Theoretical Quantification of the Modified Photoactivity of

Article pubs.acs.org/JPCC

Theoretical Quantification of the Modified Photoactivity of Photochromes Grafted on Metallic Nanoparticles Roberto Russo,† Arnaud Fihey,‡ Benedetta Mennucci,*,† and Denis Jacquemin*,‡,¶ †

Department of Chemistry, University of Pisa, Via Moruzzi 3, 56124 Pisa, Italy Chimie Et Interdisciplinarité, Synthèse, Analyse, Modélisation (CEISAM), UMR CNRS no. 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France ¶ Institut Universitaire de France, 1 rue Descartes, F-75005 Paris Cedex 05, France Downloaded via UNIV OF ALABAMA BIRMINGHAM on August 21, 2018 at 06:42:09 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: We present a quantum-mechanical study of the photoactivity of nanoscale architectures based on dithienylethene (DTE) photochromic molecules grafted onto plasmonic gold or silver nanoparticles (NPs). The effects of the metal NPs are included in each step of the quantum-mechanical description through the polarizable continuum model. By a direct comparison with measured data, we demonstrate that such a multiscale model is able to provide a reliable quantification of the spectroscopic parameters characterizing the photoactivity of the switches as well as their evolution under the influence of the plasmonic effects. In particular, both the calculated enhancement factors describing the modification of the DTE photoreactivity close to the NP and the calculated cyclization/cycloreversion quantum yields accounting for the efficiency of the photochromism are in good agreement with the experimental data. In addition, a better understanding of the photoinduced behavior of such complex nanoscaled photochromic systems is given in terms of a molecularlevel description.

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INTRODUCTION Switching the state of a chemical system with light allows a remote and precise control of the chemical and physical properties of matter. This is why several families of organic photochromes have been extensively used for conceiving molecular actuators,1,2 and for storing information in various fields of chemistry and material science.3−5 If numerous families of organic photochromic systems have been efficiently implemented in devices, dithienylethene (DTE) derivatives remain one of the most theoretically6−9 and experimentally2,10,11 studied. In DTEs the photochromism is based on the interconversion between an open and a closed isomer (see Scheme 1a). Their important thermal stability, great fatigue resistance and the fast conversion between the two states (ps scale) are several of the assets explaining the success of DTE switches.2,11−14 In order to transfer those photoswitching properties from the solution to the solid state, so that the switching becomes exploitable in nanoscaled devices, one can graft the photoactive compound onto a metallic aggregate. During the past decade, nanoparticles (NPs) of noble metals (mostly gold and silver) have been used to build such large systems. When immobilizing molecules onto such aggregates, it is possible to take advantage of the versatile optical responses of NPs, the most striking feature being the localized surface plasmon resonance (LSPR) that arises from a collective oscillation of the electrons belonging to the conduction band of the metal after an irradiation in the visible region.16,17 As this hallmark optical feature is highly dependent on both the structure of the metallic object (size and shape) and its environment (coating with © 2016 American Chemical Society

ligands, solvent, nature of the grafted photoactive molecules),18,19 a desired LSPR profile can be rather easily obtained. The enhanced electric field created by the LSPR around the NP can largely modify the optical properties of the nearby organic molecules. The use of this interaction constitutes the basis of all the surface enhanced (SE) spectroscopies, among which the SE Raman spectroscopy (SERS)20−22 and the SE fluorescence23,24 are the most commonly used. More globally, this type of hybrid systems where the molecular features are combined to the response of nanoscaled objects belongs to the increasingly popular field of “molecular plasmonics”.25−27 Two typical effects can be obtained in such hybrid architectures, due to the mutual interactions between the two components: (i) the molecular properties can affect the characteristic of the LSPR band (e.g., a shift of the peak) allowing to read indirectly the state of the switch if photochromic compounds are used;28,29 (ii) the response of the photoactive molecules can be tuned due to the presence of the enhanced electric field around the NP created by the LSPR.15,30 Along this line, a few hybrid NP-photochrome systems have been synthesized with various noble metal NPs covered with different DTE-based ligands.31,32 Upon molecular photoswitching, the change in the direct environment of the NP (refractive index) leads to a shift of the plasmon resonance band.29 In parallel, the plasmon-excitation interaction has been pointed out as responsible for the quenching of the Received: August 2, 2016 Revised: August 26, 2016 Published: August 29, 2016 21827

DOI: 10.1021/acs.jpcc.6b07776 J. Phys. Chem. C 2016, 120, 21827−21836

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The Journal of Physical Chemistry C

Scheme 1. a) Dithienylethene derivatives studied; b) hybrid system poly1@Ag, reproduced from Ref 15, Copyright 2012 WileyVCH Verlag GmbH & Co. KGaA, Weinheim

by coupling TD-DFT with (i) FDTD models,47−49 (ii) a polarizable Molecular Mechanics approach,50 and (iii) a “Discrete Interaction Model”51 similar to the DDA theory. In addition, the Polarizable Continuum Model (PCM), mainly used for the description of solvation,52 has also been successfully extended to describe the plasmonic effect of the NP on molecular properties described at the QM level.53,54 This has allowed rationalizing enhanced fluorescence,55,56 energy transfer phenomena57 and light-harvesting in proteinbased systems.58,59 Using this QM/PCM methodology, we here investigate the influence of the LSPR of NPs on the optical properties of different DTEs, and show that theoretical tools provide access to accurate spectroscopic data explaining the experimental outcomes for systems in which the metallic part is covered with a photochromic coat (a typical example is given in Scheme 1b). More specifically, we are interested in the behavior of three different photochromic systems, that nicely illustrate how NPs can affect dyes’ optical properties: (i) DTE 1 grafted onto a gold NP as a polymer shell, where the ring-opening reaction is speeded up;30 (ii) DTE 1 grafted onto a silver NP,15 that presents a blue-shifted LSPR compared to gold and; (iii) DTE 2 linked to a smaller silver NP, where the cyclization reaction is quenched.33 In this latter work, the authors stated that the energy transfer to the plasmon absorption is reasonably considered

photochromic activity of DTEs covalently grafted onto silver NPs,33 but the reversed situation was also observed: in the vicinity of gold and silver NPs, the ring-opening reaction of DTEs was found to be accelerated.15,30 Recently, theoretical studies have been devoted to the rationalization of this NP plasmon/organic excitation coupling phenomenon. Modeling the optical properties of such hybrid system, combining two objects of extremely different sizes, remains a fundamental challenge. The plasmon resonance bands of noble metal NPs have been thoroughly studied using classical electrodynamics-based methods,34 like the Discrete Dipole Approximation (DDA)35,36 or the Finite Difference Time Domain (FDTD),37 that yield accurate descriptions of the LSPR for various sizes and shapes of NPs.38,39 In parallel, Time-Dependent Density Functional Theory (TD-DFT)40,41 can be used to assess the molecular optical response of organic dyes and photochromes,42,43 as it yields a good agreement with experimental UV−visible measurements for many π-conjugated systems including DTEs,6,9,44−46 though being limited in practice to systems encompassing ca. 300 atoms. To describe the modifications of the optical signature of a chromophore in the vicinity of a nanoaggregate exhibiting a LSPR, one should therefore combine TD-DFT or other quantum-mechanical (QM) descriptions of the organic moiety to a classical treatment of the metallic part. This idea has been followed 21828


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The Journal of Physical Chemistry C as the main cause of the quenching on the metal nanoparticles, so that we focus on this phenomenon here, and other potential events, such as photooxidation are neglected. Furthermore, no estimate of the density of photochromes around the metal is given in these experimental works. Due to the curvature of the NP, one can nevertheless estimate that intermolecular dye−dye interactions are not preponderant, and also not considered in our model, an hypothesis consistent with the fact that now new UV/vis band appears for 1 grafted onto a gold NP compared to 1 in solution. The presentation of our results is organized as follows: after a description of the optical behavior of the isolated DTEs, we detail how the LSPR impacts the photoactivity of the switches by computing the enhancement factor (EF). In addition, we rationalize the experimental fall of the photocyclization quantum yield for a DTE anchored on a silver NP by quantifying the quenching through energy transfer. To the best of our knowledge, this constitutes the first attempt to theoretically describe those two types of key photophysical events for NP-photochromes systems in which LSPR plays a major role.

Γabs =

ε

(ω , R ) =

−

⎧ ⎪ 1 +Ω⎨ ⎪ω ω + ⎩

μ⃗met K0

1

(

ω ω+

R+v τ i Rτ F

)

⎫ ⎪ ⎬ ⎪ ⎭

i τ

(3)

(μ⃗sol K0)

where is the induced dipole on the NP (the solvent). Assuming that the quantum yield does not change in the presence of metal NP, the EF is obtained by comparing the quantity Γabs to the reference case (Γ0abs, assimilated to the absorption of the free DTE), namely:

EF =

Γabs 0 Γ abs

(4)

An EF value larger than 1 indicates a speeding of the photoinduced reaction due to a more efficient absorption process, in this vertical view of photochromism, while a EF below unity implies a slowed down reaction. Quantum yield. To complete the picture, however, all the processes potentially occurring after light irradiation need to be considered. For an isolated DTE we have (i) the radiative (fluorescence) and nonradiative decays, described respectively by the krad and knrad rates; (ii) the photochromic reaction for which the cyclization and cycloreversion reaction rates are respectively koc and kco. For a DTE anchored onto a NP, a supplementary process appears that corresponds to a nonradiative energy transfer from the excited-state of DTE to the metal, which can act as a quenching process for the DTE isomerization and is described by the rate kEET. In the QM/ PCM framework, as the response of the metal is complex, the EET rate is related to the imaginary component of the resulting transition energy of the combined chromophore-NP system: kEET = −2Im(ω)

(5)

Using those quantities, one can define the photocyclization quantum yield of the free-metal DTE as Φoc =

2

(

(2)

μK⃗ 0 = μK⃗ mol + μK⃗ met + μK⃗ sol0 0 0

METHODS AND COMPUTATIONAL DETAILS Methods. The theoretical background of the QM/PCM method used here is briefly summarized only, as more details are available elsewhere.55,56 In the presence of a continuum dielectric, the QM subsystem is described by an effective Hamiltonian that is the sum of the electronic Hamiltonian of the QM subsystem and a term describing the electrostatic and polarization interaction between the QM charge density and the continuum dielectric. Here the continuum description is applied to both the solvent and the metal NP. For the latter, a specificity appears has the metal NP responds as a perfect conductor to static fields and as a dielectric to dynamic fields. In our approach, it is assumed that the dielectric effect due to the ligand layer can be approximated with a continuum medium having the same characteristic of the solvent. The NPs used in this work are spheres with a diameter of 18 nm for gold and 4 or 19 nm for silver, in line with experiments.15,30,33 Their optical response is described through a local, frequencydependent dielectric function, obtained as a Drude model corrected for quantum size effects, met εexp (ω)

2

where c is the speed of light, n is the refractive index of the medium, and μ⃗K0 is the transition dipole moment between the ground and the Kth excited states. Near a metallic NP, this dipole moment has to be changed into an “effective” one:

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met

2π μ⃗ 3ℏ2cn K 0

koc koc + k rad + k nrad

(6)

and similarly for the cycloreversion reaction. In the presence of the NP this equation contains a additional term accounting for the potential quenching by EET:

)

Φoc,NP = (1)

koc + k rad

koc + k nrad + kEET

(7)

Those two general equations are adapted to specific scenarios later in this study, when specific pathways are ignored or redefined. Computational details. The ground-state geometries of the DTEs under study were optimized at the DFT level using the PBE061 global hybrid functional associated with the 631+G(d) atomic basis set. Vibrational frequencies calculations were systematically conducted at the same level of theory, to ensure that the obtained structures are true energy minima. TD-DFT was applied to access the transition properties, in combination with a range-separated hybrid functional, CAMB3LYP,62 and the 6-31+G(d) basis set, as this approach has been proven to yield accurate optical properties of DTE

where ω is the applied frequency, R is the radius of the 60 nanoparticle, εmet exp (ω) is the experimental bulk dielectric value, Ω is the plasma frequency (0.332 au for silver and 0.293 au for gold), τ is the bulk relaxation time (1320 au for silver and 306 au for gold), and vF is the Fermi velocity (0.64 au). Enhancement factor. Experimentally, the speed up of the photochromism in the presence of a NP is quantified by the enhancement factor (EF), obtained by following the change in absorption in solution for a given irradiation wavelength while assuming an unperturbed photoreaction quantum yield.30 We adopt the same point of view and evaluate the efficiency of the absorption process, by computing the Γabs rate as follows: 21829


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The Journal of Physical Chemistry C derivatives.63 Solvent effects were included in the PCM framework to match the experimental UV−visible measurement conditions (toluene, acetone or ethyl acetate), using another cavity in addition to the one of the metallic NP, this time around the organic molecule. All calculations were conducted with a locally modified version of the Gaussian09 software.64

the presence of a long nonconjugated linker ensures that direct NP-DTE interactions are trifling. Experimentally, the DTEs are linked to the metallic NP through a very flexible alkyl chain.15,30,33 To reproduce the fact that, in the experiments, the molecule can adopt a large set of orientations with respect to the NP surface, the QM/PCM data presented below correspond to values averaged over all the possible orientations: for each NP-DTE distance, the DTE was rotated (as a rigid body) following two angles, ϕ and φ, by 30 degrees increments to generate a semisphere of 49 orientations (see Figure 1b). Free DTEs. First we detail the optical properties of the free DTEs 1 and 2 to assess the ability of the QM model (TDDFT) to deliver insights into their optical properties and photoactivity. The computed relevant electronic transitions obtained for the different molecules, in both their open and closed forms, are listed in Table 1.

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RESULTS AND DISCUSSIONS The photoactive compounds under study, 1 and 215,30,33 can be experimentally switched between their open and closed forms (see Scheme 1). In addition 2 possesses fluorescent properties thanks to the anthracene moiety attached to one of the thiophene rings.33 These DTEs have been anchored covalently through a thiolate termination to metallic NPs, either of gold or silver. More specifically, DTE 1 has been grafted as a polymeric DTE coating surrounding the NP, leading to poly1@Au,30 and poly1@Ag,15 whereas photochrome 2 has been been anchored as a monomer all around a silver NP (2@Ag’).33 Those three hybrid systems are all considered in this work by placing the DTE molecule in the vicinity of a PCM sphere representing the metallic nanoparticle, in a 1:1 ratio, as can be seen in Figure 1a. In the QM/PCM model no explicit chemical interaction between the organic molecules and the metal is considered, as the electronic structure of the NP is obviously lacking. This approximation is valid as in the experimental hybrid systems,

Table 1. Relevant electronic transitions for the open and closed forms of 1 and 2, and corresponding experimental data.15,30,33 Compound

Exp. band (nm)

Wavelength (nm) ( f)

1-o

290

307 (0.13) 279 (1.50)

2-o

365

354 (0.24) 286 (0.06)

1-c

590

565 (0.52) 341 (0.25)

2-c

ca. 570

495 (0.29) 356 (0.19)

334 (0.16)

Composition HOMO→LUMO (88%) HOMO→LUMO+2 (55%) HOMO−1→LUMO+1 (38%) HOMO→LUMO (97%) HOMO−1→LUMO+1 (67%) HOMO→LUMO (96%) HOMO−1→LUMO (89%) HOMO→LUMO (97%) HOMO−1→LUMO+1 (67%) HOMO−1→LUMO (29%) HOMO−2→LUMO (88%)

For the first main absorption band of 1-o, 1-c and 2-o, theory reproduces the available experimental UV−visible data.15,30,33 The intense band in the visible domain for 2-c is located at too high energy (error of 0.3 eV) by CAM-B3LYP, though the global comparison with measured data remains satisfying. More importantly, by looking specifically at the electronic transitions of 1-o and 2-o, one can gain first insights into the photoinduced ring-closing process. Indeed, as demonstrated in several previous theoretical works,63,65 the TD-DFT electronic transitions in the UV domain and the nature of the virtual orbitals involved in those transitions can be correlated with the experimental feasibility of the photocyclization. In fact, if an excitation in the open form promotes an electron toward a virtual molecular orbital presenting a bonding interaction between the carbon atoms involved in the to-be-formed σ bond (in the closed form), one can expect the photocyclization to occur. This type of transition is then referred to as a “photochromic” transition, and the virtual orbitals involved as “photochromic orbitals”. The presence or the absence of such hallmark transition in the energy range targeted with the experimental irradiation, allows to empirically estimate the efficiency of the photoreaction.65,66

Figure 1. a) Model system to describe poly1@Au for the QM/PCM model and angles considered for the orientation screening; b) semisphere of orientations generated and; c) theoretical LSPR profiles calculated for the gold and silver NPs. 21830


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Figure 2. Representation of the key virtual molecular orbitals for 1 and 2 in their open and closed forms.

For 1-o, the first transition computed at 307 nm ( f = 0.13) populates the LUMO, represented in Figure 2. As this orbital possesses the photochromic topology, this transition is expected to yield the closed form, in agreement with the experimental outcome. In 2-o, the S0→ S1 transition involves only the LUMO that is purely localized on the anthracene moiety. The S0→ S3 transition is the first involving a photochromic orbital, namely the LUMO+1, but this excitation presents a moderate oscillator strength ( f = 0.06). For 2-o, the S0→ S1 excitation cannot directly induce the cyclization and the photochromic S3 state remains probably poorly efficient because, on the one hand, the associated f is moderate and, on the other hand, this state lies at 286 nm, significantly beyond the experimental irradiation wavelength at 365 nm.33 This fact is in line with the quite low experimental photocyclization quantum yield for 2-o (0.18) compared to other types of DTE where this yield is typically close to 0.5 under irradiation at this wavelength.2 Additionally this analysis also hints to an isomerization pathway with an intermediate step. As the first experimental photophysical event is the vertical transition triggered by the absorption of UV light, the highly dipoleallowed S0→ S1 transition is clearly the dominating initial process. We can propose that it is followed by an internal conversion (IC) to the photochromic S3 state thanks to excitedstate geometry relaxations provided that the fluorescence from S1 is slower than the IC. This would ultimately lead to 2-c. This interpretation is supported by previous analyses: the very same S1/S3 crossing has been highlighted in a theoretical work of Kryschi and co-workers who considered a similar symmetric anthracene-substituted DTE.67 The TD-DFT description of the optical properties of the closed DTEs is more straightforward. For 1-c, the first virtual orbital is spread on the full molecule and is the sole molecular orbital significantly taking part in the S0→ S1 transition (at 565 nm). The LUMO of 2-c is located on the highly conjugated closed DTE core, while the LUMO+1 is found on the anthracene moiety. They are the main virtual orbitals

respectively involved in the S0→ S1 and S0→ S2 transitions computed at 495 nm (f = 0.29) and 356 nm (f = 0.19). The second transition in 2-c is the counterpart of the S0→ S1 of the 2-o compound, located on the anthracene moiety, and almost unmodified compared to 2-o. This indicates that the direct electronic communication between the DTE and the anthracene in 2 is very weak, a logical consequence of the large twisting between those two fragments in the ground-state (see Figure 2). When irradiating 2-c in the visible, only the photochromic moiety is involved and no fluorescence is expected from the anthracene, consistent with observations in solution.33 The cycloreversion process is then more straightforward than the cyclization process in 2. As detailed in the following this rationalization of the optical properties of the free DTEs helps understanding how the photoactivity of the switches are modified by interacting with the LSPR. DTEs on metallic NPs: enhancement of the absorption. The frequency-dependent profiles of the imaginary component of the polarizability for the gold and silver nanoparticles considered in this work are shown in Figure 1c. The plasmon band is found at ca. 530 nm for the 18 nm gold NP and at 410 nm for the 19 nm silver NP: both values are in very good agreement with the experimental data.15,30 Note that for the 4 nm NP, experiments indicate a redshift of the plasmon resonance with respect to the larger NP.33 This shift can be the result of different effects, namely quantum-size and nonlocal screening effects68 which are not fully included in Drude-like models,38 and/or a change in the refractive index due to the ligand shell around the NP. Experimentally,15,30 the metallic NP was covered with a photochromic shell and the DTE-NP distance is not resolved when measuring the enhancement factor. In our QM/PCM model, several distances have been investigated to assess the area of influence of the LSPR on the molecular excitation. The distances reported in the following were measured between the centers of mass of the DTE and the NP surface. The shortest distance studied corresponds to the expected separation between the closest DTE monomer in 21831


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The Journal of Physical Chemistry C the polymer coating and the surface.15,30 The largest distance corresponds to the farthest DTE of the polymer chain and equals the thickness of the DTE polymer film itself. Gold NP. Table 2 compares the calculated and experimental EFs, for 1 in the vicinity of the 18 nm gold NP, in a range of

Such a result could be explained in terms of a limitation of the analytical-type model used in ref 30. In contrast, our QM/PCM leads to the largest enhancement around the LSPR peak, as well as smaller EFs when getting further in the red. For the open DTE, no experimental data are available. For a given distance, the computed EFs remains roughly unchanged, as the irradiation wavelengths, 313 nm, 365 or 400 nm (the two former being possibly suited to induce cyclization) are far from the LSPR peak. Only a minimal increase (from 2.30 to 2.46) is found when getting closer from the LSPR band. In that sense, tuning the irradiation wavelength to increase the EF may not be an ideal strategy for boosting the photocyclization as one has to keep targeting the previously described photochromic transition. A safer strategy would be to rely on either DTEs or NPs of different nature so that the molecular transition of interest for photochromism and the LSPR overlap naturally, a fact illustrated below for a silver NP. Silver NP. The EF values for poly1-o@Ag and poly1-c@Ag determined at different distances and irradiation wavelengths are listed in Table 3. The experimental conditions are similar to

Table 2. Enhancement factors obtained at the TD-DFT level for 1 anchored on the gold NP, in toluene, for different NPDTE distances and irradiation wavelengths, along with the available experimental values.30 Isomer

Distance (nm)

313 nm

365 nm

400 nm

1-o

1.5 6.0 9.0 17.0 Distance (nm)

2.30 1.29 1.14 1.04 550 nm

2.37 1.30 1.15 1.04 600 nm

2.46 1.31 1.15 1.04 650 nm

1.5 6.0 9.0 17.0 Exp

4.70 1.44 1.14 0.90 3.20

4.34 1.39 1.13 1.01 2.90

3.87 1.34 1.11 1.01 5.00

Isomer 1-c

Table 3. Enhancement factors obtained at the TD-DFT level for 1 anchored on the silver NP, in acetone for different NPDTE distances and irradiation wavelengths, along with the analytical values from experiments.15

distances going from 1.5 to 17 nm from the surface. Several irradiation wavelengths were considered. The experimental values of the EF indicated here were obtained by Nishi et al. using a two-component analytical model based on the change of absorption and assuming that the quantum yield of the photoreaction of the molecule remains constant.30 Those values are mean values of EF inside the enhanced area and no precise experimental distance-dependent values are available. Globally our model satisfactorily reproduces the key amplitudes of the EFs: the QM/PCM EFs are similar to the ones derived from experiments, i.e., they range from 1 to 5. The greatest EF is obtained for 1-c at 1.5 nm from the surface for a 500 nm wavelength, and attains 4.70. For 1-o the largest EF is 2.46 again for the closest NP-DTE situation, at 400 nm. In general the Γabs is much less impacted by the NP in the open form than in the closed form. This is an expected outcome as the main absorption band of 1-o lies in the UV region of the spectrum, rather far from the LSPR maximum at 530 nm. For both poly1-o@Au and poly1-c@Au, the EF is logically decreasing when the DTE is taken away from the surface of the NP, and always tends toward unity when considering the limit distance of the DTE shell, 17 nm. This is consistent with the experimental analysis in which the effect of the LSPR was assumed to become negligible before reaching the outer part of the DTE polymer shell.30 The decrease is found nonlinear through this shell by the QM/PCM model, and the EF vanishes rapidly when getting away from the metal: the enhancement value at 6 nm from the surface is already only ca. 1.3−1.4 in all cases. The experimental analysis of the absorption changes in ref 30 led to conclude that the area of effect of the LSPR was approximately 9 to 12 nm from the NP surface, in good agreement with the distance-dependent theoretical values of EF listed in Table 2), where the values of EFs clearly above one are for distances below 9 nm. For poly1-c@Au, the experimental-based model predicts a larger EF for longer wavelengths, with a maximum value of 5.00 at 650 nm, a surprising result according to the usual behavior of plasmonic effects: the closer the irradiation wavelength from the LSPR (at 530 nm), the larger the expected modification of the molecular transition dipole moment, the greater the Γabs.

Isomer

Distance (nm)

313 nm

365 nm

400 nm

1-o

1.5 8.0 11.0 Distance (nm)

3.18 1.04 1.03 450 nm

8.63 1.16 0.95 500 nm

35.9 3.52 1.99 550 nm

1.5 8.0 11.0

8.20 1.44 1.17 5.70

4.02 1.18 1.06 3.10

2.78 1.10 1.04 2.50

Isomer 1-c

Exp

those used for the poly1@Au system, the thickness of the shell being here 11 nm.15 The computed EF values are again in good agreement with their experimental counterparts. Indeed for poly1-c@Ag, depending of the wavelength, Nishi et al. determined EFs between 2.50 and 5.70, while the QM/PCM results lie in the 1.00−8.20 range. For this system, when shifting the irradiation wavelength to the red, both the experimental and calculated EFs decrease, consistently with the position of the LSPR band (410 nm). Concerning the distance dependency of the EF values, a shell of 8 nm was assumed as being the experimental limit for the effect of the NP, a part of the outer shell being not impacted by the LSPR, similarly to the poly1@Au case. The theoretical EFs for poly1c@Ag confirm this hypothesis, as they are only slightly exceeding unity at 8 nm from the surface. The comparison between the open and closed cases leads to opposite conclusions compared to the gold system: the EFs tend to be larger for 1-o than for 1-c. This is a result of the change in the LSPR position, peaking at 410 nm for the silver NP instead of 530 nm for the gold NP. Consequently, the absorption of the open DTE in the UV is now more impacted by plasmonic effects than the visible absorption of the closed isomer. For poly1-o@Ag, the EFs are increased when going from a 313 nm, to a 365 nm, and finally a 400 mn irradiation wavelength, and can attain very high values (the largest being 35.9 at 400 nm for the shortest distance). These very large EFs originate not only from the proximity of the LSPR but also 21832


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for the calculations, 10 and 20 Å as the thiolate linker used in the experiments should keep the molecule at ca. 10 Å from the surface of the NP. The theoretical Φco, 0.015 at 10 Å, is accurate as it is very close to the experimental value of 0.018. When going from 10 to 20 Å, kEET decreases by approximately 1 order of magnitude. However, this variation does not significantly impact the cycloreversion efficiency as the very large knrad mainly determines the final quantum yield. Compared to the value determined by Yamaguchi et al., the QM/PCM rate at 10 Å from the NP surface is found higher, though the dependence of kEET on the distance makes the comparison with the experimental values not straightforward. Indeed, the NP-DTE distance can vary experimentally around 10 Å due to the flexibility of the linker. Cyclization reaction. For 2-o, the ring closing was experimentally observed to be partially prevented after anchoring to the silver NP and the photocyclization quantum yield dropped from 0.18 to 0.019.33 This modification of the photoactivity was ascribed to an energy transfer from the excited open DTE to the metal NP. As detailed above, the S1 of 2-o corresponds to the intense absorption band targeted with the experimental irradiation at 365 nm, and the photochromic S3 can take part in the isomerization process after an IC crossing between these two excited-states only. In the 2-o@Ag’ case, a quenching of the fluorescence is also observed experimentally, simultaneously to the cyclization efficiency drop,33 suggesting that the population of S1 is the first step in the photochromism of 2-o. A quenching mechanism by EET from an excited-state can take place at several moments along the isomerization pathway. The expression of the photocyclization quantum yield is more complex in this open form case as two excited-states should be accounted for. In addition, we also considered the conversion from S1 to S3 characterized by the k13 rate, and the fluorescence from both states (kf1 and kf 3). Kryschi and co-workers used time-resolved spectroscopy to determine the lifetimes of the states experimentally identified as S1 and S3.67 The former has a very short lifetime (below the ps) while the latter was found to last 13 ps. As it is difficult to discard potential pathways based on these values only, and because we do not know a priori the EET rate, we considered different models that include energy transfer(s) occurring at different times after the initial light absorption by the molecule. FC → NP First, if the EET occurs from an unrelaxed S1 (kS1 ), then EET the quantum yield is expressed as follows:

from the large number of intense electronic transitions in the UV domain for the open DTE, contrasting with the single band of the closed isomer in the visible region (see Table 1). In all cases, the EFs of the open DTE are larger than one, indicating that the photocyclization process is clearly not impeded by the sole interaction between the electronic transition and the field surrounding the silver NP: this result is in good agreement with the experimental efficient formation of [email protected] In some other cases, following the excitation of the open DTE, the energy can be transferred to the metallic NP acting as an acceptor, quenching the excited-state and hence the subsequent DTE photochromism.33 Indeed, experimentally the photocyclization quantum yield of 2-o drops drastically after the grafting on a 4 nm diameter silver NP, and this phenomenon is quantified in the following Section using our QM/PCM approach. DTEs on a small silver NP, quantum yield and energy transfer. As stated in the Introduction, Yamaguchi et al.33 presented a thorough spectroscopic study of the DTE 2 free and in the vicinity of a 4 nm diameter silver NP (2@Ag’). In this study, besides variations of the absorption, modifications of the photochromism quantum yields were also investigated. In contrast to the poly1@Au and poly1@Ag hybrid systems, the silver NP is covered by thiolate-DTE monomers. As the linker is highly flexible we again considered a set of possible orientations to obtain a mean value of the kEET. Retrocyclization reaction. The ring-opening of 2-c occurs after visible irradiation that populates the first excited state. Experimentally, no difference in the efficiency of this reaction was observed with and without the NP, the cycloreversion quantum yield of the free molecule and the anchored one being respectively 0.019 and 0.018. These rather low values are typical of DTEs.2 The cycloreversion quantum yield of free 2 can be expressed following the equation given in the Methods Section, adapted by considering that the irradiation of 2-c in the visible leads to negligible fluorescence as the corresponding absorption process involves only the DTE-localized LUMO and not the anthracene moiety (see Figure 2). Therefore, we have

Φco =

kco kco + k nrad

Φco,Ag =

(8)

kco kco + k nrad + kEET

(9)

for the free and NP-anchored DTE, respectively. To estimate the two quantum yields, we use the experimental values determined in ref 67 with the help of time-resolved spectroscopy for free anthracene-substituted DTEs, that is a kco = 9.5 × 109 s−1 and a knrad = 4.9 × 1011 s−1. To those, we add the kEET calculated at the QM/PCM level to obtain the values listed in Table 4. Two NP-DTE distances have been explored

A Φoc,Ag

⎛ ⎞ koc ⎜⎜ ⎟⎟ ⎝ k f 3 + k nrad3 + koc ⎠

Table 4. Experimental33,67 and calculated rate constants (in s−1) and quantum yields for 2-c isolated and anchored on the silver NP, in ethyl acetate Free 2-c Exp 2-c@Ag’ Exp Calc. (10 Å) Calc. (20 Å)

kco

knrad

kEET

Φco

9.50 × 109 kco

4.90 × 1011 knrad

−

0.019 Φco

9.50 × 109 − −

4.90 × 1011 − −

kEET 2.80 × 1010 1.43 × 1011 1.85 × 1010

⎛ ⎞ k13 ⎜ ⎟ = ⎜k + k S1FC → NP ⎟ + + k k ⎝ f1 ⎠ nrad1 13 EET

(10)

Second, if the EET occurs after IC to the S3 only (kS3→NP EET ), one has: ⎛ ⎞ k13 B ⎟⎟ Φoc,Ag = ⎜⎜ ⎝ k f 1 + k nrad1 + k13 ⎠ ⎞ ⎛ koc ⎟ ⎜ ⎜k + k S3 → NP ⎟ ⎠ ⎝ f3 nrad3 + koc + kEET

0.018 0.015 0.018 21833

(11)


Article


Table 5. Experimental33,67 and calculated rate constants (in s−1) and quantum yields for 2-o isolated and anchored on the silver NP, in ethyl acetate System 2-o, exp 2-o@Ag’, exp 2-o@Ag’, calc ΦAoc,Ag ΦBoc,Ag ΦCoc,Ag

koc

knrad1 + kf1

6.00 × 10

10

5.50 × 10

11

k13

knrad3 + kf 3

5.60 × 10

11

2.30 × 10

10

S →NP

S →NP

3 kEET

Φco

1 kEET

−

−

− 9.10 × 1011

0.36 0.03

5.79 × 1011 − −

− − 4.21 × 1011

− 4.21 × 1011 1.97 × 1011

0.24 0.26 0.08

with good accuracy by computing, for different wavelengths, and this holds for the enhancement of the absorption process under the influence of plasmonic effects. In particular the different behaviors observed on a gold or a silver NP were rationalized: on the gold NP, the ring-opening reaction is more impacted than the ring-closing reaction, while the opposite occurs on the silver NP. The dependency on the distance between the molecule and the NP is in line with the experimental conclusions: only a fraction (ca. 40% for gold and 60% for silver) of the photochromic shell, close to the metallic surface, is impacted by the LSPR. For a DTE system bearing a fluorescent unit and anchored onto a silver NP, the photophysical processes leading to a decrease of the fluorescence and a reduction of the yield of the ring closing have been rationalized by analyzing the excited-state energy transfer between the DTE and the NP. By comparing with the experimental results, we were able to discriminate between possible alternative pathways, showing that the process in which two excited-states are involved and both are subject to energy transfer to the NP is the most likely. This theoretical work is one of the few rationalizing the photochromism of DTEs in the vicinity of metallic NPs exhibiting plasmonic effects, and the first to achieve a semiquantitative agreement with the “real-life” spectroscopic measurements. The present investigation paves the way to joint theoretical/experimental studies of hybrid systems where the interaction between the photoactive dye and the metallic architecture is first predicted from theory to design the optimal setup, and then experimentally realized. Improvements of the theoretical methodology are currently being undertaken, to consider more complex hybrid systems, for instance containing multiphotochromic molecules,1 or taking into account side reactions.69

Finally, if the EET takes place from both the S1 and the S3, one can write ⎛ ⎞ k13 ⎟ Φcoc,Ag = ⎜⎜ S1 → NP ⎟ k k k k + + + ⎝ f1 ⎠ nrad1 13 EET ⎛ ⎞ koc ⎜ ⎟ ⎜k + k S3 → NP ⎟ ⎝ f3 ⎠ nrad3 + koc + kEET

SFC→NP

1 kEET

(12)

As for the cycloreversion case, if we insert the experimental value of the constant rates67 in those equations together with the kEET obtained with the QM/PCM model, it is possible to access the photocyclization quantum yield of 2-o for each scenarios. The geometries of 2-o for the calculation of the kEET rate are chosen in accordance to the pathway under consideration. For FC 1 → NP 1→NP 3→NP kSEET , kSEET and kSEET we use respectively the ground-state FC geometry (S1 ), the relaxed geometry of S1, and the relaxed geometry of S3. In the same manner the wavelengths chosen for calculating the response of the NP depends on the pathway/ geometry considered: either 365 nm (experimental absorption of the S1 for the ground-state geometry), 420 nm (experimental emission of the S1 for the relaxed geometry of the S1) and 550 nm (experimental emission of the S3 for the relaxed geometry of S3). The calculated of kEET values for the different scenarios are listed in Table 5 for a NP-DTE distance of 10 Å and compared to the experimental values. The different kEET obtained at the QM/PCM level are all of the same order of magnitude as the experimental value, 9.10 × 1011. We underline that the experimental photocyclization quantum yields given in Table 5 is twice the observed value in solution, to take into account the presence of nonreactive parallel conformation in solution (in a 1:1 ratio with the reactive antiparallel conformer),10 while the calculation are conducted on the photoactive antiparallel conformation only. The computed ΦAoc,Ag (0.24) and ΦBoc,Ag (0.26) are ca. 10 times larger than the experimentally determined value (0.03), and only the ΦCoc,Ag value (0.08), taking into account an EET from both the S1 and S3, leads to a reasonable match with experiment. This agreement suggests that the photophysics of the 2-o@Ag’ hybrid system is better described with two separate energy transfers acting consecutively on the two involved excited-states.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]; phone: +39 (0)5 02 21 92 93. *E-mail: [email protected]; phone: +33 (0)2 51 12 55 64. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A.F. acknowledges the European Research Council (ERC, Marches 278845) for supporting his postdoctoral grant. B.M. acknowledges the European Research Council (ERC) for financial support in the framework of the Starting Grant (EnLight 277755). D.J. acknowledges the ERC and the Région des Pays de la Loire for financial support in the framework of a Starting Grant (Marches 278845) and the LUMOMAT project, respectively. All authors acknowledge the support of the CNRS

■

CONCLUSIONS Using a Quantum Mechanics/Polarizable Continuum Model approach we have shown that theory can provide reliable quantifications on the photoactivity of nanoscaled architectures based on hybrid NP-DTE photochromic systems. When a gold or a silver NP are considered, the modification of the yield of photoreaction with respect to the free dye can be reproduced 21834


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Theoretical Quantification of the Modified Photoactivity of

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