  One-body reduced density matrix functional theory (RDMFT) provides an
alternative to Density Functional Theory (DFT), able to treat static
correlation while keeping a relatively low computation scaling. Its
disadvantageous cost comes mainly from a slow convergence of the
self-consistent energy optimisation. To improve on that problem, we propose in
this work to use the hessian of the energy, including the coupling term. We
show that using the exact hessian is very effective in reducing the number of
iterations. However, since the exact hessian is too expensive to use in
practice, we test different approximations based on an inexpensive exact part
and/or BFGS updates.
