The size and shape of gold nanoparticles significantly influence their electronic and optical properties due to the phenomenon known as surface plasmon resonance SPR . Surface plasmon resonance occurs when the conduction electrons on the surface of the nanoparticle oscillate collectively in response to an incident electromagnetic radiation, such as light. This oscillation leads to strong absorption and scattering of light, which gives rise to the unique optical properties of gold nanoparticles.1. Size effect:As the size of gold nanoparticles changes, the following electronic and optical properties are affected:a. Absorption and scattering: Smaller nanoparticles have a higher absorption to scattering ratio, while larger nanoparticles scatter light more efficiently. This is because the size of the nanoparticle determines the relative contribution of absorption and scattering to the extinction cross-section.b. Surface plasmon resonance peak: The position of the SPR peak shifts with the size of the nanoparticle. As the size of the nanoparticle increases, the SPR peak redshifts i.e., moves towards longer wavelengths . This is due to the increased interaction between neighboring particles and the retardation effects in larger particles.c. Quantum confinement: In very small nanoparticles typically below 2 nm , the electronic properties are significantly influenced by quantum confinement effects. This leads to discrete energy levels and a deviation from the classical SPR behavior.2. Shape effect:The shape of gold nanoparticles also plays a crucial role in determining their electronic and optical properties:a. Anisotropy: Non-spherical nanoparticles, such as rods, triangles, or stars, exhibit anisotropic optical properties due to the different aspect ratios of their dimensions. This results in multiple SPR peaks corresponding to different plasmon modes.b. Localized surface plasmon resonance LSPR : The LSPR is highly sensitive to the shape of the nanoparticle. For example, gold nanorods exhibit two LSPR peaks one corresponding to the transverse mode short axis and the other to the longitudinal mode long axis . The longitudinal LSPR peak is highly tunable and can be shifted from the visible to the near-infrared region by changing the aspect ratio of the nanorod.c. Hotspots: Sharp edges and corners in non-spherical nanoparticles can lead to the formation of "hotspots" where the electromagnetic field is highly localized and enhanced. These hotspots can significantly enhance the local surface plasmon resonance, leading to improved performance in applications such as surface-enhanced Raman scattering SERS and plasmonic sensing.In summary, the size and shape of gold nanoparticles play a crucial role in determining their electronic and optical properties. By controlling these parameters, it is possible to tune the surface plasmon resonance and other properties for various applications in fields such as sensing, imaging, catalysis, and drug delivery.