Origins of dihydrogen binding to metal-inserted porphyrins: electric polarization and Kubas interaction

Using density functional theory calculations, we have investigated the interactions between hydrogen molecules and metalloporphyrins. A metal atom such as Ca or Ti is introduced for incorporation in the central N${}_4$ cavity. Within local density approximation (generalized gradient approximation), we find that the average binding energy of H${}_2$ to the Ca atom is about 0.25 (0.1) eV/H${}_2$ up to four H${}_2$ molecules, whereas that to the Ti atom is about 0.6 (0.3) eV per H${}_2$ up to two H${}_2$. Our analysis of orbital hybridization between the inserted metal atom and molecular hydrogen shows that H${}_2$ binds weakly to Ca-porphyrin through a weak electric polarization in dihydrogen, but is strongly hybridized with Ti-porphyrin through the Kubas interaction. The presence of $d$ orbitals in Ti may explain the difference in the interaction types.