Gradient Bundle Analysis of Electric Field Induced Changes in Electron Charge Density.

Applying an electric field (EF) to a molecule is known to induce rearrangement of its electron charge density, ρ(r). Previous experimental and computational studies have investigated effects on reactivity by using homogeneous EFs with specific magnitudes and directions to control reaction rates and product selectivity. To best incorporate EFs into experimental design, a more fundamental understanding of how EFs rearrange ρ(r) is necessary. To gain this understanding, we first applied EFs to a set of 10 diatomic and linear triatomic molecules with various constraints on the molecules to determine the importance of rotation and altering bond lengths on bond energies. In order to capture the subtle changes in ρ(r) known to occur from EFs, an extension of the quantum theory of atoms in molecules called gradient bundle (GB) analysis was employed, allowing for quantification of the redistribution of ρ(r) within atomic basins. This allowed us to calculate GB-condensed EF-induced densities using conceptual density functional theory. Results were interpreted considering relationships between the GB-condensed EF-induced densities and properties including bond strength, bond length, polarity, polarizability, and frontier molecular orbitals (FMOs).

Bond Bundle Analysis of Ketosteroid Isomerase.

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.

Computer-Assisted Design of Macrocyclic Chelators for Actinium-225 Radiotherapeutics.

Actinium-225 (225Ac) is an excellent candidate for targeted radiotherapeutic applications for treating cancer, because of its 10-day half-life and emission of four high-energy α2+ particles. To harness and direct the energetic potential of actinium, strongly binding chelators that remain stable in vivo during biological targeting must be developed. Unfortunately, controlling chelation for actinium remains challenging. Actinium is the largest +3 cation on the periodic table and has a 6d05f0 electronic configuration, and its chemistry is relatively unexplored. Herein, we present theoretical work focused on improving the understanding of actinium bonding with macrocyclic chelating agents as a function of (1) macrocycle ring size, (2) the number and identity of metal binding functional groups, and (3) the length of the tether linking the metal binding functional group to the macrocyclic backbone. Actinium binding by these chelators is presented within the context of complexation with DOTA4-, the most relevant Ac3+ binding agent for contemporary radiopharmaceutical applications. The results enabled us to develop a new strategy for actinium chelator design. The approach is rooted in our identification that Ac3+-chelation chemistry is dominated by ionic bonding interactions and relies on (1) maximizing electrostatic interactions between the metal binding functional group and the Ac3+ cation and (2) minimizing electronic repulsion between negatively charged actinium binding functional groups. This insight will provide a foundation for future innovation in developing the next generation of multifunctional actinium chelators.

Development of Density Functional Tight-Binding Parameters Using Relative Energy Fitting and Particle Swarm Optimization.

We provide a strategy to optimize density functional tight-binding (DFTB) parameterization for the calculation of the structures and properties of organic molecules consisting of hydrogen, carbon, nitrogen, and oxygen. We utilize an objective function based on similarity measurements and the Particle Swarm Optimization (PSO) method to find an optimal set of parameters. This objective function considers not only the common DFTB descriptors of binding energies and atomic forces but also incorporates relative energies of isomers into the fitting procedure for more chemistry-driven results. The quality in the description of the binding energies and atomic forces is measured based on the Ballester similarity index and relative energies through a similarity index induced by the Levenshtein edit distance to quantify the correct energetic order of isomers. Training and testing datasets were created to include all relevant chemical functional groups. The accuracy of this strategy is assessed, and its range of applicability is discussed by comparison against our previous parameterization [A. Krishnapriyan, et al., J. Chem. Theory Comput. 13, 6191 (2017)]. The improved performance of the new DFTB parameterization is validated with respect to the density functional theory large datasets QM-9 [R. Ramakrishnan, et al., Sci. Data 1, 140022 (2014)] and ANI-1 [J. S. Smith, et al., Sci. Data 4, 170193 (2017)], where excellent agreement is found between the structures and properties available in these datasets, and the ones obtained with DFTB.

Advancing Chelation Chemistry for Actinium and Other +3 f-Elements, Am, Cm, and La.

A major chemical challenge facing implementation of 225Ac in targeted alpha therapy-an emerging technology that has potential for treatment of disease-is identifying an 225Ac chelator that is compatible with in vivo applications. It is unclear how to tailor a chelator for Ac binding because Ac coordination chemistry is poorly defined. Most Ac chemistry is inferred from radiochemical experiments carried out on microscopic scales. Of the few Ac compounds that have been characterized spectroscopically, success has only been reported for simple inorganic ligands. Toward advancing understanding in Ac chelation chemistry, we have developed a method for characterizing Ac complexes that contain highly complex chelating agents using small quantities (µg) of 227Ac. We successfully characterized the chelation of Ac3+ by DOTP8- using EXAFS, NMR, and DFT techniques. To develop confidence and credibility in the Ac results, comparisons with +3 cations (Am, Cm, and La) that could be handled on the mg scale were carried out. We discovered that all M3+ cations (M = Ac, Am, Cm, La) were completely encapsulated within the binding pocket of the DOTP8- macrocycle. The computational results highlighted the stability of the M(DOTP)5- complexes.

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.

Predicting Chemical Reactivity from the Charge Density through Gradient Bundle Analysis: Moving beyond Fukui Functions.

Predicting chemical reactivity is a major goal of chemistry. Toward this end, atom condensed Fukui functions of conceptual density functional theory have been used to predict which atom is most likely to undergo electrophilic or nucleophilic attack, providing regioselectivity information. We show that the most probable regions for electrophilic attack within each atom can be predicted through analysis of gradient bundle volumes, a property that depends only on the charge density of the neutral molecules. We also introduce gradient bundle condensed Fukui functions to compare the stereoselectivity information obtained from gradient bundle volume analysis. We demonstrate this method using the test set of molecular fluorine, oxygen, nitrogen, carbon monoxide, and hydrogen cyanide.

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.

The influence of zero-flux surface motion on chemical reactivity.

Visualizing and predicting the response of the electron density, ρ(r), to an external perturbation provides a portion of the insight necessary to understand chemical reactivity. One strategy used to portray electron response is the electron pushing formalism commonly utilized in organic chemistry, where electrons are pictured as flowing between atoms and bonds. Electron pushing is a powerful tool, but does not give a complete picture of electron response. We propose using the motion of zero-flux surfaces (ZFSs) in the gradient of the charge density, ∇ρ(r), as an adjunct to electron pushing. Here we derive an equation rooted in conceptual density functional theory showing that the movement of ZFSs contributes to energetic changes in a molecule undergoing a chemical reaction. Using a substituted acetylene, 1-iodo-2-fluoroethyne, as an example, we show the importance of both the boundary motion and the change in electron counts within the atomic basins of the quantum theory of atoms in molecules for chemical reactivity. This method can be extended to study the ZFS motion between smaller gradient bundles in ρ(r) in addition to larger atomic basins. Finally, we show that the behavior of ∇ρ(r) within atomic basins contains information about electron response and can be used to predict chemical reactivity.

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.