Quenching of the Photoisomerization of Azobenzene Self-Assembled

Article pubs.acs.org/JPCC

Quenching of the Photoisomerization of Azobenzene SelfAssembled Monolayers by the Metal Substrate Enrico Benassi*,† and Stefano Corni Centro S3 CNR Istituto di Nanoscienze, via G. Campi 213/a, 41125 Modena, Italy S Supporting Information *

ABSTRACT: In this study, we aim at investigating the role played by the metal surface as a possible dissipative channel in the photoisomerization process of azobenzene-derivativebased self-assembled monolayers (azo-SAMs). In particular we compare the cases of gold and platinum. We study the excitonic transfer phenomena of two azo-derivatives (both in trans and in cis conformation) chemisorbed on Au{111} and Pt{111} to the metal surfaces. The metal effects are evaluated within the local and nonlocal regimes, showing that nonlocality in the metal response plays an important role and nonlocal accounting quenching rates are one order of magnitude smaller than the corresponding local results. The couplings are stronger for Au{111} than for Pt{111}, but for both cases the energy transfer between the molecule and the metal turns out not to be able to suppress photoisomerization.

1. INTRODUCTION Azobenzene (diphenyldiazene) exists in trans and cis isomers (Scheme 1)1−10 that can be switched one into the other by the

Scheme 2. Azo-Derivatives Investigated in This Study (with X = H, SH)a

Scheme 1. Mechanisms of trans−cis Isomerization of Azobenzene

a

directly linked over the metal surface. Since the excitonic couplings do not immediately provide information concerning the dynamic process of exciton diffusion through the material, especially because the destiny of the exciton is strongly influenced by the system geometry, then we studied not only the couplings but also the excitonic dynamics, up to the computation of the diffusivity tensor components. In that work, the (gold) surface was simply considered as the anchoring support for the active molecules. However, it may be supposed that the surface could act as an important role in the exciton transfer phenomenon. Therefore, a key question naturally arises: What is the role of the metal? In other words, does the photoisomerization process occur to a different degree when the molecules of Scheme 2 are chemisorbed on

interaction with the electromagnetic radiation. The photoisomerization capability of azobenzene and its derivatives was demonstrated to be preserved also when molecular rods incorporating the -NN- azo-group are adsorbed in compact self-assembled monolayers (azo-SAMs) on metal surfaces.11,12 There exist phenomena that may hinder the photoisomerization process. One of these may be the exciton transfer. According to a recent study,13 azobenzene chromophores in a close-packed SAM structure influence each other strongly by excitonic coupling. This and the related fast delocalization of the excitation within the SAM is suspected to contribute strongly to the suppression of the photoisomerization process because of the strong delocalization in the densely packed layer which quenches the optical excitation on an ultrafast time scale. It thus impedes molecular switching in the SAM. Recently,14 we investigated the azobenzene derivatives reported in Scheme 2, where the thio-group is a direct substituent of the phenyl ring, and thus the active molecules are © 2014 American Chemical Society

Names refer to X = H.

Received: August 14, 2014 Revised: October 9, 2014 Published: October 9, 2014 25906

dx.doi.org/10.1021/jp508246p | J. Phys. Chem. C 2014, 118, 25906−25917

The Journal of Physical Chemistry C

Article

different metals? To find an answer to this question, we compare two noble metals, which are widely employed in SAM fabrication: platinum and gold. The main phenomenon that involves the metal is the possible quenching via exciton transfer between the adsorbed molecule and the metal. This is a wellknown phenomenon that found an elegant model in the 1970s, thanks to Chance, Prock, and Silbey (the CPS model).15 This theory was also recently revised,16,17 but the main features remain; i.e., a rigorous electrodynamics treatment is followed at the expense of a strongly simplified molecular picture, where the molecule is assumed to be a point dipole. This is the reason why in this work we shall follow a different approach that improves the description of the adsorbed molecules and in particular of their electronic structure. Here we shall present and discuss the study of the metalinduced quenching of the azobenzene derivatives chemisorbed over gold and platinum, starting from an accurate evaluation of the differences in the geometrical parameters of the azoderivatives anchored over the two metals and computing the optical properties of the two kinds of systems. Moreover, another aspect that is investigated is the effect due to the dielectric environment where the photoactive molecule is immersed. Finally, the role of the nonlocal response of the metal is explored by using hydrodynamics and Lindhard− Mermin models.18

positive charges are regarded as being smeared out over the entire volume of the metal, whereas the valence electrons are free to move within this homogeneously distributed, positively charged background. Referring to Scheme 3, δv represents system-dependent small offsets between the image plane and the jellium edge in vacuo. The choice of appropriate values of δv is a delicate question. Surface state energies from photoemission and inverse photoemission measurement indicate metal-dependent locations of the image plane relative to the jellium edge δv = (−0.13 ÷ +0.26) Å.20 Low values of δv are associated with a higher total electron density of the metal, proportional to higher atomic number; e.g., δv(Au) < δv(Pt).20,21 The average position of the first layer of the metal atoms at the interface is represented by zsurf. We shall conventionally assume the normal axis origin in order to have zsurf ≡ 0. Then, in vacuo the position of the image plane is zim ≡ zsurf + d/2 + δv = d/2 + δv, where d is the distance between two metal layers (for instance, d = 2.350 Å and 2.299 Å for gold and platinum, respectively; vide infra), and d/2 is the distance between the jellium edge and the first metal layer. The arithmetic mean (“interface edge”) characterizes the position of the image plane which maps the first atomic layer of the adsorbed molecules onto the first atomic layer of the metal. A widespread approach relies on the dipole CPS model, in which an exciton within the organic layer is modeled as an oscillating point dipole whose electric field is described by dyadic Green’s functions, although more complex approaches have been proposed.18 In the limit of distances much smaller than the wavelength, the expression for the dipole−metal energy transfer (ET) rate constant as a function of the angular frequency of the dipole emission ω is15

2. METHODS If we are to provide a microscopic picture about what occurs at the metal surface when a molecule (or a solution) interacts with it, we have to take into account that the electrons in the metal rearrange to counterbalance the local electric field at the interface of the adsorbed molecules. To do this, we shall use the method of auxiliary charges, which consists of the replacement of certain elements in the original layout (in our case, the metal) with fictitious charges satisfying the boundary conditions of the problem. Specifically, the charges of the molecule chemisorbed on the metal surface are replicated, generating an image potential. The image potential can be computed under the assumption of a mirror image (with opposite sign) of the collection of all atomic charges (blurred molecule in Scheme 3). An issue discussed in the literature19 concerns the reflecting surface position choice, with respect to the outset metal atoms layer. The computation of the image potential depends on the position of the image plane. The jellium is a model describing the delocalized valence electrons in a metal, in which the

̂ (ω) = bET

qθ

(

n

3

)

4 ω c1 d1

Φ(ω) (1)

where q is the quantum yield; the orientational parameter θ is 3/2, 3/4, or 1 for perpendicular, parallel, or isotropically averaged dipole, respectively; n1 is the refractive index of the medium containing the dipole; c is the light velocity in vacuo; d1 is the distance of the dipole emitter to the mirror; and the dissipative function Φ(ω) is defined as ⎡ ε (ω) − ε1(ω) ⎤ Φ(ω) ≡ Im⎢ 2 ⎥ ⎣ ε2(ω) + ε1(ω) ⎦

Scheme 3. Representation of a Thiolated Azobenzene Molecule Adsorbed over a Metal Slab and Its Mirror Image

(2)

where εj = εj′ + iεj″ is the complex dielectric function (j = 1 for the medium containing the dipole that in our case is the adsorbed molecule; j = 2 for the metal). This model does not fully describe the properties of the system, since in general the molecule cannot be reduced to a point dipole, because of its extended nature. To overcome this difficulty, we shall couple the CPS model with a quantum mechanical model that calculates the energy transfer constant rate from the excitonic matrix. In the following we present such an extension to the CPS model, beyond the point dipole and the metal local dielectric response approximations. The excitation energy transfer (EET) molecular decay rate is given by22

∫ dr ρS →S (r) Vreact[ρS →S ](r)}

0 → Sn) Γ(S = −2Im{ EET

25907

0

n

0

n

(3)



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delicate. Such nonlocality can be accounted for by using the proper Green’s function:

where Vreact[ρS0→Sn] is the electrostatic potential generated by the metal polarization induced by the transition density ρS0→Sn itself. This is a generalization of 0 → Sn) Γ(S EET

= 2Im{μS → S ·Ereact[μS → S ]} n

0

0

.(nonloc) (r, r′) = Im

(S0 → Sn)

=

4 3

k13 2 1 μ 2 S0 → Sn q n1

the expression of the CPS model can be obtained (see eq 1). In general, using eq 3 and defining the electrostatic Green function .el (r,r′) as 1 + .Im(r, r′) ε1|r − r′|

∫ dr ∫ dr′ ρS →S (r) .Im(r, r′) ρS →S (r′)} 0

n

(7)

For instance, in the case of local metal response, we have .(loc) Im (r ,

(hydr) (bulk) εmet (ω , q) = εmet −

ε − ε1 1 r′) = − 2 ε2 + ε1 ε1|r − 9(r′)|

(8)

⎛ ε − ε1 ⎞ 1 dr = 2Im⎜ 2 ⎟ ⎝ ε2 + ε1 ⎠ ε1 ρS → S (r) ρS → S (r′)

(LM) (bulk) εmet − (ω , q) = εmet

∫ ∫ dr′

n

0

0

n

ε(bulk) met

⎛ ε − ε1 ⎞ 1 dr = 2Im⎜ 2 ⎟ ⎝ ε2 + ε1 ⎠ ε1 ρS → S (r) ρSmir→ S (r″)

∫ ∫ dr″

n

0

n

fl (z , u) ≡

|r − r″| =

2 ΦHnn ε1 (9)

ρmir S0→Sn(r″)

(12)

3Ω p2u 2fl (z , u) ⎡ i f (z , u) ⎤ (ω + i/τ )⎢ω − τ fl (z , 0) ⎥ ⎣ ⎦ l

(13)

2

⎛ z − u + 1⎞ 1 1⎧ ⎟ ⎨[1 − (z − u)2 ] log⎜ + ⎝ z − u − 1⎠ ⎩ 2 8z ⎛ z + u + 1 ⎞⎫ ⎟⎬ + [1 − (z + u)2 ] log⎜ ⎝ z + u − 1 ⎠⎭ (14)

As we mentioned in the Introduction, we are also interested in investigating the effect of the dielectric environment. Therefore, we shall consider two differing conditions, viz., the hemispace where the azoderivative resides is characterized (a) by a unitary relative dielectric constant (Scheme 4, on the left) or (b) by a continuum isotropic dielectric function of the lighting frequency determined on the basis of the dielectric properties of the azoderivative (Scheme 4, on the right). The first case represents the physical condition of an infinitely

where r″ ≡ 9 (r′) and ≡ ρS0→Sn(9 (r″)) is the transition density of the reflected molecule, Φ is the dissipative function (defined in eq 2), and Hnn ≡ ∫ dr ∫ dr″ρS0→Sn(r) ρmir S0→Sn(r″)/|r −r″| is the exciton coupling between the two electronic densities. So, in the case of local metal response, the decay rate is factored. As it can be seen, the excitonic matrix elements Hnn are multiplied by the dissipative function Φ(ω); i.e., H★(ω) = Φ(ω)H

(ω + i / τ )ω − β 2 q 2

where ≡ εmet(ω,0) + Ωp /[(ω + i/τ)ω] is the interband contribution to the bulk dielectric function, Ωp is the plasma frequency, τ ≡ 1/γ is the bulk relaxation time, β2 ≡ (3/5)νF2, νF ≡ pF/me = ℏkF/me is Fermi’s velocity, z ≡ q/(2kF), u ≡ (ω + i/τ)/(qνF), and

|r − 9(r′)|

0

Ω p2

and according to Lindhard−Mermin’s model:

and thus the decay rate has the simple form: 0 → Sn) Γ(S EET(loc)

e−q1(z + z ′− 2z12)

+∞

(6)

n

ε10(q1) + 1

0(q1) ≡ q1/π∫ dqz /(q2ε2(ω , q)), and q2 ≡ q12 + qz2. −∞ Equation 11 has been obtained from a more general expression, considering three layers, viz., the metal, the molecule, and the vacuum,18,25 and shows that, in the case of nonlocal metal response, the decay rate cannot be factored. According to the mentioned previous work,18 the value of the energy transfer rate constant can change in one direction or in its opposite depending on the level at which nonlocality is considered. The metal nonlocal permittivity is here chosen according to the hydrodynamic approximation:

the decay rate is rewritten as 0

ε10(q1) − 1

where J0 is the zero-order Bessel function of the first kind, R and R′ are the projections of r and r′, respectively, on the interface plane, z and z′ are the coordinates along the axis normal to the interface plane (so that r = R + zẑ and r′ = R′ + z′z′̂ ), z 12 is the coordinate of the interface plane,

(5)

0 → Sn) Γ(S = − 2Im{ EET

dq1 J0 (q1|R − R′|)

(11)

15

.el(r, r′) ≡

+∞

(4)

n

From eq 4 and the total decay rate ̂ btot

∫0

−1

(10)

Scheme 4. Two Cases Characterized by Different Dielectric Environments

Here we would also discuss about two other important phenomena occurring in the proximity of the metal surface: (1) the electron−hole excitation made possible by the presence of a surface23,24 and (2) the nonlocality of the metal response. Concerning the electron−hole excitation, it has been proved23,24 that the expression of the dumping contribution for a molecule in vacuo, at a certain distance from a metal surface, is proportional to EF−1/2, while concerning the nonlocality of the metal response, the question is more 25908



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system was fully relaxed until each component of the residual force on each atom was smaller than 0.03 eV/Å. Once the optimized geometries of the metal atom surfaces were obtained, the thio-1DA and thio-2DA were adsorbed on them. In particular trans and cis conformers anchored on the surface through the sulfur atom at the on-top position. Adsorbed monolayers were described by considering one molecule per unit cell adsorbed on one side only of the slab. The size surface unit cells was (10.150 × 5.860) Å2, i.e., 1.681 molecules/nm2, for gold, and (9.930 × 5.733) Å2, i.e., 1.757 molecules/nm2, for platinum. The system was fully relaxed with the same computational setup as that described earlier. The quantum mechanical (QM) PW calculations were performed using the Quantum Espresso package.40 Once the geometries and the description of the electronic structures for the single molecules were obtained, we built model homodimers, taking two identical molecules and arranging them in “specular” conformation (Figure 2). To do

diluted azo-SAM, whereas the second case mimics the different condition of a hemispace fully filled by a medium optically acting as the azo-derivative adsorbed on the metal. In both cases, the metal complex dielectric function is related to the complex refraction function nj* = nj′ + in″, by ε′j = n′j2 − n″j2 and ε″j = 2n′j n″j , and the experimental values of nj and nj″ are measured.26,27 In case b, for the thiolated 1- and 2DA the dielectric function spectra have been obtained from the UV−vis spectra,28,29 according to the procedure described in Appendix A.

3. COMPUTATIONAL DETAILS 3.1. Single Molecule Computations. In our previous work14 we obtained the relaxed molecular geometries of the 1and 2DA−X (X = H, SH; see Scheme 2), both in trans and in cis conformation, in vacuo phase, after optimization at the density functional theory (DFT)30−33 level (Figure 1). The cc-

Figure 1. Optimized geometries of thiolated 1- (top) and 2DA (bottom), in trans (left) and in cis (right) conformation.

Figure 2. Specular dimer for trans-thio-1DA.

this, we have employed the geometrical parameters computed at the PW level. The distance between the real and the image sulfur atoms was scanned between 0.750 and 6.000 Å (step = 0.125 Å). For each step, the singlet−singlet coupling matrix element was computed following the transition charge density (TCD) approach.41,42 The TCD method is designed to provide a highly accurate estimate of the Coulombic portion of the electronic coupling between two molecules. The TCD method can determine Coulombic coupling to the fullest extent allowed by the accuracy of the original quantum mechanical calculation, because it utilizes the full three-dimensional details of the transition densities. The couplings in vacuo were computed as a function of the distance and of the wavelength, introducing then the dissipative function (2). Following the approach proposed in ref 14, once the couplings are computed, we have also investigated the exciton dynamics between the original molecule and its mirror image, employing the model by Kimura et al.43−51 (See Supporting Information SI.1.) 3.3. EET to the Metal. Previous MD simulations52,53 of the thio-1DA and -2DA on the gold surface SAMs were also used for computing the coupling and the exciton dynamics parameters. A set of 120 molecules was arranged in a ∼(5 × 6) nm2 rectangular box with periodic boundary conditions applied in all three directions, to simulate SAMs. The 50 ps MD simulations were run with a time step of δt = 1 fs within the canonical ensemble (NVT) at a reference temperature of 300 K. The global dynamics were sampled each 100 steps, for a total of 5000 snapshots on the whole. For each step, the electronic couplings were computed for each molecule with its mirror image. The TCD approach41,42 was employed. For each step,

pVTZ basis set and the Becke three-parameter Lee−Yang−Parr (B3-LYP) exchange-correlation functional34 were employed. The properties of the first five singlet excited electronic states were investigated at two levels of theory: time-dependent DFT (TD-DFT) and configuration interaction (CI).35 For TD-DFT calculations, the same computational level of the geometry optimizations was used. For CI calculations, the ZINDO/ S36−38 semiempirical Hamiltonian was employed, and only the single excitations were introduced (CIS). The CI size was large enough to include all of the n, π, and π* molecular orbitals (MOs). Finally, the optimized geometries of the molecules at the first two singlet excited states were obtained at the TDDFT level. The reorganization energies (used here in the Supporting Information) were thus obtained from potential energy surfaces (PES) and from displacements along normal coordinates (DANC). (See ref 14 for the discussion about the two methods.) 3.2. Molecule Adsorption over the Metal Surface. Au{111} and Pt{111} surfaces were modeled using slabs of five atomic layers with a repeated slab geometry. The separation between successive slabs was about 100 Å. The metal slabs were optimized at the DFT level. The DFT calculations were performed using the PW9139 exchange-correlation functional. Ultrasoft pseudopotentials were used to describe electron−ion interactions, with plane-wave basis set cut-offs of 25 and 200 Ry for the smooth part of the electron wave functions and augmented electron density, respectively. The Brillouin zone was sampled with 16 special k-points (4 × 4 × 1). The entire 25909



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metal surface and the tilt angle are influenced by system size, the conformation, and the metal (Table 1). The computed tilt angles are slightly larger than those experimentally obtained.12 As already observed in previous computational studies,73,74 when the molecule is adsorbed on the gold surface, the atom(s) bounded to the sulfur atom tends to be extracted. In our specific case, this phenomenon is appreciable with the molecule being anchored on-top. Table 1 collects the values of the tilt angle (θ), the sulfur−metal bond length (b), the extraction (δ), and the sulfur−mirror distance (h), defined as

the relative distances and orientations between the molecules and the surface were used to position the charge transition density cubes and then to compute the couplings and the rate constants. We underline that the image method is applicable for calculating the electronic properties for each snapshot independently because the difference in the time scales between the nuclear motion and the electron response is very large, and the dielectric constant used for the metal is representative of the response of the electrons of the metal.

4. RESULTS AND DISCUSSION 4.1. Geometrical Structure of the System. After relaxation, the average distance between two metal layers is d = 2.350 Å and 2.299 Å for gold and platinum, respectively. If we compare these results with literature data, we see that, for gold the cell constant a = 4.070 Å, which is often overestimated in theoretical works,54−61 here is well-described (experimental value, a(exp) = 4.058 ÷ 4.080 Å).62−65 In the case of platinum, the computed cell constant a = 3.982 Å is slightly greater than the experimental value (3.924 Å)66,67 but within the range of those obtained in other theoretical studies (3.970 ÷ 4.020 Å).66−69 For many years the headgroup structure for adsorbed thiolated molecules on gold surface has been an object of study.70 Through a combined computational and experimental study on the structure of SAMs of long-chain alkyl-sulfides on gold(111), Cossaro et al.71 showed the presence of a competition between SAM ordering, driven by the lateral van der Waals interaction between alkyl chains, and disordering of interfacial gold atoms, driven by the sulfur−gold interaction. The sulfur atoms of the molecules bind at two distinct surface sites, and that of the first layer of the gold surface contains metal atom vacancies (which are partially re-distributed over different sites) as well as gold adatoms (which are laterally bound to two sulfur atoms). This work showed that some of the sulfur atoms effectively occupy an atop-like position. Here we have considered a simplified structure of the adsorption, without accounting for vacations nor adatoms, but preferring to assume such atop anchoring position as in the experimental picture.72 For the sake of completeness, we remark that for ideal surfaces, state-of-the-art DFT calculations56−60 indicate the bridge-fcc site to be the most stable, but the atop site is not far in energy. When adsorbed on the Au{111} or Pt{111} surface, thiolated 1- and 2DA undergo a small geometry change involving the moiety closer to the surface after optimization (Figure 3). The equilibrium distance between sulfur and the

h ≡ |z(S) − zsurf (M)| = b + δ

(15)

where the extraction δ along the z Cartesian axis normal to the surface plane is defined as the difference between the z value for the “extracted” atom M* and the z value for the surface (zsurf(M)), computed as the mean value of all the M atoms but M*.74 We observe that the extraction in the case of Au{111} is larger than in the case of Pt{111}, and more significant when the molecule is in trans rather than in cis conformation. Additionally, what is particularly important for our principal aim is the values of the equilibrium distances. We can observe that both thio-1DA and thio-2DA are closer when adsorbed on Au{111} than on Pt{111}, by ca. 30−40%. These values define the distances between a molecule and its mirror image via h in eq 15, for instance quantified in terms of the distance between the two sulfur atoms: dSS ′ ≡ 2dS ‐ jellium = 2h − d

(16)

The dSS′ distance increasing of platinum with respect to gold is a first element making the exciton couplings, which is a decreasing function of the distance, more significant when the molecules are adsorbed on the Au{111} surface than on the Pt{111} surface. 4.2. Exciton Couplings. To have a quantitative evaluation of the exciton couplings, we have computed them as a function of the distance between the molecule and its image. The curves are plotted in Figure 4. Since the singlet−singlet coupling matrix elements were computed following the TCD approach, on the basis of our previous work14 we can suppose that the computed values are slightly overestimated. We consider the couplings between S1(nπ*) states first. The orders of magnitude are under microelectronvolts. When the molecule is in trans conformation, the coupling is greater than in cis conformation. As already observed in different dimer geometries,14 enlarging the system sizes, we have a coupling increasing. Passing to the couplings between S2(ππ*) states, the order of magnitude increases to 10−2 eV. Moreover, the thio1DA gives greater values than the thio-2DA. This can be explained as follows. For both thio-1DA and thio-2DA, the S2 state is mainly describable in terms of only the |H,L⟩ transition. Whereas for both 1- and 2DA the HOMO state is delocalized over the entire system, the LUMO is still delocalized over the entire system for thio-1DA but is more localized on the central moiety for thio-2DA.14 Considering the greater length of the system than the inferior homologous, and due to the reciprocal spatial orientation of the two molecules, this explains why the interaction between the transition densities is weaker in the case of the larger system than the smaller one. As for H11 couplings, also for H22 couplings trans conformation is associated with larger values than cis conformation. In Table 2, we have collected the exciton couplings extracted by Figure 4 when we consider the equilibrium geometries on gold and platinum surfaces. dSS′ was evaluated according to eq

Figure 3. Optimized trans- (left) and cis-thio-1DA (right) on the Au{111} surface. 25910



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Table 1. Tilt Angle (θ), the Sulfur−Metal Bond Length (b), the Extraction (δ), and the Sulfur−Mirror Distance (h), for Thiolated trans (t)- and cis (c)-1- and 2DA, on-Top Adsorbed on a Au{111} and Pt{111} Surface Au{111} t-1DA c-1DA t-2DA c-2DA

Pt{111}

θ/deg

b/Å

δ/Å

h/Å

θ/deg

b/Å

δ/Å

h/Å

45.8 39.8 21.7 23.0

2.392 2.382 2.421 2.504

0.258 0.223 0.483 0.380

2.650 2.605 2.904 2.884

42.6 26.9 18.1 11.8

2.618 2.617 2.762 2.747

0.160 0.152 0.306 0.288

2.778 2.769 3.068 3.035

Figure 4. Electronic coupling as a function of the distance between the sulfur atom and its reflected image (dSS′). The dissipative factor is taken to be 1. Panel a refers to the S1 state and panel b to the S2 state.

Table 2. Distance between Sulfur Atom and Its Reflected Image (dSS′) and Electronic Energy Couplings between S1 (H11) and S2 (H22) States, in the Case of Gold and Platinum Mirrors, Assuming δv = 0 thio-1DA

thio-2DA

trans Au{111}

Pt{111}

dSS′/Å H11/eV H22/eV dSS′/Å H11/eV H22/eV

2.950 7.496 1.337 3.257 6.961 1.268

× 10−7 × 10−2 × 10−7 × 10−2

cis 2.860 3.045 8.160 3.239 2.563 7.060

16, i.e., assuming δv = 0. (For the time being, these couplings are not corrected with the dissipative function.) If we compare the data obtained on gold and those obtained on platinum, we can immediately note that the former are larger than the latter. This can be simply explained on the basis of the different distances. To give a quantitative estimation, we computed that, passing from platinum to gold, for trans (cis)-thio-1DA, H11 increases 10% (20%) and H22 increases 5% (16%); for trans (cis)-thio-2DA, H11 increases 5% (7%) and H22 increases 4% (7%). As already observed in our previous study,14 the average couplings calculated along the MD trajectories are significantly smaller than the couplings calculated at the equilibrium geometries. For example, in the case of trans-thio-2DA on Au{111} ⟨H11⟩ = (5.339 ± 0.116) × 10−7 eV and ⟨H22⟩ = (1.355 ± 0.383) × 10−3 eV. (The other couplings are shown in the Supporting Information, Table SI.4.1.) Now we figure the effect of the metal surface and the dielectric surrounding space from an electromagnetic point of view. To do this, we first analyze the case of the surface in contact with vacuum. We can evaluate the dissipative function from eq 2 and then compare the different metals. In Figure 5, we report a comparison of the dissipative function Φ computed for the metal−vacuum interface. We observe that Φ(Pt{111})

× 10−8 × 10−3 × 10−8 × 10−3

trans 3.458 1.124 8.470 3.837 1.071 7.950

× 10−6 × 10−3 × 10−6 × 10−3

cis 3.418 3.367 2.470 3.771 3.239 2.310

× 10−7 × 10−3 × 10−7 × 10−3

Figure 5. Comparison between dissipative function F for the metal− vacuum interface. Legend: black, (Au{111}); red, (Pt{111}).

increases as a function of the wavelength. Below ca. 450 nm, Φ(Pt{111}) is smaller than Φ(Au{111}), whereas for larger 25911



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wavelengths, Φ(Au{111}) decreases and Φ(Pt{111}) is then larger. We recall that the wavelengths experimentally used for the photoisomerization of 2DA are 360 nm (trans-to-cis) and 450 nm (cis-to-trans).11 The optical absorption of the metal depends on the interband transitions (for Au and Pt are in the blue region and in the near-UV, respectively26,27). When the adsorbed molecule has the capability of transferring energy also to the interband transition channel, the quenching is more efficient. Therefore, Au is more dissipative than Pt in the experimentally relevant region. The next step consists of evaluating the case of the metal surface in contact with a medium having the dielectric function of the systems we are studying. In Computational Details (see paragraph 2), we have already exposed the approximations and the assumptions we have done for evaluating the imaginary part of the dielectric function from the experimental UV−vis spectra. Moreover we remark on an additional aspect of our simple model. Actually, we have considered a two-media model; i.e., the space is divided into two regions, one occupied by the metal, and the other occupied by one dielectric, without taking into account that a more realistic approach should take into account a three-media model, where the metal and vacuum occupy two semiinfinite regions with the dielectric (organic molecule) in between. The real picture should be found between these two extremes, viz., the previous case, where the semispace not filled by the metal is filled by vacuum, and what we are going to show, where the results are obtained as if the semispace not filled by the metal is filled by the dielectric. We calculated the dissipative function Φ as a function of the wavelength, for the eight cases of trans (cis)-thio-1(2)DA adsorbed on a gold (platinum) surface. These results were used for obtaining the electronic couplings, according to eq 3, as a function of the distance from the reflecting metal surface and the wavelength. An example of such results is plotted in Figure 6, where the case of trans-thio-2DA (coupling between S2 states) is shown. (additional plots can be found in the Supporting Information, Figure SI.2.) Figure 7 derives from Figure 6, where the surface is cut at a fixed distance, according to the values reported in Table 2. We have sketched the comparison between corrected couplings for trans- and cis-thio-2DA as a function of the wavelength. (For trans- and cis-thio-1DA, see Supporting Information SI.3) In Figure 7, the comparison between the couplings obtained assuming the molecule immersed into an isotropic continuum medio having the same dielectric function and the case of the molecule in vacuo on the surface (infinite dilution of the SAM) is also shown. Clearly, only the wavelengths around the absorption one for each molecule (indicated by arrows in the figure) are physically relevant. Yet the dispersion of the curve shows that the value of the absorption frequency is important for determining the system behavior. We want to focus on the comparison between gold and platinum results. As expected, the shapes are qualitatively similar. We may recognize two general trends, one when the molecule is in trans conformation and the other in cis conformation. In both cases, over 500−550 nm, the curves reach a plateau. What significantly characterizes trans from cis is the presence of a deep “valley”, around the absorption wavelength. This is remarkable, both for platinum and gold. Around this value, we see a drastic decreasing of the coupling, whereas in cis conformation we haveroughly speakingan increasing behavior, until the plateau. The orders of magnitude are the same, even if Figure 7 shows the couplings obtained on platinum are always smaller. The difference in

Figure 6. Plots of the electronic H★ 22 couplings for trans-thio-2DA on gold (top) and on platinum (bottom), as a function of the distance from the reflecting metal surface and the wavelength. (Additional plots can be found in the Supporting Information, Figure SI.2.).

values is not constant, as a function of the wavelength: It is more regular in the case of cis conformers, whereas for trans it is very small in the minimum region and more pronounced in the external region of the spectrum. 4.3. Rate Constant for the EET to the Metal. A significant quantity that allows one to clarify the kinetic picture of the overall process is the rate constant for the EET process to the metal (Table 3). It is computed by employing the extended version of the CPS model, presented in Methods. (Data obtained according to Kimura et al.43−51 theory are reported in Supporting Information SI.1.) We may summarize some observations. First, we note that the rate constants are always larger for Au than Pt. In particular, for the S1 state, when the molecule is in trans (cis) conformation, the rate constant with M = Pt is about 11% (12%) of that with M = Au. The differences are even larger for the S2 state; the Pt data are around 1−2% of the Au data. The better quality of the experimental UV−vis differential spectra obtained upon photoisomerization of 2DA on Pt compared to those on Au75 is in line with our findings. Another relevant aspect is the large difference (3 orders of magnitude) between the EET rates for S1 and S2, both for trans and for cis conformers, independently by the metallic substrate. If we consider the values computed for S2 within this local response approximation, we could suppose that the EET from the molecule to the metal after excitation to S2 represents a phenomenon that hinders the photoisomerization process, certainly for Au and perhaps also for Pt. In fact, the S2−S1 decay time value scale is typically of the order of picoseconds,76−78 which means the intramolecular S2−S1 decay occurs more slowly than EET to 25912



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Figure 7. Comparison between corrected couplings for trans- and cis-thio-2DA computed at the proper dSS′ assuming the molecule surrounded by a dielectric (solid lines) or vacuum (dotted lines). Legend: black, (Au{111}); red, (Pt{111}). The arrows indicate the absorption wavelengths. (For trans- and cis-thio-1DA, see Supporting Information SI.3).

by the presence of a surface23,24 and the nonlocality of the metal response. Concerning the electron−hole excitation, since the expression of the dumping contribution for a molecule in vacuo, at a certain distance from a metal surface, is proportional to EF−1/2,23,24 and EF(Au) = 5.53 eV and EF(Pt) = 9.74 eV, gold is confirmed to be worse than platinum. We now consider the nonlocality of the metal response. By employing Drude’s model parameters from the fitting of the experimental dielectric functions (Table 4),79,80 we have calculated the complex

Table 3. Vertical Transition Energy (ΔE, eV), Wavelength (λ, nm), and Rate Constant Γ(M) EET for the EET Process According to the modified CPS Model,15 When the Molecule Is Adsorbed on a Slab of Metal M = Au, Pt (at d = de(M−S)) (Level of Theory, TD-DFT B3LYP/cc-pVTZ)a ΔE/eV trans-thio-2DA cis-thio-2DA

S1 S2 S1 S2

2.4937 2.9956 2.4591 3.3976

λ/nm

−1 Γ(Au) EET /s

497 414 504 365

× × × ×

2.70 2.33 1.36 1.23

10

10 1013 1010 1013

−1 Γ(Pt) EET/s

6.22 2.07 3.16 1.04

× × × ×

108 1011 108 1011

Table 4. Drude’s Model Parameters To Fit the Experimental Dielectric Function: Plasma Frequency (Ωp), Bulk Relaxation Time (τ), and Fermi’s Velocity (νF)

a

Data referring to Kimura et al.43−51 theory are reported in Supporting Information SI.1).

Ωp/eV

Au, and with a comparable rate with EET to Pt. However, we shall see in the next section that taking into account nonlocal effects in the metal response substantially changes this picture. At the local model level, the picture does not significantly change when we consider the average values of Γ along the MD trajectories (see Supporting Information, Table SI.4.2 and Figure SI.4.1). 4.4. Nonlocal Effects. As hinted at in Section 2, there arise two important phenomena occurring in the proximity of the metal surface, viz., the electron−hole excitation made possible

Au{111} Pt{111}

8.55 5.15

τ/ps

vF/(m s−1)

ref

0.225 0.060

1.39 × 10 1.85 × 106

77 78

6

dielectric functions for Au{111} and Pt{111}, according to the equations reported in Methods. The dielectric functions for the two metals have been used for evaluating the decay rate for the metal−molecule interface in the regime of the nonlocal metal response (hydrodynamic approximation and Lindhard−Mermin’s model). The results are plotted in Figure 8, where we 25913



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the coupling (and thus the rate) decreases (see earlier discussion and the Supporting Information), which further reduces the possible role of quenching via EET to the metal also for Au. We now compare in more detail the two nonlocal approaches. We find that results obtained by applying 11 0→S2) Lindhard−Mermin’s model (Γ(S EET(LM)(Au{111}) ∼ 3.9 × 10 −1 s at equilibrium distance) are very similar to the hydro0→S2) 11 −1 dynamics ones (Γ(S s at EET(hydr)(Au{111}) ∼ 1.3 × 10 equilibrium distance) and much smaller than the local results, while in a previous study18 Lindhard−Mermin’s model EET rates were even faster than the local results. We have performed some numerical tests by artificially changing the emission frequency, all of the rest being kept constant, and we found that for larger frequencies (i.e., deepest into the electron−hole pair (S0→S2) (S0→S2) excitation region) ΓEET(LM) do become greater than ΓEET(loc) . Therefore, the emission frequency of trans-thio-2DA is also relevant to avoid quenching via EET to the metal. Interestingly, for the S1 ← S0 transition, where the dipole component of the transition density is smaller and thus higher multipoles (providing faster-decaying electric fields) have a larger relative contribution, even at the correct S1 ← S0 transition frequency, (S0→S2) 0→S2) Γ(S EET(LM) > ΓEET(loc).

Figure 8. Log−Log plot of S2 ← S0 decay rate for metal−molecule interface in regime of local (crosses) and nonlocal metal response (filled circles = hydrodynamic approximation; empty circles = Lindhard−Mermin’s model) as a function of the distance of the center of mass of the molecule from the interface. The molecule is trans thio-2DA. Legend of colors: black (Au{111}), and red (Pt{111}).

5. SUMMARY AND CONCLUSION The role played by the metal surface as a possible dissipative channel in the photoisomerization process of azo-SAMs has been investigated. In particular we have compared Pt-SAMs and Au-SAMs. Because of the peculiar structure of the SAMs we are studying, where the active molecules are directly linked to the metal surface, we can suppose the existence of a deactivation channel for the photoisomerization process, i.e., the energy transfer to the metal that can be operatively calculated by exploiting the excitonic coupling between a molecule and its virtual reflected image. Here we studied the excitonic transfer phenomena of the p-thiolated azobenzene (diphenyldiazene, thio-1DA) and its derivative bis[(1,1′)-biphenyl-4-yl]diazene (thio-2DA) chemisorbed over gold and platinum, forming SAMs. In particular, we presented a modified version of the CPS expression, where not only the dipole is taken into account but also the entire transition density. Following the nonlocal EET theory presented previously,18 we also included nonlocal effects at the hydrodynamics and Lindhard−Mermin levels in our quenching rate calculations. The investigation began at the single molecule level, with the exploration of the electronic excited states, and then thio-1DA and thio-2DA were adsorbed on Au{111} and Pt{111} surfaces, in order to obtain the geometrical parameters for the two different kinds of SAMs. The excitonic couplings were computed for the states S1(nπ*) and S2(ππ*) and then multiplied by the dissipative function, involving the imaginary parts of the dielectric functions of the molecule and the metal, obtaining in this way the core quantity determining the rate. We observed a significantly different behavior depending on the assumed conformation (trans or cis). Moreover, the couplings were always found to be weaker in the case of adsorption on Pt than Au. This is principally due to the different values of the dissipative function and the larger distance of the molecule from the surface. Pt therefore turns out to be a better substrate to minimize the coupling. Then we studied the quenching rate. In general, we observed that the rate constant is greater for S2 than for S1, as well as it is

show the case of the S2 ← S0 transition for trans-thio-2DA. The decay rate has been computed as a function of the distance between the center of charge of the molecule (approximated by its geometric center) and the mirror plane. Such distances allow one to highlight deviations from the point-dipole-like behavior. According to our results, the decay rates at a large distance follow the expected d−3 decay, independently of the local/ nonlocal model used. In particular, for d > 20 Å ca., the dipole decay is evident and the nonlocal effects become negligible. Concerning the local approximation, we observe that the plot deviates with respect to the d−3 decay (straight line in the log− log plot) predicted by the original CPS model15 at d ∼ 20 Å (corresponding to a sulfur−metal separation of ∼10 Å) for both metals. This evidence can be explained by remembering that in our approach the molecule is treated as charge density, and not as a point dipole, and thus the deviations are essentially due to the higher-order multipoles (quadrupoles, octupoles, and so on), which are absent in the original CPS model.15 As mentioned in ref 18, the hydrodynamic approximation provides values smaller than Lindhard−Mermin’s model, and the two curves are almost parallel for both Au{111} and Pt{111}. At the (S0→S2) 0→S2) interface (d ∼ 9 Å), Γ(S EET(nonloc)(Pt{111}) < ΓEET(nonloc)(Au11}), in accordance with the calculation with the local model 13 −1 0→S2) (Γ(S (see Table 3), both within EET(loc)(Au{111}) = 2.3 × 10 s 0→S2) the hydrodynamic approximation (Γ(S EET(hydr)(Au{111}) = 1.3 × (S0→S2) 11 −1 10 s , ΓEET(hydr)(Pt{111}) = 2.1 × 109 s−1) and within 0→S2) 11 Lindhard−Mermin’s model (Γ(S EET(LM)(Au{111}) = 3.9 × 10 (S0→S2) −1 9 −1 s , and ΓEET(LM)(Pt{111}) = 4.0 × 10 s ). Yet, it can be noted that both nonlocal models give a transfer rate that is 2 orders of magnitude slower than the local one. This is an important finding, since the local results for Au would imply that quenching via EET to the metal successfully suppresses photoisomerizaton, whereas these nonlocal results show that decay to S1 (and then photoisomerization) is still effective, although for Au the quenching may indeed hamper to some extent the photoisomerization. Pt is certainly a better substrate to avoid such competition. In any case, we also remark that when the average over various MD conformations is performed, 25914



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greater when the molecules are adsorbed on Au than on Pt, confirming the picture provided by the corrected exciton coupling element. Nonlocality in the metal response plays an important role, and nonlocal accounting quenching rates are 2 orders of magnitude smaller than the corresponding local results. This also contributes, together with dynamical disorder probed here by MD, to make the EET characteristic times larger than the S1 ← S2 decay times. The couplings are stronger for Au than for Pt; for Pt we can conclude that the energy transfer to the metal does not represent an important deactivation channel, while for Au it may compete with (trans-to-cis) photoisomerization reducing the quantum yields. Further investigations concerning this topic might be finalized to explore the quenching capability of other metals. Moreover, here we have also demonstrated that the dissipative features of the metal/SAM are very sensitive to the molecular absorption frequency, which can be tuned by to the presence of substituents on the molecule (electron donating/withdrawing groups) and choosing the environment (solvent). This aspect could play an important role in the design of devices with facilitated or hindered photoisomerization aptitude.

negative−frequency response because χ(ω) is the Fourier transform of a real quantity χ(t −t′), so χ(−ω) = χ*(ω), This means χ1(ω) is an even function of frequency and χ2(ω) is an odd function, and we can therefore collapse the integration ranges to [0,+∞[. In such way the Kramers−Kronig relations are

APPENDIX A. HOW TO OBTAIN THE DIELECTRIC FUNCTION SPECTRUM FROM THE UV−VIS SPECTRUM From the definitions:

where ξ(ω) ≡ (2/π)7 {∫ +∞ dω′ ω′εj″(ω′)/[(ω′)2 − ω2]}. 0 This equation cannot be analytically solved. Therefore, we set up a recursive algorithm for obtaining a numerical solution. The solution was iteratively found, assuming an initial arbitrary (constant) guess for the real part of the dielectric function.

⎧ ⎧ +∞ ω′χ2 (ω′) ⎫ ⎪ χ (ω) = 2 7⎨ ⎬ dω′ 1 π ⎩ 0 ⎪ (ω′)2 − ω 2 ⎭ ⎨ ⎪ χ1 (ω′) ⎫ 2ω ⎧ +∞ ⎬ dω′ χ2 (ω) = − 7⎨ ⎪ ⎪ π ⎩ 0 (ω′)2 − ω 2 ⎭ ⎩

∫

∫

Thus, we can now employ these relations to solve the equation. We can substitute (A.5) into (A.2) squared: (εj″)2 = 4(n″j )2 ⎡⎣εj′ + (n″j )2 ⎤⎦

ℏc ρ εBL ̃ ΔE NA

[εj″(ω)]2 = 4[n″j (ω)]2 {ξ(ω) + [n″j (ω)]2 }

■

(A1)

■

(A2)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +39 050 509 210. fax: +39 050 563 513. Present Address †

Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy. Notes

(A3)

The authors declare no competing financial interest.

■

a complex function of the complex variable ω, where χ1(ω) and χ2(ω) are real, and suppose this function to be analytic in the upper half-plane of ω and it vanishes faster than 1/|ω| as |ω| → +∞, the Kramers−Kronig relations are given by ⎧ ⎧ +∞ χ2 (ω′) ⎫ ⎪ χ (ω) = 1 7⎨ ⎬ ω ′ d π ⎩ −∞ ω′ − ω ⎭ ⎪ 1 ⎨ ⎪ χ (ω′) ⎫ 1 ⎧ +∞ ⎬ χ2 (ω) = − 7⎨ dω′ 1 ⎪ ⎪ π ⎩ −∞ ω′ − ω ⎭ ⎩

ASSOCIATED CONTENT

Text describing EET to the metal as a special case of EET dynamics, figures showing EET couplings, as a function of the distance from the metal surface and the wavelength, plots of the EET couplings as a function of the wavelength at the proper 0→Sn) dSS′ for trans and cis thio-1DA, plot of Γ(S EET(loc) along the MD trajectory, and tables listing vertical transition energies, wavelengths, and EET process rate constants and average results along the MD trajectory. This material is available free of charge via the Internet at http://pubs.acs.org.

To use this relation, we should know the real part of the dielectric function, but this is not our case. As known, the Kramers−Kronig relations connect the real and imaginary parts of any complex function that is analytic in the upper half-plane. Being χ (ω) = χ1 (ω) + iχ2 (ω)

(A7)

S Supporting Information *

where ΔE is the transition energy (in eV), ρ is the density (expressed as number of molecules per m3), NA is Avogadro’s constant, and ε̃BL is the linear molar extinction coefficient (in L cm−1 mol−1), which appears in the well-known Beer−Lambert’s law. ε̃BL and ΔE may be measured through the experimental UV−vis spectra, or they may be theoretically estimated. (In this paper, the density was obtained from the PW calculations, whereas for ε̃BL and ΔE experimental measurement data were employed.) To obtain the imaginary part of the dielectric function, we may write εj″ = 2n″j εj′ + (n″j )2

(A6)

which now becomes

■

n″j = 10−10

(A5)

ACKNOWLEDGMENTS Funding from EU NanoSciE+ project under the Transnational grant Maecenas and computational time from CINECA under the ISCRA initiative are gratefully acknowledged. We thank M. A. Rampi and L. Bergamini for useful discussions, S. Pipolo for providing MD trajectory, and M. C. Murari for technical support in software installation and management.

∫

■

∫

(A4)

REFERENCES

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where 7 {···} denotes the Cauchy principal value. Since in most systems, the positive frequency−response determines the 25915



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Quenching of the Photoisomerization of Azobenzene Self-Assembled

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