The motivation for this question is similar in nature to the series of questions on different methods :
- What are the types of SCF?
- What are the types of MCSCF?
- What are the types of Quantum Monte Carlo?
- What are the types of ab initio Molecular Dynamics?
- What are the types of DFT?
- What are the types of DMRG?
The answers to these questions were really insightful, so I am looking for an answer that briefly describes the different variants of Perturbation Theory (PT), and the context in which they are applied on different electronic structure methods.
Rayleigh-Schrodinger perturbation theory (RSPT) is the most common form that is used, but there's also the Lennard-Jones-Brillouin-Wigner perturbation theory (BWPT). In fact, RSPT could be derived from BWPT. Again, depending the type of partitioning of the Hamiltonian, there are two variants: Moller-Plesset and Epstein-Nesbet. Then there are also many-body and diagrammatic PT. These methods have also been applied with both multi and single reference schemes as well as multi-configurational methods.
Here are a few examples of such methods:
- Second order corrections to ground state energies(the standard MPn methods)
- Perturbative corrections to CI (see for example CIS(D) by Martin Head-Gordon et al)
- CASPT2 (multireference second-order PT)