Question

What kinds of bonds does the `d_(x^2-y^2)` orbital form in transition metal complexes?

Answer 1

As it is aligned along coordinate axes, the `d_(x^2-y^2)` usually forms `sigma` bonds in preference to `pi` bonds, seeing as how ligands bond along the coordinate axes as the internuclear axes.

An example is in square planar transition metal complexes...

...or in octahedral transition metal complexes:

One "exception" (among others) is trigonal bipyramidal transition metal complexes, where the `d_(x^2-y^2)` does not quite provide a direct `sigma` interaction. In that case, it only is a partially direct overlap and not an ideal `sigma` bond.

The `d_(x^2-y^2)` orbitals would lie along the coordinate axes defined by ligand "`2`" and the wedge bond, whereas the ligands would lie on the corners of the dashed triangle.

See this answer for further detail on the `d_(x^2-y^2)` orbital.

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On the other hand, the `d_(xy)`, `d_(xz)`, and `d_(yz)` tend to form `pi` bonds, and rarely `delta` bonds.

One note here is that usually the internuclear axis is the `z` axis, but with some exceptions.

The above diagram for octahedral complexes uses the convention that in polyatomic compounds, the `bby` axis is the internuclear axis in the coordinates of the outer (non-central) atoms.