A proposed parametric quantum method based on q-exponential functions

Abstract

Fundamental issues of quantum chemistry related with parametric quantum methods (PQMs), such as, set of elementary functionals (SEF), exact energy functional, and minimax principle (MMP) are discussed in terms of elementary functionals (EF). In this work, it is shown the possibility of PQM development based on two-centers parametric elementary functionals (PEFs) obtained from simulation of analytical EFs, using q-exponential (QE) type functions. All electrons are included and NDO approximations are not considered. Comparison between analytical and PEF for H-H, C-C and C-H pairs of atoms are performed and very reasonable modeling of intraatomic ${\mathit{H}}_{\mathit{core}}$ (IH), electron-nucleus potential (V), overlap (S), and Coulomb two-center (G) integrals were obtained. Four- and three-center are proposed to be calculated by Mayer’s partition energy (MPE) approximation in terms of one- and two-centers PEFs. Trials for small molecules using PEFs and for MPE approach are presented and a scheme for a new PQM is proposed.