The quantum theory of atoms in molecules (QTAIM) as originally formulated Prof. R.F.W. Bader and coworkers is a successful method for computing atomic properties within a nonrelativistic quantum mechanical framework.[1] Prof. R.F.W. Bader and coworkers showed that QTAIM satisfies the Schwinger principle of stationary action and as such justifying its utility for computing atomic properties in a nonrelativistic setting. [1, 2] Relativity is critical when computing properties of chemical systems that include nuclei with atomic number larger than 37.[3] It has been demonstrated how to formulate QTAIM to include relativistic effects in defining a proper quantum subsystem that satisfies Schwinger's principle of stationary action for the Scalar-Relativistic Zeroth-Order Regular Approximation (SR-ZORA) Hamiltonian.[4-6] Given that the concept of an atom in a molecule is satisfied even when relativistic corrections are included a more practical question remains: What level of theory is needed to obtain an accurate computation of a property?
This of course means, what level of relativity, correlation method, and basis set is needed to for a reliable calculation of a property? In this presentation, the formulation of QTAIM from the Schwinger Principle at the nonrelativistic and SR-ZORA level of theory will be reviewed. Several properties at different levels of theory will be shown and provide intuition to properties that are sensitive to scalar-relativistic corrections, electron correlation, or both.[7]

1. Bader RFW (1990) Atoms in Molecules: A Quantum Theory. Clarendon, Oxford
2. Bader RFW, Nguyen-Dang TT (1981) Quantum-Theory of Atoms in Molecules - Dalton Revisited. 14:63-124
3. Dyall KG, - (2007) Introduction to relativistic quantum chemistry. Oxford University Press, New York
4. Anderson JSM, Ayers PW (2011) Quantum Theory of Atoms in Molecules: Results for the SR-ZORA Hamiltonian. J. Phys. Chem. A 115:13001-13006
5. Anderson JSM, Ayers PW (2018) The general setting for the zero-flux condition: The Lagrangian and zero-flux conditions that give the Heisenberg equation of motion. J. Comp. Chem. 39:1051-1058
6. Anderson JSM (2023) In:J. I. Rodríguez, F. Cortés-Guzmán and J. S. M. Anderson (eds) Advances in Quantum Chemical Topology Beyond QTAIM, Elsevier, Amsterdam, Netherlands
7. Jimenéez-Rosas CAS, Kawasaki A, Anderson JSM (2026) Disentangling the competing effects of relativity, correlation, and basis function the electron density's topology: The impacts on an atom in a molecule. In Preparation for J. Chem. Theory and Comput.