Cusp relation for the Pauli potential

In orbital-free density functional theory, only a Schrödinger-like equation has to be solved for the square root of the electron density. In this equation, however, there is an extra potential in addition to the Kohn-Sham potential, the so-called Pauli potential. Cusp relations are now presented for this Pauli potential for spherically symmetric systems.

Figure 1

Pauli potentials $v_p\left(r\right)$ and their radial derivatives $v_p^{\prime }\left(r\right)$ (in atomic units) for Be and Xe atoms near the nucleus. They have been obtained from converged densities and Kohn-Sham potentials by inverting the Euler equation (6) for $v_p\left(r\right)$, that is, using Eq. (19). Values near the nucleus are seen to agree with those [Eqs. (29) and (30)] given in Table 1.