Generalization of the Hohenberg–Kohn theorem to the presence of a magnetostatic field

The Hohenberg–Kohn theorem is generalized to the case of electrons in the presence of both an external electrostatic E(r)=−∇v(r)E(r)=−∇v(r) and magnetostatic B(r)=∇×A(r)B(r)=∇×A(r) field. For the non-degenerate ground state, it is established that the basic variables are the ground state density ρ(r)ρ(r) and physical   current density j(r)j(r) by proving the relationship between the densities {ρ(r),j(r)}{ρ(r),j(r)} and the external potentials {v(r),A(r)}{v(r),A(r)} is one-to-one  . A constrained-search proof is also provided. It is further explained why the basic variables cannot be the density ρ(r)ρ(r) and the paramagnetic   current density jp(r)jp(r) as presently thought to be the case.

► The Hohenberg–Kohn theorem is generalized to electrons in an external magnetostatic field.
► For the non-degenerate ground state, the relationship between the physical densities {ρ(r),j(r)}{ρ(r),j(r)} and potentials {v(r),A(r)}{v(r),A(r)} is one-to-one.
► A constrained-search proof is also provided.
► We explain why ρ(r)ρ(r) and the paramagnetic current density jp(r)jp(r) cannot be basic variables.