Myoglobin-Catalyzed Azide Reduction Proceeds via an Anionic Metal Amide Intermediate.

Nitrene transfer reactions catalyzed by heme proteins have broad potential for the stereoselective formation of carbon-nitrogen bonds. However, competition between productive nitrene transfer and the undesirable reduction of nitrene precursors limits the broad implementation of such biocatalytic methods. Here, we investigated the reduction of azides by the model heme protein myoglobin to gain mechanistic insights into the factors that control the fate of key reaction intermediates. In this system, the reaction proceeds via a proposed nitrene intermediate that is rapidly reduced and protonated to give a reactive ferrous amide species, which we characterized by UV/vis and Mössbauer spectroscopies, quantum mechanical calculations, and X-ray crystallography. Rate-limiting protonation of the ferrous amide to produce the corresponding amine is the final step in the catalytic cycle. These findings contribute to our understanding of the heme protein-catalyzed reduction of azides and provide a guide for future enzyme engineering campaigns to create more efficient nitrene transferases. Moreover, harnessing the reduction reaction in a chemoenzymatic cascade provided a potentially practical route to substituted pyrroles.

Automated preparation of nanoscopic structures: Graph-based sequence analysis, mismatch detection, and pH-consistent protonation with uncertainty estimates.

Structure and function in nanoscale atomistic assemblies are tightly coupled, and every atom with its specific position and even every electron will have a decisive effect on the electronic structure, and hence, on the molecular properties. Molecular simulations of nanoscopic atomistic structures therefore require accurately resolved three-dimensional input structures. If extracted from experiment, these structures often suffer from severe uncertainties, of which the lack of information on hydrogen atoms is a prominent example. Hence, experimental structures require careful review and curation, which is a time-consuming and error-prone process. Here, we present a fast and robust protocol for the automated structure analysis and pH-consistent protonation, in short, ASAP. For biomolecules as a target, the ASAP protocol integrates sequence analysis and error assessment of a given input structure. ASAP allows for p K a prediction from reference data through Gaussian process regression including uncertainty estimation and connects to system-focused atomistic modeling described in Brunken and Reiher (J. Chem. Theory Comput. 16, 2020, 1646). Although focused on biomolecules, ASAP can be extended to other nanoscopic objects, because most of its design elements rely on a general graph-based foundation guaranteeing transferability. The modular character of the underlying pipeline supports different degrees of automation, which allows for (i) efficient feedback loops for human-machine interaction with a low entrance barrier and for (ii) integration into autonomous procedures such as automated force field parametrizations. This facilitates fast switching of the pH-state through on-the-fly system-focused reparametrization during a molecular simulation at virtually no extra computational cost.

Striking the right balance of encoding electron correlation in the Hamiltonian and the wavefunction ansatz.

Multi-configurational electronic structure theory delivers the most versatile approximations to many-electron wavefunctions, flexible enough to deal with all sorts of transformations, ranging from electronic excitations, to open-shell molecules and chemical reactions. Multi-configurational models are therefore essential to establish universally applicable, predictive ab initio methods for chemistry. Here, we present a discussion of explicit correlation approaches which address the nagging problem of dealing with static and dynamic electron correlation in multi-configurational active-space approaches. We review the latest developments and then point to their key obstacles. Our discussion is supported by new data obtained with tensor network methods. We argue in favor of simple electron-only correlator expressions that may allow one to define transcorrelated models in which the correlator does not bear a dependence on molecular structure.

Uncertainty-Aware First-Principles Exploration of Chemical Reaction Networks.

Exploring large chemical reaction networks with automated exploration approaches and accurate quantum chemical methods can require prohibitively large computational resources. Here, we present an automated exploration approach that focuses on the kinetically relevant part of the reaction network by interweaving (i) large-scale exploration of chemical reactions, (ii) identification of kinetically relevant parts of the reaction network through microkinetic modeling, (iii) quantification and propagation of uncertainties, and (iv) reaction network refinement. Such an uncertainty-aware exploration of kinetically relevant parts of a reaction network with automated accuracy improvement has not been demonstrated before in a fully quantum mechanical approach. Uncertainties are identified by local or global sensitivity analysis. The network is refined in a rolling fashion during the exploration. Moreover, the uncertainties are considered during kinetically steering of a rolling reaction network exploration. We demonstrate our approach for Eschenmoser-Claisen rearrangement reactions. The sensitivity analysis identifies that only a small number of reactions and compounds are essential for describing the kinetics reliably, resulting in efficient explorations without sacrificing accuracy and without requiring prior knowledge about the chemistry unfolding.

SCINE-Software for chemical interaction networks.

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

Solving Intractable Chemical Problems by Tensor Decomposition.

Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavorable scaling with increasing molecular size. Tensor decomposition techniques can overcome such challenges by decomposing unattainably large numerical representations of chemical problems into smaller, tractable ones. In the first two decades of this century, algorithms based on such tensor factorizations have become state-of-the-art methods in various branches of computational chemistry, ranging from molecular quantum dynamics to electronic structure theory and machine learning. Here, we consider the role that tensor decomposition schemes have played in expanding the scope of computational chemistry. We relate some of the most prominent methods to their common underlying tensor network formalisms, providing a unified perspective on leading tensor-based approaches in chemistry and materials science.

Multi-Time-Scale Simulation of Complex Reactive Mixtures: How Do Polyoxometalates Form?

Understanding the dynamics of reactive mixtures still challenges both experiments and theory. A relevant example can be found in the chemistry of molecular metal-oxide nanoclusters, also known as polyoxometalates. The high number of species potentially involved, the interconnectivity of the reaction network, and the precise control of the pH and concentrations needed in the synthesis of such species make the theoretical/computational treatment of such processes cumbersome. This work addresses this issue relying on a unique combination of recently developed computational methods that tackle the construction, kinetic simulation, and analysis of complex chemical reaction networks. By using the Bell-Evans-Polanyi approximation for estimating activation energies, and an accurate and robust linear scaling for correcting the computed pKa values, we report herein multi-time-scale kinetic simulations for the self-assembly processes of polyoxotungstates that comprise 22 orders of magnitude, from tens of femtoseconds to months of reaction time. This very large time span was required to reproduce very fast processes such as the acid/base equilibria (at 10-12 s), relatively slow reactions such as the formation of key clusters such as the metatungstate (at 103 s), and the very slow assembly of the decatungstate (at 106 s). Analysis of the kinetic data and of the reaction network topology shed light onto the details of the main reaction mechanisms, which explains the origin of kinetic and thermodynamic control followed by the reaction. Simulations at alkaline pH fully reproduce experimental evidence since clusters do not form under those conditions.

Quantum Computing for Molecular Biology.

Molecular biology and biochemistry interpret microscopic processes in the living world in terms of molecular structures and their interactions, which are quantum mechanical by their very nature. Whereas the theoretical foundations of these interactions are well established, the computational solution of the relevant quantum mechanical equations is very hard. However, much of molecular function in biology can be understood in terms of classical mechanics, where the interactions of electrons and nuclei have been mapped onto effective classical surrogate potentials that model the interaction of atoms or even larger entities. The simple mathematical structure of these potentials offers huge computational advantages; however, this comes at the cost that all quantum correlations and the rigorous many-particle nature of the interactions are omitted. In this work, we discuss how quantum computation may advance the practical usefulness of the quantum foundations of molecular biology by offering computational advantages for simulations of biomolecules. We not only discuss typical quantum mechanical problems of the electronic structure of biomolecules in this context, but also consider the dominating classical problems (such as protein folding and drug design) as well as data-driven approaches of bioinformatics and the degree to which they might become amenable to quantum simulation and quantum computation.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths.

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

Pathfinder─Navigating and Analyzing Chemical Reaction Networks with an Efficient Graph-Based Approach.

While the field of first-principles explorations into chemical reaction space has been continuously growing, the development of strategies for analyzing resulting chemical reaction networks (CRNs) is lagging behind. A CRN consists of compounds linked by reactions. Analyzing how these compounds are transformed into one another based on kinetic modeling is a nontrivial task. Here, we present the graph-optimization-driven algorithm and program Pathfinder to allow for such an analysis of a CRN. The CRN for this work has been obtained with our open-source Chemoton reaction network exploration software. Chemoton probes reactive combinations of compounds for elementary steps and sorts them into reactions. By encoding these reactions of the CRN as a graph consisting of compound and reaction vertices and adding information about activation barriers as well as required reagents to the edges of the graph yields a complete graph-theoretical representation of the CRN. Since the probabilities of the formation of compounds depend on the starting conditions, the consumption of any compound during a reaction must be accounted for to reflect the availability of reagents. To account for this, we introduce compound costs to reflect compound availability. Simultaneously, the determined compound costs rank the compounds in the CRN in terms of their probability to be formed. This ranking then allows us to probe easily accessible compounds in the CRN first for further explorations into yet unexplored terrain. We first illustrate the working principle on an abstract small CRN. Afterward, Pathfinder is demonstrated in the example of the disproportionation of iodine with water and the comproportionation of iodic acid and hydrogen iodide. Both processes are analyzed within the same CRN, which we construct with our autonomous first-principles CRN exploration software Chemoton [Unsleber, J. P.; J. Chem. Theory Comput. 2022, 18, 5393-5409] guided by Pathfinder.

Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination.

We present a symmetry projection technique for enforcing rotational and parity symmetries in nuclear-electronic Hartree-Fock wave functions, which treat electrons and nuclei on equal footing. The molecular Hamiltonian obeys rotational and parity inversion symmetries, which are, however, broken by expanding in Gaussian basis sets that are fixed in space. We generate a trial wave function with the correct symmetry properties by projecting the wave function onto representations of the three-dimensional rotation group, i.e., the special orthogonal group in three dimensions SO(3). As a consequence, the wave function becomes an eigenfunction of the angular momentum operator which (i) eliminates the contamination of the ground-state wave function by highly excited rotational states arising from the broken rotational symmetry and (ii) enables the targeting of specific rotational states of the molecule. We demonstrate the efficiency of the symmetry projection technique by calculating the energies of the low-lying rotational states of the H2 and H3+ molecules.

Ultra-fast semi-empirical quantum chemistry for high-throughput computational campaigns with Sparrow.

Semi-empirical quantum chemical approaches are known to compromise accuracy for the feasibility of calculations on huge molecules. However, the need for ultrafast calculations in interactive quantum mechanical studies, high-throughput virtual screening, and data-driven machine learning has shifted the emphasis toward calculation runtimes recently. This comes with new constraints for the software implementation as many fast calculations would suffer from a large overhead of the manual setup and other procedures that are comparatively fast when studying a single molecular structure, but which become prohibitively slow for high-throughput demands. In this work, we discuss the effect of various well-established semi-empirical approximations on calculation speed and relate this to data transfer rates from the raw-data source computer to the results of the visualization front end. For the former, we consider desktop computers, local high performance computing, and remote cloud services in order to elucidate the effect on interactive calculations, for web and cloud interfaces in local applications, and in world-wide interactive virtual sessions. The models discussed in this work have been implemented into our open-source software SCINE Sparrow.

High-throughput ab initio reaction mechanism exploration in the cloud with automated multi-reference validation.

Quantum chemical calculations on atomistic systems have evolved into a standard approach to studying molecular matter. These calculations often involve a significant amount of manual input and expertise, although most of this effort could be automated, which would alleviate the need for expertise in software and hardware accessibility. Here, we present the AutoRXN workflow, an automated workflow for exploratory high-throughput electronic structure calculations of molecular systems, in which (i) density functional theory methods are exploited to deliver minimum and transition-state structures and corresponding energies and properties, (ii) coupled cluster calculations are then launched for optimized structures to provide more accurate energy and property estimates, and (iii) multi-reference diagnostics are evaluated to back check the coupled cluster results and subject them to automated multi-configurational calculations for potential multi-configurational cases. All calculations are carried out in a cloud environment and support massive computational campaigns. Key features of all components of the AutoRXN workflow are autonomy, stability, and minimum operator interference. We highlight the AutoRXN workflow with the example of an autonomous reaction mechanism exploration of the mode of action of a homogeneous catalyst for the asymmetric reduction of ketones.

Toward in silico Catalyst Optimization.

In this minireview, we overview a computational pipeline developed within the framework of NCCR Catalysis that can be used to successfully reproduce the enantiomeric ratios of homogeneous catalytic reactions. At the core of this pipeline is the SCINE Molassembler module, a graph-based software that provides algorithms for molecular construction of all periodic table elements. With this pipeline, we are able to simultaneously functionalizenand generate ensembles of transition state conformers, which permits facile exploration of the influencenof various substituents on the overall enantiomeric ratio. This allows preconceived back-of-the-envelope designnmodels to be tested and subsequently refined by providing quick and reliable access to energetically low-lyingntransition states, which represents a key step in undertaking in silico catalyst optimization.

The Apparently Unreactive Substrate Facilitates the Electron Transfer for Dioxygen Activation in Rieske Dioxygenases.

Rieske dioxygenases belong to the non-heme iron family of oxygenases and catalyze important cis-dihydroxylation as well as O-/N-dealkylation and oxidative cyclization reactions for a wide range of substrates. The lack of substrate coordination at the non-heme ferrous iron center, however, makes it particularly challenging to delineate the role of the substrate for productive O 2 activation. Here, we studied the role of the substrate in the key elementary reaction leading to O 2 activation from a theoretical perspective by systematically considering (i) the 6-coordinate to 5-coordinate conversion of the non-heme FeII upon abstraction of a water ligand, (ii) binding of O 2 , and (iii) transfer of an electron from the Rieske cluster. We systematically evaluated the spin-state-dependent reaction energies and structural effects at the active site for all combinations of the three elementary processes in the presence and absence of substrate using naphthalene dioxygenase as a prototypical Rieske dioxygenase. We find that reaction energies for the generation of a coordination vacancy at the non-heme Fe II center through thermoneutral H2 O reorientation and exothermic O 2 binding prior to Rieske cluster oxidation are largely insensitive to the presence of naphthalene and do not lead to formation of any of the known reactive Fe-oxygen species. By contrast, the role of the substrate becomes evident after Rieske cluster oxidation and exclusively for the 6-coordinate non-heme Fe II sites in that the additional electron is found at the substrate instead of at the iron and oxygen atoms. Our results imply an allosteric control of the substrate on Rieske dioxygenase reactivity to happen prior to changes at the non-heme Fe II in agreement with a strategy that avoids unproductive O 2 activation.

The transferability limits of static benchmarks.

Every practical method to solve the Schrödinger equation for interacting many-particle systems introduces approximations. Such methods are therefore plagued by systematic errors. For computational chemistry, it is decisive to quantify the specific error for some system under consideration. Traditionally, the primary way for such an error assessment has been benchmarking data, usually taken from the literature. However, their transferability to a specific molecular system, and hence, the reliability of the traditional approach always remains uncertain to some degree. In this communication, we elaborate on the shortcomings of this traditional way of static benchmarking by exploiting statistical analyses using one of the largest quantum chemical benchmark sets available. We demonstrate the uncertainty of error estimates in the light of the choice of reference data selected for a benchmark study. To alleviate the issues with static benchmarks, we advocate to rely instead on a rolling and system-focused approach for rigorously quantifying the uncertainty of a quantum chemical result.

The Exploration of Chemical Reaction Networks.

Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various algorithmic advances have shown that such structural screenings must and can be automated and routinely carried out. This will replace the standard approach of manually studying a selected and restricted number of molecular structures for a chemical mechanism. The complexity of the task has led to many different approaches. However, all of them address the same general target, namely to produce a complete atomistic picture of the kinetics of a chemical process. It is the purpose of this overview to categorize the problems that should be targeted and to identify the principal components and challenges of automated exploration machines so that the various existing approaches and future developments can be compared based on well-defined conceptual principles.

Charge-Transfer-Induced Predissociation in Rydberg States of Molecular Cations: MgAr.

Very little is known about the Rydberg states of molecular cations, i.e., Rydberg states having a doubly charged ion core. With the example of MgAr+, we present general features of the structure and dynamics of the Rydberg states of molecular cations, which we find are subject to the process of charge-transfer-induced predissociation. Our study focuses on the spectrum of low-n Rydberg states with potential-energy functions associated with the Mg+(3d and 4s) + Ar(1S0) dissociation asymptotes. In particular, we have recorded spectra of the 3dπΩ' (Ω' = 1/2, 3/2) Rydberg states, extending from the lowest (v' = 0) vibrational levels to their dissociation limits. This spectral range encompasses the region where the onset of predissociation by interaction with the mostly repulsive 2Σ and 2Π charge-transfer states associated with the Mg(3s2) + Ar+(2P1/2,3/2) dissociation asymptotes is observed. This interaction leads to very strong perturbations of the 3dπ Rydberg states of MgAr+, revealed by vibrational progressions exhibiting large and rapid variations of the vibrational intervals, line widths, and spin-orbit splittings. We attribute the anomalous sign and magnitude of the spin-orbit coupling constant of the 3dπ state to the interaction with a 2Π Rydberg state correlating to the Mg+(4p) + Ar(1S0) dissociation limit. To analyze our spectra and elucidate the underlying process of charge-transfer-induced predissociation, we implemented a model that allowed us to derive the potential-energy functions of the charge-transfer states and to quantitatively reproduce the experimental results. This analysis characterizes the main features of the dynamics of the Rydberg series converging to the ground state of MgAr2+. We expect that the results and analysis reported here are qualitatively valid for a broader range of singly charged molecular cations, which are inherently prone to charge-transfer interactions.

Immersive Interactive Quantum Mechanics for Teaching and Learning Chemistry.

The impossibility of experiencing the molecular world with our senses hampers teaching and understanding chemistry because very abstract concepts (such as atoms, chemical bonds, molecular structure, reactivity) are required for this process. Virtual reality, especially when based on explicit physical modeling (potentially in real time), offers a solution to this dilemma. Chemistry teaching can make use of advanced technologies such as virtual-reality frameworks and haptic devices. We show how an immersive learning setting could be applied to help students understand the core concepts of typical chemical reactions by offering a much more intuitive approach than traditional learning settings. Our setting relies on an interactive exploration and manipulation of a chemical system; this system is simulated in real-time with quantum chemical methods, and therefore, behaves in a physically meaningful way.

On the Predictive Power of Chemical Concepts.

Many chemical concepts can be well defined in the context of quantum chemical theories. Examples are the electronegativity scale of Mulliken and Jaffé and the hard and soft acids and bases concept of Pearson. The sound theoretical basis allows for a systematic definition of such concepts. However, while they are often used to describe and compare chemical processes in terms of reactivity, their predictive power remains unclear. In this work, we elaborate on the predictive potential of chemical reactivity concepts, which can be crucial for autonomous reaction exploration protocols to guide them by first-principles heuristics that exploit these concepts.