Conference-ICSFS-16-A TD-DFT Study of the Spectroscopic Properties of Hollow Silver Cluster

Noble metal clusters have attracted the interest of the scientific community for their particular electronic and optical properties, which are remarkably size-dependent. In fact, these systems have great potentials for technological applications such as in the development of optical devices or for medical applications, in diagnostic and therapeutic fields. As an example, in the latter case the metal nanoparticles need to be tailored in order to have strong absorption in the near infrared (NIR), since biological tissues are transparent in this spectral region. For these reasons, great efforts have been invested in developing synthetic methods to control the parameters that dictate the nanostructure applicability like shape, stability, composition and size. In this framework, the theoretical modeling can be applied for correlating the electronic and structural properties with the size and composition of these systems, in order to achieve information about the design and the tuning of the optical absorptions of the noble metal clusters. Recently, improvements in the descriptions of the relationships between structure and electronic properties were achieved for nanorod and spherical Ag clusters, using the density functional theory. Here, we extend these results to hollow nanorods and nanocages, i.e. non classic structures, demostrating that our model can predict satisfactory the formation of low-energy transitions, experimentally observed in the NIR region. [DOI: 10.1380/ejssnt.2012.530]


I. INTRODUCTION
The electronic and structural properties of metal nanoparticles are an object of increasing interest due to their potential applications in a wide range of fields like: plasmonic, sensing, nanocatalysis, nanodevices and biomedicine [1][2][3][4].For this reason, considerable efforts have been invested in developing synthetic methods to control the shape, stability and size of the metal clusters which are the parameters that dictate the applicability of the nanostructures.In this framework, theoretical modeling can be useful for the rationalization of the experimental results as well as for the design of new materials with tailored optical and electronic properties [5,6].In the case of large clusters, classical electrodynamics approach like the Mie scattering theory or the discrete dipole approximation models have been satisfactory applied [7,8].On the other hand, for smaller clusters (especially when their size is lower than of the conductance electron mean free path), the dielectric constant of the molecular aggregate becomes size dependent and firstprinciple simulations can better describe the chemicophysical properties of these systems.For example, abinitio models have been successfully applied for the prediction of structural [9,10] and electronic properties [11] of Ag n clusters based on the classic icosahedral solid cores, by using the equation of motion coupled cluster method (EOM-CC) [12] when n varies between 8 and 20 atoms or with the time dependent density functional theory (TD-DFT), which gives good agreements with experimental results [13,14].These TD-DFT simulations were early performed on Ag n aggregates where n ranged from 20 to 30 atoms [15], and more recently on cluster structures, based on tetrahedral [16] or rod [17] shapes containing up to 120 atoms.
In the present study, in order to contribute to achieve new insight on the electronic properties of these systems, we have performed DFT (geometries) and TD-DFT (excited states) calculations on non classical shapes, like nanocages or hollow nanorods, using as simple model systems the Ag n clusters (with n = 60) shown in Fig. 1.

II. THEORETICAL METHODOLOGY
All the calculations were carried out using the Gaussian 03 program package [18] and the cluster geometries were optimized using the Becke-Lee-Yang-Parr exchange correlation functional (B3LYP), whilst the basis sets used for the optimizations is based on the double zeta (DZ) Slater type wavefunctions associated to the CRENBS (36), Hay-Wadt VDZ (28) and LANL2DZ (28) pseudopotentials, taken from the EMSL Basis Set Exchange Library [19].For each pseudopotentials the number in parentheses represent the number of the Ag frozen core electrons.These basis sets were used because they allow: (i) to reduce the computational effort by reducing the number of active electrons and consequently the number of the basis functions, (ii) to have an effective treatment of the relativistic effects as in the case of the CRENBS and Hay-Wadt pseudopotentials [20,21].Instead, the TD-DFT calculations were done with the pseudopotential selected from the previous geometry optimizations using the same density functional.

A. Pseudopotential
The Ag 60 nanocage cluster (with spherical symmetry) was chosen as reference structure for testing the pseudopotentials performances in the geometry optimization.The electronic energies of the optimized structures, obtained for each basis set are shown in Table I.In order to compare the results obtained, the single point energies for the optimized cluster geometry (obtained with the CRENBS pseudopotential) are also given.We can see that, for the VDZ and LANL2DZ basis, the energy differences between the optimized and single point calculations are small (0.08 eV/atom for VDZ and 0.07 eV/atom for LANL2DZ).This implies that the results obtained to the different pseudopotentials are comparable.However, we have to emphasize that the binding energies of these clusters are greater than those of the corresponding compact structures with icosahedral, tetrahedral or nanorod shape.For example, in the latter case, for clusters similar in size to our models [17], the aggregate binding energy (evaluated with the VDZ basis set) of the solid nanorod is −1.77eV/atom, while in our case for the hollow nanorod we obtain the value of −1.17 eV/atom.Finally, the Ag-Ag bond distances obtained with the CRENBS pseudopotential are closer to those of the Ag crystals as well as with the bond lengths obtained for an similar Ag 66 nanorods structure [17] resulting from DFT calculations done with the BP86 functional.On the basis of these results, we have chosen the CRENBS pseudopotential to study the structural and electronic properties of the clusters here considered, in order to take the advantage of its higher number of frozen core electrons.

B. Optical properties
The UV-Vis absorption spectra, were simulated starting from the nanocage and nanorod optimized geometries (with the CRENBS pseudopotential) through TD-B3LYP/CRENBS calculations, where 1600 excited state were computed.This allowed to explore a spectral region up to 250 nm as shown in Fig. 2, in which the absorption spectra of the two clusters are displayed.A strong absorp- tion peak at 398 (445) nm is predicted for the nanocage (nanorod) shape, and this result is in good agreement with the plasmonic excitation experimentally observed for "bulk Ag clusters" (i.e., nanostructures devoid of internal cavities).However it is interesting to point out that, in addition to these strong peaks, low-energy allowed transitions (see the inset box of Fig. 2) with weak absorption intensities are found.In fact, for the nanocage an excitation is predicted at 926 nm and, due to the lower symmetry, different transitions are found for the hollow-nanorod structure.The nature of these electronic transitions will be discussed in the next section.Since these weak peaks are found in a low-energy spectra region the TD-B3LYP results were checked with corresponding CIS (Configuration Interaction Singles) calculations, which gives the same results.This confirms that the TD-B3LYP results are not artifact of the TD approach.
As far as the energy positions are concerned, for these clusters geometries, the predicted absorption peaks in the spectral region between 800 and 2000 nm are in good agreement with the corresponding experimental data obtained for Ag-Au nanocages [22][23][24].In fact, for these systems, in function of the amount of Ag etching, optical peaks in the range 700-1000 nm are found and those occurring at longer wavelengths (about 1000 nm) are associated with the completely hollowed structures.The less agreement found for the absorption intensity of these lowenergy transitions could be associated to symmetry effects (since for our nanocage clusters we have assumed a spherical geometry) and the relatively low size of our models with respect to the effective dimensions of the synthesized nanocage systems.

C. Electronic properties
In Fig. 3 are shown the plots of the DOS (density of states) obtained for the nanocage and nanorod clusters, through a gaussian convolution of the occupied and virtual set of the molecular orbitals, which highlights the formations of different electronic bands generated by the s, p and d atomic orbitals.
Comparison between the two structures shows, due to symmetry constraints in the AO interactions, that in the case of the nanorod a spd band-like region is interposed between two sp band-like.This implies that the nanocage electronic excitations are generated by sp → sp interband mono-excitations while, those of the nanorod, by spd → sp interband mono-excitations which implies lower excitation energies for this geometry, as found.In the previous section we have recalled that these plasmonic excitations are generated by collective electronic motions, i.e. variations of the electronic density which is largely delocalized over the cluster.Analyzing the nature of the electronic transitions which occurs at 398 (445) and 926 (1137) nm for the nanocage (nanorod) we found that they are characterized by a large number of mono-excitations (where the greatest contributions to the excited state of a single term has a weight of about 1-8%).This implies, as expected, that during these excitations large variations of the electronic density occur.In order to understand, at least qualitatively, the different behaviors of the electronic transitions predicted at high and low energy, in Fig. 4 are depicted the electronic fluxes which occur during the excitations as the sum of the mono-excitation contributions, showing on the left (right) the occupied (virtual) MO's involved.In the case of the spherical shape, we can see that the electronic excitation at 398 nm involves the whole surface but at the same time there is a zero density plane which allows to treat the nanocage as two distinct and somewhat independent moieties.Consequently a strong orientation of the electronic transition dipole (µ t ) can be achieved, and a high absorption should be associated to this excitation as predicted by the simulations and experimentally observed.On the other hand, the absorption peak at 926 nm is associated to a more delocalized and symmetric electron density variations and in this case we should expect an appreciably lower value of µ t .In fact, http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) the UV-Vis spectrum simulations predicts smaller values for the oscillator strength of these low-energy excitations.This results is in less agreements with the experimental results obtained for nanocage clusters, however, it should underlined that these structures have a lower symmetry with respect to our model.
Finally, a similar analysis holds for the nanorod as shown in Fig. 4. The electronic excitations have an axial (1137 nm) and transversal (445 nm) direction which implies small and strong values for µ t .In this case the lower symmetry (with respect to the nanocage) allows to obtain higher values of the oscillator strengths for both the excitations.

IV. CONCLUSIONS
Our modelization of the electronic properties of Agnanocages systems based of a simple model structures like Ag 60 -nanocages or Ag 60 -hollow nanorods well reproduce the experimental energy positions of the absorption peaks.In this context, the main point to underline is that, for the characterization of the plasmonic excitations, the model system can be limited to the surface atoms, or at least a few surface layers.The calculations of the absorption spectra nearby the strong excitations associated to the bulk cluster show the initial emergence of new electronic excitations in the range 900-1200 nm which are in good agreement with the experimentally observed absorption peak of the nanocages.
Next improvements in our model will include Au atoms in the cluster structures using a ratio close to that of the syntetized Ag-Au nanocages and different shapes, in order to better describe these systems.The effects of the 4s and 4p electrons on the cluster electronic properties in function of the binding energy, will be also taken into account.
FIG. 2: TD-B3LYP/CRENBS normalized absorption spectrum of the nanocage (straight line) and nanorod (dotted line).A detail of the region between 800 and 2400 nm is shown in the figure inset, where the signals are renormalized.
FIG.4: Schematic representation of the electronic transitions predicted at 926 (1137) and 398 (445) nm for the nanocage (nanorod) obtained by sum of the mono-excitation contributions to the corresponding excited states.

TABLE I :
[17]gy and Ag bond lengths of the optimized Ag60 nanocage cluster, in function of different pseudopotentials.To compare with the values of 2.736-2.968Åobtainedfor an Ag 66 nanorods[17]and the minimum Ag-Ag distance in the crystal: 2.892 Å.
a b Using the CRENBS optimized geometry.