Why the hydration energy of Au⁺ is larger for the second water molecule than the first one: Skewed orbitals overlap

Using molecular-orbital analysis, we have elucidated the quantum-chemical origin of the intriguing phenomena in sequential hydration energies of the gold cation, which is known to be the most conspicuous among all transition metals. The hydration energy of Au⁺ with the second water molecule is found to be much larger than that with the first water molecule. Owing to the large relativistic effect of gold (i.e., significant lowering of the 6s orbital energy and significant raising of the 5d orbital energy), the highest occupied molecular orbital of the hydrated gold cation has a large portion of the 6s orbital. As the electron density of the 6s orbital populates in a large outer spherical shell far off the gold nucleus, the p orbitals (or sp hybridized lone-pair orbitals) of the water molecules are able to overlap with the outer part of the 6s orbital in the dihydrated gold cation, resulting in the unusual skewed overlap of p-6s-p orbitals (not the atom-to-atom bond overlap). No previous molecular-orbital analysis has reported this peculiar skewed orbitals overlap. Since this skewed orbitals overlap is saturated with two water molecules, this property is responsible for the low coordination number of the gold ion.