Chemistry: orbital overlap

Tutoring chemistry, one might be asked about the nature of bonds. The tutor mentions hybridization and overlap.

The following is by my understanding.

I mention in my post from July 13, 2024 the idea of some atoms having more than an octet of electrons in the outer shell. The reason turns out to be that the central atom has access to a d orbital.

In the case of sulfate, the sulfur atom has twelve electrons in its outer shell. Yet, we are told that the shape-determining hybridization is sp3, so that the molecule is tetrahedral. The other two bonds are pi bonds. Then, what about those pi bonds? What orbitals do they involve?

It turns out that said pi bonds are dπ-pπ bonds, specifically from d orbitals on the sulfur atom to p orbitals on the oxygen atoms. Some d orbitals have shapes that permit them to overlap with p orbitals, making dπ-pπ bonds possible.

Source:

Haas, K. (n.d.) “Quantum Numbers and Atomic Wavefunctions.” https://chem.libretexts.org/Courses/East_Tennessee_State_University/CHEM_3110%3A_Descriptive_Inorganic_Chemistry/02%3A_Atomic_Theory/2.01%3A_Quantum_Numbers_and_Atomic_Wavefunctions#Angular_nodeschem.libretexts.org

chem.libretexts.org: “Orbital Overlap.”

chem.libretexts.org: “Hybrid Atomic Orbitals.”