Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

It is broadly recognized that intramolecular electric fields, produced by the protein scaffold and acting on the active site, facilitate enzymatic catalysis. This field effect can be described by several theoretical models, each of which is intuitive to varying degrees. In this contribution, we show that a fundamental effect of electric fields is to generate electrostatic potentials that facilitate the energetic alignment of reactant frontier orbitals. We apply this model to demystify the impact of electric fields on high-valent iron–oxo heme proteins: catalases, peroxidases, and peroxygenases/monooxygenases. Specifically, we show that this model easily accounts for the observed field-induced changes to the spin distribution within peroxidase active sites and explains the transition between epoxidation and hydroxylation pathways seen in Cytochrome P450 active site models. Thus, for the intuitive interpretation of the chemical effect of the field, the strategy involves analyzing the response of the orbitals of active site fragments, and their energetic alignment. We note that the energy difference between fragment orbitals involved in charge redistribution acts as a measure for the chemical hardness/softness of the reactive complex. This measure, and its sensitivity to electric fields, offers a single parameter model from which to quantitatively assess the effects of electric fields on reactivity and selectivity. Thus, the model provides an additional perspective to describe electrostatic preorganization and offers ways for its manipulation.

The nascent field of computationally aided molecular design will be built around the ability to make computation useful to synthetic chemists who draw on their empirically based chemical intuition to synthesize new and useful molecules. This fact poses a dilemma, as much of existing chemical intuition is framed in the language of chemical bonds, which are pictured as possessing physical properties. Unfortunately, it has been posited that calculating these bond properties is impossible because chemical bonds do not exist. For much of the computationalchemistry community, bonds are seen as mythical—the unicorns of the chemical world. Here, we show that this is not the case. Using the same formalism and concepts that illuminated the atoms in molecules, we shine light on the bonds that connect them. The real space analogue of the chemical bond becomes the bond bundle in an extended quantum theory of atoms in molecules (QTAIM). We show that bond bundles possess all the properties typically associated with chemical bonds, including an energy and electron count. In addition, bond bundles are characterized by a number of nontraditional attributes, including, significantly, a boundary. We show, with examples drawn from solid state and molecular chemistry, that the calculated properties of bond bundles are consistent with those that nourish chemical intuition. We go further, however, and show that bond bundles provide new and quantifiable insights into the structure and properties of molecules and materials.

Enzymes host active sites inside protein macromolecules, which have diverse, often incredibly complex, and atom-expensive structures. It is an outstanding question what the role of these expensive scaffolds might be in enzymatic catalysis. Answering this question is essential to both enzymology and the design of artificial enzymes with proficiencies that will match those of the best natural enzymes. Protein rigidifying the active site, contrasted with the dynamics and vibrational motion promoting the reaction, as well as long-range electrostatics (also known as electrostatic preorganization) were all proposed as central contributions of the scaffold to the catalysis. Here, we show that all these effects inevitably produce changes in the quantum mechanical electron density in the active site, which in turn defines the reactivity. The phenomena are therefore fundamentally inseparable. The geometry of the electron density-a scalar field characterized by a number of mathematical features such as critical points-is a rigorous and convenient descriptor of enzymatic catalysis and a reporter on the role of the protein. We show how this geometry can be analyzed, linked to the reaction barriers, and report in particular on intramolecular electric fields in enzymes. We illustrate these tools on the studies of electrostatic preorganization in several representative enzyme classes, both natural and artificial. We highlight the forward-looking aspects of the approach.

Bond bundle analysis is used to investigate enzymatic catalysis in the ketosteroid isomerase (KSI) active site. We identify the unique bonding regions in five KSI systems, including those exposed to applied oriented electric fields and those with amino acid mutations, and calculate the precise redistribution of electron density and other regional properties that accompanies either enhancement or inhibition of KSI catalytic activity. We find that catalytic enhancement results from promoting both inter-and intra-molecular electron density redistribution, between bond bundles and bond wedges within the KSI-docked substrate molecule, in the forward direction of the catalyzed reaction. Though the redistribution applies to both types of perturbed systems and is thus suggestive of a general catalytic role, we observe that bond properties (e.g., volume vs energy vs electron count) can respond independently and disproportionately depending on the type of perturbation. We conclude that the resulting catalytic enhancement/inhibition proceeds via different mechanisms, where some bond properties are utilized more by one type of perturbation than the other. Additionally, we find that the correlations between bond wedge properties and catalyzed reaction barrier energies are additive to predict those of bond bundles and atomic basins, providing a rigorous grounding for connecting changes in local charge density to resulting shifts in reaction barrier energy.

The fundamental construct of organic chemistry involves understanding molecular behavior through functional groups. Much of computational chemistry focuses on this very principle, but metallic materials are rarely analyzed using these techniques owing to the assumption that they are delocalized and do not possess inherent functionality. In this paper, we propose a methodology that recovers functional groups in metallic materials from an energy perspective. We characterize neighborhoods associated with functional groups in metals by observing the evolution of Bader energy of the central cluster as a function of cluster size. This approach can be used to conceptually decompose metallic structure into meaningful chemical neighborhoods allowing for localization of energy-dependent properties. The generalizability of this approach is assessed by determining neighborhoods for crystalline materials of different structure types, and significant structural defects such as grain boundaries and dislocations. In all cases, we observe that the neighborhood size may be universal-around 2-3 atomic diameters. In its practical sense, this approach opens the door to the application of chemical concepts, e.g., orbital methods, to investigate a broad range of metallurgical phenomena, one neighborhood at a time.

For the better part of a century researchers across disciplines have sought to explain the crystallography of the elemental transition metals: hexagonal close packed, body centered cubic, and face centered cubic in a form similar to that used to rationalize the structure of organic molecules and inorganic complexes. Pauling himself tried with limited success to address the origins of transition metal stability. These early investigators were handicapped, however, by incomplete knowledge regarding the structure of metallic electron density. Here, we exploit modern approaches to electron density analysis to first comprehensively describe transition metal electron density. Then, we use topological partitioning and quantum mechanically rigorous treatments of kinetic energy to account for the structure of the density as arising from the interactions between metallic polyhedra. We argue that the crystallography of the early transition metals results from charge transfer from the so called “octahedral” to “tetrahedral cages” while the face centered cubic structure of the late transition metals is a consequence of anti-bonding interactions that increase octahedral hole kinetic energy.

A novel form of charge density analysis, that of isosurface curvature redistribution, is formulated and applied to the toy problem of carbonyl oxygen activation in formaldehyde. The isosurface representation of the electron charge density allows us to incorporate the rigorous geometric constraints of closed surfaces towards the analysis and chemical interpretation of the charge density response to perturbations. Visual inspection of 2D isosurface motion resulting from applied external electric fields reveals how isosurface curvature flows within and between atoms, and that a molecule can be uniquely and completely partitioned into chemically significant regions of positive and negative curvature. These concepts reveal that carbonyl oxygen activation proceeds primarily through curvature and charge redistribution within rather than between Bader atoms. Using gradient bundle analysis—the partitioning of formaldehyde into infinitesimal volume elements bounded by QTAIM zero flux surfaces—the observations from visual isosurface inspection are verified. The results of the formaldehyde carbonyl analysis are then shown to be transferable to the substrate carbonyl in the ketosteroid isomerase enzyme, laying the groundwork for extending this approach to the problems of enzymatic catalysis.

Bond bundles are chemical bonding regions, analogous to Bader atoms, uniquely defined according to the topology of the gradient bundle condensed charge density, itself obtained by a process of infinitesimal partitioning of the three-dimensional charge density into differential zero-flux surface bounded regions. Here we use bond bundle analysis to investigate the response of the charge density to an oriented electric field in general, and the catalytic effect of such a field on Diels-Alder reactions in particular, which in this case is found to catalyze by allowing the transition state valance bond bundle configuration to be achieved earlier along the reaction pathway. Using precise numerical values, we arrive at the conclusion that chemical reactions and electric field catalysis can be understood in terms of intra-atomic charge density redistribution, i.e., that charge shifts within more so than between atoms account for the making and breaking of bonds.

Our quest to design materials often envisions as a first step the conceptual decomposition of a material into meaningful atomic scale neighborhoods. The performance of the monolithic material is then seen to arise from the combined properties of these much simpler regions. It is the nearsightedness of electronic matter (NEM) principle that provides the rigorous justification for this "divide and conquer" approach. NEM asserts that a material property may be significantly affected by a perturbation, no matter how large, only over a neighborhood of size $R$. Though NEM posits the existence of meaningful atomic scale neighborhoods, for the most part these regions are identified empirically. In this paper we propose a methodology to divide real materials into meaningful neighborhoods determined by the topology of the charge density. We generalize this approach by applying the same to determine neighborhoods representative of elemental crystalline materials and then use these neighborhoods to model the embrittling effects of bismuth atoms segregated to copper grain boundaries. We show that embrittlement is the result of impurity atom-induced enhancements of copper nearsightedness. We further suggest that just as nearsightedness plays an overlooked role mediating embrittlement, it may also be an important factor affecting a broad range of unresolved problems as apparently diverse as energy focussing phenomena and enzyme kinetics.

Normally tough structural materials may  fail catastrophically when contaminated with even minuscule quantities of ubiquitous elements such as sulfur, phosphorus or hydrogen.  These so called embrittling elements exert their influence at the tip of atomically sharp cracks where applied stress is concentrated to a degree given by the stress concentration factor.  When the concentrated stress exceeds the strength of the bonds across the crack tip, the crack will run.  Hence, an element may  embrittle a host either by decreasing bond strength and/or increasing the stress concentration.  While the effects of embrittling elements on the earlier have been extensively studied, less attention has been directed to their effects on the latter.  Here we exploit the nearsightedness of electronic matter principle to provide a measure of the stress concentration factor and study its changes in the presence of a known embrittling element.  We find that for the well studied system of copper embrittled by dilute quantities of bismuth, bismuth atoms increase the  crack tip stress concentration  by more than 60%

By leveraging the fundamental doctrine of the quantum theory of atoms in molecules — the partitioning of the electron charge density (ρ) into regions bounded by surfaces of zero flux — we map the gradient field of ρ onto a two-dimensional space called the gradient bundle condensed charge density ([Formula: see text]). The topology of [Formula: see text] appears to correlate with regions of chemical significance in ρ. The bond wedge is defined as the image in ρ of the basin of attraction in [Formula: see text], analogous to the Bader atom, which is the basin of attraction in ρ. A bond bundle is defined as the union of bond wedges that share interatomic surfaces. We show that maxima in [Formula: see text] typically map to bond paths in ρ, though this is not necessarily always true. This observation addresses many of the concerns regarding the chemical significance of bond critical points and bond paths in the quantum theory of atoms in molecules.

Our curiosity-driven desire to "see" chemical bonds dates back at least one-hundred years, perhaps to antiquity. Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric understanding of molecules and materials, heighten this desire with means and significance. Here we present a method for analyzing chemical bonds and their energy distributions in a two-dimensional projected space called the condensed charge density. Bond "silhouettes" in the condensed charge density can be reverse-projected to reveal precise three-dimensional bonding regions we call bond bundles. We show that delocalized metallic bonds and organic covalent bonds alike can be objectively analyzed, the formation of bonds observed, and that the crystallographic structure of simple metals can be rationalized in terms of bond bundle structure. Our method also reproduces the expected results of organic chemistry, enabling the recontextualization of existing bond models from a charge density perspective.

Our curiosity-driven desire to chemical bonds dates back at least one-hundred years, and perhaps back to antiquity. This desire has taken on a more practical significance as our ability to measure and predict the electron charge density continues to grow. Because the properties of molecules and materials are largely understood in terms of their bonds, gaining the ability to see chemical bonds within the charge density---a feat some insist is unattainable---would best leverage our current understanding and capabilities. Here we report the discovery of a 2D projected space, with well-defined mathematical properties, onto which a chemical bond casts an unmistakable shadow. Following the shadow back to its source in the charge density reveals the bond itself, called a bond bundle, with a precise boundary and energy. In this way, delocalized metallic bonds and organic covalent bonds alike can be objectively analyzed, compared, and visualized. The making and breaking of bonds can also be observed. We have found that our method reproduces the expected results of organic chemistry, enabling the recontextualization of existing bond models from a charge density perspective. More significantly, we go beyond the scope of chemistry by demonstrating that the crystallographic structure of simple metals can be rationalized in terms of bond bundle structure.

Large protein macromolecules in enzymatic catalysis have been shown to exert a specific electric field that reduces the reorganization energy upon barrier crossing and thus reduces the reaction free energy barrier. In this work we suggest that the charge density in the active site of an enzyme investigated using formalisms embodied by the quantum theory of atoms in molecules (QTAIM) provides a sensitive and quantum mechanically rigorous probe of electrostatic preorganization. We focus on the active site of ketosteroid isomerase, a well-studied enzyme for which electrostatic preorganization has been modeled theoretically and studied experimentally. We study the charge density in the active site and the reaction mechanism in the presence of small external electric fields of various directions and magnitudes. We show that the geometry of the full charge density is a sensitive reporter on the external field experienced by the active site. Changes are observed in the relative positions of critical points and amount of charge at critical points as a function of the field. At the same time, a subset of these features correlates linearly with the barrier of the first reaction step in catalysis. Small changes in the barrier, within 1-2 kcal/mol, are reflected in the charge density, suggesting the existence of a field - reactant state charge density - reaction barrier correlation. Hence, QTAIM can be used for the analysis of electric field in enzyme active sites, and further investigations and exploitations of the found correlations may prove useful in enzyme design where preorganization is optimized.

The Cover Feature depicts the formation and evolution of the boron-nitrogen bond bundle as borane and ammonia react to form H3B-NH3. More information can be found in the Article by T. R. Wilson et al. on page 3289 in Issue 24, 2019 (DOI: 10.1002/cphc.201900962).

For nearly a century chemical understanding has been tied to the properties of bonds, although more often than not, these bond properties are rooted in molecular orbital or valence bond representations of the electronic structure. Technological advances, however, are allowing for experimental measurements of the density via high resolution X-ray diffraction, while theoretical insights are opening the door to its direct calculation using fast and potentially versatile orbital free DFT methods. Capitalizing on these emerging tools without sacrificing orbital derived understanding has spurred a search for density based representations that deliver the same information available from the orbital perspective. We show that recent extensions of the QTAIM formalism are useful as a means of recovering some of the bond properties that have become an intrinsic part of our chemical understanding. Specifically, we compute from the density the changing bond order and bond order distribution accompanying the rotation about a double bond using the well-studied fulvene molecule as a test case. We compare the picture that emerges from this density based perspective with that stemming from molecular orbital approaches and argue that the two viewpoints are compatible.

In the traditional view, covalently bound materials differ in a fundamental way from metallic substances. Though both are built from more basic units that are, in turn, constructed from a small number of atoms, for these two materials classes the nature of these units is thought to be quite different. For covalent solids and liquids, these units are considered to be molecular, meaning that they possess properties and bonding that are retained in the condensed phase and thus they continue to be identifiable within the larger system. For metallic materials, these basic units are considered to be mere constructs that are not observable against the delocalized bonding of metals or alloys. The perceived dissimilarity of metallic and covalently bound materials has fostered distinctly different approaches to their design and improvement. Here, the delocalized view of metallic bonding is examined. This examination suggests that much of the rationale used in the design of molecular materials my be applied to metals and alloys as well.

Electrostatic preorganization is thought to be a principle factor responsible for the impressive catalytic capabilities of enzymes. The full protein structure is believed to facilitate catalysis by exerting a highly specific electrostatic field on the active site. Computationally determining the extent of electrostatic preorganization is a challenging process. We propose using the topology and geometry of the electron charge density in the enzyme's active site to asses the effects of electrostatic preorganization. In support of this approach we study the convergence of features of the charge density as the size of the active site model increases in Histone Deacetylase 8. The magnitude of charge density at critical points and most Bader atomic charges are found to converge quickly as more of the protein is included in the simulation. The exact position of critical points however, is found to converge more slowly and be strongly influenced by the protein residues that are further away from the active site. We conjecture that the positions of critical points are affected through perturbations to the wavefunctions in the active site caused by dipole moments from amino acid residues throughout the protein. We further hypothesize that electrostatic preorganization, from the point of view of charge density, can not be easily understood through the charges on atoms or the nature of the bonding interactions, but through the relative positions of critical points that are known to correlate with reactivity and reaction barriers.