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On the information obtained using Shannon’s entropy through spin density

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Abstract

In this work, we analyze the reaction \(H_{2} + H\) using Shannon’s entropy defined in terms of spin density in position and momentum spaces. We analyzed the changes in the trends obtained in terms of the first derivative of Shannon’s entropy with respect to the electron number and with respect to spin density, in the first case, we show that this result is related to Fukui’s function, while in the second case, we found that the functional derivative is related to the so-called generalized moments.

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Notes

  1. In previous work we had discussed aspects of several definitions of joint probability and conditional probability, in which we suggest that there is no a definitive definition on them, see Ref. [76].

  2. It is important to mention that in Eqs. (17) and (18) were written with the consideration of \(Q(\textbf{r})\) and \(Q(\textbf{q})\) are greater that zero, otherwise the numerical calculations are not possible. In such cases, one could use the following expressions, \(S_{r}^{\alpha \beta } = -\frac{1}{k_{Qr_{\max }}} \int \left| \left( \frac{Q(\textbf{r})}{Qr_{\max }}\right) \right| \ln \left| \left( \frac{Q(\textbf{r})}{Qr_{\max }}\right) \right| d\textbf{r}\), and \(S_{q}^{\alpha \beta } = -\frac{1}{k_{Qq_{\max }}} \int \left| \left( \frac{Q(\textbf{q})}{Qq_{\max }}\right) \right| \ln \left| \left( \frac{Q(\textbf{q})}{Qq_{\max }}\right) \right| d\textbf{q}\).

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Acknowledgements

The author wishes to thank the CONACyT, the PRODEP-SEP program for support.

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  1. Centro Universitario de los Valles, Universidad de Guadalajara, Carretera Guadalajara - Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, Mexico

    N. Flores-Gallegos

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NFG, wrote the manuscript, performed all the calculations, and did all the figures. The author reviewed the manuscript.

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Flores-Gallegos, N. On the information obtained using Shannon’s entropy through spin density. J Math Chem 61, 1532–1544 (2023). https://doi.org/10.1007/s10910-023-01481-9

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