Ligand and Solvent Effects on the Structural and Optical Properties of Au 13 L 83 + Clusters : a Density Functional Theory Study

Density functional theory (DFT) calculations have been performed to develop a systematic structural analysis of Au13L8, where L = SCH3, SeCH3, SCH2OCH3 and S(CH2)2NH2, in order to examine the influence of different ligands. Binding energy calculations indicate that the gold core is more stabilized by the ligand in the following sequence S(CH2)2NH2 > SCH2OCH3 > SeCH3 > SCH3. Natural bond orbital (NBO) analysis describes the interaction between the gold and the ligands, showing that the strongest electron donation occurs from a lone pair orbital on the sulfur and selenium atoms to the antibonding acceptor σ(Au−S) and σ(Au−Se) orbitals, respectively. The NBO analysis allowed to understand the origin of enhanced stability of the [Au13(S(CH2)2NH2)8]. Time-dependent DFT (TDDFT) calculations have been performed to simulate the optical absorption spectra of Au13L8 in gas phase and under the effect of solvents with different polarities. The absorption spectrum of [Au13(S(CH2)2NH2)8] shows a spectral profile that differs considerably from the others in gas phase and which is strongly affected by the solvent.


Introduction
2][3] Among the properties of the gold clusters, the magnetic, 4 catalytic, [5][6][7] electrochemical, 8,9 optical [10][11][12] and structural 13 ones have been intensively studied, which lead to promising applications in nanoelectronics, chemical sensing, catalysis, biomedicine, etc. [14][15][16] Many of these properties are affected by the strong relativistic effect present on gold atoms. 17,18This feature explains the trend of gold atoms to generate clusters of different sizes, in contrast with other analogous metals like silver and copper. 19In general, small Au n clusters (n = 2-10) are usually planar, 20,21 while transition structures from 2D to 3D are formed at n = 11-13 22,23 and, for n > 13, the 3D structures are predominant. 24,25mong Au clusters, the Au 13 has been focus of particular interest for being the smallest geometrically stable shell-closed structure ("magic number"). 268][29][30] The most popular one shows icosahedral (I h ) symmetry, since it is present as subunits of larger clusters, like Au 25 31 and Au 38 . 32On the other hand, the structures of smaller clusters such as Au 9 and Au 11 are observed as fragments of icosahedral Au 13 . 27,33Nonetheless, other Au 13 isomers have been studied: cuboctahedron, decahedron, planar and flake. 28,30,34Ding et al., 34 in a theoretical study, investigated through density functional theory (DFT) calculations the energetic stability of some of these geometrical structures.The results indicate that the planar structure of Au 13 is the most stable in energy.However, for the thiolate-protected Au 13 (SCH 3 ) 12 , the icosahedral geometry is the one with the lowest energy, followed by the planar, cuboctahedron and flake.
Although the icosahedral structure is perhaps the most frequently studied geometry for metallic nanoclusters, 29 we consider the octahedral (O h ) symmetry of Au 13 in this study.This can be justified in order to keep the face-centered-cubic (fcc) structure of the bulk gold that, by a spherical cut, originates the Au 13 as being the smallest gold cluster with O h symmetry.An extra motivation comes from the experimental work of Negishi and Tsukuda. 35hey prepared the Au 13 with O h symmetry in which the eight (111) facets of the gold cluster are fully passivated by eight meso-2,3-dimercaptosuccinic acid (DMSA) ligands.They also predicted a structural model for the Au 13 (DMSA) 8 cluster where the sulfur atom of the DMSA ligand is bonded to the three gold atoms of each (111) facet of the cuboctahedral Au 13 .
Beyond the geometrical structure of the gold core, another important factor exhibited by the clusters is the influence of different ligands.It has been pointed that the ligand influence interferes in many properties of the cluster. 8,9,36,37Aikens, 36 in 2010, investigated the changes in the absorption spectra of Au 25 (SPhX) 18  -induced by different ligands, X = H, F, Cl, Br, CH 3 and OCH 3 .She observed that the chemical nature of ligand slightly affects the optical absorption spectra, being the X = OCH 3 that most affects among the other ligands.In 2012, Jung et al. 8 reported through DFT/PW91 calculations the influence of different thiolate ligands in the electrochemical and thermodynamic stability of gold nanoclusters: Au 25 (SR) 18  -, Au 38 (SR) 24 and Au 102 (SR) 44 , where R(aliphatic) = CH 3 , C 6 H 13 and CH 2 CH 2 Ph, and R(aromatic) = Ph, PhF and PhCOOH.It was concluded that open-chain ligands presented a higher electrochemical and thermodynamic stability than the aromatic thiols, and the SCH 2 CH 2 Ph provides the highest stability among them.On the experimental point of view, Guo and Murray 9 analyzed the ligand effect through the redox potential of Au 38 (SPhX) 24 clusters (in which X = NO 2 , Br, H, CH 3 , OCH 3 ).The results showed that the electron acceptor ligands favor energetically the reduction instead of oxidation.A later paper, published in 2015 by Chen et al., 37 presented a strategy to obtain gold nanoclusters with varied sizes, Au 40 (MBT) 24 , Au 104 (MBT) 41  and Au 130 (MBT) 50 , and using as stabilizer the isomers ortho-, meta-, para-methylbenzenethiol (MBT), respectively.They concluded that the nanocluster size decreases as the position of methyl group in MBT ligand goes from para to ortho, which is caused by steric hindrance of the group CH 3 with the interfacial Au−S bond.
9][40][41][42][43] From the structural point of view, Jiang et al. 39 showed that solvents with higher polarity tend to form thiolate clusters with smaller sizes due to hydrogen bonding interactions.Recently, Thanthirige et al. 43 observed the characteristics of the absorption spectra of bi-icosahedral Au 25 clusters in ethanol and toluene, under different temperatures.At room temperature the results were similar for both solvents.But, at 78 K, it was observed a different behavior in the absorption spectrum profile between the solvents: when the toluene had been substituted by ethanol, there was a red-shift of the lowest energy band, and also new peaks appear in the 400 nm region.
Therefore, this work reports a systematic theoretical investigation, at DFT level, about the influence of different ligands and the solvent effect on the structural and optical properties of cuboctahedral Au 13 3+ cluster capped with one ligand on each face (111).The choice of the triply charged metal cluster is motivated by the article of Nobusada 44 who explains that the monolayer-protected metal clusters (MPCs) are usually synthesized in solvents, where there are counterpart negative ions, such as halogens, in such an environment.Thus, compounds in ionic forms, such as Au 13 L 8 k+ + k Cl -, are also present together with neutral compounds Au 13 L 8 .Furthermore, to avoid performing DFT calculations taking into account the high-spin state (i.e., the quartet state) of the neutral Au 13 L 8 , the Au 13 L 8 3+ was chosen.Therefore, we investigated the system Au 13 L 8 3+ , where L = SCH 3 , SeCH

Methodology
All calculations have been performed on the framework of DFT 45 as implemented in the ORCA program package. 46he electronic structure of the excited states and related optical properties of all molecular systems were calculated with time dependent density functional theory (TDDFT) methodology. 47The Becke's three-parameter exchange functional combined with Lee, Yang and Parr (LYP) correlation functional, known as B3LYP, [48][49][50] was employed in all calculations carried out here.The 6-311++G(d,p) basis set 51 was used for the H, S, C, N, O and Se atoms, while for the gold atoms the Los Alamos effective-core potential (ECP) LANL2DZ basis set 52 were applied.All geometries were fully optimized considering the Au 13 L 8 3+ clusters in gas phase or under the effect of the solvents.The default convergence criteria were used in all geometry optimizations (energy change: 5.0 × 10 -6 E h , maximum gradient: 3.0 × 10 -4 E h /bohr, root-mean-square (RMS) gradient: 1.0 × 10 -4 E h /bohr, maximum displacement: 4.0 × 10 -3 bohr and RMS displacement: 2.0 × 10 -3 bohr).The initial geometry used in the optimization calculations was built from the optimized structure of the cuboctahedral Au 13 3+ in gas phase in which the pre-optimized ligand is added to each of the eight (111) facets of the gold cluster.Excitations to the lowest 50 states were evaluated for the optical spectra.The absorption spectra were fit with a Gaussian function with a half width at half maximum (HWHM) of 0.13 eV.To improve computational speed of the excited states, the RIJCOSX 53 approximation was applied.The conductor-like polarizable continuum model (C-PCM) 54,55 was used for the treatment of implicit solvation effects on the absorption spectra.Finally, the natural bond orbital (NBO) analysis 56 was employed to obtain the natural charges and the charge transfer between the metallic cluster and the ligands using the commercially available Gaussian09 software package. 57The NBOs of several selected clusters were plotted using the GaussView program. 58

Structural properties-structure and stability
The optimized geometry of the Au 13 L 8 3+ , where L = SCH 3 , SeCH 3 , SCH 2 OCH 3 and S(CH 2 ) 2 NH 2 , is presented in Figure 1 and the respective structural parameters are summarized in Table 1.The uncertainties in Table 1 are calculated as the standard deviation of the set of all chemically equivalent structural parameters in the cluster.The structures of [Au 13 (SCH 3 ) 8 ] 3+ and [Au 13 (SeCH 3 ) 8 ] 3+ are optimized within O h molecular symmetry, while for the SCH 2 OCH 3 and S(CH 2 ) 2 NH 2 ligands, it is observed a light compression along one of the 4-fold axes reducing the cluster symmetry from O h to D 4h .
Analyzing the results of [Au 13 (SCH 3 ) 8 ] 3+ with the ones from its similar selenolate cluster, [Au 13 (SeCH 3 ) 8 ] 3+ , it can be noted some structural differences between them.The average length of the Au-Se bond is larger than the Au-S bond in the [Au 13 (SCH 3 ) 8 ] 3+ cluster.This increase is attributed to the larger covalent radius of the Se atom (r = 1.20 Å) in contrast to the S atom (r = 1.05 Å).The same behavior is observed in the average distance of Se-C (1.987 Å) and S-C (1.846 Å) bonds.The substitution of the thiolate ligands SCH 3 by the selenolate SeCH 3 promotes an increase of the average distance between the central and surrounding gold atoms (Au C -Au S ) and between two surrounding neighboring gold atoms (Au S -Au S ).Thus, it is expected that this substitution affects not only the structural characteristics of the cluster, but also the electron density distribution and the molecular orbital energies. 59Comparing the calculated geometrical parameters of the [Au 13 (SCH 3 ) 8 ] 3+ with those from the other thiolate clusters, it can be observed that the substitution of the SCH 3 ligand by SCH 2 OCH 3 or S(CH 2 ) 2 NH 2 changes slightly the structural parameters of thiolate-protected gold clusters.This result is in agreement with the study of Weerawardene and Aikens, 2 who showed that the replacement of a large aromatic ligand (the 4-tert-butylbenzenethiol, TBBT) by a small aliphatic ligand (SCH 3 ) does not cause significative changes in the geometric parameters of Au 20 R 16 , R = CH 3 and TBBT.
In order to investigate the stabilization of the cuboctahedral Au 13 clusters, the binding energies, E b , in the following reaction were computed: Au 13 3+ + 8L → Au 13 L 8

3+
. These values are defined as per L unit and they are shown in Table 1.Among all ligands studied in this work, the results clearly show that S(CH 2 ) 2 NH 2 is the one which stabilizes the Au 13 3+ cluster with more efficiency, followed by SCH 2 OCH 3 , SeCH 3 , SCH 3 , respectively.
Structural properties-natural bond orbitals analysis NBO analysis provides an accurate method for studying intra-and inter-molecular bonding and interaction among bonds, and also provides information about charge transfer or conjugative interaction in molecular systems. 56In this study, the NBO method has been performed to quantify the donor-acceptor interactions between the gold cluster and the thiolate or selenolate ligands.Three types of donor-acceptor interactions were estimated through the second-order perturbation stabilization energy, E(2), whose values are listed in Table 2, for all clusters investigated in this study.The NBO donor-acceptor overlaps of such interactions are presented in Figure 2, for the particular case of [Au 13 (SCH 3 ) 8 ] 3+ .The results analyzed below are directed to the thiolate clusters, but a similar discussion can be considered to the selenolate cluster replacing sulfur atoms by selenium.From Table 2, one can see that two donor-acceptor interactions show that the 3p lone pair electrons of the sulfur atom (n S ) can transfer to either the 6p empty lone pair orbital of surrounding gold atom ( ) or to the antibonding σ * orbital in the Au s -S bond.However, the electron transfer from n S to is more favored than to .This is demonstrated by the higher second-order perturbation stabilization energy E(2) of .It is important to observe that the dominant donor-acceptor charge transfer interactions belong to adjacent subsystems.The third interaction presented in Table 2 indicates a donation of electrons from the bonding σ orbital in the  (SCH 3 ) 8 ] 3+ .This result is consistent with the shorter S-Au distance for the thiolate clusters containing the amine and ether groups, as one can see in Table 1.

Optical properties-ligand effects
In order to evaluate the effect of different ligands on the optical properties, we have performed TDDFT calculations to obtain the optical spectrum of Au 13 L 8 3+ , L = SCH 3 , SeCH 3 , SCH 2 OCH 3 and S(CH 2 ) 2 NH 2 .Although the [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ and [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ present a D 4h symmetry due to a light compression along one of the 4-fold axes, their quasi-degenerate molecular orbitals will be grouped according to the corresponding in the O h symmetry: a 2u + e u → t 1u , b 2g + e g → t 2g and b 1g + a 1g → e g .This will allow a standard interpretation for the spectral profile of the four clusters investigated in this study.
Firstly, the optical absorption spectrum of [Au 13 (SCH 3 ) 8 ] 3+ is compared with its similar selenolate cluster, [Au 13 (SeCH 3 ) 8 ] 3+ .Thus, for these two systems, the calculated optical spectrum and the energy diagram of Kohn-Sham molecular orbitals (MO) with their respective atomic orbital (AO) contributions are shown in Figures 3A  and 3B.
As one can see in Figures 3A and 3B, the absorption spectra of both systems show three feature peaks assigned as b, c and d.The transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO), which is a forbidden a 1g → a 1g transition, is designed as peak a and it occurs at 2.04 eV for [Au 13 (SCH 3 ) 8 ] 3+ and 1.87 eV for [Au 13 (SeCH 3 ) 8 ] 3+ .The HOMO-LUMO gap value decreases from [Au 13 (SCH 3 ) 8 ] 3+ to [Au 13 (SeCH 3 ) 8 ] 3+ , which correlates with a red-shift of the absorption spectrum.Atomic orbital composition analyses reveal that the HOMO is composed almost exclusively from the one central Au(6s) atomic orbital, while the LUMO presents a preferential contribution from the surrounding Au(6s) and also from S(3s) or Se(4s) atomic orbitals, as it can be seen in their respective diagrams (Figures 3A and  3B).The Au(6s) contribution in HOMO and LUMO orbitals The medium intensity peak assigned as b refers to the electronic transition from HOMO to the triply degenerate LUMO+1 and it is located at 2.40 and 2.25 eV for the thiolate and selenolate systems, respectively.The LUMO+1 is mostly composed from the surrounding Au unoccupied 6s and 6p orbitals.Thus, the HOMO → LUMO+1 excitation induces electric charge transfer from the central gold atom to the surrounding ones.
A strong peak, indicated by c in both spectra of [Au 13 (SCH 3 ) 8 ] 3+ and [Au 13 (SeCH 3 ) 8 ] 3+ occurs, respectively, at 3.35 eV (oscillator strength, f = 0.155) and 3.18 eV (f = 0.140).Thus, the red-shift of 0.17 eV to the c peak keeps the same magnitude that is observed for the other peaks assigned in Figures 3A and 3B.The reason for this is that the replacement of the sulfur by the selenium atoms promotes, in general, a regular energy destabilization of the whole set of molecular orbitals, being more pronounced for the occupied (0.32 eV) than for the unoccupied orbitals (0.08 eV).Among the unoccupied molecular orbitals, the LUMO+2 shows a more considerable energy destabilization (0.15 eV) causing a reordering of this orbital with LUMO+3 which is very close in energy.Thus, the c peak in [Au 13 (SCH 3 ) 8 ] 3+ and [Au 13 (SeCH 3 ) 8 ] 3+ refers to the electronic transition from HOMO to LUMO+3 and LUMO+2, respectively.The LUMO+3 orbital of the thiolate cluster and its equivalent LUMO+2 orbital of selenolate cluster have a majoritarian composition of the S and Se atomic orbitals, respectively, as seen in Figures 4a and 4b.Therefore, the c peak is attributed to the electronic transition which induces electric charge transfer from the central metal to the ligands.The analysis of the relative intensities of b, c and d peaks in the spectrum of Figures 3A and 3B reveals that such a charge transfer from the central metal to the ligands is responsible for the high intensity of c peak.
The highest energy feature absorption peak but with low intensity, assigned as d in Figures 3A and 3B, are located at 3.96 eV (f = 0.008) and 3.70 eV (f = 0.005), respectively.This peak is attributed to the electronic transition HOMO-2 → LUMO+1.The doubly degenerate HOMO-2 is composed mainly by the central Au(5d) atomic orbitals.Thus, the electronic transition related to the d peak corresponds to an electric charge redistribution from the central metal to the surrounding ones, as it was also observed for the d peak.
A similar analysis, as it was done above for the optical absorption spectra of thiolate and selenolate clusters, is expected for the spectrum of the thiolate cluster that contains the ether functional group, i.e., [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ .Its absorption spectrum and MO energy diagram are shown in Figure 3C.Three peaks assigned as b, c and d are observed in such spectrum and they occur at 2.46, 3.28 and 4.00 eV, respectively.Similar to the [Au 13 (SeCH 3 ) 8 ] 3+ spectrum, the b and c peaks are also attributed to the electronic transitions HOMO → LUMO+1 and HOMO → LUMO+2, respectively.The three orbitals involved in these transitions also present a closely related composition of the AO's as those discussed above for the [Au 13 (SeCH 3 ) 8 ] 3+ cluster.
A slight difference between the absorption spectra of the [Au 13 (SCH 3 ) 8 ] 3+ and [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ is noticed for the weak peak d.The d peak in the spectrum of the thiolate cluster containing the ether group has a contribution of both electronic transitions: HOMO-2 → LUMO+1 and HOMO-3 → LUMO.The extra contribution of the electronic transition HOMO-3 → LUMO originates a subtle asymmetry in the band structure.The HOMO-3 orbital is composed almost exclusively from the ligand orbitals, that is, C(2s), O(2p) and H(1s), as seen in the energy diagram of Figure 3C.Thus, while the electronic transition HOMO-2 → LUMO+1 induces an electric charge transfer from the central Au to the surrounding ones, the HOMO-3 → LUMO is concerned to an electric charge redistribution from the ligands to the surrounding metals.
T h e o p t i c a l a b s o r p t i o n s p e c t r u m o f [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ and the respective orbital energy diagram are presented in Figure 3D.Three absorption peaks b, e and c are located, respectively, at 2.09, 2.80 and 3.37 eV.Compared with the previous spectra discussed above, the b peak is similarly attributed to the electronic transition HOMO → LUMO+1 and it also occurs at the lowest energy position.The c peak, regarding to the electronic transition HOMO → LUMO+3, keeps with the largest oscillator strength but it appears with the highest energy position while the d peak is not observed in the spectrum of the cluster containing the amine group.However, a new peak assigned as e lies in the energy position between the peaks b and c.The e peak is attributed mainly to the electronic transition HOMO-2 → LUMO+1.The HOMO-1 and HOMO-2 show a distinct composition from those verified for the other systems, being mostly composed from the N(2p) atomic orbitals.For the [Au 13 (SCH 3 ) 8 ] 3+ , [Au 13 (SeCH 3 ) 8 ] 3+ and [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ , there is an average energy gap of 1.66 eV between the HOMO (central Au(6s)) and HOMO-1 (central Au(5d)).For the [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ , due to the energy proximity between the valence orbitals of the isolated fragments (Au 13 3+ and S(CH 2 ) 2 NH 2 ), the orbitals composed strictly from the ligands containing the amine group appear between the orbitals with atomic character of the central gold, Au(6s) and Au(5d).Thus, the HOMO-2 → LUMO+1 transition is related to an electric charge transfer from the amine group to the metals.A more significant contribution of the ligands in the composition of HOMO, HOMO-1 and HOMO-2 of [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ enhances the relative intensity of b and e peaks in relation to the c peak.

Optical properties-solvent effects
The effect of solvation on the optical absorption spectra of Au 13 L 8 3+ , L = SCH 3 , SeCH 3 , SCH 2 OCH 3 and S(CH 2 ) 2 NH 2 was taken into account using the C-PCM implicit solvation model.The absorption spectra of the clusters in solvents of different polarities are shown in Figure 5.
As one can see in Figures 5A, 5B and 5C, the evolution of the spectra when the solvent polarity is increased show a similar trend for the clusters: [Au 13 (SCH 3 ) 8 ] 3+ , [Au 13 (SeCH 3 ) 8 ] 3+ and [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ .The solvent effect is more pronounced for the c peak for which is observed a red-shift of 0.16 eV for [Au 13 (SCH 3 ) 8 ] 3+ and [Au 13 (SeCH 3 ) 8 ] 3+ and 0.08 eV for [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ , as the solvent polarity is increased from gas phase to water.This result may be explained by considering that the electronic transition corresponding to c peak comprises the LUMO+3 (for [Au 13 (SCH 3 ) 8 ] 3+ ) or its equivalent LUMO+2 (for [Au 13 (SeCH 3 ) 8 ] 3+ and [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ ), which presents a composition with the most significant contribution from the ligands which would be greatly affected by the solvent.The red-shift of c peak can be rationalized as a result of the LUMO+3 or LUMO+2 orbital energy being less destabilized than the HOMO energy by the more polar solvent field, reducing the energy difference between these orbitals.As the solvent polarity increases, going from gas phase to water, and using the MO energies of the ground electronic states, it is observed that the increase in energy of such unoccupied orbitals are 6.87 eV for [Au 13 (SCH 3 ) 8 ] 3+ , 6.69 eV for [Au 13 (SeCH 3 ) 8 ] 3+ and 5.46 eV for [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ , while the increase in energy of HOMO for these three clusters are 7.04, 6.80 and 6.21 eV, respectively.
A distinct result is observed in the optical spectrum of [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ when the solvent effect is included, see Figure 5D.For this system, the solvent effect promotes a blue-shift of b and e peaks with increasing the solvent polarity.The b peak undergoes a blue-shift of 0.17 eV going from the [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ in gas phase to water, while for the e peak this shift is of 0.60 eV.This pronounced blueshift of e peak results in its overlapping with c peak for higher solvent polarity.The electronic transitions regarding to the b and e peaks are, respectively, HOMO → LUMO+1 and HOMO-2 → LUMO+1.Thus, as the solvent polarity increases, increases also the energy difference between the orbitals involved in such electronic transitions caused by a progressive destabilization of the HOMO-2, HOMO and LUMO+1 energies, being more pronounced for the latter.The increase in energy of the HOMO-2, HOMO and LUMO+1, calculated from the MO energies of the ground electronic states, are 5.18, 5.83 and 5.96 eV, respectively, going from the [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ in gas phase to under the effect of water.
For the cluster containing the amine group it is observed that due to its significant contribution from the ligands, the unoccupied orbital LUMO+1 would be greatly affected by the solvent.Contrary to what was observed for the previous clusters, the solvent does not promote a significative shift of the c peak in the optical spectrum of [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ .The c peaks corresponds to the HOMO → LUMO+3 electronic transition.As the solvent polarity increases from gas phase to water, the HOMO and LUMO+3 energies undergo a progressive and closer destabilization of 5.83 and 5.90 eV, respectively, keeping almost unchanged the energy difference between these orbitals.Due to this, the solvent does not affect significantly the position of c peak.

Conclusions
In this study, we employed density functional theory to investigate the effect of different ligands on the structural and optical properties of Au 13 L 8 , with L = SCH 3 , SeCH 3 , SCH 2 OCH 3 and S(CH 2 ) 2 NH 2 .Firstly, we showed that the geometric parameters of the thiolate clusters are affected slightly with the variation of the ligand, while a more pronounced change is observed comparing the thiolate and selenolate clusters.The average of binding energies for the four clusters considered in this study has the order of (−3.20 eV) > (−3.15 eV) > (−3.10 eV) > (−3.05 eV).The NBO analysis show that the secondorder perturbation stabilization energy, E(2), of the dominant donor-acceptor charge transfer interaction, , presents the same trend as binding energies: (68.95 kcal mol -1 ) > (67.95 kcal mol -1 ) > (54.78 kcal mol -1 ) > (49.36 kcal mol -1 ).Both results demonstrate that the ligand containing the amine group shows an enhanced capacity to stabilize the Au 13 3+ cluster.The optical absorption spectra have been simulated for the Au 13 L 8 3+ in gas phase and under the effect of solvents with different polarities.The absorption spectra of [Au 13 (SCH 3 ) 8 ] 3+ , [Au 13 (SeCH 3 ) 8 ] 3+ and [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ show a similar profile, where the c peak, which is more affected by the solvent, presents a more pronounced red-shift as the solvent polarity increases.The optical spectrum of [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ shows a spectral profile that differs considerably from the others in gas phase where an extra peak, designed by e, is observed.The absorption spectrum of the cluster containing the amine group is strongly affected by the solvent, where a progressive blue-shift is observed for b and e peaks with the increase of the solvent polarity.
was performed on the Laboratório de Computação de Alto Desempenho of UFS (LCAD-UFS).

Figure 3 .
Figure 3. Theoretical absorption spectrum and the respective Kohn-Sham (KS) orbital level diagram of (A) [Au 13 (SCH 3 ) 8 ] 3+ ; (B) [Au 13 (SeCH 3 ) 8 ] 3+ ; (C) [Au 13 (SCH 2 OCH 3 ) 8 ] 3+ and (D) [Au 13 (S(CH 2 ) 2 NH 2 ) 8 ] 3+ clusters.Each KS orbital is drawn to indicate the relative contributions (line length with color labels) of the atomic orbitals.The orbital symmetry is indicated within O h point group for (A) and (B) and within D 4h point group for (C) and (D).The quasi-degenerate KS orbitals in D 4h symmetry are grouped according to the O h correlation table: a 2u + e u → t 1u , b 2g + e g → t 2g and b 1g + a 1g → e g .The energy values of each peak are specified in the absorption spectra.