Tangential Ligand-Induced Strain in Icosahedral Au₁₃

Abstract

A quantitative comparison of first principles calculations with extended X-ray absorption fine structure and transmission electron microscopy measurements provides strong evidence that Au13 nanocrystals are stabilized in a slightly distorted icosahedral structure by on-top phosphine ligands and a combination of on-top and bridging thiol ligands. Importantly, the ligands change the icosahedral strain (i.e., the radial−tangential bond length ratio) significantly, with the tangential bonds within the Au core exhibiting much more disorder than the radial ones.

Effect of Ligands on the Geometric and Electronic Structure of Au13 Clusters

“…As we have seen this bond length expansion, also known as compressive strain, is a result of the charge transfer from Au-Au bonds to Au-ligand bonds. At this point, it is worth comparing our results with the findings of Guliamov et al, 23 who also found a compressive strain in icosahedral Au 13 , except that the surface Au-Au bonds were more strongly perturbed than the radial ones, which led them to conclude that a resultant icosahedral geometry should be a distorted one. The difference from our result can be easily attributed to the effect of the S atom in their mixed ligand (PH 3 /SCH 3 ) which adsorbs at the bridge site between two neighboring Au atoms, thereby perturbing the surface Au-Au bond more than the others.…”

“…As to adsorption sites, we place the phosphines either on top of Au atoms or in the bridge sites between two neighboring Au atoms, although from the latter position they are always found to move to on-top sites during the energy minimization process used to obtain relaxed structures for the ion cores, in agreement with previous theoretical calculations and experiment. [18][19][20]23 It is noteworthy that we do not see the formation of hydrogen bonds for the phosphine ligands, such as those reported for ligands like ammonia and acetone. 31,32 Figure 2 shows the relaxed geometries of the clusters upon the adsorption of six phosphines.…”

“…22 In the case of Au 13 , ab initio calculations of bond lengths together with data from EXAFS (extended X-ray adsorption fine structure) measurement show that ligands induce substantial tangential (as compared to radial) strain, which leads to a distorted icosahedral structure. 23 While this particular study provides insights into the structural changes induced by ligands on the Au 13 nanocluster, they do not venture into the details of electronic structural changes which may answer the question why ligands induce stabilization of the icosahedral structure. To develop a rationale for the same we have carried out a systematic examination of the electronic structure of four chosen Au 13 structures in clean form and in the presence of phosphines, the ligand of choice in several experiments.…”

“…[18][19][20] An obvious reason for the discrepancy may be that the Au 13 clusters observed in experiment are prepared in ligand-resolved solution. For example, ligands such as (PMe 2 Ph) 10 In theoretical studies of the effect of ligands on the stability of Au clusters, [21][22][23] it is generally viewed that ligands play an important role by promoting further the hybridization of the Au valence bands. 21 In particular, for the Au 11 cluster, Spivey et al have concluded that the larger degrees of freedom in the 3D geometries provide a better mixing of the d orbitals of Au with the ligand orbitals than is the case for the 2D structures.…”

Theoretical investigations on the structure–property relationships of Au13and AuxM13−xnanoclusters

“…For example, Kronik et al successfully synthesized Au 13 (PPh 3 ) 4 (SC 12 H 25 ) 4 , and found that the co-protection of thiolates and phosphine ligands leads to the slight distortion of the icosahedral structure. 13 Similarly, Wei and co-workers recently found that the framework of Au 13 (PPh 3 ) 4 (SC 12 H 25 ) 4 is signicantly disturbed by the solvent environment. They found that changing the solvent from ethanol to hexane induces the dissociation of the anionic SR ligands, and the rearrangement of the icosahedral core structure to a face-centred cubic (FCC) structure.…”