Exact Factorization-Based Density Functional Theory of Electrons and Nuclei.

The ground state energy of a system of electrons (r=r_{1},r_{2},…) and nuclei (R=R_{1},R_{2},…) is proven to be a variational functional of the electronic density n(r,R) and paramagnetic current density j_{p}(r,R) conditional on R, the nuclear wave function χ(R), an induced vector potential A_{µ}(R) and a quantum geometric tensor T_{µν}(R). n, j_{p}, A_{µ} and T_{µν} are defined in terms of the conditional electronic wave function Φ_{R}(r). The ground state (n,j_{p},χ,A_{µ},T_{µν}) can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing effective scalar and vector potentials v_{s}(r) and A_{xc}(r) that depend parametrically on R, (ii) the Schrödinger equation for χ(R), and (iii) Euler-Lagrange equations that determine T_{µν}. The theory is applied to the E⊗e Jahn-Teller model.