Theoretical prediction of a new stable structure of Au 28 (SR) 20 cluster

Chiral Inversion of Au40(SR)24 Nanocluster Driven by Rotation of Gold Tetrahedra in the Kekulé-like Core

Studying the chiral characteristics and chiral inversion mechanisms of gold nanoclusters is important to promote their applications in the field of chiral catalysis and chiral recognition. Herein, we investigated the chiral inversion process of the Au40(SR)24 nanocluster and its derivatives using density functional theory calculations. The results showed that the chiral inversion process can be achieved by rotation of tetrahedra units in the gold core without breaking the Au-S bond. This work found that Au40 nanoclusters protected by different ligands have different chiral inversion mechanisms, and the difference is mainly attributable to the steric effects of the ligands. Moreover, the chiral inversion of the derivative clusters (Au34, Au28, and Au22) of the Au40 nanocluster can also be accomplished by the rotation of the Au4 tetrahedra units in the gold core. The energy barrier in the chiral inversion process of gold nanoclusters increases with the decrease of Au4 tetrahedra units in the gold core. This work identifies a chiral inversion mechanism with lower reaction energy barriers and provided a theoretical basis for the study of gold nanocluster chirality.

Structural predictions of three medium-sized thiolate-protected gold nanoclusters Au44(SR)30, Au56(SR)32, and Au60(SR)34

The knowledge of structural evolution among thiolate-protected gold nanoclusters is not only helpful for understanding their structure-property relationship but also provides scientific evidence to rule-guided structure predictions of gold nanoclusters. In this paper, three new atomic structures of medium-sized thiolate-protected gold nanoclusters, i.e. Au44(SR)30, Au56(SR)32, and Au60(SR)34, are predicted based on the grand unified model and ring model. Two structural evolution rules, i.e., Au44(SR)28 + [Au12(SR)4] → Au56(SR)32 + [Au12(SR)4] → Au68(SR)36 and Au44(SR)30 + [Au8(SR)2] → Au52(SR)32 + [Au8(SR)2] → Au60(SR)34 + [Au8(SR)2] → Au68(SR)36, are explored. The generic growth patterns underlying both sequences of nanoclusters can be viewed as sequential addition of four and three highly stable tetrahedral Au4 units on the cores, respectively. In addition, density functional theory calculations show that these three newly predicted gold nanoclusters have very close formation energies with their adjacent structures, large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps, and all-positive harmonic vibration frequencies, indicating their high stabilities.

Assembling Au4 Tetrahedra to 2D and 3D Superatomic Crystals Based on Superatomic-Network Model

Thiolate-protected gold nanoclusters (denoted as Au _m (SR) _n or Au _n L _m ) have received extensive attention both experimentally and theoretically. Understanding the growth mode of the Au₄ unit in Au _m (SR) _n is of great significance for experimental synthesis and the search for new gold clusters. In this work, we first build six clusters of Au₇(AuCl₂)₃, Au₁₂(AuCl₂)₄, Au₁₆(AuCl₂)₆, Au₂₂(AuCl₂)₆, and Au₃₀(AuCl₂)₆ with the Au₄ unit as the basic building blocks. Density functional theory (DFT) calculations show that these newly designed clusters have high structural and electronic stabilities. Based on chemical bonding analysis, the electronic structures of these clusters follow the superatom network (SAN) model. Inspired by the cluster structures, we further predicted an Au₄ two-dimensional (2D) monolayer and a three-dimensional (3D) crystal using graphene and diamond as templates, respectively. The computational results demonstrate that the two structures have high dynamic, thermal, and mechanical stabilities, and both structures exhibit metallic properties according to the band structures calculated at the HSE06 level. The chemical bonding analysis by the solid-state natural density partitioning (SSAdNDP) method indicates that they are superatomic crystals assembled by two electron Au₄ ^- superatoms. With this construction strategy, the new bonding pattern and properties of Au _n L _m are studied and the structure types of gold are enriched.

Structural Prediction of Anion Thiolate Protected Gold Clusters of [Au28+7n(SR)17+3n]− (n = 0-4)

Structural prediction of thiolate-protected gold nanocluster (AuNCs) with diverse charge states can enrich the understanding of this species. Till now, most expementally synthesized or theoretically predicted AuNCs structures own neutral total charge. In this work, a series of gold nanoclusters with negative total charge including [Au28(SR)17]−, [Au35(SR)20]−, [Au42(SR)23]−, [Au49(SR)26]−, and [Au56(SR)29]− are designed. Following crystallized [Au23(SR)16]- prototype structure, the inner core of the newly predicted clusters are obtained through packing crossed Au7. Next, proper protecting thiolate ligands are arranged to fullfil the duet rule to obtain Au3(2e) and Au4(2e). Extensive analysis indicates these cluster own high stabilities. Molecular orbital analysis shows that the orbitals for the populations of the valence electron locate at each Au3(2e) and Au4(2e), which demonstrates the reliability the GUM model. This work should be helpful for enriching the structural diversity of AuNCs.

Isomer dynamics of the [Au6(NHC-S)4]2+ nanocluster

The use of metal nanoclusters is strongly reliant on their size and configuration; hence, studying the potential isomers of a cluster is extremely beneficial in understanding their performance. In general, the prediction and identification of isomer structures and their properties can be challenging and computationally expensive. Our work describes an investigation to find local isomers for the previously experimentally characterized small gold cluster [Au₆(NHC-S)₄]²⁺ protected by bidentate mixed carbene-thiolate ligands. We employ the molecular dynamics simulation method where the interatomic forces are calculated from density functional theory. We find several isomers that are more stable than the isomer corresponding to the experimental crystal structure, as well as a significant impact of the finite-temperature atom dynamics on the electronic structure and optical properties. Our work highlights the growing need to investigate ligand-stabilized metal clusters to uncover isomerism and temperature effects on their properties.

An Au2S network model for exploring the structural origin, evolution, and two-electron (2e-) reduction growth mechanism of Aun(SR)m clusters

An Au₂S network model was proposed to study the structural origin, evolution, and formation mechanism of the Au_n(SR)_m clusters containing quasi-face-centered-cubic (fcc) cores. The Au-S framework structures of 20 quasi-fcc gold clusters had been determined from the Au₂S network. Based on the Au₂S network, some new quasi-fcc clusters, such as 8e^- clusters Au₂₄(SR)₁₆, Au₂₆(SR)₁₈, Au₂₆(SR)₁₉ ^-, Au₂₉(SR)₂₁, Au₃₀(SR)₂₂, and Au₃₂(SR)₂₄, and a class of Au_24+8n(SR)_20+4n (n = 1, 2, 3, …) clusters were predicted. Furthermore, by studying the evolution of Au-S frameworks, it was possible to construct molecular-like reaction equations to account for the formation mechanism of quasi-fcc gold clusters, which indicated that the formation of quasi-fcc gold clusters can be understood from the stepwise 2e^--reduction cluster growth pathways. The present studies showed that the Au₂S network model provided a "parental" Au-S network for exploring the structural evolution of the quasi-fcc Au_n(SR)_m clusters. Moreover, it was possible to study the formation pathways of the Au_n(SR)_m clusters by studying the evolution of their Au-S frameworks.

Chiral Au22(SR)17-: a new ligand-binding strategy for structural prediction of thiolate-protected gold nanocluster

A new atomic structure of chiral thiolate-protected gold nanocluster Au22(SR)17- is predicted on the basis of the new ligand-binding strategy, namely, redistributing the Au-S "staple" motifs on the well-known Au10 core from previously laboratory-determined Au21(SR)15 crystal structure. Density functional theory calculations show that this structure is very likely the realistic structure for the synthesized Au22(SR)17-.

Modulation of the Double-Helical Cores: A New Strategy for Structural Predictions of Thiolate-Protected Gold Nanoclusters

A fundamental understanding of the structural growth of thiolate-protected gold nanoclusters not only benefits experimental synthesis but also will advance the methodology for structural predictions and for rational design of highly stable nanoclusters. Herein, we report numerous new structures (11 total) of thiolate-protected gold nanoclusters predicted from theoretical modulation of the double-helical cores of experimentally determined nanoclusters. Among these newly predicted structures, Au₃₂(SR)₂₂, Au₄₀(SR)₂₆, and Au₄₈(SR)₃₀ are obtained by adding a defective layer containing 4 gold atoms on a structural sequence of experimentally crystallized nanoclusters, namely, Au₂₈(SR)₂₀, Au₃₆(SR)₂₄, and Au₄₄(SR)₂₈. The generic growth pattern underlying this sequence of nanoclusters can be viewed as adding the highly stable tetrahedral Au₄ unit on the double-helical cores. Likewise, the other eight newly predicted structures, including two groups of isomeric structures corresponding to the sequence of experimentally determined Au₂₈(SR)₂₀, Au₃₆(SR)₂₄, Au₄₄(SR)₂₈, and Au₅₂(SR)₃₂ nanoclusters, are successfully predicted. Density functional theory calculations show that these 11 newly predicted nanoclusters exhibit large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps and all-positive harmonic vibrational frequencies, suggesting their high chemical stabilities. Additional analyses on the structures and properties suggest that these newly predicted nanoclusters are very likely to be synthesized in the laboratory. Confirmation by experiments would validate the new strategy for structural prediction of thiolate-protected gold nanoclusters by taking advantage of a large structure database of crystallized ligand-protected gold nanoclusters with a variety of gold cores.

Structural predictions of thiolate-protected gold nanoclusters via the redistribution of Au–S “staple” motifs on known cores

Four structures of gold nanoclusters were predicted via the redistribution of Au–S motifs on known cores.

Fusion growth patterns in atomically precise metal nanoclusters

Atomically precise nanoclusters of coinage metals in the 1-3 nm size regime have been intensively pursued in recent years. Such nanoclusters are attractive as they fill the gap between small molecules (<1 nm) and regular nanoparticles (>3 nm). This intermediate identity endows nanoclusters with unique physicochemical properties and provides nanochemists opportunities to understand the fundamental science of nanomaterials. Metal nanoparticles are well known to exhibit plasmon resonances upon interaction with light; however, when the particle size is downscaled to the nanocluster regime, the plasmons fade out and step-like absorption spectra characteristic of cluster sizes are manifested due to strong quantum confinement effects. Recent research has revealed that nanoclusters are commonly composed of a distinctive kernel and a surface-protecting shell (or staple-like metal-ligand motifs). Understanding the kernel configuration and evolution is one of the central topics in nanoscience research. This Review summarizes the recent progress in identifying the growth patterns of atomically precise coinage nanoclusters. Several basic kernel units have been observed, such as the M₄, M₁₃ and M₁₄ polyhedrons (where, M = metal atom). Among them, the tetrahedral M₄ and icosahedral M₁₃ units are the most common ones, which are adopted as building blocks to construct larger kernel structures via various fusion or aggregation modes, including the vertex- and face-sharing mode, the double-strand and alternate single-strand growth, and cyclic fusion of units, as well as the fcc-based cubic growth pattern. The identification of the kernel growth pathways has led to deeper understanding of the evolution of electronic structure and optic properties.

Face-Centered-Cubic Ag Nanoclusters: Origins and Consequences of the High Structural Regularity Elucidated by Density Functional Theory Calculations

Face-centered-cubic (FCC) silver nanoclusters (NCs) adopting either cubic or half-cubic growth modes have been recently reported, but the origin of these atomic assembly patterns and how they are achieved, which would inform our understanding of larger FCC silver nanomaterials, are both unknown. In this study, the cubic and half-cubic growth modes have been unified based on common structural characteristics, and differentiated depending on the starting blocks (cubic vs. half cubic). In both categories, the silver atoms adopt octahedral Ag₆ , linear AgS₂ (in projection drawing), or tetrahedral AgS₃ P binding modes, and the sulfur atoms adopt T-shaped SAg₃ and orthogonal SAg₄ modes. An additional T-shaped AgS₃ mode is oriented on the surface edge in cubic NCs to complete the cubic framework. Density functional theory calculations indicated that the high structural regularity originates from the strong diffusing capacity of the Ag(5d) and S(3p) orbitals, and the angular momentum distribution of the formed superatomic orbitals. The equatorial orientation of μ⁴ -S or μ⁴ -Ag determines whether growth stops or continues. In particular, a density-of-states analysis indicated that the octahedral silver atoms are chemically more reactive than the silver atoms in the AgS₃ P motif, regardless of whether the parent NC functions as an electron donor or acceptor.

Growth-Rule-Guided Structural Exploration of Thiolate-Protected Gold Nanoclusters

Understanding the structure and structure-property relationship of atomic and ligated clusters is one of the central research tasks in the field of cluster research. In chemistry, empirical rules such as the polyhedral skeleton electron pair theory (PSEPT) approach had been outlined to account for skeleton structures of many main-group atomic and ligand-protected transition metal clusters. Nonetheless, because of the diversity of cluster structures and compositions, no uniform structural and electronic rule is available for various cluster compounds. Exploring new cluster structures and their evolution is a hot topic in the field of cluster research for both experiment and theory. In this Account, we introduce our recent progress in the theoretical exploration of structures and evolution patterns of a class of atomically precise thiolate-protected gold nanoclusters using density functional theory computations. Unlike the conventional ligand-protected transition metal compounds, the thiolate-protected gold clusters demonstrate novel metal core/ligand shell interfacial structures in which the Au _m(SR) _n clusters can be divided into an ordered Au(0) core and a group of oligomeric SR[Au(SR)] _x ( x = 0, 1, 2, 3, ...) protection motifs. Guided by this "inherent structure rule", we have devised theoretical methods to rapidly explore cluster structures that do not necessarily require laborious global potential energy surface searches. The structural predictions of Au₃₈(SR)₂₄, Au₂₄(SR)₂₀, and Au₄₄(SR)₂₈ nanoclusters were completely or partially verified by the later X-ray crystallography studies. On the basis of the analysis of cluster structures determined by X-ray crystallography and theoretical prediction, a structural evolution diagram for the face-centered-cubic (fcc)-type Au _m(SR) _n clusters with m up to 92 has been preliminarily established. The structural evolution diagram indicates some basic structural and electronic evolution patterns of thiolate-protected gold nanoclusters. The fcc Au _m(SR) _n clusters show a genetic structural evolution pattern in which each step of cluster size increase results in the formation of another Au₄ tetrahedron or Au₃ triangle unit in the Au core, and every increase of a structural unit in the Au core leads to an increase of two electrons in the whole cluster. The unique one- or two-dimensional cluster size evolution, the isomerism of the Au-S framework, and the formation of a double-helical and cyclic tetrahedron network in the fcc Au _m(SR) _n clusters all can be addressed from this evolution pattern. The summarized cluster structural evolution diagrams enable us to further explore more stable cluster structures and understand their structure-electronic structure-property relationships.

Application of Electronic Counting Rules for Ligand-Protected Gold Nanoclusters

Understanding special stability of numerous ligand-protected gold nanoclusters has always been an active area of research. In the past few decades, several theoretical models, including the polyhedral skeletal electron pair theory (PSEPT), superatom complex (SAC), and superatom network (SAN), among others, have been developed for better understanding the stabilities and structures of selected ligand-protected gold nanoclusters. This Account overviews the recently proposed grand unified model (GUM) to offer some new insights into the structures and growth mechanism of nearly all crystallized and predicted ligand-protected gold nanoclusters. The main conceptual advancement of the GUM is identification of the duet and octet rules on the basis of the "big data" of 70+ reported ligand-protected gold nanoclusters. According to the two empirical rules, the cores of the gold nanoclusters can be regarded as being composed of two kinds of elementary blocks (namely, triangle Au₃ and tetrahedron Au₄), each having 2 e closed-shell valence electrons (referred as Au₃(2 e) and Au₄(2 e)), as well as the secondary block (icosahedron Au₁₃) with 8 e closed-shell valence electrons (referred as Au₁₃(8 e)). The two elementary blocks (Au₃(2 e) and Au₄(2 e)) and the secondary block (Au₁₃(8 e)), from electron counting point of view, can be regarded as an analogy of the highly stable noble-gas atoms of He and Ne, respectively. In each elementary block, the Au atoms exhibit three different valence-electron states (i.e., 1 e, 0.5 e, and 0 e), depending on the type of ligands bonded with these Au atoms. Such three valence-electron states are coined as three "flavors" of gold (namely, bottom, middle, and top "flavor"), a term borrowed from the quark model in the particle physics. Upon application of the duet and octet rules with accounting the three valence states of gold atoms, the Au₃(2 e), Au₄(2 e), and Au₁₃(8 e) blocks can exhibit 10 (denoted as Δ₁-Δ₁₀), 15 (denoted as T₁-T₁₅), and 91 (denoted as I₁-I₉₁) variants of valence states, respectively. When packing these blocks (with distinct electronic states) together, it forms the gold core of ligand-protected gold nanocluster. As such, the special stabilities of the ligand-protected gold nanoclusters are explained based on the local stability of each block. With GUM, rich and complex structures of ligand-protected gold nanoclusters have been analyzed through structure anatomy. Moreover, the growth of these clusters can be simply viewed as sequential addition of the blocks, rather than as addition of the gold atoms. Another useful application of the GUM is to analyze the structural isomerism. The three types of isomerism for the gold nanoclusters, i.e., core, staple, and complex isomerism, can be considered as an analogy of chain, point, and functional isomerism (known in organic chemistry), respectively. GUM can be applied to predict new clusters, thereby guiding experimental synthesis. Indeed, a number of ligand-protected gold nanoclusters with high stabilities were rationally designed based on the GUM.