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Abstract
Modern quantum chemistry can make quantitative predictions on an immense array of
chemical systems. However, the interpretation of those predictions is often complicated
by the complex wave function expansions used. Here we show that an exceptionally simple
algebraic construction allows for defining atomic core and valence orbitals, polarized
by the molecular environment, which can exactly represent self-consistent field wave
functions. This construction provides an unbiased and direct connection between quantum
chemistry and empirical chemical concepts, and can be used, for example, to calculate
the nature of bonding in molecules, in chemical terms, from first principles. In particular,
we find consistency with electronegativities (χ), C 1s core-level shifts, resonance
substituent parameters (σR), Lewis structures, and oxidation states of transition-metal
complexes.