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Tsallis q ‐exponentials as atomic orbitals in two‐electron systems
Author(s) -
Lombardo Giuseppe Marcello
Publication year - 2021
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26489
Subject(s) - atomic orbital , exponential function , gaussian , basis set , electron , exponential type , physics , atomic physics , quantum mechanics , statistical physics , mathematics , mathematical analysis , molecule
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 ≥ E 0, with E 0 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.