Exact Factorization-Based Density Functional Theory of Electrons and Nuclei

The ground state energy of a system of electrons (r =r₁,r₂,…) and nuclei (R =R₁,R₂,… ) 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_{μ ν}(R ) . n , j_p, A_μ and T_{μ ν} are defined in terms of the conditional electronic wave function Φ_R(r ). The ground state (n ,j_p,χ ,A_μ,T_{μ ν}) 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_{μ ν}. The theory is applied to the E ⊗e Jahn-Teller model.