Ionization potentials of neutral atoms and positive ions in the limit of large atomic number

The many-electron Schrödinger equation allows one to make predictions for the nonrelativistic ionization potentials of both highly charged positive atomic ions and neutral atoms in the limit of large atomic number $Z$. Beginning with theoretical configuration interaction data on both Li- and Be-like positive atomic ions by K.T. Chung et al. [Phys. Rev. A 45, 7766 (1992); Phys. Rev. A 47, 1740 (1993)], their nonrelativistic first ionization potentials $I$ are plotted in the form of $I∕Z^2$ versus $1∕Z$. In these two sequences, it is then clear that ${\lim }_{Z\to \infty }(I∕Z^2)$ remains finite and that this limit is approached essentially linearly. Interpretation is afforded by means of the so-called $1∕Z$ expansion of atomic theory. The question of the behavior of the nonrelativistic ionization potentials for large $Z$ is then addressed for neutral atoms. We perform density functional theory (DFT) calculations using the local density approximation with Dirac exchange and neglecting Coulomb correlation for the heavy actinides as well as for the rare gas and alkali atoms from $Z=10$ up to $Z=291$. Our results suggest that there is a nonzero value for ${\lim }_{Z\to \infty }I$ for both the noble gases and the alkalis, the second one implying that there is a lower bound of about $2.56\mathrm{eV}$ to the ionization potential of any nonrelativistic neutral atom. We also explore an alternative approach via the one-body potential $V\left(r\right)$ of DFT by calculating the eigenenergies of the highest occupied atomic orbital in neutral atoms. Finally, relativistic corrections needed to compare measured ionization potentials to the predictions from the Schrödinger equation are briefly considered.

Figure 1

Ionization potentials of the Li isoelectronic series calculated by Chung et al. [7] as a function of the inverse of the atomic number. The curve is a fit to Eq. (5).

Figure 2

Ionization potentials of the Be isoelectronic series calculated by Chung et al. [8] as a function of the inverse of the atomic number. The curve is a fit to Eq. (5).

Figure 3

Ionization potentials of neutral rare gas atoms as a function of the atomic number calculated with the LDA approximation to DFT neglecting relativistic and correlation effects. The line is merely a guide for the eye.

Figure 4

Ionization potentials of heavy actinides as a function of the atomic number calculated with the LDA approximation to DFT neglecting relativistic and correlation effects. The line is merely a guide for the eye.

Figure 5

Ionization potential in atomic units for the rare gas and alkali atom series in the $10⩽Z⩽291$ range, calculated using the LDA neglecting Coulomb correlation. The curves are fits to Eq. (10) for the heavy and ultra-heavy atoms in these series.

Figure 6

Binding energies in a.u. of the highest occupied $s$ and $p$ states in the Thomas-Fermi (dashed lines) and Thomas-Fermi-Dirac (solid lines) potentials for the rare gas atoms (interpolated from [22]). The lines are only a guide for the eye.

Figure 7

Energy of the highest occupied atomic orbital (HOAO) and ionization potential (I) in absolute value and in atomic units for the rare gas atom series, calculated using the LDA neglecting Coulomb correlation both within the nonrelativistic (dashed lines) and the scalar relativistic (solid lines) approximations. Experimental ionization potentials from [30] are given for comparison. The lines are only a guide for the eye.

Figure 8

Energy of the highest occupied atomic s orbital eigenenergy (HOAO) and ionization potential (I) in absolute value and in atomic units for the heavy actinides, calculated using the LDA neglecting Coulomb correlation both within the nonrelativistic (dashed lines) and the scalar relativistic (solid lines) approximations. Experimental ionization potentials from [30] are given for comparison. The lines are only a guide for the eye.