The equivalence of the Piris Natural Orbital Functional 5 (PNOF5) and the antisymmetrized product of strongly orthogonal geminal theory

We show that a recently proposed natural orbital functional by Piris et al. PNOF5, is equivalent to the antisymmetrized product of strongly orthogonal geminal (APSG) approach if expansion of geminals is limited to two-dimensional subspaces. Consequently, the PNOF5 energy is bounded from below by the APSG value and by the exact ground state energy. Additionally, the PNOF5 inherits both the advantages of the ASPG functional such as variationality, qualitatively correct potential energy curves or (near) size-consistency as well as its most severe deficiency which is underestimation of dynamic (intergeminal) electron correlation.