Dissociation curves from variational second order density matrices : an Atoms in Molecules perspective

Most (relatively) routine quantum chemical calculations use either the wave function or the electron density as basic entity. On the other hand, for a Hamiltonian with at most pairwise interactions, the second order density matrix (2- DM) suffices for an exact description of the system. A logical step is to optimize the 2-DM by minimization of the energy. Unfortunately, not every 2-DM is related to a proper wave function and one needs to constrain the optimization using so-called N-representability constraints. We present results of a P, Q and G constrained optimization of the 2-DM and discuss potential energy surfaces obtained for the 14-electron systems N2, CO, NO+ and CN-. The surfaces are in apparently good agreement with energy data from Full CI but analysis of the atoms in the molecules in the 2-DM approach reveal an important chemical flaw. Even at very large separations, up to 20 Å, the atoms have fractional occupancies. This observation will be shown to be a consequence of the poor energy versus occupancy curves for fractional numbers of electrons resulting in the chemically wrong dissociation behavior.

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