  Although mean field theories have been very successful to predict a wide
range of properties for solids, the discovery of high temperature
superconductivity in cuprates supported the idea that strongly correlated
materials cannot be qualitatively described by a mean field approach. After the
original proposal by Anderson, there is now a large amount of numerical
evidence that the simple but general resonating valence bond (RVB) wave
function contains just those ingredients missing in uncorrelated theories, so
that the main features of electron correlation can be captured by the
variational RVB approach. Strongly correlated antiferromagnetic (AFM) systems,
like Cs2CuCl4, displaying unconventional features of spin fractionalization,
are also understood within this variational scheme. From the computational
point of view the remarkable feature of this approach is that several
resonating valence bonds can be dealt simultaneously with a single determinant,
at a computational cost growing with the number of electrons similarly to more
conventional methods, such as Hartree-Fock or Density Functional Theory.
Recently several molecules have been studied by using the RVB wave function; we
have always obtained total energies, bonding lengths and binding energies
comparable with more demanding multi configurational methods, and in some cases
much better than single determinantal schemes. Here we present the paradigmatic
case of benzene.
