As an AI language model, I cannot perform quantum chemical calculations directly. However, I can provide you with a general understanding of the effect of size and shape on the electronic and optical properties of gold nanoparticles.Gold nanoparticles exhibit unique electronic and optical properties due to their size, shape, and the quantum confinement effect. The quantum confinement effect arises when the size of the nanoparticle is smaller than the electron's de Broglie wavelength, which leads to quantization of the energy levels. This effect is responsible for the size-dependent properties of gold nanoparticles.1. Size effect:As the size of the gold nanoparticles decreases, the energy gap between the highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO increases. This leads to a blue shift in the absorption spectrum, meaning that the nanoparticles absorb light at shorter wavelengths as their size decreases. Additionally, smaller nanoparticles exhibit higher surface-to-volume ratios, which can enhance their catalytic and sensing properties.2. Shape effect:The shape of gold nanoparticles also plays a crucial role in determining their electronic and optical properties. Spherical and triangular gold nanoparticles exhibit different surface plasmon resonance SPR properties due to the difference in their geometries.Spherical gold nanoparticles:Spherical gold nanoparticles exhibit a single SPR band, which is primarily due to the dipole oscillation of the conduction electrons. The SPR peak position is highly sensitive to the size of the nanoparticles and the dielectric environment surrounding them.Triangular gold nanoparticles:Triangular gold nanoparticles, on the other hand, exhibit multiple SPR bands due to the presence of different types of plasmon modes, such as dipolar and higher-order multipolar modes. The SPR peaks for triangular nanoparticles are more sensitive to the aspect ratio ratio of height to base length and the sharpness of the vertices.In summary, the electronic and optical properties of gold nanoparticles are highly dependent on their size and shape. Smaller nanoparticles exhibit a blue shift in the absorption spectrum, and the SPR properties are influenced by the geometry of the nanoparticles. To obtain a more accurate and detailed understanding of these properties, quantum chemical calculations should be performed using appropriate computational methods and software.