  We report an implementation of self-consistent Green's function many-body
theory within a second-order approximation (GF2) for application with molecular
systems. This is done by iterative solution of the Dyson equation expressed in
matrix form in an atomic orbital basis, where the Green's function and
self-energy are built on the imaginary frequency and imaginary time domain
respectively, and fast Fourier transform is used to efficiently transform these
quantities as needed. We apply this method to several archetypical examples of
strong correlation, such as a H$_{32}$ finite lattice that displays a highly
multireference electronic ground state even at equilibrium lattice spacing. In
all cases GF2 gives a physically meaningful description of the metal to
insulator transition in these systems, without resorting to spin-symmetry
breaking. Our results show that self-consistent Green's function many-body
theory offers a viable route to describing strong correlations while remaining
within a computationally tractable single-particle formalism.
