Hyper Valence Theory and Multicenter Bonding:

Hyper Valence Theory is a concept that describes the formation of molecules that have more than eight electrons in their outermost shell. In such molecules, the central atom can form bonds with more than four atoms or groups.

Multicenter Bonding is a type of chemical bonding in which more than two atoms participate in the formation of a bond. In other words, it involves the sharing of electrons between three or more atoms.

Answer Explanation:

Out of the given options, only SF4 has multicenter bonding. Let's understand why SF4 has multicenter bonding:

1. Molecular Geometry: The molecular geometry of SF4 is trigonal bipyramidal. The central atom (Sulfur) is surrounded by four Fluorine atoms and one lone pair of electrons.

2. Hybridization: The Sulfur atom in SF4 undergoes sp3d hybridization to form five hybrid orbitals. These hybrid orbitals participate in the formation of bonds with the surrounding Fluorine atoms.

3. Bonding: In SF4, the four Fluorine atoms form a single bond with the central Sulfur atom. However, each Fluorine atom shares its electron with two hybrid orbitals of the Sulfur atom. Thus, the bond in SF4 involves three atoms (one Sulfur and two Fluorine atoms) and two electrons.

4. Multicenter Bonding: As mentioned earlier, multicenter bonding involves the sharing of electrons between three or more atoms. In SF4, the bond formation involves three atoms (one Sulfur and two Fluorine atoms) and two electrons. Hence, SF4 has multicenter bonding.

Conclusion:

From the above explanation, it is clear that only SF4 has multicenter bonding among the given options. Therefore, the correct answer is option 'A'.