New mechanistic insights into the Claisen rearrangement of chorismate – a Unified Reaction Valley Approach study

The influence of model building schemes and molecular dynamics sampling on QM-cluster models: the chorismate mutase case study

Most QM-cluster models of enzymes are constructed based on X-ray crystal structures, which limits comparison to in vivo structure and mechanism. The active site of chorismate mutase from Bacillus subtilis and the enzymatic transformation of chorismate to prephenate is used as a case study to guide construction of QM-cluster models built first from the X-ray crystal structure, then from molecular dynamics (MD) simulation snapshots. The Residue Interaction Network ResidUe Selector (RINRUS) software toolkit, developed by our group to simplify and automate the construction of QM-cluster models, is expanded to handle MD to QM-cluster model workflows. Several options, some employing novel topological clustering from residue interaction network (RIN) information, are evaluated for generating conformational clustering from MD simulation. RINRUS then generates a statistical thermodynamic framework for QM-cluster modeling of the chorismate mutase mechanism via refining 250 MD frames with density functional theory (DFT). The 250 QM-cluster models sampled provide a mean ΔG‡ of 10.3 ± 2.6 kcal mol-1 compared to the experimental value of 15.4 kcal mol-1 at 25 °C. While the difference between theory and experiment is consequential, the level of theory used is modest and therefore "chemical" accuracy is unexpected. More important are the comparisons made between QM-cluster models designed from the X-ray crystal structure versus those from MD frames. The large variations in kinetic and thermodynamic properties arise from geometric changes in the ensemble of QM-cluster models, rather from the composition of the QM-cluster models or from the active site-solvent interface. The findings open the way for further quantitative and reproducible calibration in the field of computational enzymology using the model construction framework afforded with the RINRUS software toolkit.

Reaction mechanism - explored with the unified reaction valley approach

One of the ultimate goals of chemistry is to understand and manipulate chemical reactions, which implies the ability to monitor the reaction and its underlying mechanism at an atomic scale. In this article, we introduce the Unified Reaction Valley Approach (URVA) as a tool for elucidating reaction mechanisms, complementing existing computational procedures. URVA combines the concept of the potential energy surface with vibrational spectroscopy and describes a chemical reaction via the reaction path and the surrounding reaction valley traced out by the reacting species on the potential energy surface on their way from the entrance to the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting species is registered by a change in the normal vibrational modes spanning the reaction valley and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction, with curvature minima reflecting minimal change and curvature maxima indicating the location of important chemical events such as bond breaking/formation, charge polarization and transfer, rehybridization, etc. A decomposition of the path curvature into internal coordinate components or other coordinates of relevance for the reaction under consideration, provides comprehensive insight into the origin of the chemical changes taking place. After giving an overview of current experimental and computational efforts to gain insight into the mechanism of a chemical reaction and presenting the theoretical background of URVA, we illustrate how URVA works for three diverse processes, (i) [1,3] hydrogen transfer reactions; (ii) α-keto-amino inhibitor for SARS-CoV-2 Mpro; (iii) Rh-catalyzed cyanation. We hope that this article will inspire our computational colleagues to add URVA to their repertoire and will serve as an incubator for new reaction mechanisms to be studied in collaboration with our experimental experts in the field.

Best Practices on QM/MM Simulations of Biological Systems

During the second half of the 20th century, following structural biology hallmark works on DNA and proteins, biochemists shifted their questions from "what does this molecule look like?" to "how does this process work?". Prompted by the theoretical and practical developments in computational chemistry, this led to the emergence of biomolecular simulations and, along with the 2013 Nobel Prize in Chemistry, to the development of hybrid QM/MM methods. QM/MM methods are necessary whenever the problem we want to address involves chemical reactivity and/or a change in the system's electronic structure, with archetypal examples being the studies of an enzyme's reaction mechanism and a metalloprotein's active site. In the last decades QM/MM methods have seen an increasing adoption driven by their incorporation in widely used biomolecular simulation software. However, properly setting up a QM/MM simulation is not an easy task, and several issues need to be properly addressed to obtain meaningful results. In the present work, we describe both the theoretical concepts and practical issues that need to be considered when performing QM/MM simulations. We start with a brief historical perspective on the development of these methods and describe when and why QM/MM methods are mandatory. Then we show how to properly select and analyze the performance of the QM level of theory, the QM system size, and the position and type of the boundaries. We show the relevance of performing prior QM model system (or QM cluster) calculations in a vacuum and how to use the corresponding results to adequately calibrate those derived from QM/MM. We also discuss how to prepare the starting structure and how to select an adequate simulation strategy, including those based on geometry optimizations as well as free energy methods. In particular, we focus on the determination of free energy profiles using multiple steered molecular dynamics (MSMD) combined with Jarzynski's equation. Finally, we describe the results for two illustrative and complementary examples: the reaction performed by chorismate mutase and the study of ligand binding to hemoglobins. Overall, we provide many practical recommendations (or shortcuts) together with important conceptualizations that we hope will encourage more and more researchers to incorporate QM/MM studies into their research projects.

Mechanistic Details of the Sharpless Epoxidation of Allylic Alcohols—A Combined URVA and Local Mode Study

In this work, we investigated the catalytic effects of a Sharpless dimeric titanium (IV)–tartrate–diester catalyst on the epoxidation of allylalcohol with methyl–hydroperoxide considering four different orientations of the reacting species coordinated at the titanium atom (reactions R1–R4) as well as a model for the non-catalyzed reaction (reaction R0). As major analysis tools, we applied the URVA (Unified Reaction Valley Approach) and LMA (Local Mode Analysis), both being based on vibrational spectroscopy and complemented by a QTAIM analysis of the electron density calculated at the DFT level of theory. The energetics of each reaction were recalculated at the DLPNO-CCSD(T) level of theory. The URVA curvature profiles identified the important chemical events of all five reactions as peroxide OO bond cleavage taking place before the TS (i.e., accounting for the energy barrier) and epoxide CO bond formation together with rehybridization of the carbon atoms of the targeted CC double bond after the TS. The energy decomposition into reaction phase contribution phases showed that the major effect of the catalyst is the weakening of the OO bond to be broken and replacement of OH bond breakage in the non-catalyzed reaction by an energetically more favorable TiO bond breakage. LMA performed at all stationary points rounded up the investigation (i) quantifying OO bond weakening of the oxidizing peroxide upon coordination at the metal atom, (ii) showing that a more synchronous formation of the new CO epoxide bonds correlates with smaller bond strength differences between these bonds, and (iii) elucidating the different roles of the three TiO bonds formed between catalyst and reactants and their interplay as orchestrated by the Sharpless catalyst. We hope that this article will inspire the computational community to use URVA complemented with LMA in the future as an efficient mechanistic tool for the optimization and fine-tuning of current Sharpless catalysts and for the design new of catalysts for epoxidation reactions.

Accelerating Ab Initio Quantum Mechanical and Molecular Mechanical (QM/MM) Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semiempirical QM/MM Hamiltonian

Molecular dynamics (MD) simulations employing ab initio quantum mechanical and molecular mechanical (ai-QM/MM) potentials are considered to be the state of the art, but the high computational cost associated with the ai-QM calculations remains a theoretical challenge for their routine application. Here, we present a modified protocol of the multiple time step (MTS) method for accelerating ai-QM/MM MD simulations of condensed-phase reactions. Within a previous MTS protocol [Nam J. Chem. Theory Comput. 2014, 10, 4175], reference forces are evaluated using a low-level (semiempirical QM/MM) Hamiltonian and employed at inner time steps to propagate the nuclear motions. Correction forces, which arise from the force differences between high-level (ai-QM/MM) and low-level Hamiltonians, are applied at outer time steps, where the MTS algorithm allows the time-reversible integration of the correction forces. To increase the outer step size, which is bound by the highest-frequency component in the correction forces, the semiempirical QM Hamiltonian is recalibrated in this work to minimize the magnitude of the correction forces. The remaining high-frequency modes, which are mainly bond stretches involving hydrogen atoms, are then removed from the correction forces. When combined with a Langevin or SIN(R) thermostat, the modified MTS-QM/MM scheme remains robust with an up to 8 (with Langevin) or 10 fs (with SIN(R)) outer time step (with 1 fs inner time steps) for the chorismate mutase system. This leads to an over 5-fold speedup over standard ai-QM/MM simulations, without sacrificing the accuracy in the predicted free energy profile of the reaction.

Uranium: The Nuclear Fuel Cycle and Beyond

This review summarizes the recent developments regarding the use of uranium as nuclear fuel, including recycling and health aspects, elucidated from a chemical point of view, i.e., emphasizing the rich uranium coordination chemistry, which has also raised interest in using uranium compounds in synthesis and catalysis. A number of novel uranium coordination features are addressed, such the emerging number of U(II) complexes and uranium nitride complexes as a promising class of materials for more efficient and safer nuclear fuels. The current discussion about uranium triple bonds is addressed by quantum chemical investigations using local vibrational mode force constants as quantitative bond strength descriptors based on vibrational spectroscopy. The local mode analysis of selected uranium nitrides, N≡U≡N, U≡N, N≡U=NH and N≡U=O, could confirm and quantify, for the first time, that these molecules exhibit a UN triple bond as hypothesized in the literature. We hope that this review will inspire the community interested in uranium chemistry and will serve as an incubator for fruitful collaborations between theory and experimentation in exploring the wealth of uranium chemistry.

BF3–Catalyzed Diels–Alder Reaction between Butadiene and Methyl Acrylate in Aqueous Solution—An URVA and Local Vibrational Mode Study

In this study we investigate the Diels–Alder reaction between methyl acrylate and butadiene, which is catalyzed by BF3 Lewis acid in explicit water solution, using URVA and Local Mode Analysis as major tools complemented with NBO, electron density and ring puckering analyses. We considered four different starting orientations of methyl acrylate and butadiene, which led to 16 DA reactions in total. In order to isolate the catalytic effects of the BF3 catalyst and those of the water environment and exploring how these effects are synchronized, we systematically compared the non-catalyzed reaction in gas phase and aqueous solution with the catalyzed reaction in gas phase and aqueous solution. Gas phase studies were performed at the B3LYP/6-311+G(2d,p) level of theory and studies in aqueous solution were performed utilizing a QM/MM approach at the B3LYP/6-311+G(2d,p)/AMBER level of theory. The URVA results revealed reaction path curvature profiles with an overall similar pattern for all 16 reactions showing the same sequence of CC single bond formation for all of them. In contrast to the parent DA reaction with symmetric substrates causing a synchronous bond formation process, here, first the new CC single bond on the CH2 side of methyl acrylate is formed followed by the CC bond at the ester side. As for the parent DA reaction, both bond formation events occur after the TS, i.e., they do not contribute to the energy barrier. What determines the barrier is the preparation process for CC bond formation, including the approach diene and dienophile, CC bond length changes and, in particular, rehybridization of the carbon atoms involved in the formation of the cyclohexene ring. This process is modified by both the BF3 catalyst and the water environment, where both work in a hand-in-hand fashion leading to the lowest energy barrier of 9.06 kcal/mol found for the catalyzed reaction R1 in aqueous solution compared to the highest energy barrier of 20.68 kcal/mol found for the non-catalyzed reaction R1 in the gas phase. The major effect of the BF3 catalyst is the increased mutual polarization and the increased charge transfer between methyl acrylate and butadiene, facilitating the approach of diene and dienophile and the pyramidalization of the CC atoms involved in the ring formation, which leads to a lowering of the activation energy. The catalytic effect of water solution is threefold. The polar environment leads also to increased polarization and charge transfer between the reacting species, similar as in the case of the BF3 catalyst, although to a smaller extend. More important is the formation of hydrogen bonds with the reaction complex, which are stronger for the TS than for the reactant, thus stabilizing the TS which leads to a further reduction of the activation energy. As shown by the ring puckering analysis, the third effect of water is space confinement of the reacting partners, conserving the boat form of the six-member ring from the entrance to the exit reaction channel. In summary, URVA combined with LMA has led to a clearer picture on how both BF3 catalyst and aqueous environment in a synchronized effort lower the reaction barrier. These new insights will serve to further fine-tune the DA reaction of methyl acrylate and butadiene and DA reactions in general.

Capturing Individual Hydrogen Bond Strengths in Ices via Periodic Local Vibrational Mode Theory: Beyond the Lattice Energy Picture

Local stretching force constants derived from periodic local vibrational modes at the vdW-DF2 density functional level have been employed to quantify the intrinsic hydrogen bond strength of 16 ice polymorphs, ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI, XII, XIII, XIV, XV, XVII, and XIX, that are stable under ambient to elevated pressures. Based on this characterization on 1820 hydrogen bonds, relationships between local stretching force constants and structural parameters such as hydrogen bond length and angle were identified. Moreover, different bond strength distributions, from uniform to inhomogeneous, were observed for the 16 ices and could be explained in relation to different local structural elements within ices, that is, rings, that consist of different hydrogen bond types. In addition, criteria for the classification of hydrogen bonds as strong, intermediate, and weak were introduced. The latter was used to explore a different dimension of the water-ice phase diagram. These findings will provide important guidelines for assessing the credibility of new ice structures.

Theoretical Insights into [NHC]Au(I) Catalyzed Hydroalkoxylation of Allenes: A Unified Reaction Valley Approach Study

Hydroxylation is an effective approach for the synthesis of carbon-oxygen bonds and allylic ethers. The [NHC]Au(I) catalyzed intermolecular hydroalkoxylation of allene was studied at the DFT and Coupled Cluster level of theory. Using the Unified Reaction Valley Approach (URVA), we carry out a comprehensive mechanistic analysis of [NHC]Au(I)-catalyzed and noncatalyzed reactions. The URVA study of several possible reaction pathways reveal that the [NHC]Au(I) catalyst enables the hydroalkoxylation reaction to occur via a two step mechanism based upon the Au ability to switch between π- and σ-complexation. The first step of the mechanism involves the formation of a CO bond after the transition state with no energy penalty. Following the CO bond breakage, the OH bond breaks and CH bond forms during the second step of the mechanism, as the catalyst transforms into the more stable π-Au complex. The URVA results were complemented with local vibrational mode analysis to provide measures of intrinsic bond strength for Au(I)-allene interactions of all stationary points, and NBO analysis was applied in order to observe charge transfer events along the reaction pathway. Overall, the π-Au C═C interactions of the products are stronger than those of the reactants adding to their exothermicity. Our work on the hydroxylation of allene provides new insights for the design of effective reaction pathways to produce allylic ethers and also unravels new strategies to form C-O bonds by activation of C═C bonds.

Chorismate- and isochorismate converting enzymes: versatile catalysts acting on an important metabolic node

Chorismate and isochorismate represent an important branching point connecting primary and secondary metabolism in bacteria, fungi, archaea and plants. Chorismate- and isochorismate-converting enzymes are potential targets for new bioactive compounds, as well as valuable biocatalysts for the in vivo and in vitro synthesis of fine chemicals. The diversity of the products of chorismate- and isochorismate-converting enzymes is reflected in the enzymatic three-dimensional structures and molecular mechanisms. Due to the high reactivity of chorismate and its derivatives, these enzymes have evolved to be accurately tailored to their respective reaction; at the same time, many of them exhibit a fascinating flexibility regarding side reactions and acceptance of alternative substrates. Here, we give an overview of the different (sub)families of chorismate- and isochorismate-converting enzymes, their molecular mechanisms, and three-dimensional structures. In addition, we highlight important results of mutagenetic approaches that generate a broader understanding of the influence of distinct active site residues for product formation and the conversion of one subfamily into another. Based on this, we discuss to what extent the recent advances in the field might influence the general mechanistic understanding of chorismate- and isochorismate-converting enzymes. Recent discoveries of new chorismate-derived products and pathways, as well as biocatalytic conversions of non-physiological substrates, highlight how this vast field is expected to continue developing in the future.

Barnes Update Applied in the Gauss-Newton Method: An Improved Algorithm to Locate Bond Breaking Points

A mechanochemical reaction is a reaction induced by mechanical energy. A general accepted model for this type of reaction consists of a first-order perturbation on the associated potential energy surface (PES) of the unperturbed molecular system due to mechanical stress or pulling force. Within this theoretical framework, the so-called optimal barrier breakdown points or optimal bond breaking points (BBPs) are critical points of the unperturbed PES where the Hessian matrix has a zero eigenvector that coincides with the gradient vector. Optimal BBPs are "catastrophe points" that are particularly important because their associated gradient indicates how to optimally harness tensile forces to induce reactions by transforming a chemical reaction into a barrierless process. Building on a previous method based on a nonlinear least-squares minimization to locate BBPs (Bofill et al., J. Chem. Phys. 2017, 147, 152710-10), we propose a new algorithm to locate BBPs of any molecular system based on the Gauss-Newton method combined with the Barnes update for a nonsymmetric Jacobian matrix, which is shown to be more appropriate than the Broyden update. The efficiency of the new method is demonstrated for a multidimensional model PES and two medium size molecular systems of interest in enzymatic catalysis and mechanochemistry.

Exploring the Mechanism of Catalysis with the Unified Reaction Valley Approach (URVA)—A Review

The unified reaction valley approach (URVA) differs from mainstream mechanistic studies, as it describes a chemical reaction via the reaction path and the surrounding reaction valley on the potential energy surface from the van der Waals region to the transition state and far out into the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting molecules is registered by a change in their normal vibrational modes and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction with curvature minima reflecting minimal change and curvature maxima, the location of important chemical events such as bond breaking/forming, charge polarization and transfer, rehybridization, etc. A unique decomposition of the path curvature into internal coordinate components provides comprehensive insights into the origins of the chemical changes taking place. After presenting the theoretical background of URVA, we discuss its application to four diverse catalytic processes: (i) the Rh catalyzed methanol carbonylation—the Monsanto process; (ii) the Sharpless epoxidation of allylic alcohols—transition to heterogenous catalysis; (iii) Au(I) assisted [3,3]-sigmatropic rearrangement of allyl acetate; and (iv) the Bacillus subtilis chorismate mutase catalyzed Claisen rearrangement—and show how URVA leads to a new protocol for fine-tuning of existing catalysts and the design of new efficient and eco-friendly catalysts. At the end of this article the pURVA software is introduced. The overall goal of this article is to introduce to the chemical community a new protocol for fine-tuning existing catalytic reactions while aiding in the design of modern and environmentally friendly catalysts.

A new way of studying chemical reactions: a hand-in-hand URVA and QTAIM approach

Bond formation and bond cleavage processes are central to a chemical reaction. They can be investigated by monitoring changes in the potential energy surface (PES) or changes in the electron density (ED) distribution ρ(r) taking place during the reaction. However, it is not yet clear how the corresponding changes in the PES and ED are related, although the connection between energy and density has been postulated in the famous Hohenberg-Kohn theorem. Our unified reaction valley approach (URVA) identifies the locations of bond formation/cleavage events along the reaction path via the reaction path curvature peaks and their decomposition into the internal coordinate components associated with the bond to be formed or cleaved. One can also investigate bond formation/cleavage events using the quantum theory of atoms-in-molecule (QTAIM) analysis by monitoring changes in the topological properties of ρ(r) and the associated Laplacian ∇2ρ(r). By a systematic comparison of these two approaches for a series of ten representative chemical reactions ranging from hydrogen migration to cycloaddition reactions and gold(i) catalysis, we could for the first time unravel the PES-ED relationship. In the case of a bond formation, all changes in the ED occur shortly before or at the corresponding curvature peak, and in a bond cleavage, the ED changes occur at or shortly after the curvature peak. In any case, the ED changes always occurred in the vicinity of the curvature peak in accordance with the Hohenberg-Kohn theorem. Our findings provide a comprehensive view on bond formation/cleavage processes seen through the eyes of both the PES and ED and offer valuable guidelines on where to search for significant ED changes associated with bond formation or cleavage events.

Quantitative Assessment of Tetrel Bonding Utilizing Vibrational Spectroscopy

A set of 35 representative neutral and charged tetrel complexes was investigated with the objective of finding the factors that influence the strength of tetrel bonding involving single bonded C, Si, and Ge donors and double bonded C or Si donors. For the first time, we introduced an intrinsic bond strength measure for tetrel bonding, derived from calculated vibrational spectroscopy data obtained at the CCSD(T)/aug-cc-pVTZ level of theory and used this measure to rationalize and order the tetrel bonds. Our study revealed that the strength of tetrel bonds is affected by several factors, such as the magnitude of the σ-hole in the tetrel atom, the negative electrostatic potential at the lone pair of the tetrel-acceptor, the positive charge at the peripheral hydrogen of the tetrel-donor, the exchange-repulsion between the lone pair orbitals of the peripheral atoms of the tetrel-donor and the heteroatom of the tetrel-acceptor, and the stabilization brought about by electron delocalization. Thus, focusing on just one or two of these factors, in particular, the σ-hole description can only lead to an incomplete picture. Tetrel bonding covers a range of -1.4 to -26 kcal/mol, which can be strengthened by substituting the peripheral ligands with electron-withdrawing substituents and by positively charged tetrel-donors or negatively charged tetrel-acceptors.