Global Method for Electron Correlation

The current work presents a new single-reference method for capturing at the same time the static and dynamic electron correlation. The starting-point is a determinant wavefunction formed with natural orbitals obtained from a new interacting-pair model. The latter leads to a natural orbital functional (NOF) capable of recovering the complete intra-pair, but only the static inter-pair correlation. Using the solution of the NOF, two new energy functionals are defined for both dynamic ($E^{dyn}$) and static ($E^{sta}$) correlation. $E^{dyn}$ is derived from a modified second-order Møller\textendash Plesset perturbation theory (MP2), while $E^{sta}$ is obtained from the static component of the new NOF. Double counting is avoided by introducing the amount of static and dynamic correlation in each orbital as a function of its occupation. As a result, the total energy is represented by the sum $\tilde{E}_{hf}+E^{dyn}+E^{sta}$, where $\tilde{E}_{hf}$ is the Hartree-Fock energy obtained with natural orbitals. The new procedure called NOF-MP2 scales formally as $O(M^{5})$ ($M$: number of basis functions), and is applied successfully to the homolytic dissociation of a selected set of diatomic molecules, paradigmatic cases of near-degeneracy effects. Its size-consistency has been numerically demonstrated for singlets. The values obtained are in good agreement with the experimental data.