Chapter 3: Electronic Structure Methods for the Computation of Electronic States

This chapter is about the physical and conceptual aspects of electron correlation in the excited state. We will use a common theoretical framework for the main electronic structure methods that are currently in use for excited state computation. This theoretical approach is based upon an effective Hamiltonian. Diagrammatic methods will be used to identify the important types of contribution to the correlation problem for excited states without the need for detailed algebraic development. The role of the semi-internal correlation in the excited state will be emphasized and methods like TD-DFT will be formulated in terms of effective integrals. The choice of the active space for excited state computation is also discussed within the CASSCF and the RASSCF approaches using strategy based on natural bond orbitals. In the last part of this chapter we will also look into the development of methods that use a coherent superposition of electronic states and thus lead to electron dynamics. Now that attosecond lasers are capable of populating such a superposition of states, this topic is at the frontier between physics and chemistry.