Computational chemistry has made remarkable progress in the last couple of decades due to the availability of better and more powerful computers. However, there is definitely more room for improvement. There are problems in material science and biology that require 102 to 104 atoms to be considered and the importance of such systems cannot be over-emphasized. Addressing such systems with ab-initio methods is still a quantum chemist’s dream. ¨ Brute force solutions of the Schrodinger equation are not possible for reasonably interesting and important systems due to the large number of Slater determinants that have to be stored in a computer’s memory. Thus electronic structure theorists have made chemically and mathematically intuitive approximations to simplify the problems. A particularly difficult class of systems that is very interesting to the theoretical and experimental chemists is the strongly correlated systems. High Tc superconductors, nanotubes, graphene sheets, transition metal complexes and photosynthetic materials all fall under this category. These systems are too large to be treated by traditional quantum chemical methods. Another reason why such systems have not been studied sufficiently by ab-initio method is that they comprise of complicated strong electron-electron correlation (and therefore the name strongly correlated), thus, making them impossible to be qualitatively defined by a molecular orbital picture, which has been a quantum chemist’s fa- vorite tool for a long time now. Therefore, in this thesis, we have tried to develop, improve and apply methods for treating such strongly correlated systems. The thesis is broadly divided into two parts. In the first part, we discuss the orbital optimized DMRG method developed to treat static correlation in large strongly correlated systems. In the next part we discuss the two methods that can treat dynamic correlation in such complicated systems.