text: (r λ2)/(32Jcluster) 
  (Sj3 
  · 
  × 
  − Pjk)Sj2 
  Pjk)[0 
  Sk4) 
  −  · 
  Pjk gives the same result. 
  In summary the second order perturbation from λ[Sj2 
  · 
  (Sj3  Sj4) + r Sk2  (Sj3  Sj4)] is 
  
  where Hcluster j are given by (2), λx,y,z Hperturbation x,y,z 
  are given above. Plug in relevant equations we get (16) 
  in Subsection IV B. 
  
  ×  · 
  
  × 
  λ2 
  32Jcluster  r λ2 
  16Jcluster · 
  k + r2 τ x  τ z 
  j τ z 
  (τ x 
  k + 
  j −  −  − 