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 wave function 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 intrapair, but only the static interpair correlation. Using the solution of the NOF, two new energy functionals are defined for both dynamic ($E^{\mathrm{dyn}}$) and static ($E^{\mathrm{sta}}$) correlation. $E^{\mathrm{dyn}}$ is derived from a modified second-order Møller-Plesset perturbation theory (MP2), while $E^{\mathrm{sta}}$ 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 ${\tilde{E}}_{\text{HF}}+E^{\mathrm{dyn}}+E^{\mathrm{sta}}$, where ${\tilde{E}}_{\text{HF}}$ is the Hartree-Fock energy obtained with natural orbitals. The new procedure called NOF-MP2 scales formally as $O(M^5)$ (where $M$ is the 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. The size consistency has been numerically demonstrated for singlets. The values obtained are in good agreement with the experimental data.

Figure 1

Potential energy curves (cc-pVTZ).

Figure 2

Potential energy curves for $H_2$.