Topological and AIM analyses beyond the Born-Oppenheimer paradigm: New   opportunities
  The multi-component quantum theory of atoms in molecules (MC-QTAIM) analysis is done on methane, ethylene, acetylene and benzene as selected basic hydrocarbons. This is the first report on applying the MC-QTAIM analysis on polyatomic species. In order to perform the MC-QTAIM analysis, at first step the nuclear-electronic orbital method at Hartree-Fock level (NEO-HF) is used as a non-Born-Oppenheimer (nBO) ab initio computational procedure assuming both electrons and protons as quantum waves while carbon nuclei as point charges in these systems. The ab initio calculations proceed substituting all the protons of each species first with deuterons and then tritons. At the next step, the derived nBO wavefunctions are used for the "atoms in molecules" (AIM) analysis. The results of topological analysis and integration of atomic properties demonstrate that the MC-QTAIM is capable of deciphering the underlying AIM structure of all the considered species. Also, the results of the analysis for each isotopic composition are distinct and the fingerprint of the mass difference of hydrogen isotopes is clearly seen in both topological and AIM analyses. This isotopic distinction is quite unique in the MC-QTAIM and not recovered by the orthodox QTAIM that treats nuclei as clamped particles. The results of the analysis also demonstrate that each quantum nucleus that forms an atomic basin resides within its own basin. The confinement of quantum nuclei within a single basin is used to simplify the basic equations of the MC-QTAIM paving the way for future theoretical studies. 
Mohammad Goli and Shant Shahbazian
physics.chem-ph