Unicorns, Rhinoceroses and Chemical Bonds.

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.

Geometry of Charge Density as a Reporter on the Role of the Protein Scaffold in Enzymatic Catalysis: Electrostatic Preorganization and Beyond.

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.

Principles Determining the Structure of Transition Metals.

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.

Observing the 3D Chemical Bond and its Energy Distribution in a Projected Space.

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.

Charge Density in Enzyme Active Site as a Descriptor of Electrostatic Preorganization.

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.

Quantified electrostatic preorganization in enzymes using the geometry of the electron charge density.

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.

Nearsightedness of Oxygen-Containing Functional Groups.

Matter is nearsighted, that is, for a fixed chemical potential, the charge density is only sensitive to perturbations within a radius R. While it is known that the resultant change in the density at point r0 from some perturbation at some other point R (Δn(r0,R)) is a monotonically decreasing function, a plausible range of a chemically significant Δn(r0,R) and the value of R needed to cause these perturbations has not been well studied. Using the functional group, which upon satisfying the necessary atoms/bonds specific to that functional group retains a characteristic chemistry, this paper provides an initial study into the magnitude of both Δn and R, the radius beyond which to affect a given property. Values for Δn are shown to be robust across a variety of DFT functionals and provide a framework for the transfer of the functional group concept to other disciplines, such as metallurgy.

Predictive methods for computational metalloenzyme redesign - a test case with carboxypeptidase A.

Computational metalloenzyme design is a multi-scale problem. It requires treating the metal coordination quantum mechanically, extensive sampling of the protein backbone, and additionally accounting for the polarization of the active site by both the metal cation and the surrounding protein (a phenomenon called electrostatic preorganization). We bring together a combination of theoretical methods that jointly offer these desired qualities: QM/DMD for mixed quantum-classical dynamic sampling, quantum theory of atoms in molecules (QTAIM) for the assessment of electrostatic preorganization, and Density Functional Theory (DFT) for mechanistic studies. Within this suite of principally different methods, there are both complementarity of capabilities and cross-validation. Using these methods, predictions can be made regarding the relative activities of related enzymes, as we show on the native Zn2+-dependent carboxypeptidase A (CPA), and its mutant proteins, which are hypothesized to hydrolyze modified substrates. For the native CPA, we replicated the catalytic mechanism and the rate in close agreement with the experiment, giving validity to the QM/DMD predicted structure, the DFT mechanism, and the QTAIM assessment of catalytic activity. For most sequences of the modified substrate and tried CPA mutants, substantially worsened activity is predicted. However, for the substrate mutant that contains Asp instead of Phe at the C-terminus, one CPA mutant exhibits a reasonable activity, as predicted across the theoretical methods. CPA is a well-studied system, and here it serves as a testing ground for the offered methods.

Histone Deacetylase 8: Characterization of Physiological Divalent Metal Catalysis.

Histone deacetylases (HDACs) are responsible for the removal of acetyl groups from histones, resulting in gene silencing. Overexpression of HDACs is associated with cancer, and their inhibitors are of particular interest as chemotherapeutics. However, HDACs remain a target of mechanistic debate. HDAC class 8 is the most studied HDAC, and of particular importance due to its human oncological relevance. HDAC8 has traditionally been considered to be a Zn-dependent enzyme. However, recent experimental assays have challenged this assumption and shown that HDAC8 is catalytically active with a variety of different metals, and that it may be a Fe-dependent enzyme in vivo. We studied two opposing mechanisms utilizing a series of divalent metal ions in physiological abundance (Zn(2+), Fe(2+), Co(2+), Mn(2+), Ni(2+), and Mg(2+)). Extensive sampling of the entire protein with different bound metals was done with the mixed quantum-classical QM/DMD method. Density functional theory (DFT) on an unusually large cluster model was used to describe the active site and reaction mechanism. We have found that the reaction profile of HDAC8 is similar among all metals tested, and follows one of the previously published mechanisms, but the rate-determining step is different from the one previously claimed. We further provide a scheme for estimating the metal binding affinities to the protein. We use the quantum theory of atoms in molecules (QTAIM) to understand the different binding affinities for each metal in HDAC8 as well as the ability of each metal to bind and properly orient the substrate for deacetylation. The combination of this data with the catalytic rate constants is required to reproduce the experimentally observed trend in metal-depending performance. We predict Co(2+) and Zn(2+) to be the most active metals in HDAC8, followed by Fe(2+), and Mn(2+) and Mg(2+) to be the least active.

Molecular Design for Tuning Work Functions of Transparent Conducting Electrodes.

In this Perspective, we provide a brief background on the use of aromatic phosphonic acid modifiers for tuning work functions of transparent conducting oxides, for example, zinc oxide (ZnO) and indium tin oxide (ITO). We then introduce our preliminary results in this area using conjugated phosphonic acid molecules, having a substantially larger range of dipole moments than their unconjugated analogues, leading to the tuning of ZnO and ITO electrodes over a 2 eV range as derived from Kelvin probe measurements. We have found that these work function changes are directly correlated to the magnitude and the direction of the computationally derived molecular dipole of the conjugated phosphonic acids, leading to the predictive power of computation to drive the synthesis of new and improved phosphonic acid ligands.

A full topological analysis of unstable and metastable bond critical points.

Researchers are developing conceptually based models linking the structure and dynamics of molecular charge density to certain properties. Here we report on our efforts to identify features within the charge density that are indicative of instability and metastability. Towards this, we use our extensions to the quantum theory of atoms in molecules that capitalize on a molecule's ridges to define a natural simplex over the charge density. The resulting simplicial complex can be represented at various levels by its 0-, 1-, and 2-skeleton (dependent sets of points, lines, and surfaces). We show that the geometry of these n-skeletons retains critical information regarding the structure and stability of molecular systems while greatly simplifying charge density analysis. As an example, we use our methods to uncover the fingerprints of instability and metastability in two much-discussed systems, that is, the di-benzene complex and the He and adamantane inclusion complex.

Reactive cluster model of metallic glasses.

Though discovered more than a half century ago metallic glasses remain a scientific enigma. Unlike crystalline metals, characterized by short, medium, and long-range order, in metallic glasses short and medium-range order persist, though long-range order is absent. This fact has prompted research to develop structural descriptions of metallic glasses. Among these are cluster-based models that attribute amorphous structure to the existence of clusters that are incommensurate with crystalline periodicity. Not addressed, however, are the chemical factors stabilizing these clusters and promoting their interconnections. We have found that glass formers are characterized by a rich cluster chemistry that above the glass transformation temperature promotes exchange as well as static and vibronic sharing of atoms between clusters. The vibronic mechanism induces correlated motions between neighboring clusters and we hypothesize that the distance over which these motions are correlated mediates metallic glass stability and influences critical cooling rates.

Better alloys with quantum design.

Alloy discovery and development is slowed by trial and error methods used to identify beneficial alloying elements. This fact has led to suggestions that integrating quantum theory and modeling with traditional experimental approaches might accelerate the pace of alloy discovery. We report here on one such effort, using advances in first principles computation along with an evolving theory that allows for the partitioning of charge density into chemically meaningful structures, alloying elements that improve the adhesive properties of interfaces common to high strength steels have been identified.

Bond bundles and the origins of functionality.

We briefly review the method by which the electron charge density of atomic systems is decomposed into unique volumes called bond bundles, which are characterized by well-defined and additive properties. We then show that boundaries of bond bundles topologically constrain their chemical reactivity. To illustrate this fact, we model the response of the bond bundles of ethane and ethene to electrophilic attack and from the results of these models posit that functional group properties can be inferred from the shapes of their bond bundles. By relating functionality to bond bundle shape, it is possible to see subtle changes in chemical reactivity that are otherwise difficult to explain, as is illustrated by comparing bond bundles through a series of impact sensitive polynitroaromatic molecules.

Topological catastrophe and isostructural phase transition in calcium.

We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find, at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure.

The irreducible bundle: further structure in the kinetic energy distribution.

Modern molecular sciences are often concerned with the properties and dynamics of chemical bonds. With the ability to experimentally measure charge density, there is a pressing need to find the relationships between charge density and the properties of chemical bonds. Here we show molecules can be partitioned into unique bond volumes characterized by well defined properties. Moreover, this partitioning recovers unrecognized structure in the kinetic energy distribution.

The topologies of the charge densities in Zr and Ru.

We report on the atomic scale phenomena responsible for the variation of oxygen solubility in Zr and Ru. First-principles calculations reveal that the topologies of the charge densities in these hexagonal close-packed metals are distinct. Neither element was found to possess the topology of the prototype, Mg. There are 12 bond paths terminating at each Ru atom. These are the bonds between nearest neighbors. Only five bond paths terminate at each Zr atom and the Zr atoms are not bound to one another. Instead, they are bonded through non-nuclear maxima. As a result, channels of low charge density that can accommodate oxygen anions are present in Zr.

Electronic selection rules controlling dislocation glide in bcc metals.

The validity of the structure-property relationships governing the low-temperature deformation behavior of many bcc metals was brought into question with recent ab initio density functional studies of isolated screw dislocations in Mo and Ta. These relationships were semiclassical in nature, having grown from atomistic investigations of the deformation properties of the group V and VI transition metals. We find that the correct form for these structure-property relationships is fully quantum mechanical, involving the coupling of electronic states with the strain field at the core of long a/<2111> screw dislocations.

Topology of the spin-polarized charge density in bcc and fcc iron.

We report the first investigation of the topology of spin-polarized charge density, specifically in bcc and fcc iron. While the total spin-density is found to possess the topology of the non-magnetic prototypical structures, the spin-polarized charge densities of bcc and high-spin fcc iron are atypical. In these cases, the two spin densities are correlated: the spin-minority electrons have directional bond paths and deep minima, while the spin-majority electrons fill these holes, reducing bond directionality. The presence of distinct spin topologies allows us to show that the two phase changes seen in fcc iron (paramagnetic to low-spin and low-spin to high-spin) are different. The former follows the Landau symmetry-breaking paradigm and proceeds without a topological transformation, while the latter involves a topological catastrophe.