@Huan Yang thank you so much for your answer yes i know the factors that affect on plasmonic absorption but i want to know an exact physical explanation for it

Sanaz Mirzaeipary

A change in pH affects the aggregation of gold nanoparticles, like other nanoparticles. The quanta of plasmon oscillations are called plasmons. During aggregation, the surface of the nanoparticles changes. Therefore, plasmon oscillations and spectrum change. Aggregation of gold nanoparticles leads to a contrasting change in the color of the solutions from ruby ​​red to purple or blue (depending on the size of the aggregates). This process is accompanied by the appearance of a new peak in the absorption spectra in the longer wavelength region and a decrease in the intensity of the absorption band at 520 nm. The majority of currently known optical sensors based on gold nanoparticles and spectrophotometric methods for determining inorganic ions and organic compounds using them are based on the effect of changing the degree of aggregation.

dear @Yuri Mirgorod thank you for your good answer, i'd appreciate it if you tell me formula