Azimuthal Dichroism in Near-Edge X-ray Absorption Fine Structure

Article pubs.acs.org/JPCC

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

ETSF, CNISM, Dipartimento di Scienza dei Materiali, Università 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-ray absorption fine structure (NEXAFS) spectrum of molecules on the photon electric field direction is investigated by means of first-principles simulations based on density functional theory with the transition-potential approach. In addition to the well-known dependence of the NEXAFS resonances on the orientation of the electric field with respect to the molecular plane, we demonstrate that for planar molecules with sufficient in-plane anisotropy such as pentacene a dichroic effect is found with a splitting of the σ* resonance as a function of the azimuthal orientation of the photon electric field in the molecular plane. The σ* splitting is investigated as a function of the length of acenes and closely related molecules. A proper assignment of such spectral features guided by theory together with variable polarization experiments may allow one to completely determine the orientation of molecules at interfaces.

■

INTRODUCTION Understanding and controlling the geometric alignment of molecules at an interface is of the utmost importance to optimize the properties of organic electronic devices.1,2 As an example, for planar organic molecules such as many poliaromatics, their orientation controls the superposition of the π-electron states with the wave functions of facing systems, hence determining the efficiency of charge transfer among the molecules, and with a substrate. Additionally, a proper accommodation of the first organic layer at a hybrid interface is highly desirable because that can seed subsequent optimally oriented molecular growth as well as influence the alignment of the electronic energy levels at the interface.3 The latter aspect, associated with the molecular orientation of the thin film, can affect the heterojunction processes, such as the light absorption strength, and the charge and exciton transport in organic photovoltaic cells.4 The current−voltage characteristics of a single layer of planar organic molecules such as nickel phthalocyanine depends on the molecular orientation.5 In organic light-emitting diodes, molecules completely parallel to the substrate effectively increase the light-out efficiency.6 The molecular orientation can be accessed by different experimental techniques. Possibly, the most direct one is the imaging of species through scanning tunnelling microscopy (STM). However, this technique is intrinsically limited to the very first layer of an organic film and requires some electrical conductivity, so it may be difficult to apply to thick insulating substrates. In the framework of organic thin films, one of the most commonly adopted methods is near-edge X-ray absorption spectroscopy (NEXAFS),7 which displays several interesting features. In particular, its element specificity follows © 2013 American Chemical Society

that of the core energies, and it is solely sensitive to the organic material, when performed at the carbon K-edge for a C-free substrate. The intensity of the NEXAFS resonances depends on the angle between the incoming photon electric field and the transition dipole moment of the molecular orbitals. Hence, provided that the molecules within an overlayer display a preferential orientation, the latter one can be determined from the intensity variation of the corresponding NEXAFS electronic transitions, as taken for different angles between the photon beam polarization and the surface plane.7,8 This procedure is commonly used to determine the tilting angle of the molecules with respect to the normal.9−14 In the NEXAFS analysis the researcher is required to associate features in the spectrum with transitions where the dipole moment is known: for example, the lower-energy peaks at the C K-edge of a planar aromatic molecule are generally due to 1s−π* transitions, hence their intensity is maximized for the electric field perpendicular to the molecular plane, while 1s−σ* transitions require larger energy. However, it was recently demonstrated for the case of heteroaromatics that fluorinated phthalocyanines exhibit the opposite behavior at the F K-edge and a significant overlap of π* and σ* resonances at the N K-edge, thus calling for theoretical support to avoid misleading interpretation of measurements.15 The knowledge of the orientation of the π system only fixes the polar angle of the experimental frame with respect to the normal to the molecular plane, ẑ, while leaving the azimuthal Received: December 20, 2012 Revised: February 28, 2013 Published: March 12, 2013 6632

dx.doi.org/10.1021/jp312569q | J. Phys. Chem. C 2013, 117, 6632−6638

The Journal of Physical Chemistry C

Article

direction (rotation of molecules around ẑ) unknown. For a full determination of the molecular orientation by a NEXAFS experiment, the in-plane σ* resonances should be resolved (which requires a molecule displaying significant in-plane anisotropy) and assigned properly. The possibility to achieve this additional contribution is the focus of the present paper, where we consider planar, anisotropic molecules such as the acenes and we determine the polarized NEXAFS spectrum of the isolated molecule by first-principle simulations. A direct comparison with experiments in the gas phase is not viable since these measurements yield the average of the molecular orientations. Nevertheless, our results can be representative of weakly adsorbed molecules, as shown in the case of pentacene by making reference to recent experiments for adsorption on dielectric16 and metal surfaces.17 The paper is structured as follows. We first overview the theoretical method and then present results for pentacene. Eventually, we analyze the applicability to other molecules such as shorter acenes and the limitations of the theoretical approach.

included in the lowest unoccupied KS state when computing the energy levels. For the above reasons, the HCH method is chosen 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 binding energy for the i state (with eigenvalues measured from the vacuum level). If one is interested in relative energy scales, the core level shift (CLS) for the inequivalent sites is to be computed only. This has the advantage of being easily accessible to DFT calculations, also within the pseudopotential (PP) method, by using a PP with a full core hole for the ionized atom; the calculation is repeated for each inequivalent site, and the CLS among the atoms is given by the respective total energy difference.25 Hence, our final expression for the transition energy is hν = εf (N − 1/2; ni = 1/2, nf = 0) + ΔEi + Eiavg

where ΔEi is the CLS with respect to the site average of the core electron binding energy, Eavg i . The latter term is a constant which we do not evaluate and will be taken as the energy reference for the spectra reported here. Absolute energy scales within a DFT framework are otherwise accessible through the so-called ΔKohn−Sham approach.26 Spectra arising from atoms of the same species are computed by repeating the above procedure with the core hole at the various atomic sites and are summed up to obtain the total spectrum of the molecule. To compute the spectrum taking matrix elements into account, we adopt the Fermi golden rule with the transition amplitude given by the dipole operator directed along the photon beam polarization, evaluated between i and f KS states. Energy conservation follows from eq 4.8,27 We use the xspectra28 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 reconstructing the unoccupied wave functions in the core region by means of the projector augmented wave method30 within the frozen-core approximation. The use of plane waves makes the description of the continuum part of the spectrum straightforward. Still, the summation over the final states would limit for computational reasons the energy range accessible to the calculation especially for large simulation cells. That expensive summation is avoided by adopting a recursion method based on the Lanczos algorithm.28,31 The ionic and electronic structures of the molecules were then computed by DFT with the PBE exchange correlation functional.32 Norm-conserving PPs with kinetic energy cutoff of 90 Ry were used for structural relaxations and total energy differences, e.g., when computing the CLS. We checked, however, that the spectra presented below are converged already for a cutoff of 50 Ry, and that was used for the xspectra calculation. Neutral, HCH-ionized, and FCH-ionized PPs were used for C to determine the molecular geometry, the NEXAFS spectrum, and the CLS, respectively, hence including relaxation of core states of the ionized atom owing to the core hole. All were generated with a Martins−Troullier33 pseudization scheme with 2s and 2p electrons in the valence and pseudization radii of 0.794 Å. Each one of the molecules under study was placed in a periodically repeated orthorhombic supercell which includes 11 Å of vacuum in each direction. This is largely sufficient to minimize intermolecular interactions when evaluating the ground state density, potential, and energy.

■

THEORY From the point of view of Kohn−Sham (KS) density functional theory (DFT), the energy of the photon absorbed in a transition from the ground state to an excited one can be written as the total energy difference of the two states hν = Etot(N ; ni = 0, nf = 1) −Etot(N ; ni = 1, nf = 0)

(1)

where the second term on the right-hand side is the groundstate energy of the N-electron system and the first one the total energy with one electron promoted from the initially occupied level i to an empty level f. We note that, in comparison to optical excitations, the much more localized character of the core level allows one to treat the hole wave function in the exciton statically. Following Slater18 and by using Janak’s theorem,19 this can be rewritten in terms of the Kohn−Sham eigenvalues εi and εf at half filling, hν = εf (N ; ni = 1/2, nf = 1/2) −εi(N ; ni = 1/2, nf = 1/2)

(2)

including screening effects up to second order in the occupation numbers. This approach is however impractical for generating a complete NEXAFS spectrum including the continuum part because it requires a separate calculation of the electronic structure of the system for each final-state orbital. Accordingly, Triguero et al.20 have proposed the so-called transition-potential approach as an approximation to Slater’s one, by neglecting the fractional occupation of the state f in the calculation hν = εf (N − 1/2; ni = 1/2, nf = 0) −εi(N − 1/2; ni = 1/2, nf = 0)

(4)

(3)

This approach, defined as the half core hole (HCH) approximation, has been applied successfully to a wide range of systems and recently reviewed. 21 It was generally demonstrated to be more accurate than alternative ones,22,21 such as the full core hole (FCH)23 approximation which differs from the HCH approach by setting ni = 0 in eq 3 or the excited core hole method (XCH)24 where the excited electron is 6633



Article

Larger cells would be needed to describe the continuum part of the spectrum, where states would suffer from confinement effects. We found that converged results with respect to supercell size could be alternatively and more efficiently obtained by introducing a sampling of the ficticious Brillouin zone, with at least one k point every 0.3 Å−1 in each direction, already with this moderate vacuum volume. Since in xspectra eigenvalues are referred to the Fermi level EF (here set to the middle of the HOMO−LUMO gap), a separate calculation with a cubic supercell was run to determine the vacuum level within the Makov−Payne method.34 The spectra were computed with an energy-independent Lorentzian broadening of 0.2 eV which is introduced as an imaginary part iγ to the transition energy.28 For plotting purposes, we have followed the energy-dependent broadening scheme21 adopted by many authors; namely, we take γ = 0.2 eV for valence energies up to EF + 5 eV, γ = 1.0 eV for energies higher than EF + 25 eV, and a linear dependence of γ on energy in between.

■

RESULTS We present the calculated NEXAFS spectra for pentacene in the gas phase and compare them with the experimental results and previous calculations.35 Since the molecule has six inequivalent C atoms (see Figure 1), to sum their contributions

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

Figure 2. (a) NEXAFS of gas-phase pentacene (Pc). The shaded area is the total spectrum (3 × the spherical average). The solid, dashed, and dotted lines label transitions with the photon electric field along the x̂, ŷ, and ẑ axes as defined in the inset. (b) Experimental spectrum16 for one monolayer of pentacene on rutile TiO2(110) for the 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 vertical bars mark the position of σ* resonances along the long and short axis of the molecules, respectively.

to the total spectrum properly one has to take into account the corresponding chemical shifts, as outlined in the previous section. We recall that the absolute energy scale is not accessible here, and our results are referred to the averaged C 1s photoemission energy. The chemical shifts are reported in Figure 1 and show good agreement with previous calculations and experiments:35 the most bound core levels are found for atom numbers 2 and 4, in the valleys, and the least bound ones for atom numbers 1 and 3 in the top positions; the two external atoms 5 and 6 have intermediate values. Small shifts like those observed here influence only marginally the overall simulated spectrum, but they can in general have a larger effect, e.g., when the C atoms are bound to different functional groups (for example the F-bound carbon atoms are shifted by about +1.5 eV 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 by discussing the total (spherically averaged) spectrum as measurable in the gas phase. As already mentioned, our energy reference is the average core level photoionization threshold,

whose absolute value is not computed here. The lower energy multiplets, commonly known as LUMO and LUMO+1, are mainly due to transitions from the 1s orbital to empty molecular π* orbitals. They can be generally assigned to the LUMO and LUMO+1 states of the molecule with the HCH in the various inequivalent sites, although matrix elements can dampen the contribution of the true LUMO making it inactive in NEXAFS. For example, we found that in the case of C(1) the LUMO does not contribute to NEXAFS since it is odd with respect to the yz plane [defined as in Figure 2(a)] and hence has no weight on the 2pz wave functions of C(1). We recall that these transitions to bound states are in the discrete part of the spectrum but appear broadened due to the smearing technique and split because of the contributions by inequivalent atoms. 6634



Article

monolayer.16 Hence, to a first approximation, calculated NEXAFS spectra with E ∥ x̂, ŷ, and ẑ should be representative of measurements taken with the E ∥ [001], [11̅0], and [110], respectively, providing an ideal benchmark for our study. The comparison of our simulations with the experimental findings for one monolayer of pentacene adsorbed on TiO2(110) is deduced from Figure 2(a) and (b). One clearly notices a remarkable agreement between the relative energy scales of the computed and measured spectra, as well as for the spectral intensities. The agreement is particularly striking when comparing the spectra taken with the electric field in the surface plane ([001] and [11̅0] azimuths), which are dominated by the strong σ* resonance displaying a difference of ≈1.5 eV between the σx* and σy* components, indicated in the figure as vertical bars. When molecules are in contact with the surface of metals, a rehybridization of the molecular orbitals takes place. This yields a significant distortion and broadening of the spectral features, hence making a direct comparison with gas-phase calculations more difficult. Nevertheless, our results can be used to highlight azimuthal dichroism in interpreting previous experiments for pentacene adsorbed on the Au(110) surface,17 as we illustrate here. For this system two commensurate phases are formed in the monolayer range, with (3 × 6) and (6 × 8) periodicity, respectively.42 Molecules in the (3 × 6) phase lay perfectly flat on the surface with the long axis oriented along the [001] direction.17,43 Although the NEXAFS resonances display a large broadening, particularly for the 1s−π* transitions around 285 eV, a residual (≈0.5 eV) azimuthal dichroism is observed for E in 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 three is perfectly normal to the surface lying on its long edge, oriented along [11̅0], while the others are aligned as in the (3 × 6) phase. As a consequence of this admixture, experimental spectra17 reprinted in Figure 2(d) for the electric field along the three main crystallographic directions include contributions from transitions with dipole moment along different molecular axes for edge-on and flat-lying molecules. In particular, the peaks in the E ∥ [001] spectrum at about 285 eV mostly account for 1s−π* (LUMO and LUMO+1) transitions due to the edge-on molecules; their structure, as compared to the broad one observed in the (3 × 6) phase, shows that this molecular species is less rehybridized. Most interesting in the present context are the other two electric field directions. In particular, the prominent feature in the E ∥ [11̅0] spectrum at about 294 eV mixes σx* transitions from edge-on molecules with σy* transitions from flat-lying ones. Conversely, the shallow peak at about 292.3 eV for E ∥ [110] results from the sum of σ*y transitions from edge-on molecules and a structureless decay for transitions with E perpendicular to the molecular plane from flat-lying ones [see the corresponding line in Figure 2(c)]. Hence, the 1.7 eV energy difference between the two features discussed above and marked in Figure 2(d) by vertical bars is an indication of the σx*−σy* dichroism in the NEXAFS spectrum of edge-on molecules, in excellent agreement with the simulations. This strict correspondence of our simulations with the experimental observations for pentacene adsorbed on both dielectric and metal substrates demonstrates the validity of our approach and its applicability to determine the full molecular orientation directly from polarized NEXAFS spectra.

The much broader feature above vacuum is assigned to transitions to σ* orbitals.7 The energy positions of the spectral features (the LUMO and LUMO+1 are centered at about −5 and −3 eV, the σ* peak at +5 eV relative to the photoionization threshold) are in very good agreement with the experimental findings.35 Our calculations also produce a peak close to the ionization threshold, marked by ⊕ in Figure 2(a), which was not observed, neither in the gas phase nor in the solid state and thin films. We will come back to this later. Previous calculations of this system35 were performed with the static exchange method (STEX) where full exchange is accounted. We observe that the energy positions of those NEXAFS peaks are similar to ours. The dependence of the C 1s spectrum of pentacene on the light polarization orientation was not discussed theoretically in the literature to our knowledge. Obviously such an effect cannot be detected in the randomly distributed molecules in the gas phase, but it allows one to determine the orientation of molecules in the condensed phase by means of polarized experiments.8 So Figure 2(a) also reports the spectrum when three different light polarizations are involved, namely, with the electric field E parallel to the x̂, ŷ, and ẑ axis. This further confirms the π* character of the LUMO and LUMO+1 multiplets and the σ* resonance in the xy-plane. Most interesting in our context is the splitting of the σ* peak in two resonances according to the light polarization: we observe that transitions with E parallel to the long axis of the molecule, x̂, can be found at higher energies (by ≈2 eV) than those with E parallel to the short axis, ŷ. We denote these transitions as σ*x and σy*, respectively. The origin of the energy difference between σ*x and σ*y resonances (azimuthal dichroism) is 2-fold. On the one hand, shorter C−C distances are found for atom pairs along the x̂ axis than for pairs along ŷ (on average 1.40 and 1.45 Å, respectively, in good agreement with X-ray results39), and a shortening of the C−C bond length is associated to an increased energy of the σ* resonance.40 On the other hand, the molecule being much longer in one direction is another source of anisotropy. The two factors contribute almost equally to the dichroism, as we deduce by the simulation of the spectrum of a pentacene molecule with all C−C distances fixed to an averaged value (not shown), resulting in a σ* 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 the plane, provided that the interaction (charge transfer) with the supporting substrate does not affect the molecular orbitals significantly. To validate our statement, we need variable polarization experiments on a well-ordered structure grown on a 2-fold symmetry substrate (rectangular unit cell) where the molecular orientation can be checked by complementary techniques. These requirements are fulfilled for the monolayer phase of pentacene adsorbed on the rutile TiO2(110).16 There, polarized NEXAFS spectra were taken jointly with STM measurements, so that the geometrical configuration could be fully determined. This strongly anisotropic substrate is characterized by rows of protruding O atoms running along the [001] direction,41 inducing a long-range ordering of the molecules with their long axis parallel to that direction and the molecular plane slightly tilted off the surface by 25° around the long axis.16 The molecule−substrate interaction was found to leave the molecular orbitals almost unaffected: indeed, the NEXAFS resonances of the bare pentacene molecules are observed down to the smallest detail since the very first 6635



■

Article

DISCUSSION Since the observation of azimuthal dichroism requires some molecular anisotropy, it is interesting to investigate how the position of σ* resonances corresponding to transitions with different electric field depends on the molecular species. To this purpose, we simulated the NEXAFS spectrum for acenes and other representative molecules. The same numerical setup as described in the Theory section was taken, with the vacuum portion of the supercell being constant and the k-point sampling adjusted accordingly. Results are collected and compared to the ones of pentacene in Figure 3. For all molecules, 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, the rotationally averaged computed spectrum is in good agreement with gas-phase experiments.44 Here we access also the polarized spectra; however, the high symmetry of the molecule results in the σ* resonance almost independent of the in-plane electric field direction, as can be seen in Figure 3(a). Some splitting in the E ∥ x and E ∥ y resonance positions is instead found for larger acenes, starting from anthracene which is reported in Figure 3(c). We remark that a systematic study of the NEXAFS spectrum of the acenes in the gas phase is available in the literature,45 but there the dichroism in the spectrum was not investigated. Other anisotropic molecules may exhibit dichroism 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 when taken 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 ∥ ẑ around the photoionization threshold, marked by ⊕ in Figure 2(a). The absence of that peak in the measurements for the adsorbed molecule as shown in Figure 2(b)−(d) would not be sufficient to draw any conclusion, but a comparison to gasphase measurements35 where it is also missing clearly identifies it as spurious. This points out the possible major limits of the current theoretical approach. Since the spectrum we compute is a slight modification (due to the matrix elements) of the unoccupied portion of the density of states (DOS) with p character at the ionized atom in the presence of the HCHmodified potential (HCH-DOS), an analysis of that DOS in the relevant energy region will be representative of the quality of the spectrum to be expected by different approaches. The electronic DOS is critically influenced by the approximate exchange correlation functional adopted in the calculations (here PBE), while the exact Kohn−Sham spectrum could provide a better description of the true quasiparticle one.46 In particular, the electron affinity is typically overestimated by mean-field approaches.47 This can result in the presence of spurious bound states which should rather be resonances in the continuum: one finds consequently spurious sharp peaks in the computed NEXAFS spectrum in the energy region right below the 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 spectrum due to ionization of C(2) together with its PBE density of states. Here only the NEXAFS spectra polarized with E ∥ ẑ and the pz DOS are discussed. In the latter one a state (indicated by “b” in the figure) is found close to the vacuum level which contributes to the ⊕ peak in the NEXAFS spectrum below the threshold, as observed in Figure 2(a). Its wave function is very localized on the molecule, as shown in Figure 4(b). Similar observations hold for C atom numbers 4 and 6. The spurious character of such a state and its dependence on the computational approach are further confirmed by a calculation of the HCH-DOS by other more refined approaches. As an example, we use here the hybrid functional PBE0,48 which includes a portion of Hartree− Fock like exchange. This is expected to produce better results for the spectroscopy of a wide range of systems including pentacene molecules, even though a residual rigid shift of the electronic states with respect to the true quasi-particle excitations is still observed.49 Notice that here we are more concerned about the inaccuracy of valence states with respect to the vacuum level (which may induce the features discussed here) 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. 6636



Article

with special emphasis on its dependence on the azimuthal angle which is commonly overlooked. Major inaccuracies of the method emerged around the photoionization threshold as a result of approximate functionals in DFT. Gas-phase results can be applied to condensed phases on weakly interacting substrates, at least as the relative position of the main features is involved, and this is validated by a remarkable agreement between our simulations and the NEXAFS measures for highly ordered pentacene arrays on TiO2(110) and Au(110). Across the acenes, the σ* resonance splits into two components according to the direction of the photon electric field in the plane. We observe that the feature involving mainly C p-states oriented along the long molecular axis is located at larger energy than that associated to states along the short axis. The difference becomes negligible in benzene, the spectrum being invariant for in-plane rotations, but not in pyrazine where stronger intensity is found for electric field along the N−N axis. In conclusions, our results show that by identifying spectral features, possibly aided by theoretical results, and by making comparison to polarized NEXAFS experiments one could determine the orientation not only of the molecular plane but also of the molecules within that plane.

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

■

of hybrid functionals.38 The PBE0 HCH-DOS, reported in Figure 4(a), shows a shift of the states at higher energies, and the one of interest here shifted above the vacuum level. Conversely, we notice that the character of the states in the lower-energy part of the spectrum (LUMO/LUMO+1 structures) is very similar in the two approaches, as can be seen by a comparison of the corresponding wave functions in Figure 4(c),(d). Similarly, resonances at higher energies (such as the σ* of relevance to the present article) are described more properly by the mean-field approach than states close to the photoionization threshold since their character is less dependent on the precise energy position. A description avoiding the mean-field approximation could be chosen to overcome the above limitations and obtain a good evaluation of the spectrum in the full energy range. To this respect, nonempirical optimally tuned hybrid density functionals have recently proved to be very accurate in describing quasi-particle excitations in molecules. 49 However, the implementation of the Fock operator in the iterative (Lanczos) calculation of the spectrum (as it would be needed for a hybrid functional NEXAFS calculation) would increase severely the computational requirements of the present plane-wave method,28 while the use of a Gaussian basis set could not help because the delocalized states at high energy would not be well represented. Similarly, if one is willing to proceed through a direct calculation of the states, only the first unoccupied ones could be conveniently obtained since the description of the continuum portion of the spectrum up to a relatively low energy would already require thousands of states to be explicitly included. The approach taken here hence appears as a good compromise between accuracy and computational cost for the description of the main spectral features, bearing in mind that inaccuracies about the ionization threshold are likely expected.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS Computational resources were made available in part by CINECA (application code HP10C3YWUA). REFERENCES

(1) Witte, G.; Wöll, C. J. Mater. Res. 2004, 19, 1889−1916. (2) Sirringhaus, H.; Brown, P.; Friend, R.; Nielsen, M.; Bechgaard, K.; Langeveld-Voss, B.; Spiering, A.; Janssen, R.; Meijer, E.; Herwig, P.; de Leeuw, D. Nature 1999, 401, 685−688. (3) Koch, N. ChemPhysChem 2007, 8, 1438−1455. (4) Rand, B. P.; Cheyns, D.; Vasseur, K.; Giebink, N. C.; Mothy, S.; Yi, Y.; Coropceanu, V.; Beljonne, D.; Cornil, J.; Brédas, J.-L.; Genoe, J. Adv. Funct. Mater. 2012, 22, 2987−2995. (5) Dey, S.; Pal, A. J. Org. Electron. 2012, 13, 1499−1505. (6) Yokoyama, D.; Sakaguchi, A.; Suzuki, M.; Adachi, C. Org. Electron. 2009, 10, 127−137. (7) Stöhr, J. NEXAFS spectroscopy; Springer-Verlag: Berlin, 1996. (8) Brouder, C. J. Phys.: Condens. Matter 1990, 2, 701−738. (9) Solomon, J.; Madix, R.; Stöhr, J. Surf. Sci. 1991, 255, 12−30. (10) Hu, W.; Tao, Y.; Hsu, Y.; Wei, D.; Wu, Y. Langmuir 2005, 21, 2260−2266. (11) Sohnchen, S.; Lukas, S.; Witte, G. J. Chem. Phys. 2004, 121, 525−534. (12) Betti, M. G.; Kanjilal, A.; Mariani, C. J. Phys. Chem. A 2007, 111, 12454−12457. (13) Hanel, K.; Sohnchen, S.; Lukas, S.; Beernink, G.; Birkner, A.; Strunskus, T.; Witte, G.; Wöll, C. J. Mater. Res. 2004, 19, 2049−2056. (14) Floreano, L.; Cossaro, A.; Gotter, R.; Verdini, A.; Bavdek, G.; Evangelista, F.; Ruocco, A.; Morgante, A.; Cvetko, D. J. Phys. Chem. C 2008, 112, 10794−10802. (15) de Oteyza, D. G.; Sakko, A.; El-Sayed,; Goiri, E.; Floreano, L.; Cossaro, A.; Garcia-Lastra, J. M.; Rubio, A.; Ortega, J. E. Phys. Rev. B 2012, 86, 075469. (16) Lanzilotto, V.; Sanchez-Sanchez, C.; Bavdek, G.; Cvetko, D.; Lopez, M. F.; Martin-Gago, J. A.; Floreano, L. J. Phys. Chem. C 2011, 115, 4664−4672.

■

CONCLUSIONS Taking into account pentacene as a relevant test case, we have demonstrated the effectiveness of DFT approaches based on the transition potential approximation to describe the dichroism in the NEXAFS spectrum of aromatic molecules, 6637



Article

(17) Bavdek, G.; Cossaro, A.; Cvetko, D.; Africh, C.; Blasetti, C.; Esch, F.; Morgante, A.; Floreano, L. Langmuir 2008, 24, 767−772. (18) Slater, J. C.; Mann, J. B.; Wilson, T. M.; Wood, J. H. Phys. Rev. 1969, 184, 672−694. (19) Janak, J. F. Phys. Rev. B 1978, 18, 7165−7168. (20) Triguero, L.; Pettersson, L. G. M.; Ågren, H. Phys. Rev. B 1998, 58, 8097−8110. (21) Leetmaa, M.; Ljungberg, M. P.; Lyubartsev, A.; Nilsson, A.; Pettersson, L. G. M. J. Electron Spectrosc. Relat. Phenom. 2010, 177, 135−157. (22) Cavalleri, M.; Odelius, M.; Nordlund, D.; Nilssonab, A.; Pettersson, L. G. M. Phys. Chem. Chem. Phys. 2005, 7, 2854−2858. (23) Hetenyi, B.; Angelis, F. D.; Giannozzi, P.; Car, R. J. Chem. Phys. 2004, 120, 8632−8637. (24) Prendergast, D.; Galli, G. Phys. Rev. Lett. 2006, 96, 215502. (25) Pehlke, E.; Scheffler, M. Phys. Rev. Lett. 1993, 71, 2338−2341. (26) Kolczewski, C.; Puttner, R.; Plashkevych, O.; Agren, H.; Staemmler, V.; Martins, M.; Snell, G.; Schlachter, A.; Sant’Anna, M.; Kaindl, G.; Pettersson, L. J. Chem. Phys. 2001, 115, 6426−6437. (27) Taillefumier, M.; Cabaret, D.; Flank, A.-M.; Mauri, F. Phys. Rev. B 2002, 66, 195107. (28) Gougoussis, C.; Calandra, M.; Seitsonen, A. P.; Mauri, F. Phys. Rev. B 2009, 80, 075102. (29) Giannozzi, P.; et al. J. Phys.: Condens. Matter 2009, 21, 395502. (30) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953−17979. (31) Lanczos, C. J. Res. Natl. Bur. Stand. 1952, 49, 33−53. (32) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (33) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993−2006. (34) Makov, G.; Payne, M. C. Phys. Rev. B 1995, 51, 4014−4022. (35) Alagia, M.; Baldacchini, C.; Betti, M. G.; Bussolotti, F.; Carravetta, V.; Ekström, U.; Mariani, C.; Stranges, S. J. Chem. Phys. 2005, 122, 124305. (36) Cabellos, J. L.; Mowbray, D. J.; Goiri, E.; El-Sayed, A.; Foreano, L.; de Oteyza, D. G.; Rogero, C.; Ortega, J. E.; Rubio, A. J. Phys. Chem. C 2012, 116, 17991−18001. (37) Ohta, T.; Fujikawa, T.; Kuroda, H. Bull. Chem. Soc. Jpn. 1975, 48, 2017−2024. (38) Lopata, K.; Van Kuiken, B. E.; Khalil, M.; Govind, N. J. Chem. Theory Comput. 2012, 8, 3284−3292. (39) Campbell, R. B.; Robertson, J. M.; Trotter, J. Acta Crystallogr. 1961, 14, 705−711. (40) Stohr, J.; Sette, F.; Johnson, A. Phys. Rev. Lett. 1984, 53, 1684− 1687. (41) Diebold, U. Surf. Sci. Rep. 2003, 48, 53−229. (42) Floreano, L.; Cossaro, A.; Cvetko, D.; Bavdek, G.; Morgante, A. J. Phys. Chem. B 2006, 110, 4908−4913. (43) Guaino, P.; Carty, D.; Hughes, G.; McDonald, O.; Cafolla, A. Appl. Phys. Lett. 2004, 85, 2777−2779. (44) Rennie, E. E.; Kempgens, B.; Köppe, H. M.; Hergenhahn, U.; Feldhaus, J.; Itchkawitz, B. S.; Kilcoyne, A. L. D.; Kivimaki, A.; Maier, K.; Piancastelli, M. N.; Polcik, M.; Rudel, A.; Bradshaw, A. M. J. Chem. Phys. 2000, 113, 7362−7375. (45) Ågren, H.; Vahtras, O.; Carravetta, V. Chem. Phys. 1995, 196, 47−58. (46) Carrascal, J.; Ferrer, J. Phys. Rev. B 2012, 85, 045110. (47) Blase, X.; Attaccalite, C.; Olevano, V. Phys. Rev. B 2011, 83, 115103. (48) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158−6170. (49) Refaely-Abramson, S.; Sharifzadeh, S.; Govind, N.; Autschbach, J.; Neaton, J. B.; Baer, R.; Kronik, L. Phys. Rev. Lett. 2012, 109, 226405.

6638


Azimuthal Dichroism in Near-Edge X-ray Absorption Fine Structure

Recommend Documents