Azimuthal Dichroism in Near-Edge X‑ray Absorption Fine StructureSpectra of Planar MoleculesGuido Fratesi,*,† Valeria Lanzilotto,‡ Luca Floreano,‡ and Gian Paolo Brivio†

†ETSF, CNISM, Dipartimento di Scienza dei Materiali, Universita di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy‡CNR-IOM, Laboratorio TASC, Basovizza SS-14, Km 163.5, I-34149 Trieste, Italy

ABSTRACT: The dependence of the near-edge X-rayabsorption fine structure (NEXAFS) spectrum of moleculeson the photon electric field direction is investigated by meansof first-principles simulations based on density functionaltheory with the transition-potential approach. In addition tothe well-known dependence of the NEXAFS resonances onthe orientation of the electric field with respect to themolecular plane, we demonstrate that for planar moleculeswith sufficient in-plane anisotropy such as pentacene a dichroiceffect is found with a splitting of the σ* resonance as a functionof the azimuthal orientation of the photon electric field in themolecular plane. The σ* splitting is investigated as a functionof the length of acenes and closely related molecules. A proper assignment of such spectral features guided by theory togetherwith variable polarization experiments may allow one to completely determine the orientation of molecules at interfaces.

■ INTRODUCTION

Understanding and controlling the geometric alignment ofmolecules at an interface is of the utmost importance tooptimize the properties of organic electronic devices.1,2 As anexample, for planar organic molecules such as manypoliaromatics, their orientation controls the superposition ofthe π-electron states with the wave functions of facing systems,hence determining the efficiency of charge transfer among themolecules, and with a substrate. Additionally, a properaccommodation of the first organic layer at a hybrid interfaceis highly desirable because that can seed subsequent optimallyoriented molecular growth as well as influence the alignment ofthe electronic energy levels at the interface.3 The latter aspect,associated with the molecular orientation of the thin film, canaffect the heterojunction processes, such as the light absorptionstrength, and the charge and exciton transport in organicphotovoltaic cells.4 The current−voltage characteristics of asingle layer of planar organic molecules such as nickelphthalocyanine depends on the molecular orientation.5 Inorganic light-emitting diodes, molecules completely parallel tothe substrate effectively increase the light-out efficiency.6

The molecular orientation can be accessed by differentexperimental techniques. Possibly, the most direct one is theimaging of species through scanning tunnelling microscopy(STM). However, this technique is intrinsically limited to thevery first layer of an organic film and requires some electricalconductivity, so it may be difficult to apply to thick insulatingsubstrates. In the framework of organic thin films, one of themost commonly adopted methods is near-edge X-rayabsorption spectroscopy (NEXAFS),7 which displays severalinteresting features. In particular, its element specificity follows

that of the core energies, and it is solely sensitive to the organicmaterial, when performed at the carbon K-edge for a C-freesubstrate. The intensity of the NEXAFS resonances depends onthe angle between the incoming photon electric field and thetransition dipole moment of the molecular orbitals. Hence,provided that the molecules within an overlayer display apreferential orientation, the latter one can be determined fromthe intensity variation of the corresponding NEXAFS electronictransitions, as taken for different angles between the photonbeam polarization and the surface plane.7,8 This procedure iscommonly used to determine the tilting angle of the moleculeswith respect to the normal.9−14 In the NEXAFS analysis theresearcher is required to associate features in the spectrum withtransitions where the dipole moment is known: for example,the lower-energy peaks at the C K-edge of a planar aromaticmolecule are generally due to 1s−π* transitions, hence theirintensity is maximized for the electric field perpendicular to themolecular plane, while 1s−σ* transitions require larger energy.However, it was recently demonstrated for the case ofheteroaromatics that fluorinated phthalocyanines exhibit theopposite behavior at the F K-edge and a significant overlap ofπ* and σ* resonances at the N K-edge, thus calling fortheoretical support to avoid misleading interpretation ofmeasurements.15

The knowledge of the orientation of the π system only fixesthe polar angle of the experimental frame with respect to thenormal to the molecular plane, z, while leaving the azimuthal

Received: December 20, 2012Revised: February 28, 2013Published: March 12, 2013

Article

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direction (rotation of molecules around z) unknown. For a fulldetermination of the molecular orientation by a NEXAFSexperiment, the in-plane σ* resonances should be resolved(which requires a molecule displaying significant in-planeanisotropy) and assigned properly. The possibility to achievethis additional contribution is the focus of the present paper,where we consider planar, anisotropic molecules such as theacenes and we determine the polarized NEXAFS spectrum ofthe isolated molecule by first-principle simulations. A directcomparison with experiments in the gas phase is not viablesince these measurements yield the average of the molecularorientations. Nevertheless, our results can be representative ofweakly adsorbed molecules, as shown in the case of pentaceneby making reference to recent experiments for adsorption ondielectric16 and metal surfaces.17 The paper is structured asfollows. We first overview the theoretical method and thenpresent results for pentacene. Eventually, we analyze theapplicability to other molecules such as shorter acenes and thelimitations of the theoretical approach.

■ THEORYFrom the point of view of Kohn−Sham (KS) density functionaltheory (DFT), the energy of the photon absorbed in atransition from the ground state to an excited one can bewritten as the total energy difference of the two states

ν = = =

− = =

h E N n n

E N n n

( ; 0, 1)

( ; 1, 0)

i f

i f

tot

tot(1)

where the second term on the right-hand side is the ground-state energy of the N-electron system and the first one the totalenergy with one electron promoted from the initially occupiedlevel i to an empty level f. We note that, in comparison tooptical excitations, the much more localized character of thecore level allows one to treat the hole wave function in theexciton statically. Following Slater18 and by using Janak’stheorem,19 this can be rewritten in terms of the Kohn−Shameigenvalues εi and εf at half filling,

ν ε

ε

= = =

− = =

h N n n

N n n

( ; 1/2, 1/2)

( ; 1/2, 1/2)

f i f

i i f (2)

including screening effects up to second order in theoccupation numbers. This approach is however impracticalfor generating a complete NEXAFS spectrum including thecontinuum part because it requires a separate calculation of theelectronic structure of the system for each final-state orbital.Accordingly, Triguero et al.20 have proposed the so-calledtransition-potential approach as an approximation to Slater’sone, by neglecting the fractional occupation of the state f in thecalculation

ν ε

ε

= − = =

− − = =

h N n n

N n n

( 1/2; 1/2, 0)

( 1/2; 1/2, 0)

f i f

i i f (3)

This approach, defined as the half core hole (HCH)approximation, has been applied successfully to a wide rangeof systems and recently reviewed.21 It was generallydemonstrated to be more accurate than alternative ones,22,21

such as the full core hole (FCH)23 approximation which differsfrom the HCH approach by setting ni = 0 in eq 3 or the excitedcore hole method (XCH)24 where the excited electron is

included in the lowest unoccupied KS state when computingthe energy levels. For the above reasons, the HCH method ischosen here.It should be noted that the second term on the right-hand

side of eq 3, taken with its sign, is the core electron bindingenergy for the i state (with eigenvalues measured from thevacuum level). If one is interested in relative energy scales, thecore level shift (CLS) for the inequivalent sites is to becomputed only. This has the advantage of being easilyaccessible to DFT calculations, also within the pseudopotential(PP) method, by using a PP with a full core hole for the ionizedatom; the calculation is repeated for each inequivalent site, andthe CLS among the atoms is given by the respective totalenergy difference.25 Hence, our final expression for thetransition energy is

ν ε= − = = + Δ +h N n n E E( 1/2; 1/2, 0)f i f i iavg

(4)

where ΔEi is the CLS with respect to the site average of thecore electron binding energy, Ei

avg. The latter term is a constantwhich we do not evaluate and will be taken as the energyreference for the spectra reported here. Absolute energy scaleswithin a DFT framework are otherwise accessible through theso-called ΔKohn−Sham approach.26 Spectra arising fromatoms of the same species are computed by repeating theabove procedure with the core hole at the various atomic sitesand are summed up to obtain the total spectrum of themolecule.To compute the spectrum taking matrix elements into

account, we adopt the Fermi golden rule with the transitionamplitude given by the dipole operator directed along thephoton beam polarization, evaluated between i and f KS states.Energy conservation follows from eq 4.8,27 We use thexspectra28 code of the Quantum-ESPRESSO distribution.29

There, plane wave basis sets and pseudopotentials are used,with a ficticious 3D periodicity for molecules in the gas phase.The transition matrix element is expressed by reconstructingthe unoccupied wave functions in the core region by means ofthe projector augmented wave method30 within the frozen-coreapproximation. The use of plane waves makes the descriptionof the continuum part of the spectrum straightforward. Still, thesummation over the final states would limit for computationalreasons the energy range accessible to the calculation especiallyfor large simulation cells. That expensive summation is avoidedby adopting a recursion method based on the Lanczosalgorithm.28,31

The ionic and electronic structures of the molecules werethen computed by DFT with the PBE exchange correlationfunctional.32 Norm-conserving PPs with kinetic energy cutoff of90 Ry were used for structural relaxations and total energydifferences, e.g., when computing the CLS. We checked,however, that the spectra presented below are convergedalready for a cutoff of 50 Ry, and that was used for the xspectracalculation. Neutral, HCH-ionized, and FCH-ionized PPs wereused for C to determine the molecular geometry, the NEXAFSspectrum, and the CLS, respectively, hence including relaxationof core states of the ionized atom owing to the core hole. Allwere generated with a Martins−Troullier33 pseudizationscheme with 2s and 2p electrons in the valence andpseudization radii of 0.794 Å. Each one of the moleculesunder study was placed in a periodically repeated orthorhombicsupercell which includes 11 Å of vacuum in each direction. Thisis largely sufficient to minimize intermolecular interactionswhen evaluating the ground state density, potential, and energy.

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Larger cells would be needed to describe the continuum part ofthe spectrum, where states would suffer from confinementeffects. We found that converged results with respect tosupercell size could be alternatively and more efficientlyobtained by introducing a sampling of the ficticious Brillouinzone, with at least one k point every 0.3 Å−1 in each direction,already with this moderate vacuum volume. Since in xspectraeigenvalues are referred to the Fermi level EF (here set to themiddle of the HOMO−LUMO gap), a separate calculationwith a cubic supercell was run to determine the vacuum levelwithin the Makov−Payne method.34 The spectra werecomputed with an energy-independent Lorentzian broadeningof 0.2 eV which is introduced as an imaginary part iγ to thetransition energy.28 For plotting purposes, we have followed theenergy-dependent broadening scheme21 adopted by manyauthors; namely, we take γ = 0.2 eV for valence energies upto EF + 5 eV, γ = 1.0 eV for energies higher than EF + 25 eV,and a linear dependence of γ on energy in between.

■ RESULTSWe present the calculated NEXAFS spectra for pentacene inthe gas phase and compare them with the experimental resultsand previous calculations.35 Since the molecule has sixinequivalent C atoms (see Figure 1), to sum their contributions

to the total spectrum properly one has to take into account thecorresponding chemical shifts, as outlined in the previoussection. We recall that the absolute energy scale is notaccessible here, and our results are referred to the averaged C1s photoemission energy. The chemical shifts are reported inFigure 1 and show good agreement with previous calculationsand experiments:35 the most bound core levels are found foratom numbers 2 and 4, in the valleys, and the least bound onesfor atom numbers 1 and 3 in the top positions; the two externalatoms 5 and 6 have intermediate values. Small shifts like thoseobserved here influence only marginally the overall simulatedspectrum, but they can in general have a larger effect, e.g., whenthe C atoms are bound to different functional groups (forexample the F-bound carbon atoms are shifted by about +1.5eV with respect to C(2) and C(4) in perfluorinated pentacene,36

and the shift is larger than 2 eV for fluorobenzene37,38).We are now in the position to evaluate the NEXAFS

spectrum, which is reported in Figure 2(a). We start bydiscussing the total (spherically averaged) spectrum asmeasurable in the gas phase. As already mentioned, our energyreference is the average core level photoionization threshold,

whose absolute value is not computed here. The lower energymultiplets, commonly known as LUMO and LUMO+1, aremainly due to transitions from the 1s orbital to emptymolecular π* orbitals. They can be generally assigned to theLUMO and LUMO+1 states of the molecule with the HCH inthe various inequivalent sites, although matrix elements candampen the contribution of the true LUMO making it inactivein NEXAFS. For example, we found that in the case of C(1) theLUMO does not contribute to NEXAFS since it is odd withrespect to the yz plane [defined as in Figure 2(a)] and hencehas no weight on the 2pz wave functions of C

(1). We recall thatthese transitions to bound states are in the discrete part of thespectrum but appear broadened due to the smearing techniqueand split because of the contributions by inequivalent atoms.

Figure 1. CLS of pentacene in the gas phase with individualcontributions from the six inequivalent atoms (marked by the verticalbars) numbered as in the inset. The solid line is a pseudo-Voigt profile:50% Gaussian (0.2 eV standard deviation) plus 50% Lorentzian (0.2eV width). The XPS average energy is set to zero.

Figure 2. (a) NEXAFS of gas-phase pentacene (Pc). The shaded areais the total spectrum (3 × the spherical average). The solid, dashed,and dotted lines label transitions with the photon electric field alongthe x , y, and z axes as defined in the inset. (b) Experimentalspectrum16 for one monolayer of pentacene on rutile TiO2(110) forthe electric field along the high-symmetry crystallographic axes. (c)and (d) Experimental spectrum17 for the (c) (3 × 6) and (d) (6 × 8)phase of pentacene adsorbed on Au(110). Solid and dashed verticalbars mark the position of σ* resonances along the long and short axisof the molecules, respectively.

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The much broader feature above vacuum is assigned totransitions to σ* orbitals.7 The energy positions of the spectralfeatures (the LUMO and LUMO+1 are centered at about −5and −3 eV, the σ* peak at +5 eV relative to the photoionizationthreshold) are in very good agreement with the experimentalfindings.35 Our calculations also produce a peak close to theionization threshold, marked by ⊕ in Figure 2(a), which wasnot observed, neither in the gas phase nor in the solid state andthin films. We will come back to this later. Previous calculationsof this system35 were performed with the static exchangemethod (STEX) where full exchange is accounted. We observethat the energy positions of those NEXAFS peaks are similar toours.The dependence of the C 1s spectrum of pentacene on the

light polarization orientation was not discussed theoretically inthe literature to our knowledge. Obviously such an effectcannot be detected in the randomly distributed molecules inthe gas phase, but it allows one to determine the orientation ofmolecules in the condensed phase by means of polarizedexperiments.8 So Figure 2(a) also reports the spectrum whenthree different light polarizations are involved, namely, with theelectric field E parallel to the x , y, and z axis. This furtherconfirms the π* character of the LUMO and LUMO+1multiplets and the σ* resonance in the xy-plane. Mostinteresting in our context is the splitting of the σ* peak intwo resonances according to the light polarization: we observethat transitions with E parallel to the long axis of the molecule,x , can be found at higher energies (by ≈2 eV) than those withE parallel to the short axis, y. We denote these transitions as σx*and σy*, respectively. The origin of the energy differencebetween σx* and σy* resonances (azimuthal dichroism) is 2-fold.On the one hand, shorter C−C distances are found for atompairs along the x axis than for pairs along y (on average 1.40and 1.45 Å, respectively, in good agreement with X-rayresults39), and a shortening of the C−C bond length isassociated to an increased energy of the σ* resonance.40 On theother hand, the molecule being much longer in one direction isanother source of anisotropy. The two factors contributealmost equally to the dichroism, as we deduce by the simulationof the spectrum of a pentacene molecule with all C−Cdistances fixed to an averaged value (not shown), resulting in aσ* splitting approximately half of the one shown in Figure 2(a).This azimuthal dichroism of the in-plane polarization signal

can be used to determine the orientation of the molecule in theplane, provided that the interaction (charge transfer) with thesupporting substrate does not affect the molecular orbitalssignificantly. To validate our statement, we need variablepolarization experiments on a well-ordered structure grown ona 2-fold symmetry substrate (rectangular unit cell) where themolecular orientation can be checked by complementarytechniques. These requirements are fulfilled for the monolayerphase of pentacene adsorbed on the rutile TiO2(110).

16 There,polarized NEXAFS spectra were taken jointly with STMmeasurements, so that the geometrical configuration could befully determined. This strongly anisotropic substrate ischaracterized by rows of protruding O atoms running alongthe [001] direction,41 inducing a long-range ordering of themolecules with their long axis parallel to that direction and themolecular plane slightly tilted off the surface by 25° around thelong axis.16 The molecule−substrate interaction was found toleave the molecular orbitals almost unaffected: indeed, theNEXAFS resonances of the bare pentacene molecules areobserved down to the smallest detail since the very first

monolayer.16 Hence, to a first approximation, calculatedNEXAFS spectra with E ∥ x , y, and z should be representativeof measurements taken with the E ∥ [001], [110], and [110],respectively, providing an ideal benchmark for our study. Thecomparison of our simulations with the experimental findingsfor one monolayer of pentacene adsorbed on TiO2(110) isdeduced from Figure 2(a) and (b). One clearly notices aremarkable agreement between the relative energy scales of thecomputed and measured spectra, as well as for the spectralintensities. The agreement is particularly striking whencomparing the spectra taken with the electric field in thesurface plane ([001] and [11 0] azimuths), which aredominated by the strong σ* resonance displaying a differenceof ≈1.5 eV between the σx* and σy* components, indicated inthe figure as vertical bars.When molecules are in contact with the surface of metals, a

rehybridization of the molecular orbitals takes place. This yieldsa significant distortion and broadening of the spectral features,hence making a direct comparison with gas-phase calculationsmore difficult. Nevertheless, our results can be used to highlightazimuthal dichroism in interpreting previous experiments forpentacene adsorbed on the Au(110) surface,17 as we illustratehere. For this system two commensurate phases are formed inthe monolayer range, with (3 × 6) and (6 × 8) periodicity,respectively.42 Molecules in the (3 × 6) phase lay perfectly flaton the surface with the long axis oriented along the [001]direction.17,43 Although the NEXAFS resonances display a largebroadening, particularly for the 1s−π* transitions around 285eV, a residual (≈0.5 eV) azimuthal dichroism is observed for Ein the surface plane (see Figure 2(c)).The azimuthal dichroism is even more evident in the (6 × 8)

phase of pentacene/Au(110), where one molecule out of threeis perfectly normal to the surface lying on its long edge,oriented along [110], while the others are aligned as in the (3 ×6) phase. As a consequence of this admixture, experimentalspectra17 reprinted in Figure 2(d) for the electric field along thethree main crystallographic directions include contributionsfrom transitions with dipole moment along different molecularaxes for edge-on and flat-lying molecules. In particular, thepeaks in the E ∥ [001] spectrum at about 285 eV mostlyaccount for 1s−π* (LUMO and LUMO+1) transitions due tothe edge-on molecules; their structure, as compared to thebroad one observed in the (3 × 6) phase, shows that thismolecular species is less rehybridized. Most interesting in thepresent context are the other two electric field directions. Inparticular, the prominent feature in the E ∥ [110] spectrum atabout 294 eV mixes σx* transitions from edge-on molecules withσy* transitions from flat-lying ones. Conversely, the shallowpeak at about 292.3 eV for E ∥ [110] results from the sum ofσy* transitions from edge-on molecules and a structureless decayfor transitions with E perpendicular to the molecular planefrom flat-lying ones [see the corresponding line in Figure 2(c)].Hence, the 1.7 eV energy difference between the two featuresdiscussed above and marked in Figure 2(d) by vertical bars isan indication of the σx*−σy* dichroism in the NEXAFSspectrum of edge-on molecules, in excellent agreement withthe simulations. This strict correspondence of our simulationswith the experimental observations for pentacene adsorbed onboth dielectric and metal substrates demonstrates the validity ofour approach and its applicability to determine the fullmolecular orientation directly from polarized NEXAFS spectra.

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■ DISCUSSION

Since the observation of azimuthal dichroism requires somemolecular anisotropy, it is interesting to investigate how theposition of σ* resonances corresponding to transitions withdifferent electric field depends on the molecular species. To thispurpose, we simulated the NEXAFS spectrum for acenes andother representative molecules. The same numerical setup asdescribed in the Theory section was taken, with the vacuumportion of the supercell being constant and the k-pointsampling adjusted accordingly. Results are collected andcompared to the ones of pentacene in Figure 3. For allmolecules, the lower-energy peaks correspond to the 1s−π*transitions, as expected, and at larger energy the σ* resonance is

found, on which we focus next. Starting from benzene, therotationally averaged computed spectrum is in good agreementwith gas-phase experiments.44 Here we access also the polarizedspectra; however, the high symmetry of the molecule results inthe σ* resonance almost independent of the in-plane electricfield direction, as can be seen in Figure 3(a). Some splitting inthe E ∥ x and E ∥ y resonance positions is instead found forlarger acenes, starting from anthracene which is reported inFigure 3(c). We remark that a systematic study of the NEXAFSspectrum of the acenes in the gas phase is available in theliterature,45 but there the dichroism in the spectrum was notinvestigated. Other anisotropic molecules may exhibit dichro-ism of a different kind: for example, if we take pyrazine(C4H4N2), one cannot identify a splitting in the σ* resonance,but the intensity of that feature is about twice as large whentaken with E parallel to the N−N axis (see Figure 3(f)).We now return to the theoretical results for gas-phase

pentacene, especially focusing on the peak found for E ∥ z around the photoionization threshold, marked by ⊕ in Figure2(a). The absence of that peak in the measurements for theadsorbed molecule as shown in Figure 2(b)−(d) would not besufficient to draw any conclusion, but a comparison to gas-phase measurements35 where it is also missing clearly identifiesit as spurious. This points out the possible major limits of thecurrent theoretical approach. Since the spectrum we compute isa slight modification (due to the matrix elements) of theunoccupied portion of the density of states (DOS) with pcharacter at the ionized atom in the presence of the HCH-modified potential (HCH-DOS), an analysis of that DOS in therelevant energy region will be representative of the quality ofthe spectrum to be expected by different approaches. Theelectronic DOS is critically influenced by the approximateexchange correlation functional adopted in the calculations(here PBE), while the exact Kohn−Sham spectrum couldprovide a better description of the true quasiparticle one.46 Inparticular, the electron affinity is typically overestimated bymean-field approaches.47 This can result in the presence ofspurious bound states which should rather be resonances in thecontinuum: one finds consequently spurious sharp peaks in thecomputed NEXAFS spectrum in the energy region right belowthe threshold, as is observed in the case of pentacene.To highlight the effect of the overestimated electron affinity

in the simulated spectrum, Figure 4(a) reports the spectrumdue to ionization of C(2) together with its PBE density of states.Here only the NEXAFS spectra polarized with E ∥ z and the pzDOS are discussed. In the latter one a state (indicated by “b” inthe figure) is found close to the vacuum level which contributesto the ⊕ peak in the NEXAFS spectrum below the threshold,as observed in Figure 2(a). Its wave function is very localizedon the molecule, as shown in Figure 4(b). Similar observationshold for C atom numbers 4 and 6. The spurious character ofsuch a state and its dependence on the computational approachare further confirmed by a calculation of the HCH-DOS byother more refined approaches. As an example, we use here thehybrid functional PBE0,48 which includes a portion of Hartree−Fock like exchange. This is expected to produce better resultsfor the spectroscopy of a wide range of systems includingpentacene molecules, even though a residual rigid shift of theelectronic states with respect to the true quasi-particleexcitations is still observed.49 Notice that here we are moreconcerned about the inaccuracy of valence states with respectto the vacuum level (which may induce the features discussedhere) than to absolute energy scales, also improved by the use

Figure 3. Simulated NEXAFS spectra of (a) benzene, (b) naphthalene,(c) anthracene, (d) tetracene, (e) pentacene, and (f) pyrazine.

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of hybrid functionals.38 The PBE0 HCH-DOS, reported inFigure 4(a), shows a shift of the states at higher energies, andthe one of interest here shifted above the vacuum level.Conversely, we notice that the character of the states in thelower-energy part of the spectrum (LUMO/LUMO+1structures) is very similar in the two approaches, as can beseen by a comparison of the corresponding wave functions inFigure 4(c),(d). Similarly, resonances at higher energies (suchas the σ* of relevance to the present article) are described moreproperly by the mean-field approach than states close to thephotoionization threshold since their character is less depend-ent on the precise energy position.A description avoiding the mean-field approximation could

be chosen to overcome the above limitations and obtain a goodevaluation of the spectrum in the full energy range. To thisrespect, nonempirical optimally tuned hybrid density func-tionals have recently proved to be very accurate in describingquasi-particle excitations in molecules.49 However, theimplementation of the Fock operator in the iterative (Lanczos)calculation of the spectrum (as it would be needed for a hybridfunctional NEXAFS calculation) would increase severely thecomputational requirements of the present plane-wavemethod,28 while the use of a Gaussian basis set could nothelp because the delocalized states at high energy would not bewell represented. Similarly, if one is willing to proceed througha direct calculation of the states, only the first unoccupied onescould be conveniently obtained since the description of thecontinuum portion of the spectrum up to a relatively lowenergy would already require thousands of states to be explicitlyincluded. The approach taken here hence appears as a goodcompromise between accuracy and computational cost for thedescription of the main spectral features, bearing in mind thatinaccuracies about the ionization threshold are likely expected.

■ CONCLUSIONSTaking into account pentacene as a relevant test case, we havedemonstrated the effectiveness of DFT approaches based onthe transition potential approximation to describe thedichroism in the NEXAFS spectrum of aromatic molecules,

with special emphasis on its dependence on the azimuthal anglewhich is commonly overlooked. Major inaccuracies of themethod emerged around the photoionization threshold as aresult of approximate functionals in DFT. Gas-phase results canbe applied to condensed phases on weakly interactingsubstrates, at least as the relative position of the main featuresis involved, and this is validated by a remarkable agreementbetween our simulations and the NEXAFS measures for highlyordered pentacene arrays on TiO2(110) and Au(110). Acrossthe acenes, the σ* resonance splits into two componentsaccording to the direction of the photon electric field in theplane. We observe that the feature involving mainly C p-statesoriented along the long molecular axis is located at largerenergy than that associated to states along the short axis. Thedifference becomes negligible in benzene, the spectrum beinginvariant for in-plane rotations, but not in pyrazine wherestronger intensity is found for electric field along the N−N axis.In conclusions, our results show that by identifying spectralfeatures, possibly aided by theoretical results, and by makingcomparison to polarized NEXAFS experiments one coulddetermine the orientation not only of the molecular plane butalso of the molecules within that plane.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: guido.fratesi@mater.unimib.it.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSComputational resources were made available in part byCINECA (application code HP10C3YWUA).

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Figure 4. Pentacene with HCH on atom C(2), indicated by the arrowin panel (b). In panel (a) we report the NEXAFS spectrum with E ∥ zby PBE (dotted line) and the pz DOS on C(2) computed by differenttheoretical approaches, PBE and PBE0 (shaded areas). Horizontalsegments mark the KS HOMO−LUMO gap. Panels (b), (c), and (d)show the wave function corresponding to the DOS peak indicated bythe same label in panel (a).

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