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Ligand-Enhanced Optical Response of Gold Nanomolecules and Its Fragment Projection Analysis: The Case of Au (SR) 30

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Luca Sementa, Giovanni Barcaro, Oscar Baseggio, Martina De Vetta, Amala Dass, Edoardo Aprà, Mauro Stener, and Alessandro Fortunelli J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12029 • Publication Date (Web): 24 Jan 2017 Downloaded from http://pubs.acs.org on January 25, 2017

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The Journal of Physical Chemistry

Ligand-Enhanced Optical Response of Gold Nanomolecules and Its Fragment Projection Analysis: The Case of Au30(SR)18 Luca Sementa1, Giovanni Barcaro1, Oscar Baseggio2, Martina De Vetta2, Amala Dass3, Edoardo Aprà4, Mauro Stener2,*, Alessandro Fortunelli1,* 1

CNR-ICCOM & IPCF, Consiglio Nazionale delle Ricerche, Pisa, I-56124, Italy Dip. di Scienze Chimiche e Farmaceutiche, Università di Trieste, Trieste, I-34127, Italy 3 Department of Chemistry and Biochemistry, University of Mississippi, Oxford, MS 38677, United States 4 Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O.Box 999, K8-91, Richland, WA 99352, United States 2

Abstract Here we investigate via first-principles simulations the optical absorption spectra of three different Au30(SR)18 monolayer-protected clusters (MPC): Au30(StBu)18, Au30(SPh)18, and Au30(SPhpNO2)18. Au30(StBu)18 is known in the literature and its crystal structure is available. In contrast, Au30(SPh)18 and Au30(SPh-pNO2)18 are two species that have been designed by replacing the tertbutyl organic residues of Au30(StBu)18 with aromatic ones so as to investigate the effects of ligand replacement on the optical response of Au nanomolecules. In analogy with a previously studied Au23(SR)16- anionic species – despite distinct differences in charge and chemical composition, a substantial ligand-enhancement of the absorption intensity in the optical region is obtained also for the Au30(SPh-pNO2)18 MPC. The use of conjugated aromatic ligands with properly chosen electron withdrawal substituents and exhibiting steric hindrance so as to also achieve charge decompression at the surface is therefore demonstrated as a general approach to enhance MPC photo-absorption intensity in the optical region. Additionally, we here subject the ligand-enhancement phenomenon to a detailed analysis based on fragment projection of electronic excited states and on induced transition densities, leading to a better understanding of the physical origin of this phenomenon, thus opening avenues to its more precise control and exploitation.

*

Corresponding authors – email: [email protected], [email protected]

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Introduction

The optical properties of metal nanoclusters and nanoparticles have attracted considerable interest since a long time1 and are still at the center of both fundamental science and practical applications2,3,4,5. Central in shaping the response of metal nanostructures to electromagnetic fields is the nature of metallic bond, which allows for low-lying electronic excited states and large polarizability of electrons thereby involved6, thus giving rise – for extended systems or sufficiently large nanoparticles – to Plasmon Resonances or Surface Plasmon Resonances (SPR), i.e., collective excitations of metal conduction electrons and correspondingly strong absorption bands in the visible/near-UV region7. For the smaller clusters, in the range of 1-2 nanometers in diameter, quantum confinement however produces non-negligible finite gaps at the Fermi level, and in general a decrease of polarizability and intensity of the optical response. This effect is also often reinforced by the presence of a coating shell of ligands, which is needed to protect and stabilize the clusters, but which can also further confine and reduce mobility of metal electrons. Both effects (quantum confinement and coating, producing optical damping) are found in the field of monolayer-protected metal clusters (MPC) or metal nanomolecules, i.e., coated metal nanoclusters with a well defined stoichiometry5,8,9,10,11, on which we focus in particular in the present work. Despite this general framework, examples of brightly colored coated or monolayerprotected small metal clusters have nevertheless been proved to exist and have been reported in the literature, such as the ‘green gold’ MPC12,13,14, while other clusters give rise to intense colored luminescence, such as Au22 15,16 and Au18 17. Three phenomena can counteract the tendency to quench the absorption strength in MPC and resurrect absorption intensity of small and medium-sized metal clusters in the optical region, which is most important in several perspective applications of these compounds. First, plasmonic-coupling effects, i.e., the interaction between dipolar excitations of nearby particles which gives rise to optically bright (strengthened) and dark (weakened) electronic excited states18,19,20. Second, alloying two or more different metals can produce a fine tuning of energy levels leading to increased polarizability, see e.g. Ref.21 for a recent review, as suggested experimentally in a few examples22,23,24, although the corresponding theoretical interpretation and analysis is still debated25,26,27,28. Focusing on MPC similar in size to those hereafter investigated, for alloying of the well studied Au25(SR)18 we refer to the detailed discussion in Ref.21, while more recently also Ag alloying in Au18 has been studied29,30.


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Third, the optical response of coated metal clusters and specifically MPC – for definitiveness let’s consider the case of gold nanomolecules and let’s define their stoichiometry as AuM(SR)N – can be tuned by varying the nature and number of thiolated ligands. One effect in this respect is certainly caused by changes in geometry. Changing the ligands can in fact induce a distorsion of the gold core in a rather complex way, as extensively investigated in Ref.17, where it has been shown that ligands containing oxygen atoms or phenyl rings can induce important structural deformations mediated by van der Waals interactions. Such ligands can also produce an enhancement of absorption intensity, consistent with the finding of the present and previous work31 (also the ligand effects on IR and Raman spectra has been studied32). However, a more substantial amplification can be obtained by finely modulating the interaction and alignement of energy levels among the metal core, the Au/S shell, and the organic R residues. This effect has been theoretically predicted for Au23(SPh-pNO2)16 anionic clusters, designed in a process starting from Au25(SH)18 MPC31. Crucial in this approach is the synergic combination of “charge decompression” (i.e., the reduction in the density of the ligands at the surface of the Au core) and electron conjugation due to properly chosen aromatic organic residues (coupling excitations in the Au(core)/AuS(shell) with those in the organic residues): combining these two effects can in fact increase substantially the mobility of valence electrons via quantummechanical interaction and resonance between the metal core and the aromatic ligand shell, thus giving rise to a “ligand-enhancement” of optical absorption quantitatively much stronger than that achieved otherwise. Indeed, evidence that theoretical predictions in Ref.31 are grounded and that such a ligand-enhancement phenomenon can indeed be observed experimentally has appeared in the literature33. However, it should be noted that the interpretation given in Ref.33 is different from the one here proposed. In general, it appears that the theme of the effect of ligands on the optical properties of MPC is a subject of great interest in recent literature17,34,35, including the effect on the optical absorption of small glod clusters of various ligands with electron donor or withdrawal properties36, but a comprehensive treatment is still lacking. To make progress in this field it is thus important to achieve a deeper understanding in terms of both basic principles and practical viability. Here we pursue this third avenue (i.e., the charge-decompression/electron-conjugation approach, the line of research explored in Ref.31), and make progress by: (a) selecting a Au30(SR)18 neutral cluster whose crystal structure has been solved13,14 and which is significantly different from the Au23(SR)16- anionic species investigated in Ref.31, (b) showing that a striking ligandenhancement of its absorption intensity in the optical region is analogously obtained also for this rather different species by choosing similar organic residues, and (c) subjecting the ligandACS Paragon Plus Environment

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enhancement phenomenon to an in-depth analysis via an original approach based on fragment projection of electronic response. In this way we thus simultaneously demonstrate the generality of the approach and better understand its physical origin, thus opening avenues to its more precise control and exploitation e.g. in sensing37 or photocatalytic38 applications. The article is organized as follows. In Sec. 2 we present the method of fragment projection and describe computational details, Sec. 3 reports results and discussion, while conclusions are summarized in Sec. 4.


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2. Computational Details and Fragment Projection Approach The geometry of Au30(StBu)18, Au30(SPh)18 and Au30(SPh-pNO2)18 nanomolecules were optimized by using the Plane-Wave QuantumEspresso software39 in conjunction with ultra-soft pseudopotentials40 and the PBE xc-functional41. All Au30(SR)18 species for which optical spectra were simulated were assumed to be neutral, however a background positive charge was added to compensate for the charge of the species in periodic calculations when calculating electron affinity or ionization potential. A cubic unit cell with a length of 50 a.u. (1 a.u.=0.529 Å) was used. Values of 20 and 200 Ry (1 Ry=13.606 eV) were used as the cut-off for the selection of the plane wave basis sets for describing the kinetic energy and the electronic density, respectively. Calculations were performed at the Gamma point and spin-restricted for neutral species and spin-unrestricted for charged species, by applying a Gaussian smearing of the Kohn-Sham levels of 0.002 Ry. This value is small enough to prevent fractional occupation numbers at converged geometries. The initial geometry of Au30(StBu)18 used as input to structural optimization was taken from Ref.13, while the initial geometries of Au30(SPh)18 and Au30(SPh-pNO2)18 nanomolecules were generated from the Au30(StBu)18 one by erasing all C, H atoms except the C atoms bound to S and building up phenyl or pNO2-phenyl residues in place of these C atoms before fully optimizing the structure. All the structures belongs to the C1 point group, so it was not possible to exploit any symmetry in the calculations. The photoabsorption spectra of the systems here considered were calculated by employing a recent TDDFT algorithm based on the extraction of the spectrum from the imaginary part of the complex polarizability42. This algorithm is particularly suited to the present study because, apart from being very efficient computationally thus allowing us to treat large systems43,44, is not hampered by the limitations of conventional Casida method45 in which only a limited number of eigenvalues of the Casida matrix can be extracted so that it is difficult or impossible to reach the high-energy region of the spectrum. Moreover, although formulated in terms of the transition density, the complex polarizability TDDFT algorithm supports a set of analysis tools which allow for a complete assignment of the spectral features to specific electron transitions. In detail, the complex polarizability TDDFT algorithm consists in calculating the photoabsorption spectrum    point by point, from the imaginary part of the dynamical polarizability    :

   

4 Im   c

(1)


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The polarizability    is calculated for complex frequency, i.e.   r  ii , where the real part  r is the scanned photon frequency and  i is the imaginary part which corresponds to a broadening of the discrete lines and can be interpreted as a pragmatic inclusion of the excited states finite lifetime. In this work a value of 0.15 eV has been chosen for i , which corresponds to a Lorentzian broadening with FWHM equal to twice i . This procedure introduces an arbitrary quantity  i and prevents the analysis of the spectrum by discrete lines. The complex polarizability TDDFT algorithm is implemented in a local version of the ADF code. The LB94 exchangecorrelation (xc-) model potential46 has been employed to obtain the Kohn-Sham orbitals and eigenvalues, scalar relativistic effects are included at the Zero Order Regular Approximation (ZORA) level47, while the exchange-correlation kernel in the TDDFT equations is approximated by the adiabatic local density (ALDA) approximation48 taking the derivative of the VWN LDA XC potential49. The basis sets here employed consist of Slater Type Orbitals (STO) of TZP size included in the ADF database, as well as the corresponding density-fitting auxiliary functions as employed in the ADF code50. The complex polarizability algorithm typically uses a subset of the ADF fitting functions to save computer time as some fitting functions are not necessary for an accurate description of the photoabsorption spectrum. For comparison, absorption spectra have been also calculated using standard ADF code which employs the Casida method and results of these calculations are reported in Figure 4 and in Figure S1 of the Supporting Information (SI). Moreover, concerning Au30(StBu)18, it has been shown in previous work that the present methodology produces a fair description of the absorption spectrum13, so that the same level of accuracy is expected also for the other species considered in the present work, for which – unfortunately – experimental data are not yet available. It can be recalled in fact that the LB94 xcfunctional displays the correct asymptotic behaviour since supports the Coulombic tail and is thus superior to standard gradient-corrected xc-functionals in optical simulations of gold clusters51. Circular Dichroism (CD) profiles have been calculated in the length gauge employing the expressions recently given for the complex polarizability TDDFT algorithm52. Again, the theoretical predictions of chirality still await experimental confirmation as Au30(StBu)18 enantiomers have not been separated yet. The spectra have been analysed in terms of induced density as well as with an original fragment projection analysis, as discussed hereafter. The induced density or transition density53 is the first-order time-dependent density generated by the external electromagnetic field, which takes into account the response of the system to the external perturbation, and will be used in the next section to visualize the form and


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localization of the electronic excitations corresponding to peaks in absorption intensity in our systems. Details about the calculation of the induced density within the formalism of the complex polarizability algorithm can be found in Ref.42. It should be noted that – within our formalism – we evaluate the induced density associated not with a single transition but with a Lorentzian average of all transitions with a FWHM of 0.30 eV. Additionally, in the present work we introduce and apply to our systems an original fragment projection analysis, tailored at better understanding the interplay among excitations belonging to the metal cluster and coating shell in determining the optical response of MPC. The idea is to fragment a given system into – say – two pieces or fragments that will be named M and L for convenience, and to express the absorption spectrum as a sum of 4 terms, corresponding to MM, ML, LM, LL transitions. To achieve this, we start by recalling that in the TDDFT formalism an excited state is described as a linear combination of one-electron excited configurations45:

(2)

where i is an occupied orbital, a is a virtual orbital,

is a Slater determinant generated from the

ground state one by replacing orbital i with orbital a, and expansion of the excited state. The

is the corresponding coefficient in the

coefficients (squared) are commonly used in the Casida

method to assign the spectral features obtained from TDDFT to specific one-electron excited configurations, as the squared

sum to 1. Here we further analyse

in terms of fragments via

the Mulliken analysis of molecular orbitals, obtained from the normalization condition:

(3)

(4)

(5) where in Eqs. (3-5)  are indexes running over the basis set, onto basis functions μ,

are the coefficients of orbital i

are the elements of the overlap matrix, and F is an index running over

fragments (M and L in the present case of only two fragments).


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Now, the oscillator strength in the optical spectrum is proportional to the imaginary part of the polarizability and to the squared modulus of dipole transition moment between the ground and the excited states, e.g., along the z direction of the field:

(6)

where Pi a corresponds to the ia element of the induced density matrix. Since the coefficients

are

normalized and the sum of the orbital populations sum to 1, we finally obtain the following relations:

(7)

where in Eq. (7) :

(8)

The quantities given in Eq. (8) are energy dependent (since the coefficients

are energy

dependent) and sum up to 1 if summed over all the initial (F) and final (G) fragments. The analysis of the spectra in terms of fragments then splits the absorption spectrum according to the partial contributions given by Eq. (8), multiplying the photo-absorption profile by the quantity MFG. Clearly, more sophisticated fragment decomposition schemes than the present one based on Mulliken projection can be devised, and will be explored in future work. To implement the fragment projection analysis within the complex polarizability algorithm, we recall that the diagonal elements of the dynamical polarizability tensor e.g. along the z direction can be expressed as (see Eq. 34 in Ref. 41):

occ virt

 zz      i z  a Pi a i

(9)

a

From Eq. (9) it is possible to obtain the coefficients

to be employed in Eqs. (2,6,8). In

fact by combining Eq. (6) for the oscillator strength, it can be seen that the coefficients must be proportional to the density matrix elements, and can be obtained by normalization:


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(10)


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3. Results and discussion As anticipated in the introduction we select a Au30(StBu)18 neutral cluster whose crystal structure has been solved13,14 and which is significantly different from the Au23(SR)16- anionic species investigated in Ref.31, and we apply to this cluster and its photo-absorption spectra a theoretical analysis in which we replace the StBu thiolates with aromatic thiolates (SR) or with aromatic thiolates exhibiting electron withdrawal groups (Ph-pNO2), to investigate whether the phenomenon of ligand-enhancement of absorption intensity in the optical region occurs also for this rather different (both in terms of stoichiometry and charge) species. To illustrate the structural characteristics of these species, we report in the top-right part of Figure 1 a schematic picture of the (Au,S) skeleton of Au30(StBu)18, in which the Au atoms in the staples are depicted with different colors as belonging to monomeric or trimeric units, and in the rest of the first two rows of Figure 1 schematic picture of the three clusters in which only the H atoms are not reported for the sake of clarity. For convenience of the reader, the Cartesian coordinates of these atomistic models are also reported in full in the SI. On these geometries, TDDFT calculations of optical and rotatory activity have been performed. Figure 2 reports the corresponding photo-absorption profiles outcome of these calculations. Strikingly, the minor intensity in the optical region of Au30(StBu)18 (the integral of oscillator strength in the optical region, i.e., below 3 eV, for this MPC is 5.79), is greatly enhanced already for Au30(SPh)18, (integrated intensity of f = 22.79) and becomes a prominent and intense, broad peak in Au30(SPh-pNO2)18, whose integrated oscillator strength below 3 eV is 51.13. So, along the series, we obtain the following relative ratio of the oscillator strength up to 3 eV, taking Au30(StBu)18 as a reference – 1 : 3.9 : 8.8. In practice, the presence of the aromatic ring enhances the absorption roughly by a factor of four, which is further more than doubled when the nitro groups are added in para positions. This theory-predicted effect due to the chemical nature of the ligands is appealing since it changes the spectral features in terms of both photoabsorption band energy positions and intensity, properties which are here tuned by playing with the chemical nature of the ligands. This finding calls for an experimental confirmation and can represent a step forward to the design of materials with given optical properties. It is worth noting that the structures of the clusters here employed in the simulation of the optical spectrum are fully optimized, but starting from initial geometries basically taken from the experimental structure of Au30(StBu)18. We cannot exclude that changing the ligands could bring about a significant change in the structure of the cluster, as shown in some systems54, although for other MPC the structure of the metallic core is not affected by the nature of the ligands: for example


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Au36(SR)24 MPC55 is known to keep the same structure55,56,57,58,59 with three different ligands : R=Ph55,59, R=Ph-tBu56,57, and R=Cyclopentyl58, and the same may happen for Au30(SR)18. In short, since the details of observed effects on the optical spectra derive from both electronic as well as structural features – as discussed in depth in previous work32 –, the assumption of an unaltered geometrical framework may represent a limitation of the present study. However, as we will see in the following, the presence of “dark” states in the Au(core)/AuS(shell) which can interact and enter in resonance with excitations in the organic residues is a general phenomenon which should be qualitatively independent of the detailed structure of the cluster, as long as it is such that it does not hinder electron delocalization via conjugation. From Figure 2 we also see that the accuracy of the present computational approach is basically validated by comparison with experiment: see e.g. the agreement of the maximum of absorption for Au30(StBu)18 at ≈2 eV with respect to experiment13. For the validation of the approach for predicting dichroism we refer to the Au38(SC2H4C6H5)24 case discussed in Ref.52. A conventional analysis of the KS orbitals involved in the optical transitions of Au30(StBu)18 has also been already considered previously, and we will not report it here again, see in particular Figure 5 of Ref.13, in which it was found that the HOMO has mainly Au 6s, occupied orbitals below HOMO have mainly S 3p and Au 5d contributions, while unoccupied orbitals have mainly Au 6s Au 6p and S 3p contributions. To further understand the photo-absorption trend along the series of three clusters here investigated and in particular the effect of the chemical nature of the ligands, we employ a fragment projection analysis as described in Section 2 (to which we refer for the analytic formulae thereby provided). The goal and outcome of this procedure is to split the absorption spectrum into partial contributions corresponding to MM, ML, LM or LM components. In this procedure, the system is first partitioned into two fragments: M (where M stands for metal but can include also other elements as discussed below) and L (where L stands for ligand but can also be more freely defined). The projection analysis then allows one to assess (M, L) projection components of each holeelectron pairs by projecting both the hole and the electron onto M and L fragments, thus giving rise to four different partial contributions to the electron excitation, according to the pair (initial fragment  final fragment), i.e., to ascribe to each particular absorption peak 4 partial contributions: MM, ML, LM, and LM, as outlined in Sec. 2. It is important to remind that the cluster orbitals are rather delocalized, being contributed by basis functions pertaining to both metal and ligand atoms. A contribution such as for example ML therefore does not correspond to a classical Charge Transfer (CT) transition from metal to ligand, but it rather indicates that in the given transition there is a partial contribution from occupied ACS Paragon Plus Environment

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metal orbitals to unoccupied ligand orbitals. In a classical CT transition one would in fact expect 100% contribution of type ML or ML, a situation which never happens in Figure 3 (see below). This note is important to rule out CT transitions which are notoriously not properly described at the TDDFT level. The results of this fragment projection analysis for the clusters here considered are reported in Figure 3. Each column of Figure 3 correspond to a MPC cluster, while the rows correspond to three different possibilities of fragment definition. The definition of the M and L fragment is in fact arbitrary, but can be suggested by simple chemical considerations. A natural choice is to take all the Au atoms as the M fragment and including all the other atoms into the ligand L fragment – this choice corresponds to the central row, designated as M = Au. However, it should be considered that the Au atoms belonging to the staple units are strongly involved in Au-S bonds and have an oxidation state closer to +1 than neutral, so that they are expected to behave differently with respect to the gold atoms belonging to the cluster core with oxidation state closer to zero. For this reason, in the second ligand definition reported in the bottom row of Figure 3, we consider only the Au atoms of the cluster core as belonging to the M fragment, while the Au atoms in the staple shell belong to the fragment L, together with the atoms of the thiolate ligands. Finally, to focus on the effect of the conjugation connected with the aromaticity of the ligands, we have also considered as a third possibility (top row of Figure 3) the fragment M as built of all Au and S atoms, so that only the phenyl or the nitro-phenyl residues are included into the definition of the L fragment. Such a choice is clearly meaningful only for the two clusters containing the aromatic thiols, and is not applied to the alkyl Au30(S-tBu)18 cluster which does not contain any aromatic moieties, and the consequently empty top/right panel of Figure 3 is left for a label inset. For convenience of the reader, in the bottom row of Figure 1 we provide schematic pictures of the three different ligand definitions, in which we depict only the (Au,S,C) skeleton – where the C atoms are the ones directly attached to the S atoms –, and we color in light blue the atoms belonging to the M fragment, and in green those belonging to the L fragment, respectively. It is convenient to start the discussion of Figure 3 from the central row, that is, with the M fragment corresponding to all Au atoms and the L fragment to the SR thiolates. For the Au30(StBu)18 cluster the splitting of absorption onto the four partial contributions is rather uniform and a slight maximum in intensity located at about 3.35 eV is the only apparent feature. Going to the Au30(SPh)18 cluster one finds again a more or less homogeneous distribution with an increase in strength of all 4 components with a slight predominance of LM and LL transition in e.g. the feature at 3 eV, suggesting a mechanism of ‘electron injection’ from the ligands into the metal. For this cluster it is interesting to compare the fragment analysis using M=Au with the one using M =


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Au(core). In the latter case we observe that most MM contribution is shifted to the LL contribution and nearly disappears, while the other components are basically constant. This suggests that the MM photoabsorption contributions for M=Au were in fact excitations among Au atoms belonging to the staples, while LM and ML excitations basically did not involve these Au atoms in the staples. This effect is also present in the Au30(StBu)18 cluster, but is less evident due to the lesser intensity of the absorption profile. Finally considering the Au30(SPh)18 cluster with the M=Au,S fragment definition for the projections, we find an obvious increase of MM contributions (transition between and within Au and S) but also an important ML contribution. This finding is interesting, because clearly indicates that the virtual orbitals of the aromatic ring begin to play an important role, starting from the feature at 3 eV and at higher energy. The M=Au analysis of the Au30(S-PhNO2)18 cluster displays a strong feature at 2.6 eV, which is ascribed for more than a half to the LL partial contribution. Interestingly, in the M=Au,S fragment projection, the main contribution of the strong band at 2.6 eV comes from ML excitations, with the LM contribution nearly disappearing. The fact that LM contribution is nearly absent for the M=Au,S fragment proves that there is no charge injection in this case from the aromatic ligands, in tune with the electron withdrawing character of the NO2 group. The fact the largest contribution is ML for M=Au,S to be contrasted with LL for M=Au instead demonstrates that the huge and broad peak at 2.6 eV is dominated by transitions from S to the aromatic rings, with also a component of transitions from Au to the aromatic rings as well. It can also be recalled that the photo-absorption of the free ligands in this energy range is confined to a sharp peak around 2.9-3.2 eV depending on the xc-functional31, so the observed feature of a broad and intense absorption peak in the optical region is univocally singled out as a consequence of the orbital coupling between the gold core, the Au/S staple shell and the ligand electronic structure. More precisely, the analysis of the assignment of the low energy absorption band (around 2.0 eV) in the green gold nanomolecule12,13,14 indicates that such band is ascribed to a transition from the Au-S bond to virtual orbitals belonging to the gold cluster. The presence of the aromatic ring introduces an interaction between the * orbitals of the ligands and both the empty and occupied orbitals of the gold core. The result is two-fold: a lowering of the transition energy due to the lowering of the final empty state but also an enhanced intensity due to the more effective delocalization of charge and dipole overlap between the initial Au-Au and Au-S bonds and the final state, that now is also contributed by the ligands and therefore gives a higher overlap with the initial Au-Au and Au-S orbital. This interpretation is consistent also with the effect of the nitro group substitution: in fact, the presence of a strongly electronegative group lowers further the empty orbitals and increases the delocalization onto the ligands and participation of the ligands to the optical phenomenon, the effect ACS Paragon Plus Environment

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is therefore a shift of the maximum to lower energy and a much higher intensity absorption. To go into finer structural detail, one can apply an analysis similar to that used in previous work17,32,34,35,36 and observe that the replacement of StBu with SPh or SPh-pNO2 ligands also induces fine changes in the structural arrangement. The Au-S distances are typically only slightly perturbed by ≈0.01 Å. However, the Au-Au distances between the Au(core) and Au(staple) atoms are similar in the two conjugated ligands but are larger by ≈0.075 Å in the StBu case, essentially because of the larger steric hindrance of the latter, while, correspondingly, the Au-Au distances in the core increase by ≈0.011 Å. This ligand-enhancement phenomenon may be called “rebirth of the plasmon resonance” (or “plasmon rebirth” for simplicity) as hinted in Ref.31, in order to distinguish the present ligand effect from the size effect which instead promotes the “birth” of the plasmon60. However this expression may be misleading, as the present ligand-enhancement phenomenon clearly does not possess the features of a classical surface plasmon. This is evident from a simple inspection of the left-handside of Figure 4 in which we report the discrete TDDFT spectra calculated with the Casida algorithm, extracting the lowest 600 eigenvalues for each cluster. What comes out clearly from this figure are two effects: (i) the position of very many discrete transitions is shifted from the highenergy region well into the optical region as a consequence of the interaction phenomena discussed above, and (ii) these excitations are “revived”, i.e., their intensity is increased: in this connection it is useful to recall that most of these transitions are damped due to the s/d coupling in the Au atom brought about by relativistic effects61. Despite this convergence of many excitations in the same energy range, there is no merging of the transitions into a single peak corresponding to a collective excitation of all the valence electrons as in a classic plasmon resonance, and it is more appropriate to speak of a resonance phenomenon between the Au core, the Au/S shell and the organic residues. As discussed in Ref.31, this resonance is favoured by a synergic combination of a proper alignment of energy levels and overlap between the different components of the MPC, and a “charge decompression” effect. Such charge decompression is associated with a greater sparsity of the ligands at the surface of the metal cluster, induced by steric hindrance. This sparsity is useful to increase the polarizability of the valence electrons, both the metal free electrons and the electrons confined in Au-S bonds, thus increasing absorption intensity (here the role and importance of this effect is masked by the fact that the three clusters here considered share the same density of ligands at the interface). To make these arguments more quantitative, we first see from the left-hand-side of Figure 4 that the spanned energy range narrows along the series. In fact in Au30(StBu)18 the energy of the first and the 600th eigenvalues are 1.30 and 4.11 eV, respectively, whereas they are 1.18 and 3.51


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eV, respectively, for R = Ph, and 0.98 and 2.74 eV, respectively, for R = Ph-pNO2. These values correspond to an average density of 214, 258 and 341 transitions per eV along the series, meaning that the R = Ph and R = Ph-pNO2 ligands increase by 20% and by 59%, respectively, the density of states with respect to R = tBu. This effect adds up to the increase in oscillator strength due to the conjugation effect discussed previously and which is responsible for a further increase intensity by a factor ≈5. In the central panel of Figure 4 we also report the transition densities53 obtained with the complex polarizability method calculated at the energy of the spectral features identified with vertical arrows in Figure 2 (the energy values are reported in the figure as well for clarity). Such plots correspond to the Z-electric dipole component, which supports the spectral feature under study in all three clusters (as seen from the partial photo-absorption profiles distinguished according the electric dipole components in Figures S2, S3 and S4 of the SI). It is apparent that while for R = tBu the transition density is localized near the Au-S chemical bonds, for the aromatic ligands the transition density is much more delocalized, as an effect of the empty final orbitals which are mixed between gold and ligands, in agreement with the outcome of the previous fragment analysis. It is also apparent that for R = Ph-pNO2 the transition density is delocalized but less diffuse than for R = Ph, which can be ascribed to the presence of electronegative and electron withdrawing nitro groups, which leave the carbon atoms of the ligands less shielded and therefore more electron-attracting, so the empty orbitals and the transition density becomes more bounded to the carbon atoms of the ligands. In the right-hand-side column of Figure 4 for comparison we report the same analysis for the tiny features at 2.00 eV, 1.80 eV and 1.30 eV for R = tBu, R = Ph, and R = Ph-pNO2, respectively. In this case the features are supported by the X-electric dipole components (see the Figures S2, S3 and S4 of the SI). The behavior is qualitatively similar to the Z-dipole component: an increase in delocalization is found going from the alkyl to the aromatic ligand, and a strong compactness of the transition density is induced by the nitro groups. We can conclude the analysis observing that all the tools employed (fragment projection, density of transitions and transition density) are consistent with each other and purports to give a clear rationalization of the effect of the chemical nature of the ligands on the “plasmon rebirth” or better ligand-resonance phenomenon. In passing, as a reference we also report the adiabatic ionization potential (IP) and electron affinity (EA) of the clusters here investigated, i.e., the energy lost to extract or gained to add an electron to the cluster, respectively, by keeping the geometry frozen at the one optimized for the neutral species. The ionization potentials of Au30(StBu)18, Au30(SPh)18, and Au30(SPh-pNO2)18 nanomolecules are: 6.80 eV, 6.95 eV, 8.98 eV, respectively, while the electron affinities are: 2.88 eV, 3.47 eV, 5.45 eV, respectively. Interestingly, these quantities follow a monotonous behavior as


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a function of conjugation and electron withdrawal strength, and reach their largest values for Au30(SPh-pNO2)18, which has an ionization potential larger by 3 eV and an electron affinity larger by 2 eV with respect to Au30(SPh)18. It is then to be expected that Au30(SPh-pNO2)18 will be negatively charged except in strongly oxidizing conditions5. Finally, we briefly introduce here a few remarks on optical absorption anisotropy, a topic which we have recently started exploring62 and will be discussed in detail in future work. As apparent from Figure S2 of the SI, Au30(StBu)18 exhibits a significant absorption anisotropy, i.e., a significantly different absorption intensity along the three Cartesian direction of the exciting electric field. This is indeed consistent with the intrinsic absence of symmetry elements (all the clusters belong to the C1 point group), and can be understood as an effect of the asymmetric distribution of thiolate ligands around its metal core, however with non-trivial features. Optical anisotropy is in fact large in Au30(StBu)18 but much smaller in Au30(SPh)18 and Au30(SPh-pNO2)18 (Figures S3, S4 of the SI, respectively). The reason of such a decrease of anisotropy for the conjugated species can be rationalized as being due to the intense enhancement of absorption and electron delocalization on the organic residues in the excited states, which revive all Au(core)/AuS(shell) excitations in the original cluster via resonance with ligand as discussed above, but also make the induced density oscillations more homogeneous in the three Cartesian directions, thus reducing optical anisotropy. Finally we also calculated the Circular Dicroism spectra of Au30(StBu)18, Au30(SPh)18, and Au30(SPh-pNO2)18 and report them in Figure S5. Interestingly, from an inspection of this figure it can be drawn that ligand-enhanced resonance, at variance with anisotropy, does not decrease the chiro-optical activity of the Au30(SR)18 MPC. On the opposite, one observes an almost identical dichroism among the three clusters in the range between 3 and 4 eV, while for lower energies the maximum of Au30(StBu)18 at 2.8 eV is shifted to 2.5 eV in Au30(SPh)18 and, even more interestingly, the minimum of Au30(StBu)18 at 3.1 eV with almost zero dichroism is shifted to 3.0 eV and enhanced to -350·10-40 esu2cm2 in Au30(SPh)18. In the same energy range Au30(SPh-pNO2)18 gives the lowest dichroism, but this cluster becomes the most dichroic for very low energies, namely below 2 eV. The behavior of the dichroism along the series is therefore more complex than that of absorption. In this respect it is worth noting that in some circumstances it has been observed a reduction of the CD signal in the presence of structural distortion, like for example the effect of the chiral BINAS ligand in Au25.63 Such complexity might also turn useful in chiro-optical applications.


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4. Conclusions and perspectives

We have conducted a first-principles investigation on the optical absorption on a series of three Au30(SR)18 clusters: starting from the known and fully characterized Au30(StBu)18, other two systems, namely Au30(SPh)18 and Au30(SPh-pNO2)18, have been designed by replacing the tertbutyl alkylic group with two aromatic ones exhibiting or not electron withdrawal substituents. This investigation has allowed us to assess the dependence of the optical response of Au nanomolecules onto the chemical nature of the ligands34, in particular focusing on the most striking features31, i.e., electron conjugation, charge decompression, and electronegativity effects. It has so been found that the oscillator strength in the optical region (integrated below 3 eV) is amplified by a factor of 8.8 in going form R=tBu to R=Ph-pNO2. To identify the driving force responsible of such amplification, we have analysed in detail the electronic characteristics of these species and their absorption spectrum, also introducing an approach based on fragment projection of electronic excited states as here calculated within the TDDFT formalism and therefore described as a linear combination of one-electron excited determinants. Such fragment projection analysis has been implemented within the complex polarizability algorithm that has been here employed to perform TDDFT calculations, but is of course applicable using any other TDDFT approach. From the comparison of the fragment projection analysis on the series of the three clusters, performed with three different possible definitions of the (M,L) fragment pairs (metal=M, ligand=L), it has been possible to better understand the mutual role of conjugation and electronegativity in the optical absorption of the protected gold clusters. More specifically, for R = Ph a mechanism of ‘charge injection’ from the ligands to the metal has been identified, which disappears in R = SPh-pNO2. In this latter system the energetic stabilization of the  and * orbitals of the ligands promotes a delocalization of both occupied and virtual orbitals of the cluster giving rise to a strongly red-shifted absorption spectrum, while simultaneously strongly increasing the intensity of the optical peaks. The analysis of the transition density plots in correspondence of the energies of the most prominent spectral features confirms the delocalization effects already identified by the projection analysis, with the further observation of a characteristic “compactness” or reduction in the diffuse extension of the transition density when the nitro groups are present on the phenyl rings. It is also further clarified how the ligand-enhancement phenomenon here investigated is not a classic plasmonic effect, since it does not give rise to a focusing of absorption intensity into a single resonance, but rather a resonance effect, due to an effective energy alignment and overlap of


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the orbitals of the metal core, Au/S shell, and ligand orbitals. It is worth underlining the usefulness of efficient TDDFT algorithms and available analysis tools that makes TDDFT particularly adequate for the description of the ligand-enhancement phenomenon, providing its comprehensive description. Finally, also the anisotropy as well as the circular dichroism have been briefly considered: the “plasmon rebirth”, or better resonance, effect damps anisotropy due to the more effective delocalization of the transitions, whereas, in contrast, the circular dichroism is not damped along the series but simply red shifted, in parallel with the behavior of photoabsorption. In short, we here demonstrate the generality of the ligand-enhancement optical phenomenon described in Ref.31, understand why combining charge decompression and electron conjugation effects give rise to enhancements quantitatively larger than that obtained via previous 34 or successive17,35,36 analyses, and better clarify the physical origin of this phenomenon, thus opening avenues to its more precise control and exploitation e.g. in sensing37 or photocatalytic38 applications. Work is in progress to explore these possibilities.

ASSOCIATED CONTENT Supporting Information. Comparison of simulated TDDFT spectra using the Casida and approaches, decomposition of TDDFT spectra into Cartesian components, Circular Dicroism spectra, and Cartesian coordinates of the systems here considered. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements Computational research was performed in part using EMSL, a DOE Office of Science User Facility sponsored by the Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory, and PNNL Institutional Computing at Pacific Northwest National Laboratory. Support from CINECA supercomputing centre within the ISCRA programme is also gratefully acknowledged. This work has been supported by Università degli Studi di Trieste, Finanziamento di Ateneo per progetti di ricerca scientifica, FRA2014.


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Page 24 of 29

Figure Captions Figure 1. Schematic pictures of: Au30S18 skeleton (top-left); Au30(StBu)18 (top-right); Au30(SPh)18 (middle-left); Au30(SPh-pNO2)18 (middle-right); and of the M//L fragment definitions showing the Au30(SC)18 skeleton: Au20(core)//Au10(staples)(SR)18 (left); Au30//(SR)18 (middle); Au30(S)18//R18 (right). In top and middle rows hydrogen atoms are omitted for clarity, S in red, C in brown, and Au in yellow except in Au30S18 skeleton where Au in the core are yellow, Au in trimeric staples pink, and Au in monomeric staples are in blue. M fragments are in light blue, L fragments in green. Figure 2. TDDFT photoabsorption spectra of Au30(StBu)18, Au30(SPh)18, and Au30(SPh-pNO2)18, calculated with the complex polarizability algorithm. The arrows indicates the most salient spectra features at 3.35 eV, 3.00 eV and 2.60 eV for the three clusters respectively. Figure 3. Fragment analysis (see text for details) of the photoabsorption spectra of Au30(StBu)18, Au30(SPh)18 and Au30(SPh-pNO2)18. Figure 4. Left column: TDDFT discrete photoabsorption spectra of Au30(StBu)18, Au30(SPh)18, and Au30(SPh-pNO2)18, calculated with the Casida algorithm. Central and right columns: transition densities calculated with the complex polarizability algorithm at the energy corresponding to the absorption maxima (also reported as “E” values in the figure): Z-dipole component in the central column, X-dipole component in the right column, respectively.


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Fig. 1


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5 Au30(SR)18

R=tBut R=Ph R=PhNO2

4 3

f

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2 1 0 0

1

2

3

4

5

E (eV)

Fig. 2


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Au30(S-Ph)18

Au30(S-PhNO2)18 4 3

L -> L L->M M->L M->M

3 M = Au, S

2

2

1

1

Au30(S-tBut)18 13

2

3

4

1

2

3

4

0 4

3 3 2

2

1

f

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


2

1

M = Au

1 0 4

3 3

3 M = Au(core)

2

2

1

2

1

1 0

1

2

3

4

1

2

3

4

1

2

3

4

E (eV)

Fig. 3


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X component

Z component

0.10

Au30(S-tBut)18

E = 3.35 eV

Au30(S-Ph)18

E = 3.00 eV

E = 2.00 eV

0.05

0.00

E = 1.80 eV

0.10

f

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0.05

0.00

E = 1.30 eV

Au30(S-PhNO2)18

E = 2.60 eV

0.05

0.00 0

1

2

3

4

5

6

E (eV)

Fig. 4 ACS Paragon Plus Environment

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TOC Ligand-enhanced optical absorption of Au30(SR)18 monolayer-protected clusters


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Ligand-Enhanced Optical Response of Gold ... - ACS Publications

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