Reciprocity theorems and pseudoelectric fields for ab initio force calculations

We present a method for constructing a pseudoelectric field at each paint in space, which gives the force on a classical ion due to its local or nonlocal pseudopotential interaction with a quantum electronic system. Our derivation extends a classical reciprocity theorem used by Hellmann and Feynman for purely Coulombic interactions to a family of generalized electron-ion potentials, which are useful for efficient electronic structure studies. The method is computationally efficient and it should be particularly useful for structural relaxation and molecular dynamics studies of complex systems.