Analytical nuclear gradient and derivative coupling theories for multireference perturbation methods

Electron correlations should be appropriately included in quantum chemistry calculations to accurately describe the energy and wave functions. In multiconfigurational methods, the reference functions are written as linear combinations of multiple electronic configurations to describe static correlations. Using the multiconfigurational reference functions, it is also possible to correct for dynamical correlations using various methods. Geometry optimizations and dynamics simulations are among the most prominent applications of quantum chemistry methods. Such applications become much more straightforward when analytical nuclear gradients are available. Many efficient algorithms for computing analytical nuclear gradients and derivative coupling using multireference perturbation theories (MRPTs) have recently been developed. This work aims to provide a comprehensive and easy-to-follow review of analytical gradient theories and the properties of methods for obtaining analytical gradients and derivative coupling methods using MRPTs. We also briefly review the practical applications of these methods in performing nonadiabatic dynamics simulations.