Correspondence: Reply to 'On the bonding in ligand-protected gold clusters'

Isomerism effects in relaxation dynamics of Au24(SR)16thiolate-protected gold nanoclusters

Understanding the excited state behavior of isomeric structures of thiolate-protected gold nanoclusters is still a challenging task. In this paper, based on grand unified model and ring model for describing thiolate-protected gold nanoclusters, we have predicted four isomers of Au₂₄(SR)₁₆nanoclusters. Density functional theory calculations show that the total energy of one of the predicted isomers is 0.1 eV lower in energy than previously crystallized isomer. The nonradiative relaxation dynamics simulations of Au₂₄(SH)₁₆isomers are performed to reveal the effects of structural isomerism on relaxation process of the lowest energy states, in which that most of the low-excited states consist of core states. In addition, crystallized isomer possesses the shorter e-h recombination time, whereas the most stable isomer has the longer recombination time, which may be attributed to the synergistic effect of nonadiabatic coupling and decoherence time. Our results could provide practical guidance to predict new gold nanoclusters for future experimental synthesis, and stimulate the exploration of atomic structures of same sized gold nanoclusters for photovoltaic and optoelectronic devices.

Mechanistic Insights into Oxidation-Induced Size Conversion of [Au6(dppp)4]2+ to [Au8(dppp)4Cl2]2

Oxidation-induced conversion of gold nanoclusters is an important strategy for preparing novel atomically precise clusters and elucidating the kinetic correlations of different clusters. Herein, the oxidation-induced growth from [Au6(dppp)4]2+ to [Au8(dppp)4Cl2]2+ (reported by Konishi and co-workers) has been studied by density functional theory calculations. A successive oxidation → Cl- coordination → oxidation → Cl- coordination sequence occurs first to activate the Au6 structure, resulting in the high Au(core)-Au(corner) bond cleavage activity and the subsequent formation of [Au2(dppp)2Cl]+ and [Au4(dppp)2Cl]+ fragments. Then, the dimerization of two Au4 fragments and the rearrangement of the diphosphine coordination occur to generate the thermodynamically stable [Au8(dppp)4Cl2]2+ products. The proposed mechanism agrees with the experimental outcome for the fast reaction rate and the residual of the Au2 components. Specifically, a multivariate linear regression analysis indicates the strong correlation of the oxidation potential of Au6, Au8, Au23, and Au25 clusters with the HOMO energy, the number of Au atoms, and cluster charge state. The main conclusions [e.g., oxidation-induced Au(corner)-Au(core) bond activation, easy 1,2-P transfer steps, etc.] of this study might be widely applicable in improving our understanding of the mechanism of other cluster-conversion reactions.

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.