Bounds for the second and the third derivatives of the electron density at the nucleus

Abstract

Lower bound for ${\bar{\rho }}^{\prime \prime }(0)$, the second derivative of the spherically averaged atomic electronic density at the nucleus, and upper bound for ${\bar{\rho }}^{\prime \prime \prime }(0)$, the third derivative, are obtained respectively. It is shown that, for the ground state, ${\bar{\rho }}^{\prime \prime }(0)\ge 10/3Z^2\rho (0)$ and ${\bar{\rho }}^{\prime \prime \prime }(0)\le -14/3Z^3\rho (0)$ where $Z$ is the charge of the nucleus, and $\rho (0)$ is the electron density at the nucleus. Tighter bounds for ${\bar{\rho }}^{\prime \prime }(0)$ and ${\bar{\rho }}^{\prime \prime \prime }(0)$ are also reported which are valid for both the ground state and excited states. Explicit illustration with the example of one-electron atomic ions is given.

4 pages

References in corpus (1)

• Exchange and correlation near the nucleus in density functional theory