photon electron interaction such that the photon energy does not correspond to any state change Although I've read answers to similar questions, they did not answer my doubt:
If a photon has an energy less than that required to move an electron from one energy level to another, then what happens when the electron and photon collide? Is the photon absorbed, or does it by some mysterious method, just pass through the electron?
 A: Electrons can either be free, or bound in an atom/molecule/lattice.
If free there exists the Compton scattering, 

It results in a decrease in energy (increase in wavelength) of the photon (which may be an X ray or gamma ray photon), called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering exists, in which a charged particle transfers part of its energy to a photon.

For an electron to exist in energy levels, it has to be bound to a nucleus. In that case an impinging photon scatters with the whole atom, not with the bound electron. If the energy of the photon matches a difference in energy levels, the photon will be absorbed, and the electron will be in a higher energy level. But the scattering is with the whole system.
The electrons may be  bound in an atom/molecule/lattice and if the photon energy is not appropriate for a change in energy levels and absorption, the photon scatters elastically off the combined field of the atom/molecule /lattice:
There is rayleigh scattering:

Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. It is Rayleigh scattering off the molecules of the air which gives us the blue sky. 


In terms of photons, it is the photon elastically scattering over the combined field of the atoms/molecules/lattice

Rayleigh scattering can be considered to be elastic scattering since the photon energies of the scattered photons is not changed. Scattering in which the scattered photons have either a higher or lower photon energy is called Raman scattering. Usually this kind of scattering involves exciting some vibrational mode of the molecules, giving a lower scattered photon energy, or scattering off an excited vibrational state of a molecule which adds its vibrational energy to the incident photon. 

A: The atoms have what are called absorption spectra. In other words, if one would scan through all the wavelengths (which is proportional to the energy per photon), one would find that the atoms of a particular element absorb light with certain wavelengths much better than others. Those wavelengths for which light is better absorbed, correspond to the transitions for the electrons between different energy levels of that type of atom. 
So to say this differently, if I illuminate an atom with light that has an energy (per photon) equal to the energy of a particular transition of that atom, then the light will be more readily absorbed by the atom. On the other hand, if I illuminate this atom with light that has an energy (per photon) that is nowhere near any transition of this atom, then the light would tend to pass by it without being absorbed. In the latter case the material made of those atoms would be transparent to light at that wavelength. 
