Control of Coherences and Optical Responses of PigmentâProtein

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The Control of Coherences and Optical Responses of Pigment-Protein Complexes by Plasmonic Nanoantennae Stefano Caprasecca, Ciro Achille Guido, and Benedetta Mennucci J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00828 • Publication Date (Web): 25 May 2016 Downloaded from http://pubs.acs.org on May 26, 2016

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The Journal of Physical Chemistry Letters

The Control of Coherences and Optical Responses of Pigment-Protein Complexes by Plasmonic Nanoantennae Stefano Caprasecca,∗ Ciro A. Guido, and Benedetta Mennucci∗ Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy E-mail: [email protected]; [email protected]

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gated using a self-consistent multiscale strategy, combining Time-Dependent Density Functional Theory (TD-DFT) calculations with a classical but atomistic polarizable embedding for the the protein matrix and a polarizable continuum model for the metal nanorod. 17–21 The molecular details of the exciton – plasmon interactions at the basis of the experimental observations are unveiled by comparing a hierarchy of models in which the excitonic nature of the system is artificially changed by switching on and off the couplings among the components and allowing either a monomeric or a dimeric description of the minimal excitonic unit. LH2 consists of two transmembrane apoproteins, called the α and β apoproteins, containing 27 bacteriochlorophylls a (BChls) arranged in a highly symmetric way: they form two circular subaggregates, the B800 and B850 rings, where, respectively, weak and strong couplings are in action between the BChl units (see Figure 1). This structure provides the absorption properties of the complex in the low-frequency region with a unique excitonic signature, with the two rings being responsible for the bands at ca. 800 nm and 850 nm, respectively while the emission only occurs from the B850 ring. 23 The whole absorbing system is too large to tackle with a single electronic structure calculation, and we therefore resorted to an excitonic approximation, where the Hamiltonian of the entire system is constructed using excitation energies localized on the different BChls and their interactions, the electronic couplings (see Supporting Information). Various excitonic models are here applied and compared to understand in more details the plasmonic effects on the cascade of physical processes activated by the light absorption. These models can be divided into two sets, M and D. In the models belonging to the M set, where ‘M’ stands for ‘monomer’, each BChl is treated individually at TDDFT level, in the presence of the protein scaffold and of the surrounding BChls, represented classically as polarizable Molecular Mechanics atoms (MMPol), each described by a fixed charge and an isotropic polarizability. 24 Only the first excited state (Qy ) for each BChl is considered, resulting in an exci-

tonic Hamiltonian matrix dimensioned 27×27. It has been argued that this approach may not be valid for the strongly coupled B850 ring, 25 where charge-transfer (CT) excitations can play a role. 26 For this reason, the D set of models, where ‘D’ stands for ‘dimer’, has been devised: the 18 BChls of ring B850 are not studied individually, but are grouped into 9 dimers instead, each dimer comprising two adjacent monomers. The B850 BChls are usually labeled as either α or β, depending on the noncovalent binding to the α and β apoprotein, and they alternate in the B850 ring structure. The αβ couple, usually identified as a “natural” subunit, 27 is used as the basis for the dimeric model. In this case, the two lowest excited states of each B850 dimer, arising from the combination of the Qy states of the two BChls, were considered. The B800 BChls, on the other hand, were considered individually, as in the M set. Both in the M and D sets, three different classes of models were applied. In the first class (models M-All and D-All), the whole 27 × 27 excitonic matrices are diagonalized, obtaining a set of 27 excitonic states. In the second class (models MSep and D-Sep), the excitonic matrices are not diagonalized as a whole; instead, the two submatrices comprising the B800 and B850 units are diagonalized independently. This procedure prevents mixing between different rings, and produces two sets of excitonic states, localized on either ring. In the third class (models M-850 and D-850), only the sub-matrices comprising the B850 units are diagonalized, to obtain 18 excitonic states, while no excitonic treatment is carried out on the B800 BChls, which are left uncoupled. The upper diagonal part of the excitonic matrix obtained for models M is shown in Figure 1 (a). The electronic couplings follow a regular pattern: each B850 unit is strongly coupled (V > 400 cm−1 ) to the two neighboring units, and fairly well coupled (V ≈ 100 cm−1 ) to the two units further away along the ring. The B800 units are only weakly coupled with each other (V ≈ 50 cm−1 ). Inter-ring coupling is also observed, between each B800 unit and the closest unit on the B850 ring (V > 50 cm−1 ). In the D models, each B850 dimer couples strongly


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Table 1: Absorption enhancement due to the presence of the metal in the hotspot configuration, at various distances and tilt angles. The monomer-based calculations are reported. The results for the dimer-based calculations (D = 5 nm, θ = 90) are 19.4, 19.1 and 18.7 for D-All, DSep and D-850 models, respectively. Dist./nm 5 5 5 5 5 5 5 6 7 8 10 15 20

Tilt/deg 0 15 30 45 60 75 90 90 90 90 90 90 90

M-All 0.1 1.1 4.1 8.4 12.8 17.1 19.6 16.8 14.5 12.5 9.5 5.0 2.8

M-Sep 0.1 1.1 4.0 8.1 12.4 16.6 19.1 16.4 14.2 12.3 9.3 4.9 2.8

most completely quenched (AE = 0.1) when the tilt angle θ is 0◦ . Once this angle is increased, the absorption increases too and is enhanced by nearly 20 times when θ = 90◦ . This behavior can be explained in terms of the transition dipoles of the two B800 excitonic states, on which the absorption rates depend. While the excitonic transition dipoles are not affected by the metal, the polarization of the metal NR generates an induced complex transition dipole, µmet . When θ = 0◦ the vectorial combination of the two dipoles is almost null, and the absorption rate is quenched. When θ 6= 0, the total dipole moment is largely increased, and the absorption is enhanced, with a maximum AE at θ = 90◦ . When the metal–LH2 distance is increased, with θ fixed at 90◦ , the absorption enhancement reduces. Interestingly, the NR affects the emission process in a parallel way, so that the combined effect on absorption and emission is synergically enhanced. The fluorescence quantum yield, defined as the ratio between photons emitted and photons absorbed, depends on the interplay of the plasmonic effects on the radiative and non-radiative rates (see the Supporting Information). When considering the two emissive states, S2 and S3 , their radiative and non-radiative rates may behave differently at varying tilt angles and distances. For instance, in the particular configuration studied, both non-radiative ones increase slightly with the tilt angle and decay more than exponentially with the distance (see Figures 4 (a) and (b)). Instead, the radiative decay rates of the two states are very different. In particular, ΓRad is two orders of magnitude larger 3 Rad than Γ2 , and overcomes the corresponding non-radiative rate at θ 6= 0◦ . In such cases the total quantum yield is enhanced by the metal. The individual contributions of the two emissive states to the QY vary when the LH2 system is rotated around its C9 axis; however, the total QY remains unaltered, as one would intuitively expect from symmetry considerations. If we now focus on the optimal tilt angle, and we analyze the distance dependence, we see that the QY shows a maximum at D = 8 nm (QY ≈ 0.75) (see Figure 4 (d)). The synergic behavior of the AE and QY at

M-850 0.3 1.3 4.2 8.2 12.4 16.4 18.7 16.1 13.9 12.0 9.1 4.8 2.7

sorbing), and the D values are exactly equivalent to their M counterparts. The same dimeric picture is instead expected to affect the emissive state, due to the possible role of CT states in the B850 ring. As a matter of fact, a small reduction (12% — 14%) in the QY can be found by comparing the monomerand dimer-based models, with a consequent reduction of the FE. The composition of excitonic states is unaltered. This supports the conclusion that the presence of CT states does not significantly affect the nature and position of the excitonic states, which are equally well described in terms of monomeric or dimeric units. We note, however, that the present approach does not explicitly account for the effect of the metal on the role of CT states as additional dissipative channels: 26 these channels (if active) are implicitly accounted for through the intrinsic non-radiative decay rates, ΓNRad,◦ , which are derived from the experimental QY◦ . Concerning the effect of the LH2 – NR setups, we here focus on the M-Sep model; the results corresponding to the other models are reported in the Supporting Information. If the LH2 system is kept at a fixed distance from the metal surface (5 nm), the absorption is al-


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Figure 4: Top: Radiative and non-radiative decay rates of emissive states S2 and S3 in model M-Sep: (a) scan over tilt angles, distance kept at 5 nm; (b) scan over distances, tilt angle kept at 90◦ . The rates reported on the y axis are in logarithmic scale. Bottom: Quantum yield: (c) scan over tilt angles, distance kept at 5 nm; (d) scan over distances, tilt angle kept at 90◦ . varying distances and tilt angles causes the final FE to be largest at close NR – LH2 distances and θ = 90◦ , in the hotspot configuration, where an enhancement of almost 130 is observed. The fluorescence reduces at smaller angles, and is completely switched off at θ = 0◦ ; it decreases monotonically with the distance. Figure 5 shows a pictorial summary of all the rates of interest for the LH2 alone (a) and for two different LH2 – NR arrangements determined by different values of the tilt angle θ (b, c). The figure refers only for the monomerbased M-Sep model, the parallel analysis for the M-All and M-*50 models is reported in the Supporting Information. The presence of the metal can either quench the absorption, or enhance it with respect to the isolated case, as the circle under ‘Summary’ shows (its area is proportional to the total absorption rate). The symmetry of the states is conserved when the tilt angle is 0◦ , and is instead broken when it moves to 90◦ . In the lat-

ter case, the absorption rate of of one of the two states increases, while that of other reduces, as a result of the metal response. The lines connecting each absorbing to each emissive states shows how the photons absorbed are transferred. In all cases, it is possible to note an asymmetry in such transfer rates, which is due to the different couplings between absorbing and emissive states. Since the transition densities are only marginally affected by the presence of the metal, the transfer rates remain unperturbed when the NR is placed next to the LH2, at any value of the tilt angle. Concerning the emission process, the radiative decay is completely quenched at θ = 0◦ (b), as the arrows down from the emissive states show. Straight and wiggly arrows indicate radiative and non-radiative decays, respectively. Conversely, when θ = 90◦ (c), the asymmetric interaction with the metal causes one of the two emissive states to increase its radiative rate by one order of magnitude (as we also noted when


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S2 (quantum efficiencies are 80% and 5%, respectively). As remarked before, however, any other arrangement obtained through a formal rotation around the C9 axis, while affecting the individual states, would not modify the total absorption and emission properties of the system. At θ = 90◦ , the combined effect of the metal on these properties produces a large FE > 100. We have here presented a QM-based investigation of the excitonic processes in LH2 when interacting with gold nanorods by combining TD-DFT with classical polarizable descriptions of the protein matrix and the NR. By comparing a hierarchy of models where the excitonic units are modified (from the single BChl to the dimer) and selected couplings are switched on or off, we have revealed how the excitons interact with plasmons to give the observed dramatic enhancement in the fluorescence. We have shown that such an enhancement is possible only in “hot-spot” LH2-NR arrangements and a fundamental role is played by the orientation of LH2 with respect to the NR surface. The results also clearly indicate that, even at short LH2 – NR distances, the coherence nature of the excitonic states are only slightly perturbed by the nanorod and their delocalization length is not significantly affected. Finally, the multiscale description has been used to justify the applicability of the classical dipolar analyses commonly used in the interpretation of the experiments. The obtained results suggest that, if a fine tuning of the coherences is desired, a set-up has to be used where the dimension of the nanoparticle is comparable with that of the LH complex: in that case in fact we expect that the plasmonic effects will be able to differentiate among the different chromophoric units on the basis of their relative position and orientation. In such a way a direct effect of the nanoparticle on the composition of the excitonic states will be possible in addition to the ”larger” scale enhancements seen here. As a result, quantum relaxations and dephasing effects, 36–39 which have been neglected here as not affected by the nanoparticle, are expected to become relevant.

the ring plane. The same is true for the emission process. It is worth noting here that the actual orientation of these dipoles is irrelevant. Each pair of dipoles should instead be viewed only as a basis of the vector space containing all vectors lying on the B800 or B850 ring plane. Indeed, this is confirmed by the fact that a rotation around the C9 axis of LH2, while modulating the metal effect on each state of a degenerate pair, does not affect the macroscopic behavior of the system, and both AE and QY remain unaltered upon such rotation. We can then try to model the excitonic properties of the whole LH2 system using a classical approach based on the two pairs of transition dipoles, shown in Figure 5 under ‘Dipoles’. In the absence of the metal (panel a), the absorption rates of the absorbing states are the same, so the photons are captured equally by S11 and S12 . The transfer process to the emissive states, at lower energy, is governed by the electronic couplings (minimally affected by the NR). Particularly, S11 couples more strongly with S2 , vice versa for the S12 and S3 pair. Note however that since S11 and S12 are degenerate, and so are S2 and S3 , the effective transfer rate to the B850 states is the sum of the four rates: k eff = k11→2 + k11→3 + k12→2 + k12→3 . The emission from S2 and S3 , when the metal is not present, is also very low, with an efficiency of 10%. The fluorescence quenching observed with the NR at θ = 0◦ (panel b) can be explained both in terms of quenched absorption (see the shrinking circle areas in Figure 5) and in terms of inefficient emission (QY ∼ 0). 35 In this orientation the axis of the NR is parallel to the C9 axis of LH2, and therefore perpendicular to the molecular transition dipoles, which lie on the ring planes. Consequently, the metal quenches both absorption and emission, as the sum of molecular and metal-induced dipoles is nearly zero. When instead the LH2 is at θ = 90◦ (panel c), the metal main axis lies on the LH2 ring plane and can enhance the total transition dipoles of the four states. In the particular case shown, the dipoles of the two absorbing states S11 and S12 are similarly enhanced, while the dipole moment of S3 is much more enhanced than that of


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Supporting Information Available: Computational details. Description of the different excitonic models used. Overview of the model used to describe the plasmonic nanoparticle. Description of the kinetic model used to simulate the optical processes. Additional data on the calculated absorption and fluorescence enhancements. Additional analysis on the role of the charge-transfer states. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Acknowledgement The authors gratefully thank Niek van Hulst for the many suggestions and the fruitful discussion on the comparison with experiments. Stefano Corni is also acknowledged for the useful comments on the manuscript and Oliviero Andreussi for his contribution to the computational model. The European Research Council (ERC) is acknowledged for financial support in the framework of the Starting Grant (EnLight-277755).

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