Exploiting the hessian for a better convergence of the SCF RDMFT procedure

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.