Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

Abstract

We have previously proposed a simple empirical equation to reproduce the literature values of the ionization energies of oneelectron to four-electron atomic ions with very good agreement. However, we used a potential energy approach in our equation, which has no theoretical basis. is paper discusses an alternative kinetic energy expression for one to �ve electrons with simple corrections for relativistic and Lamb shi effects and for two-to-�ve electron ions additional effects including electron relaxation and residual interactions. For calculated values of one-electron (hydrogen-like) and two electron (helium like) atomic ions, the difference with the literature values is typically 0.001% or less. Agreement with the literature values for three-, four-, and �ve-electron ions is 99% or better. First electron affinities calculated by our expression also agree fairly well with generally recommended values. ese results show that there is strong evidence that our methodology can be developed to reliably predict, with fairly good accuracy, ionization energies of multielectron atomic ions that have not been measured.

Renaissance of Bohr's Model Via Derived Alternative Equation

“…One needs to add that with the advent of quantum theory according to Lang and Barry [13], the two particle problem can be solved exactly, and the kinetic energy of the electron in a hydrogen atom or hydrogen-like ion can be calculated using the Schrödinger equation. However, there has been research into other methods for the determination of ionization energies of atoms, one-, two, three-, four-, and five-electron ions [13,14].…”

Methods of Calculating Ionization Energies of Multielectron (Five or More) Isoelectronic Atomic Ions

“…Therefore, the ionization energy can be represented as [15] $\begin{array}{c}\frac{\mathrm{normal1}}{n^{\mathrm{normal2}}}\mu \left(J_k-J_l-J_t\right)+E_r=E_k-E_l-E_t+E_r,\end{array}$ where n is the principal quantum number and μ is the reduced mass and are provided in Table 2. E k , E l , and E t represent J k , J l , and J t multiplied by 1/ n 2 μ , respectively.…”

“…The attractive energy between the proton and the remaining electron(s) changes because of the change in screening experienced by the remaining electron(s) before and after ionization, [15] and this transition/relaxation energy is a function of $\begin{array}{c}\frac{n^{\mathrm{normal2}}}{\mathrm{normal4}}\left(\frac{\mathrm{normal1}}{\mathrm{normal2}}{m}_o{\left(v_o\left(Z-S_{\mathrm{normal1}}\right)\right)}^{\mathrm{normal2}}-\frac{\mathrm{normal1}}{\mathrm{normal2}}{m}_o{\left(v_o\left(Z-S_{\mathrm{normal2}}\right)\right)}^{\mathrm{normal2}}\right),\end{array}$ where S 1 is the screening constant for the remaining electron(s) after ionization and S 2 is the screening constant for the remaining electron(s) before ionization.…”

“…We assume that there are two opposite and competing residual electron-electron interactions, and this is discussed in detail in previous work and is not fully reproduced here [15]. In summary, there are temporary asymmetric distributions of electrons (e.g., they may be nearer to each other or further apart than average).…”

“…The biggest absolute difference is 0.086 eV (to 3 decimal places) from a calculated value of 5469.95 eV or 0.00164% [15]. …”