Core-valence stockholder AIM analysis and its connection to nonadiabatic effects in small molecules

A previous theory of separation of motions of core and valence fractions of electrons in a molecule [J. R. Mohallem et al., Chem. Phys. Lett. 501, 575 (2011)] is invoked as basis for the useful concept of Atoms-in-Molecules (AIM) in the stockholder scheme. The output is a new tool for the analysis of the chemical bond that identifies core and valence electron density fractions (core-valence stockholder AIM (CVSAIM)). One-electron effective potentials for each atom are developed, which allow the identification of the parts of the AIM which move along with the nuclei (cores). This procedure results in a general method for obtaining effective masses that yields accurate non-adiabatic corrections to vibrational energies, necessary to attain cm^-1 accuracy in molecular spectroscopy. The clear-cut determination of the core masses is exemplified for either homonuclear (H₂⁺, H₂) or heteronuclear (HeH⁺, LiH) molecules. The connection of CVSAIM with independent physically meaningful quantities can resume the question of whether they are observable or not.