Jahn-Teller effect in density-functional theory

Jahn and Teller used degenerate perturbation theory to prove that open shell molecules with symmetry Jahn-Teller distort. In that vein, we have developed a perturbative approach to computing Jahn-Teller distortions in Kohn-Sham density-functional theory, starting from a symmetrized molecule with an electronic shell closed by fractional occupation numbers. The resulting highly symmetric state is an energy extremum but not necessarily a minimum. 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. As a demonstration, we solve the resulting equations for ten electrons in a superatomlike harmonic-oscillator potential.

Figure 1

Original electron density of the superatom per ${\mathrm{bohr}}^3$ (left) and the change in density overlaid with the quadropole potential as it undergoes a Jahn-Teller distortion (right).