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. 2017 Jul 7;8:15988.
doi: 10.1038/ncomms15988.

Thermodynamic Stability of Ligand-Protected Metal Nanoclusters

Free PMC article

Thermodynamic Stability of Ligand-Protected Metal Nanoclusters

Michael G Taylor et al. Nat Commun. .
Free PMC article


Despite the great advances in synthesis and structural determination of atomically precise, thiolate-protected metal nanoclusters, our understanding of the driving forces for their colloidal stabilization is very limited. Currently there is a lack of models able to describe the thermodynamic stability of these 'magic-number' colloidal nanoclusters as a function of their atomic-level structural characteristics. Herein, we introduce the thermodynamic stability theory, derived from first principles, which is able to address stability of thiolate-protected metal nanoclusters as a function of the number of metal core atoms and thiolates on the nanocluster shell. Surprisingly, we reveal a fine energy balance between the core cohesive energy and the shell-to-core binding energy that appears to drive nanocluster stabilization. Our theory applies to both charged and neutral systems and captures a large number of experimental observations. Importantly, it opens new avenues for accelerating the discovery of stable, atomically precise, colloidal metal nanoclusters.

Conflict of interest statement

The authors declare no competing financial interests.


Figure 1
Figure 1. Optimized geometries of the experimentally synthesized metal nanoclusters.
(a) Au18SR14 (ref. 29), (b) Au20SR16 (ref. 25), (c) Au24SR20 (ref. 30), (d) Au28SR20 (ref. 32), (e) Au30S(SR)18 (ref. 19), (f) Au36SR24 (ref. 33), (g) Au38SR24q (ref. 34), (h) Au38SR24t (ref. 65) and (i) Au102SR44 (ref. 35). nc represents the number of core metal atoms while nShellInt represents the number of shell-to-core interactions. Ligands (S-CH3) are shown in stick representation while core and shell atoms, in ball and stick, have been coloured yellow and blue, respectively. In b,c, shell Au atoms which do not interact with the core have been coloured red and are shown in stick representation, while in a,i shell Au atoms which were previously identified as core are coloured darker blue. In e,h, shell sulfur atoms which are not directly bound to a shell Au atom are shown as brown balls.
Figure 2
Figure 2. Parity between core cohesive energy and the shell-to-core BE.
The corresponding structures of the Aun(SR)m NCs are presented in Fig. 1 except from the optimized structures of (i) [Au25SR18] (ref. 31), (ii) [Cu25SR18] and (iii) [Ag25(SPhMe2)18] (ref. 36) NCs, which are shown as insets in the graph. For i–iii, nc=13 metal atoms (Au/Cu/Ag) and nShellInt=12 as in Fig. 1. The shell metal atoms are shown in blue, whereas, the Cu and Ag core metal atoms are shown in red and green, respectively. Here, all the Au and Ag NCs reported have been experimentally determined. The Cu NC structure is hypothetical, optimized from the Au NC analogous structure (i).
Figure 3
Figure 3. Nanocluster stability–morphology relations.
(a) Core CE and shell-to-core BE versus nc−1/3 (number of core metal atoms) for cores of thermodynamically stable magic number Au NCs. (b) Core CE and shell-to-core BE versus average coordination numbers (CNs) for cores of Au NCs. (c) Shell-to-core BE and average core CN versus the ratio of total Au atoms and S atoms in the shells and (d) global minima gas phase Au clusters and cores of Au NCs. From Figs 1 and 2, the Au NC cores contain: Au18SR14=8, Au20SR16=7, Au24SR20=8, [Au25SR18]=13, Au28SR14=14, Au30S(SR)14=17, Au36SR24=20, Au38SR24q, t=23 and Au102SR44=77 Au atoms.
Figure 4
Figure 4. Nanocluster stoichiometry relations.
(a) Number of ligands (m) and nShellInt versus nc2/3 for all NCs of Fig. 3. The inset graph shows the nShellInt versus m behaviour. (b) Predicted stoichiometric trend between number of ligands (m) and total Au (n) atoms of the NCs. The predictions were made using the relations shown in a. The black line represents the best fit, whereas, the surrounding red lines the standard error in the prediction. The purple square points represent experimentally stable NCs used in our calculations to develop the model, whereas, the blue circles represent other experimentally stable NCs identified in literature.

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    1. Daniel M. C. & Astruc D. Gold nanoparticles: assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology. Chem. Rev. 104, 293–346 (2004). - PubMed
    1. Sardar R., Funston A. M., Mulvaney P. & Murray R. W. Gold nanoparticles: past, present, and future†. Langmuir 25, 13840–13851 (2009). - PubMed
    1. Zhu Y., Qian H., Drake B. A. & Jin R. Atomically precise Au25(SR)18 nanoparticles as catalysts for the selective hydrogenation of alpha,beta-unsaturated ketones and aldehydes. Angew. Chem. Int. Ed. Engl. 49, 1295–1298 (2010). - PubMed
    1. Brust M., Walker M., Bethell D., Schiffrin D. J. & Whyman R. Synthesis of thiol-derivatised gold nanoparticles in a two-phase liquid-liquid system. J. Chem. Soc. Chem. Commun. 801–802 (1994).
    1. Chen Y., Zeng C., Kauffman D. R. & Jin R. Tuning the magic size of atomically precise gold nanoclusters via isomeric methylbenzenethiols. Nano Lett. 15, 3603–3609 (2015). - PubMed

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