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

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.