Bond breaking and bond formation: how electron correlation is captured in many-body perturbation theory and density-functional theory.

For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e.

Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation.

Self-consistent correlation potentials for H(2) and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations.

Open-shell reduced density matrix functional theory.

Open-shell reduced density matrix functional theory is established by investigating the domain of the exact functional. For spin states that are the ground state, a particularly simple set is found to be the domain. It cannot be generalized to other spin states.

A new scheme to calculate isotope effects.

We present a new scheme to calculate isotope effects. Only selected frequencies at the target level of theory are calculated. The frequencies are selected by an analysis of the Hessian from a lower level of theory.

A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation.

A recently proposed series of corrections to the earliest JK-only functionals has considerably improved the prospects of density matrix functional theory (DMFT). Still, the most advanced of these functionals (correction C3) requires a preselection of the terms in the pair density Gamma(r(1),r(2)) involving the bonding and antibonding natural orbitals (NOs) belonging to an electron pair bond. Ideally, a DMFT functional should only depend on the NOs and their occupation numbers, and we propose a functional with an occupation number driven weighing of terms in the pair density.