Whither the density in DFT calculations?: The continuing development of density functional theory (DFT) has greatly expanded the size and complexity of molecules amenable to computationally tractable simulation. The conventional metric of success for new functionals has been the accuracy of their calculated energies. Medvedev et al. examined how well these functionals calculate electron density across a series of neutral and cationic atoms (see the Perspective by Hammes-Schiffer). Although historically the accuracies of energy and density have improved in tandem, certain recent functionals have sacrificed fidelity to the true density. Science , this issue p. 49 ; see also p. 28

Understanding the interplay of multiple components (steric, electrostatic, stereoelectronic, dispersive, etc.) that define the overall energy, structure, and reactivity of organic molecules can be a daunting task. The task becomes even more difficult when multiple approaches based on different physical premises disagree in their analysis of a multicomponent molecular system. Herein, we will use a classic conformational “oddity”, the anomeric effect, to discuss the value of identifying the key contributors to reactivity that can guide chemical predictions. After providing the background related to the relevant types of hyperconjugation and a brief historic outline of the origins of the anomeric effect, we outline variations of its patterns and provide illustrative examples for the role of the anomeric effect in structure, stability, and spectroscopic properties. We show that the complete hyperconjugative model remains superior in explaining the interplay between structure and reactivity. We will use recent controversies regarding the origin of the anomeric effect to start a deeper discussion relevant to any electronic effect. Why are such questions inherently controversial? How to describe a complex quantum system using a model that is “as simple as possible, but no simpler”? What is a fair test for such a model? Perhaps, instead of asking “who is right and who is wrong?” one should ask “why do we disagree?”. Stereoelectronic thinking can reconcile quantum complexity with chemical intuition and build the conceptual bridge between structure and reactivity. Even when many factors contribute to the observed structural and conformational trends, electron delocalization is a dominating force when the electronic demand is high (i.e., bonds are breaking as molecules distort from their equilibrium geometries). In these situations, the role of orbital interactions increases to the extent where they can define reactivity. For example, negative hyperconjugation can unleash the “underutilized” stereoelectronic power of unshared electrons (i.e., the lone pairs) to stabilize a developing positive charge at an anomeric carbon. This analysis paves the way for the broader discussion of the omnipresent importance of negative hyperconjugation in oxygen-containing functional groups. From that point of view, the stereoelectronic component of the anomeric effect plays a unique role in guiding reaction design.

Although carbon is the central element of organic chemistry, oxygen is the central element of stereoelectronic control in organic chemistry. Generally, a molecule with a C–O bond has both a strong donor (a lone pair) and a strong acceptor (e.g., a σ*_C–O orbital), a combination that provides opportunities to influence chemical transformations at both ends of the electron demand spectrum. Oxygen is a stereoelectronic chameleon that adapts to the varying situations in radical, cationic, anionic, and metal-mediated transformations. Arguably, the most historically important stereoelectronic effect is the anomeric effect (AE), i.e., the axial preference of acceptor groups at the anomeric position of sugars. Although AE is generally attributed to hyperconjugative interactions of σ-acceptors with a lone pair at oxygen (negative hyperconjugation), recent literature reports suggested alternative explanations. In this context, it is timely to evaluate the fundamental connections between the AE and a broad variety of O-functional groups. Such connections illustrate the general role of hyperconjugation with oxygen lone pairs in reactivity. Lessons from the AE can be used as the conceptual framework for organizing disjointed observations into a logical body of knowledge. In contrast, neglect of hyperconjugation can be deeply misleading as it removes the stereoelectronic cornerstone on which, as we show in this review, the chemistry of organic oxygen functionalities is largely based. As negative hyperconjugation releases the “underutilized” stereoelectronic power of unshared electrons (the lone pairs) for the stabilization of a developing positive charge, the role of orbital interactions increases when the electronic demand is high and molecules distort from their equilibrium geometries. From this perspective, hyperconjugative anomeric interactions play a unique role in guiding reaction design. In this manuscript, we discuss the reactivity of organic O-functionalities, outline variations in the possible hyperconjugative patterns, and showcase the vast implications of AE for the structure and reactivity. On our journey through a variety of O-containing organic functional groups, from textbook to exotic, we will illustrate how this knowledge can predict chemical reactivity and unlock new useful synthetic transformations.

Kepp argues in his Comment, among other concerns, that the atomic densities we have considered are not relevant to molecular bonding. However, this does not change the main conclusion of our study, that unconstrained fitting of flexible functional forms can make a density functional more interpolative but less widely predictive.