Density Functional Theory Study of the Conformation and Optical

Article pubs.acs.org/JPCA

Density Functional Theory Study of the Conformation and Optical Properties of Hybrid Aun−Dithienylethene Systems (n = 3, 19, 25) Arnaud Fihey,* Benedikt Kloss, Aurélie Perrier,* and François Maurel Laboratoire Interfaces, Traitements, Organisation et Dynamique des Systèmes (ITODYS), CNRS UMR 7086, Université Paris Diderot Sorbonne Paris Cité, Bâtiment Lavoisier, 15 rue Jean Antoine de Baïf, 75205 Paris Cedex 13, France S Supporting Information *

ABSTRACT: We present a theoretical study of Aun−dithienylethene hybrid systems (n = 3, 19, 25), where the organic molecule is covalently linked to a nanometer-scaled gold nanoparticle (NP). We aim at gaining insights on the optical properties of such photochromic devices and proposing a size-limited gold aggregate model able to recover the optical properties of the experimental system. We thus present a DFTbased calculation scheme to model the ground-state (conformation, energetic parameters) and excited-state properties (UV−visible absorption spectra) of this type of hybrid systems. Within this framework, the structural parameters (adsorption site, orientation, and internal structure of the photochrome) are found to be slightly dependent on the size/shape of the gold aggregate. The influence of the gold fragment on the optical properties of the resulting hybrid system is then discussed with the help of TD-DFT combined with an analysis of the virtual orbitals involved in the photochromic transitions. We show that, for the open hybrid isomer, the number of gold atoms is the key parameter to recover the photoactive properties that are experimentally observed. On the contrary, for hybrid closed systems, the three-dimensional structure of the metallic aggregate is of high impact. We thus conclude that Au25 corresponds to the most appropriate fragment to model nanometer-sized NP−DTE hybrid device.

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resonances,9,10 and the irradiation wavelength6 but also on the nature of the photochrome.5 In 2006, Feringa’s group synthesized a series of hybrid systems where the DTE unit is directly anchored via a thiol termination to a 2 nm diameter thiol-protected gold nanoparticle (NP).12 In that case, the optical properties of the molecular-sized gold aggregate are not dominated by surface plasmon resonances.13 For DTE linked to the NP through a phenyl aromatic ring, the photochromic properties are preserved whereas choosing a thiophene linker inhibits the ring-closure reaction (Figure 1). Experimentally, the hybrid system corresponds to a single monolayer of DTE molecules coating the 2 nm NP. One can thus rationalize these effects by incriminating a quenching of the excited states, due to energy transfers between different DTE units. However, in the past, by using a “simple” theoretical model made of one single DTE unit grafted onto a NP, we have shown that the modification of the photochrome electronic structures due to the grafting onto the nanoparticule can rationalize the loss or preservation of the photoswitching properties, without taking into account dynamical effects observed upon photoexcitation.14,15 The behavior of such hybrid systems is thus not trivial and theoretical studies can bring helpful information to understand the photoreactivity of DTEs grafted on Au clusters.

INTRODUCTION In the presence of an external stimuli (heat, light, chemical environment), photochromic compounds undergo a reversible transformation between two isomers. Those two forms generally possess different chemical and/or physical properties (redox potential, conductance, refractive index, magnetic properties, acid−base equilibrium constants, absorption, emission). Among the numerous families of photochromic compounds, diarylethenes (DAs) and especially dithienylethenes (DTEs) are widely studied both experimentally and theoretically, due to their interesting characteristics.1−4 Actually, they can undergo a cyclization and retrocyclization process respectively under UV and visible irradiation, and both resulting compounds are stable at room temperature. As these two forms can be assimilated to “on” and “off” states, they constitute promising candidates for molecular switches in nanoscaled optoelectronic devices. To this purpose, one has to immobilize DTEs, for instance within a polymer matrix or onto a metallic aggregate (electrode, surface, nanoparticle).5−10 In the following, the organic/metallic assembly made of a DTE immobilized on a gold surface will be referred to as a hybrid system. Within the last ten years, different experimental studies have been dedicated to the description of the interactions between the organic and metallic moieties within these hybrid compounds. These studies have shown that these interactions are highly dependent not only on the distance between the photochrome and the metallic aggregate,11 the size of the gold NP and the possible interaction with the NP surface plasmon © XXXX American Chemical Society

Received: February 12, 2014 Revised: June 5, 2014

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dx.doi.org/10.1021/jp501542m | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Figure 1. Representation of (a) isolated DTE systems and (b) Aun−DTE hybrid compounds.

Figure 2. Representation of the different gold NPs and fragments.

Although this “single DTE−NP” system is a model of choice for theoretical studies thanks to the simplicity of the linker, modeling such hybrid compounds remains challenging. As a matter of fact, a 2 nm diameter gold NP encompassing about 250 atoms, a full ab initio treatment becomes rapidly unfeasible due to the large number of electrons. Because these hybrid systems present no symmetry properties, calculations are rapidly not affordable in terms of computational cost, convergence problems, and number of excited states to handle to access optical properties. Furthermore, within the density functional theory (DFT) framework, the choice of a functional to describe simultaneously the metallic and organic part is not straightforward. Concerning the structural parameters, GGA (general gradient approximation) and hybrid functionals can provide a satisfying description of both the organic and metallic geometrical properties.16−18 On the contrary, for the UV−vis spectrum, there is no method that can provide an accurate description of the optical properties of both the NP and the photochrome. In a recent work dedicated to pyrene immobilized on a Au25 cluster,18 we have focused our attention on the modification of the absorption spectrum of the chromophore after grafting. In that framework, we have chosen to work with the CAM-B3LYP functional which is the method of choice to deal with organic chromophores.19 We have previously investigated this type of Aun−DTE hybrid systems with very few gold atoms14,15 and shown that if the cluster is large enough (n = 13), a qualitative description of the NP−DTE interactions can be reached. We are now

concerned with increasing the cluster size to provide a more realistic model. Therefore, the present DFT study aims at (i) proposing a computational scheme to treat such compounds and (ii) determining the effect of the size and structure of the gold aggregate on the geometry and optical properties of the anchored DTE. Our final objective consists in finding the smallest gold nanocluster model able to describe and analyze the optical properties of a DTE grafted onto a NP. To this purpose, hybrid systems Aun−photochrome are studied, where n increases from 3 to 25 (n = 3, 19, 25) (Figure 1). For each gold aggregate, both the open and closed forms of the DTE anchored onto the surface through a thiophene linker (open form, of; closed form, cf) are considered. To model the metallic environment close to the DTE, the NP fragments are extracted from fully optimized 2 nm structures and are thus realistic gold fragments, corresponding to the edge of the NP. Because adsorption of the thiol group is known to occur favorably on Au(111) surfaces,20−22 all fragments are orientated as (111) crystallographic planes and constitute either the first or the two first layers of the NP surface. The choice of our fragments enlightens the effect of the change from an extremely small cluster (Au3) to a “surface-like” cluster (Au19) and a two-layer cluster (Au25). This work is organized as follows: first, a brief description of the properties of the isolated DTE of interest is given. Then, the study focuses on the Aun−DTE hybrid systems: the geometrical and optical properties are successively discussed. B



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COMPUTATIONAL DETAILS

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OPTICAL PROPERTIES OF DTE MOLECULES Our two-step computational scheme is first tested on the isolated DTE. Experimentally, UV−visible absorption data are available for a photochrome substituted with a −COCH3 group (Figure 1). The calculated electronic transitions can then be compared to the absorption measurements in toluene for the open (of-COCH3) and closed forms (cf-COCH3). The computed lowest energy transitions are found respectively at 321 nm for of-COCH3 and 605 nm for cf-COCH3 and are thus in good agreement with the experimental wavelengths (respectively 330 and 600 nm), with a deviation of +0.11 eV for the open isomer and −0.02 eV for the closed one. This small error validates the choice of our computational scheme to study the DTE optical properties. Within the hybrid structure, the organic moiety corresponds to a R = H substitution pattern in Figure 1 and hereafter, we will focus our attention on this system. Figure 3 presents the

Two successive computational steps were applied to obtain the structures and UV−visible absorption properties of gold− photochrome hybrid systems. First, geometry optimizations have been carried out with the Amsterdam Density Functional (ADF) code,23 using the BP86 GGA functional and Slater-type orbitals under the zeroth order regular approximation (ZORA) relativist Hamiltonian,24 in vacuo. This method has been successfully used to model a large range of gold nanoclusters.25−27 For gold atoms, core electrons have been frozen and the 19 valence electrons were treated with a DZ Slater-type basis set. For C, H, and S, a triple-ζ plus polarization (TZP) has been used. Geometries of the gold fragments were extracted from the structure of a complete cuboctahedral Au249 nanoparticle for the Au6 and Au25 cluster and from a cuboctahedral Au201 NP for the Au19 cluster (Figure 2). The starting geometries for the optimizations of Au249 (2 nm diameter) and Au201 (1.8 nm diameter) NP are obtained from the fcc bulk phase of gold, following a Wulff’s construction,28 to obtain a simili-spheric structure, which is then fully optimized with DFT at the BP86/ DZ level with D4h symmetry. Au6 and Au25 fragments correspond respectively to the first and the two first (111) layers of the Au249 NP. Au19 is the first (111) layer of the Au201 NP. Additionally, a triangular Au3 fragment has been taken into account as an example of a highly molecular perspective. An overview of the different metallic structures used in this work is given in Figure 2. During relaxations of the hybrid systems, gold atoms were kept frozen. We thus neglect the surface reorganization, although it is considered significant for gold.29,30 This constraint is actually a necessary approximation to keep the Au19 and Au25 clusters in the conformations extracted from the complete Au NP. In a second step, to compute the optical properties, we performed time dependent-DFT (TD-DFT) calculations31−33 using Gaussian 09 package.34 As we want to address the effect of the Au cluster on the DTE optical properties for both the open and closed forms, we have chosen a reliable method for the computation of the absorption properties of conjugated organic photoswitches, which is the combination of a rangeseparated hybrid functional with the description of solvent effects by a continuum model.18,19 The range-separated hybrid functional CAM-B3LYP35 was then preferred, allowing to describe charge transfer phenomena, highly expected in such hybrid compounds.16,17 The LANL2DZ pseudopotential and basis set36 for the description of gold atoms and a 6-31G(d) basis set for C, H, and S constitute a basis set combination suitable for all sizes of hybrid compound, considering computational resources limitations. Solvent effects have been introduced by the mean of a polarizable continuum model (PCM)37,38 in its nonequilibrium formalism, considering either toluene for the isolated DTE or dichloromethane for the hybrid systems. A total of 100, 200, and 250 excited states were computed respectively for Au3−DTE, Au19−DTE, and Au25− DTE hybrid systems. Computing such a large number of excited states is necessary to reach transitions involving the organic part, beyond the numerous low energetic metal-tometal transitions. All theoretical spectra are convoluted with a Gaussian function (fwhm = 0.12 eV).

Figure 3. UV−visible absorption spectra of of (red, dashed line) and cf (blue) calculated at the PCM(Toluene)-CAM-B3LYP/6-31G(d)// BP86/TZP level.

theoretical absorption spectra for the two corresponding isomers, of and cf. A description of the most intense electronic transitions can be found in Table 1. For of and cf, the less Table 1. Most Intense Electronic Transitions Calculated at the PCM(Toluene)-CAM-B3LYP/6-31G(d)//BP86/TZP Level for of and cf: Wavelengths (λ), Oscillator Strengths ( f), and State Description system

λ (nm)

f

orbital composition

of

319

1.00

274

0.40

599

0.78

HOMO−1 → LUMO (38%) HOMO → LUMO (36%) HOMO → LUMO+2 (45%) HOMO → LUMO (19%) HOMO → LUMO

cf

energetic transition is also the most intense one. The lowest energetic transition of of is composed of HOMO−1 → LUMO and HOMO → LUMO monoelectronic excitations. The maximum absorption of cf corresponds to a HOMO → LUMO excitation. For the two isomers, frontier molecular orbitals involved in these transitions are presented in Figure 4. For the open form, the HOMO and LUMO present a strong localization on one side of the DTE moiety, because of the asymmetry in the substitution of the two thiophene aromatic arms (−CH3 on one side and −SH on the other side). The HOMO−1 is more delocalized and presents electronic density on the overall molecule. For the more conjugated closed form cf, the asymmetry slightly impacts the frontier orbitals: both the C



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Figure 4. Frontier molecular orbitals of of and cf (threshold: 0.02 au).

Figure 5. Description of the adsorption parameters (upper part). For clarity, only one thiophene group of the DTE molecule is represented. Stable methanethiol adsorption site for Au19 and Au25 (lower part). Color code: yellow, gold; pink, sulfur; gray, carbon; white, hydrogen. The second layer of Au25 is displayed in a wireframe fashion.

the closed form, the first step of the cycloreversion reaction corresponds to a HOMO → LUMO transition, yielding a loss of bonding electronic density on the C−C bond. In the following, the promotion of an electron toward a virtual orbital presenting the expected topology for either the open-ring or closed-ring DTE will be denoted as a photochromic transition. Consequently, the theoretical investigation of the photochromic properties will rely on the analysis of the virtual orbital topologies and on the research of the photochromic transitions in the computed spectra. The presence (respectively

HOMO and the LUMO are delocalized over the whole πsystem. DTE frontier orbitals actually constitute a reliable indicator of the photochromic reactivity. In previous works,39−41 we have shown that, for a large range of photochromic open-ring DTEs, the first step of the cyclization reaction corresponds to the promotion of an electron toward a virtual orbital presenting a significant density on at least one of the reactive carbon atom(s) (red-circled carbons in Figure 1) as well as a bonding character for the to-be-formed C−C bond. On the contrary, for D



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Table 2. Computed Adsorption Geometrical Parameters for Au19−DTE and Au25−DTE Systems (Definition of the Different Parameters in Figure 5) distances Au−S (Å)

angles (deg)

system

1

2

3

4

plane-S

tilt

twist

shift from the bridge position (Å)

Au25−of Au25−cf Au19−of Au19−cf

2.92 2.90 3.53 3.60

3.93 4.00 3.43 3.52

2.77 2.80 2.82 2.77

2.89 2.92 2.76 2.99

2.46 2.48 2.50 2.78

68.9 69.2 62.1 64.6

8.0 4.0 5.0 2.0

0.7 0.8 −0.1 0.1

Figure 6. Conformations of Au19−DTE and Au25−DTE systems. For each system, both frontal and lateral views are reported.

A small methanethiol fragment is first considered, with different starting geometries. These are the bridge, top, and hollow positions (depicted in Figure 5), which are the three adsorption sites known for thiols on Au(111).42,29 Regardless of the starting geometry, the stable position for −SCH3 is found to be on a bridge site for Au19 and halfway between bridge and hollow site for Au25, in accordance with previously published DFT results.42 Adsorption of DTE on Aun (n = 3, 9, 15). In the next step, the methyl moiety is replaced by the DTE and a further geometry optimization is carried out. One has to note that this step was highly complicated due to SCF convergence issues, a well-known computational bottleneck for gold−organic hybrid systems. For a given hybrid system, the adsorption site did not change when going from the methanethiol fragment to the whole anchored DTE and the adsorption parameters are summarized in Table 2. Geometries of Au3−DTE hybrid systems have already been studied in a previous work.14 Considering the highly molecular structure of this gold cluster, the relaxation would inevitably lead to a top position, with the sulfur atom in the Au3 plane. Hence, the sulfur position for this system was kept fixed, in the conformation found for Au25−DTE systems, to ensure a surface-like adsorption site. Au3−DTE adsorption parameters are thus not given in Table 2 and not discussed in the following. The main difference between Au19 and Au25 clusters lies in the adsorption site, as described above for the methanethiol group. Indeed, for Au25, the interaction with the gold atom of the second layer lying below the hollow site can explain the translation of the sulfur adsorption site from the bridge toward the hollow position. The optimized orientation of DTE grafted onto Au19 and Au25 corresponds to tilt angles close to 65° (Figure 6), in agreement with a previous study.15 Table 2 shows that both tilt angles and twist angles are slightly affected by the

absence) of such an electronic transition in the absorption spectrum will be used as a criterion to determine the preservation (respectively loss) of the DTE photoreactive properties within the hybrid system. Here, for of, regarding the contribution of the reactive carbons, the LUMO possesses a weak bonding character. Indeed, one can identify a weak bonding interaction between the two reactive carbon atoms by reducing the isodensity threshold to 0.01 au. The HOMO−1/HOMO → LUMO transition computed at 319 nm is thus a photochromic transition. One can draw the same conclusions for the cf first excited state.

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AUN−DTE HYBRID SYSTEMS Structural and Electronic Properties. Adsorption of a Methanethiol on Aun (n = 3, 9, 15). The first step toward the construction of hybrid systems is the study of possible thiol adsorption sites on the NP fragments. The Aun (n = 3, 19, 25) fragments come from either Au201 or Au249 NPs, which have been optimized, starting from a bulk fcc phase cuboctahedral structure with a starting interatomic distance of 2.88 Å. After relaxation and extraction of the fragments, we observe a bond contraction with respect to the bulk distance resulting from the lowest coordination of some gold atoms, transcribing the “edge effect”. The relaxed mean distance is found to be the same for Au19 and Au25: 2.73 Å. The relaxed distance between the two Au(111) layers for Au25 is 2.26 Å instead of 2.36 Å in the bulk. The adsorption is defined by the position of the sulfur atom on the surface (distance to the surface and projected position in the plane; here quantified by the distances to the four nearest gold atoms and the displacement with respect to the bridge position) as well as the tilt angle between the first S−C bond and the normal to the surface and the twist angle between the surface and the plane of the first thiophene ring. These adsorption parameters are sketched in Figure 5. E



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size of the metallic cluster. The internal structural parameters of the of and cf DTE subunits are given in Table 3, for the isolated Table 3. Main Geometric Parameters for of and cf in Their Isolated and Anchored Conformationsa of Au3−of Au19−of Au25−of cf Au3−cf Au19−cf Au25−cf

d (Å)

ξ1 (deg)

ξ2 (deg)

ξ3 (deg)

ξ4 (deg)

3.59 3.58 3.63 3.63 1.54 1.55 1.55 1.55

46.6 42.4 45.1 42.6 8.2 8.4 10.4 9.9

47.7 40.3 42.7 42.5 9.0 10.1 10.1 9.5

26.4 34.0 13.2 12.9 0.8 11.9 1.7 11.9

21.6 25.9 17.2 19.4 10.3 0.3 1.6 0.3

d is the distance between the reactive carbons. ξ1 and ξ2 are the C1C2C3C4 and the C2C1C3′C4′ dihedral angles, ξ3 and ξ4 are the S1C5C6C7 and the S1′C5′C6′C7′. See Figure 1 for the atom numbering.

a

Figure 7. Band structure of gold fragments and molecular energy levels of of and cf isomers.

similar, and there are only minor energy shifts for the last occupied orbitals. This result suggests convergence of the electronic structure when going from Au25H to Au52. For Au19H, some subgaps are not perfectly reproduced in important regions (considering Au52 as a reference structure), for example, between the HOMO energies of of and cf. However, the 19 atoms aggregate can still be considered to be qualitatively close to Au52. Both Au6 and Au3H obviously fail to describe the overall band structure and the frontier orbital positions, due to their limited number of gold atoms and thus their few energy levels (Au6−DTE systems are not considered in the TD-DFT section due to their open-shell electronic structure). Previous theoretical studies showed oscillating behavior of the HOMO− LUMO gaps for small cluster sizes,44,45 explaining the large difference between Au6 and Au3H. According to the analysis of the fragment orbital energies (which is a straightforward but simple approach), we expect a better description of the targeted NP−DTE system for Au19 and Au25 hybrid systems than for their Au3 and Au6 counterparts. This hypothesis will be validated in the following TD-DFT section, by comparing the theoretical spectra of Au3−of/cf, Au19−of/cf, and Au25−of/cf.

and anchored conformations. The distance d between the two reactive carbons (red circle carbons in Figure 1) is known to be a key empirical parameter for the efficiency of the photocyclization of the open isomer:43 ring closure is no longer possible if d is larger than 4.2 Å. This distance remains close to 3.6 Å and is thus not significantly impacted by the adsorption on the different clusters. In the same way, the dihedral angles ξ1 and ξ2, which are also a descriptor of the ring-opening/closure reaction, are slightly modified after grafting onto the cluster (the uttermost change is 5). On the contrary, the torsion angle ξ3 between the first and the second thiophene rings of the DTE lateral chain is highly impacted by the environment of the molecule, especially for the open form. For instance, ξ3, decreases from 34° for Au3−of to 13.2 for Au19−of, as a consequence of the steric effect brought by this extended gold plane This should lead to a significant change in the electronic structure and thus in the optical properties of the of anchored conformation compared to those of its isolated conformation. Finally, the electronic energy difference between the closedring and the open-ring isomers remains in the same order of magnitude for the isolated DTE and for the three DTE−gold hybrid systems: 8.5 kcal mol−1 for cf/of, 10.7 kcal mol−1 for Au3−cf/of, 9.5 kcal mol−1 for Au19−cf/of and 10.7 kcal mol−1 for Au25−cf/of, always in favor of the open isomer. There is thus no effect of the anchoring on the relative stability of the DTE isomers. Electronic Structure. The interaction between the gold cluster and the photochrome may be rationalized by analyzing fragment interaction diagrams of the isolated organic and metallic fragments. The idea is to intuit the electronic structure of a Aun−DTE system by comparing the orbital diagrams of the two fragments forming the hybrid moiety, namely the Aun cluster on the one side and the photochromic molecule on the other side. One has to note that, for metallic systems presenting an odd number of gold atoms, the Aun fragment is an open shell system. Therefore, a hydrogen atom localized on the sulfur adsorption site has been added to obtain closed-shell systems and ensure the simplicity of the comparison. Figure 7 shows the different NP fragment (Au3H, Au6, Au19H, Au25H, and Au52) band structures and compares them to the photochrome of/cf MO energy levels. Au52 (a third layer is added to Au25) was included in the scheme to show the evolution of the band structure with growing fragment size. The overall band structures of Au25H and Au52 are qualitatively

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UV−VISIBLE SPECTRA Description of the Open Form Absorption Spectra. Figure 8 shows the calculated UV−visible spectra for for Aun− of systems with n = 3, 19, and 25. The DTE (in its anchored geometry), NP, and hybrid system spectra are superimposed to provide a better understanding of the perturbation. For each system, the different absorption bands are sorted as metal-tometal, photochrome-to-photochrome or charge transfer excitations. Generally, metal-to-metal transitions become by far the most frequent type of transitions with growing cluster size. Furthermore, photochrome-to-metal charge transfer transitions are found for all the systems in the infrared region. These bands arise from the limited size of the cluster aggregate and should not be present in the experimental absorption measurements.14 In the following, only transitions that involve a non-negligible contribution of the photochrome (larger than approximatively 20%) are discussed. Details of these transitions are given in Table 4. Molecular orbitals involved in these excitations and presenting an important contribution on the DTE are depicted in Figure 9. For the three different systems, one can note that the electronic transitions of the DTE subunit, in its Aun−of conformation (green line in Figure 8), is systematically redF



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Figure 8. Theoretical absorption spectra of Au3−of (top left), Au19−of (top right), and Au25−of (down). The DTE spectrum is in green, the gold cluster spectrum is in dotted black line, and the hybrid system spectrum is in red (the stick spectrum is also represented). For the latter, green sticks are transitions populating DTE orbitals and photochromic transitions wavelengths are marked with a star *.

other hand, the transition at 317 nm relies on an electronic excitation to the LUMO+12, the latter orbital presenting a weakly antibonding interaction between the two reactive C atoms and thus not matching the photochromic criteria. In the case of Au25−of, the spectrum does not contain transitions with considerable DTE fragment contribution, except for an excitation at 313 nm with a 0.37 oscillator strength value. This intense transition promotes an electron toward the LUMO+17, which shows an antibonding interaction between the reactive carbons. Thus, this excitation cannot be identified as a photochromic transition. The first virtual orbital with a photochromic topology is the LUMO+16 (Figure 9). However, it is not significantly involved (i.e., the percentage contribution is trifling) in weak transitions (i.e., the oscillator strength value is small). Aside from the “surface” type of conformation, another stable conformation can be found for Au25−of where the photochrome is grafted onto the edge of the gold fragment. This conformation is found to be lower in energy, by 8.2 kcal mol−1 at the CAM-B3LYP level. One should, however, expect an inversion of stability between those two structures for a large NP, where steric effects would have a

shifted with respect to the free molecule spectrum presented in the “isolated DTE” section (Table 1). This difference is clearly related to the variation of the dihedral angle ξ3 and hence a modification of the conjugation path after grafting onto the metallic aggregate. For Au3−of (Figure 8), the spectrum of the hybrid system cannot be seen as a simple addition of the DTE and cluster optical properties. The most intense transition, peaking at 308 nm, corresponds to the promotion of an electron toward the LUMO+2, which topologically matches the of LUMO, with a bonding interaction between the reactive carbons. It is thus a photochromic transition. Moreover, at 281 nm, one can identify a second intense photochromic transition that enables the promotion of an electron toward the LUMO+5, the counterpart of the of LUMO+2. Among the 200 transitions computed for Au19−of, only three significantly involve excitations localized on the photochrome moiety. They peak at 333, 331, and 317 nm, with a low oscillator strength value (around 0.2). The transitions at 331 and 333 nm involve weakly (respectively 11% and 15%) the LUMO+9, which presents a photochromic topology. On the G



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Table 4. Description of the Most Relevant Electronic Transitions for the Hybrid Open Systems in the 300−400 nm Region (Photochromic Transitions in Bold, More Details in Table 1) system

λ (nm)

f

orbital composition

Au3−of

334

0.31

331 308 281

0.34 0.54 0.35

386 386 385 383 345

0.41 0.74 0.68 0.29 0.21

333

0.19

331

0.18

317 394

0.21 0.36

390

0.59

375 313

0.26 0.37

HOMO → LUMO+3 (26%) HOMO−15 → LUMO+1 (20%) HOMO−17 → LUMO (16%) HOMO → LUMO+3 (37%) HOMO−1 → LUMO+2 (79%) HOMO → LUMO+5 (29%) HOMO−1 → LUMO+5 (15%) HOMO−2 → LUMO+3 (13%) HOMO−2 → LUMO+4 (30%) HOMO−2 → LUMO+3 (25%) HOMO−2 → LUMO+5 (32%) HOMO−4 → LUMO+4 (13%) HOMO−24 → LUMO+1 (13%) HOMO−2 → LUMO+6 (14%) HOMO−1 → LUMO+9 (11%) HOMO−1 → LUMO+9 (15%) HOMO−2 → LUMO+8 (13%) HOMO−3 → LUMO+12 (36%) HOMO → LUMO+11 (17%) HOMO−23 → LUMO (13%) HOMO−25 → LUMO (17%) HOMO−24 → LUMO (15%) HOMO−16 → LUMO+1 (24%) HOMO−3 → LUMO+17 (50%)

Au19−of

Au25−of

Figure 10. Theoretical absorption spectra of Au25−of in its “surface” and “border” conformations.

same conclusions can thus be drawn concerning the loss of the photochromic properties. From the study of the hybrid open isomers, a clear difference arises between the optical properties of Au3−DTE on one side and Au19−DTE/Au25−DTE on the other side. The photochromic transitions of the isolated molecule are recovered in the Au3−of spectrum. They are the most intense transitions and are not mixed with any nearby metal-to-metal transitions. On the contrary, for Au19−of and Au25−of, the photochromic transitions are embedded by metal-to-metal transitions. As a consequence, for Au25, the photochromic transition of the isolated DTE completely disappears, whereas for Au19 a weak transition is preserved at ca. 330 nm. However, this transition is surrounded by a multitude of stronger metal-to-metal transitions. Experimentally, the impossibility to photocyclize the DTE unit can thus be explained by the vanishing of the photochromic transitions. Hence, the critical parameter to model properly the interaction between the photochrome and the metallic aggregate is identified as the ability to reproduce the high density of relatively intense metal-to-metal transitions

Figure 9. Relevant virtual molecular orbitals of the open hybrid systems (isodensity value of 0.02 au for Au3 and 0.01 for the others).

more important contribution. The comparison of the spectra of Au25−of in its “surface” and “border” conformation is shown in Figure 10. The global shapes of the spectra are similar; the same transitions involving the photochrome-localized virtual orbitals are found in both cases. The relative contribution of the gold and DTE fragments to the hybrid molecular orbitals slightly changes, which may explain the small variations between the two spectra. For this second conformation, the H



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expected in the 300−400 nm region for a nanometer-sized NP. Only Au19 and Au25 clusters enable us to recover the experimental observations; thus only Au19−cf and Au25−cf optical properties will be described and discussed in the following. Description of the Closed Form Absorption Spectra. The theoretical spectra of Au19−cf and Au25−cf are compared in Figure 9, with an emphasis on the 550−750 nm region, where the photochromic transition of the closed isomer is expected to be found. For the closed isomers, like the open-ring case, there is a bathochromic shift of the isolated DTE electronic transitions in its Aun−cf conformation (green line in Figure 11) compared to those of the “isolated DTE” section (Table 1). For example, for cf, the HOMO → LUMO transition (λ = 599 nm in toluene) is shifted toward 673 nm for the anchored geometry on Au25 and toward 719 nm on Au19. By study of the frontier orbital energy levels, it appears that this shift is caused by a destabilization of the HOMO and a stabilization of the LUMO. This can be rationalized by the

evolution of the DTE bond distances after grafting onto the NP, which directly impacts the bonding or antibonding contributions within these two molecular orbitals (the bond distances are reported and discussed in the Supporting Information). For Au19−cf, the absorption band between 600 and 700 nm is mainly composed of two intense metallic transitions, at λ = 629 nm with an oscillator strength f = 0.43 and at λ = 672 nm with f = 0.18 (Table 5). In between, the transition peaking at Table 5. Description of the Most Relevant Electronic Transitions for the Hybrid Closed Systems in the 500−800 nm Region (Photochromic Transitions in Bold, More Details in Table 1) system

λ (nm)

f

orbital composition

Au3−cf

656

0.54

572

0.18

Au19−cf

671

0.18

Au25−cf

656 628 775

0.11 0.43 0.37

695

0.23

651

0.42

593

0.16

HOMO → LUMO+2 (50%) HOMO−1 → LUMO (20%) HOMO → LUMO+2 (35%) HOMO → LUMO+1 (19%) HOMO−1 → LUMO+1 (13%) HOMO−3 → LUMO+2 (42%) HOMO−4 → LUMO (24%) HOMO → LUMO+3 (76%) HOMO−4 → LUMO+1 (52%) HOMO−2 → LUMO+4 (22%) HOMO → LUMO+4 (20%) HOMO−2 → LUMO+2 (17%) HOMO−6 → LUMO (42%) HOMO−5 → LUMO (21%) HOMO → LUMO+6 (19%) HOMO → LUMO+8 (24%) HOMO−7 → LUMO (24%)

656 nm is relatively weak (f = 0.11) and corresponds to a HOMO → LUMO+3 excitation, comparable to the lowest energetic transition of the cf molecule in terms of molecular orbital topology. Following our criteria, it can be seen as a photochromic transition. For Au25−cf, the metal-to-metal transitions are less intense in this region of the spectrum. The most intense excitation (λ = 651 nm, f = 0.42) promotes an electron toward the LUMO+6 and LUMO+8 (43% of the total excitation), which both present a cf photochromic topology. Hence, for both Au25−cf and Au19−cf, a photochromic transition is found, nearly at the same wavelength (656 and 651 nm). However, for the latter system, the presence of this excitation is not clearly interpretable as a preservation of the photochromic properties due to its weak oscillator strength in the proximity of stronger metal to metal transitions. The difference between Au25 and Au19 is clearly caused by the absorption profile of the gold fragment in the 600−700 nm region. For instance, for Au19, the very strong metallic transition at 629 nm involves occupied and virtual molecular orbitals delocalized over the whole gold plane (see for instance the HOMO−4 and LUMO+1 in Figure 12). The presence of these transitions is due to the planar organization of the gold cluster and disappears if one considers a multilayer metallic aggregate. Choosing to model a gold NP by a planar cluster can thus induce some artifacts in the visible−near IR region due to the enhancement of “in plane” localized excitations.

Figure 11. Theoretical absorption spectra of Au19−cf (upper part) and Au25−cf (lower part). See Figure 8 for more details. I



Article

Figure 12. Relevant virtual molecular orbitals of the closed hybrid systems (isodensity value of 0.02 au for Au3 and 0.01 for the others).

■

CONCLUSION This study aims at modeling the optical properties of a dithienylethene photoswitch grafted onto a gold nanoparticle. To reduce the computational burden and recover the experimental trends with the smallest metallic aggregate possible, we have investigated the influence of the shape and size of small gold clusters on the DTE photochromic properties. We have first investigated the adsorption site of thiol-substituted DTE for different metallic clusters. For Aun (n = 19 and 25), the binding site lies in the vicinity of the bridge site: the influence of the cluster shape/size on the adsorption site is negligible. Concerning the optical properties, we have shown that the representation of the high density of metallic states in the 300−400 nm region is crucial to understand the preservation or the loss of the of photochromic properties. Whereas Au3 results to be inappropriate to model this high density of states, Au19 and Au25, representing respectively a planar fragment and a two-layer structure, produce similar results, suggesting that the three-dimensional arrangement of the gold atoms is less important than the number of gold atoms to reproduce the interactions between the metallic and the organic moieties in the near UV region. Inversely, the arrangement of the gold cluster is critical to model the optical properties of closed-ring hybrid systems. For Au19, the presence of low energetic metallic transitions, resulting from the planar arrangement of the gold atoms, interferes with the cf photochromic transition. Using such a model can thus lead to a false prediction of the photochromic activity. Therefore, Au25 is considered as the best fragment possible to understand and predict the optical properties of a nanoscaled NP−DTE object. For the considered photochrome, the Au25 model can rationalize why the ring-opening is preserved and the ringclosure impeded. In the former case, an electron can be promoted toward a virtual orbital presenting the required photochromic topology, whereas for the latter, there is no efficient way to populate such a hallmark orbital. Our present work thus shows the extreme dependence of the size and

organization of the metallic cluster on the computation of the excited-state properties of the hybrid system. Hence, within our framework, we consider that the modification of the electronic structure of the photochrome due to the grafting onto the metallic moiety is responsible for the loss of photochromic activity. Even so, with one photochromic unit immobilized on the cluster, our model cannot consider the influence of possible intermolecular quenching mechanism on the loss/preservation of the photoactive properties. We now plan to investigate such a feature.

■

ASSOCIATED CONTENT

S Supporting Information *

The detailed geometries of cf in the different conformations (gas phase and onto the different clusters) are available in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

■

AUTHOR INFORMATION

Corresponding Authors

*A. Fihey: e-mail, arnaud.fi[email protected]. *A. Perrier: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This research used resources of the GENCI-CINES/IDRIS (Grant c2011086680). REFERENCES

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