The two-component quantum theory of atoms in molecules (TC-QTAIM): tensor formulation and its implications

In this contribution, the tensor formulation of the two-component quantum theory of atoms in molecules is addressed in detail. The subsystem hypervirial and the regional atomic theorems are presented in their local forms enabling one to introduce the tensor formulation easily. Accordingly, the two-component force, virial, torque, power, current and continuity theorems are introduced. Then, by proposing a model wavefunction for quantum nuclei, the nuclear stress tensor density is analytically evaluated. Based on the derived analytical stress tensor density, the regional nuclear properties are also computed analytically and their asymptotic trend at the infinite nuclear mass limit is inspected. It is demonstrated that in the infinite nuclear mass limit, the nuclear contribution in basin properties is null, while electronic contributions reduce to that computed within context of the orthodox quantum theory of atoms in molecules. Subsequently, the regional energies as well as the regional components of the potential energy are derived for two-component systems. The computed analytical equation for the nuclear contribution in basin energies is of particular importance. Finally, the electric dipole moment of a typical two-component system is decomposed into electronic/nuclear charge transfer and polarization contributions revealing the fine structure of the charge density distribution for both electrons and quantum nuclei.