Surface vibration correlation with d-electron (hole) per atom ratio (d-bandfilling) in CO chemisorption on supported transition metal particles: Dominance of hund's rule and d-electron degeneracy in real supported catalysts

The findings of Guerra and Schulman (ref.1) of a correlation between force constant of metal-CO chemisorbed species (admolocules) with the number of d-holes per atom (1-number of d-electrons per atom, or d-bandfilling) of the transition metal particle (supported) surface is treated using the ten-fold degenerate Hubbard (ref.2) (TDHM) and Anderson (TDAM) (ref.3) models developed for magnetic and Mott metal-insulator transition problems in transition metals, alloys and compounds. Their experimental finding that via infrared spectroscopy on the CO adsorbed species (admolecule) bond, the infrared surface vibrational frequency, CO bond order and CO bond force constant were nearly linear versus the number of d-holes per transition metal surface atom is easily explained via the TDHM and TDAM via their inherent d-bandfilling dependent (alloy specific) Coulomb and exchange enhanced coupling strength between d-electrons or d-holes (ref.4). Even the Fulde (ref.5) correction to the number of d-electrons (holes) per $\text{surface}$ atom as a function of transition metal particle size does not change the excellent agreement, but merely renormalizes the measured functional properties versus d-hole per atom ratio for a suite of equally fine sized transition metal particles. So it seems that in admolecule chemisorption (at least for CO) the degenerate electronic properties of the surface dominate the vibrational and bonding properties of the admolecular species rather completely.