Geometric Quantification of Chirality in Ligand-Protected Metal Clusters

Abstract

Chirality has been found as a relevant property of nanomaterials, including ligand-protected metal clusters and nanorods. This property not only is crucial in nanotechnology developments related to asymmetric catalysis and chiroptical phenomena but also generates fundamental questions on the existence of chirality at the nanoscale. In fact, X-ray total structure determination, electron diffraction studies, NMR, and circular dichroism spectroscopies as well as theoretical calculations performed on gold clusters protected with thiolate or phosphine ligands have confirmed the existence of chiral structures in the size range of 18−144 Au atoms. In this work, we realize a comparative analysis of the degree or amount of chirality existing in chiral ligand-protected gold clusters (LPGC), through a geometric quantification, using the Hausdorff chirality measure (HCM). The calculated HCM values provide a quantitative framework to compare, classify, and gain insight into the origin of chirality. Interestingly, these values are consistent with the current knowledge on the different sources of chirality: achiral cores and chiral arrangement of ligands in, for example, Au 102 (SR) 44 and Au 38 (SR) 24 or intrinsically chiral cores, like in Au 52 (SR) 32 and Au 20 protected with phosphine ligands. Our calculations are also helpful to assign an index of chirality and classify as chiral several recently synthesized and structurally solved LPGC that in first instance were not identified as such. The calculated HCM values are used to extract trends on how chirality is spatially distributed in LPGC and correlate them with optical activity measurements. The main trend indicates that the Au−S interface has the dominant role in the chirality of LPGC.

Diverse Chiral Scaffolds from Diethynylspiranes: All‐Carbon Double Helices and Flexible Shape‐Persistent Macrocycles

“…The chirality index increases rapidly for ( P 4 )‐ 2 when traveling in the PES from θ =0° to 30° and 60° (HCM=0.011, 0.121, and 0.152, respectively). This indicates that the flexibility of ( P 4 )‐ 2 gives rise to structures with a broad range of chiralities, as has been found in chiral ligand‐protected gold clusters . Remarkably, a great relative increase in the HCM is observed when comparing a single helix from ( P 2 )‐ 1 with itself (HCM=0.110 and 0.163, respectively, see Figure , for more information, see the Supporting Information).…”

“…Herein, we present both enantiomers of all‐carbon double helix 1 and chiral flexible shape‐persistent macrocycle 2 bearing two and four axially chiral spiranic building blocks, respectively (Scheme ). Moreover, the chirality of these fascinating structures has been geometrically quantified through the Hausdorff chirality measure (HCM) …”

“…With the purpose of gaining insight into the chirality of these novel structures, a geometrical quantification of their index of chirality was performed . This calculation, based on the HCM to quantify chirality, shows that the HCM value for the diethynylspirane building block is identical to that of a single helix from ( P 2 )‐ 1 (HCM=0,110), and almost identical to that of the D 4 symmetric conformer of ( P 4 )‐ 2 (HCM=0.011). The chirality index increases rapidly for ( P 4 )‐ 2 when traveling in the PES from θ =0° to 30° and 60° (HCM=0.011, 0.121, and 0.152, respectively).…”

Evaluation of bonding, electron affinity, and optical properties of M@C28 (M = Zr, Hf, Th, and U): Role of d‐ and f‐orbitals in endohedral fullerenes from relativistic DFT calculations

“…For comparison, the optical properties were calculated with the PBE functional (Supporting Information) which gave similar results. Calculation of optical properties with PBE and LB94, among other GGA functional, has been shown to provide reliable results in comparison to experimental data in several cluster structures …”

“…Calculation of optical properties with PBE and LB94, among other GGA functional, has been shown to provide reliable results in comparison to experimental data in several cluster structures. [44][45][46][47][48][49] The EDA [50] on the basis of the Morokuma2Ziegler scheme, [33][34][35] was used to evaluate the nature of the endohedral bonding. The dissociation energy (D e ) can be directly related to the total interaction energy (DE tot ) by taken into account both preparation energy, from the structural desestabilization of the fullerene host, DE prep , and the instantaneous interactions between the selected fragments, DE int , which leads to the following relation:…”