ARTICLE pubs.acs.org/JPCC
Enhancement of Ultraviolet Photoinduced Energy Transfer Near Plasmonic Nanostructures Ioannis Thanopulos,*,† Emmanuel Paspalakis,‡ and Vassilios Yannopapas‡ † ‡
Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens 116 35, Greece Department of Materials Science, School of Natural Sciences, University of Patras, Patras 265 04, Greece ABSTRACT: We show that photoinduced intermolecular energy transfer can be greatly enhanced in the UV frequency range in proximity to plasmonic metamaterials. The rate of the resonance energy transfer for a molecular donor-acceptor system with absorption and emission transition lines in the vacuum UV near metal-coated dielectric nanospheres is calculated by a rigorous first-principle electromagnetic Green’s tensor technique. Exemplary donor-acceptor systems based on fullerenes and organic compounds are discussed. The electronic transition spectra of the donor-acceptor molecules are obtained by ab initio calculations.
’ INTRODUCTION Photoinduced intermolecular energy transfer, often known as resonance energy transfer (RET), is a fundamental photophysical process whereby an electronically excited donor molecule transfers its excitation energy to an acceptor molecule by a nontrivial mechanism.1 It is often distinguished between two cases, namely, (radiationless) short-range transfer, which is also called F€orster transfer2 and (radiative) long-range transfer. The radiationless transfer is predominant when the distance R between the donor and the acceptor molecules is small compared with the wavelength λ of the light related to the energy transfer, R/λ , 1, and the corresponding free-space transfer rate behaves as R-6 due to the instantaneous (longitudinal) Coulombic interaction between the donor and acceptor.1 In the case that R/λ . 1, the radiative longrange transfer dominates over the radiationless process, and the observed R-2 dependence of the transfer rate can be regarded as being the result of emission and reabsorption of real (transverse) photons. The radiative and radiationless energy transfer, however, are special cases of a unified theory within a rigorous approach in the framework of multipolar quantum electrodynamics.3 Metamaterials are manmade structures that offer unprecedented control over the propagation of electromagnetic (EM) waves by proper engineering of the effective electric permittivity and magnetic permeability. Exotic phenomena that are not met in naturally occurring materials such as negative refraction, nearfield amplification, superlensing, and cavity super-resonance have been demonstrated with the advent of metamaterials.4 Because the operation of metamaterials is based on electric and magnetic resonances of its unit elements, EM radiation becomes strongly localized in small volumes in such cases. In the presence of metamaterials, the RET can thus change from its free-space value, offering the possibility for control of the RET, with respect to potential applications, for example, in high-efficiency light-harvesting r 2011 American Chemical Society
systems,5 quantum computing,6 and quantum networks,7 just to name a few. In this work, we predict a significant enhancement of the RET in the UV 5-7 eV photon energy range in the presence of a 2D array of metal-coated dielectric nanospheres shown in Figure 1. Our results are based on rigorous calculations of the EM Green’s tensor.8,9 We also present molecules with absorption and emission in the UV frequency range, as potential candidates for demonstrating the RET enhancement as discussed here. The corresponding transition spectra are obtained by ab initio theory. We note that the change of the RET rate within a suitable environment, albeit different than metamaterials, has been investigated experimentally and theoretically in previous works.10-14
’ RESULTS AND DISCUSSION The RET transfer rate w for a donor-acceptor pair of molecules A and B in the presence of dispersing and absorbing media, where initially (finally) the molecule A is in the excited (ground) state and the molecule B is in the ground (excited) state, is given, within second-order perturbation theory, by15 Z abs w ¼ dωwðωÞσem ð1Þ A ðωÞσ B ðωÞ with wðωÞ ¼
2π ω4 † jdA 3 GðrA , rB , ωÞ 3 dB j2 p2 ε20 c4
ð2Þ
abs In eqs 1 and 2, σem A (ω) and σB (ω) denote the (one-photon) emission spectrum of molecule A and the (one-photon)
Received: July 15, 2010 Revised: January 13, 2011 Published: March 02, 2011 4370
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Figure 1. Metal-coated dielectric nanosphere (a) and a 2D array of such spheres [side-view in scheme (b) and top-view in scheme (c)] used in this work (color online).
absorption spectrum of molecule B respectively, and dA( dBA) and dB( dBB) stand for the electronic electric dipole vectors of the transition between the lower and the upper electronic states in molecules A and B, respectively. In the spirit of second-order perturbation theory used for the derivation of the above abs equations, σem A (ω), σB (ω), dA and dB are considered in free 15 space. In eq 2, G(rA,rB,ω) is the classical EM Green's tensor between the position ra of molecule A and the position rB of molecule B. We however note that the above approach is not valid in the case of strong coupling between a molecule and a metallic nanoparticle. However, as recent studies have indicated,16 for molecular electric dipoles of about 1-2 au (here and below au stands for atomic units), as it is the case in this study (below), the weak-coupling assumption in general holds at molecule-nanoparticle distances larger than 5-6 nm. We thus consider our discussion below to apply when the distance of each molecule from the nanostructure is larger than 5-6 nm because, beyond that value, it can be justifiably assumed that eq 2 holds in our case. We also note that, in surface-enhanced Raman spectroscopy (SERS), which involves absorption and emission of single photons in the presence of nanoparticles similarly to the process discussed here, the SERS effect is a linear optical effect, although the local field enhancement is highly nonlinear.17 Therefore, we do not expect that local field enhancement would invalidate the use of eq 1; in particular, at distances larger than 5-6 nm. Below, we focus our discussion on the enhancement of w(ω), relatively to its free-space value w0(ω), defined as w ~ ðωÞ
wðωÞ w0 ðωÞ
ð3Þ
which we denote as RET in Figures 2 and 3 for simplicity; in eq 3, w0(ω) is given by15 2 !2 2π ω3 ω 2 G w0 ðωÞ ¼ 2 K ð4Þ c p 4πε0 c3 with ! ω i 1 1 G G ðqÞ ¼ exp ðiqRÞ 2 2 - - 3 3 c qR qR q R
ð5Þ
when RB B rA - B r B and K = dBA 3 dBB - 3((dBA 3 RB)/(R)) ((dBB 3 RB)/(R)), for real-valued electric dipole transition moments. Evidently, the orientations of the dBA, dBB, and RB are crucial for calculating the wh0 for a specific orientation of the
molecules A and B relative to the 2D array of nanospheres, as given in Figure 1. In Figure 1, we schematically show a 2D array of touching metal-coated dielectric nanoparticles. The dielectric core in each nanosphere [scheme (a)] has a radius Sc and the dielectric constant equals ε = 12, corresponding to semiconducting materials. S = 21.9 nm stands for the total nanosphere radius. The plasmonic (metallic) shell around the dielectric core has a thickness of S - Sc = 4.38 nm. The dielectric function of the shell is provided by a Drude-type electric permittivity given by εðωÞ ¼ 1 -
ω2p ω2 þ iωγ
ð6Þ
where pωp = 8.99 eV is the bulk plasma frequency and ‘pγ = 0.45 eV is the loss factor; these values are modeled close to the corresponding values for gold. To calculate w~(ω) between two molecules in the presence of a metal-coated nanosphere or a plane of such spheres we need to calculate the corresponding EM Green's tensor appearing in eq 2. For the case of a single metal-coated sphere, the formalism is based on the Mie scattering problem8 and for the case of the lattice of nanospheres the Green's tensor is calculated on the basis of a layer-multiple-scattering technique.9,18 In Figure 2, we show w~(ω) due to the presence of a single metal-coated dielectric nanosphere described above, as a function of both frequency (photon energy) and distance (of each molecule from the sphere). It is evident that around 6.5 eV, w(ω) is about 7 times greater than the corresponding vacuum value. This is due to the excitation of surface plasmons at the metallic nanoshell. Actually, there are two (dipolar) surface plasmons for a metallic nanoshell;19,20 a low-frequency particle-like resonance in which case the surface plasmon is localized around the metalvacuum interface and a higher-frequency cavity-like resonance where the surface plasmon is localized around the metal-dielectric interface. Because of the high permittivity of the dielectric core and the small thickness of the plasmonic nanoshell, the particle-like resonance lies in the near-infrared regime and it will not concern us here. We note, in addition, that the use of coreshell metal particles, in contrast to pure metallic nanostructures, at the particular choice of material parameters (high-index core material and small shell thickness) provides maximum RET enhancement for realistic laboratory conditions. Also, the dependence of the w~(ω) maximum on the dielectric core and the nanoshell thickness allows for tuning of the RET enhancement to a desired spectral region. We can further increase w ~(ω) for two molecules when we employ a lattice of touching metal-coated dielectric nanospheres as described above. This is evident from Figure 3 where w(ω) can become about 15 times larger than the corresponding value in free-space when both molecules are placed close to the plane of spheres. This is due to the fact that a periodic plane of such spheres acts as near-field metamaterial lens for p-polarized EM modes.4 In this case, the near-field emitted by a point source (in our case an excited molecule) placed at one side, say the left side, of the plane of spheres, is amplified within the plane when transmitted to a receiver at the right side (in our case a molecule in ground state). In this way, the metamaterial (plane of spheres) compensates the decay of the near-field in vacuum and enables the efficient RET between two molecules despite the considerably large distance between them (always compared with the case where the molecules are placed in free space). The w(ω) can be 4371
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Figure 2. Enhancement of RET with respect to its free-space value, w~(ω), as function of photon energy and distance from the nanosphere surface, for a pair of molecules separated by a single metal-coated dielectric nanosphere lying in the middle of the way between the two molecules (color online). The sphere radius is 21.9 nm and the plasmonic shell thickness is 4.38 nm. Figure 4. (color online) Upper part: The C60 (left) and C76 (right) fullerenes. Lower part: The pyrene (left) and dithiapyrene (right) organic molecules. Hydrogen (white), carbon (gray), and sulfur (gold) atoms are shown.
Table 1. Spectroscopic Data for Strong (Oscillator Strength fB g 0.1) Singlet Absorption Lines (with 3-fold Degeneracy) of C60 in the 4-7 eV Frequency Range E/eV
4.08
5.30
6.38
dB /a.u. -0.58 0.80 -1.02 1.31 -1.23 1.60 -1.21 1.40 -1.70 x
dBy/a.u.
0.64 1.15 0.55 0.90 -1.35 -1.77 -1.14 0.23
0.83
dBz/a.u. -1.14 0.23 0.83 1.81 1.56 -0.27 -2.06 -1.39 0.33 |d BB|/a.u. 2.03 2.03 2.03 5.79 5.79
Figure 3. Enhancement of RET with respect to its free-space value, w~(ω), as function of photon energy and distance from the surface of a 2D array as in part b of Figure 1 for a pair of molecules, when the 2D array is located halfway between the two molecules (color online). The radius and the metallic shell thickness are as in Figure 2 and the 2D lattice constant is 2 21.9 = 43.8 nm.
further increased if materials with higher dielectric constant are used as a core. We note that the predicted enhancement of RET cannot be rationalized primarily as a cascade energy transfer process,23 including just two RET steps in tandem, because the nanoparticle, or the 2D nanoparticle-array, is not treated as a quantum mechanical system, with two or more levels. Its presence is treated in a classical way through a dielectric function; there is no single dipole attributed to the nanoparticle(s) considered. Of course, one could design a cascade RET process including three molecules, A, B and C, with C being located halfway between A and B, for which the RET rate A f C f B equals numerically, by proper choice of the dipole of molecule C, to the enhanced transfer RET rate A f B due to the presence of the nanoparticle(s) located middle-way between A and B. However, the two approaches cannot be considered in general conceptually equivalent, in our opinion. We now present the absorption and emission electronic line spectra of exemplary molecules with singlet electronic transitions
fB
0.204
0.752
5.79
6.27
6.27
6.27
0.980
in the UV part of the EM spectrum. The spectroscopic data for each emission line are obtained at the optimized geometry of the corresponding excited state. We consider the fullerenes, C60 and C76, and the organic molecules, pyrene and dithiapyrene, shown in Figure 4 as potential candidates for demonstrating the enhancement of the RET as predicted here. These molecules play also prominent role as donor or acceptor units of electronic energy and charge transfer processes24,25 in optoelectronic applications. For, quite often, the electron transfer process from an organic donor to a fullerene acceptor takes place in two steps, with a first RET step, to be followed by a charge transfer process.24 Thus, the two competitive channels, electron transfer versus RET, contribute likely to charge generation in organometallic optoelectronic devices. One might thus take advantage of RET manipulation, either by attempting to enhance its rate, as here, or by controlling its directionality,26 to design such devices more efficiently. The C60 molecule features reduced absorption in the visible spectral region; its absorption line spectrum, however, shows very strong transitions in the UV frequency range between 4 and 7 eV. In Table 1, the spectroscopic data for the strongest, that is with oscillator strength g0.1, singlet transitions in the electronic spectrum of C60 are summarized according to our calculations. Our results are obtained by the time-dependent density functional theory (TD-DFT) at the B3LYP/3-21G* level of theory, as 4372
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Figure 5. x (blue), y (red), and z (green) components of strong, with oscillator strength fB g 0.1 (black), electric dipole absorption moments in C76 from the ground electronic state to singlet electronic excited states in the 5-7 eV frequency range (color online).
Table 2. Spectroscopic Data for Strong (Oscillator Strength fA g 0.1) Singlet Emission Lines of Pyrene and Dithiapyrene in the 5-7 eV Frequency Range pyrene E/eV
5.20
6.14
dxA/a.u. -2.70 -2.63
dithiapyrene 7.02
5.16
5.54
0.00
1.46
0.71
-0.20 -1.88
5.89
6.26
-0.58 -0.95
7.00 1.56
-1.14 -1.00
dyA/a.u.
0.00
0.00
0.00
dzA/a.u.
0.00
0.00
-2.32
0.00
0.00
0.00
0.00
0.00
fA
0.928
1.046
0.920
0.275
0.548
0.557
0.338
0.593
1.88
implemented in the Gaussian 09 electronic structure calculation package,27 with the C60 equilibrium geometry optimized at the same theoretical level. We have also calculated the absorption line spectrum of the chiral C76 molecule,28 which due to its lower symmetry (D2) with respect to C60 (Ih), has more transition lines in the energy range of interest here. Our results on C76 are obtained by ab initio methods at the same level of theory as for the line spectrum of C60. In Figure 5, we present the electric dipole absorption moments between the ground electronic state of C76 and singlet electronic excited states with energy between 5 and 7 eV with oscillator strength fB g 0.1. We note that our calculated spectra are in good agreement with experimental work,22,28 as well as other theoretical work,29,30 albeit at a different level of ab initio theory. The pyrene and dithiapyrene molecules, which are shown on the lower part of Figure 4 respectively, are widely used donor compounds in RET and electron transfer processes.25,31 In Table 2, we summarize the spectroscopic data for the emission lines of the pyrene and dithiapyrene, with oscillator strength fA g 0.1 in the 5-7 eV frequency range of interest to this work. Our results are obtained by ab initio methods at the TD-DFT/ B3LYP/6-31G* level of theory.27 We note that previous theoretical work on these molecules32 has addressed the spectra of lowlying excited states, below 4 eV. In our case, RET values can be obtained using the results of Figure 3 and eq 3 and eq 4 at the transition frequencies ω and for the transition dipoles dBA and dBB, as given in Table 1 and Table 2. For that purpose, we provide in Figure 6, the |G (q)|, in the energy and distance range relevant to the UV enhancement as
Figure 6. |G (q)| for the energy and distance range relevant to the UV enhancement as discussed in this work (color online).
discussed above, needed for obtaining the w0(ω) value at any particular configuration of the two molecules A and B relative to the 2D array. abs The vibronic spectra, σem A (ω) and σB (ω), as required in eq 1, are hardly obtainable theoretically21 for such large molecules as abs discussed here. We thus present the σem A (ω) and σB (ω) in a semiquantitative way by calculating the corresponding spectra, as the sum of Gaussian-shaped bands with 0.1 eV full width at halfmaximum (fwhm), where each band is positioned at the corresponding line transition frequency and weighted according to the corresponding line oscillator strength. The thus obtained abs (normalized) σem A (ω) and σB (ω) for A = {pyrene, dithiapyrene} and B = {C60,C76} are shown in Figure 7. Extended spectral range is demonstrated, for which significant overlap of the emission and absorption spectra of these molecules exists. As noted above, all results presented here are thought of being at molecule-nanosphere distances larger than 5 nm, in order for the weak-field assumption used in the derivation of eq 1 to hold. This implies that the free space emission spectrum σem A (ω) is not broadened by a significant change of the spontaneous emission 4373
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Figure 7. Semiquantitative absorption and emission (normalized) spectra for C60, C76, pyrene, and dithiapyrene, as superposition of Gaussian bands with fwhm = 0.1 eV centered at the positions obtained by ab initio calculations, in proportion to their oscillator strengths (color online).
rate in molecule A due to the presence of the nanostructures at such distances. Nevertheless, a small change of σem A (ω) can be incorporated by calculating the spontaneous emission rate in such cases perturbatively, within the weak-field assumption,15 which can be then added to σem A (ω) in a purely ad hoc fashion. We however could take into consideration such perturbative effects in a purely empirical manner within our approach of calculating the emission spectrum as described above because the fwhm of each band in our treatment is adjusted in an ad hoc way, too.
’ CONCLUSIONS In this work, we show that photoinduced intermolecular energy transfer can be enhanced over an order of magnitude relative to its vacuum value in the 5-7 eV UV frequency range in proximity to plasmonic metamaterials. The RET enhancement is calculated by a rigorous first-principle electromagnetic Green’s tensor technique. Exemplary RET donor-acceptor systems based on fullerenes and organic compounds are introduced and the optical properties of these molecules are obtained by ab initio calculations. The enhancement of RET in the presence of metamaterials has potential applications on the control of electronic energy transfer in numerous optoelectronic devices. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT I.T. acknowledges financial support from the EU-FP7 programme under Grant Agreement No. PIRG03-GA-2008-230943 (COPET). V.Y. acknowledges support from the EU-FP7 programme under Grant Agreement No. 228455-NANOGOLD.
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