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

Abstract

AbstractThe 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.