  The main flaw of the well-known Brinkman-Rice description, obtained through
the Gutzwiller approximation, of the paramagnetic Mott transition in the
Hubbard model is in neglecting high-energy virtual processes that generate for
instance the antiferromagnetic exchange $J\sim t^2/U$. Here we propose a way to
capture those processes by combining the Brinkman-Rice approach with a
variational Schrieffer-Wolff transformation, and apply this method to study the
single-band metal-to-insulator transition in a Bethe lattice with infinite
coordination number, where the Gutzwiller approximation becomes exact. We
indeed find for the Mott transition a description very close to the real one
provided by dynamical mean-field theory; an encouraging result in view of
possible applications to more involved models.
