A first principles density functional investigation of ligand-protected eight atom gold nanoclusters

Relativistic effect is an important aspect for gold. 1s electron of gold reaches a speed about 58% of that of light and electronic mass at this 1s orbital also increases by an amount of 20%. Thus the 1s orbital shrinks and similar effect takes place for s orbitals of higher quantum number. The relativistic to nonrelativistic ratios of the orbital radii (described by 〈r〉R/〈r〉NR) for neutral gold becomes 0.880 for 1s, 0.873 for 2s, 0.900 for 3s, 0.911 for 4s, 0.907 for 5s, 0.827 for 6s [1]. Thus, 6s orbital shrinks more than 1s. Fig. 5.1 shows a plot of 〈r〉R/〈r〉NR of the 6s orbital for several elements from the periodic table. This radial function shows a minima at gold and platinum. Similar contraction also takes place for p orbital. Contraction of s or p results from the direct relativistic effect while indirect relativistic orbital expansion also plays crucial role in gold cluster stability [2]. d or f orbitals are hardly affected because of the centrifugal potential I(I + 1)/r2 where I is the azimuthal quantum number and r is the radius. As a result, effective potential of d or f orbital is more effectively screened due to such relativistic contraction of s, p orbitals. As a result of such interesting relativistic effect, 6s orbital or gold shrinks while 5d is pushed ∗This chapter is based on the article : AIP Advances 1, 032150 (2011).


Chapter
A first principles density functional investigation of ligand-protected eight atom gold nanoclusters * -------

Background
Relativistic effect is an important aspect for gold.1s electron of gold reaches a speed about 58% of that of light and electronic mass at this 1s orbital also increases by an amount of 20%.Thus the 1s orbital shrinks and similar effect takes place for s orbitals of higher quantum number.The relativistic to nonrelativistic ratios of the orbital radii (described by r R / r N R ) for neutral gold becomes 0.880 for 1s, 0.873 for 2s, 0.900 for 3s, 0.911 for 4s, 0.907 for 5s, 0.827 for 6s [1].Thus, 6s orbital shrinks more than 1s.Fig. 5.1 shows a plot of r R / r N R of the 6s orbital for several elements from the periodic table.
This radial function shows a minima at gold and platinum.Similar contraction also takes place for p orbital.Contraction of s or p results from the direct relativistic effect while indirect relativistic orbital expansion also plays crucial role in gold cluster stability [2].d or f orbitals are hardly affected because of the centrifugal potential I(I + 1)/r 2 where I is the azimuthal quantum number and r is the radius.As a result, effective potential of d or f orbital is more effectively screened due to such relativistic contraction of s, p orbitals.As a result of such interesting relativistic effect, 6s orbital or gold shrinks while 5d is pushed away from the nucleus.Study of Au cluster thus forms an active area of research.The properties exhibited by the gold clusters are found to be extremely sensitive to the size, structure and dimension of the cluster.This led to extensive research to determine the size N at which the 3D geometries become energetically more favorable over the 2D geometries.
Several experimental and theoretical studies have predicted this number to fall in a range from 6 to 13 [4][5][6][7][8][9][10][11][12][13][14][15][16].For anionic and cationic gold clusters the 2D-3D transitions are observed to occur at N = 13 and N = 8, respectively.Theoretical calculations for neutral clusters have predicted the transition to occur at six [4], seven [5,6], eight [7,8], as well as in the range from 11-15 atom clusters [9][10][11][12][13][14][15][16].It has been anticipated that the different methods and models adopted to determine the cluster size at which the 2D-3D transition takes place can possibly be one of the reasons for the large spread in the obtained results (from 6-15).Gold clusters are reported to retain their planar structures to cluster sizes larger compared to Ag and Cu clusters which remain planar upto 7 atom cluster sizes only [17].This has been anticipated to occur due to the relativistic effect in gold which results in a strong sd-hybridization leading to a delocalization of the d-electrons over the volume of the cluster which in turn produces a stronger d-d interaction of neighboring Au atoms [17].However, the clusters observed in experiments are prepared in ligand-resolved solution.
"passivators", originally employed to check the growth of the clusters which otherwise would grow to large sizes, appear to play a more active role in terms of determining the structure of the cluster primarily by influencing the surface geometry through a change of surface chemistry.This has lead to several theoretical studies involving cluster together with ligands.Considering small Au atoms, particularly those falling in the range of crossover transition between 2D-like to 3D-like geometry theoretical studies have been carried out for 11-atom and 13-atom clusters [18,19].The studies indicate that the structure of small gold clusters are altered substantially in the presence of ligands, in the sense the planar geometries predicted by calculations for bare clusters were found to be stabilized in 3D-like geometries upon ligation.The rational for the stabilization of markedly different geometries were traced to Au-ligand covalency.

Motivation behind the project
In 2008, Au 8 has been prepared by etching with "excess" † glutathione [32].Strong bluishgreen luminescence has been noticed in glutathione capped Au 8 with excitation and emission maxima 370 and 465 nm respectively.Such fluorescent property suggests that glutathione capped Au 8 complex is not metallic.But the experimental structural analysis has not been provided for this magic cluster which have also been predicted by several studies to be a possible case for 2D-3D crossover.In the present study based on first principles density functional theory (DFT) calculations, we investigate the effect of ligand capping on the results of the earlier studies on the stabilization of 2D and 3D geometries.In this present study, we have considered the ligand molecule as ethyl mercaptan (CH 3 -CH 2 SH), a small structure of glutathione (HO 2 CCH 2 NHCOCH(NH 2 )CH 2 CH 2 CONHCH(CO 2 H)-CH 2 SH) , the ligand which was used for the synthesis of the 8-atom clusters [32].

Computational Details
All our calculations were performed by using the PWscf (plane wave self consistent field) code of the QUANTUM ESPRESSO [33,34] distribution.The wave functions in this † During etching in presence of "excess" thiol, structural composite follows two distinct mechanism: during first mechanism, unstable gold-thiol molecules form Au-SR (SR : sulfur S within an organic radical R) polymers [30].Second mechanism is the formation of stable gold nanoclusters with smaller size.Such a process of conversion of larger unstable nanoclusters to smaller stable size is termed as "core-size conversion" [31].
code are expanded in a basis consisting of plane waves.An energy cut-off of 680 eV was chosen for the plane wave based wave functions to converge the binding energies.
Relativistic spin-orbit coupling increases the binding energies of all clusters.But the relative stability between different structures was not significantly altered.Thus, Scalar relativistic ultrasoft pseudopotentials [35] was considered for the calculations.Exchange correlation functional was treated under LDA scheme as parametrized by Perdew and Zunger [36].
Binding energy per gold atom was calculated by the mathematical expression : where E Au 8 is the total energy of the 8 atom gold cluster, E Au is the energy of an isolated Au atom.The interaction energy E I of the ligand capped molecules was defined as: where E (Au 8 +N Lig ) is the total energy of the Au 8 cluster covered with N number of ligand chains and E Lig is the total energy of the isolated ligand.The ionization potentials (IP) and the electron affinities (EA) have been calculated as: where E N −1 , E N +1 and E N are the total energies of the anionic, cationic and neutral clusters respectively.For vertical IPs and EAs, the total energies were obtained at the optimized coordinates of the neutral cluster with a difference in the number of electrons and for adiabatic IPs and EAs, the geometries were relaxed.s-d hybridization index is calculated according to Ref [38]: where w l i,s and w I i,d are the squares of the projections of the i-th Kohn-Sham orbital onto the s and d spherical harmonics respectively, centered on the I-th atom integrated over a sphere whose radius is equal to half the nearest neighbor bond distances of the cluster.

Results and Discussions
In order to study the gold-sulfur interface of Au 8 (SR) n (R = CH 3 − CH 2 H), we have to understand their structural properties.Thus, at first, we will discuss the optimized structures.

Structural stability of clusters
8 gold ions can be rearranged in various ways.We started our calculations by considering only minimum energy configuration of Au 8 available in literature [12,[38][39][40][41][42].Considering planner 2D geometry of Au 8 we found that edge-bridge rhombus (star) structure (left structure of top panel in Fig 5 .2) is most stable among the planner geometry.Binding energies were calculated by using the formula 5.1.Binding energy of triangle-capped hexagonal (hex) structure (second figure of top panel in Fig 5 .2) is 0.01 eV/atom was found to be less compared to that of "star" structure.From the binding energy concept, we can clearly conclude that rest two 2D planner geometry of Au 8 are much more unstable, thus they have been put aside in this current project.From the stability point of view, both star and hex structure are in tough competition, irrespective of basis set or exchange correlation functional or choice of pseudopotentials [12,40,41,43], while bicapped distorted octahedron is reported to be the only stable non-planner 3D geometry of Au 8 [12,40,43].So, in the following discussions, we will focus on only star, hex and 3D bicapped-distorted octahedron structure of 8 atom gold nanocluster.
In order to study the ligand capped structures, first we have to know the amount of ligand coverage ie.number of ligand chains to be attached as well as the preferable gold sites for the ligand molecules.Considering star structure, it can be seen that (see Fig. 5.2) this structure has two in-equivalent sites, corner site ( pointed as 1, 2, 3, 4) and top site (ponied as 5, 6, 7, 8).Top sites have two nearest Au ions, while corner ions are shared in between 4 gold ions.Single ligand chain attached to the a site, increases the stability of the complex, while ligation at corner site detaches the mercaptan molecule from that site and after force optimization, we found that the ligand chain is attached to a top site, nearest to that corner site (see Fig. 5.2).In conclusion, gold ion with 4 or higher order nearest neighbors is less inactive to the lignd chain.To check the higher order ligand activity of the star structure, we considered Au-S to be 2.38 Å [44] and ∠ S-Au-S as 160 • [45].Our calculations suggested that top site of star structure can attach, at best two ligand molecule, so that full ligaton resulted in the structure shown in the left figure of bottom panel in Fig. 5.2.Optimization reduces the Au-S bond-lengths to 2.47 Å, while ∠ S-Au-S is changed to 111.02 • .Next we focus on the hex structure.Atom sitting at the top of the triangle (marked as 1 in middle of the bottom panel in Fig. 5.2) has two nearest neighbors, thus two ligand chain can be attached to that site, which after optimization increases the stability.Atom 2 and 3 don't react with the mercaptan chain, may be due to the absence of any dangling bond (4 nearest neighbors).Atom sites 4, 5, 6 and 7 attach maximum single chain of mercaptan, while site 8 with 5 nearest neighbors doesn't react with ligand.Thus, full ligand coverage results into the structure shown in the middle diagram of bottom panel in Fig. 5.2.Finally we consider the non-planner geometry of Au 8 .Within this structure, sites marked as 2, 3, 7 and 8 have 3 nearest neighbors, while 1, 4, 5 and 6 sites are located at more than 3 nearest neighbors positions.Considering sites 2, 3, 7 and 8, except site marked as 7, rest attach two ligand chains, site 7 does not prefer to attach any ligand.Thus, three nearest neighbor sites in non-planner geometry attach a pair of ligands which is energetically restricted for planner geometry like the hex structure.In hex structure separation between 2 three nearest neighbor sites is ∼ 2.62 Å, while same for 3D becomes 4.38 Å ie.ligand capped non-planner structure is much more closely packed with ligand chains leading to less ligand-ligand interaction.

Energetics
Energetics of bare and ligand capped systems are summarized in table 5.1.Numbers within the bracket stand for results obtained within PBE-GGA.Bare planner 2D hex and non-planner (3D)structures become energetically degenerate within LDA.Although 2D hex and 3D structures are covered with 6 number of mercaptan chains, E I of ligand capped hex structure is greater than 3D structure by 0.18 eV per ethyl mercaptan chain.PBE-GGA also shows similar type of trend.Then we will discuss about the first adiabatic and vertical ionization potentials (IP) and electron affinities (EA) of both bare and ligand capped complex system by using equation 5.  Relaxation lowers the IPs and increases the EAs (see Table 5.2) irrespective of bare or ligand-capped clusters.Both EAs and IPs decreases compared with the bare component, indicating that the ligand capping increases the stability of the structures.Such reduction is weaker for 3D geometry compared to planner structures.Thus, passivation is stronger for the planner geometry suggesting that ligand capped planner geometry is much more stable compared to the non-planner (3D) structure

sd hybridization
Stability of the individual cluster and their ligand capped complexes can be explained in terms of the sd hybridization index.Calculated sd hybridization index for bare star, hex and non-planner structure become 1.98, 2.10 and 1.75 respectively.Thus, sd hybridization become stronger for planner 2D geometry.Ligand capped molecules show decrease in the value of sd hybridization index [46].After ligand attachment, sd hybridization index for star, hex and 3D complexes become 1.24, 1.48, 1.16 respectively.Although values of sd hybridization decreases after ligation, the trend remains almost same for both bare and ligand capped structures.

Density of states
Next we discuss about the density of states (DOS) of each bare cluster system and their ligand capped complexes.From Fig. 5.3, it can be easily seen that S-[s,p] and C-p states appear at lower energies, which also hybridize with Au-d states resulting from the bonding nature of Au and the ligand molecule.HOMO-LUMO gaps for both star and hex complexes increases after ligand attachment, while for non-planner geometry, this energy gap gets reduced.Thus, attachment of ligand increases the stability for planner geometry over the 3D structure.The quantitative values of HOMO-LUMO gaps are summarized in table 5.1.

HOMO-LUMO charge densities
Now, we focus on the charge densities accumulated at the HOMO and LUMO.This analysis will mainly reflect the DOS nature.From

Bonding charge density
In order to study the bonding nature of the ligand molecule and gold cluster, we have studied the bonding charge densities or the charge density differences.Bonding charge density ρ diff has been calculated by using the mathematical expression 5.6, (5.6) where ρ complex is the charge density of ligand capped complexes, ρ cluster stands for charge density of bare cluster and ρ ligand is ligand charge density.All sets of values are calculated within same structural supercell.So, in other words, during the calculations, we first calculate the charge density of the ligand-cluster complex (ρ complex ).Then using the same supercell we calculate the charge densities of individual ligands (ρ ligand , i = ligand number) and the bare cluster (ρ cluster ).Fig. 5.5 shows bonding charge density plots, in which red and cyan regions denote charge accumulated and charge-depleted regions respectively.
These plots shares important electronic aspect regarding the charge-accumulated regions.
Charge transfer from the metal cluster to the Au-S bonds results in a strong covalent bond between the Au and S atoms.Ligand protected star cluster shows strong charge accumulation in the Au-S bonds as well as in the S-S bridges.The six-ligand protected hex cluster shows similar types of behavior ie.charge lost from the Au and S atoms accumulate at the center of the bond between Au and S atoms.This accumulation is stronger for the 2D hex system than the 3D structure (Fig. 5.5) supporting the enhanced stability of the 2D systems over the 3D.

Conclusion
Applying first principles DFT calculations we have studied the effect of ligand attachment to 8-atom Au-clusters.This magic numbered cluster has already been experimentally synthesized.We have chosen the ligand molecule to be ethyl mercaptan which is similar to the sulfur tail of glutathione, the ligand which was used for the synthesis of the 8atom clusters [32].In the experimental scenario, the solvent molecules interact with the tail part of the ligands leaving the cluster-ligand interaction unperturbed, as the clusterligand interaction (bonding) involves only the head part of the ligand [47,48].During our study this solvent effect is neglected completely and simplified form of ligand molecule is considered with shortened tail part.Our study in this respect represents mainly the cluster-ligand interaction through the bonding nature of gold and sulfur.Our studies suggests that attachment of ethyl mercaptan ligands to Au 8 increases the stability of the planner geometries over that of the non-planner structure.

Figure 5 . 2 :
Figure 5.2: Toppanel :: planner (2D) geometry of bare gold nanoclusters with correspondingbinding energy E B (eV/atom).Left and second left structures are termed as star and hex.Middlepanel :: inactivity of 4 nearest neighbor gold site to a mercaptan chain.If we attach any ligand chain to some corner site, after force optimization, ligand chain goes to nearest top site.Bottompanel :: ligand capped cluster configurations.From left to right: four double ligand chains attached to the four top atoms of the star cluster, six ligand chains attached to selective atoms of the hex cluster and the 3D cluster capped by three double ligand chains.
3 and 5.4.The vertical IPs and EAs are

Fig. 5 . 4 ,
it is seen that corner centered HOMO states of bare star structure shows dominant Au: d x 2 −y 2 nature while same for top sites bears mainly Au: d xy character.This feature remains almost same after ligand attachment .For hex structure, center atom of the hexagon shows mainly Au: d x 2 −y 2 character.This HOMO charge density remains more or less similar when ligands are attached.Considering non-planner structure, HOMO states are mainly centered on the sites marked as 2, 3, and 8 which moves to the site 7 after ligation.Next we will discuss about LUMO charge densities.Considering star structure, sd hybridized LUMO charges, centered on the 4 top sites, move to the ligand site after ligation ie.all dangling bonds of this bare gold cluster are successfully passivatd by the ethyl mercaptan chains.The edge atoms of the hex cluster which in bare condition show accumulation of sd-hybridized charge density, similarly get rid of the accumulated charge upon ligand attachment by shifting them to the ligand chains.The sites where ligand is not attached, such sd-hybridization character

Figure 5 . 4 :
Figure 5.4: HOMO and LUMO charge density distributions has been plotted at one-third the maximum of iso-value for bare and ligand protected star (panel A), hex (panel B) and 3D (panel C) clusters.

Figure 5 . 5 :
Figure 5.5: Charge density difference plots for one-third the maximum of iso-value of star (a) hex (b) and 3D (c) ligand-protected clusters.Charge accumulated and depleted regions have been shaded by Red and cyan colors .

Table 5 . 1 :
Binding energies E B (in eV/atom) of bare clusters (B) and the interaction energies E I (in eV/ligand) of the ligand capped clusters (WL).E g is the HOMO-LUMO energy gap in eV.The numbers within the brackets for E B (B)/E I (WL) indicate results obtained using PBE-GGA
calculated with a difference in electron count keeping the same structure between the two calculations.The adiabatic IPs and EAs are obtained by optimization of the structures.