A Hierarchy of Static Correlation Models

It is commonly accepted in the scientific literature that the static correlation energy, Estat, of a system can be defined as the exact correlation energy of its valence electrons in a minimal basis. Unfortunately, the computational cost of calculating the exact correlation energy within a fully optimized minimal basis grows exponentially with system size, making such calculations intractable for all but the smallest systems. However, analogous to single-reference methods, it is possible to systematically approximate both the treatment of electron correlation and flexibility of the minimal basis to reduce computational cost. This yields a hierarchy of methods for calculating Estat, ranging from coupled cluster methods in a minimal atomic basis up to full valence complete active space methods with a minimal molecular orbital basis constructed from a near-complete atomic orbital basis. By examining a variety of dissociating diatomics, along with equilibrium and transition structures for polyatomic systems, we show that standard coupled cluster models with minimal atomic basis sets (e.g., STO-3G) offer a convenient and cost-effective hierarchy of black box estimates for Estat in small- to medium-sized systems near their equilibrium geometries. To properly describe homolytic bond dissociation, it is better to use a more flexible basis set expansion so that each atomic orbital can effectively adapt to its molecular environment.