Pedro Salvador

Classical chemical concepts—such as the chemical bond, oxidation state, aromaticity, donor–acceptor interactions—are inherently heuristic. While they lack precise, mathematically defined formulations, they remain indispensable for describing, rationalizing, and predicting chemical behavior. This duality represents a fundamental challenge: bridging the conceptual language of chemistry with the rigorous formalism of quantum chemistry. In this work, we discuss the use of effective fragment orbitals (EFOs) and their occupations as a powerful and versatile tool to address this gap. The EFOs generalize Mayer's effective atomic orbitals (eff-AOs) to molecular fragments, providing a direct orbital-level representation of fragment-based electron density from the molecular wavefunction, without any additional fragment reference calculations. By analyzing the EFOs and their associated occupation numbers, we obtain a rigorous yet chemically intuitive picture of electronic structure. We will show that key chemical concepts can be quantitatively extracted from this framework, including oxidation states via spin-resolved EFO populations, donor–acceptor interactions, inductive and mesomeric effects as distinct orbital interaction patterns induced by substituents, mechanistic rationalization of reaction pathways, and electronic structure features relevant to spin-crossover properties. By translating qualitative chemical concepts into well-defined orbital descriptors, EFOs offer a unified language that connects chemical intuition with first-principles quantum chemistry.