  The relative stability of the singlet, triplet, and quintet spin states of
Iron(II) porphyrin (FeP) represents a challenging problem for electronic
structure methods. While it is currently accepted that the ground state is a
triplet, multiconfigurational wavefunction-based methods predict a quintet, and
density functional approximations vary between triplet and quintet states,
leading to a prediction that highly depends on the features of the method
employed. The recently proposed Global Natural Orbital Functional (GNOF) aims
to provide a balanced treatment between static and dynamic correlation, and
together with the previous Piris Natural Orbital Functionals (PNOFs), allowed
us to explore the importance of each type of correlation in the stability order
of the states of FeP with a method that conserves the spin of the system. It is
noteworthy that GNOF correlates all electrons in all available orbitals for a
given basis set; in the case of the FeP with a double zeta basis set as used in
this work; this means that GNOF can properly correlate 186 electrons in 465
orbitals, significantly increasing the sizes of systems amenable to
multiconfigurational treatment. Results show that PNOF5, PNOF7s and PNOF7
predict the quintet to have a lower energy than the triplet state; however, the
addition of dynamic correlation via second-order Moller-Plesset corrections
(NOF-MP2) turns the triplet state to be lower than the quintet state, a
prediction also reproduced by GNOF that incorporates much more dynamic
correlation than its predecessors.
