Describing dynamic electron correlation beyond a large active space.

The pursuit of quantitatively accurate electron correlation calculations for realistic large strongly correlated systems presents significant theoretical and computational challenges. These challenges stem primarily from two fundamental aspects: the inherent complexity of treating static correlations within extensive active spaces and the additional difficulty of incorporating dynamic correlation effects from the external space. In this comprehensive perspective, we systematically review and analyze state-of-the-art methodologies that address dynamic correlation beyond large active spaces, with particular emphasis on approaches that circumvent the computational burden associated with high-order reduced density matrices. Through careful classification, we have organized these advanced techniques into seven distinct categories. To illustrate the practical application and comparative performance of these newly developed methods, we present a detailed case study involving the calculation of potential energy curves for the neodymium oxide (NdO) molecule. It is our expectation that this work will not only provide valuable insights for future multi-reference calculations in large strongly correlated systems but also stimulate the development of innovative methodologies specifically tailored for handling extensive active spaces in multi-reference calculations.