A unified view of ligand-protected gold clusters as superatom complexes

Abstract

Synthesis, characterization, and functionalization of self-assembled, ligand-stabilized gold nanoparticles are long-standing issues in the chemistry of nanomaterials. Factors driving the thermodynamic stability of well documented discrete sizes are largely unknown. Herein, we provide a unified view of principles that underlie the stability of particles protected by thiolate (SR) or phosphine and halide (PR(3), X) ligands. The picture has emerged from analysis of large-scale density functional theory calculations of structurally characterized compounds, namely Au(102)(SR)(44), Au(39)(PR(3))(14)X(6)(-), Au(11)(PR(3))(7)X(3), and Au(13)(PR(3))(10)X(2)(3+), where X is either a halogen or a thiolate. Attributable to a compact, symmetric core and complete steric protection, each compound has a filled spherical electronic shell and a major energy gap to unoccupied states. Consequently, the exceptional stability is best described by a "noble-gas superatom" analogy. The explanatory power of this concept is shown by its application to many monomeric and oligomeric compounds of precisely known composition and structure, and its predictive power is indicated through suggestions offered for a series of anomalously stable cluster compositions which are still awaiting a precise structure determination.

Fig. 1.

Core-shell structure of the Au₁₀₂(p-MBA)₄₄ cluster. (a and b) Space-filling (a) and ball-and-stick (b) representations of the Au₁₀₂(p-MBA)₄₄ nanoparticle. Au, orange; S, yellow; C, gray; O, red; H, white. (c and d) Two views of the 40-atom surface of the Au₇₉ core, together with the passivating Au₂₃(p-MBA)₄₄ mantle. The cationic Au atoms in the mantle are depicted by the smaller orange spheres. The “structure defects” at the core–mantle interface [two Au atoms with two Au–S bonds, and a long RS–(AuSR)₂ unit] are highlighted by the ellipse. (e) Close-up of the protecting RS–(AuSR)_x unit with x = 1 or 2. (f and g) Two views of the Au₇₉ core, which has a symmetry of D_5h (within 0.4-Å tolerance).

Fig. 2.

Electronic structure analysis of the Au₁₀₂(p-MBA)₄₄ cluster. (a) The radial dependence of the integrated induced charge Q(R) upon removing (red curve) and adding (green curve) one electron to the neutral Au₁₀₂(p-MBA)₄₄ cluster (Upper), and the radial distribution of atoms (Lower). The dashed line indicates a midpoint between the surface of Au₇₉ core and the Au-thiolate layer. Q(R) = 4π ∫^R Δρ(r) r² dr, where Δρ(r) = ρ⁰(r) − ρ^q(r) is the induced charge difference from two density functional theory (DFT) calculations for the neutral and charged particle. (b) The angular-momentum-projected local electron density of states (PLDOS) (projection up to the I symmetry, i.e., l = 6) for the Au₇₉ core in Au₁₀₂(p-MBA)₄₄. (c) The angular-momentum-projected electron density of states (PDOS) for the bare Au₇₉ without the Au-thiolate layer. (d) A cut-plane visualization of the LUMO state of the Au₁₀₂(p-MBA)₄₄ cluster. Note the H symmetry (10 angular nodes) at the interface between the Au₇₉ core and the Au-thiolate layer. In b, the zero energy corresponds to the middle of the HOMO–LUMO gap, whereas in c the zero energy is at the HOMO level (dashed lines). For plotting PLDOS/PDOS curves, each individual electron state is displayed by a Gaussian smoothing of 0.03 eV. Shell-closing electron numbers are indicated in b and c.

Fig. 3.

Structure of phosphine-chloride- and phosphine-thiolate-protected Au₃₉ and Au₁₁ clusters. (a) The Au₃₉Cl₆(PH₃)₁₄⁻ cluster. (b) The Au₃₉ core. (c) The Au₁₁Cl₃(PH₃)₇ cluster. (d) The Au₁₁(SMe)₃(PH₃)₇ cluster. The Au core symmetries (with tolerance) are as follows: a, Au₃₉, D₃ (within 0.2 Å); c, Au₁₁, C_3v (0.2 Å); d, Au₁₁, C_3v (0.2 Å). Au, orange; Cl, green; S, yellow; P, blue; H, white.

Fig. 4.

Superatom shell closures for 8 and 34 electrons in Au₁₁ and Au₃₉ clusters. The angular-momentum-projected local density of electron states (PLDOS) (projection up to the I symmetry, i.e., l = 6) for the gold core of phosphine-halide- and phosphine-thiolate-protected clusters is shown. (a) Au₁₁(PH₃)₇Cl₃. (b) Au₁₁(PH₃)₇(SMe)₃. (c) Au₃₉(PH₃)₁₄Cl₆⁻. The zero energy in each figure corresponds to the middle of the HOMO–LUMO gap (dashed line). Shell-closing electron numbers are indicated. Each individual electron state is displayed by a Gaussian smoothing of 0.07 eV.