A relationship between atomic correlation energy of neutral atoms and generalized entropy

Abstract

In a previous article, hereafter named as Paper I, we have showed a relationship between atomic correlation energy of neutral atoms with 2 < Z < 29 and Tsallis entropy. In this article, we generalize this relation showing the link between the atomic correlation energy and a general form of entropy obtained from deformed algebra. The results evidence the role of both q and D parameters of the general entropy, in terms of contribution of the long-range interactions in the correlation energy. The q and D values, obtained as best fit of the atomic correlation energies 2 < Z < 29, indicate that this general form of entropy reduces to the Tsallis one, reproducing well the trend of the correlation energy for low Z. Moreover, as a consequence of these values of the parameters, the state atomic wave function is more localized with respect to the wave function calculated in the limit of Shannon entropy. V C 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: [2390][2391][2392][2393][2394][2395][2396][2397] 2011 Key words: electron correlation; entropy; deformed algebra W ithin the many-electron theory of atoms, molecules, solids, and so forth, an important consequence of the electron-electron repulsion is the so-called electron-correlation. The energetic measure of the electron-correlation is the correlation energy, defined as the difference between the exact non relativistic total energy and the HartreeFock energy, E c ¼ E exp À E HF . This physical quantity is because of the impossibility to solve analytically the Schrödinger equation for a many-electron system, because of the electron-electron potential V ee . In the framework of the density functional theory (DFT), the simplest approximation for E c is given within the local spin density approximation (LSD):where qðrÞ ¼ q " ðrÞ þ q # ðrÞ is the electron density and e c ðq " ðrÞ; q # ðrÞÞ is the correlation energy per particle of an electron gas with uniform spin-densities q # ðrÞ and q " ðrÞ.

Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

“…In addition, Tsallis statistics emerges in several systems of ultracold atoms . Furthermore, these quantities provide different perspectives to statistic mechanics, entropic uncertainty relations, electron correlation, orbital‐free density functional theory (DFT), and other applications …”

“…[9][10][11][12][13][14][15] In addition, Tsallis statistics emerges in several systems of ultracold atoms. [16][17][18][19] Furthermore, these quantities provide different perspectives to statistic mechanics, [20][21][22][23][24][25][26] entropic uncertainty relations, [27][28][29] electron correlation, [30][31][32][33][34][35][36][37][38][39][40][41] orbital-free density functional theory (DFT), [42,43] and other applications. [44][45][46][47][48][49][50][51][52][53][54] In particular, by treating the electron density as a continuous probability distribution, these quantities are naturally extended to the position space and applied to numerous types of potential [55]…”

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

“…Furthermore, Tsallis statistics is relevant to certain systems of ultracold atoms [124][125][126][127]. Moreover, these IT quantities are applied to investigate electron correlation [30,31,33,39,72,[128][129][130][131][132][133][134][135][136] and various molecular properties as well [28,36,45,48,49,[59][60][61]72,73]. Calculated with the highly correlated Hylleraas wave functions, the results in this work then serve as a useful and reliable reference for the various applications mentioned above.…”

Rényi’s divergence as a chemical similarity criterion

“…In chemistry, the use of the ideas of information theory started in the 1970s, and these studies were principally focused on the study of atoms and simple systems using Shannon's entropy in position and momentum spaces; in the 1990s, with the advantages of computers, it was possible to extend these studies to simple molecules and some simple chemical processes. In this line, it was also possible to show that Shannon's entropy can be related to some important concepts of quantum chemistry, such as the chemical reactivity, electron correlation, and structural stability of the molecules [8][9][10][11][12][13][14][15][16][17].…”