  Multireference electron correlation methods describe static and dynamical
electron correlation in a balanced way, and therefore, can yield accurate and
predictive results even when single-reference methods or multiconfigurational
self-consistent field (MCSCF) theory fails. One of their most prominent
applications in quantum chemistry is the exploration of potential energy
surfaces (PES). This includes the optimization of molecular geometries, such as
equilibrium geometries and conical intersections, and on-the-fly photodynamics
simulations; both depend heavily on the ability of the method to properly
explore the PES. Since such applications require the nuclear gradients and
derivative couplings, the availability of analytical nuclear gradients greatly
improves the utility of quantum chemical methods. This review focuses on the
developments and advances made in the past two decades. To motivate the
readers, we first summarize the notable applications of multireference electron
correlation methods to mainstream chemistry, including geometry optimizations
and on-the-fly dynamics. Subsequently, we review the analytical nuclear
gradient and derivative coupling theories for these methods, and the software
infrastructure that allows one to make use of these quantities in applications.
The future prospects are discussed at the end of this review.
