Light Absorption of Contacted Molecules - American Chemical Society

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Light Absorption of Contacted Molecules: Insights and Impediments from Atomistic Simulations Thomas A. Niehaus,*,†,‡ Thomas Frauenheim,§ and Björn Korff‡,§ †

Institut Lumière Matière, CNRS UMR5306, Université Lyon 1, Université de Lyon, 69622 Villeurbanne CEDEX, France Department of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany § BCCMS, University of Bremen, 28359 Bremen, Germany ‡

ABSTRACT: The absorption spectrum of a prototypical organic molecule (hydroquinone) in contact with semi-infinite metallic nanowires is investigated by means of atomistic parameter-free simulations. We employ an open boundary Liouville-van Neumann approach in conjunction with approximate time-dependent density functional theory to reveal changes in absorbance with respect to the gas phase spectrum. It is found that molecule−metal hybridization leads to state specific shifts in the band maxima and significant broadening. In addition, the line shape acquires a nonsymmetrical Fano character for strong molecule−metal coupling. As the strong plasmonic response of the metal leads overshadows molecular excitations, we show that construction of a differential cross section for the junction with and without embedded molecule effectively uncovers hidden spectral features.

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INTRODUCTION Metal−molecule hybrid systems play an important role in the growing fields of nano-optics1 and nanoelectronics.2 This is due to the tunability of collective plasmonic excitations in the metal with associated strong field enhancements in its proximity. Molecules, on the other hand, offer rich diversity in geometrical and electronic structure. The coupling of both leads to improved means of characterization like in surface enhanced Raman scattering (SERS)3 and to novel technologies as molecular electronics. The latter deals with electronic transport through metal−molecule−metal bridges and has been extensively studied in the past.4 Questions of reproducibility and control remain however and hamper the commercialization of such electronic devices. Instead of application of static electric fields like in conventional field effect transistors, irradiation of the junction by UV−visible light promises additional means of control.5 This is for example realized in molecular photoswitches,6 where electronic excitation leads to changes in the molecular structure and transmission. Light absorption and emission may also be used to characterize the junction in addition to elastic and (phonon related) inelastic tunneling spectroscopy.7 Molecular fingerprints have already been identified in electroluminescence from scanning probe setups8−12 or in Raman scattering from break junctions.13−15 The optical properties of metal−molecule hybrids have been the topic of several theoretical studies in the past. The response of larger metal nanoparticles is usually well described at a classical level.16 Hence multiscale approaches combining electrodynamics with first-principles electronic structure © XXXX American Chemical Society

calculations for the molecule were successfully used to explain SERS.17,18 In these studies often time-dependent density functional theory (TD-DFT)19 is used in the quantum part, because it provides an excellent trade-off between accuracy and numerical efficiency. For smaller metal particles and/or stronger coupling to the molecule a full quantum description of the compound system is required.20 In the mentioned studies the focus is on finite systems. In order to describe electronic transport in molecular junctions one has to deal with open boundary conditions that allow for electrons entering and leaving the central device region. This scenario is effectively treated using the nonequilibrium Green’s function (NEGF) formalism.4 In this framework, pioneering theoretical work on illuminated junctions has been put forward by Nitzan and Galperin.21−23 Their model based approach addresses light absorption and emission as well as Raman scattering in biased junctions in a unified framework. Recently, Galperin and Tretiak derived a connection between NEGF and TD-DFT in the frequency domain to determine absorption spectra.24 This formalism was however not yet applied to realistic junctions. In a very recent study, NEGF is combined with time domain TDDFT for the prototypical Au−benzene−Au junction.25 The results show clear broadening of the absorption due to metal− molecule binding compared to the spectrum for the isolated molecule. Recent efforts to treat the radiation field in second quantization which leads to an electron-photon self-energy that Received: December 17, 2015 Revised: February 9, 2016

A

DOI: 10.1021/acs.jpcc.5b12355 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C fits naturally in the NEGF formalism should also be mentioned. First applications of this idea in a TD-DFT context have already appeared.26 While the theoretical framework to describe irradiated molecular junctions is in place, there are few studies which apply these techniques to study realistic atomistic models. Our goal here is to fill this gap and provide an investigation for the absorption spectrum of a hydroquinone molecule contacted to an aluminum nanowire for varying polarization of the incoming light and different contact distances. In this way the influence of metal−molecule coupling on the absorption spectrum can be systematically studied. On the way several practical problems have to be overcome which have not yet been documented in the literature.

Figure 1. Hydroquinone coupled to two Al nanowires for several lead distances. Shown are only atoms in the device region.

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ensure a smooth transition of the potential from the central region to the leads. Similar systems have been extensively studied in the context of molecular electronics. Results for static and time-dependent transport simulations are available and provide an additional characterization of the junction.29,32−34 In order to investigate the dependence of the molecular absorption on the environment provided by the metallic contacts, we perform calculations for different molecule-lead distances d as shown in Figure 1. Starting from DFTB optimized geometries for infinite contact separation, the simulation models have been obtained by rigidly shifting the lead atoms without further structural relaxation. Clearly, such high-symmetry structures do not necessarily reflect the conditions in real measurements. In break junction transport experiments, as an example, several configurations are typically realized and lead to differing conductance values. In addition, deprotonation of the molecule may occur at shorter lead distance to ensure more stable metal−molecule binding.35 On the positive side, the idealized geometries studied here enable a systematic and transparent analysis and may be replaced by more realistic models in the future. In order to compute the photoabsorption cross section we proceed as follows. First, the device region is initially perturbed by a weak external electric field E⃗ (t) of short duration (deltakick), which populates the full manifold of excited states.36 Appreciable molecular absorption is expected only for excitation along the long or short axis of hydroquinone. For light polarization in the x direction (see Figure 1) the field is realized through the boundary conditions for the solution of the Poisson equation, i.e., a time-dependent bias V = −Ex(t)d is applied to the junction. Due to technical constraints, the same approach is not possible for excitation in the y direction. [In our current implementation Dirichlet boundary conditions may be set on the yz plane of the Poisson box but not on perpendicular planes.] Instead we resort to the electric dipole approximation which should be a reasonable approach for radiation in the visible range of moderate strength. We hence add the following term to the DFTB Hamiltonian

METHOD In order to describe the electron dynamics of a molecular system contacted with two semi-infinite metallic leads, we use the Liouville-van Neumann approach introduced by Chen and co-workers.27 Originally, this method was developed in the context of DFT and later adapted to the approximate density functional based tight-binding (DFTB) method.28 A detailed account of this implementation which is also used in the present study is given elsewhere.29 Similar to implementations of static transport in the Landauer framework, the simulation model is divided into a central device part and two leads (L,R) which are periodically replicated to infinity on both sides of the finite device region. At t = 0 the full system is in equilibrium at a common chemical potential. Applying a time-dependent external field or bias V(t) then leads to changes of the electron density according to (in atomic units) i

∂ σ(t ) = [H(t ), σ(t )] − i ∑ Q α(t ) ∂t α = L,R

(1)

Equation 1 describes the time evolution of the reduced Kohn−Sham density matrix σ(t) for the device region. The matrices Qα(t) account for all effects introduced by the metallic leads, including the shift and broadening of molecular orbitals (MO) as well as the possibility of electrons leaving and entering the device region. An explicit expression for Qα(t) based on the Keldysh nonequilibrium Green’s function formalism was derived in ref 27 in the wide band limit. It involves the surface Green’s function of the leads, the lead-molecule coupling, and the time-dependent bias. The Qα(t) are therefore not just empirical parameters but explicitly include details of the electronic structure for the computational model at hand. At each time step the density matrix σ(t) is used to compute the electron density ρ(t), followed by solution of the Poisson equation to provide a consistent potential in the device region. This potential is used to update the DFTB Hamiltonian H(t) during the propagation.29 A minimal set of four pseudoatomic basis functions are used to represent the heavy elements apart from hydrogen (one basis function) and the PBE exchangecorrelation functional30 was used in the construction of the Hamiltonian.28,31 The simulation models used in the present study are depicted in Figure 1. We consider a hydroquinone molecule that is symmetrically positioned in between Al nanowires of finite cross sections. The simulation cell for the (periodically repeated) leads includes 72 Al atoms while the device region consists of the molecule and 36 additional Al atoms. This is to

ΔHμν = −Ey(t )⟨ϕμ|rŷ |ϕν⟩

(2)

1 ≈− Ey(t )Sμν(RA , y + RB , y); μ ∈ A , ν ∈ B (3) 2 where ϕμ,ϕν denote atomic orbitals, r̂ is the position operator, S is the overlap matrix, and R⃗ N is the position vector of atom N. The approximate form eq 3 avoids the explicit evaluation of dipole matrix elements. For static electric fields it has already been used earlier in the DFTB context.37 Equation 1 is subsequently integrated with a time step of 5 as using a fourth order Runge−Kutta method for a total B

DOI: 10.1021/acs.jpcc.5b12355 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C simulation time of 70 fs. The external field leads to changes in the electron density which we estimate using Mulliken charges 1 2

qA (t ) =

the irreducible representation, n indexes states of same representation, and p denotes the direction of the transition dipole. States at the TD-DFTB and TD-PBE level carry the same label if they coincide in MO composition. It turns out that TD-DFTB and TD-PBE are in excellent agreement below 7.5 eV. Above this value, the 5Byu state does not show up in the TDDFTB spectrum, because it involves polarization functions on the hydrogen atoms not present in the basis set. In addition, the states of A symmetry have no oscillator strengths. This latter artifact could in principle be remedied by a recent extension of the TD-DFTB method.43 Since these higher excited states are not essential for the further discussion, we continue with the present scheme. Contacted Case: Excitation Perpendicular to Transport Direction. We now turn to the results for the contacted molecule and first discuss the case of excitation with an electric field in the y direction. The inset of Figure 3 shows the

∑ ∑ (σμν(t )Sνμ + σνμ(t )Sμν) μ∈A

ν

(4)

These charges are used to evaluate the induced dipole moment μ⃗ (t ) =

∑ (qA (t ) − qA (0))RA⃗ A

(5)

where the sum runs over all atoms in the device region. Numerical Fourier transforms then lead to the dipole polarizability αii(ω) = μi(ω)/Ei(ω) and the absorption cross section σ(ω) according to38 σii(ω) =

4πω Im[αii(ω)], i ∈ {x , y} c

(6)

By virtue of the terms Qα in eq 1, this approach takes the coupling of the finite device region to the infinitely extended metallic contacts fully into account.

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RESULTS AND DISCUSSION Gas Phase Spectrum. Before discussing the contacted system, we shortly validate the accuracy of the approximate DFTB method for the isolated hydroquinone molecule in the gas phase. To this end the spectrum is computed using frequency domain TD-DFTB40,41 as implemented in a development version of the dftb+ code.42 Solving for the linear density response in the frequency domain by means of the RPA (a.k.a. Casida) equations offers important information. It allows for a straightforward characterization of individual excited states in terms of molecular orbital (MO) contributions and point group symmetries. Such calculations are equivalent to the real time propagation of eq 1, in the sense that they provide the same spectrum, if the device region consists of only the molecule and the contact terms Qα are neglected. We compare the TD-DFTB results to first-principles TDPBE with a basis set of triple-ζ quality with polarization functions (TZVP) in Figure 2. Hydroquinone possesses C2h symmetry and features dipole allowed Au and Bu singlet excited states. The former are polarized in z-direction and only very weakly allowed. For later reference we label states according to the scheme nIp based on the TD-PBE results. Here I indicates

Figure 3. Differential absorption cross section Δσ(ω) for excitation in y-direction at different contact distances. Inset: Cross section for the full device σM+C(ω) and contacts only σC(ω) at d = 13.88 Å. The stick spectrum is obtained from TD-DFTB calculations for the molecule in the gas phase.

absorption spectrum for distance d = 13.88 Å. The response of the device region is dominated by the absorption of the metallic region with a broad feature around 6 eV. Due to the limited size of the simulation box, a full plasmon is not yet fully developed although the excited states in this energy region show already contributions from a large number of single-particle transitions.44 Superimposed are signatures of molecular absorption at 4.33 eV (1Byu), 6.80 eV (4Byu), and 7.88 eV (6Byu) which correspond to the y-polarized states of the isolated molecule. Increasing the device region to include larger fractions of the metallic leads would render the detection of molecule specific signatures even more difficult. Using a minimal device region of molecule plus only few metal atoms as done in ref 25 only masks this principle problem. The finite cross section of a laser spot will always excite also the contacts in a nanojunction which overshadows the molecular response. To circumvent this problem, we compute the differential absorption cross section Δσ = σM+C − σC. Here σM+C is the cross section for the full device and σC is the one for the device at the same contact distance but without embedded molecule. Figure 3 shows that this approach effectively uncovers the molecular features. For large contact distance, Δσ(ω) approaches the spectrum of hydroquinone in the gas phase. In this case the width of the peaks arises solely from the finite propagation time in the simulations. For smaller lead distances,

Figure 2. Absorption spectrum of hydroquinone in the gas phase at the TD-DFTB level compared to TD-DFT results with the PBE functional and TZVP basis set. Peak spectra have been Lorentzian broadened. TD-DFT calculations have been performed with the Turbomole code.39 C

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Figure 4. Participating MO in the dominant single particle transition of the excited states 1Byu and 4Byu for the isolated (left of each graph) and the contacted case (right of each graph, d = 9.28 Å). An isovalue of 0.01 was used in all cases.

conditions play an important role in this case and complicate the theoretical description considerably. The inset of Figure 5

the MO start to overlap with the metallic states, giving rise to energetic shifts and broadening of discrete molecular states into resonances. This in turn leads to modified peak positions and additional broadening in the absorption spectrum. Going from d = 19.88 to 9.28 Å, the state 4Byu shifts by 0.05 eV and broadens by 0.04 eV (full width at half-maximum), while the state 6Byu even shifts by 0.41 eV and broadens by 0.10 eV. Both states develop a blueshifted sideband at smaller lead distance. The lowest state 1Byu loses considerable strength at d = 9.88 Å and diminishes completely at d = 9.28 Å. Given that fluorescence usually occurs out of the lowest excited state according to Kasha’s rule, our calculations predict a quenching of radiative return to the ground state in this system. In order to rationalize these changes, we compute the spectrum using the frequency domain TD-DFTB method for a finite cluster which consists of the device region only. Because the infinite leads are not properly accounted for in these calculations, the spectrum (not shown here) differs from the one depicted in Figure 3 obtained with the correct open boundary conditions. Still the spectra are similar enough to extract and identify the single particle states that contribute most significantly. Figure 4 presents the relevant MO for the 1Byu and 4Byu state with and without the lead. Even at a distance of d = 9.28 Å the MO of the contacted system bear a strong resemblance with the ones of the isolated molecule. The state 1Byu is characterized as a π → π* transition from the highest occupied MO (HOMO) to the lowest unoccupied MO (LUMO) of hydroquinone. The LUMO remains largely unchanged upon coupling to the Al nanowire while the HOMO exhibits considerable hybridization with metal states. The reverse is true for the 4Byu state. Here the electron state LUMO+1 hybridizes, whereas the hole state HOMO−1 is unaffected. In both cases the previously observed reduction of oscillator strength for stronger coupling can be understood to originate from the significantly reduced overlap between initial and final MO. We attribute the negative signal in the differential cross section (Figure 3) around 6 eV to a similar effect. This spectral region is dominated by absorption of the metallic nanowire. Coupling to the molecule leads to increased delocalization of metal states and reduced absorption in the compound system. Contacted Case: Excitation in Transport Direction. Next, we discuss the absorption characteristics for light polarized in the x direction. As we will see, the open boundary

Figure 5. Absorption cross section σred(ω) from the reduced dipole moment (see main text) for excitation in the x direction at different contact distances. Inset: Total cross section for the full device σtot(ω), cross section due to displacement current σdis(ω) and corrected cross section σcor(ω) all at d = 9.28 Å.

shows the cross section which is obtained by direct application of eq 6 as before (labeled σtot(ω) in the figure). The spectrum features extended regions of negative values for σtot(ω), which should not be interpreted as signifying light emission in the junction. Instead, the time-dependent electric field leads to a displacement current, which involves a constant charging and decharging of the metallic part in the device region. Computations of the frequency dependent admittance Y(ω) for structurally similar junctions indeed show that transport is capacitive over a large energy range.33,34 In this way a timedependent dipole moment develops, which is out of phase with the external field and leads to the negative regions in σtot(ω). Since the displacement current is not associated with electronic absorption, one needs to disentangle the dipole moment due to polarization from the one due to lead charging. This can only be achieved with additional approximations. Thinking about the junction as a nanocapacitor, we evaluate the total charge on the plates according to Q̂ l / r(t ) =

∑ A∈l/r

D

qA(t )

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Although absorption spectroscopy of molecular junction networks has been experimentally demonstrated,49 the measurement of light absorption at the single molecule level is technologically demanding. Setting questions of light focusing and junction heating aside, our simulations provide evidence that the spectrum is dominated by metal absorption which make molecular fingerprints difficult to detect. The theoretical description is further complicated by the reactive nature of the device that require corrections for displacement currents. Once these difficulties are overcome, optical junction spectroscopy holds great promise to provide useful information about metal−molecule−metal hybrids. Our simulations indicate a strong dependence of the absorption profile on the junction geometry, which could be used in conjunction with elastic and inelastic transport measurements for an improved characterization of molecular devices. In this context the absorption of contacted molecules under bias becomes relevant. Efforts to perform simulations in this nonequilibrium regime are currently under way.

Here the sum runs over the Al atoms of the nanowire on the left (l) or right (r) side of the device region. As expected for this symmetrical device, we find that overall charge neutrality, i.e., Q̂ l = −Q̂ r, holds to very high precision in our numerical simulations. Defining also R̂⃗ l/r = ∑A∈l/r R⃗ A, we arrive at μ⃗ dis = Q̂ l R̂⃗ l + Q̂ r R̂⃗ r for the dipole moment due to the displacement current. Inserting this expression into eq 6 gives rise to σdis(ω) (Figure 5) which is indeed strictly negative. Admittedly, this approach is motivated by classical considerations. It should be less accurate for large inhomogeneities of the lead material or strong metal-molecule coupling. In the latter case the division of the device region into separate parts is less well-defined. We are now in the position to investigate changes in the charge density only due to electron−hole excitations. The dipole moment μ⃗cor = μ⃗ tot − μ⃗ dis gives rise to the corrected cross section σcor(ω) in the inset of Figure 5. We find that the absorption spectrum after correction is now positive over the full frequency range. This result shows that the displacement current contributes significantly to the computed spectrum and is responsible for the spurious negative features. Unfortunately this correction scheme is not quantitative. Attempts to form the differential cross section based on σcor(ω), as done for excitation along the y axis, lead to large numerical noise for short contact distances. This is related to the mentioned approximations for the displacement current contribution. In order to single out molecular spectral features we follow a different route. Instead of computing μ⃗ (t) for the full device region according to eq 5, we restrict the sum to atoms in the molecule. The spectrum based on this reduced dipole is free of artifacts due to lead charging as shown in Figure 5. On the downside it does not correspond to an observable that is easily accessible in experiment. With this grain of salt, inspection of Figure 5 reveals that the selection rules for the isolated hydroquinone remain intact for the contacted system. Only the states 2Bxu at 5.36 eV and 3Bxu at 6.51 eV show significant oscillator strength for excitation along the x-axis. The latter state exhibits a red shift of 0.17 eV and significant broadening of roughly 0.5 eV for the shortest lead distance, while the 2Bxu diminishes completely. An interesting finding is related to the line shape of the 3Bxu state. Starting with a distance of d = 13.88 Å, it develops into a nonsymmetrical Fano-like form. This feature is attributed to the coupling of the discrete molecular states to the continuous set of metal states. Fano lineshapes have been reported earlier for systems with strong exciton− plasmon coupling.45−48 Even though the device region in the present simulation consists only of a few metal atoms, the open boundary conditions naturally support the emergence of these unusual spectral features.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33 (0)47243 1571. Fax: +33 (0)47243 1130. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Deutsche Forschungsgemeinschaft (SPP 1243, “Quantum transport at the molecular scale”) is gratefully acknowledged.

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REFERENCES

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SUMMARY In summary, we employed a Liouville−van Neumann approach in conjunction with an approximate TD-DFT method to investigate the optical absorption spectrum of a benzene derivative in close contact with metallic reservoirs. As expected, molecular excited states undergo energetic shifts as well as significant broadening if the molecule-lead distance is reduced. For the shortest distances even a complete quenching of absorption may occur. These changes with respect to the gas phase spectrum are highly nonuniform and state specific. Bands can either shift to the red or to the blue and the obtained lineshapes differ significantly from a simple Lorentzian broadening due to molecule-lead coupling. This highlights the necessity for atomistic calculations of irradiated junctions. E

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DOI: 10.1021/acs.jpcc.5b12355 J. Phys. Chem. C XXXX, XXX, XXX−XXX