Need commutator that rotates centers 180 degrees on D face.

[rjohnson_8ball]

(RLD2R'L'D)2 is the simpliest.

That is the one I use. If you perform the commutator [ [R L, D2], D ]
and apply an extra D2 afterward, you get
((R L D2 L' R' D2) D (D2 R L D2 L' R') D' )(D2)
which is (R L D2 L' R' D)*2. Did I do it okay?

 

[deadalnix]

Like this, it's a double permutation of group composed by one corner and one edge. It's an elegant way to see it as a commutaor !

 

[Stefan]

For understanding, I like this best: [ L R d2 R' L', U ]
It's also a double swap of corner-edge pairs (in the U layer) and more direct.

 

[rjohnson_8ball]

For understanding, I like this best: [ L R d2 R' L', U ]
It's also a double swap of corner-edge pairs (in the U layer) and more direct.

Would that need a U2 applied afterward?
((L R d2 R' L') U (L' R' d2 R L) U') U2

 

[Stefan]

Yes of course. Just wanted to show a more understandable way for the pair swaps.

Oh and you made a mistake unwinding my commutator notation alg. Your alg does something different, resulting in a nice pattern. Can be done shorter, though.