Why do shape and size have the greatest effect on the optical properties of nanoparticles?

The LSPR properties of nanoparticles depend on a number of factors, including shape, size, material, crystal structure, dielectric environment, etc. However, it has been consistently shown that shape and size have the greatest effect on the optical properties of nanoparticles. Exactly WHY, however, is this true? Does anyone have an explanation at the molecular level?




As Surface Plasmon Resonance phenomenon is mainly seen in metal nanoparticles, I don't know whether this answer will help you? The size dependent optical phenomenon of semiconductor nanoparticles (e.g., $\ce{CdS}$) can be explained using the [effective mass approximation model](http://inbt.jhu.edu/igert/jc_Semiconductor_Quantum_Dots.ppt). 


![enter image description here](https://i.stack.imgur.com/G3GSL.png)
where r is radius of the particle (the rest details of the above equation can be find in the link).


so the energy gap is inversely proportional to the radius of the particle.


![enter image description here](https://i.stack.imgur.com/ioGki.png)


When the radius of the particle decreases, the [band gap increases so it will emit high energy wavelength](http://en.wikipedia.org/wiki/Quantum_dot) (i.e., wavelength in blue region) and when the particle size is large the energy gap will be less so it will emit light in red region (lesser energy).


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Optical properties of nanoparticles come from electronic spectra of one excited electron trapped within. The energy levels in the spectra are derived from lengths of waves, that resonates with energy well within particle. Of course, this lengths depends on size and form of the resonator. Note: this IS oversimplification, but it allows to grab the concept.


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