HohenbergKohn theorem including electron spin
Abstract
The HohenbergKohn theorem is generalized to the case of a finite system of N electrons in external electrostatic E(r)=∇v(r) and magnetostatic B(r)=∇×A(r) fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density ρ(r) and physical current density j(r) and the potentials {v(r),A(r)}. The possible manytoone relationship between the potentials {v(r),A(r)} and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables are {ρ(r),j(r)}, and explicitly employing the bijectivity between {ρ(r),j(r)} and {v(r),A(r)}, the further extension to Nrepresentable densities and degenerate states is achieved via a PercusLevyLieb constrainedsearch proof. A {ρ(r),j(r)}functional theory is developed. Finally, a Slater determinant of equidensity orbitals which reproduces a given {ρ(r),j(r)} is constructed.
 Publication:

Physical Review A
 Pub Date:
 October 2012
 DOI:
 10.1103/PhysRevA.86.042502
 Bibcode:
 2012PhRvA..86d2502P
 Keywords:

 31.15.E;
 31.10.+z;
 03.65.w;
 Densityfunctional theory;
 Theory of electronic structure electronic transitions and chemical binding;
 Quantum mechanics