Dynamic effects on organic reactivity—Pathways to (and from) discomfort

A Strategy for Modeling Nonstatistical Reactivity Effects: Combining Chemical Activation Estimates with a Vibrational Relaxation Model

The kinetics of many chemical reactions can be readily explained with a statistical approach, for example, using a form of transition state theory and comparing calculated Gibbs energies along the reaction coordinate(s). However, there are cases where this approach fails, notably when the vibrational relaxation of the molecule to its statistical equilibrium occurs on the same time scale as the reaction dynamics, whether it is caused by slow relaxation, a fast reaction, or both. These nonstatistical phenomena are then often explored computationally using (quasi)classical ab initio molecular dynamics by calculating a large number of trajectories while being prone to issues such as zero-point energy leakage. On the other side of the field, we see resource-intensive quantum dynamics simulations, which significantly limit the size of explorable systems. We find that using a Fermi's golden rule type of model for vibrational relaxation, based on anharmonic coupling constants, we can extract the same qualitative information while giving insights into how to enhance (or destroy) the bottlenecks causing the phenomena. We present this model as a middle ground for exploring complex nonstatistical behavior, capable of treating medium-sized organic molecules or biologically relevant fragments. We also cover the challenges involved, in particular quantifying the excess energy in terms of vibrational modes. Relying on readily available electronic structure methods and providing results in a simple master equation form, this model shows promise as a screening tool for opportunities in mode-selective chemistry without external control.

Revisiting a classic carbocation - DFT, coupled-cluster, and ab initio molecular dynamics computations on barbaralyl cation formation and rearrangements

Density functional theory computations were used to model the formation and rearrangement of the barbaralyl cation (C9H+ 9). Two highly delocalized minima were located for C9H+ 9, one of C s symmetry and the other of D 3h symmetry, with the former having lower energy. Quantum chemistry-based NMR predictions affirm that the lower energy structure is the best match with experimental spectra. Partial scrambling was found to proceed through a C 2 symmetric transition structure associated with a barrier of only 2.3 kcal mol-1. The full scrambling was found to involve a C 2v symmetric transition structure associated with a 5.0 kcal mol-1 barrier. Ab initio molecular dynamics simulations initiated from the D 3h C9H+ 9 structure revealed its connection to six minima, due to the six-fold symmetry of the potential energy surface. The effects of tunneling and boron substitution on this complex reaction network were also examined.

Rearrangement, Elimination, and Ring-Opening Reactions of Cyclopropyl-Substituted Nitrenium Ions: A Computational and Experimental Investigation

N-(4-Biphenylyl)-N-cyclopropyl nitrenium ion 5 and N-benzyl-N-cyclopropyl nitrenium ion (6) were generated through photolysis of their corresponding N-aminopyridinium ion photoprecursors. In the case of 5, stable products result from a combination of cyclopropyl ring expansion (N-biphenylazetium ion) and ethylene elimination (biphenylisonitrilium ion). When present in high concentrations, methanol can add to the cyclopropyl ring-forming N-3-methoxypropyl-N-biphenyl iminium ion. In contrast, the only detectable product from the N-benzyl-N-cyclopropyl nitrenium ion (6) is benzylisonitrile, resulting from the elimination of ethylene. Density functional theory (DFT) calculations predict the product distributions from the more stable biphenyl system 5 with reasonable accuracy. However, product distributions from the less stable benzyl system 6 are forecast with less accuracy.

Woodward-Hoffmann or Hoffmann-Woodward? Cycloadditions and the Transformation of Roald Hoffmann from a "Calculator" to an "Explainer"

On May 1, 1965, Roald Hoffmann and R. B. Woodward published their second joint communication, Selection Rules for Concerted Cycloaddition Reactions, in the Journal of the American Chemical Society. Herein is presented a historical analysis of Woodward and Hoffmann's determination of the mechanism of cycloadditions. This analysis is based on thorough analyses with Roald Hoffmann of his 1964 and 1965 laboratory notebooks and his archived documents and on numerous in-person, video, and email interviews. This historical research pinpoints several seminal moments in chemistry and in the professional career of Hoffmann. For example, now documented is the fact that Woodward and Hoffmann had no anticipation that their collaboration would continue after the publication of their first 1965 communication on electrocyclizations. Also pinpointed is the moment in Hoffmann's professional and intellectual trajectories that he became a full-fledged, equal collaborator with Woodward and Hoffmann's transition from a "calculator" to an "explainer."

PyDFT-QMMM: A modular, extensible software framework for DFT-based QM/MM molecular dynamics

PyDFT-QMMM is a Python-based package for performing hybrid quantum mechanics/molecular mechanics (QM/MM) simulations at the density functional level of theory. The program is designed to treat short-range and long-range interactions through user-specified combinations of electrostatic and mechanical embedding procedures within periodic simulation domains, providing necessary interfaces to external quantum chemistry and molecular dynamics software. To enable direct embedding of long-range electrostatics in periodic systems, we have derived and implemented force terms for our previously described QM/MM/PME approach [Pederson and McDaniel, J. Chem. Phys. 156, 174105 (2022)]. Communication with external software packages Psi4 and OpenMM is facilitated through Python application programming interfaces (APIs). The core library contains basic utilities for running QM/MM molecular dynamics simulations, and plug-in entry-points are provided for users to implement custom energy/force calculation and integration routines, within an extensible architecture. The user interacts with PyDFT-QMMM primarily through its Python API, allowing for complex workflow development with Python scripting, for example, interfacing with PLUMED for free energy simulations. We provide benchmarks of forces and energy conservation for the QM/MM/PME and alternative QM/MM electrostatic embedding approaches. We further demonstrate a simple example use case for water solute in a water solvent system, for which radial distribution functions are computed from 100 ps QM/MM simulations; in this example, we highlight how the solvation structure is sensitive to different basis-set choices due to under- or over-polarization of the QM water molecule's electron density.

Revisiting Textbook Azide-Clock Reactions: A "Propeller-Crawling" Mechanism Explains Differences in Rates

An ongoing challenge to chemists is the analysis of pathways and kinetics for chemical reactions in solution, including transient structures between the reactants and products that are difficult to resolve using laboratory experiments. Here, we enabled direct molecular dynamics simulations of a textbook series of chemical reactions on the hundreds of ns to μs time scale using the weighted ensemble (WE) path sampling strategy with hybrid quantum mechanical/molecular mechanical (QM/MM) models. We focused on azide-clock reactions involving addition of an azide anion to each of three long-lived trityl cations in an acetonitrile-water solvent mixture. Results reveal a two-step mechanism: (1) diffusional collision of reactants to form an ion-pair intermediate; (2) "activation" or rearrangement of the intermediate to the product. Our simulations yield not only reaction rates that are within error of experiment but also rates for individual steps, indicating the activation step as rate-limiting for all three cations. Further, the trend in reaction rates is due to dynamical effects, i.e., differing extents of the azide anion "crawling" along the cation's phenyl-ring "propellers" during the activation step. Our study demonstrates the power of analyzing pathways and kinetics to gain insights on reaction mechanisms, underscoring the value of including WE and other related path sampling strategies in the modern toolbox for chemists.

Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree-Fock exchange. These results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

Running Wild through Dirhodium Tetracarboxylate-Catalyzed Combined CH(C)-Functionalization/Cope Rearrangement Landscapes: Does Post-Transition-State Dynamic Mismatching Influence Product Distributions?

A special type of C-H functionalization can be achieved through C-H insertion combined with Cope rearrangement (CHCR) in the presence of dirhodium catalysts. This type of reaction was studied using density functional theory and ab initio molecular dynamics simulations, the results of which pointed to the dynamic origins of low yields observed in some experiments. These studies not only reveal intimate details of the complex reaction network underpinning CHCR reactions but also further cement the generality of the importance of nonstatistical dynamic effects in controlling Rh2L4-promoted reactions.

Monitoring the Evolution of Relative Product Populations at Early Times during a Photochemical Reaction

Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps toward understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species among the emerging reaction products. Here, we show that mega-electronvolt ultrafast electron diffraction in combination with ab initio molecular dynamics calculations offer a powerful route to determining time-resolved populations of the various isomeric products formed after UV (266 nm) excitation of the five-membered heterocyclic molecule 2(5H)-thiophenone. This strategy provides experimental validation of the predicted high (∼50%) yield of an episulfide isomer containing a strained three-membered ring within ∼1 ps of photoexcitation and highlights the rapidity of interconversion between the rival highly vibrationally excited photoproducts in their ground electronic state.

Discovery and bioinspired total syntheses of unprecedented sesquiterpenoid dimers unveiled bifurcating [4 + 2] cycloaddition and target differentiation of enantiomers

[4 + 2] cycloaddition has led to diverse polycyclic chiral architectures, serving as novel sources for organic synthesis and biological exploration. Here, an unprecedented class of cadinane sesquiterpene [4 + 2] dimers, henryinins A-E (1-5), with a unique 6/6/6/6/6-fused pentacyclic system, were isolated from Schisandra henryi. The divergent total syntheses of compounds 1-5 and their enantiomers (6-10) were concisely accomplished in eight linear steps using a protection-free approach. Mechanistic studies illustrated the origin of selectivity in the key [4 + 2] cycloaddition as well as the inhibition of reaction pathway bifurcation via desymmetrization. The chemical proteomics results showed that a pair of enantiomers shared common targets (PRDX5 C100 and BLMH C73) and had unique targets (USP45 C588 for 4 and COG7 C419 for 9). This work provides experimental evidence for the discovery of unprecedented cadinane dimers from selective Diels-Alder reaction and a powerful strategy to explore the biological properties of natural products.

Portable Models for Entropy Effects on Kinetic Selectivity

Differences in entropies of competing transition states can direct kinetic selectivity. Understanding and modeling such entropy differences at the molecular level is complicated by the fact that entropy is statistical in nature; i.e., it depends on multiple vibrational states of transition structures, the existence of multiple dynamically accessible pathways past these transition structures, and contributions from multiple transition structures differing in conformation/configuration. The difficulties associated with modeling each of these contributors are discussed here, along with possible solutions, all with an eye toward the development of portable qualitative models of use to experimentalists aiming to design reactions that make use of entropy to control kinetic selectivity.

Kinetic Analysis of a Reaction Path Network Including Ambimodal Transition States: A Case Study of an Intramolecular Diels-Alder Reaction

This study proposes a methodology for the kinetic analysis of a reaction path network including ambimodal transition states (TSs), through which an ensemble of trajectories bifurcates to multiple minima in a phenomenon called dynamical bifurcation. The proposed methodology consists of three techniques: an automated reaction path search to construct a reaction path network including ambimodal TSs, an ab initio molecular dynamics simulation to evaluate the branching ratio, and the definition of rate constants incorporating this ratio. Applying the procedure to a Diels-Alder reaction, it was found that the inclusion of dynamical bifurcations is necessary to explain the experimental reaction yield of a byproduct. In addition, it was verified that the products take 10¹³ s to reach thermal equilibrium and that the experimental selectivity is determined by the dynamical bifurcations.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

Examining the Research on Business Information-Entropy Correlation in the Accounting Process of Organizations

Open business organizations, where information flows, is shared, and exchanged, are more prepared to adapt and survive chaos, uncertainty, and entropy, so they will be more predisposed to change management. The aim of this study is to analyze research trends at the international level on business information-entropy correlation in the accounting process of organizations. Mathematical and statistical techniques were applied to 980 articles during the period 1974-2020, obtaining results on the scientific productivity of the driving agents of this topic: authors, research institutions, countries/territories, and journals. Five lines of research were identified during the period analyzed, which mainly study information theory, maximum entropy, information entropy, decision-making, and enthalpy. Future research should focus on analyzing the evolution of this topic, which forms new thematic axes related to bitcoin market efficiency, business hierarchy information, business model evaluation systems, catastrophic economic collapse, corporate diversification, CSR reports affecting accounting conservatism, economic income accounting, and information loss. Currently, the research presents an upward trend, which allows a growing interest in the subject to be deduced in the academic and scientific community worldwide.