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

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

2007-09-27

arxiv.org/abs/0709.4311v2

Physics

Atomic Physics

4 pages

Scientific paper

10.1088/1751-8113/41/8/085305

Lower bound for ${\bar \rho}''(0)$, the second derivative of the spherically averaged atomic electronic density at the nucleus, and upper bound for ${\bar \rho}'''(0)$, the third derivative, are obtained respectively. It is shown that, for the ground state, ${\bar \rho}''(0) \ge {10/3} Z^2 \rho(0)$ and ${\bar \rho}'''(0) \le -{14/3}Z^3 \rho(0)$ where $Z$ is the charge of the nucleus, and $\rho(0)$ is the electron density at the nucleus. Tighter bounds for ${\bar \rho}''(0)$ and ${\bar \rho}'''(0)$ 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.

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