The pdb file generally contains about 1000 atoms without hydrogen and my computer is not able to handle such a large number of atoms as i have planed to use Gaussian 09 for my work. So How many atoms should i consider for doing a proper research
That is a hard question because I feel it depends on your intents. For example:
1) You are planning on understand something particular to the active site in a localized manner, so, you might be able to run DFT calculations on a structural model of that region, including the copper center and the ligands as a convenient approach.
2) You are planning on studying properties that depend on hundreds of atoms, well, that would be better done in a QM/MM approach that could get very expensive depending on the size of the protein.
This indicates that there are different approaches that could be employed for such a system, so I'd define the research idea and find some articles on similar studies to understand how they were done and then study the feasibility regarding the computational resources, like:
Article Active site structures and the redox properties of blue copp...
Article Spectroscopic and DFT Studies of Second Sphere Variants of t...
I am to run dft calculations in the region very near to the active site. Will the electronic properties get effected if I didn't consider the atoms other than copper center and ligands??
It will affect your results to some extent, so you'll have to define your research as a structural model study of the enzyme's active site. There's no shame in defining approximations to make the computational cost affordable.
Also, you have to keep in mind that each approximation has its flaws and that you have to double check every result to make sure it goes according the chemical/biological intuition. If you find "non expected" results you might have to seek a more complete approach to define if the results are due to a bad modelling design or if the system behaves in that way.
Approximations are ok when everything goes well, the problem is when you get anything you don't expect, mostly because you have the burden of proof.