The Jahn-Teller effect in density functional theory

Using degenerate perturbation theory, Jahn and Teller proved that open-shell molecules with symmetry distort into lower symmetry configurations. Extending this proof to Kohn-Sham (KS) density functional theory (DFT) is not straightforward because of the nonlinear Coulomb and exchange-correlation potentials. These potentials affect the relationship between nuclear symmetry and electronic degeneracy, altering degenerate perturbation theory itself. Using our recently developed degenerate density functional perturbation theory, we define a perturbative approach to Jahn-Teller distortions for KS DFT. We use fractional occupation numbers to symmetrize the initial electron density, artificially stabilizing the nuclei in the highest possible symmetry. Using second-order perturbation theory, we find the changes in geometry that occur when the symmetry of the electron density is broken to form a state with integer occupation numbers. This methodology allows us to retain many of the computational benefits of working in higher symmetry. We demonstrate the resulting equations in a system of ten electrons in a superatom-like harmonic oscillator potential.