The confined helium atom: An information–theoretic approach

• Published in: International journal of quantum chemistry Vol. 124; no. 4
• Main Authors: Estañón, C. R., Montgomery, H. E., Angulo, J. C., Aquino, N.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.02.2024; Wiley Subscription Services, Inc
• Subjects: confined helium atom; Correlation; disequilibrium; Entropy (Information theory); Fisher information; Fisher–Shannon complexity; Helium atoms; Hylleraas coordinates; Kullback–Leibler entropy; Shannon entropy; Tsallis entropy; Wave functions
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.27358

In this article, we study the helium atom confined in a spherical impenetrable cavity by using informational measures. We use the Ritz variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius r0$$ {r}_0 $$. As trial wave functions we use one uncorrelated function and five explicitly correlated basis sets in Hylleraas coordinates with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback–Leibler entropy, Tsallis entropy, disequilibrium and Fisher–Shannon complexity, as a function of r0$$ {r}_0 $$. We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. As expected these entropic measures are less sensitive to electron correlation in the strong confinement regime (r0<1$$ {r}_0<1 $$ a.u.). Tsallis entropy for the helium atom confined in a spherical impenetrable cavity with electronic correlation.