Modeling the MoFe nitrogenase system with broken symmetry density functional theory

Spiers Memorial Lecture: Quantum chemistry, classical heuristics, and quantum advantage

We describe the problems of quantum chemistry, the intuition behind classical heuristic methods used to solve them, a conjectured form of the classical complexity of quantum chemistry problems, and the subsequent opportunities for quantum advantage. This article is written for both quantum chemists and quantum information theorists. In particular, we attempt to summarize the domain of quantum chemistry problems as well as the chemical intuition that is applied to solve them within concrete statements (such as a classical heuristic cost conjecture) in the hope that this may stimulate future analysis.

Calculating the chemical mechanism of nitrogenase: new working hypotheses

The enzyme nitrogenase converts N₂ to NH₃ with stoichiometry N₂ + 8H⁺ + 8e^- → 2NH₃ + H₂. The mechanism is chemically complex with multiple steps that must be consistent with much accumulated experimental information, including exchange of H₂ and N₂ and the N₂-dependent hydrogenation of D₂ to HD. Previous investigations have developed a collection of working hypotheses that guide ongoing density functional investigations of mechanistic steps and sequences. These include (i) hypotheses about the serial provision of protons and their conversion to H atoms bonded to S and Fe atoms of the FeMo-co catalytic site, (ii) the migration of H atoms over the surface of FeMo-co, (iii) the roles of His195, (iv) identification of three protein channels, one for the ingress of N₂, a separate pathway for the passage of exogenous H₂ (D₂) and product H₂ (HD), and a hydrophilic pathway for egress of product NH₃. Two additional working hypotheses are described in this paper. N₂ passing along the N₂ channel approaches and binds end-on to the exo coordination position of Fe2, with favourable energetics when FeMo-co is pre-hydrogenated. This exo-Fe2-N₂ is apparently not reduced but has a promotional role by expanding the reaction zone. A second N₂ can enter via the N₂ ingress channel and bind at the endo-Fe6 position, where it is surrounded by H atom donors suitable for the N₂ → NH₃ conversion. It is proposed that this endo-Fe6 position is also the binding site for H₂ (generated or exogenous), accounting for the competitive inhibition of N₂ reduction by H₂. The HD reaction occurs at the endo-Fe6 site, promoted by N₂ at the exo-Fe2 site. The second hypothesis concerns the most stable electronic states of FeMo-co with ligands bound at Fe2 and Fe6, and provides a protocol for management of electronic states in mechanism calculations.

Structures and reaction dynamics of N2 and H2 binding at FeMo-co, the active site of nitrogenase

The chemical reactions occurring at the Fe₇MoS₉C(homocitrate) cluster, FeMo-co, the active site of the enzyme nitrogenase (N₂ → NH₃), are enigmatic. Experimental information collected over a long period reveals aspects of the roles of N₂ and H₂, each with more than one type of reactivity. This paper reports investigations of the binding of H₂ and N₂ at intact FeMo-co, using density functional simulations of a large 486 atom relevant portion of the protein, resulting in 27 new structures containing H₂ and/or N₂ bound at the exo and endo coordination sites of the participating Fe atoms, Fe2 and Fe6. Binding energies and transition states for association/dissociation are determined, and trajectories for the approach, binding and separation of H₂/N₂ are described, including diffusion of these small molecules through proximal protein. Influences of surrounding amino acids are identified. FeMo-co deforms geometrically when binding H₂ or N₂, and a procedure for calculating the energy cost involved, the adaptation energy, is introduced here. Adaptation energies, which range from 7 to 36 kcal mol^-1 for the reported structures, are influenced by the protonation state of the His195 side chain. Seven N₂ structures and three H₂ structures have negative binding free energies, which include the estimated entropy penalties for binding of N₂, H₂ from proximal protein. These favoured structures have N₂ bound end-on at exo-Fe2, exo-Fe6 and endo-Fe2 positions of FeMo-co, and H₂ bound at the endo-Fe2 position. Various postulated structures with N₂ bridging Fe2 and Fe6 revert to end-on-N₂ at endo positions. The structures are also assessed via the calculated potential energy barriers for association and dissociation. Barriers to the binding of H₂ range from 1 to 20 kcal mol^-1 and barriers to dissociation of H₂ range from 3 to 18 kcal mol^-1. Barriers to the binding of N₂, in either side-on or end-on mode, range from 2 to 18 kcal mol^-1, while dissociation of bound N₂ encounters barriers of 3 to 8 kcal mol^-1 for side-on bonding and 7 to 18 kcal mol^-1 for end-on bonding. These results allow formulation of mechanisms for the H₂/N₂ exchange reaction, and three feasible mechanisms for associative exchange and three for dissociative exchange are identified. Consistent electronic structures and potential energy surfaces are maintained throughout. Changes in the spin populations of Fe2 and Fe6 connected with cluster deformation and with metal-ligand bond formation are identified.

Spin-Regulated Electron Transfer and Exchange-Enhanced Reactivity in Fe4 S4 -Mediated Redox Reaction of the Dph2 Enzyme During the Biosynthesis of Diphthamide

The [4Fe-4S]-dependent radical S-adenosylmethionine (SAM) proteins is one of large families of redox enzymes that are able to carry a panoply of challenging transformations. Despite the extensive studies of structure-function relationships of radical SAM (RS) enzymes, the electronic state-dependent reactivity of the [4Fe-4S] cluster in these enzymes remains elusive. Using combined MD simulations and QM/MM calculations, we deciphered the electronic state-dependent reactivity of the [4Fe-4S] cluster in Dph2, a key enzyme involved in the biosynthesis of diphthamide. Our calculations show that the reductive cleavage of the S-C_(γ) bond is highly dependent on the electronic structure of [4Fe-4S]. Interestingly, the six electronic states can be classified into a low-energy and a high-energy groups, which are correlated with the net spin of Fe4 atom ligated to SAM. Due to the driving force of Fe4-C_(γ) bonding, the net spin on the Fe4 moiety dictate the shift of the opposite spin electron from the Fe1-Fe2-Fe3 block to SAM. Such spin-regulated electron transfer results in the exchange-enhanced reactivity in the lower-energy group compared with those in the higher-energy group. This reactivity principle provides fundamental mechanistic insights into reactivities of [4Fe-4S] cluster in RS enzymes.

Spin-Orbit Coupling Changes the Identity of the Hyper-Open-Shell Ground State of Ce+, and the Bond Dissociation Energy of CeH+ Proves to Be Challenging for Theory

Cerium (Ce) plays important roles in catalysis. Its position in the sixth period of the periodic table leads to spin-orbit coupling (SOC) and other open-shell effects that make the quantum mechanical calculation of cerium compounds challenging. In this work, we investigated the low-lying spin states of Ce⁺ and the bond energy of CeH⁺, both by multiconfigurational methods, in particular, SA-CASSCF, MC-PDFT, CASPT2, XMS-PDFT, and XMS-CASPT2, and by single-configurational methods, namely, Hartree-Fock theory and unrestricted Kohn-Sham density functional theory with 34 choices of the exchange-correlation functional. We found that only CASPT2, XMS-CASPT2, and SA-CASSCF (among the five multiconfigurational methods) and GAM, HCTH, SOGGA11, and OreLYP (among the 35 single-configuration methods) successfully predict that the SOC-free ground spin state of Ce⁺ is a doublet state, and CASPT2 and GAM give the most accurate multireference and single-reference calculations, respectively, of the excitation energy of the first SOC-free excited state for Ce⁺. We calculated that the ground doublet state of Ce⁺ is an intra-atomic hyper-open-shell state. We calculated the spin-orbit energy (E^SO) of Ce⁺ by the five multiconfigurational methods and found that E^SO calculated by CASPT2 is the closest to the experimental value. Taking advantage of the availability of an experimental D₀ for CeH⁺ as a way to provide a unique test of theory, we showed that all the multiconfigurational methods overestimate D₀ by at least 246 meV (5.7 kcal/mol), and only three functionals, namely, SOGGA, MN15, and GAM, have an error of D₀ that is less than 200 meV (5 kcal/mol).

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe²⁺, Fe³⁺, and Co³⁺, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF₂, FeCl₂, and CoF₂. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

Survey of the Geometric and Electronic Structures of the Key Hydrogenated Forms of FeMo-co, the Active Site of the Enzyme Nitrogenase: Principles of the Mechanistically Significant Coordination Chemistry

The enzyme nitrogenase naturally hydrogenates N2 to NH3, achieved through the accumulation of H atoms on FeMo-co, the Fe7MoS9C(homocitrate) cluster that is the catalytically active site. Four intermediates, E1H1, E2H2, E3H3, and E4H4, carry these hydrogen atoms. I report density functional calculations of the numerous possibilities for the geometric and electronic structures of these poly-hydrogenated forms of FeMo-co. This survey involves more than 100 structures, including those with bound H2, and assesses their relative energies and most likely electronic states. Twelve locations for bound H atoms in the active domain of FeMo-co, including Fe–H–Fe and Fe–H–S bridges, are studied. A significant result is that transverse Fe–H–Fe bridges (transverse to the pseudo-threefold axis of FeMo-co and shared with triply-bridging S) are not possible geometrically unless the S is hydrogenated to become doubly-bridging. The favourable Fe–H–Fe bridges are shared with doubly-bridging S. ENDOR data for an E4H4 intermediate trapped at low temperature, and interpretations in terms of the geometrical and electronic structure of E4H4, are assessed in conjunction with the calculated possibilities. The results reported here yield a set of 24 principles for the mechanistically significant coordination chemistry of H and H2 on FeMo-co, in the stages prior to N2 binding.

The mechanism for nitrogenase including all steps

Nitrogen in the air is turned into biologically useful ammonia by the nitrogenase enzyme. The leading member of this group has a cofactor with one molybdenum and seven irons linked together by sulfurs. The structure that binds N₂ has a triply protonated carbide and a rotated homocitrate. Both these structural changes are necessary for the activation.

Bimetallic Complexes Supported by a Redox-Active Ligand with Fused Pincer-Type Coordination Sites

The remarkable chemistry of mononuclear complexes featuring tridentate, meridionally chelating "pincer" ligands has stimulated the development of ligand frameworks containing multiple pincer sites. Here, the coordination chemistry of a novel pentadentate ligand (L(N3O2)) that provides two closely spaced NNO pincer-type compartments fused together at a central diarylamido unit is described. The trianionic L(N3O2) chelate supports homobimetallic structures in which each M(II) ion (M = Co, Cu, Zn) is bound in a meridional fashion by the bridging diarylamido N atom and O,N-donors of the salicyaldimine arms. The metal centers are also coordinated by a mono- or bidentate auxiliary ligand (L(aux)), resulting in complexes with the general form [M2(L(N3O2))(L(aux))2](+) (where L(aux) = 1-methyl-benzimidazole (1MeBI), 2,2'-bipyridine (bpy), 4,4'-dibromo-2,2'-bipyridine (bpy(Br2)), or (S)-2-(4-isopropyl-4,5-dihydrooxazolyl)pyridine (S-(iPr)OxPy)). The fused nature of the NNO pincer sites results in short metal-metal distances ranging from 2.70 Å for [Co2(L(N3O2)) (bpy)2](+) to 3.28 Å for [Zn2(L(N3O2)) (bpy)2](+), as revealed by X-ray crystallography. The complexes possess C2 symmetry due to the twisting of the aryl rings of the μ-NAr2 core; spectroscopic studies indicate that chiral L(aux) ligands, such as S-(iPr)OxPy, are capable of controlling the helical sense of the L(N3O2) scaffold. Since the four- or five-coordinate M(II) centers are linked solely by the amido moiety, each features an open coordination site in the intermetallic region, allowing for the possibility of metal-metal cooperativity in small-molecule activation. Indeed, the dicobalt(II) complex [Co2(L(N3O2)) (bpy(Br2))2](+) reacts with O2 to yield a dicobalt(III) species with a μ-1,2-peroxo ligand. The bpy-containing complexes exhibit rich electrochemical properties due to multiple metal- and ligand-based redox events across a wide (3.0 V) potential window. Using electron paramagnetic resonance (EPR) spectroscopy and density functional theory (DFT), it was determined that one-electron oxidation of [Co2(L(N3O2)) (bpy)2](+) results in formation of a S = 1/2 species with a L(N3O2)-based radical coupled to low-spin Co(II) centers.

Broken-Symmetry DFT Computations for the Reaction Pathway of IspH, an Iron-Sulfur Enzyme in Pathogenic Bacteria

The recently discovered methylerythritol phosphate (MEP) pathway provides new targets for the development of antibacterial and antimalarial drugs. In the final step of the MEP pathway, the [4Fe-4S] IspH protein catalyzes the 2e(-)/2H(+) reductive dehydroxylation of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate (HMBPP) to afford the isoprenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). Recent experiments have attempted to elucidate the IspH catalytic mechanism to drive inhibitor development. Two competing mechanisms have recently emerged, differentiated by their proposed HMBPP binding modes upon 1e(-) reduction of the [4Fe-4S] cluster: (1) a Birch reduction mechanism, in which HMBPP remains bound to the [4Fe-4S] cluster through its terminal C4-OH group (ROH-bound) until the -OH is cleaved as water; and (2) an organometallic mechanism, in which the C4-OH group rotates away from the [4Fe-4S] cluster, allowing the HMBPP olefin group to form a metallacycle complex with the apical iron (η(2)-bound). We perform broken-symmetry density functional theory computations to assess the energies and reduction potentials associated with the ROH- and η(2)-bound states implicated by these competing mechanisms. Reduction potentials obtained for ROH-bound states are more negative (-1.4 to -1.0 V) than what is typically expected of [4Fe-4S] ferredoxin proteins. Instead, we find that η(2)-bound states are lower in energy than ROH-bound states when the [4Fe-4S] cluster is 1e(-) reduced. Furthermore, η(2)-bound states can already be generated in the oxidized state, yielding reduction potentials of ca. -700 mV when electron addition occurs after rotation of the HMBPP C4-OH group. We demonstrate that such η(2)-bound states are kinetically accessible both when the IspH [4Fe-4S] cluster is oxidized and 1e(-) reduced. The energetically preferred pathway gives 1e(-) reduction of the cluster after substrate conformational change, generating the 1e(-) reduced intermediate proposed in the organometallic mechanism.

Use of Broken-Symmetry Density Functional Theory To Characterize the IspH Oxidized State: Implications for IspH Mechanism and Inhibition

With current therapies becoming less efficacious due to increased drug resistance, new inhibitors of both bacterial and malarial targets are desperately needed. The recently discovered methylerythritol phosphate (MEP) pathway for isoprenoid synthesis provides novel targets for the development of such drugs. Particular attention has focused on the IspH protein, the final enzyme in the MEP pathway, which uses its [4Fe-4S] cluster to catalyze the formation of the isoprenoid precursors IPP and DMAPP from HMBPP. IspH catalysis is achieved via a 2e-/2H+ reductive dehydroxylation of HMBPP; the mechanism by which catalysis is achieved, however, is highly controversial. The work presented herein provides the first step in assessing different routes to catalysis by using computational methods. By performing broken-symmetry density functional theory (BS-DFT) calculations that employ both the conductor-like screening solvation model (DFT/COSMO) and a finite-difference Poisson-Boltzmann self-consistent reaction field methodology (DFT/SCRF), we evaluate geometries, energies, and Mössbauer signatures of the different protonation states that may exist in the oxidized state of the IspH catalytic cycle. From DFT/SCRF computations performed on the oxidized state, we find a state where the substrate, HMBPP, coordinates the apical iron in the [4Fe-4S] cluster as an alcohol group (ROH) to be one of two, isoenergetic, lowest-energy states. In this state, the HMBPP pyrophosphate moiety and an adjacent glutamate residue (E126) are both fully deprotonated, making the active site highly anionic. Our findings that this low-energy state also matches the experimental geometry of the active site and that its computed isomer shifts agree with experiment validate the use of the DFT/SCRF method to assess relative energies along the IspH reaction pathway. Additional studies of IspH catalytic intermediates are currently being pursued.

Utilizing a dynamical description of IspH to aid in the development of novel antimicrobial drugs

The nonmevalonate pathway is responsible for isoprenoid production in microbes, including H. pylori, M. tuberculosis and P. falciparum, but is nonexistent in humans, thus providing a desirable route for antibacterial and antimalarial drug discovery. We coordinate a structural study of IspH, a [4Fe-4S] protein responsible for converting HMBPP to IPP and DMAPP in the ultimate step in the nonmevalonate pathway. By performing accelerated molecular dynamics simulations on both substrate-free and HMBPP-bound [Fe₄S₄]²⁺ IspH, we elucidate how substrate binding alters the dynamics of the protein. Using principal component analysis, we note that while substrate-free IspH samples various open and closed conformations, the closed conformation observed experimentally for HMBPP-bound IspH is inaccessible in the absence of HMBPP. In contrast, simulations with HMBPP bound are restricted from accessing the open states sampled by the substrate-free simulations. Further investigation of the substrate-free simulations reveals large fluctuations in the HMBPP binding pocket, as well as allosteric pocket openings – both of which are achieved through the hinge motions of the individual domains in IspH. Coupling these findings with solvent mapping and various structural analyses reveals alternative druggable sites that may be exploited in future drug design efforts.

Drug resistance has recently entered into media conversations through the lens of MRSA (methicillin-resistant Staphylococcus aureus) infections, but conventional therapies are also failing to address resistance in cases of malaria and other bacterial infections, such as tuberculosis. To address these problems, we must develop new antibacterial and antimalarial medications. Our research focuses on understanding the structure and dynamics of IspH, an enzyme whose function is necessary for the survival of most bacteria and malaria-causing protozoans. Using computer simulations, we track how the structure of IspH changes in the presence and absence of its natural substrate. By inspecting the pockets that form in the normal motions of IspH, we propose a couple new routes by which new molecules may be developed to disrupt the function of IspH. It is our hope that these structural studies may be precursors to the development of novel therapies that may add to our current arsenal against bacterial and malarial infections.