I want to briefly know, how theoretically IR and Raman spectrum of a particular optimised structure is estimated using DFT. Actually I want to know what is the basic theory behind this in a brief way.
It is very difficult to reply both briefly and rigorously to such a question on RG. Nevertheless, there are a few papers and reviews on this topics you might be interested into. In order of publication, I would suggest:
1) Article Vibrational frequency prediction using density functional theory
It is indeed hard it is to explain it briefly. Basically, you have to change the displacement of a given atom, this changes the electric field and generates a force (k), which is related to the frequency in the FTIR. I may have oversimplified the process, and I am sure there are other ways to compute the frequency. You might be interested in this paper: https://hal.archives-ouvertes.fr/hal-00906659/document