  We present a detailed discussion of self-energy embedding theory (SEET) which
is a quantum embedding scheme allowing us to describe a chosen subsystem very
accurately while keeping the description of the environment at a lower cost. We
apply SEET to molecular examples where commonly our chosen subsystem is made
out of a set of strongly correlated orbitals while the weakly correlated
orbitals constitute an environment. Such a self-energy separation is very
general and to make this procedure applicable to multiple systems a detailed
and practical procedure for the evaluation of the system and environment
self-energy is necessary. We list all the intricacies for one of the possible
procedures while focusing our discussion on many practical implementation
aspects such as the choice of best orbital basis, impurity solver, and many
steps necessary to reach chemical accuracy. Finally, on a set of carefully
chosen molecular examples, we demonstrate that SEET which is a controlled,
systematically improvable Green's function method can be as accurate as
established wavefunction quantum chemistry methods.
