  The self-energy embedding theory (SEET), in which the active space
self-energy is embedded in the self-energy obtained from a perturbative method
treating the non-local correlation effects, was recently developed in our
group. In SEET the double counting problem does not appear and the accuracy can
be improved either by increasing the perturbation order or by enlarging the
active space. This method was first calibrated for the 2D Hubbard lattice
showing promising results. In this paper, we report an extension of SEET to
quantum chemical ab initio Hamiltonians for applications to molecular systems.
The self-consistent second-order Green's function (GF2) method is used to
describe the non-local correlations, while the full configuration interaction
(FCI) method is carried out to capture strong correlation within the active
space. Using few proof-of-concept examples, we show that SEET yields results of
comparable quality to $n-$electron valence state second-order perturbation
theory (NEVPT2) with the same active space, and furthermore, the full active
space can be split into smaller active spaces without further implementation.
Moreover, SEET avoids intruder states and does not require any high-order
reduced density matrices. These advantages show that SEET is a promising method
to describe physical and chemical properties of challenging molecules requiring
large active spaces.
