Shannon Entropy in LS-Coupled Configuration Space for Ni-like Isoelectronic Sequence.

Jian-Jie Wan,Jie Gu,Jiao Li,Na Guo

doi:10.3390/e24020267

Abstract

The Shannon entropy in an LS-coupled configuration space has been calculated through a transformation from that in a jj-coupled configuration space for a Ni-like isoelectronic sequence. The sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction have been presented for adjacent levels. It is shown that eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, and both of them are a sufficient condition for information exchange, which is the same as the case of the jj-coupled configuration space. It is found that the structure of sudden change from jj-coupled into LS-coupled configuration spaces through the LS-jj transformation is invariant for Shannon entropy along the isoelectronic sequence. What is more, in an LS-coupled configuration space, there are a large number of information exchanges between energy levels whether with or without strong configuration interaction, and most of the ground and single excited states of Ni-like ions are more suitable to be described by a jj-coupled or other configuration basis set instead of an LS-coupled configuration basis set according to the configuration mixing coefficients and their Shannon entropy. In this sense, Shannon entropy can also be used to measure the applicability of a configuration basis set or the purity of atomic state functions in different coupling schemes.

Highlights

Shannon information entropy [1] has been used to describe a large variety of physical concepts nowadays and to elucidate the physical and chemical properties of atomic and molecular systems
In our previous work [24,25], the atomic state wavefunction was expressed by an expansion of the jj-coupled configuration basis set, which is obtained by using the relativistic configuration interaction (RCI) with relativistic one-electron orbitals and multiconfiguration Dirac–Hartree–Fock (MCDHF) methods with the relativistic electron orbitals generated by the self-consistent field procedure [27,28,29,30,31]
All figures present the Shannon entropies for the levels in the LS-coupled configuration space, configuration weights and eigenlevel anticrossing for selected levels and the unique notation of each level has been given in these figures according to the configuration mixing coefficients

Summary

Introduction

Shannon information entropy [1] has been used to describe a large variety of physical concepts nowadays and to elucidate the physical and chemical properties of atomic and molecular systems. In our previous work [24,25], we have found the following in a jj-coupled configuration space: (1) The sudden change of Shannon entropy is a sufficient and necessary condition for the eigenlevel anticrossing in a given configuration space whether the total angular momentum and parity JP of the adjacent levels is the same or not, with the help of which it is easy to determine the position of eigenlevel anticrossing; the transition probabilities can be changed dramatically around the anticrossing of eigenlevel, and strongly induced transition in an external electromagnetic field can take place; (2) The sudden change of Shannon entropy is a sufficient condition for information exchanges whether JP of the adjacent levels is the same or not; (3) There is no necessary causal relationship between the eigenlevel anticrossing and strong configuration interaction in isoelectronic sequences.

Theoretical Considerations

Results and Discussion

Summary and Outlook