Quantum Chemistry has reached a state where most physical properties of molecules can be easily and accurately calculated—for example, DFT calculations of molecular structure, reaction mechanisms, and reaction energetics have become routine complements to organic chemistry.
However, the techniques behind these calculations afford no easy way of "making sense" of the computed quantities, like orbitals and wave functions. Additionally, many central empirical concepts of chemistry, including concepts as basic as partial charges, bond orders, or even covalent bonds themselves, have no consensus physical definition.
In the ab initio community, the connection between calculations and empirical concepts has therefore long been ignored, if not straight out denied. We here argue that, once we properly define what is an "atomic orbital" in a molecule, quantities representing most other empirical concepts can be straight-forwardly derived from simple physical arguments, and then easily calculated. In this sense, we show how our Intrinsic Atomic Orbital (IAO) technique gives rise to partial charges and bond orders, and to bond orbitals, which represent the electron pairs of Lewis structures (σ- and π-bonds). Even curly-arrow reaction mechanisms can be readily derived!
Based on selected examples of both us and others, we how IAOs allow the analysis of bonding in novel and exotic chemical species, and how the method played a key role in understanding metal-catalyzed reaction mechanisms.