Characteristics of ground state electronic structures of ionized atoms and rules of their orbital competitions

Abstract

Ionized atoms widely exist in plasmas, and studies of properties of ionized atoms are the foundations of frontier science researches such as astrophysics and controlled nuclear fusions. For example, the information about the ground configurations of atoms is required for accurately calculating the physical quantities such as energy levels and dynamical processes. The configurations for different ionized atoms can be obtained with the photo-electron energy spectrum experiment, however it is very time-consuming to obtain so many data of all ions. Therefore the more economical theoretical study will be of great importance. As is well known, the configurations of neutral atoms can be determined according to Mendeleev order while those of highly ionized atoms are hydrogen-like due to the strong Coulombic potential of their nuclei. Then with the variations of ionization degree and atomic number along the periodic table, there would appear the interesting competitions between electronic orbitals. Although some theoretical results exist for ions 3 Z 118, 3 Ne 105 (where Z is the atomic number and Ne is the electron number), there are many errors in the results for highly ionized atoms. Therefore, the ground configurations of ionized atoms and their orbital competitions still deserve to be systematically studied. Based on the independent electron approximation, we calculate the energy levels of all possible competition configurations of all the neutral and ionized atoms in the extended periodic tables (2 Z 119) by Dirac-Slater method. Then the ground configurations are determined by calculating the chosen lowest total energy. The advantages of Dirac- Slater method are as follows. 1) It has been shown that the Dirac-Slater calculation is accurate enough for studying the ground properties of atoms, such as the 1st threshold, and that higher accuracy will be obtained for highly ionized atoms, because the electron correlation becomes less important. 2) Furthermore, with Dirac-Slater method we can obtain the localized self-consistent potential, thereby we can study the orbital competition rules for different atoms. Using the three of our designed atomic orbital competition graphs, all of our calculated ground configurations for over 7000 ionized atoms are conveniently expressed. We systematically summarize the rules of orbital competitions for different elements in different periods. We elucidate the mechanism of orbital competition (i.e., orbital collapsing) with the help of self-consistent atomic potential of ionized atoms. Also we compare the orbital competition rules for different periods of transition elements, the rare-earth and transuranium elements with the variation of the self-consistent filed for different periods. On this basis, we summarize the relationship between the orbital competitions and some bulk properties for some elements, such as the superconductivity, the optical properties, the mechanical strength, and the chemistry activities. We find that there exist some abnormal orbital competitions for some lowly ionized and neutral atoms which may lead to the unique bulk properties for the element. With the ground state electronic structures of ionized atoms, we can construct the basis of accurate quasi-complete configuration interaction (CI) calculations, and further accurately calculate the physical quantities like the energy levels, transition rates, collision cross section, etc. Therefore we can meet the requirements of scientific researches such as the analysis of high-power free-electron laser experiments and the accurate measurement of the mass of nuclei.

Interesting Features of Ionization Potentials for Elements ( Z ≤ 119) along the Periodic Table

“…More specif-ically, the calculated first IPs of the outermost orbitals along the periodic table are in good agreement with the experimental measurements except for 64 Gd, 90 Th and 93 Np due to the local approximations of exchange interactions adopted in our RSCF method. [9] For the inner shell orbitals, the good accuracies can be achieved within a few percent. Therefore, it should be useful to select x-ray energies for elementspecific and spatially resolved analysis of materials.…”

“…These differences mainly originate from local approximations of exchange interactions in the RSCF method. [9] The variation of the first IPs along the periodic tables (PT) can be understood since the IP is the absolute value of the orbital energy according to Koopmans' theorem, which can be expressed as [10] IP th…”

“…Entering the 4th row starting at 𝑍 = 19, similarly the first IP curve of the 4𝑠 orbital of 19 K drops first, and then increases for 20 Ca. For the first transition elements starting at 𝑍 = 21 with the 3𝑑 orbital collapsing as valence orbitals [9] from 21 Sc to 29 Cu, the first IP curve of the 4𝑠 orbital varies smoothly due to the changes of ESCs, ∆𝜎 4𝑠 (Sc, Ti, . .…”

“…., or Cu) of the 4𝑠 orbital is about one owing to the screening of the inner localized 3𝑑 electrons compared with the atomic number increase ∆𝑍 = 1. Note that there are sudden drops of the IP curve of the 3𝑑 orbitals at 𝑍 = 24 and 29 since the changes of the GEConf occur, i.e., from 23 V (3𝑑 3 4𝑠 2 ) through 24 Cr (3𝑑 For the rare-earth elements starting at 𝑍 = 57 with the 4𝑓 orbital collapsing as valence orbitals [9] from 57 La to 71 Lu, the first IP curve of the 6𝑠 orbital varies smoothly due to the changes of ESCs, ∆𝜎 6𝑠 (La, Ce, . .…”

“…1. The occupation of 5𝑑 electron in 64 Gd can be regarded as an isolated case, [9] while the 5𝑑 electron will begin to be filled in systematically after 71 Lu. To display variations of 5𝑑 orbitals along the rare-earth elements and the third transition elements, the orbital energies of unoccupied 5𝑑 electrons from 59 Pr to 70 Yb are also shown in Fig.…”