An immediate optical feature of colloidal quantum dots is their coloration. While the material which makes up a quantum dot defines its intrinsic energy signature, the nanocrystal's quantum confined size is more significant at energies near the band gap. Thus quantum dots of the same material, but with different sizes, can emit light of different colors. The physical reason is the quantum confinement effect.

The larger the dot, the redder (lower energy) its fluorescence spectrum. Conversely, smaller dots emit bluer (higher energy) light. The coloration is directly related to the energy levels of the quantum dot. Quantitatively speaking, the bandgap energy that determines the energy (and hence color) of the fluorescent light is inversely proportional to the size of the quantum dot.

Recent articles in nanotechnology and in other journals have begun to suggest that the shape of the quantum dot may be a factor in the coloration as well, but as yet not enough information is available.

Please find, another practical example of Optical  Properties of Gold Nanoparticles as an attached file.

Consider for a moment the particle in a box, the nanoparticle should be considered as a box. In general when a box becomes larger the energy levels become closer together.

I see no reason why the nanoparticles should not be any different in this regard to polycyclic aromatic hydrocarbons such as napthalene, anthracene etc and also conjugated polyenes such as butadiene and ethylene.

It is simply due to the quantum confinement. As the aradius,R, of a nanoparticle changes the photon energy of the first absorbance peak changes accordingly. As explained above this is related to the modulation in the energy levels. This results in different optical properties. For this effect to be seen the R needs to be lower than Bohr radius to be considered in that region of optical changes due to quantum confinement. And basically they are named as Quantum dots for this reason.

Please, see the following chapter on Theory of Size-Dependent Optical Properties that is directly based on CdSe experiments.

http://scholar.lib.vt.edu/theses/available/etd-04262005-181042/unrestricted/Ch2Theory.pdf

this process occurs due to the crystal array of the nanoparticle and quantum confinement. Photons absorbed on smallest nano crystals produces  emissions with short wavelength (no energy leaking), on larger crystals there are a little loss of energy because the photon transfer between two elements Cd and Se (more layers on the crystal) producing large wavelength emissions. In solution, maybe can occur a non linear optics effect too.

The energy structure is a result of the geometrical confinement quantum effect. If, in addition, the nanoparticle is a multi-layer structure, the heteroepitaxial strain becomes important. More details (see also absorption coefficient of colloidal quantum dot solutions) in:

http://www.sciencedirect.com/science/article/pii/S0009261414006678

http://arxiv-web3.library.cornell.edu/abs/1408.4972

As the size of the CdSe particles appresoaches its Bohr exciton diameter the particles are termed as quantum dots. For quantum dots as size decreases the band gap increases and the wavelength of absorption shift to blue region. So the colour changes with size of CdSe Quantum dots

The size of QDs depends on the strength of the confinement potentials offered by the joint venture of the applied magnetic and electric field. As the confinement potential increases the radius of the Dot center (R) decreases. As a result the energy gap between two successive band increases. Consequently, photon with high energy is absorbed. So the blue shift in noticed as the dot size diminishes. So we can say that, the color of QDs depends on its size intimately. 

Sincerely thank to all experts for your constructive answers and valuable reference.