In these theoretical studies, the long-standing puzzle of CO on transition metal surfaces is attributed to charge-transfer between CO and the metal site, with the preferential hollow site resulting from the enhanced back-donation of the metal d-orbitals to CO's 2π* orbital. Shifting the LUMO of CO's 2π* orbital higher can potentially re-orient the HOMO-LUMO gap to revert to the correct 5σ-metal interaction for the atop site. Studies by Gajdos, et. al. and Patra, et. al. add a Hubbard U parameter to surmount difficulties of the PBE functional, but note that the determination of U to be empirical. Total energies calculated within the random phase approximation, using LDA eigenfunctions and eigenvalues, seems to fare much better. In the same work, densities of states were also presented, and showed improvement relative to DFT.