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Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

by Jen-Hao Ou 1,2,* and Yew Kam Ho 1
1
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
2
Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
*
Author to whom correspondence should be addressed.
Atoms 2019, 7(3), 70; https://doi.org/10.3390/atoms7030070
Received: 10 June 2019 / Revised: 5 July 2019 / Accepted: 11 July 2019 / Published: 18 July 2019
Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α . View Full-Text
Keywords: Shannon entropy; Rényi entropy; Tsallis entropy; Onicescu information energy; singly excited states; helium; Hylleraas wave functions; singlet–triplet reversal Shannon entropy; Rényi entropy; Tsallis entropy; Onicescu information energy; singly excited states; helium; Hylleraas wave functions; singlet–triplet reversal
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Ou, J.-H.; Ho, Y.K. Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium. Atoms 2019, 7, 70.

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