Role of Organic Ligands Orientation on the Geometrical and Optical

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Role of Organic Ligands Orientation on the Geometrical and Optical Properties of Au (SCH) 25

3

180

Mirko Vanzan, and Stefano Corni J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01797 • Publication Date (Web): 03 Aug 2018 Downloaded from http://pubs.acs.org on August 5, 2018

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The Journal of Physical Chemistry

Role of Organic Ligands Orientation on the Geometrical and Optical Properties of Au25(SCH3)180 Mirko Vanzan and Stefano Corni* Department of Chemical Sciences, University of Padova, Via Marzolo 1, 35131 Padova, Italy

ABSTRACT: The role of the organic groups orientation on the geometrical and optical properties in neutral Au25 nanocluster have been analyzed through density functional theory (DFT) and timedependent density functional theory (TDDFT) simulations. Starting from two different X-ray diffraction (XRD) resolved structures which differ in the ligands orientation, we optimized the methyl substituted neutral nanoclusters at the B3LYP//6-31G (d,p)/LANL2DZ level finding remarkable differences on the bonds length and the symmetry of the gold kernels. Despite these differences, the TDDFT estimated absorption features of the two clusters are quite similar, showing that ligands orientation brings negligible effects on nanoclusters optical properties. All obtained results are in good agreement with available experimental data.

INTRODUCTION During the past 10 years, the study of thiolate-protected gold nanoclusters has become one of the most promising and exciting research field in nanoscience.1 The ultra-small space occupied by the gold atoms (< 2 nm) induces strong quantum confinement effects which gives them unique properties in terms of electronic energy levels distributions, absorption profiles, photoluminescence, intrinsic magnetism, catalytical capabilities and nonlinear optical features2–9 making them promising

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candidates for applications in catalysis, energy conversion, chemical sensors and nanobiomedicine to name a few.10–13 Among all gold based nanoclusters, [Au25(SR)18]q (R = organic ligand) received the most extensive attention14,15 since it was one of the first case of fully resolved crystal structure when q = -1.16 This structure consists of an icosahedral inner Au13 core surrounded by six dimeric staples which contain the reminder of the gold and sulphur atoms and give to the cluster an almost D2h arrangement.17 The ligands are connected to the S atoms and act like a coating layer, as pictured in Figure 1. Regarding the neutral form of the cluster (q = 0), further XRD investigations revealed that its structure is very similar to its anionic counterpart3,18 but not identical.

A

B

Figure 1. (A) Stick and ball model of [Au25(SCH3)18]0. Au atoms are coloured in pink, S in yellow, C in azure and H in white. The 13 gold core atoms are represented by the bigger balls. (B) Possible orientation of the organic ligands with respect to the staple plane. U = Up, D = Down. This colour code is consistent in all the figures presented in this work. Indeed, notwithstanding the main framework is the same, the neutral cluster is paramagnetic due to its open-shell configuration.19 Moreover, such cluster exhibits a Jahn-Teller effect20 which lows


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down the core symmetry and remove the degeneracy of the frontier orbitals observed in its anionic counterpart.21,22 The optical properties of these systems were deeply studied both from an experimental and a theoretical point of view finding that the neutral and -1 charged nanoclusters have almost the same absorption profile.3 In the case of -1 charged nanoclusters the absorption features were fully characterized in terms of single particles transitions among different molecular orbital levels through TDDFT tecniques23,24 but a similar systematic analysis has not be performed yet for the neutral cluster form. There is also another aspect of these clusters that deserve some attention. Each organic ligand stemming from a sulphur atom may have two different orientations with respect to the staple (Au-SAu) plane (see Fig. 1), that may even confer a chiral nature to the cluster. Experimental structures did show different orientations, and the role of the organic ligands orientation on the core structural features and the optical properties of the neutral clusters remains still unknown. These effects are certainly not appreciable at room temperature (the ligand flipping with respect to the staples plane require about 0.45 eV25), but they would become stronger and notable in low temperature applications. Therefore, the aim of this work is to analyse and quantify the contribution of the organic ligands orientation with respect to the staples to the geometrical and optical features of [Au25(SR)18]q when q = 0. From now we will omit the square brackets and the charge state since we will always refer to the neutral nanocluster. We choose to perform our calculations on the methyl-substituted nanocluster Au25(SCH3)18. This choice has the main goal of limiting the differences between the optimized structures to the orientation of the ligands with respect to the staples, and thus focusing our investigation on this point. In turn, such orientation is determined by the nature of the complete ligands, in particular by their interchain interactions.18 To be meaningful, our computational procedure must (and indeed does) preserve such original orientation. Moreover, the choice of using



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methyl groups minimizes the computational work while maintain the organic character of the chain groups. For saturated alkyl chain substituents, shortening the organic substituent chains, with respect to available absorption spectra, is not a drastic approximation, because it was demonstrated that changing the alkyl chains length modifies only slightly the optical proprieties of these molecules.17 To single out the effect of the organic ligand orientation we analysed the geometry and the optical features of two Au25(SCH3)18 nanoclusters whose starting geometries come from different XRD resolved structures and present different ligand orientations. We will call A and B the structure obtained from the starting geometry presented in ref.16 (ammonium salt of [Au25(SCH2CH2Ph)18]-) and ref.18 ([Au25(SCH2CH3)18]0) respectively. In both cases the charge state was set to 0. COMPUTATIONAL DETAILS Geometrical structure optimizations were carried through spin-unrestricted DFT calculations with Gaussian 09.26 In these calculations the hybrid functional B3LYP was used together with the LANL2DZ relativistic corrected pseudopotentials and basis sets27 for the gold atoms, while the 631G (d,p) basis set was used for all other atoms. This computational level was validated in previous computational studies.28–30 Since it is well known that the gold core has low force constant vibrations31, the default SCF thresholds on the maximum force and maximum displacement were tightened to 10-4 eV/Å and 10-6Å respectively. No external constrain were adopted. Excitation energies and their composition in terms of single electron transitions were computed at the equilibrium geometries with the linear response TDDFT method as implemented in Gaussian 09. The computations were performed adopting the same calculation level as for geometry optimizations. Excitations were evaluated to the lowest 250 states in cluster A rather than the lowest 200 states in cluster B. The UV-VIS spectra convolution were obtained with GaussSum0332 adopting gaussian functions with a width at half-maximum of 0.12 eV. No implicit solvation model was employed, since it was previously demonstrated that solvent effects are minimal, at least within the


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implicit solvation approach.17 RESULTS AND DISCUSSION Organic Ligands Orientation. The starting geometries of cluster A and B differ for the ligands spatial arrangement. In particular in nanocluster B the organic ligands have a centre-symmetrical arrangement while in A this symmetry is lacking, as shown in Figure 2. The origin of this difference is not clear but is probably connected to the presence of the counter ion. Indeed, a visual inspection on the original XRD resolved structure, show that the ligand orientation seems to be the correct one to get space for it. This difference may be given by the presence of ammonium ion in the crystal structure of A, which locally modify the nanocluster geometry. Since the optimization algorithm is not able to overcome the internal energy barrier that separate different methyl orientations (ca. 0.45eV from previous simulations25) the initial ligands arrangement are preserved during the optimizations.

Figure 2. Side views of the two optimized Au25(SCH3)18 nanoclusters A and B. Each column (a, b, c) shows a different opposite pair of staples (the other staple planes are omitted for clarity). Notice that the CH3 groups have a centre-symmetrical arrangement in B but not in A case.



a

A

B

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b

c

D

D

D

D

D

U

D

U

D

D

U

U

D

D

U

U

U

U

D

D

U

U

D

U

D

U

D

U

D

U

U

U

D

D

D

U

Table 1. Arrangement of the CH3 groups with respect to the staples planes in cluster in A and B. Letters a, b, c are referred to different opposite staples pair as pictured in Figure 2. Letters U (up) and D (down) indicate the methyl orientations with respect to the plane. A characterization of methyl groups disposition is presented in Table 1. This analysis clearly shows the centre-symmetric disposition of CH3 in cluster B which is lacking in A. In the next sections, we will show how these different arrangements affect the nanocluster geometrical and optical properties. Analysis of the Nanoclusters Geometries. In order to verify if the optimized structures correspond to energy minima configurations, we calculated the vibrational frequencies for both clusters, adopting the same computational level of the optimizations. The computed IR absorption spectra are pictured in Figure S1. These calculations gave no imaginary vibrational frequencies, demonstrating that the optimized structures are indeed equilibrium geometries. To concisely describe the geometrical features of a structure as complex as these gold nanoclusters, we analyse in both optimized nanoclusters the length of five different kinds of bond (each set groups together chemically-equivalent bonds) and compare it with the ones recovered by the experimental XRD structure of Au25(SCH2CH3)18 presented in ref.18 indicated by E (Experimental) from now on. Notice that this structure is the starting geometry of the DFT geometrical optimization for cluster B. All


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average bond length values together are summarized in Table 2. In the Table we also indicate as error bars, using a notation introduced in ref.33, the standard deviation within the given set of bonds. Such error bars have nothing to do with experimental or computational errors, but it is rather a compact way to represent how inhomogeneous is each set.

Bond type

Number of bonds

A

B

E

Aucenter− Aushell

12

2.912±0.010

2.912±0.014

2.793±0.006

Aushell − Aushell

30

3.06±0.11

3.06±0.11

2.94±0.09

Aushell − Sterminal

12

2.485±0.017

2.484±0.016

2.372±0.020

Austaple − Sterminal

12

2.391±0.003

2.391±0.001

2.301±0.008

Austaple − Scentral

12

2.395±0.003

2.395±0.001

2.299±0.013

Table 2. Average bond distance in angstrom for B3LYP//6-31G (d, p)/LANL2DZ optimized clusters and for the experimental one. Bonds type are defined on the basis of Figure 1. Length in Armstrong. The error bars indicate the standard deviation of the set of bonds. Comparing the calculated structures A and B, we note that the average bond lengths are almost identical. The high values of standard deviation in Aushell − Aushell indicate that the gold core is heavily distorted. This can be correlated to the presence of a first order Jahn-Teller (JT) effect. The presence of this effect will be discussed later. Let us now compare the computed geometry with the experimental one. Notwithstanding the bond lengths are all consistently overestimated in the optimized structures with respect to the experimental one, a general agreement on the relative errors bars is notable. In particular, the most distorted region seems to be the gold core in the experimental structure too. The overestimation of the average bond lengths is likely due to the adopted xc functional (B3LYP). In fact, it is well known that the latter tends to overestimate the Au-Au bond distance in bulk gold.34 Moreover, while A and B geometries were obtained in gas phase, where no confinement takes place, the experimental structure is affected by the crystal environment which might induce non-negligible confinement effects and affect the nanocluster geometry. 7 ACS Paragon Plus Environment


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Comparing the error bars it can be seen that, in cluster E, the dispersion of Austaple − Sterminal and Austaple − Scentral bond lengths, is smaller in the corresponding optimized structure B (and in A too). These larger spreads indicate a modification of the bond lengths of the staples which is directly connected to the formation of aurophilic bonds among the core and the gold atoms of the staples. The presence of this bonds were noticed in other experimental structures in both neutral3 and charged23 form. Unfortunately, aurophylic bonds are dominated by dispersion interactions35 which are not well described by the adopted xc functionals. This is likely the reason why the calculated structures appear more symmetrical (i.e., less distorted) than the experimental one. A deeper analysis on the icosahedral core was made in order to quantify the distortion of the kernels and understand if these distortions are due only to a pure JT effect, or if there is also a contribution coming from the ligand arrangements. In particular, following the analysis in ref.33 we compared pairs of Aushell-Aushell bonds placed on opposite sides of the core. The results of this analysis are summarized in Table 3, and are pictorially depicted in Fig. 3 where a colour maps similar to those used in ref.20 are exploited.

Figure 3. Heat maps of the length of kernels edges. M = Model of Au13 gold kernel. Bond with different length are pictured as the color code placed on the bottom. All length values are in Angstrom.


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A Au (X) - Au (X)

Distance

5 - 10

3.214

4 - 11

3.149

10 - 13

2.968

7-4

2.964

6-9

3.001

12 - 3

2.954

9-8

3.110

2-3

3.181

8 - 13

3.002

2-7

2.942

2-5

2.964

8 - 11

3.002

5-3

3.261

9 - 11

3.208

Differences

B

E

Distance Differences

Distance Differences

3.108

0.065

3.108 2.955

0.004

2.955 2.961

0.047

2.961 3.112

0.071

3.112 3.013

0.060

3.013 2.964

0.038

2.964 3.307

0.053

3.307

0.000

0.000

0.000

0.000

0.000

0.000

0.000

2.986 2.986 2.951 2.951 2.955 2.955 3.002 3.002 2.928 2.928 2.954 2.954 3.114 3.114

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Table 3. Bond length analysis performed on the core of the optimized and experimental neutral clusters. Data in angstrom. Numbering refers to Figure 3M. From Figure 3 it is clear that all of the analysed kernels cannot be represented by a regular icosahedron since all bonds has different length. However, a regular pattern can be found in clusters B and E where, leaving out the difference on absolute values, every bond has the same length of its opposite, meaning that the cores distortions are centre-symmetrical. This is fully compatible with the presence of a pure JT effect which breaks the icosahedral symmetry in order to stabilize the otherwise degenerate ground state. B is the cluster where the ligands are also arranged in a symmetric way, an arrangement that preserves the core symmetry we are analysing here. This symmetry is instead lacking in A, and indeed for this cluster, opposite bonds have different lengths,



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with differences up to 0.071 Å which is the 2.3% of the average bond length. Therefore, the orientation of the organic ligands does have a structural effect on the core. To provide a reference value, the changes in bond length passing from the ground to the excited states for [Au25(SR)18]- is on the order of 0.1 Å.33 On a group symmetry point of view, these data together shows that, neglecting some minor differences between bonds, the [Au25(SCH3)18]0 core of all analysed clusters have a D3d symmetry character (instead of the ideal Ih group) which is anyway more symmetrical than the D2h of the whole nanocluster.20 In order to investigate the consequence of the JT effect, and of the ligand orientation, we analysed the energy level distribution of the optimized clusters. As highlighted in Table 4, the energetic levels are quite similar between A and B (they differ by 0.030 eV at most), thus we reported in Figure 4 the average energy level distribution calculated on the two cluster’s frontier orbitals.

E [eV] SOMO-2

SOMO-1

SOMO

LUMO

LUMO+1

ALPHA

-5.179

-5.116

-4.905

-2.908

-2.895

BETA

-5.140

-5.077

-4.086

-2.847

-2.829

ALPHA

-5.187

-5.145

-4.884

-2.920

-2.906

BETA

-5.144

-5.107

-4.063

-2.866

-2.840

A

B

Table 4. Energies of frontiers orbital of B3LYP//6-31G (d, p)/LANL2DZ optimized clusters. SOMO = Single Occupied Molecular Orbital; LUMO = Lowest Unoccupied Molecular Orbital.


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Figure 4. Average of the frontiers orbitals electronic configurations of the B3LYP//6-31G (d, p)/LANL2DZ [Au25(SCH3)18]0 optimized nanoclusters. Since we adopted an unrestricted scheme for the structures optimization, the orbital energies are different if we consider the (alpha and beta) spin polarized orbital pairs. Looking at Figure 4 it is noticeable a splitting between spin orbitals in the three almost degenerate SOMOs. We recall that on the basis of superatom model21 the three SOMOs should be degenerate (without counting the whole cluster symmetry) since they have P-like character. In neutral cluster, both the open-shell character and the JT effect contribute to decrease the orbital symmetry, and remove the degeneracy observed in the mono-negative charged closed-shell [Au25(SR)18]-1 systems.2 We have also to point out the effect of spin-orbit coupling on orbital energies that has been very recently estimated to be 0.14 eV and that it is not accounted for here.30 Our focus is in fact in comparing the effects of two different arrangements of substituents, rather than accurately targeting a specific experimental measurement. A point that has not been discussed yet is the relation between the different ligand orientations and the electric dipole of the molecule. Indeed, while in cluster B there is not unbalanced charges, the asymmetrical arrangement of the methyl groups in cluster A allows the presence of a non-zero



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electric dipole moment in the ground state. The components and module are summarized in Table 5 and the corresponding vector is pictured in Figure 5 with respect to the core orientation. µx [D]

µy [D]

µz [D]

|µ|[D]

1.6278

-4.0938

-3.4170

5.5754

Table 5. Electric dipole moment components and module of cluster A. Values in Debye. The coordinate reference system is that used in Figure 5 The presence of an intrinsic electric dipole moment, of appreciable magnitude, connected to the spatial arrangement of the organic chains, can play an important role in the behaviour of a system composed on many nanoclusters, especially when they are packed (like in the crystal) and/or in low temperature conditions.

Figure 5. Electric dipole moment vector and Au13 kernel of cluster A. The color code of the axes is as follows: x = red, y = green, z = blue. Analysis of the Optical Properties. The relation between ligands orientation and optical response can be identified by a comparative analysis of clusters A and B TDDFT computed spectra. Indeed, since the two clusters were optimized at the same level of theory, the small differences in terms of molecular orbital transitions compositions are linked to the differences in the organic units arrangement. In Figure 6 we reported both computed absorption profiles and the overlaid spectra. No relative normalization of the spectra was performed in order to mark possible differences in terms of


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absorption intensities. In both spectra, we pointed out with letters the most significant transitions. The criterion adopted to define a significant transition was correlated to their oscillator strengths. In particular, in A case we took as significant transition the ones with oscillator strengths greater than 0.025. As consequence, in order to provide a meaningful comparison, we took the same excitations for B. Other excitations were accounted if their oscillator strengths were higher than 0.020 and if their excitation energies were far from a previous identified significant excitation by ±0.01 eV at most. Finally, peak s was considered significant since it is referred to the optical α-SOMO → αLUMO gap. Significant excitations compositions in terms of single particle transitions are reported in Table 6 together with their optical parameters.

Figure 6. From left to right: TDDFT computed absorption spectra for cluster A and B respectively, calculated at the B3LYP//6-31G/LANL2DZ geometry. Lastly, the overlaid computed absorption spectra for cluster A and B at the B3LYP//6-31G/LANL2DZ geometry. Latin letters indicate the main absorption peaks. The original oscillator strengths are magnified by 10 times to ease their visualization. Looking at Figure 6, the first impression is that the two spectra are very similar. In particular major peaks s, a and d occur almost at the same excitation energies in both cases (the maximum difference is only 0.02 eV). These correspondences arise from the compositions of the peaks since, as resumed in Table 6, they are composed by almost the same transitions. In particular the excitation



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composition coincides in peaks s and differs by only α-SOMO-2 → α-LUMO+1 transition on peaks a which are present in B but not in A. Regarding d peaks the situation is quite more complicated since it is composed by two significative excitations in cluster A rather than the three of cluster B (see Figure 6). Although the main molecular orbital transitions constituting cluster A d peaks are all included in cluster B, the opposite is not true.

Peak

Energy [eV]

Oscillator strength

Major involved transitions d/(sp+d) % character ratio

d/(sp+d) % character ratio

s

1.37

0.008

S(A)->L(A) (78%) S(A)->L+1(A) (16%)

11.9

14.5

a

1.77

0.031

S-2(A)->L(A) (22%) S-1(B)->L+1(B) (13%) S-1(B)->L+2(B) (22%)

6.0

14.5

A d1

3.17

0.023

S-14(A)->L(A) (23%) S-13(B)->L+2(B) (14%)

7.1

14.7

d2

3.18

0.047

S-2(A)->L+6(A) (20%)

5.9

15.6

s

1.35

0.005

S(A)->L(A) (48%) S(A)->L+1(A) (22%)

10.7

18.5

0.035

S-2(A)->L(A) (17%) S-2(A)->L+1(A) (17%) S-1(B)->L+1(B) (27%) S-1(B)->L+2(B) (16%)

5.6

20.8

S-14(A)->L(A) (15%) S-1(A)->L+6(A) (25%) S-13(B)->L+1(B) (24%) S(B)->L+7(B) (19%)

8.1

12.0

a

1.76

B d1

3.18

0.097

d2

3.19

0.085

S-13(B)->L+2(B) (56%)

7.2

25.6

d3

3.20

0.034

S-2(A)->L+6(A) (46%) S-1(B)->L+7(B) (39%)

7.0

10.6

Table 6. Optical parameters of the main transitions giving rise to s, a and d peaks in A and B absorption profiles. S = SOMO, L = LUMO, A = alpha, B = beta.


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and

d/(sp+d) % character ratio are the percentage of the core atoms d-basis functions

squared coefficients over the sum of both sp and d coefficients for the initial (i) and final (f) states. A deeper analysis on the minor excitations compositions show that the missing transitions are present in nearby (and less intense) excitations, spread in a range of ± 0.04 eV with respect to the major excitations, both for peaks a and d. This is reasonable: cluster B is more symmetric than A due to the ligand arrangement, therefore some transitions that are degenerate by symmetry in cluster B may not be (and indeed are not) exactly degenerate in cluster A. However, when a reasonable broadening for each excitation is taken into account, the absorption intensities of the excitations are practically superimposable. The largest intensity difference (peak a) is about 0.03 units over 0.26. In order to characterize the nature of the excitations and compare it with the bulk gold ones, we analysed the sp and d contributions of the initial and final states on the gold core atoms, adopting intraband and interband terminology (as done before in the literature23,29). This terminology is not strictly correct because the level distribution is clearly discrete and therefore cannot be considered as a continuous band. Unfortunately, since atomic-centred gaussian basis functions are not an orthonormal basis set, there is not a rigorous way to obtain the sp and d character from the initial and final states compositions. However, we performed this estimation by summing the square moduli of sp and d basis functions coefficients of each involved molecular orbital. Finally, to obtain suitable indications on the sp or d character of the involved states, we calculated the percentage of the d character over the sum of both sp and d coefficients defined here above,

that is the ratio

reported in Table 6 and 7. Looking at the nature of the excitations, the molecular orbital transitions which constitute peaks s, a and d have approximately the same

value both on initial and final

states, so they coherently point to the mixed inter/intraband nature of these excitations. Indeed, according to Table 6, in A every state has a d character which is up to the 15.6% of the whole 15 ACS Paragon Plus Environment


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excitation nature while in B this ratio raise up to 25.6%. This means that none of the accounted state has a pure sp or d character so the excitations are not pure interband or intraband process. Although transitions are mainly sp → sp (intraband), the arrival states of the excitations peaks s, a, and d have non-negligible d characters (up to 25.6%). Thus, these transitions can be considered as mixed intraband/interband excitations. Looking at the other major peaks, the main differences between A and B take place on peaks b and c. In order to understand in detail how these peaks differ in terms of single molecular transitions, we reported in Table 7 their main physical features. Starting from peaks b, it can be seen that it is more pronounced in cluster A than in cluster B. This can be explained on the basis of the involved molecular orbital excitations: in cluster A this peak is composed by two main excitations which involves many molecular orbitals states and have almost the same strengths. Instead, despite in cluster B the peak is also composed by two different excitations, the first of them (b1) has an oscillator strength 3.7 times smaller than the second one (b2). This means that only one of the two excitations contribute sizably to the global peak and so the shape of the two peaks are different. A deeper analysis on excitation compositions between A and B, reveals that b principal transitions occur almost through the same energy levels, but they have different weights. Moreover, the molecular orbital transition α-SOMO-2 → α-LUMO+2 which is present in A is not included among the major transitions of cluster B peaks. Similarly, the transitions β-SOMO → β-LUMO+3 and βSOMO-1 → β-LUMO+3 which are present in cluster B are not included in A case. It is important to point out that these transitions are not really missing; only they occur at slightly different excitation energy values with oscillator strengths that are lower by more than 2.5 times the main ones. Regarding the nature of the excitations, in both cases peaks b represent an almost pure sp → sp intraband excitations.


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Peak

Energy [eV]

Oscillator strength

Major involved transitions



b1

2.58

0.020

S-1(A)->L+2(A) (14%) S(A)->L+4(A) (14%) S(B)->L+4(B) (22%)

7.0

7.9

b2

2.60

0.026

S-2(A)->L+2(A) (19%) S-1(B)->L+3(B) (24%)

6.9

7.8

c

2.91

0.042

S-2(A)->L+4(A) (24%) S-1(B)->L+5(B) (32%)

5.9

7.1

b1

2.58

0.007

S-1(A)->L+2(A) (15%) S-1(B)->L+3(B) (13%) S(B)->L+3(B) (20%)

6.7

8.8

6.9

8.9

A

B

b2

2.59

0.026

S-1(A)->L+2(A) (10%) S(A)->L+4(A) (10%) S-1(B)->L+3(B) (10%) S(B)->L+3(B) (16%) S(B)->L+4(B) (10%)

c1

2.89

0.072

S-1(A)->L+4(A) (20%) S(B)->L+5(B) (23%)

5.6

6.4

c2

2.90

0.065

S-2(A)->L+4(A) (18%) S-1(B)->L+5(B) (22%)

5.6

6.5

Table 7. Optical parameters of the main transition constituting b and c peaks in absorption profiles. S = SOMO, L = LUMO, A = alpha, B = beta.

and

d/(sp+d) % character

ratio are the percentage of the core atoms d-basis functions squared coefficients over the sum of both sp and d coefficients for the initial (i) and final (f) states. At odds with b, peak c is more intense in B than A. This arises because in B the global excitation is composed mainly by two transitions (rather than one in cluster A) that have oscillator strengths greater than c transition in cluster A (0.071 and 0.065 vs 0.042). In terms of molecular orbitals composition, the c peak in cluster A corresponds to peak c2 in cluster B. Instead, peak c1 has not a direct correspondence in A major transitions since the molecular orbital excitations involved, in cluster A, are spread over many minor excitations in the 2.88-2.87 eV range. Finally, also in this case the nature of the excitations is conserved between A and B, since they are also pure sp → sp 17 ACS Paragon Plus Environment


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intraband excitations. Globally, despite the discussed minor differences, the two spectra show approximately the same absorption profiles and so the different methyl group orientations give negligible modifications in the nanocluster’s optical properties. Taking into account that the important excitations for the lowest transitions are mainly localized on the gold kernel, and that the geometry of the latter is sensitive to the different ligand arrangements (see Table 3), some changes in the optical spectrum could be expected. Nevertheless, the geometry distortions are not extensive, and the spectral changes turned out to be limited. The obtained spectra are qualitatively comparable with the ones obtained by the calculations on -1 charged nanoclusters. By a comparison with the profiles reported in ref.17,29 it can be show that all major peaks have the same energies of the -1 charged case, notwithstanding differences introduced by using different xc functionals and ligands, that can introduce errors of several hundredths of electronvolts in excitation energies.17 This is in line with the experimental evidence that the absorption profiles of negatively charged and neutral Au25 gold nanoclusters are almost equal.3 However, an insight on the peak compositions show that the peak which corresponds to HOMOLUMO gap in charged clusters has a direct counterpart in peak a of neutral cluster profile but not in peaks s which is missed in the charged cluster case. This directly means that the optical gap in -1 charged clusters is bigger than in neutral clusters. This is a direct consequence of the presence of the extra electron. Indeed in monocharged case, despite the extra electron destabilize all orbitals, it fills the HOMO set, making it lightly more stable. On the other side, LUMOs are destabilized because any virtual electron added to a closed shell system is less stable than one added in an open shell configuration. Among neutral and monocharged cases, the nature of the excitations are always comparable in most of the cases, except for peaks d where, while in neutral cluster it is made primarily on intraband transitions, in literature it has been considered as an interband excitation for the negatively charged cluster.23,29 In the latter references the argument used to support this conclusion relies to the well-known optical absorption of bulk gold which shows interband 18 ACS Paragon Plus Environment

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transitions below 470 nm, while at higher wavelengths it behaves as a Drude-like metal with pure intraband transitions.36 However, notwithstanding there is non-negligible contribution of interband transitions, our (approximate) estimate demonstrates that the character of all neutral clusters excitations is mostly composed by sp → sp transitions. The computed spectra are comparable to the experimental spectra too, as reported in Figure 7. Despite the experimental spectrum37 was obtained in a dichloromethane solution of cluster Au25(S CH2CH3)18 which has longer organic ligands than B, the global shape is the same. Therefore, we named all recognizable peaks with the same letters adopted above in order to ease the comparisons. The letter assignment on the experimental spectrum was performed on the basis of similarities in excitation energies and peaks intensities.

Figure 7. – Computed and experimental UV-VIS spectra of Au25 nanocluster. Experimental spectrum adapted from ref.37 In the experimental spectrum the excitation s and b are missing. However, the experimental conditions lead to peak widths larger than the 0.12 eV FWHM adopted in the simulated spectra (FWHM is an arbitrary parameter in these TDDFT calculations, and in principle could also be different for the various bands). As reported in Figure S3, with a larger FWHM of about 0.24 eV 19 ACS Paragon Plus Environment


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peak s is barely visible and the two close peaks b and c merge into a single peak (called c because of the similarity with peak c of computed spectrum), which is exactly what is obtained in the experimental spectrum. Despite these little differences, a comparison between the excitation energies of the principal peaks clearly shows that the predicted excitation energies of peaks a, c and d agree with the experiment. More in details, while peaks a and d differ by only 0.04 eV (they fall at 1.80 eV and 3.14 eV respectively in the experimental spectrum), greater difference among peaks c (2.75 eV in the experimental spectrum) may indicate that the experimental peak is a combination of b and c peaks of cluster B, as discussed here above. Overall, the good agreement indicates the appropriateness of the calculation setup used in the present work. In order to test the role of the functional on the optical features, we also computed the absorption spectrum of cluster B at the CAM-B3LYP//6-31G/LANL2DZ level. The obtained spectrum (reported in Figure S1) presents several differences from the experimental data, as already noticed by Azarias et. al.29 CONCLUSIONS A systematic study performed on the geometry of two different Au25(SCH3)18 structures optimized through an unrestricted scheme at the B3LYP//6-31G/LANL2DZ level, gives useful information on the effects that concur to create the equilibrium nanocluster geometry. First of all, we found that the clusters (independently from the ligand orientation) are affected by a first order Jahn-Teller effect as expected due to their open-shell configuration. This effect approximately reduces the core symmetry from Ih to D3d (neglecting the further symmetry reduction given by the staples). These findings were already observed in experimental structures and other calculations,16,18,33 which indeed show the same distortions. After that, we demonstrated that different orientations of the organic ligands (coming from different nanoclusters), bring the simulations into equilibrium structures that also differ for the geometry of the core. In particular, the structures with a non-centre symmetric arrangement of the CH3 on the staples16 have a more distorted gold core. This behaviour is also


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correlated to the generation of a weak electric dipole moment in the ground state. However, this phenomenon does not affect the energy level arrangement, which are quite similar in both structures. The TDDFT computed optical absorption spectra reveal that the two clusters have almost the same optical features since they agree in peaks distributions, molecular orbital compositions and nature of the excitations. This demonstrates that the organic ligands orientations, while creating measurable distortions of the core geometry, bring negligible effects on the nanoclusters optical absorption properties, even though the excitations that are important for the lowest transitions are localized on the gold kernel. An insight on the excitations nature reveal that all excitations are mainly composed of intraband sp → sp like transitions. However, the peaks called s (1.36 ÷ 1.37 eV), a (1.76 ÷ 1.77 eV) and d (3.17 ÷ 3.20 eV) show non-negligible interband characters which can constitute up to the 25% of the whole excitation nature. The calculated spectra are compatible with both experimental and previously calculated absorption profiles. In particular, we noticed minimal differences with respect to the negatively charged nanoclusters. This is in line with the experimental evidence that negatively charged and neutral clusters have almost the same absorption profiles. However, the transitions involved in the main absorption peaks are not exactly the same considering neutral or negative nanoclusters. Moreover the intra/interband nature of some of the main excitations are different among neutral and -1 clusters. In particular peak d, which appears at around 3.20 eV, has an intraband feature in the negatively charged cluster while it has a mixed intra-interband nature in neutral cluster. ASSOCIATED CONTENT Supporting Information TDDFT computed spectrum of [Au25(SCH3)18]0 (structure B) at the CAM-B3LYP//6-31G/LANL2DZ level; TDDFT computed spectrum of [Au25(SCH3)18]0 (structure B) with a larger FWHM; Calculated IR spectra of the clusters



Page 22 of 26

AUTHOR INFORMATION Corresponding Author *Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT SC thanks MIUR-FARE for funding under the grant Plasmochem. REFERENCES (1)

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Role of Organic Ligands Orientation on the Geometrical and Optical

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