Supercubes, Supersquares, and Superrods of Face-Centered Cubes (FCC): Atomic and Electronic Requirements of [M_m(SR)_l(PR′₃)₈]^q Nanoclusters (M = Coinage Metals) and Their Implications with Respect to Nucleation and Growth of FCC Metals

Understanding the nucleation and growth pathways of nanocrystallites allows precise control of the size and shape of functional crystalline nanomaterials of importance in nanoscience and nanotechnology. This paper provides a detailed analysis of the stereochemical and electronic requirements of three series of nanoclusters based on face-centered cubes (fcc) as the basic building blocks, namely, 1-, 2-, and 3-D assemblages of fcc to form superrods (n), supersquares (n²), and supercubes (n³). The generating functions for calculating the numbers (and arrangements) of surface and interior metal atoms, as well as the number and dispositions of the ligands, for these particular sequences of fcc metal clusters of the general formula [M_m(SR)_l(PR′₃)₈]^q (where M = coinage metals; SR = thiolates (or group XI ligands), and PR′₃ = phosphines) are presented. An electron-counting scheme based on the jelliumatic shell nodel, a variant of the jellium model, predicts the electron requirements and hence the chemical compositions that are critical in the design and synthesis of the next generation of giant nanoclusters in the nanorealm. The ligand binding specificities, which are keys to effective surface ligand control of the size and shape of these nanoclusters, are defined. Finally, a connection is made with regard to the growth of fcc metals, n³, from fcc supercubes (n < 10) to fcc nanocrystallites/particles (10 < n < 10²) and to fcc bulk phase (n > 10²).