Perspective: multi-configurational methods in bio-inorganic chemistry

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.

Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]- Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the ΔE is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect ΔE. Our best revised single-reference CC estimates for ΔE are 85-91 kJ/mol, including energy corrections to account for contributions beyond triples, core-valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree-Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82-84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, r2SCAN with 10-13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The r2SCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC ΔE results within 2 kJ/mol.

Second and Outer Coordination Sphere Effects in Nitrogenase, Hydrogenase, Formate Dehydrogenase, and CO Dehydrogenase

Gases like H2, N2, CO2, and CO are increasingly recognized as critical feedstock in "green" energy conversion and as sources of nitrogen and carbon for the agricultural and chemical sectors. However, the industrial transformation of N2, CO2, and CO and the production of H2 require significant energy input, which renders processes like steam reforming and the Haber-Bosch reaction economically and environmentally unviable. Nature, on the other hand, performs similar tasks efficiently at ambient temperature and pressure, exploiting gas-processing metalloenzymes (GPMs) that bind low-valent metal cofactors based on iron, nickel, molybdenum, tungsten, and sulfur. Such systems are studied to understand the biocatalytic principles of gas conversion including N2 fixation by nitrogenase and H2 production by hydrogenase as well as CO2 and CO conversion by formate dehydrogenase, carbon monoxide dehydrogenase, and nitrogenase. In this review, we emphasize the importance of the cofactor/protein interface, discussing how second and outer coordination sphere effects determine, modulate, and optimize the catalytic activity of GPMs. These may comprise ionic interactions in the second coordination sphere that shape the electron density distribution across the cofactor, hydrogen bonding changes, and allosteric effects. In the outer coordination sphere, proton transfer and electron transfer are discussed, alongside the role of hydrophobic substrate channels and protein structural changes. Combining the information gained from structural biology, enzyme kinetics, and various spectroscopic techniques, we aim toward a comprehensive understanding of catalysis beyond the first coordination sphere.

Modern multireference methods and their application in transition metal chemistry

Transition metal chemistry is a challenging playground for quantum chemical methods owing to the simultaneous presence of static and dynamic electron correlation effects in many systems. Wavefunction based multireference (MR) methods constitute a physically sound and systematically improvable Ansatz to deal with this complexity but suffer from some conceptual difficulties and high computational costs. The latter problem partially arises from the unfavorable scaling of the Full Configuration Interaction (Full-CI) problem which in the majority of MR methods is solved for a subset of the molecular orbital space, the so-called active space. In the last years multiple methods such as modern variants of selected CI, Full-CI Quantum Monte Carlo (FCIQMC) and the density matrix renormalization group (DMRG) have been developed that solve the Full-CI problem approximately for a fraction of the computational cost required by conventional techniques thereby significantly extending the range of applicability of modern MR methods. This perspective review outlines recent advancements in the field of MR electronic structure methods together with the resulting chances and challenges for theoretical studies in the field of transition metal chemistry. In light of its emerging importance a special focus is put on the selection of adequate active spaces and the concomitant development of numerous selection aides in recent years.

Successes, challenges, and opportunities for quantum chemistry in understanding metalloenzymes for solar fuels research

Overview of the rich and diverse contributions of quantum chemistry to understanding the structure and function of the biological archetypes for solar fuel research, photosystem II and hydrogenases.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

X-ray Crystallography and Vibrational Spectroscopy Reveal the Key Determinants of Biocatalytic Dihydrogen Cycling by [NiFe] Hydrogenases

[NiFe] hydrogenases are complex model enzymes for the reversible cleavage of dihydrogen (H₂). However, structural determinants of efficient H₂ binding to their [NiFe] active site are not properly understood. Here, we present crystallographic and vibrational‐spectroscopic insights into the unexplored structure of the H₂‐binding [NiFe] intermediate. Using an F₄₂₀‐reducing [NiFe]‐hydrogenase from Methanosarcina barkeri as a model enzyme, we show that the protein backbone provides a strained chelating scaffold that tunes the [NiFe] active site for efficient H₂ binding and conversion. The protein matrix also directs H₂ diffusion to the [NiFe] site via two gas channels and allows the distribution of electrons between functional protomers through a subunit‐bridging FeS cluster. Our findings emphasize the relevance of an atypical Ni coordination, thereby providing a blueprint for the design of bio‐inspired H₂‐conversion catalysts.

Biomimetic heterobimetallic architecture of Ni(ii) and Fe(ii) for CO2 hydrogenation in aqueous media. A DFT study

In this work, density functional theory has been employed to design a heterobimetallic catalyst of Ni(ii) and Fe(ii) for the effective CO2 hydrogenation to HCOOH. Based on computational results, our newly designed catalyst is found to be effective for such conversion reactions with free energy as low as 14.13 kcal mol-1 for the rate determining step. Such a low value of free energy indicates that the NiFe heterobimetallic catalyst can prove to be very efficient for the above said conversion. Moreover, the effects of ligand substitutions at the active metal center and the effects due to various spin states are also explored, and can serve as a great tool for the rational design of NiFe catalyst for CO2 hydrogenation.

Theoretical Studies of Nickel-Dependent Enzymes

The advancements of quantum chemical methods and computer power allow detailed mechanistic investigations of metalloenzymes. In particular, both quantum chemical cluster and combined QM/MM approaches have been used, which have been proven to successfully complement experimental studies. This review starts with a brief introduction of nickel-dependent enzymes and then summarizes theoretical studies on the reaction mechanisms of these enzymes, including NiFe hydrogenase, methyl-coenzyme M reductase, nickel CO dehydrogenase, acetyl CoA synthase, acireductone dioxygenase, quercetin 2,4-dioxygenase, urease, lactate racemase, and superoxide dismutase.

Computational Approach to Molecular Catalysis by 3d Transition Metals: Challenges and Opportunities

Computational chemistry provides a versatile toolbox for studying mechanistic details of catalytic reactions and holds promise to deliver practical strategies to enable the rational in silico catalyst design. The versatile reactivity and nontrivial electronic structure effects, common for systems based on 3d transition metals, introduce additional complexity that may represent a particular challenge to the standard computational strategies. In this review, we discuss the challenges and capabilities of modern electronic structure methods for studying the reaction mechanisms promoted by 3d transition metal molecular catalysts. Particular focus will be placed on the ways of addressing the multiconfigurational problem in electronic structure calculations and the role of expert bias in the practical utilization of the available methods. The development of density functionals designed to address transition metals is also discussed. Special emphasis is placed on the methods that account for solvation effects and the multicomponent nature of practical catalytic systems. This is followed by an overview of recent computational studies addressing the mechanistic complexity of catalytic processes by molecular catalysts based on 3d metals. Cases that involve noninnocent ligands, multicomponent reaction systems, metal-ligand and metal-metal cooperativity, as well as modeling complex catalytic systems such as metal-organic frameworks are presented. Conventionally, computational studies on catalytic mechanisms are heavily dependent on the chemical intuition and expert input of the researcher. Recent developments in advanced automated methods for reaction path analysis hold promise for eliminating such human-bias from computational catalysis studies. A brief overview of these approaches is presented in the final section of the review. The paper is closed with general concluding remarks.

Extremely large differences in DFT energies for nitrogenase models

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen avaiable for other organisms. It contains a complicated MoFe7S9C(homocitrate) cluster in its active site. Many computational studies with density-functional theory (DFT) of the nitrogenase enzyme have been presented, but they do not show any consensus - they do not even agree where the first four protons should be added, forming the central intermediate E4. We show that the prime reason for this is that different DFT methods give relative energies that differ by almost 600 kJ mol-1 for different protonation states. This is 4-30 times more than what is observed for other systems. The reason for this is that in some structures, the hydrogens bind to sulfide or carbide ions as protons, whereas in other structures they bind to the metals as hydride ions, changing the oxidation state of the metals, as well as the Fe-C, Fe-S and Fe-Fe distances. The energies correlate with the amount of Hartree-Fock exchange in the method, indicating a variation in the amount of static correlation in the structures. It is currently unclear which DFT method gives the best results for nitrogenase. We show that non-hybrid DFT functionals and TPSSh give the most accurate structures of the resting active site, whereas B3LYP and PBE0 give the best H2 dissociation energies. However, no DFT method indicates that a structure of E4 with two bridging hydride ions is lowest in energy, as spectroscopic experiments indicate.

The Challenging in silico Description of Carbon Monoxide Oxidation as Catalyzed by Molybdenum-Copper CO Dehydrogenase

Carbon monoxide (CO) is a highly toxic gas to many living organisms. However, some microorganisms are able to use this molecule as the sole source of carbon and energy. Soil bacteria such as the aerobic Oligotropha carboxidovorans are responsible for the annual removal of about 2x108 tons of CO from the atmosphere. Detoxification through oxidation of CO to CO2 is enabled by the MoCu-dependent CO-dehydrogenase enzyme (MoCu-CODH) which-differently from other enzyme classes with similar function-retains its catalytic activity in the presence of atmospheric O2. In the last few years, targeted advancements have been described in the field of bioengineering and biomimetics, which is functional for future technological exploitation of the catalytic properties of MoCu-CODH and for the reproduction of its reactivity in synthetic complexes. Notably, a growing interest for the quantum chemical investigation of this enzyme has recently also emerged. This mini-review compiles the current knowledge of the MoCu-CODH catalytic cycle, with a specific focus on the outcomes of theoretical studies on this enzyme class. Rather controversial aspects from different theoretical studies will be highlighted, thus illustrating the challenges posed by this system as far as the application of density functional theory and hybrid quantum-classical methods are concerned.

Reaction Mechanism of [NiFe] Hydrogenase Studied by Computational Methods

[NiFe] hydrogenases catalyze the reversible conversion of molecular hydrogen to protons and electrons. This seemingly simple reaction has attracted much attention because of the prospective use of H₂ as a clean fuel. In this paper, we have studied the full reaction mechanism of this enzyme with various computational methods. Geometries were obtained with combined quantum mechanical and molecular mechanics (QM/MM) calculations. To get more accurate energies and obtain a detailed account of the surroundings, we performed big-QM calculations with 819 atoms in the QM region. Moreover, QM/MM thermodynamic cycle perturbation calculations were performed to obtain free energies. Finally, density matrix renormalisation group complete active space self-consistent field calculations were carried out to study the electronic structures of the various states in the reaction mechanism. Our calculations indicate that the Ni-L state is not involved in the reaction mechanism. Instead, the Ni-C state is reduced by one electron and then the bridging hydride ion is transferred to the sulfur atom of Cys546 as a proton and the two electrons transfer to the Ni ion. This step turned out to be rate-determining with an energy barrier of 58 kJ/mol, which is consistent with the experimental rate of 750 ± 90 s^-1 (corresponding to ∼52 kJ/mol). The cleavage of the H-H bond is facile with an energy barrier of 33 kJ/mol, according to our calculations. We also find that the reaction energies are sensitive to the size of the QM system, the basis set, and the density functional theory method, in agreement with previous studies.

Comprehensive reaction mechanisms at and near the Ni-Fe active sites of [NiFe] hydrogenases

[NiFe] hydrogenase (H2ase) catalyzes the oxidation of dihydrogen to two protons and two electrons and/or its reverse reaction. For this simple reaction, the enzyme has developed a sophisticated but intricate mechanism with heterolytic cleavage of dihydrogen (or a combination of a hydride and a proton), where its Ni-Fe active site exhibits various redox states. Recently, thermodynamic parameters of the acid-base equilibrium for activation-inactivation, a new intermediate in the catalytic reaction, and new crystal structures of [NiFe] H2ases have been reported, providing significant insights into the activation-inactivation and catalytic reaction mechanisms of [NiFe] H2ases. This Perspective provides an overview of the reaction mechanisms of [NiFe] H2ases based on these new findings.

QM/MM Investigation of the Role of a Second Coordination Shell Arginine in [NiFe]-Hydrogenases

[NiFe]-hydrogenases are highly efficient catalysts for the heterolytic splitting of molecular hydrogen (H₂). The heterobimetallic cysteine-coordinated active site of these enzymes is covered by a highly conserved arginine residue, whose role in the reaction is not fully resolved yet. The structural and catalytic role of this arginine is investigated here using QM/MM calculations with various exchange-correlation functionals. All of them give a very consistent picture of the thermodynamics of H₂ oxidation. The concept of the presence of a neutral arginine and its direct involvement as a Frustrated Lewis Pair (FLP) in the reaction is critically evaluated. The arginine, however, would exist in its standard protonation state and perform a critical role in positioning and slightly polarizing the substrate H₂. It is not directly involved in the heterolytic processing of H₂ but guides its approach and reduces its flexibility during binding. Upon substitution of the positively charged arginine by a charge-conserving lysine residue, the H₂ binding position remains unaffected. However, critical hydrogen bonding interactions with nearby aspartate residues are lost. In addition, the H₂ polarization is unfavorable and the reduced side-chain volume may negatively affect the kinetics of the catalytic process.

Jensen HJ, Hedegård ED. Exploration of H2 binding to the [NiFe]-hydrogenase active site with multiconfigurational density functional theory

The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions.

From Enzymes to Functional Materials-Towards Activation of Small Molecules

The design of non-noble metal-containing heterogeneous catalysts for the activation of small molecules is of utmost importance for our society. While nature possesses very sophisticated machineries to perform such conversions, rationally designed catalytic materials are rare. Herein, we aim to raise the awareness of the overall common design and working principles of catalysts incorporating aspects of biology, chemistry, and material sciences.