We introduce new and robust decompositions of mean-field Hartree–Fock and Kohn–Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure–property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.
The reason for this is that the centre of the electronic density associated with a given atom (of which the partial charge is the essential measured quantity) will not necessarily coincide with the corresponding nuclear coordinates, e.g., when constituent atoms carry lone pairs.
In the iterative optimization of IBOs used in the present work, a PM localization power (p = 2) has been used throughout, cf. Appendix D of Ref. 178.
The choice of IAO over Mulliken partial charges are justified in Fig. S6 of the supplementary material, in which the former are shown to vary continuously along the symmetric stretch in H2O while also giving rise to smoothly varying atom-RDM1s.