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.