Shannon entropy as a predictor of avoided crossing in confined atoms

Abstract

Avoided crossing is one of the unique spectroscopic features of a confined atomic system. Shannon information entropy of the ground state and some of the excited states of confined H atom as a predictor of avoided crossing is studied in this work. This is accomplished by varying the strength of the confinement and examining structure properties like ionization energy and Shannon information entropy. Along with the energy level repulsion at the avoided crossing, Shannon information entropy is also exchanged between the involved states. This work also addresses a question: In addition to that regarding localization, what other property of the system can be extracted from Shannon entropy? Insightful connection is discovered between Shannon entropy and the average value of confinement potential, Coulomb potential, and kinetic energy.

Coulomb correlation and information entropies in confined helium-like atoms

“…Quantum mechanical properties of confined systems are influenced by properties of confinement cage, for instance, the energy spectra and the polarizability experience significant changes [37,38]. With the increment of computational processing capacity and development of modern techniques for the effective confinement, this topic remains to be of interest [39][40][41][42][43][44][45][46][47][48][49][50]. In previous researches, we use the entropy sum to investigate the regions of the confined harmonic oscillator [51] and confined hydrogenic-like atoms [21] where the confinement effects has major impact.…”

Electronic structure and dynamics of confined atoms

“…in both of these works. Figure 1 shows evolution of the energy levels of 1s to 3s subshells with variation of the depth of the confinement well [74,86], and the corresponding ASW results are also shown in the figure; very good agreement between all three results is seen. For smaller confinement depths, the 1s electronic energy is unaffected; it remains the same as the binding energy in free H-atom.…”

“…(7), with A = 0. The GASW model potential has been used to investigate photoionization dynamics of confined hydrogen and argon [25] and to investigate Shannon entropy in avoided crossings of energy levels of confined hydrogen [86]. Among the potentials discussed above, there are two classes of potentials: (1) having depth of ∼0.3 a.u.…”

“…The Gaussian amplitude was varied to illustrate the 1s-4d energy level variation of H@C 60 . Building on earlier work [100], a slightly different model potential, the GASW model, has also been employed recently to study the energy levels of low-lying states of H@C 60 [86] using the finite difference method. r c is 6.7 a.u.…”

“…This is because the amplitude of the 1s wave function is nearly zero in the region of the con- Fig. 1 Evolution of ionization energy of 1s, 2s, and 3s levels of confined H atom as a function of the strength of the confinement well using a ASW (solid line) and GASW (dashed line) model potentials [86] and b ASW (solid line) and Gaussian (dashed line) confinement [74] fining square well potential. On the other hand, the 2s and 3s wave functions have significant amplitudes in this region, and hence, their eigen-energies are affected in response to even small changes in the potential.…”