Vibrational Entanglement through the Lens of Quantum Information Measures.

We introduce a quantum information analysis of vibrational wave functions to understand complex vibrational spectra of molecules with strong anharmonic couplings and vibrational resonances. For this purpose, we define one- and two-modal entropies to guide the identification of strongly coupled vibrational modes and to characterize correlations within modal basis sets. We evaluate these descriptors for multiconfigurational vibrational wave functions which we calculate with the n-mode vibrational density matrix renormalization group algorithm. Based on the quantum information measures, we present a vibrational entanglement analysis of the vibrational ground and excited states of CO2, which display strong anharmonic effects due to the symmetry-induced and accidental (near-) degeneracies. We investigate the entanglement signature of the Fermi resonance and discuss the maximally entangled state arising from the two degenerate bending modes.

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.

Nanoscale chemical reaction exploration with a quantum magnifying glass.

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a "quantum magnifying glass" that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

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.

A human-machine interface for automatic exploration of chemical reaction networks.

Autonomous reaction network exploration algorithms offer a systematic approach to explore mechanisms of complex chemical processes. However, the resulting reaction networks are so vast that an exploration of all potentially accessible intermediates is computationally too demanding. This renders brute-force explorations unfeasible, while explorations with completely pre-defined intermediates or hard-wired chemical constraints, such as element-specific coordination numbers, are not flexible enough for complex chemical systems. Here, we introduce a STEERING WHEEL to guide an otherwise unbiased automated exploration. The STEERING WHEEL algorithm is intuitive, generally applicable, and enables one to focus on specific regions of an emerging network. It also allows for guiding automated data generation in the context of mechanism exploration, catalyst design, and other chemical optimization challenges. The algorithm is demonstrated for reaction mechanism elucidation of transition metal catalysts. We highlight how to explore catalytic cycles in a systematic and reproducible way. The exploration objectives are fully adjustable, allowing one to harness the STEERING WHEEL for both structure-specific (accurate) calculations as well as for broad high-throughput screening of possible reaction intermediates.

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.

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.

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.

Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations.

We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general, high-dimensional model representations of potential energy surfaces. For this purpose, we extend the vDMRG framework to support vibrational Hamiltonians expressed in the so-called n-mode second-quantization formalism. The resulting n-mode vDMRG method offers full flexibility with respect to both the functional form of the PES and the choice of the single-particle basis set. We leverage this framework to apply, for the first time, vDMRG based on an anharmonic modal basis set optimized with the vibrational self-consistent field algorithm on an on-the-fly constructed PES. We also extend the n-mode vDMRG framework to include excited-state-targeting algorithms in order to efficiently calculate anharmonic transition frequencies. We demonstrate the capabilities of our novel n-mode vDMRG framework for methyloxirane, a challenging molecule with 24 coupled vibrational modes.

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.

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.

Lifelong Machine Learning Potentials.

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years, a vast number of MLPs have been trained from scratch because learning additional data typically requires retraining on all data to not forget previously acquired knowledge. Additionally, most common structural descriptors of MLPs cannot represent efficiently a large number of different chemical elements. In this work, we tackle these problems by introducing element-embracing atom-centered symmetry functions (eeACSFs), which combine structural properties and element information from the periodic table. These eeACSFs are key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pretrained MLP to arrive at a continuously adapting lMLP, because a predefined level of accuracy can be ensured. To extend the applicability of an lMLP to new systems, we apply continual learning strategies to enable autonomous and on-the-fly training on a continuous stream of new data. For the training of deep neural networks, we propose the continual resilient (CoRe) optimizer and incremental learning strategies relying on rehearsal of data, regularization of parameters, and the architecture of the model.

Quantum chemical data generation as fill-in for reliability enhancement of machine-learning reaction and retrosynthesis planning.

Data-driven synthesis planning has seen remarkable successes in recent years by virtue of modern approaches of artificial intelligence that efficiently exploit vast databases with experimental data on chemical reactions. However, this success story is intimately connected to the availability of existing experimental data. It may well occur in retrosynthetic and synthesis design tasks that predictions in individual steps of a reaction cascade are affected by large uncertainties. In such cases, it will, in general, not be easily possible to provide missing data from autonomously conducted experiments on demand. However, first-principles calculations can, in principle, provide missing data to enhance the confidence of an individual prediction or for model retraining. Here, we demonstrate the feasibility of such an ansatz and examine resource requirements for conducting autonomous first-principles calculations on demand.

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.

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.

Corresponding Active Orbital Spaces along Chemical Reaction Paths.

The accuracy of reaction energy profiles calculated with multiconfigurational electronic structure methods and corrected by multireference perturbation theory depends crucially on consistent active orbital spaces selected along the reaction path. However, it has been challenging to choose molecular orbitals that can be considered corresponding in different molecular structures. Here, we demonstrate how active orbital spaces can be selected consistently along reaction coordinates in a fully automatized way. The approach requires no structure interpolation between reactants and products. Instead, it emerges from a synergy of the Direct Orbital Selection orbital mapping ansatz combined with our fully automated active space selection algorithm autoCAS. We demonstrate our algorithm for the potential energy profile of the homolytic carbon-carbon bond dissociation and rotation around the double bond of 1-pentene in the electronic ground state. However, our algorithm also applies to electronically excited Born-Oppenheimer surfaces.

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.

Second-Order Self-Consistent Field Algorithms: From Classical to Quantum Nuclei.

This work presents a general framework for deriving exact and approximate Newton self-consistent field (SCF) orbital optimization algorithms by leveraging concepts borrowed from differential geometry. Within this framework, we extend the augmented Roothaan-Hall (ARH) algorithm to unrestricted electronic and nuclear-electronic calculations. We demonstrate that ARH yields an excellent compromise between stability and computational cost for SCF problems that are hard to converge with conventional first-order optimization strategies. In the electronic case, we show that ARH overcomes the slow convergence of orbitals in strongly correlated molecules with the example of several iron-sulfur clusters. For nuclear-electronic calculations, ARH significantly enhances the convergence already for small molecules, as demonstrated for a series of protonated water clusters.