On the squared spin-orbit correction to the positronium fine-structure   splitting
  In the recent paper by Zhang the order $\alpha^4 R_{\infty}$ corrections to the positronium P levels were reconsidered. Those calculations confirm our corresponding results, except for the contribution due to the squared spin-orbit interaction. We present here a new derivation of our previous result for this last correction, this derivation being to our opinion both simple and convincing. 
I.B. Khriplovich, A.I. Milstein and A.S. Yelkhovsky