Chemical Information From the Ehrenfest Force Field Based on Reduced Density Matrix Functional Theory

The Ehrenfest force (EhF) field, which acts on the electron distribution of molecules, offers a force-based framework to probe chemical bonding beyond conventional energy or orbital perspectives. However, its evaluation from correlated wavefunction methods is computationally demanding, limiting applications to small systems. Here we assess Reduced Density Matrix Functional Theory (RDMFT) as an alternative approach to approximate the exchange-correlation contribution to the EhF field. The Fock-Dirac approximation to the pair density from Kohn-Sham pseudo-determinants is also tested. Using a range of natural orbital functionals, we perform a topological analysis of the EhF and its exchange-correlation component in representative molecules from simple diatomics to polyatomic systems. Results show that RDMFT successfully reproduces essential features of the exact force field, including covalent basins and directional bonding patterns, while highlighting limitations in strongly correlated cases. This work establishes RDMFT-based approximations as a practical route to extend the applicability of Ehrenfest force analysis to larger and more complex molecular systems.