Unraveling the slopes of photoluminescence: where calculus meets clusters

Abstract

Noble metal nanoclusters are vital for advancing research in biology, electronics, catalysis, and several other fields, as they can produce different properties with a variety of geometric and electronic changes. A few properties that have garnered interest are absorption and photoluminescence. Atomically precise nanoclusters have large energetic gaps, rather than a more bulk-like structure which has small energy gaps between bands. As large energetic gaps promote radiative emission, understanding the electronic structure leads to the creation of more emissive materials for bioimaging, sensing, and other applications. As clusters continue to be synthesized with different sizes, shapes, and ligand shell structures, it is imperative to understand absorption and emission properties and be able to tune them for the advancement of nanomaterials. Thus, it is critical to be able to model the electronically excited states in these systems. One of the most popular methods to model these clusters is time-dependent density functional theory (TDDFT). In this dissertation, DFT is used to model geometric and electronic structure, and TDDFT is used to model optical and photoluminescent properties to analyze the structure-property relationships as a result of a specific change to the system. Initially, ligand effects are analyzed through three examples: the ligand exchange mechanism of Ag₂₉(BDT)₁₂ to Ag₂₉(DHLA)₁₂, the influence of the chiral ligand structure in Au₁₈(S-Adm)₈(SbPh₃)₄Br₂, and the role of the stibine as a protecting ligand in [Au₆(SbP₃)₂]²⁺ and how it differs from the phosphine protected [Au₆(PPh₃)₆]²⁺ cluster. As heteroatom dopants have recently become a popular way to further tailor the structure-property relationships, the role of the Pt dopant on Au₂₄Pt(SR)₁₈ compared to the well-studied [Au₂₅(SR)₁₈]⁻ cluster will be discussed, in addition to the role of Ni, Pt, Au and Cu dopants in Ag₂₉(BDT)₁₂ clusters. As theory becomes an essential tool in deciphering photoluminescent mechanisms in noble metal nanoclusters, the dual emission mechanism of Au₁₄Cd(S-Adm)₁₂ will be examined, as well as the unique emission mechanisms that arise from different ligand choices in small alkynyl protected Au₂₂ nanoclusters. TDDFT has proved to be a great theoretical model as it is relatively accurate compared to experiments in a wide range of chemical species. Unfortunately, modelling photophysical and photochemical processes with TDDFT becomes substantially more computationally expensive in large molecular systems and nanoparticles when properties other than energy are required. It is therefore vital to develop methods that solve the scaling problem for excited state energy calculations in TDDFT but retain a similar accuracy. Time-dependent density functional theory plus tight binding (TDDFT+TB) uses a monopole approximation for the transition density in the excited states. As a result, TDDFT+TB reproduces linear response TDDFT results 100x faster than TDDFT in large plasmonic NCs, keeping the electronic excitation energy within 0.10 eV of TDDFT. This method seems optimal for the calculation of excited states properties, however, no one had derived and implemented the analytical excited state gradient derivation to help chemists gain insights into the minimum points on the excited state potential energy surface for insight into photoluminescent mechanisms. To acknowledge both the application and method development sides in understanding noble metal nanoclusters, this dissertation has two main research prongs. Initially, the role of geometry and electronic structure in optical and photoluminescent properties is ascertained for various nanoclusters with different sizes, shapes, ligand structures, charge states and heteroatom dopants. Second, the analytical gradients for TDDFT+TB will be discussed, which enables more efficient modelling.