  The original formulation (Phys. Rev. Lett. 119, 063002, 2017) of the natural
orbital functional - second-order M{\o}ller-Plesset (NOF-MP2) method is based
on the MP2 that uses the canonical Hartree-Fock molecular orbitals. The current
work presents a reformulation of the dynamic energy correction based on the
orbital-invariant MP2, which allows to attain both dynamic and static
correlations even for those systems with strong orbital localizability and
significant multiconfigurational character. To improve the reference Slater
determinant formed with natural orbitals, the natural orbital functional that
generates them is also modified to take into account only the inter-pair static
correction. This more general NOF-MP2 is able to dissociate properly noble gas
dimers, which remain as non-bound species within the canonical formulation.
Test calculations in a selected set of 30 polyatomic molecules demonstrate a
substantial improvement not only of the relative energies but also of the total
energies calculated with the NOF-MP2 method.
