  The current work presents a natural orbital functional (NOF) for electronic
systems with any spin value independent of the external potential being
considered, that is, a global NOF (GNOF). It is based on a new two-index
reconstruction of the two-particle reduced density matrix for spin multiplets.
The emergent functional describes the complete intrapair electron correlation,
and the correlation between orbitals that make up both the pairs and the
individual electrons. The interorbital correlation is composed of static and
dynamic terms. The concept of dynamic part of the occupation numbers is
introduced. To evaluate the accuracy achieved with GNOF, calculation of a
variety of properties is presented. They include the total energies and energy
differences between the ground state and the lowest-lying excited state with
different spin of atoms from H to Ne, ionization potentials of the first-row
transition-metal atoms (Sc-Zn), and the total energies of a selected set of 55
molecular systems in different spin states. GNOF is also applied to the
homolytic dissociation of selected diatomic molecules in different spin states
and to the rotation barrier of ethylene, both paradigmatic cases of systems
with significant multi-configurational character. The values obtained agree
with those reported at high level of theory and experimental data.
