Informational energy as a measure of electron correlation

Rényi's divergence as a chemical similarity criterion

In this work, a new version of Rényi's divergence is presented. The expression obtained is used as a tool to identify molecules that could share some chemical or structural properties, and a data basis set of 1641 molecules is used in this study. Our results suggest that this new form of Rényi divergence could be a useful tool that will eventually permit complementary studies in which the main goal is to obtain molecules with similar properties.

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

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 .

Generalized Shannon’s entropies in position and momentum spaces

In this report, we present three generalized expressions of Shannon’s entropy using the electron densities of position and momentum spaces. Such expressions were obtained using the definition of deformed logarithm introduced by Tsallis. We show that only one expression fulfils the dimensionless criterion, it is strictly positive overall space and follows a growing behavior with respect to the electron number. We also found that by using some values of [Formula: see text], it is possible to reproduce the general trends of the radial distribution in position space and momentum space of the neon atom.