Multi‐Configurational Reference Perturbation Theory with a CASSCF Reference Function

The purpose of the present chapter is to give students a detailed introduction to time-independent multi-configurational reference perturbation theory (MRPT), in particular the CASPT2 method, one of the standard tools for the study of excited states of molecular systems of small to intermediate size. To achieve this, in as closed a form as possible, we believe that the chapter should begin with the very basics of Rayleigh–Schrödinger (RS) and Møller–Plesset (MP) perturbation theory (PT) before we present the MRPT. The multi-configurational version of perturbation theory has many features and flaws which are either a direct consequence of the original Rayleigh–Schrödinger formulation, or due to the choice of the zeroth order Hamiltonian. These flaws or peculiarities have to be clearly identified and understood before we proceed toward the more elaborate multi-configurational reference perturbation theories. This is then followed by a section dedicated to the most popular versions of single-state multi-configurational reference perturbation theory. Here we again present the formulation of these methods and also address the various problems they encounter. Multi-state versions of perturbation theory are today based on effective Hamiltonian approximations. Hence, these deserve their own treatment due to the fact that this approach introduces its own kind of features and problems, which need to be addressed separately. At the very end of this chapter we summarize and present an outlook on the subject of MRPT.