Reciprocity Theorems for Ab Initio Force Calculations
  We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules. 
C. Wei, Steven P. Lewis, E. J. Mele, and Andrew M. Rappe (University   of Pennsylvania)