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 jp(r,R) conditional on R, the nuclear wave function χ(R), an induced vector potential Aμ(R) and a quantum geometric tensor Tμν(R). n, jp, Aμ and Tμν are defined in terms of the conditional electronic wave function ΦR(r). The ground state (n,jp,χ,Aμ,Tμν) can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing effective scalar and vector potentials vs(r) and Axc(r) that depend parametrically on R, (ii) the Schrödinger equation for χ(R), and (iii) Euler-Lagrange equations that determine Tμν. The theory is applied to the E-e Jahn-Teller model.