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Programmable manipulation of inorganic–organic interfacial electronic properties of ligand-functionalized plasmonic nanoparticles (NPs) is the key parameter dictating their applications such as catalysis, photovoltaics, and biosensing. Here we report the localized surface plasmon resonance (LSPR) properties of gold triangular nanoprisms (Au TNPs) in solid state that are functionalized with dipolar, conjugated ligands. A library of thiocinnamate ligands with varying surface dipole moments were used to functionalize TNPs, which results in ∼150 nm reversible tunability of LSPR peak wavelength with significant peak broadening (∼230 meV). The highly adjustable chemical system of thiocinnamate ligands is capable of shifting the Au work function down to 2.4 eV versus vacuum, i.e., ∼2.9 eV lower than a clean Au (111) surface, and this work function can be modulated up to 3.3 eV, the largest value reported to date through the formation of organothiolate SAMs on Au. Interestingly, the magnitude of plasmonic responses and work function modulation is NP shape dependent. By combining first-principles calculations and experiments, we have established the mechanism of direct wave function delocalization of electrons residing near the Fermi level into hybrid electronic states that are mostly dictated by the inorganic–organic interfacial dipole moments. We determine that both interfacial dipole and hybrid electronic states, and vinyl conjugation together are the key to achieving such extraordinary changes in the optoelectronic properties of ligand-functionalized, plasmonic NPs. The present study provides a quantitative relationship describing how specifically constructed organic ligands can be used to control the interfacial properties of NPs and thus the plasmonic and electronic responses of these functional plasmonics for a wide range of plasmon-driven applications. 

We propose an Euler transformation that transforms a given [Formula: see text]-dimensional cell complex [Formula: see text] for [Formula: see text] into a new [Formula: see text]-complex [Formula: see text] in which every vertex is part of the same even number of edges. Hence every vertex in the graph [Formula: see text] that is the [Formula: see text]-skeleton of [Formula: see text] has an even degree, which makes [Formula: see text] Eulerian, i.e., it is guaranteed to contain an Eulerian tour. Meshes whose edges admit Eulerian tours are crucial in coverage problems arising in several applications including 3D printing and robotics. For [Formula: see text]-complexes in [Formula: see text] ([Formula: see text]) under mild assumptions (that no two adjacent edges of a [Formula: see text]-cell in [Formula: see text] are boundary edges), we show that the Euler transformed [Formula: see text]-complex [Formula: see text] has a geometric realization in [Formula: see text], and that each vertex in its [Formula: see text]-skeleton has degree [Formula: see text]. We bound the numbers of vertices, edges, and [Formula: see text]-cells in [Formula: see text] as small scalar multiples of the corresponding numbers in [Formula: see text]. We prove corresponding results for [Formula: see text]-complexes in [Formula: see text] under an additional assumption that the degree of a vertex in each [Formula: see text]-cell containing it is [Formula: see text]. In this setting, every vertex in [Formula: see text] is shown to have a degree of [Formula: see text]. We also present bounds on parameters measuring geometric quality (aspect ratios, minimum edge length, and maximum angle of cells) of [Formula: see text] in terms of the corresponding parameters of [Formula: see text] for [Formula: see text]. Finally, we illustrate a direct application of the proposed Euler transformation in additive manufacturing.