuracy for solids not yet fully established.

cRPA15 Correlation energy employing the random-phase approximation.

Presently the most sophisticated approximation to the correlation energy in DFT.

“Seamless” treatment of vdW interactions at all distances for molecules and solids.

Remarkable performance for lattice constants (1.4%) and bulk moduli of solids (11%).53

Computationally expensive (applicable to systems <100 atoms).

So far done non-self-consistently, thus results are sometimes sensitive to input orbitals (DFT-LDA, DFT-PBE, etc.).

GW G: Green’s function. W: Screened Coulomb interaction.

Many-body approach for the calculation of the photoemission spectrum.

Quasi-particle (electron and hole) energies in agreement with experimental photoelectron spectroscopies.

Calculations of total energies still rare.So far done non-self-consistently,

thus results are sometimes sensitive to input orbitals (DFT-LDA, DFT-PBE, etc.).

ACFD16 Adiabatic-connection fluctuation-dissipation theorem.

Connects the independent-electron Kohn-Sham system with the full quantum many-body electronic system.

Allows obtaining exact xc functional in DFT. Equivalent to the full solution of the quantum many-body problem.

Calculations not feasible for any real system.

Table II. Brief Description, Advantages, and Shortcomings of Wave Function–Based Electronic Structure Methods.

Method Description Advantages Shortcomings

Wave function–based Methods that directly employ Well-defined hierarchy of Accurate methods are electronic structure the electronic wave function approximations toward exact very expensive in computationalmethods with 3N coordinates, where N treatment of exchange time and memory requirements.

is the number of electrons. and correlation.

HF Hartree-Fock. Self-consistent Free from self-interaction error. No correlation energy included.exact-exchange method. The Considerably underestimates“base” for all quantum chemical the binding in moleculesapproaches. and solids.

Highly problematic for metals.No vdW interactions.

MP2 Møller-Plesset second-order Accurate molecular geometries. VdW interactions perturbation theory. Can be applied to systems overestimated by 30%–50%.

Wave function–based method to of up to ~500 atoms.include correlation energy on VdW interactions approximately top of HF. included.

MP2+ΔvdW14 MP2 with the C6[n]R−6 vdW Same computational cost as MP2. Requires cutoff function at short energy correction. Similar accuracy for intermolecular distances.

interactions as with veryexpensive CCSD(T).

CCSD(T) Coupled cluster method with Remarkable accuracy for Computationally very expensive single, double, and perturbative intermolecular binding energies (applicable to systems oftriple electron excitations. and geometries. 20–50 light atoms).

Considered “gold standard” Seamless inclusion of all electron Not directly applicable toin quantum chemistry. correlation effects, including solid-state systems.

vdW interactions.11




and wave function–based theoretical meth-ods used in this work, along with theiradvantages and shortcomings.

The HF method does not describe thedispersion interaction by definition, sincedispersion arises solely from electron corre-lation. Thus, higher level approaches builton top of HF need to be employed, such asMøller-Plesset second-order perturbationtheory (MP2), or the coupled clustermethod.11 Unfortunately, coupled clustertheory with single, double, and perturba-tive triple excitations (CCSD(T))—the quantum-chemical “gold standard”—becomes unfeasible for systems larger thanabout 50 light atoms (and even for the sim-plest periodic systems) due to its steepincrease in computational cost with systemsize. More affordable MP2 calculations(applicable up to ∼200–500 light atoms withstate-of-the-art implementations) unfortu-nately overestimate the dispersion energyby nearly a factor of two for π-π stacked systems,12 though corrections for this prob-lem have been recently proposed.13,14

DFT calculations are used routinely tostudy the structure and electronic proper-ties of interfaces, being applicable to systems comprising tens of thousands ofelectrons. In principle, DFT is exact.However, in practice, the xc energy func-tional has to be approximated, and alsostate-of-the-art (semi-)local or hybrid xcfunctionals do not properly account for thedispersion interaction. An exact routetoward the description of vdW interac-tions in DFT is provided by the adiabatic-connection fluctuation-dissipation (ACFD)theorem,15,16 which connects the independent-electron Kohn-Sham system with a fullyinteracting electronic many-body system.Full ACFD-DFT calculations, however, areunfeasible, hence approximations must beemployed. The most promising route iscombining the exact treatment of exchangewith the random-phase approximationfor electron correlation (EX+cRPA), whichhas recently gained popularity.9,15,17,18

However, even EX+cRPA is computation-ally intensive and so far can only beapplied to rather small systems (clustersand periodic systems with less than about100 light atoms). Furthermore, EX+cRPA isstill an approximation to the exact treat-ment of exchange and correlation, and it issometimes sensitive to the input orbitals(LDA, PBE).

Motivated by the need to address largerand more complex systems, numerousother, more feasible, approaches havebeen proposed for including vdW interac-tions in DFT. Among the most promisingones, one may distinguish the Langreth-Lundqvist density functional (vdW-DF)19–21 on the one hand (described in the

next paragraph) and corrections based ona summation of dispersion energy contri-butions between all atoms in the system(DFT-D and DFT+vdW)22–24 on the other.Both routes describe the long-rangevdW interaction and, at atomic overlapregions, link it to a “standard” exchange-correlation functional.

Langreth et al. developed the vdW-DFfunctional over the last decade.19–21 Likethe RPA, it is based on the ACFD theorem.Characteristic for DFT calculations, thecorresponding nonlocal correlationenergy contribution is obtained from theelectron density only. The local electroncorrelation is treated by LDA, while theexchange energy is described by the gen-eralized gradient approximation (GGA) tothe xc functional, specifically the so-calledrevPBE25 functional. The approach is veryattractive, as it is derived from first princi-ples and does not rely on empiricalparameters or fitting. With recent imple-mentations,26,27 its computational effi-ciency is comparable to that of standardDFT-GGA calculations. However, espe-cially for intermolecular interactions, theperformance of vdW-DF is not spectacu-lar, as can be seen in Figures 1 and 2. Theimprovement of vdW-DF is an activeresearch field, and recent developmentsyield better accuracy by employing differ-ent exchange functionals than revPBE forthe short range and/or by introducingparameters fitted to high-level quantum-chemical binding energies.28,29

The alternative DFT-D approach simplyadds the interatomic dispersion energycontributions to DFT total energies, typi-cally only considering the leading-orderC6Rij

−6 term, where Rij is the distancebetween atoms i and j, and C6 is the associ-

ated dispersion coefficient. The DFT-Dapproach has gained popularity afterGrimme showed that accurate results forintermolecular interactions can beachieved, and DFT-D can be connected todifferent functionals.22 The main short-coming of previous DFT-D formulations isthe high level of empiricism, requiringat least two fitting parameters for everyelement in the periodic table. Furthermore,different possible hybridization/oxidationstates of atoms in different chemical orgeometrical environments were notaccounted for. Recently, several groupshave proposed different solutions to theseissues.24,30−32 In particular, Tkatchenko andScheffler developed a method to obtainaccurate dispersion coefficients and vdWradii directly from the ground-state molec-ular or condensed matter electron density(DFT+vdW method).24 This approachstarts from high-level quantum-chemistrycalculations for free atoms, and then thechanges that result from the interactionsbetween atoms are obtained from the elec-tron density of the polyatomic system.There is a single parameter remaining inthe DFT+vdW method, the vdW radiusscaling. This parameter defines the linkageof the R−6 vdW interaction and the DFTfunctional, as originally proposed byHobza and co-workers.23 This linkage isachieved by introducing a so-called damp-ing function that multiplies the Rij

−6 inter-action and smoothly cuts it off at shortinteratomic distances. This function and itsonset parameter, the vdW radius, remainthe main weakness of the approach.A strength of the DFT+vdW method andof the general DFT-D concept is that theycan be easily coupled to different xc func-tionals. Later in this section, we restrict the

Figure 1. Performance of different approximate electronic structure methods for thedescription of the binding-energy curves of (a) argon (Ar) and (b) krypton (Kr) dimers. Thereference results are given by CCSD(T)—coupled cluster method with single, double, andperturbative triple electron excitations. See Tables I and II for a detailed explanation ofdifferent electronic structure methods.14,20,24




discussion to the PBE xc functional, andtherefore label the approach as PBE+vdW(PBE-D when using the approach byGrimme22). PBE is used since it is a non-empirical xc functional that yields accurateresults for both molecules and solids.Let us note that the concept of the semi-empirical correction also has been carriedover to quantum-chemical methods, suchas MP2, with success.14

To illustrate the performance of vdW-DF and PBE+vdW methods, we show inFigure 1 the binding-energy curve for theargon and krypton dimers—fundamentalvdW-bonded systems. The reference cal-culations refer to CCSD(T), and they typi-cally reproduce experimental data withina few percent. All calculations are fullyconverged, with estimated deviations ofless than 1 meV from the complete basisset limit. The vdW-DF overestimates boththe equilibrium distance (by 0.2–0.3 Å)and the binding energy (by 40%–60%).There are two main reasons for these devi-ations: the errors in the calculated C6 dis-persion coefficients (∼20%) and the use ofthe revPBE functional for the local regime.The PBE+vdW method also overbinds,but with somewhat smaller error. Therecently developed dispersion-correctedMP2 approach (MP2+ΔvdW)14 consis-tently achieves CCSD(T)-quality at signif-icantly smaller computational cost.Similar conclusions hold for the whole S22database of noncovalent interactions

introduced by Hobza et al.,12 as shown inFigure 2. Most members of the quantumchemistry community consider this data-base to be arguably the most accurate forintermolecular interactions; it containsconverged CCSD(T) results for the bind-ing energies of 22 organic dimers, includ-ing vdW, electrostatic, and hydrogenbonding. The standard PBE functional significantly underestimates the bindingenergies with a mean absolute error(MAE) of 114 meV. In contrast, MP2 over-estimates the dispersion interactions,yielding considerable error for vdW-bonded systems with a MAE of 33 meV.The vdW-DF functional underestimatesthe binding in hydrogen-bonding systemswith a MAE of 59 meV on the S22 data-base. Its performance can be improved bychoosing a different DFT exchange func-tional, however this comes at the expenseof significantly larger errors in case ofvdW-bonding.27 The PBE+vdW methodfurther reduces the error on the S22 data-base to 13 meV, showing similar accuracyfor hydrogen and vdW-bonded systems.Finally, MP2+ΔvdW yields an almost neg-ligible MAE of 3 meV from the CCSD(T)reference data.

It is widely assumed that vdW interac-tions have a minor direct effect on the elec-tronic structure. While the semi-empiricalDFT-D methods do not affect the electronicstructure by construction, a self-consistentvdW-DF approach, in principle, can mod-

ify the electronic structure. However, thechanges due to vdW interactions werefound to be very small for selected testcases.33 In contrast, it is well known thatthe influence of vdW interactions on thegeometry of molecules can be significant.Obviously, such geometry changes will, inturn, have a profound influence on theelectronic structure. In some cases, GGAdensity functionals, when using the correct(experimental) geometry, are sufficient toyield electronic properties in qualitativeagreement with experiment, but, in manycases, hybrid functionals, which include afraction of HF exchange, are needed for anappropriate description. Recently, thisissue has been illustrated for the exampleof metal-phthalocyanine dimers.34 Whileboth methods, PBE+vdW and PBE-hybrid+vdW, yielded essentially the samegeometry, only the hybrid functional couldreproduce experimental photoemissionspectra. We remark in passing that accu-rate many-body approaches (such as GW,where G is Green’s function and W is thescreened Coulomb interaction) can beused as well for calculating the electronicspectrum,35 and this is, in fact, the moregeneral and systematic route. However,the discussion of such approaches isbeyond the scope of the present article.

Organic/Inorganic InterfacesAfter reviewing the methodology, we

will now address the role of vdW forces forbonding at organic/inorganic interfaceswith the π-conjugated molecule PTCDAadsorbed on Ag(111) as an example. Thechemical structure of PTCDA is shown atthe bottom right of Figure 3. This is one ofthe best characterized metal/organic inter-faces, both experimentally and theoreti-cally.36 Regarding the geometric andelectronic structure of the interface, the fol-lowing key parameters are known fromexperimental investigations of the highlyordered room-temperature phase:1. The molecular monolayer adsorbs at adistance of 2.86 Å from the surface with thecarboxylic oxygen atoms, which arelocated at the corner of the molecule, 0.18Å below the carbon backbone, indicativeof a covalent attraction.37 These resultswere obtained from x-ray standing wavemeasurements which, for well-orderedsystems, allow a determination of atomicpositions within a few hundredths of an Å.2. The formerly lowest unoccupiedmolecular level (LUMO) of the PTCDAmolecule is located right at the Fermi level(EF) in the adsorbate system.38 Its partialoccupation reflects a metal to moleculeelectron transfer.3. At the same time, the work function ofthe Ag(111) surface increases by 0.1 eV at

Figure 2. Performance of different approximate electronic structure methods on the bindingenergies of 22 dimers with noncovalent intermolecular interactions (S22 database).12 Thereference values are given by CCSD(T)—coupled cluster method with single, double, andperturbative triple electron excitations. See Tables I and II for a detailed explanation ofdifferent electronic structure methods. The MP2+ΔvdW method has only been applied to a subset of 16 systems, for which atomic projection of dispersion coefficients ispossible.12,14,22,24,27




monolayer coverage.38 Considering thatweakly interacting non-polar moleculestypically lower the work function by0.5–1.0 eV due to the so-called push-backeffect,39 the increase observed here reflectsthe electron-accepting properties ofPTCDA at this surface. The term “push-back” refers to the fact that Pauli repulsionbetween the occupied states of the mole-cule and the substrate leads to a mutualpolarization that reduces the surfacedipole of the metal substrate and, as a con-sequence, its work function.39

4. The adsorption energy of PTCDA can-not be verified directly in desorptionexperiments, as this requires that the mol-ecule desorbs as a whole, while PTCDAdesorbs in fragments. However, a verysimilar molecule, which is half the size ofPTCDA, has an adsorption energy onAg(111) of 1.2 eV.40 Thus, the adsorptionenergy of PTCDA is expected to bearound 2.4 eV.

As a first step, we address the perform-ance of DFT-PBE for describing the elec-tronic structure of the monolayer. Thecalculations were performed by constrain-ing the carbon atoms to be located at theexperimentally determined position whilefully optimizing all remaining degrees of

freedom.8 In agreement with experiment,the oxygen atoms are found 0.11 Å belowthe carbon backbone. The position of theLUMO for the adsorbed molecule is dis-played in Figure 3, as inferred from the den-sity of states projected onto the orbitals ofthe free molecule (projected density of statesor PDOS). The corresponding maximum isright below the Fermi level, and, hence, alarge fraction of the metal-LUMO hybridorbitals are occupied in agreement with UPSdata. The highest-occupied molecularorbital (HOMO) level is calculated to be 1.2eV below the LUMO, which also compareswell with the experimental value of about1.5 eV. As (semi-)local exchange-correlationfunctionals, such as DFT-PBE, underesti-mate the bandgap of PTCDA and moleculesin general (due to self-interaction andthe missing discontinuity of the exchange-correlation potential), the good agreementfound for the adsorbate case may appearsurprising. However, as noted previously,upon adsorption, the formerly emptyLUMO became more delocalized and frac-tionally occupied, which can be expectedto partly remove this underestimation.Furthermore, as shown by Neaton and co-workers,41 (semi-)local exchange-correlationfunctionals miss a correlation contribution

arising from surface polarization. This stabi-lizes the LUMO and destabilizes the HOMOand, therefore, partly compensates theremaining self-interaction error.

Due to the metal-molecule interaction,the potential felt by electrons at the inter-face is modified, as indicated in Figure 3. Tothe left, it is plotted for the bare Ag slab(blue, dotted line) and for the interface (red,full line). The work function Φ0 of the bareAg surface is defined as the differencebetween the Fermi level and the vacuumlevel at the uncovered surface. The workfunction Φ of the covered surface is givenby the vacuum level to the right of the totalsystem, and we find that it has increased byabout 0.2 eV compared to Φ0, in reasonableagreement with experiment (0.1 eV). As wealso had seen that most of the LUMO-derived DOS got filled by electrons, thischange of the work function might appearrather small. Indeed, a more extensiveanalysis8 shows that the work functionincrease due to the LUMO filling is coun-teracted by electron back transfer, Paulirepulsion, and bending of the molecule.Moreover, also some charge (~0.5 elec-trons) is transferred from the metal to themolecule, which weakens the push-backeffect. A similar agreement with experi-mental observations has been found forPTCDA on Cu(111) and Au(111).8 On thelatter surface, the LUMO remains essen-tially unoccupied, reflecting that Φ0 ofAu(111) is larger than that of Ag(111), andthe work function is reduced.

The PBE functional fails when describ-ing the correct adsorption distance andenergy. The energy is repulsive every-where, as shown in Figure 4 as a functionof distance. Hence, PBE underestimatesthe bonding strength for PCTDA atAg(111) and fails as severely with respectto energetics and geometry as for purelyvdW-bound systems. Again, this findingholds true also for PTCDA adsorbed ontoCu(111) and Au(111)8 and was observedfor these surfaces and also for other mole-cules such as benzene or azobenzene.3−5

On more reactive surfaces, such asCu(110), PBE can give rise to binding (e.g.,for a thiophene ring7 or a benzene ring6).However, in all cases, inclusion of vdWforces has been found to strongly modifyadsorption energies and distances.

As explained in the previous section,there are several ways to incorporate vdWinteractions to improve on PBE calcula-tions. Figure 4a shows results for PTCDAon Ag(111) using the vdW-DF approach.The nonlocal vdW energy, Enl, is negative(i.e., attractive) and decreases monotoni-cally with increasing distance. At the exper-imental binding distance, the contributionfrom this quantity amounts to several eVs.

Ene

rgy

(eV

)

Energy (eV

)

–4

–3

–2

–1

EF

LUMO1

0

–1

–2HOMO

o

o

o

o

o

o

PDOS (eV–1)

0

Φ0 Φ

1

2

3

4

5

a c

b d

Figure 3. (a) Plane-averaged electrostatic potential of the substrate without (dotted line) andwith (solid line) the adsorbed PTCDA (perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride)monolayer. The work function of the bare Ag surface is given by Φ0 and that of the coveredsurface by Φ. (b) Side view of the metal/organic interface with the slab being modeled with fourlayers on the left and the monolayer adsorbed onto the right surface. (c) Projected density ofstates (PDOS) onto the LUMO (lowest unoccupied molecular level) and the HOMO (highestoccupied molecular orbital) of PTCDA. (d) Illustration of the chemical structure of PTCDA.




The total interaction energy obtained byvdW-DF displays a pronounced minimumof about 2 eV per molecule at a bondingdistance of 3.5 Å. Hence, vdW-DF givesrealistic adsorption energies but overesti-mates adsorption distances as alreadyfound in the previous section for intermol-ecular interactions.

Results obtained by different semi-empir-ical methods3–5 and EX+cRPA9 are shown inFigure 4b. All curves exhibit a sizable mini-mum in the adsorption energy, but thespread between the methods is consider-able, with adsorption energies rangingbetween 2 to 4 eV and adsorption distancesbetween 3 and 3.5 Å. The two main differ-ences between DFT-D and DFT+vdW arethe use of different C6 coefficients and differ-ent damping functions. Both DFT-D andDFT+vdW methods do not yet describe the

screening of the vdW interaction by themetal bulk, thus the application to metalsrepresents an approximation. These aspectsand the applicability of different DFT-Dmethods to the modeling of adsorption onmetal surfaces were discussed in detail.3–5

For the vdW-DF method, the influence ofapproximations, such as the use of revPBEfor the exchange part, the approximate treat-ment for the polarizability (plasmon-polemodel), and the neglect of electron-densitygradient terms in the correlation energy, stillneeds to be examined. Lastly, we notethat for computational feasibility, someassumptions and approximations wererequired also when applying the EX+cRPAapproach.9 A common trend for all methodsis the overestimation of binding distances.For a correct description of interface phe-nomena, this geometry uncertainty is prob-lematic, as it can lead to qualitative errors inthe electronic structure. For example, asshown in Figure 4c, the peak maximum ofthe LUMO-related PDOS moves throughthe Fermi level only at adsorption distancesbelow 3 Å, and the peak position and widtharound the experimental equilibrium geom-etry depend sensitively on the adsorbatedistance.8 Extending the vdW-DF to investi-gations to Au and Cu substrates8 reveals lit-tle influence of the substrate on the bondingdistances. This is, however, in contrast to theexperimental findings that place the mole-cule much closer to the substrate in the Cucase than for Au. Hence, while the discussedmethods give much more realistic bindingenergies and distances than PBE, they stillneed to be improved for a reliable first- principles description of the geometry.

Relevance of vdW Interactions for Organic Devices

Obviously, the careful control of interfaceproperties is crucial for the function oforganic devices;43 for example, they deter-mine injection and extraction barriers inlight-emitting diodes, thin-film transistors,and solar cells. Consequently, a variety ofprocedures has been developed to tune theelectronic characteristics of interfacestoward optimum functionality. These tech-niques include, among others, the usage ofSAMs,44,45 redox-doping,46 or the depositionof (sub)monolayers of strong electronacceptors or donors.47,48 To optimize suchtechniques and to allow for a rationaldesign of new organic molecules, an in-depth understanding of interfaces also at anatomistic level is important.49,50 So far, this isbest obtained by a combined theoreticaland experimental approach (see References51 and 52). For strongly bonded systems,such as 2-(4-dicyanomethylene-2,3,5,6-tetrafluoro-cyclohexa-2,5-dienylidene)- malononitrile (F4TCNQ) on noble metals51

or covalently bonded SAMs,52 excellentresults for geometry and electronic struc-ture can be obtained in the framework ofDFT using (semi-)local exchange-correlationfunctionals. However, for the vast majorityof the practically relevant systems, a properinclusion of vdW interactions is essential forobtaining reasonable adsorption geome-tries, as already illustrated in the previoussections. Unfortunately, despite the successof present procedures, their accuracy is stillnot sufficient to credit them with predictivepower.

The structure of covalently bondedSAMs is also affected by vdW interactionssimilar to single molecule adsorptiongeometries. For example, it has beenfound52 that PBE calculations underesti-mate the tilt-angle measured by near-edgex-ray adsorption for a well-orderedanthracene selenolate SAM on Au(111),while the overestimation of the intermolec-ular interactions in LDA results in a tilt thatis too large. Preliminary studies employingDFT-D indicate that the inclusion of vdWinteractions gives rise to an intermediatesituation in better agreement with theexperiment.52 Such issues can becomeimportant for SAM-induced work-functionchanges when using molecules bearing sig-nificant long-axis dipole moments.

Moreover, situations exist in which theinclusion of vdW forces affects the relativeenergetics of different adsorption geometriesof an organic/inorganic system. A prototyp-ical example here is azobenzene,3–5 whichcan occur in the cis- or the trans-conforma-tion. Standard DFT calculations predict thatfor adsorption on Ag(111), the cis-conforma-tion is energetically more favorable. ThevdW interactions, however, stabilize thetrans-conformation to a larger amount thanthe cis-isomer because of its larger contactarea with the surface; the amount of stabi-lization is high enough here where the trans-isomer becomes the global minimum. As thecis-trans isomerization changes both themolecular dipole moment and the interac-tion with the substrate, this affects theadsorption-induced work function.

Summary and OutlookVan der Waals (vdW) interactions are

ubiquitous intermolecular forces that playa crucial role in determining the geometryof interfaces, and, consequently, have alarge effect on the functionality of organicdevices. Recently, several promisingmethods (DFT+vdW and vdW-DF) havebeen developed to include vdW interac-tions in density-functional theory calcula-tions at moderate or no additionalcomputational cost. For the interactionbetween atoms and small molecules,“chemical accuracy” of 1 kcal/mol can

Figure 4. (a) Adsorption energy forPTCDA (perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride)adsorbed onto Ag(111) whenemploying PBE and vdW-DF.6 Alsoshown is Enl, which is the non-localcorrelation term in vdW-DF. Theexperimental value is indicated by thehorizontal red line labeled “exp.” (b) Adsorption energy obtained with PBE-D,3 PBE+vdW,3 and EX+cRPA.7(c) Position of the LUMO (lowestunoccupied molecular level) relative tothe Fermi level. The red line indicatesthe peak maximum, while the peakwidth is evidenced in yellow. Note thatthe width does not decrease to zero athigh adsorption distances, as aminimum width is required in thedensity-functional theory calculations ofmetals. D, adsorption distance.




be achieved with some vdW-correctedmethods. Unfortunately, this is not yet thecase for organic/inorganic interfaces.

With the example of PTCDA on Ag(111),we have illustrated that the Perdew-Burke-Ernzerhof (PBE) functional can cap-ture the relevant features in the interfacialcharge density, and the resulting work-function change is obtained quite reliably.A prerequisite, however, hence the essenceof a successful vdW approach, is to prop-erly describe the adsorption geometry. Thelatter has a profound effect on the push-back, the metal-to-molecule charge trans-fer, as well as on the magnitude andorientation of intrinsic or adsorption-induced molecular dipole moments. Inspite of the promising approaches cur-rently available for treating vdW interac-tions, the obtained results show aconsiderable spread. Part of the shortcom-ings can be related to the underlyingapproximations and the fact that the treat-ment of metallic systems is still an openissue. The huge demand for an equally fea-sible as well as reliable scheme has trig-gered tremendous activities in thisresearch field in view of which majorimprovements can be expected in thefuture.

AcknowledgmentsWe acknowledge financial support from

the Marie Curie Network SMALL, theAustrian Science Fund (FWF), projectsP9714 and P20972-N20. A.T. thanks theAlexander von Humboldt (AvH)Foundation. We acknowledge the KavliInstitute of Theoretical Physics at theUniversity of California, Santa Barbara,where part of this paper was written (sup-ported in part by the National ScienceFoundation under Grant No. PHY05-51164).

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van der Waals Interactions Between Organic Adsorbates and ... · van der Waals Interactions Between Organic Adsorbates and at Organic/Inorganic Interfaces Alexandre Tkatchenko, Lorenz