Mechanistic Principles of Hydrogen Evolution in the Membrane-Bound Hydrogenase

The membrane-bound hydrogenase (Mbh) from Pyrococcus furiosus is an archaeal member of the Complex I superfamily. It catalyzes the reduction of protons to H2 gas powered by a [NiFe] active site and transduces the free energy into proton pumping and Na+/H+ exchange across the membrane. Despite recent structural advances, the mechanistic principles of H2 catalysis and ion transport in Mbh remain elusive. Here, we probe how the redox chemistry drives the reduction of the proton to H2 and how the catalysis couples to conformational dynamics in the membrane domain of Mbh. By combining large-scale quantum chemical density functional theory (DFT) and correlated ab initio wave function methods with atomistic molecular dynamics simulations, we show that the proton transfer reactions required for the catalysis are gated by electric field effects that direct the protons by water-mediated reactions from Glu21L toward the [NiFe] site, or alternatively along the nearby His75L pathway that also becomes energetically feasible in certain reaction steps. These local proton-coupled electron transfer (PCET) reactions induce conformational changes around the active site that provide a key coupling element via conserved loop structures to the ion transport activity. We find that H2 forms in a heterolytic proton reduction step, with spin crossovers tuning the energetics along key reaction steps. On a general level, our work showcases the role of electric fields in enzyme catalysis and how these effects are employed by the [NiFe] active site of Mbh to drive PCET reactions and ion transport.

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

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

Metal- and ligand-substitution-induced changes in the kinetics and thermodynamics of hydrogen activation and hydricity in a dinuclear metal complex

Catalytic function in organometallic complexes is achieved by carefully selecting their central metals and ligands. In this study, the effects of a metal and a ligand on the kinetics and thermodynamics of hydrogen activation, hydricity degree of the hydride complex, and susceptibility to electronic oxidation in bioinspired NiFe complexes, [NiIIX FeII(Cl)(CO)Y]+ ([NiFe(Cl)(CO)]+; X = N,N'-diethyl-3,7-diazanonane-1,9-dithiolato and Y = 1,2-bis(diphenylphosphino)ethane), were investigated. The density functional theory calculations revealed that the following order thermodynamically favored hydrogen activation: [NiFe(CO)]2+ > [NiRu(CO)]2+ > [NiFe(CNMe)]2+ ∼ [PdRu(CO)]2+ ∼ [PdFe(CO)]2+ ≫ [NiFe(NCS)]+. Moreover, the reverse order thermodynamically favored the hydricity degree.

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.

Understanding the initial events of the oxidative damage and protection mechanisms of the AA9 lytic polysaccharide monooxygenase family

Lytic polysaccharide monooxygenase (LPMO) is a new class of oxidoreductases that boosts polysaccharide degradation employing a copper active site. This boost may facilitate the cost-efficient production of biofuels and high-value chemicals from polysaccharides such as lignocellulose. Unfortunately, self-oxidation of the active site inactivates LPMOs. Other oxidoreductases employ hole-hopping mechanisms as protection against oxidative damage, but little is generally known about the details of these mechanisms. Herein, we employ highly accurate theoretical models based on density functional theory (DFT) molecular mechanics (MM) hybrids to understand the initial steps in LPMOs' protective measures against self-oxidation; we identify several intermediates recently proposed from experiment, and quantify which are important for protective hole-hopping pathways. Investigations on two different LPMOs show consistently that a tyrosine residue close to copper is crucial for protection: this explains recent experiments, showing that LPMOs without this tyrosine are more susceptible to self-oxidation.

How does multi-reference computation change the catalysis chemistry? DFT and CASPT2 studies of the Cu-catalysed coupling reactions between aryl iodides and β-diketones

The molecular mechanism of a Cu-catalysed coupling reaction was theoretically studied using density functional theory (DFT) and the complete active space self-consistent field method followed by the second-order perturbation theory (CASSCF/CASPT2) to investigate the effects of the strong electron correlation of the Cu centre on the reaction profile. Both DFT and CASSCF/CASPT2 calculations showed that the catalytic cycle proceeds via an oxidative addition (OA) reaction, followed by a reductive elimination (RE) reaction, where OA is the rate-determining step. Although the DFT-calculated activation energies of the OA and RE steps are highly dependent on the choice of functionals, the CASSCF/CASPT2 results are less affected by the choice of DFT-optimised geometries. Therefore, with a careful assessment based on the CASSCF/CASPT2 single-point energy evaluation, an optimal choice of the DFT geometry is of good qualitative use for energetics at the CASPT2 level of theory. Based on the changes in the electron populations of the 3d orbitals during the OA and RE steps, the characteristic features of the DFT-calculated electronic structure were qualitatively consistent with those calculated using the CASSCF method. Further electronic structure analysis by the natural orbital occupancy of the CASSCF wavefunction showed that the ground state is almost single-reference in this system and the strong electron correlation effect of the Cu centre can be dealt with using the MP2 or CCSD method, too. However, the slightly smaller occupation numbers of the 3dπ orbital in the course of reactions suggested that the electron correlation effect of the Cu(III) centre appears through the interaction between the 3dπ orbital and the C-I antibonding σ* orbital in the OA step, and between the 3dπ orbital and the Cu-C antibonding σ* orbital in the RE step.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

A local pair-natural orbital-based complete-active space perturbation theory using orthogonal localized virtual molecular orbitals

The multireference second-order perturbation theory (CASPT2) is known to deliver a quantitative description of various complex electronic states. Despite its near-size-consistent nature, the applicability of the CASPT2 method to large, real-life systems is mostly hindered by large computational and storage costs for the two-external tensors, such as two-electron integrals, amplitudes, and residuum. To this end, Menezes and co-workers developed a reduced-scaling CASPT2 scheme by incorporating the local pair-natural orbital (PNO) representation of the many-body wave functions using non-orthonormal projected atomic orbitals (PAOs) into the CASPT theory [F. Menezes et al., J. Chem. Phys. 145, 124115 (2016)]. Alternatively, in this paper, we develop a new PNO-based CASPT2 scheme using the orthonormal localized virtual molecular orbitals (LVMOs) and assess its performance and accuracy in comparison with the conventional PAO-based counterpart. Albeit the compactness, the LVMOs were considered to perform somewhat poorly compared to PAOs in the local correlation framework because they caused enormously large orbital domains. In this work, we show that the size of LVMO domains can be rendered comparable to or even smaller than that of PAOs by the use of the differential overlap integrals for domain construction. Optimality of the MOs from the CASSCF treatment is a key to reducing the LVMO domain size for the multireference case. Due to the augmented Hessian-based localization algorithm, an additional computational cost for obtaining the LVMOs is relatively minor. We demonstrate that the LVMO-based PNO-CASPT2 method is routinely applicable to large, real-life molecules such as Menshutkin SN2 reaction in a single-walled carbon nanotube reaction field.

Energetics for CO2 Reduction by Molybdenum-Containing Formate Dehydrogenase

The level of carbon dioxide in the atmosphere has increased in a dangerous way during the past century. Methods to decrease this level are therefore of high interest at present. Inspiration to do so in an efficient way could come from biological systems. Molybdenum-containing formate dehydrogenase (Mo-FDH) is one of the most interesting enzymes in this respect. For example, the reduction potential required is not very low. The normal reaction catalyzed by Mo-FDH is actually the opposite one of oxidizing formate to CO₂. However, recent electrochemical studies have shown that the reaction can be reversed by a moderate lowering of the reduction potential. The goal of the present study has been to study the full mechanism of Mo-FDH, particularly in the most interesting direction of reducing CO₂, which has not been done before. The methods used are the same as those that have been shown to give excellent results for redox enzymes in all cases they have been tested. The results obtained for Mo-FDH are also in excellent agreement with the experimental results.

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.

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = −2JS_i · S_j) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term jS², the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H₂ under a covalent bond dissociation, C, O, Si, NH, OH⁺, CH₂, NF, O₂, and triple bond dissociated N₂ molecule revealed that the BxB can compute the J value within 1 kcal mol⁻¹ of errors with less computational costs than conventional quantum phase estimation-based approaches.

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol⁻¹ of energy tolerance.

Accurate Ring Strain Energy Calculations on Saturated Three-Membered Heterocycles with One Group 13-16 Element

Accurate ring strain energy (RSE) data for parent (CH₂)₂X rings are reported, where X are group 13-16 elements (El) in their lowest oxidation state, from the second to the sixth row, with their covalence completed by bonds to H. They are obtained from appropriate homodesmotic and hyper-homodesmotic reactions at different levels up to the CCSD(T) level, thus providing a benchmark of high-quality reference RSE values, as well as acceptably accurate faster lower-level options. Derivatives of indium, thallium, and lead cannot be properly described by a three-member ring connectivity, because they display a unique donor-acceptor structure from an ethylene π(C═C) orbital to an empty p orbital of a metallylene subunit. The RSE of groups 13 and 14 heterocycles increases on descending in the group (except for Ga and Ge), while it decreases for groups 15 and 16. The latter is presumably due to a strain-releasing mechanism favored by the increase of p-character at the sp³-type atomic orbital used by El in the endocyclic El-C bonds, %p(El)_El-C, originated by the tendency of the El lone pairs in groups 15-16 to increase their s-character. This strain-releasing mechanism does not exist in heavier tetrels, which keep almost unchanged the p-character in the endocyclic bonds at El, whereas for triels the p-character is still lower owing to their sp²-like hybridization. Remarkable linear correlations were found between the RSE and either the above-mentioned %p(El)_El-C, the distal C-C bond distance or the relaxed force constants for the endocyclic bond angles.

[NiFe], [FeFe], and [Fe] hydrogenase models from isomers

The study of hydrogenase enzymes (H₂ases) is necessary because of their importance to a future hydrogen energy economy. These enzymes come in three distinct classes: [NiFe] H₂ases, which have a propensity toward H₂ oxidation; [FeFe] H₂ases, which have a propensity toward H₂ evolution; and [Fe] H₂ases, which catalyze H^- transfer. Modeling these enzymes has so far treated them as different species, which is understandable given the different cores and ligand sets of the natural molecules. Here, we demonstrate, using x-ray analysis and nuclear magnetic resonance, infrared, Mössbauer spectroscopies, and electrochemical measurement, that the catalytic properties of all three enzymes can be mimicked with only three isomers of the same NiFe complex.

Improving the Light-Induced Spin Transition Efficiency in Ni(II)-Based Macrocyclic-Ligand Complexes

The structural stability and photoabsorption properties of Ni(II)-based metal-organic complexes with octahedral coordination having different planar ligand ring structures were investigated employing density functional theory (DFT) and its time-dependent extension (TD-DFT) considering the M06 exchange-correlation functional and the Def2-TZVP basis set. The results showed that the molecular composition of different planar cyclic ligand structures had significant influences on the structural stability and photoabsorption properties of metal-organic complexes. Only those planar ligands that contained aromatic rings met the basic criteria (thermal stability, structural reversibility, and appropriate excitation frequency domain) for light-induced excited spin state trapping, but their spin transition efficiencies were very different. While, in all three aromatic cases, the singlet electronic excitations induced charge distribution that could help in the singlet-to-triplet spin transition, and triplet excitations, which could assist in the backward (triplet-to-singlet) spin transition, was found only for one complex.

Structure of Diferrocenyl Thioketone: From Molecule to Crystal

Ferrocenyl-functionalized thioketones have recently been recognized as useful building blocks for sulfur-containing compounds with potential applications in materials chemistry. This work is devoted to a single representative of such thioketones, namely diferrocenyl thioketone (Fc₂CS), whose structure has been determined here for the first time. Both X-ray crystallography and a wide variety of quantum-chemical methods were used to explore the structure of Fc₂CS. In addition to the X-ray structure determination, intermolecular interactions occurring in the crystal structure of Fc₂CS were examined in detail by quantum-chemical methods. These methods were also an invaluable tool in studying the molecular structure of Fc₂CS, from the gas phase to solutions and to its crystal. Intramolecular interactions governing the conformational behavior of an isolated Fc₂CS molecule were deduced from quantum-chemical analyses carried out in orbital space and real space. Our experimental and theoretical results indicate that the main structural features of an isolated Fc₂CS molecule in its lowest-energy geometry are retained both upon solvation and in the crystal. The tilt of ferrocenyl groups is only slightly affected by crystal packing forces that are dominated by dispersion. Nonetheless, a network of intermolecular interactions, such as H···H, C···H and S···H, was detected in the Fc₂CS crystal but each of them is fairly weak.

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.

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.

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.

Hydrogen bonding effect between active site and protein environment on catalysis performance in H2-producing [NiFe] hydrogenases

The interaction between the active site and the surrounding protein environment plays a fundamental role in the hydrogen evolution reaction (HER) in [NiFe] hydrogenases. Our density functional theory (DFT) findings demonstrate that the reaction Gibbs free energy required for the rate determining step decreases by 7.1 kcal mol^-1 when the surrounding protein environment is taken into account, which is chiefly due to free energy decreases for the two H⁺/e^- addition steps (the so-called Ni-SIa to I1, and Ni-C to Ni-R), being the largest thermodynamic impediments of the whole reaction. The variety of hydrogen bonds (H-bonds) between the amino acids and the active site is hypothesised to be the main reason for such stability: H-bonds not only work as electrostatic attractive forces that influence the charge redistribution, but more importantly, they act as an electron 'pull' taking electrons from the active site towards the amino acids. Moreover, the electron 'pull' effect through H-bonds via the S^- in cysteine residues shows a larger influence on the energy profile than that via the CN^- ligands on Fe.

The oxygen reduction reaction on [NiFe] hydrogenases

Oxygen tolerance capacity is critical for hydrogen oxidation/evolution catalysts.

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.

Theoretical investigation of aerobic and anaerobic oxidative inactivation of the [NiFe]-hydrogenase active site

The extraordinary capability of [NiFe]-hydrogenases to catalyse the reversible interconversion of protons and electrons into dihydrogen (H₂) has stimulated numerous experimental and theoretical studies addressing the direct utilization of these enzymes in H₂ production processes.

QM/MM Study of the Conversion of Oxophlorin into Verdoheme by Heme Oxygenase

Heme oxygenase is an enzyme that degrades heme, thereby recycling iron in most organisms, including humans. Pervious density functional theory (DFT) calculations have suggested that iron(III) hydroxyheme, an intermediate generated in the first step of heme degradation by heme oxygenase, is converted to iron(III) superoxo oxophlorin in the presence of dioxygen. In this article, we have studied the detailed mechanism of conversion of iron(III) superoxo oxophlorin to verdoheme by using combined quantum mechanics and molecular mechanics (QM/MM) calculations. The calculations employed the B3LYP method and the def2-QZVP basis set, considering dispersion effects with the DFT-D3 approach, obtaining accurate energies with large QM regions of almost 1000 atoms. The reaction was found to be exothermic by -35 kcal/mol, with a rate-determining barrier of 19 kcal/mol in the doublet state. The protein environment and especially water in the enzyme pocket significantly affects the reaction by decreasing the reaction activation energies and changing the structures by providing strategic hydrogen bonds.

Quantum chemical approaches to [NiFe] hydrogenase

The mechanism by which [NiFe] hydrogenase catalyses the oxidation of molecular hydrogen is a significant yet challenging topic in bioinorganic chemistry. With far-reaching applications in renewable energy and carbon mitigation, significant effort has been invested in the study of these complexes. In particular, computational approaches offer a unique perspective on how this enzyme functions at an electronic and atomistic level. In this article, we discuss state-of-the art quantum chemical methods and how they have helped deepen our comprehension of [NiFe] hydrogenase. We outline the key strategies that can be used to compute the (i) geometry, (ii) electronic structure, (iii) thermodynamics and (iv) kinetic properties associated with the enzymatic activity of [NiFe] hydrogenase and other bioinorganic complexes.

H2binding to the active site of [NiFe] hydrogenase studied by multiconfigurational and coupled-cluster methods

CCSD(T) and DMRG-CASPT2 calculations show that H₂prefers to bind to Ni rather than to Fe in [NiFe] hydrogenase.

Hydrogenase Enzymes and Their Synthetic Models: The Role of Metal Hydrides

Hydrogenase enzymes efficiently process H2 and protons at organometallic FeFe, NiFe, or Fe active sites. Synthetic modeling of the many H2ase states has provided insight into H2ase structure and mechanism, as well as afforded catalysts for the H2 energy vector. Particularly important are hydride-bearing states, with synthetic hydride analogues now known for each hydrogenase class. These hydrides are typically prepared by protonation of low-valent cores. Examples of FeFe and NiFe hydrides derived from H2 have also been prepared. Such chemistry is more developed than mimicry of the redox-inactive monoFe enzyme, although functional models of the latter are now emerging. Advances in physical and theoretical characterization of H2ase enzymes and synthetic models have proven key to the study of hydrides in particular, and will guide modeling efforts toward more robust and active species optimized for practical applications.

Why is a proton transformed into a hydride by [NiFe] hydrogenases? An intrinsic reactivity analysis based on conceptual DFT

The hydrogen evolution reaction (HER) catalysed by [NiFe] hydrogenases entails a series of chemical events involving great mechanistic interest.

Theoretical Study of the Dissociation Energy of First-Row Metallocenium Ions

The bond dissociation energy of a series of metallocenium ions, i.e., the energy difference of the reaction MCp2(+) → MCp(+) + Cp· (with M = Ti, V, Cr, Mn, Fe, Co, and Ni), was studied by means of multiconfigurational perturbation theory (CASPT2, RASPT2, NEVPT2) and restricted coupled cluster theory (CCSD(T)). From a comparison between the results obtained from these different methods, and a detailed analysis of their treatment of electron correlation effects, a set of MCp(+)-Cp binding energies are proposed with an accuracy of 5 kcal/mol. The computed results are in good agreement with the experimental data measured by threshold photoelectron photoion coincidence (TPEPICO) spectroscopy but disagree with the more recent threshold collision-induced dissociation (TCID) experiments.