Tsallis q‐exponentials as atomic orbitals in two‐electron systems

• Published in: International journal of quantum chemistry 2021-03, Vol.121 (5), p.n/a
• Main Author: Lombardo, Giuseppe Marcello
• Format: Article
• Language: English
• Subjects: atomic orbitals; Chemistry; Correlation analysis; correlation energy; Entropy (Information theory); Exact solutions; Exponential functions; he‐like ions; Mathematical analysis; Orbitals; Parameters; Physical chemistry; Quantum physics; Shannon entropy
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.26489

The use of simple q‐exponential functions, derived from Tsallis entropy distribution, as basis set of atomic orbitals, is explored within the non‐relativistic limit. As compared to Gaussian or to STO (Slater type orbitals) basis set, considering q as variational parameter, q‐exponentials functions lower considerably the energy of two electron systems, always respecting the Ritz variation principle, where E ≥ E0, with E0 being the true energy. The q parameter attains the highest value of 1.209 for Z = 1 (H−) slowly going down toward 1 as Z grows (for Z = 36 q = 1.005225, Kr+34). Interestingly, the correlation energy as determined considering the exact solution by the calculations of Pekeris with the current ones, shows a regular variation as a function of the q parameter. Moreover, the study confirms the link between correlation energy and Shannon information entropy. Use of Tsallis q‐exponential functions as atomic orbitals is explored on two‐electron systems within the independent particle model. It is shown that these functions bring to a good description of these atoms and ions with the possibility to attain electron correlation energy models dependent on the q parameter that finely reproduce the correlation energy of these systems.