Thanks for the clarification of your intent.
I am including some photos for completeness so that we have some actual data on the thread rather than oft repeated quotes about allelopathy associated with black walnut. In fact simply searching for allelopathy on google brings up several links on Juglans Nigra.
The first photo is that of the tree itself, the next two are of the leaf structure and of the fruit. The final one show a Rhododendron growing vigorously around 3 feet from the tree trunk.
Rhodies are supposedly very sensitive to black walnut.
I also have a large fig tree growing in the trees dripline.
Grass grows fine under the tree.
To me, the western red cedar is far more toxic than Juglans Nigra. Nothing will grow under it.